Preface Wide bandgap Ill-nitrides differ from the rest of III-V compound semiconductors in many aspects. They cover a broad range of optical spectrum including the ultraviolet portion; their most thermodynamically stable structure is wurtzite; they exhibit strong piezoelectric fields; they are chemically and physically strong, etc. In addition to these inherent peculiarities, there are many technical challenges associated with the growth and processing of these materials. Most specifically, lack of commercially available native substrates has forced the researchers to use substrates with mismatched lattice constants and thermal expansion coefficients. New ideas have had to be developed in order to reduce the number of dislocations present in the resulting material grown atop these substrates. Doping problems also, especially p-type doping, had plagued the development of these materials for a long time. All these substantial differences have separated Ill-nitrides from the rest of III-V materials and they are generally discussed independently. In the past few years, due to the great number of potential applications (Figure 1), Ill-nitrides have been studied vigorously and as a result significant advancements have taken place in this field. InGaN-based blue LEDs have found their market in full color displays and white lighting; blue laser diodes will be used in the next generation highcapacity CD/DVD read/write systems; UV LEDs and photodetectors have seen tremendous improvements in their properties and it will not be long before they are commercially available to be used for detection of biochemical agents, early missile threat warning, air/water purification, or even higher quality white lighting. Also these materials
High capacity optical data storage
Early missile threat warning
Detection of biochemical agents
Water purification
White lighting
Power line monitoring
Figure 1. Some of the potential applications of Ill-nitrides.
Mobile wireless communications
I
Flame monitoring
vi
Preface
have been successfully utilized to constitute high-frequency high-power transistor for RF transmission purposes. The aim of this book is to gather some of the most crucial information on properties and applications of Ill-nitrides in one place in the form of a handbook for the benefit of the nitride community. The book chapters cover a broad range of subjects from the material growth technology to devices such as light emitters, photodetectors, and high-power highfrequency applications. In addition, some of the other interesting properties of Ill-nitrides such as ferromagnetism, negative differential resistance, and phonon/electron-phonon interactions will be discussed. Several distinguished scientists have contributed their knowledge to this book and they have tried not only to present a historical review of the Ill-nitrides, but also to offer up-to-date advancements and future directions towards better understanding of these materials. Manijeh Razeghi Northwestern University, USA Mohamed Henini Nottingham University, UK
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 1
Introduction M. Razeghi^ and M. Henini'' ^Department of Electrical and Computer Engineering, Center for Quantum Devices, Northwestern University, Cook Room 4051, 2220 Campus Drive, Evanston, IL 60208-3129, USA ^School of Physics and Astronomy, University of Nottingham, NG7 2RD, UK
1.1.
INTRODUCTION
Wide bandgap Ill-nitrides, including (AI,Ga,In)-N, have seen enormous success in their development especially in the latest stages of the 20th century. Many substantial problems had to be overcome before these materials could constitute useful devices. High density of dislocations due to the lack of lattice-matched substrates and low doping efficiency were the most challenging problems that researchers in this area had to face. At the beginning, it was hard to believe that a material with a dislocation density in the order of 10^10^^ cm~^ would become the building block of many viable devices. However, thanks to the hard work of researches in this field, today blue/violet light-emitting diodes and laser diodes based on (Al,In,Ga)-N have been successfully commercialized. Blue/green LEDs have already found their market in full-color LCD displays and traffic lights, while blue LDs are expected to shortly replace red lasers in the current CD/DVD read/write systems. The unique properties of Ill-nitrides lead to a range of applications from optoelectronic devices to high-power electronics. The wide bandgap of GaN makes this material suitable not only for light emitting source but also for high-temperature applications. GaN and its alloys have the potential to form high power electronics such as transistors or thyristors. UV solar-blind photodetectors based on AlGaN have been demonstrated by several groups [1]. These detectors have applications in early missile threat detection and interception, chemical and biological threat detection, UV flame monitoring, and UV environmental monitoring. Due to the polar nature of the Ga-N bond, GaN does not possess inversion symmetry. Thus, when GaN is subject to an alternating electric field, the induced polarization is not symmetric. This property of GaN can be used in non-linear optics applications such as second-harmonic generation [2]. The same lack of inversion symmetry results in a huge piezoelectric field. There are some other conceivable
E-mail addresses:
[email protected] (M. Razeghi),
[email protected] (M. Henini).
2
Optoelectronic Devices: Ill-Nitrides
applications for Ill-nitrides such as surface acoustic wave generation [3], acousto-optic modulator [4], and devices that utilize negative electron affinity [5]. Group Ill-nitride materials are different from some conventional semiconductors such as silicon (Si) and GaAs in a sense that under ambient conditions, the thermodynamically stable structure is wurtzite. Although zinc blende structure for GaN or InN could exist by forcing the film to grow on {001} crystal planes of cubic substrates, the intrinsic tendency of Ill-nitrides is to form a wurzite structure with a hexagonal symmetry. The large difference in electronegativity between the group III elements and nitrogen (Al = 1.18, Ga = 1.13, In = 0.99, N = 3.0) leads to very strong chemical bonds in Ill-nitride material system which together with a wide direct energy gap is the origin of some interesting properties of Ill-nitrides [6]. Ill-nitrides have a bandgap energy tunable from 6.2 eV for AIN to 3.4 eV for GaN to 2 eV or below for InN (The energy gap of InN has been the subject of many debates and it is not agreed upon yet. There have been some recent reports on the bandgap energy of InN being as narrow as 0.7 eV) [7,8]. This corresponds to a wavelength range of 200-650 nm or higher, covering a broad spectral range, from UV to visible. Figure 1.1 demonstrates where Ill-nitride compound semiconductors stand compared to other semiconductors in the space of lattice constant-bandgap energy.
ZnS ZnO
0
•
Direct Bandgap
•
Indirect Bandgap
MgSe
A
C UJ
CdTe
InN* InSb — I —
3.0
I
3.5
4.0
I
1
4.5
1
1
-
5.0
7.0
Lattice Constant (A)
Figure 1.1. Bandgap energy vs. lattice constant of Ill-nitride family and some of the other ffl-V and II-VI compound semiconductors. Note: Bandgap of InN has been reported to be as narrow as 0.7 eV (InN* on the graph).
Introduction Table 1.1. Some of the important physical parameters of Ill-nitrides and sapphire Parameter Lattice constant, a (A) Lattice constant, c (A) Energy gap (eV) Thermal conductivity (W/cm K) Thermal expansion coefficient. a, (10-^K-^) Thermal expansion coefficient, a, (10"^K"^) Electron effective mass, m* (mg) Heavy hole effective mass, m^h (mo) Dielectric constant (so)
GaN
AIN
3.189 5.186 3.44 1.3 4.3 (17-477°C)
3.112 4.982 6.2 2.0 5.27 (20-800°C)
4.0 (17-477°C)
4.15 (20-800°C)
0.2 0.8 8.9
0.4 3.5 8.5
InN 3.545 5.703 1.9
AI2O3
4.758 12.991
-
-
0.3
5.6 (280°C)
-
3.8 (280°C)
7.7 (20-500°C)
0.11 1.6 15.3
-
Direct and indirect bandgap semiconductors are represented by triangles and circles, respectively. The direct bandgap of Ill-nitrides is one of their most beneficial features for optoelectronic device applications. In addition, the wide bandgap of Ill-nitrides results in a low intrinsic carrier density which in turn leads to low leakage and low dark current, especially important for photodetectors and high-temperature electronics. It is also known that Ill-nitrides are very robust materials with high melting points and mechanical strength. Adding to the list the ability to resist radiation damage yields a material system suitable for high-frequency, high-power and high-temperature applications. Some of the physical properties of Ill-nitrides are listed in Table 1.1. The data are complied from Refs. [9-11]. Some of the parameters for sapphire (the most widely used substrate for growth of Ill-nitrides) are also listed in this table. Owing to their direct bandgap, Ill-nitrides are promising candidates for optical devices such as laser diodes (LDs), light-emitting diodes (LEDs), and photodetectors. Not long ago, blue/violet LDs with lifetime of over 10,000 h were successfully demonstrated [12] and consequently commercialized. Implementation of blue LDs into CD/DVD read/write systems in computers will increase the data storage capacity by five times. This enhancement will become even larger when using UV LDs instead. The diameter of the focused laser beam is directly proportional to the laser wavelength. A, and inversely proportional to the numerical aperture, NA, of the imaging lens (Figure 1.2). The spot area is the square of the spot diameter:
A oc
VNAJ
Optoelectronic Devices: Ill-Nitrides
' Spot size Figure 1.2.
Illustration of a compact disc and a focused laser beam for read/write purpose.
The maximum areal density is the number of bits per spot, b, per spot area, A:
It has been several years since GaN/InGaN blue LEDs found their market in automotive dashboard lighting, full-color LED displays, indicator lighting, and LCD back lighting (Figure 1.3). The success in mass production of these highly efficient high-brightness InGaN/GaN blue LEDs basically put an end to II-VI (ZnSe/ZnS) blue LED research. UV solar-blind photodetectors have also been demonstrated in AlGaN/GaN material systems. Early missile threat warning, detection of chemical/biological agents, flame detection, power line monitoring, and non-line-of-sight (NLOS) communication (when combined with UV light emitters) are among the most important applications of solarblind photodetectors. In addition to optical devices, a lot of advances have taken place in the area of highpower, high-frequency power transistors for RF transmission applications, thanks to the high thermal conductivity, high melting point, low dielectric constant, and high breakdown voltage of Ill-nitrides. GaN HEMTs can alleviate many of the problems associated with the current LDMOS technology for mobile wireless communications due to their inherently higher transconductance, good thermal management and higher cut-off frequencies. The GaN HEMT technology aims at applications such as ship-board, airborne and ground RADARs, high-performance space electronics, base station transmitters, C-band Satcom, Ku-K band VSAT and broadband satellites, LMDS and digital radio. GaN HEMTs are capable of generating high power per unit area that translates into smaller devices with higher impedances. Also their high breakdown voltage enables them to operate at high voltages eliminating the need for voltage conversion. In addition, due to their high electron velocity, high-frequency operation is possible. These
Introduction
Figure 1.3. GaN-based blue/green LEDs have been used for traffic lights, LCD back lighting, and full-color LED displays (image of US cellular field in Chicago, courtesy of www.diamond-vision.com).
properties combined with the direct nature of their bandgap have made the GaN family a promising candidate for high-power high-frequency electronics. Although not studied in as much details as InGaN-based blue light emitters, AlGaNbased UV LEDs have also been investigated by several groups and emitters with wavelengths as short as 267 runs have been demonstrated [13]. There are numerous applications for ultraviolet light emitters. White LEDs for efficient, low-cost lighting, high-density optical data storage, water purification, portable chemical and biological agent detection/analysis systems, and NLOS communication are a few of them. Currently available incoherent UV light sources include high-intensity arc discharge lamps and fluorescent lamps. Table 1.2 summarizes advantages and disadvantages of these two technologies along with those of Ill-nitride-based UV LEDs. By combining UV LEDs and UV photodetectors, a compact system that can immediately identify certain biological agents is possible. In principle, many biological agents fluoresce when excited by a UV light source. The fluorescence emission is normally several nanometers longer than the excitation wavelength. For instance. Figure 1.4 shows the absorption and emission spectra of Phenylalanine. In this example, a UV light source with a monochromatic emission at 257 nm along with a UV photodetector with a band pass-like detection spectra peaked at around 280 nm can form a system capable of detecting this particular agent (Figure 1.5). A series of such
Optoelectronic Devices: Ill-Nitrides Table 1.2. Advantages and disadvantages of (Al,In,Ga)-N based UV LEDs compared to the existing technologies Technology
Disadvantages
Advantages
High-intensity arc discharge lamps
High power
Fluorescent lamps
Efficient
Ill-nitride UV LEDs
Compact, low power consumption, efficient, low turn-on, easy for system integration, resistant to radiation damage and magnetic fields, light, inexpensive
Requires bulky power supply, short lifetime, high power consumption Linear sources (hard to focus their light) Immature technology
LED/photodetector sub-systems each tuned at a particular wavelength of interest can be used to detect a range of biological agents. There is a need for a secure means to send messages in the field using low-power communication systems, a requirement that cannot be met with conventional RF radios. Covert communication is made possible by UV sources that exploit the solar-blind region
257.5 nm
eHjN^ ^co^e 279.5 nm
Phenylalanine Absorption Fluorescence
*0^4Am I
300
I
400
>ii"^"»» »*'
I
500
600
700
Wavelength (nm) Figure 1.4.
Absorption and fluorescence curves of phenylalanine peak at 257.5 and 279.5 nm, respectively.
Introduction UV photodetector
UV light
Cloud of unknown agent Figure 1.5.
^^^
^
"
Fluorescence
Basic representation of a system for detection of biochemical hazards.
located at 280 nm and below. In this region of the spectrum, the terrestrial solar flux is essentially zero, and the very low background can be used for NLOS communications over distances up to 250 m. The strong extinction coefficient (high scattering, high absorption) of the signal in the UV makes it difficult to detect these emissions from a distance, particularly in the forward direction. The success of such a portable UV frequency communicator unit depends on the availability of a compact, powerful and energy-efficient optical source. Blue/UV LEDs are also currently being utilized to generate white light. LEDproduced white light is cheap, durable, and more efficient than currently used light sources. One of the important applications of white LEDs is in medical illuminators. Most surgical systems are based on incandescent Ught bulbs. These light sources are simple to use, easily dimmable, and have a low initial cost. However, they are also sensitive to shock and vibration, sensitive to voltage variations, have short lifetime, consume too much power, and are inefficient (10-20 ImAV). On the other hand, Hght sources based on LED technology have long lifetime, are compact, efficient, and durable, and require low maintenance. There are three common methods for generation of white light: one method is to combine red, green, and blue (RGB) colors in order to achieve white color. Although this method can be very efficient and allows for a very good color rendering, some problems such as color mixing and existence of the yellow-green gap are yet to overcome. Another way of generating white light is to use blue color together with yellow phosphorus. This method is simple and exhibits good color rendering. However, it is limited on efficiency due to phosphorus conversion efficiency and self-absorption. In addition, multi-phosphor versions are needed to improve color rendering. The third and last approach is to use UV LED pumped RGB phosphors. In this case, white light is determined by phosphors only (tolerant to LED variation), excellent color rendering is possible, and it is easy to manufacture.
8
Optoelectronic
Devices:
Ill-Nitrides
One of the newest GaN-related research topics is the GaN-based diluted magnetic semiconductors (DMS). Spin polarizers, spin transistors, and ultra-dense non-volatile semiconductor memory are among the new class of devices and circuits based on magnetic semiconductors. In this regard, GaAs DMS has been studied more extensively. However, the Curie temperature of (Ga,Mn)As is low ( ~ 110 K). (Ga,Mn)N DMS on the other hand, has been shown to have Curie temperatures exceeding room temperature [14,15], which shows promise for realization of room temperature spintronics devices based on GaN DMS. A number of renowned scientists have contributed their knowledge to this book. A variety of useful information on some of the important properties and applications of Ill-nitrides has been collected in this book and our hope is that the scientific community will find this information helpful.
REFERENCES [1] Razeghi, M. (2002) Proc. IEEE, 90, 1006. [2] Miragliotta, J. & Wickenden, D.K. (1998) in Non-linear Optical Properties of GaN 50 B, Eds. Pankove, I. & Moustakas, T.D., Academic Press, San Diego. [3] Duffy, M.T., Wang, C.C, O'Clock, G.D., McFarlane, S.H., III & Zanzucchi, P.J. (1973) /. Electron. Mater., 2, 359. [4] Lotsch, H.K.V. & Schroter, F. (1970) Das Laser-Farbfensehen. Laser, 2, 37. [5] Pankove, J.I. & Schade, H.E.P. (1974) Appl. Phys. Lett., 25, 53. [6] Razeghi, M. (1998) Int. J. High Speed Electron. Syst., 9, 161. [7] Davydov, V.Y., Klochikhin, A.A., Emtsev, V.V., Ivanov, S.V., Vekshin, V.V., Bechstedt, F., FurthmuUer, J., Harima, H., Mudryi, A.V., Hashimoto, A., Yamamoto, A., Aderhold, J., Graul, J. & Haller, E. (2002) Phys. Stat. Sol. (b), 230, R4. [8] Wu, J., Walukiewicz, W., Wu, K.M., Ager, J.W., IE, Haller, E.E., Lu, H., Schaff, W.J., Saito, Y. & Nanishi, Y. (2002) Appl. Phys. Lett., 80, 3967. [9] Madelung, O. Ed. (1991) Semiconductors: Group IV Elements and III-V Compounds, Springer, Berlin. [10] Madelung, O. (1996) Semiconductors—Basic Data, l""^ Edition Springer, Berlin. [11] Leszczynski, M., Suski, T., Perlin, P., Teisseyre, H., Grzegory, I., Bockowski, M., Jun, J., Porowski, S. & Major, J. (1995) J. Phys., D28, A149. [12] Nakamura, S., Senoh, M., Nagahama, S., Iwasa, N., Yamada, T., Kiyoku, H., Sugimoto, Y., Kozaki, T., Umemoto, H., Sano, M. & Chocho, K. (1997) Jpn. J. Appl. Phys., 36, L1568. Part 2. [13] Yasan, A., McClintock, R., Mayes, K., Darvish, S.R., Kung, P. & Razeghi, M. (2003) Appl. Phys. Lett., 83, 4701. [14] Dietl, T., Ohno, H., Matsukura, F., Cibert, J. & Ferrand, D. (2000) Science, 287, 1019. [15] Reed, M.L., El-Masry, N.A., Stadelmaier, H.H., Ritmus, M.K., Reed, M.J., Parker, C.A., Roberts, J.C. & Bedair, S.M. (2001) Appl. Phys. Lett., 79, 3473.
optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 2
The Rise of Ill-nitrides: An Introduction Patrick Kung Department ofECE, Center for Quantum Devices, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA
The nitrides of group III metal elements or "Ill-nitrides" (or "III-N") commonly refer to aluminum nitride (AIN), gallium nitride (GaN), indium nitride (InN) and their alloys, all of which are compounds of nitrogen—the smallest group V element in the Periodic Table and an element with one of the highest values of electronegativity. Long regarded as a scientific curiosity, Ill-nitrides have now earned a most respected place in the science and technology of compound semiconductors, as well as modem electronic and optoelectronic devices. Unlike more conventional semiconductors, such as silicon (Si) or gallium arsenide (GaAs) which have a diamond or zinc-blende structure with a cubic symmetry, Ill-nitride semiconductors crystallize in their most stable form into a wurtzite crystallographic structure (Table 2.1) with nitrogen atoms forming a hexagonal close packed (hep) structure and the group III atoms occupying half of the tetrahedral sites available in the hep lattice [1,2]. Ill-Nitrides are polar crystals as they do not have a center of symmetry [3]. They thus possess many other potentially useful properties such as piezoelectricity [4], pyroelectricity [5] and non-linear optical properties [6,7]. The large difference in electronegativity between the group III and group V elements (Al = 1.18, G a = 1.13, In = 0.99, N = 3.1) results in very strong chemical bonds within the Ill-nitride material system, which is at the origin of most of the exceptional Ill-nitride physical properties (listed in Table 2.2); that have increasingly spurred interest within the research community. Most importantly, AlInGaN compounds exhibit a direct bandgap energy that can be continuously tailored between 0.7 and 6.2 eV, which corresponds to a wavelength range from 1.78 ixm to 200 nm and thus covers the near infrared, visible or near ultraviolet spectral bands. Figure 2.1 compares the bandgap energy versus lattice constants of Ill-nitrides with that of various semiconductors. Furthermore, because the intrinsic carrier concentration is an exponential function of the energy gap and the temperature, wide bandgap Ill-nitride semiconductors have a much lower intrinsic carrier concentrations over a larger temperature range than Si or GaAs. This results in lower leakage and dark currents, which is especially important in photodetectors
E-mail address:
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9
10
Optoelectronic Devices: Ill-Nitrides Table 2.1. Crystallographic data of Ill-nitrides III-N Structure type Crystal system Space group Origin
Wurtzite Hexagonal P6T,mc (No. 186) 3ml; (N^~): positions: 2b site symmetry: 3m» (ai,a2,«3) = (0,0,0.375) (III^^): positions: 2b site symmetry: 3m« (ai,a2,«3) = (0,0,0)
Coordination
and electronic devices. Another consequence of the strong chemical bonding is the physical (high melting points, mechanical strength) and chemical stability of these materials. These also enjoy high thermal conductivity. Their effective masses are higher than conventional semiconductors, thus leading to lower carrier mobilities, but this is made up for by the highsaturated electron drift velocities predicted for this material system. The refractive indices of Ill-nitrides are lower compared to narrower gap semiconductors, which results in a lower
Table 2.2. Physical properties of Ill-nitride materials
300 K energy gap (eV) Lattice constant, a (A) Lattice constant, c (A) Thermal expansion coefficient a^ (10~^K~*) Thermal expansion coefficient a, (10"^ K~') Electron effective mass, mg (mo) Hole effective mass, m^ (mo) Refractive index, n
AIN
GaN
6.2 3.112 4.982 5.27 (20-800°C)
3.44 3.189 5.186 4.3 (17-477°C)
0.7 3.545 5.703 5.6 (280°C)
4.15 (20-800°C)
4.0 (17-477°C)
3.8 (280°C)
0.2
0.11 0.5 (mhh) 0.17 (mih) 2.56 (1,0 fxm) 3.12 (0.66 |xm)
1100 -23.0 10.0
e(0)
2.2 (0.60 \xm) 2.5 (0.23 iJim) 9.14
e(oo)
4.84
Thermal conductivity, K (W/cm K) Melting point (°C) ^(f (kcal/mol) Heat capacity. Cp (cal/mol K)
2.0
0.8 2.35 (1.0 (Jim) 2.60 (0.38 |xm) 10.4 (ElIc) 9.5 (E 1 c) 5.8(Ellc) 5.4 (E 1 c) 1.7-1.8
3000 -68.2 7.6
>1700 -33.0 9.7
InN
9.3
The Rise of Ill-nitrides: An Introduction
11
A Direct Bandgap
6 1
•
Indirect Bandgap
5 H
>
ZnS
4 -\
ZnO
MgSe
• (D C LJJ Q. CD D) T3 C TO GQ
3 H
InN*
~-|— 3.0
I
3.5
4.0
'
I 4.5
'
\ 5.0
5.5
7.0
Lattice Constant (A) Figure 2.1. Bandgap energy versus lattice constant of various semiconductors, including Ill-nitrides. The bandgap energy of InN was recently reported to be 0.7 eV instead of earlier reported 2 eV.
reflectivity at the interface. This is an advantage for photodetector efficiency, but a disadvantage when trying to achieve lasers with low threshold currents. The historical development of Ill-nitrides can be punctuated by the series of milestones listed in Table 2.3, grouped into four phases. For a large part, the research work has often taken example from the development of GaAs-based compounds, first for the fundamental reason that GaN and GaAs are both III-V semiconductor compounds with a direct bandgap and secondly for the practical reason that the technology of GaAs could be adapted to manufacture GaN compounds—up to a certain extent. Phase I corresponds to the major part of the 20th century, before 1960. Although the first AIN, GaN and InN compounds were synthesized as early as 1907 [8], 1910 [9] and 1932 [10], respectively, i.e. much earlier than conventional GaAs and Si semiconductors, no significant progress could be reported until the end of the 1960s. This was mainly due to the fact that Ill-nitride crystals had been very difficult to synthesize. Thanks to the development of modem epitaxial growth techniques, it was possible during the Phase II (1960- 1970s) period to demonstrate the first growth of GaN thin films by hydride vapor phase epitaxy (HVPE) in 1969 [11]. This was quickly followed in 1971 with the first metalorganic chemical vapor deposition (MOCVD) [12] and then the first
12
Optoelectronic Devices: Ill-Nitrides
Table 2.3. Historical milestones in the development of Ill-nitride semiconductors Phase I
1907 1910 1932
Synthesis of AJN Synthesis of InN Synthesis of GaN
Phase II
1969 1971
1974 1975 1976
Epitaxy of GaN, by HVPE MOCVD of GaN Stimulated emission in GaN (needles) by optical pumping Metal-insulator-semiconductor GaN-based LED MBE of GaN MBE of AIN Bulk ALN crystals
Phase III
1983 1986 1989
Concept of low temperature buffer layer MOVPE of crystalUne GaN using AIN buffer layer P-type GaN using LEEBI
Phase IV
1990 1991
Stimulated emission by optical pumping of high-quality GaN GaN buffer by MOCVD GaN p - n junction blue LED P-type AlGaN 2DEG at AlGaN/GaN interface High-quality InGaN GaN photoconductor P-type GaN using thermal anneaUng AlGaN/GaN HEMT or HFET GaN MESFET, MISFET Schottky barrier GaN photodiode Conmiercial candela class blue InGaN LEDs Bulk GaN crystals GaN/SiC HBT (GaN/SiC heterointerface) Microwave HFET, MISFET Microwave GaN MESFET Conunercial candela class "bluish-green" InGaN LED P-type InGaN GaN-AIN SIS junction detector AlGaN/GaN HFET photodetector GaN p - n junction photodiode Pulsed operation blue laser diode 410 nm InGaN yellow LED Commercial "pure green" InGaN LEDs Ion implanted GaN JFET Doped channel AlGaN/GaN HEMT AlGaN photoconductor White LED using phosphors First continuous wave blue laser diode Complete range of AlGaN photoconductors Ultraviolet LED
1992
1993
1994
1995
1996
1997
(continued)
The Rise of Ill-nitrides: An Introduction
13
Table 2.3. Continued
1998
1999
2000
2001 2002
2003 2004
10,000 h lifetime RT CW InGaN violet LD Schottky barrier AlGaN photodiode AlGaN/GaN HBT GaN MOSFET GaN p - i - n 32 X 32 focal plane array Visible blind AlGaN p - i - n photodiode Sample shipment of blue-violet laser diode Solar blind AlGaN p - i - n photodiode GaN p - i - n 128 X 128 focal plane array GaN avalanche photodiodes MOSHFET in AlGaN (metal-oxide semiconductor heterostructure FET) Commercialization of blue-violet laser diode InN bandgap determined to be 0.7 eV 256 X 256 AlGaN solar blind focal plane array AlGaN UV LEDs at 280 nm Sample shipment of UV laser diodes at 375 nm AlGaN UV LEDs at 265 nm AlGaN UV laser at 350.9 nm
molecular beam epitaxy (MBE) of GaN in 1974 [13]. The first epitaxial growth of AIN was reported in 1975 [14]. The quality of these GaN crystals was sufficient to enable the study of their optical properties. In particular, the first observation of stimulated emission from GaN needles was observed in 1971 [15], prefiguring the demonstration of a blueultraviolet wavelength laser diode 20 years later. However, as it was still impossible to realize bulk Ill-nitride crystals, the epitaxial process had to be performed on non-native substrates and the quality of the GaN films was very poor. Phase III of the development stage of Ill-nitrides, spanning the 1980s, can be considered as the critical period when two fundamental breakthroughs were made. The first one was the introduction of the concept of a low-temperature nucleation layer which permitted the growth of smooth GaN thin films on a foreign substrate in 1983 [16]. This was followed by the demonstration of high-quality crystalline GaN films in 1986 [17]. The second breakthrough was the demonstration of p-type GaN films through low-energy electron beam irradiation (LEEBI) to activate p-type dopants in 1989 [18]. The p-type activation process was later refined in 1992 using thermal annealing [19]. Phase IV corresponds to the period from 1990 until today. It experienced the most dramatic and spectacular research and development work in Ill-nitride based compound semiconductor science and technology to date [20-33]. It is clear that understanding and controlling the optical properties of Ill-nitrides have been the first and primary driving force behind the research work in an effort to realize blue and green light-emitting diodes (LEDs) and laser diodes (LDs). Such components had long been desired in order to achieve bright full color electroluminescent displays, traffic lighting, automobile lighting, and higher
14
Optoelectronic Devices: Ill-Nitrides
density optical data storage. Now, wide bandgap Ill-nitride semiconductors have truly become the cornerstone technology for such devices, supplanting technologies such as silicon carbide (SiC) for blue LEDs, AlInGaP for green LEDs, and zinc selenide for blue and green LDs, even though these had been much more mature and well developed and had already been commercialized at the time the GaN material quality was still poor. This impressive research and development work culminated with the commercialization of candela class GaN-based blue LEDs in 1993 [34] and the realization of the first GaN-based laser diode under pulse operation in 1995 [35,36]. Since then, the development of lasers has followed an accelerated course, with milestones such as the demonstration of continuous wave operation [37], a lifetime of 10,000 h in 1997 [38], which led to the successful conMnercialization of room temperature continuous wave blue-violet laser diodes in 2001 [34]. One instrumental element in realizing long lifetime lasers was the development of lateral epitaxial overgrowth as a method to reduce dislocations in heteroepitaxially grown GaN [39,40]. The performance and reliability of these lasers have been sufficient to allow mass production and start establishing the basic specifications of a standard for next generation high-density optical disk video recordings. One of the leading standard format currently being developed, called "Blu-ray Disc", is expected to make possible "the recording, rewriting and playback of up to 27 GB of data on a single-sided, single-layer 12 cm CD/DVD-size disc using a 405 nm blue-violet laser" [41,42]. These scientific and commercial successes in realizing blue LEDs and lasers, accomplished in such a short period of time, have since spurred a plethora of activity associated with Ill-nitrides. For example, the first yellow/amber LED based on InGaN have been reported in 1995 [43]. Subsequently, the most commercially significant development since then has been the demonstration of a novel light source in 1996 in the form of a white LED that combined a blue LED and a phosphor coating [44]. The potential of this technology as a cheap, low energy consumption, more environmentally friendly solid-state light source has led to a large effort in the US called the "National Next Generation Lighting Initiative" that involves industry, universities and national laboratories [45]. Another current challenge for light emitters is to push the Ill-nitride technology to shorter wavelengths (below 340 nm) for applications such as laser-induced fluorescence of chemical/biological agents, water purification and non-line-of-sight communications. For these purposes, AlGaN ultraviolet LEDs emitting at 340 and 280 nm with increasing powers have been consistently reported [46-50]. Furthermore, AlGaN LED emitting at a wavelength as low as 267 nm have been successfully demonstrated in 2003 [51]. Sample shipments of UV laser diodes with wavelength as short as 375 nm have been initiated in 2002 [34]. And the shortest wavelength laser diode emitting at 350.9 nm was also recently demonstrated [52]. A further area of research with growing interest is that of visible-blind and solar-blind ultraviolet (UV) photodetectors based on Ill-nitrides for use in many applications such as covert space-to-space communications, early missile threat warning, UV astronomy.
The Rise of Ill-nitrides: An Introduction
15
chemical and biological agent detection, flame detection, engine and furnace monitoring [53,54]. Such devices can also be used for autocorrelation measurements [55]. The visible or solar blindness is the property that the photodetector is sensitive to UV light while being (ideally) insensitive to visible or solar light, and is a key parameter for photodetectors which are expected to detect UV light in a strong visible and/or infrared background. Compared to existing solid-state or other technologies, Ill-nitride semiconductors can lead to devices that are cheaper, more efficient and more robust. After the first report of a GaN ultraviolet photodetector in 1992 [56], that of GaN p - n junction photodiode in 1995 [57], and the demonstration of metal-semiconductor-metal GaN photodetectors [58], the entire range of AlGaN photodetectors has been demonstrated in 1996 with cut-off wavelengths from 200 to 365 nm [59-61], followed by the demonstration of AlGaN p - i - n photodiodes [62-65] and by the realization of increasingly larger size focal plane arrays between 1999 and 2002 [66-68]. With the recent report that the bandgap of InN is only 0.7 eV, there is likely to be a growing interest in Ill-nitrides for high-efficiency solar cells [69]. In addition to optoelectronic devices, Ill-nitrides have a proven potential for RFmicrowave-millimeter wave as well as high-power electronic devices in order to revolutionize high-power electrical energy control, conversion, and distribution, as well as to support applications such as all electric vehicles, wireless communications and radar technology. Two figures of merit generally used to characterize materials for electronic devices can be used to explain the interest that the research community has for Ill-nitrides. The first one, the Johnson figure of merit JFM = {E^VJlTff, where E^ is the breakdown voltage and V^ is the saturation velocity, is related to the electronic properties of materials. It characterizes the frequency-power trade-off, since high frequency usually requires small device dimension while high power need large device size. The Keyes figure of merit, KFM = ajicvjlire)^^^, where OY is the thermal conductivity of the materials and 8 is its dielectric constant, is related to the material thermal properties. It characterizes the device size and thermal resistance trade-off. The values are generally normalized to Si. The values for the JFM and KFM, listed in Tables 2.4 and 2.5, respectively [70], confirm GaN-based semiconductors are very promising for electronic devices. Table 2.4. Comparison of the Johnson figures of merit of different materials [70] Material
E^iWIcm)
n (cm/s)
Si GaAs GaN 6H-SiC 3C-SiC Diamond
3X10^ 4X10^ 50 X 10^ 40 X 10^ 40 X 10^ 100 X 10^
1.0 X 2.0 X 2.7 X 2.0 X 2.0 X 2.7 X
10^ 10^ 10^ 10^ 10^ 10^
[{E^V,)liTf
(VW)
9.1 X 10^^ 64.8 X 10^^ 18466 X 10^^ 6485 X 10^^ 6485 X 10^^ 73863 X 10^^
Ratio to silicon 1.0 7.1 2029 712 712 8117
16
Optoelectronic Devices: Ill-Nitrides
Table 2.5. Comparison of the Keyes figures of merit of different materials [70] Material
o-T (300 K) (W/cm)
V, (cm/s)
er
ajiVJe.y^ (W/cm^V^^)
Ratio to silicon
Si GaAs GaN 6H-SiC 3C-SiC Diamond
1.5 0.5 1.3 5.0 5.0 20.0
1.0X10^ 2.0 X 10^ 2.7 X 10^ 2.0 X 10^ 2.0 X 10^ 2.7 X 10^
11.8 12.8 9 9.7 9.7 5.5
13.8 X 10^ 6.25 X 10^ 22.5 X 10^ 71.8 X 10^ 71.8 X 10^ 443.1 X 10^
1.0 0.45 1.6 5.2 5.2 32.1
The first experimental indication of this potential came with the reported observation of a two-dimensional electron gas at AlGaN/GaN heterointerface in 1992 [71]. The subsequent year saw the demonstration of AlGaN/GaN high-electron mobility transistors [72]. And in 1998, the first AlGaN/GaN heterojunction bipolar transistor was reported [73].
Table 2.6. Comparison of the lattice properties and energy gaps of ni-nitrides with potential substrate materials [69,70] Formula name (crystal symmetry)
GaN (hexagonal) AIN (hexagonal) InN (hexagonal) AI2O3 (trigonal) 4H-SiC (hexagonal) 6H-SiC (hexagonal) LiGa02 (orthorhombic) LiAlOi (tetragonal) ZnO (hexagonal) MgO (cubic) Si (cubic) GaAs (cubic) GaP (cubic)
Lattice constants (A)
a = 3.1891; c = 5.1855 a = 3.112; c = 4.982 a = 3.5365; c = 5.7039 a = 4.758; c = 12.991 a = 3.073; c = 10.053 fl = 3.081; c = 15.117 a = 5.402; b = 6.372; c = 5.007 a = 5.1715; c = 6.2840 a = 3.253; c = 5.213 4.216 5.4310202 5.65325 5.4512
Plane with nearest match to (0001) GaN
Effective a lattice constant (A)
Lattice mismatch with GaN (%)
Energy gap
(^GaN ~ '^subV'^sub
(0001)
3.1891
0
3.44
(0001)
3.112
2.47
6.2
(0001)
3.53656
-9.82
0.7
(0001) rotated 30° (0001)
2.747
16.09
>8.5
3.073
3.77
3.20
(0001)
3.081
3.51
2.86
(001)
3.119, 3.186
2.25, 0.10
(100)
6.81, 1.50
(0001)
2.986, 3.142 3.253
-1.97
3.44 (1.6 K)
(111) (111) (111) (111)
2.981 3.840 3.99745 3.8546
4.93 -16.96 -20.22 -17.26
7.9 1.1242 1.424 2.26
The Rise of Ill-nitrides: An Introduction
17
Table 2.7. Comparison of the thermal properties of Ill-nitrides with potential substrate materials, including their thermal expansion coefficient or TEC {d^), thermal conductivity, and melting point [70] Formula name
a-a(10-^K-^) 0-1000°C
Mismatch with GaN by cooling 1000°C (%) (TECcaN ~ TECsub) X (-1000 K)
Thermal conductivity (W/cm K)
Melting temperature (°C)
GaN AIN InN
5.6 (0 to 600°C) 5.7 5.7 (300°C) 8.6 4.46 4.44 -7
0 0.01 0.01 0.30 -0.11 -0.12 0.14
1.7-1.8 2.0 4.9 0.3
>1700 3000 1100 2015
AI2O3
4H-SiC 6H-SiC LiGaOs LiAlOs ZnO MgO Si GaP GaAs
7.8 13.85 3.90 4.7 6.7
0.22 0.83 -0.17 -0.09 0.11
4.9
0.36 1.3 1.1 0.5
-1600 -1700 -2000 2800 1412 1470 1240
Looking into the future, as InN exhibits the highest saturation velocity of all Ill-nitride compounds, as high as 4.2 X 10^ cm/s, InN is a highly potential material for the fabrication of high-speed field effect transistors. To support all these exceptional technological endeavors, epitaxial growth techniques have significantly improved. Indeed, instead of adapting existing equipment originally used for GaAs, which may have been useful for the demonstration stage, new MOCVD and MBE growth apparatus have been engineered to accommodate and facilitate the growth of Ill-nitrides, including high growth temperatures and in situ monitoring in MOCVD. Bulk GaN substrates have been successfully grown first in 1994 [74], using high-pressure and high-temperature growth techniques. Since then, easier methods have been developed which also led to large bulk crystals. Hundreds of micrometer thick GaN films are now grown by HVPE on a foreign substrate, followed by an epitaxial lift-off and polishing to obtain a quasi-bulk single crystal. AIN substrates are now also being developed, with higher quality than originally reported in the 1970s [75], in order to support the drive toward shorter wavelength optoelectronics. However, the quality, dimension, availability and cost of these substrates are still too high for widespread use. This is why, to date, the quasientirety of Ill-nitride thin films are still grown on non-native substrates and the choice of the most appropriate substrate material is still an issue. In Tables 2.6 and 2.7, the physical properties of several candidate substrate materials are compared with those of Ill-nitrides,
18
Optoelectronic
Devices:
Ill-Nitrides
including their lattice mismatch with GaN and the thermal mismatch when cooling by 1000°C. Three substrates stand out to be the most promising ones: silicon (Si), 6H silicon carbide (6H-SiC) and sapphire (AI2O3) [20-24,26,28,40]. The choice of Si remains a desirable approach because it is the most widely used electronic material, is widely available in large areas and is very cheap. However, it does not have a crystal structure and physical properties similar to Ill-nitrides, and exhibits a lattice mismatch of ~ 17% with GaN. Silicon carbide presents the closest match with Ill-nitrides (lattice mismatch with GaN is only 3.5%) out of the three candidates but SiC substrates are still expensive in comparison with other alternative substrates, although the technology is progressing rapidly to bring prices down thanks mainly to the commercial thrust from Ill-nitride based devices. Sapphire offers a compromise between these two extremes as it is the most widely used substrate to date; high-quality wafers are widely available and are cheaper than SiC, and it has a similar hexagonal crystal symmetry as Ill-nitrides. In summary, after nearly a century since the first synthesis of AIN, Ill-nitride semiconductors have become one cornerstone of modem optoelectronic and electronic devices thanks to a spectacular research and development in the last 20 years. It is still too early to estimate their scientific and economic impact, but one can confidently say that it is not less significant than that of gallium arsenide. REFERENCES [1] Kung, P., Sun, C.J., Saxler, A., Ohsato, H. & Razeghi, M. (1994) Crystallography of epitaxial growth of wurtzite-type thin films on sapphire substrates. J. Appl. Phys., 75, 4515. [2] Sun, C.J., Kung, P., Saxler, A., Ohsato, H., Razeghi, M. & Haritos, K. (1994) A crystallographic model of (00*1) aluminum nitride epitaxial thin film growth on (00*1) sapphire substrate. J. Appl Phys., 75, 3964. [3] Daudin, B., Rouviere, J.L. & Arlery, M. (1996) Polarity determination of GaN films by ion channeling and convergent beam electron diffraction. Appl. Phys. Lett., 69, 2480. [4] Bemardini, F., Fiorentini, V. & Vanderbilt, D. (1997) Spontaneous polarization and piezoelectric constants of III-V nitrides. Phys. Rev. B, 56, R10024. [5] Bykhovski, A.D., Kaminski, V.V., Shur, M.S., Chen, Q.C. & Khan, M.A. (1996) Pyroelectricity in gallium nitride thin films. Appl. Phys. Lett., 69, 3254. [6] Miragliotta, J., Wickenden, D.K., Kistenmacher, T.J. & Bryden, W.A. (1993) Linear- and nonlinear-optical properties of GaN thin films. J. Opt. Soc. Am. B, 10, 1447. [7] Hahn, D.N., Kiehne, G.T., Wong, G.K.L., Ketterson, J.B., Kung, P., Saxler, A. & Razeghi, M. (1999) Phase-matched optical second-harmonic generation in GaN and AIN slab waveguides. J. Appl. Phys., 85, 2497. [8] Fichter, F. (1907) Uber aliminiumnitride. Z Anorg. Chem., 54, 322. [9] Fischer, F. & Schroter, F. (1910) Berichte der Deutschen Chemischen Gesellschaft, 43, 1465. [10] Johnson, V.C, Parsons, J.B. & Crew, M.C. (1932) /. Phys. Chem., 36, 2588. [11] Maruska, H.P. & Tietjen, J.J. (1969) The preparation and properties of vapor-deposited singlecrystalUne GaN. Appl. Phys. Lett., 15, 327.
The Rise of Ill-nitrides: An Introduction
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[12] Manasevit, H.M., Erdmann, P.M. & Simpson, W.I. (1971) The use of metalorganics in the preparation of semiconductor materials. IV. The nitrides of aluminum and gallium. /. Electrochem. Soc, 118, 1864. [13] Akasaki, I. et al. (1974) MITI report in Japanese only; Akasaki, I., Hayashi, I., 1976, Ind. Set. TechnoL, 17, 48. [14] Yoshida, S., Misawa, S. & Itoh, A. (1975) Epitaxial growth of aluminum nitride films on sapphire by reactive evaporation. Appl. Phys. Lett., 26, 461. [15] Dingle, R., Shaklee, K.L., Leheny, R.F. & Zetterstrom, R. (1971) Stimulated emission and laser action in gallium nitride. Appl. Phys. Lett., 19, 5. [16] Yoshida, S., Misawa, S. & Gonda, S. (1983) Improvements on the electrical and luminescent properties of reactive molecular beam epitaxially grown GaN films by using AlN-coated sapphire substrates. Appl. Phys. Lett., 42, 427. [17] Amano, H., Sawaki, N., Akasaki, I. & Toyoda, Y. (1986) Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AIN buffer layer. Appl. Phys. Lett., 48, 353. [18] Amano, H., Kito, M., Hiramatsu, K. & Akasaki, I. (1989) P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI). Jpn. J. Appl. Phys., 28, L2112. [19] Nakamura, S., Mukai, T., Senoh, M. & Iwasa, N. (1992) Thermal annealing effects on p-type Mg-doped GaN films. Jpn. J. Appl. Phys., 31, L139. [20] Sun, C.J. & Razeghi, M. (1993) Comparison of the physical properties of GaN thin films deposited on (0112) and (0001) sapphire substrates. Appl. Phys. Lett., 63, 973. [21] Sun, C.J., Kung, P., Saxler, A., Ohsato, H., Bigan, E., Razeghi, M. & Gaskill, D.K. (1994) Thermal stability of GaN thin films grown on (0001) AI2O3, (0112) AI2O3 and (OOOl)si 6HSiC substrates. J. Appl. Phys., 76, 236. [22] Saxler, A., Kung, P., Sun, C.J., Bigan, E. & Razeghi, M. (1994) High quality aluminum nitride epitaxial layers grown on sapphire substrates. Appl. Phys. Lett., 64, 399. [23] Dovidenko, K., Oktyabrsky, S., Narayan, J. & Razeghi, M. (1996) Aluminum nitride films on different orientations of sapphire and silicon. /. Appl. Phys., 79, 2439. [24] Kung, P., Saxler, A., Zhang, X., Walker, D., Wang, T.C., Ferguson, I. & Razeghi, M. (1995) High quahty AIN and GaN epilayers grown on (00*1) sapphire, (100) and (111) sihcon substrates. Appl. Phys. Lett., 66, 2958. [25] Saxler, A., Walker, D., Kung, P., Zhang, X., Razeghi, M., Solomon, J., Mitchel, W. & Vydyanath, H.R. (1997) Comparison of trimethylgallium and triethylgallium for the growth of GaN. Appl. Phys. Lett., 71, 3272. [26] Zhang, X., Kung, P., Saxler, A., Walker, D., Wang, T.C. & Razeghi, M. (1995) Growth of Al^Gai_;,N:Ge on sapphire and silicon substrates. Appl. Phys. Lett., 67, 1745. [27] Zhang, X., Kung, P., Saxler, A., Walker, D., Wang, T. & Razeghi, M. (1995) Photoluminescence study of GaN. Acta Phys. Polonica A, 88, 601. [28] Kung, P., Saxler, A., Zhang, X., Walker, D., Lavado, R. & Razeghi, M. (1996) Metalorganic chemical vapor deposition of monocrystalline GaN thin films on p-LiGa02 substrates. Appl. Phys. Lett., 69, 2X16. [29] Zhang, X., Kung, P., Saxler, A., Walker, D. & Razeghi, M. (1996) Observation of room temperature surface-emitting stimulated emission from GaN:Ge by optical pumping. /. Appl. Phys.,m, 65AA. [30] Zhang, X., Walker, D., Saxler, A., Kung, P., Xu, J. & Razeghi, M. (1996) Observation of inversion layers at AIN-Si interfaces fabricated by metal organic chemical vapour deposition. Electron. Lett., 32, 1622.
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[31] Kung, P., Saxler, A., Walker, D., Rybaltowski, A., Zhang, X., Diaz, J. & Razeghi, M. (1998) GalnN/GaN multi-quantum well laser diodes grown by low-pressure metalorganic chemical vapor deposition. MRS Internet J. Nitride Semicond. Res., 3 (1). [32] Saxler, A., Mitchel, W.C., Kung, P. & Razeghi, M. (1999) Aluminum gallium nitride shortperiod superlattices doped with magnesium. Appl. Phys. Lett., 74, 2023. [33] Yasan, A., McClintock, R., Darvish, S.R., Lin, Z., Mi, K., Kung, P. & Razeghi, M. (2002) Characteristics of high quality p-type Al;,Gai_;,N/GaN superlattices. Appl. Phys. Lett., 80,2108. [34] http://www.nichia.co.jp/info/history.html. [35] Akasaki, L, Amano, H., Sota, S., Sakai, H., Tanaka, T. & Koike, M. (1995) Stimulated emission by current injection from an AlGaN/GaN/GaInN quanmm well device. Jpn. J. Appl. Phys., 34, L1517. [36] Nakamura, S., Senoh, M., Nagahama, S.I., Iwasa, N., Yamada, T., Matsushita, T., Kiyoku, H. & Sugimoto, Y. (1996) InGaN-based multi-quantum-well-structure laser diodes. Jpn. J. Appl. Phys., 35, L74. [37] Nakamura, S., Senoh, M., Nagahama, S.I., Iwasa, N., Yamada, T., Matsushita, T., Sugimoto, Y. & Kiyoku, H. (1996) Continuous-wave operation of InGaN multi-quantum-well-structure laser diodes at 233 K. Appl. Phys. Lett., 69, 3034. [38] Nakamura, S., Senoh, M., Nagahama, S.I., Iwasa, N., Yamada, T., Matsushita, T., Kiyoku, H., Sugimoto, Y., Kozaki, T., Umemoto, H., Sano, M. & Chocho, K. (1997) InGaN/GaN/AlGaNbased laser diodes with modulation-doped strained-layer superlattices. Jpn. J. Appl. Phys., 36, L1568. [39] Usui, A., Sunakawa, H., Sakai, A. & Yamaguchi, A.A. (1997) Thick GaN epitaxial growth with low dislocation density by hydride vapor phase epitaxy. Jpn. J Appl. Phys., 36, L899. [40] Kung, P., Walker, D., Hamilton, M., Diaz, J. & Razeghi, M. (1999) Lateral epitaxial overgrowth of GaN films on sapphire and silicon substrates. Appl. Phys. Lett., 74, 570. [41] http://www.blu-ray.com. [42] New Blu-ray DVD format uses blue-violet lasers to achieve 27 GB recording capacity, http:// www.compoundsemiconductor.net (20 February 2002). [43] Nakamura, S., Senoh, M., Iwasa, N. & Nagahama, S.I. (1995) High-brightness InGaN blue, green and yellow light-emitting diodes with quanmm well structures. Jpn. J. Appl. Phys., 34, L797. [44] Sato, Y., Takahashi, N. & Sato, S. (1996) Full-color fluorescent display devices using a nearUV Hght-emitting diode. Jpn. J Appl. Phys., 35, L838. [45] http://lighting.sandia.gov/Xhghtinginit.htm. [46] Yasan, A., McClintock, R., Mayes, K., Darvish, S.R., Kung, P. & Razeghi, M. (2002) Topemission ultraviolet light-emitting diodes with peak emission at 280 nm. Appl. Phys. Lett., 81,801. [47] Yasan, A., McClintock, R., Mayes, K., Darvish, S.R., Zhang, H., Kung, P., Razeghi, M., Lee, S.K. & Han, J.Y. (2002) Comparison of ultraviolet light-emitting diodes with peak emission at 340 nm grown on GaN substrate and sapphire. Appl. Phys. Lett., 81, 2151. [48] Yasan, A., McChntock, R., Mayes, K., Darvish, S.R., Kung, P., Razeghi, M. & Molnar, R.J. (2002) 280 nm UV LEDs grown on HVPE GaN substrates. Opto-Electron. Rev., 10, 67. [49] Yasan, A., McChntock, R., Mayes, K., Kim, D.H., Kung, P. & Razeghi, M. (2003) Photoluminescence study of AlGaN-based 280 nm ultraviolet light-emitting diodes. Appl. Phys. Lett., 83, 4083. [50] Mayes, K., Yasan, A., McClintock, R., Shiell, D., Darvish, S.R., Kung, P. & Razeghi, M. (2004) High power 280 nm AlGaN light emitting diodes based on an asymmetric single quantum well. Appl. Phys. Lett., 84, 1046.
The Rise of lU-nitrides: An Introduction
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[51] Yasan, A., McClintock, R., Mayes, K., Shiell, D., Gautero, L., Darvish, S.R., Kung, P. & Razeghi, M. (2003) 4.5 mW operation of AlGaN-based 267 nm deep-ultraviolet light-emitting diodes. Appl Phys. Lett., 83, 4701. [52] lida, K., Kawashima, T., Miyazaki, A., Kasugai, H., Mishima, S., Honshio, A., Miyake, Y., Iwaya, M., Kamiyama, S., Amano, H. & Akasaki, I. (2004) 350.9 nm UV laser diode grown on low-dislocation-density AlGaN. Jpn. J. Appl. Phys., 43, L499. [53] Razeghi, JVl. & Rogalski, A. (1996) Semiconductor ultraviolet detectors. /. Appl. Phys. Appl. Phys. Rev., 79, 7433. [54] Razeghi, M. (2002) Short wavelength solar-blind detectors: status, prospects, and markets. Proceedings of IEEE, Wide Bandgap Semicond. Devices: The Third Generation Semiconductor Comes of Age, 90, 1006. [55] Streltsov, A., Moll, K.D., Gaeta, A., Kung, P., Walker, D. & Razeghi, M. (1999) Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode. Appl. Phys. Lett., 75, 3778. [56] Asif Khan, M., Kuznia, J.N., Olson, D.T., Van Hove, J.M., Blasingame, M. & Reitz, L.F. (1992) High-responsivity photoconductive ultraviolet sensors on insulating single-crystal GaN epilayers. Appl. Phys. Lett., 60, 2917. [57] Zhang, X., Kung, P., Walker, D., Piotrowski, J., Rogalski, A., Saxler, A. & Razeghi, M. (1995) Photovoltaic effects in GaN structures with p - n junction. Appl. Phys. Lett., 67, 2028. [58] Walker, D., Monroy, E., Kung, P., Wu, J., Hamilton, M., Sanchez, F.J., Diaz, J. & Razeghi, M. (1999) High-speed, low-noise metal-semiconductor-metal ultraviolet photodetectors based on GaN. Appl. Phys. Lett., 74, 762. [59] Kung, P., Zhang, X., Walker, D., Saxler, A., Piotrowski, J., Rogalski, A. & Razeghi, M. (1995) Kinetics of photoconductivity in n-type GaN photodetector. Appl. Phys. Lett., 67, 3792. [60] Walker, D., Zhang, X., Kung, P., Saxler, A., Javadpour, S., Xu, J. & Razeghi, M. (1996) AlGaN ultraviolet photoconductors grown on sapphire. Appl. Phys. Lett., 68, 2100. [61] Walker, D., Zhang, X., Saxler, A., Kung, P., Xu, J. & Razeghi, M. (1997) A^Gai-^N (0 < X < 1) ultraviolet photodetectors grown on sapphire by metal-organic chemical-vapor deposition. Appl. Phys. Lett., 70, 949. [62] Walker, D., Saxler, A., Kung, P., Zhang, X., Hamilton, M., Diaz, J. & Razeghi, M. (1998) Solar blind GaN p - i - n photodiodes. Appl. Phys. Lett., 72, 3303. [63] Monroy, E., Hamilton, M., Walker, D., Kung, P., Sanchez, F.J. & Razeghi, M. (1999) Highquality visible-blind AlGaN p - i - n photodiodes. Appl. Phys. Lett., 74, 1171. [64] Walker, D., Kumar, V., Mi, K., Sandvik, P., Kung, P., Zhang, X.H. & Razeghi, M. (2000) Solar-blind AlGaN photodiodes with very low cutoff wavelength. Appl. Phys. Lett., 76, 403. [65] McClintock, R., Yasan, A., Mayes, K., Shiell, D., Darvish, S.R., Kung, P. & Razeghi, M. (2004) High quantum efficiency AlGaN solar-blind photodetectors. Appl. Phys. Lett., 84,1248. [66] Yang, B., Heng, K., Li, T., Collins, C.J., Wang, S., Dupuis, R.D., Campbell, J.C., Schurman, M.J. & Ferguson, I.T. (2000) 32 X 32 ultraviolet Alo.1Gao.9N/GaN p - i - n photodetector array. /. Quantum Electron., 36, 1229. [67] Brown, J.D., Boney, J., Matthews, J., Srinivasan, P. & Schetzina, J.F. (2000) UV-specific (320-365 nm) digital camera based on a 128 X 128 focal plane array of GaN/AlGaN p - i - n photodiodes. MRS Internet J. Nitride Semicond. Res., 5, 6. [68] Lamarre, P., Hairston, A., Tobin, S.P., Wong, K.K., Sood, A.K., Reine, M.B., Pophristic, M., Birkham, R., Ferguson, I.T., Singh, R., Eddy, C.R., Jr., Chowdhury, U., Wong, M.M., Dupuis, R.D., Kozodoy, P. & Tarsa, E.J. (2001) AlGaN UV focal plane arrays. Phys. Stat. Sol. (a), 188, 289.
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Devices:
Ill-Nitrides
[69] Bhuiyan, A.G., Hashimoto, A. & Yamamoto, A. (2003) Indium nitride (InN): a review on growth, characterization, and properties. /. Appl Phys., 94, 2779. [70] Kung, P. & Razeghi, M. (2000) Ill-Nitride wide bandgap semiconductors: a survey of the current status and future trends of the material and device technology. Opto-Electron. Rev., 8, 201. [71] Asif Khan, M., Kuznia, J.N., Van Hove, J.M., Pan, N. & Carter, J. (1992) Observation of a twodimensional electron gas in low pressure metalorganic chemical vapor deposited GaNAl^Gai-;,N heterojunctions. Appl Phys. Lett., 60, 3027. [72] Asif Khan, M., Bhattarai, A., Kuznia, J.N. & Olson, D.T. (1993) High electron mobility transistor based on a GaN-Al^^Gai-^^N heterojunction. Appl. Phys. Lett., 63, 1214. [73] Ren, F., Abemathy, C.R., Van Hove, J.M., Chow, P.P., Hickman, R., Klaasen, J.J., Kopf, R.F., Cho, H., Jung, K.B., La Roche, J.R., Wilson, R.G., Han, J., Shul, R.J., Baca, A.G. & Pearton, S.J. (1998) 300°C GaN/AlGaN heterojunction bipolar transistor. MRS Internet I. Nitride Semicond. Res., 3, 41. [74] Teisseyre, H., Perlin, P., Suski, T., Grzegory, I., Porowski, S., Jun, J., Pietraszko, A. & Moustakas, T.D. (1994) Temperature dependence of the energy gap in GaN bulk single crystals and epitaxial layer. J. Appl. Phys., 76, 2429. [75] Gerlich, D., Dole, S.L. & Slack, G.A. (1986) Elastic properties of aluminum nitride. J. Phys. Chem. Solids, 47, 437.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 3
The Evolution of Nitride Semiconductors Satoshi Kamiyama, Hiroshi Amano and Isamu Akasaki Faculty of Science and Technology, High-Tech Research Center, and Nano-Factory, Meijo University, 1-501 Shiogamaguchi, Tempaku-ku, Nagoya 468-8502, Japan
It had been believed for long time that it was almost impossible to grow a high-quality GaN single crystal. This difficulty was overcome with low-temperature deposited buffer layer technology. This achievement opened up the pioneering path to the discovery of p-type conduction, control of n-type conductivity and verification of quantum size effects. These breakthroughs have led to the novel and high-performance devices such as high-efficiency blue, green and white light-emitting diodes, long-lived blue-violet lasers, low-noise UV detectors and high-speed transistors. Furthermore, UV-LEDs, which have recently been focused on as a leading edge of frontier application, have been improved by the reduction of threading dislocation density in an AlGaN layer. A device with external quantum efficiency of 1.4% at 363 nm peak wavelength has been demonstrated that could be used in such applications as lighting equipment in combination with three-color phosphors, exciting light sources of optical catalyst and so on. All of these nitride-based devices are able to operate in a harsh environment because of their toughness. They should also enable a great saving in energy and are suitable for the protection of the environment. Nitride semiconductors and their devices are expected to contribute significantly to the future of our world.
3.1.
INTRODUCTION
Group-Ill nitride semiconductors have been recognized as among the most promising materials for optical devices in the short-wavelength region because of their wide bandgap with direct transition. Since the AlGaInN system can cover a very wide wavelength range, from 200 nm to more than 1700 nm, it is also applicable not only to the short-wavelength devices but also the long-wavelength ones, as shown in Figure 3.1. The high electronsaturation velocity in GaN is also suitable for application in high-speed and high-power electronic devices. The superior physical and chemical stability of the nitride
E-mail address:
[email protected] (I. Akasaki).
23
24
Optoelectronic Devices: Ill-Nitrides 8
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In-plane Lattice Constant (nm) Figure 3.1. Direct bandgap energy as a function of in-plane lattice constant in AlGaInN system.
semiconductors will enable them to operate in harsh environments. Moreover, nitridebased devices are the most "environmentally friendly" ones available. To produce such novel devices, it is essential to grow high-quality nitride single crystals and to control their electrical conductivity. However, it has been quite difficult to grow high-quality epitaxial GaN films with a specular surface free from cracks. Moreover, its conductivity had never been controlled and, hence, many researchers retired from the nitride field. In the second half of the 1980s, there were two important breakthroughs: the development of extremely high-quality GaN single crystal with a specular surface free from cracks [1] and the discovery of p-type GaN together with the ability to fabricate a p - n junction light-emitting diode (LED) [2]. These breakthroughs have led to such developments as high-performance blue and green LEDs, violet laser diodes (LDs), ultraviolet (UV)-photodetectors (PDs) and field effect transistors (FETs). Very recently, the development of UV light-emitting devices has been focused on for frontier applications, such as lighting equipment in combination with three-color phosphors, light sources of high-density optical data-storage systems and excitation sources for optical catalysts. Many significant results concerned with the UV lightemitting devices have been reported in recent years. In this chapter, the evolution of group-Ill nitride semiconductors and blue lightemitting devices is reviewed. The recent advances of the crystal growth methods for
The Evolution of Nitride Semiconductors
25
low-dislocation-density and high-performance UV light-emitting diodes are also described.
3.2. NITRIDE RESEARCH IN THE EARLY DAYS
In 1969, Maruska and Tietjen succeeded in growing the first GaN single crystal on a sapphire substrate by hydride vapor phase epitaxy (HVPE) [3]. They also found that GaN has a direct-transition bandstructure with a bandgap energy of about 3.39 eV. This accelerated and inspired further research on GaN (Figure 3.2(a)). Dingle et al. demonstrated optically pumped UV stimulated emission from a GaN crystal at 2 K [4]. The first bluish-green LED having a metal-insulator-semiconductor (MIS) structure was developed by Pankove et al. in 1971 [5]. Ejder reported energy dispersion of the refractive index of GaN in 1971 [6]. In 1974, Monemar reported the temperature dependence of exciton recombination energy in GaN grown by HVPE [7].
1—'—\—'—\—'—r Source INSPEC Keyword GaN As of 1999 1000 h Laser diode (CW) h
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study of V luminescence'
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stimulated e emission RT
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_ HVPE GaN W
(B)
31:
(C)
(D)
-rr*-»r
_L ^ L 1965 1970 1975 1980 1985 1990 1995 2000 Calendar year Figure 3.2. Number of publications concerned with nitrides and their devices over the years.
26
Optoelectronic Devices: Ill-Nitrides (b)
IN, Figure 3.3.
Surface morphology of (a) GaN directly grown on a sapphire substrate and (b) GaN grown using LT-buffer layer on a sapphire substrate.
In contrast to traditional III-V compounds such as GaAs and InP, however, it was quite difficult to grow high-quality epitaxial GaN film and in particular, film with a flat surface free from cracks (Figure 3.3(a)). This was mainly due to the large lattice and thermal mismatches between the GaN epitaxial layer and the sapphire substrate. Moreover, the high residual electron concentration in GaN made it quite difficult to achieve p-type conduction and to control the conductivity of n-type GaN. As a result, many researchers withdrew from the field of research on nitride semiconductors (Figure 3.2(b)). One of the authors (LA.) started working on GaN in 1973, and grew single-crystalline GaN by molecular beam epitaxy in 1974 [8]. In 1981, he developed fairly bright bluishgreen MIS LED based on GaN grown by HVPE [9]. The emission wavelength was 495 nm and the external quantum efficiency T7ext was about 0.12%, which was a new record. This LED had the first flip-chip-type electrode so that we were able to fabricate it more easily. This LED, however, was not commercialized because the operating voltage, which is determined by the thickness of the insulating layer, ranged from several to 10 V and could not be controlled. However, he determined to continue to struggle with this difficult system at that time.
3.3.
BREAKTHROUGHS IN CRYSTAL GROWTH
In 1985, an extremely high-quality GaN with a specular surface free from cracks on a sapphire substrate was achieved by pioneering a low-temperature-deposited (LT-)buffer layer technology in the metal-organic vapor phase epitaxy (MOVPE) [1]. The essence of this method is to insert a slightly softer material between the epitaxial layer and the highly mismatched substrate in order to reduce the interfacial free energy. The surface morphology of GaN was dramatically improved by using an LT-AlN-buffer layer. The GaN film grown with the LT-buffer layer on a sapphire substrate is quite transparent and it has a specular surface free from cracks, as shown in Figure 3.3(b). The X-ray diffraction profiles [10] and photoluminescence (PL) property [11] showed that the crystalline quality of GaN was also significantly improved by using the LT-buffer layer.
The Evolution of Nitride Semiconductors
27
The residual electron concentration of the GaN grown with the LT-buffer layer was reduced to the order of 10^^ cm~^ (and soon after, to the order of 10^^ cm~^). Simultaneously, the electron mobility was greatly improved [12]. All of these results show clearly that, by inserting the LT-buffer layer, not only the crystalline quality but also the electrical and optical properties of GaN can be dramatically improved at the same time. In 1989, for the first time, distinct p-type GaN with low resistivity was discovered in Mg-doped GaN on the LT-buffer layer with low-energy electron-beam irradiation (LEEBI) [2]. Immediately, the first p - n junction UV (edge emission) and violet LED [2] were demonstrated. A p-type AlGaN and a p-type GaInN were also achieved in 1991 [13] and 1994 [14], respectively. In 1992, Nakamura succeeded in making p-type GaN by thermal annealing in a N2 atmosphere of Mg-doped GaN using Cp2Mg [15]. Regarding n-type doping, researchers attempted doping with SiH4 in 1986 [16], but it was difficult to control the conductivity due to the high density of residual donors. We also succeeded in controlling the conductivity of n-type nitrides using high-quality GaN or AlGaN grown with the LT-buffer layer in combination with SiH4 doping [17,18]. The electron concentration could be linearly controlled from an undoped level to 10^^ cm~^ without deterioration of surface morphology when the SiH4 flow rate was varied. Thus, essential technologies for the achievement of nitride-based devices were established in this period. These breakthroughs caused the transition from decline to prosperity in research on nitrides, which can be called the "Renaissance" in research on nitrides, as seen in Figure 3.2(c).
3.4. EVOLUTION OF NITRIDE-BASED BLUE LIGHT-EMITTING DEVICES Since the accomplishments of two important milestones, everything has progressed very quickly and work in the field began to grow tremendously. The high-crystalline nitrides have led to a revolutionary change in the optical properties of nitride materials and devices. Figure 3.4 shows the chronological change of the external quantum efficiency, T7ext of nitride-based blue LEDs. 7]^^^ had been saturated at about 0.1% before the breakthroughs were reached. It began to increase steeply after the success in growing high-quality nitride crystal, which resulted in the p - n junction LED. In 1992, rj^^^ of 1.5% was achieved [19], and in 1993, the first nitride-based blue LED was commercialized. At present, blue and green LEDs have rj^^^ of more than 20 and 10%, respectively. The LEDs are much brighter than incandescent lamps. A i7ext of 32% for a violet LED offers a promising excitation source for phosphors. Figure 3.5 shows the threshold power, Pth^ for optically pumped stimulated emission from nitrides over the years. Before 1985, the stimulated emission using optical excitation was obtained only at low temperatures and Pth was very high. After the two breakthroughs
28
Optoelectronic Devices: Ill-Nitrides
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1995\ 2000 Commercial LED
Calendar Year Figure 3.4. Chronological change of the external quantum efficiency, i7ext of nitride-based blue LEDs.
mentioned above, stimulated emission was achieved at RT and Pth began to decrease exponentially. Then the first lasing operation with pulsed current injection was achieved in 1995 [20] and a LD having continuous-wave operation was announced in 1996 [21]. By 1998, an estimated lifetime of 10"^ h had been achieved [22], becoming commercially available in 1999. One can see that the performance of light-emitting devices and the number of related publications (Figure 3.2) scale with each other.
3.5.
PROGRESS IN THE STUDY OF NITRTOE-BASED QUANTUM STRUCTURES
In a related activity, in 1991, a quantum size effect was verified by Itoh et al. [23] using an AlGaN/GaN quantum well, which was grown on high-quality GaN. A high electron
The Evolution of Nitride Semiconductors ^ •
29
Stimulated emission (low temperature) Stimulated emission (room temperature)
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2000
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Calendar Year Figure 3.5. Threshold power, P^YI for optically pumped stimulated emission from nitrides over the years.
mobility of a two-dimensional electron gas in AlGaN/GaN heterostructure was reported by Khan et al. in 1991 [24]. In 1993, Sakai et al. reported the theoretical band lineups of binary alloys of AIN, GaN and InN [25], which indicated that both AlGaN/GaN and GalnN/GaN systems have the type-I heterostructure. In 1994, it was shown that the wavelength dependence of the refractive indices of AlGaN and GaInN was suitable for optical confinement in DH or SCH structures [26]. A large piezoelectric field of about 5X10^ V/cm, which is induced by lattice mismatch, was observed in a GaN/AlN/GaN heterostructure in 1993 [27].
30
Optoelectronic Devices: Ill-Nitrides
The GalnN/GaN multi-quantum well (MQW), which is currently used as an active layer in nitride-based LDs, was first reported in 1995 [28-30]. Since then, peculiar properties of GaInN have been revealed. Despite the strong compressive strain of more than 1% in GaInN layers grown on GaN, it was found to be grown coherently, even in MQWs [31]. It was found that the bandedge photoluminescence intensity from GaInN MQW was greatly increased when the width of the wells was small [29,30], which was later qualitatively explained by the quantum-confined Stark effect (QCSE), due to the presence of the piezoelectric field [32].
3.6.
REDUCTION OF THREADING DISLOCATION DENSITY
3,6.1 GaN The reduction of threading dislocations in a GaN layer has been a focus of activity. The GaN grown on a sapphire substrate with the LT-buffer layer still contains dislocations, as many as 10^-10^^ cm~^.These dislocations are considered to be a major cause of the degradation of LDs which operate at high current density of 2 - 4 kA/cm^, and may pose an obstacle to the high-performance of PDs and TRs. Various technologies have been developed for the reduction of the dislocation density in a GaN layer, which are summarized in Figure 3.6. One is the application of a method
Akasaki's group Direct growth
Rough surface: Many cracks Dislocation density > 10'"'' cm'^
(until 1985)
Residual donor cone. > 10^^ cm-^ LT-buffer technology LT-buffer
Specular surface: Free from cracks
GaN
Dislocation density 10^-10''° cm"^
(1986) Sapphire
^
Residual donor cone. <10^^cm'^
%
Multi-LT-Buffer ('98)
^
Mass Transport ('99)
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I
Sapphire
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LT-buffer ^
LT-buffer
\/)teaNil Sapphire
LT-buffer
Figure 3.6. Technologies for the reduction of the dislocation density in GaN layer.
The Evolution of Nitride Semiconductors
31
(later called micro-channel epitaxy (MCE)) proposed by Nishinaga et al. in 1988 [33]. A variety of methods similar to MCE have been reported for the reduction of the dislocation density in nitrides, the most important being the epitaxial lateral overgrowth (ELO) techniques. Usui et al. developed a thick GaN layer with a dislocation density as low as 10^ cm~^ grown by HVPE using an ELO technique [34]. Later, Nakamura et al. fabricated a LD in the low dislocation region of ELO-GaN, and reported an estimated hfetime of more than 10"^ h [22]. Today, reduction of dislocation density in nitrides has been achieved by a variety of methods based on ELO. Another approach was developed for the reduction of the dislocation density to as low as 10^ cm~^ over the entire wafer using a LT-interlayer technology in 1998 [35]. A mass transport of nitrides in 1999 [36] and direct growth on a grooved substrate (GS) covered with a LT-buffer layer in 2000 [37] were proposed for the partial reduction of dislocation density. These three methods, developed by us and shown in the frame in Figure 3.6, do not require the use of a Si02 mask, which may diffuse into the crystal and may act as an obstacle. These methods enable us to reduce the dislocation density to the order of 10^ cm~l 3.6.2 AlGaN For the realization of a low-dislocation-density AlGaN layer, which is very important for UV light-emitting devices, as discussed in Section 3.7, other modified approaches are necessary. A difficulty in the reduction of the dislocations in AlGaN is mainly caused by a low diffusion length of Al atoms or Al-containing molecules on the surface of the substrate during the crystal growth. This makes it impossible to grow crystals selectively on the windows between dielectric masks in the ELO technique. Two methods have been developed for the reduction of the threading dislocation density in AlGaN, as shown in Figure 3.7. The first method (Figure 3.7(a)) is similar to the method using periodically grooved substrate described in Figure 3.6 [38]. In this method, however, it is possible to relax the lattice mismatch between underlying GaN and overgrown AlGaN layers by insertion of the LT-AIN interlayer [39]. A dislocation density as low as in the order of 10^ cm~^ was partially obtained in Alo.2Crao.8N, which was confirmed by both plan-view TEM image (not shown) and the dark spots in the CL image. Furthermore, the overgrown AlGaN layer is not cracked at all, due to the effect of the LT-AlN interlayer. In the method with periodically grooved GaN and the LT-AIN interlayer, only the AlGaN over the trenched regions has a low dislocation density, and the AlGaN over terrace regions still has as many as 10^^ cm~^ dislocations [38]. For the further reduction of dislocations in a whole AlGaN layer without cracks, the second method was demonstrated [40]. This crystal growth method comprises a first GaN epitaxial growth on sapphire substrate, a second selective growth of GaN seed crystals through (lIOO) Si02 stripe masks and a third planarized growth of Alo.22Gao.78N through an LT-AIN interlayer. After the first growth, Si02 stripe masks along with (1100) axis.
32
Optoelectronic Devices: Ill-Nitrides (a)
(b) Alo.2Gao.8N
Alo.isGaosiN
LT-AIN
LT-AIN Interlayer
'Si02 GaN
GaN LT-Buffer
LT-Buffer Layer Sapphire (0001)
Sapphire (0001)
© <1'100>
10 ^m
Dark spot
Figure 3.7. Technologies for the reduction of the dislocation density in AlGaN layer (a) a method using a periodically grooved substrate and the LT-AIN interlayer, (b) a method using selectively grown GaN seed crystals with (1122) facets and the LT-AIN interlayer. Photographs are surface cathode-luminescence images, where the dark spots show the threading dislocations.
where the width and spacing are both 5 |ULm, were formed on the GaN surface. In the second step, the GaN seed crystals were selectively grown on the window, and they have a cross-sectionally triangular shape with (1122) facets under an optimum growth condition. The dislocations in both GaN seed crystals and AlGaN layers are bent laterally, and, therefore, the whole area has dislocation density as low as 2 X 10^ cm"^, which was confirmed by the CL image [40]. In the point of view of the area of active region, the first method is convenient for the fabrication of UV-LDs, and the second is suitable for the UV-LEDs or UV-PDs.
3.7. UVLED 3.7.1 Difficulty of High-efficiency UV-LED Recently, development of UV-light-emitting devices has been seen as the next target. They are applicable to lighting equipment combining three-color phosphors, a light source of a high-density optical data-storage system, an exiting source of an optical catalyst, a sensing device in biological use and so on. However, the external quantum efficiency of UV-LEDs grown on a sapphire substrate is much lower than that of blue and green LEDs by a factor of more than two orders. Although visible or near-UV light-emitting diodes (LEDs) with GaInN quantum well active layer have high efficiency due to the effect
The Evolution of Nitride Semiconductors
33
of an In-rich cluster [41], UV LEDs with wavelengths shorter than 370 nm have very low efficiency because of a lack of In-rich clusters. The active layer of UV light-emitting devices basically comprises In-free materials, such as AlGaN, due to the requirement of a wide bandgap, so carriers can easily diffuse into non-radiative recombination centers at or around threading dislocations. On the other hand, an AlGaInN quaternary active layer is expected to have both UV bandedge emission and high quantum efficiency with In-rich clusters, and it is applied to active layers in UV-LEDs [42,43]. However, the crystalline quality of the quaternary alloy is thought to be inferior, so that the efficiency of UV LEDs having AlGaInN active layer is still very low. 3 J,2 Wavelength Variation of UV-LED with Low Dislocation Density The growth technologies described in the previous section are expected to have a potential for realization of UV-LEDs with high quantum efficiency. We applied the growth technology shown in Figure 3.7(b) to the fabrication of all UV-LEDs [40]. Figure 3.8 shows the schematic device structure, where an n-Alo.15Gao.85N first cladding layer (0.3 jxm), an active layer, a p-Alo.4Gao.6N blocking layer (20 nm), a p-Al;cGai_;cN second cladding layer (0.2-0.4 |jLm) and a p"^-GaN (0.05 jxm) contact layer were successively grown on the Alo.15Gao.85N base layer. The material of the active layer and composition of p-Al^^Gai-^^N second cladding layer are varied with changing emission wavelength as mentioned below. A Ni/Au semi-transparent p-contact and an Au bonding pad electrode were deposited on the p-side, and a Ti/Al n-contact was formed on the n-side. Under the Au bonding pad, a thin Ti layer is deposited just on the p^-GaN contact layer in order to reduce the current injection there. Four kinds of active layers (summarized in Table 3.1) were used in UV LEDs for the variation of emission Semi-trans, p-contact p-pad contact , f ^ ^ ^^ p+-contact layer p-Alo.4Gao.6N C I Active layer . n-contact ^^^
LT-AIN interlayer GaN seed crystal
. p-pad contact Semi-trans, p-contact " n-contact
LT-buffer layer
Figure 3.8.
Schematic device structure of UV LED grown on high-quality AlGaN base layer with low dislocation density. Right-hand side shows a top view of UV LED.
34
Optoelectronic Devices: Ill-Nitrides Table 3.1. Structural parameters of UV-LEDs with different emission wavelength LED (a) (b) (c) (d)
Active layer
p-cladding layer
GaN (60 nm) MQW (GaN:3 nm) Alo.1Gao.9N (60 nm) Alo.i6Gao.84N (60 nm)
Alo.15Gao.85N (0.4 |xm) Alo.2Gao.8N (0.2 fxm) Alo.25Gao.75N (0.2 |xm) Alo.3Gao.7N (0.2 |xm)
wavelength. The active layers are made of (a) bulk GaN, (b) GaN/Alo.o8Gao.92N:Si MQW, (c) bulk Alo.ioGao.9oN and (d) bulk Alo.i6Gao.84N. The AIN molar fractions of p-Al;,Gai_;,N second cladding layer are 0.15 for (a), 0.2 for (b), 0.25 for (c) and 0.3 for (d), respectively. All the bulk active layers are undoped. The thickness of p-Al^^Gai-^^N second cladding layer is 0.4 |xm in LED (a) and that of others is 0.2 jxm. The peak wavelengths of electroluminescence under 50 mA (DC) drive are 363, 352, 338 and 323 nm for LEDs (a), (b), (c) and (d), respectively. The output power as a function of peak wavelength at 50 mA (DC) bias is shown in Figure 3.9. All LEDs have output powers of more than 0.1 mW, and they are greatly dependent on the peak wavelength. With shortening of the wavelength, output power is linearly reduced. This may partly be due to the deterioration of current spread in p-layers, which must lead to the reduction of light extraction from the device. The output power of the 363-nm device with GaN active layer has a maximum output power of 1.2 mW. This output power is still much lower
1.4
-
LED (a)
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lf=50mA(DC), RT 1
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340
350
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1
1
360
370
Wavelength (nm) Figure 3.9. Wavelength variation of output powers at 50-mA operating current.
The Evolution of Nitride Semiconductors
20
40
60
35
80
Forward Current [mA] Figure 3.10.
Output power and operating voltage as a function of forward current of modified 363 nm UV LED with high light extraction efficiency.
than those of violet and blue LEDs with GaInN active layers. Some problems may remain, such as the still-unsolved non-radiative recombination in active layers and low light-extraction efficiency caused by poor current spread in p-layers and light absorption in p'^-GaN contact layer or semi-transparent metals. 3,7,3 Improvement of External Quantum Efficiency for 363-nm LED We modified the device structure of the 363-nm LED for the improvement of light-extraction efficiency [44]. It has a Si02 current blocking layer inserted between the p'^-GaN contact layer and the bonding pad electrode and a mesh-type p-side contact. The Si02 current blocking layer is placed just under the bonding pad so only current injection under the pad, which causes an absorption loss of emitting light, is blocked. The injection current can easily spread along the semi-transparent p-contact and p-Alo.15Gao.85N cladding layer. Therefore, no light is emitted under the bonding pad and light extraction efficiency may be improved. Compared with the conventional device, a uniform light emission image is obtained in the modified device. The wide emitting area is attributed to the grid-type p-side contact. V-I and L-I curves of these LEDs are shown in Figure 3.10. High output powers of 2.3 mW at 50 mA and 4.7 mW at 100 mA are achieved in the modified LED. The maximum external quantum efficiency is as high as 1.4%. Considering the absorption loss in the underlying GaN layer, this efficiency is quite high. When the transparent underlying layer and backside extraction configuration are used, the external quantum efficiency is expected to improve with at least one order of magnitude.
36
Optoelectronic Devices: Ill-Nitrides
3.8. CONCLUSION The dramatic improvement of the crystalline quality of nitrides through the pioneering of the LT-buffer layer technology and the realization of p-type conduction gave rise to a "Renaissance" in the research of nitride semiconductors. The breakthroughs have led to high-performance blue, green, and white LEDs, violet LDs, FETs and UV-PDs. All of these nitride-based devices are robust and will potentially enable a tremendous saving of energy. Today, the performance of these devices is still improving, following steady progress in the areas of crystal growth, processing and fundamental physics. Further progress is required for expansion of device applications toward the frontier regions. As a next promising nitride-based device, high-efficiency UV-LEDs using Alo.22Gao.78N base layer with low dislocation density have been demonstrated. The new crystal growth method with GaN seed crystal with (1122) facets and lateral growth of Alo.22Grao.78N through LT-interlayer enables the overgrown Alo.22Gao.78N to have a low dislocation density of 2 X 10^ cm~^ and be crack-free over whole wafer. The UV-LEDs grown on the high-quality Alo.22Gao.78N base layer have high output powers of more than 0.1 mW at 50 mA drive in a wide range of wavelengths from 323 to 363 nm. Further improvement of the efficiency is achieved using a modified device structure, which avoids light absorption loss at the bonding pad electrode. The highest output power of 4.7 mW at 100 mA driving current is obtained with 363 nm emission wavelength. In conclusion, the evolution of nitride semiconductors, the most environment friendly materials available, will have a great impact on the future world.
ACKNOWLEDGEMENTS The authors have the pleasure to thank T. Takeuchi, M. Iwaya, S. Nitta, C. Wetzel, S. Yamaguchi and T. Detchprohm for their good collaboration.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]
Amano, H., Sawaki, N., Akasaki, I. & Toyoda, T. (1986) Appl Phys. Lett., 48, 353. Amano, H., Kito, M., Hiramatsu, K. & Akasaki, I. (1989) Jpn. J. Appl. Phys., 28, L2112. Maruska, H.P. & Tietjen, J.J. (1969) Appl. Phys. Lett., 15, 327. Dingle, R., Shaklee, K.L., Leheny, R.F. & Zetterstrom, R.B. (1971) Appl. Phys. Lett., 19, 5. Pankove, J.I., Miller, E.A., Richman, D. & Berkeyheiser, J.E. (1971) /. Lumin., 4, 63. Ejder, E. (1971) Phys. Stat. Sol. (a), 6, 445. Monemar, B. (1974) Phys. Rev. B, 10, 676. Akasaki, I. & Hayashi, I. (1976) Kogyo Gijutsu, 17, 48 in Japanese. Ohki, Y., Toyoda, Y., Kobayashi, H. & Akasaki, I. (1981) Inst. Phys. Conf. Ser., 63, 479.
The Evolution of Nitride Semiconductors
37
[10] Koide, Y., Itoh, N., Itoh, K., Sawaki, N. & Akasaki:, I. (1988) Jpn. J. Appl Phys., 27, 1156. [11] Naniwae, K., Itoh, S., Amano, H., Itoh, K., Hiramatsu, K. & Akasaki, I. (1990) /. Cryst. Growth, 99, 381. [12] Akasaki, I., Amano, H., Koide, Y., Hiramatsu, K. & Sawaki, N. (1989) /. Cryst. Growth, 98, 209. [13] Akasaki, I. & Amano, H. (1992) Mater Res. Soc. Symp. Proc, 242, 383. [14] Yamasaki, S., Asami, S., Shibata, N., Koike, M., Tanaka, T., Amano, H. & Akasaki, I. (1995) Appl Phys. Lett., 66, 1112. [15] Nakamura, S. (1991) Jpn. J. Appl. Phys., 30, L1705. [16] Sayyah, K., Chung, B.C. & Gershenzon, M. (1986) /. Cryst. Growth, 77, 424. [17] Akasaki, I., Amano, H., Kitoh, M., Hiramatsu, K., Sawaki, N., (1989) 175th Electrochemical Society Meeting. [18] Murakami, H., Asahi, T., Amano, H., Hiramatsu, K., Sawaki, N. & Akasaki, I. (1991) /. Cryst. Growth, 115, 648. [19] Akasaki, L, Amano, H., Itoh, K., Koide, N. & Manabe, K. (1992) Inst. Phys. Conf. Ser, 129, 851. [20] Akasaki, I., Amano, H., Sota, S., Sakai, H., Tanaka, T. & Koike, M. (1995) Jpn. J Appl. Phys., 34, L1517. [21] Nakamura, S., Senoh, M., Nagahama, S., Iwasa, N., Yamada, T., Matsushita, T., Kiyoku, H. & Sugimoto, Y. (1996) Jpn. J Appl. Phys., 35, L74. [22] Nakamura, S., Senoh, M., Nagahara, S., Iwasa, N., Yamada, T., Matsushita, T., Kiyoku, H., Sugimoto, Y., Nozaki, T., Umemoto, H., Sano, M. & Chocho, K. (1998) Jpn. J Appl. Phys., 37, L627. [23] Itoh, K., Kawamoto, T., Amano, H., Hiramatsu, K. & Akasaki, I. (1991) Jpn. J Appl. Phys., 30, 1924. [24] Khan, M.A., Van Hove, J.M., Kuznia, J.N. & Olson, D.T. (1991) Appl. Phys. Lett., 58, 2408. [25] Sakai, S., Ueta, Y. & Tarauchi, Y. (1993) Jpn. J Appl. Phys., 32, 4413. [26] Akasaki, I. & Amano, H. (1994) Mater Res. Soc. Symp. Proc, 339, 443. [27] Bykhovski, A., Gelmont, B. & Shur, M. (1993) /. Appl. Phys., 74, 6734. [28] Nakamura, S., Senoh, M., Iwasa, N., Nagahama, S., Yamada, T. & Mukai, T. (1995) Jpn. J Appl. Phys., 34, L1332. [29] Akasaki, L, Amano, H. & Suemune, I. (1995) Proceedings of the International Conference on Silicon Carbide and Related Materials, Kyoto, MoA-I-2. [30] Amano, H. & Akasaki, I. (1995) Extended Abstracts International Conference on Solid State Devices and Materials, Osaka, vol. 7, p. 683. [31] Takeuchi, T., Takeuchi, H., Sota, S., Sakai, H., Amano, H. & Akasaki, I. (1997) Jpn. J Appl. Phys., 36, L177. [32] Takeuchi, T., Sota, S., Katsuragawa, M., Komori, M., Takeuchi, H., Amano, H. & Akasaki, I. (1997) Jpn. J Appl. Phys., 36, L382. [33] Nishinaga, T., Nakano, T. & Zhang, S. (1988) Jpn. J Appl. Phys., 27, L964. [34] Usui, A., Sunakawa, H., Sakai, A. & Yamaguchi, A.A. (1997) Jpn. J Appl. Phys., 36, L899. [35] Iwaya, M., Takeuchi, T., Yamaguchi, S., Wetzel, C , Amano, H. & Akasaki, I. (1998) Jpn. J Appl. Phys., 37, 316. [36] Nitta, S., Kariya, M., Kashima, T., Yamaguchi, S., Amano, H. & Akasaki, I. (1999) Abstracts of Third International Symposium on Control of Semiconductor Interfaces, Karuizawa, B305. [37] Yano, M., Detchprohm, T., Nakamura, R., Sano, S., Mochizuki, S., Nakamura, T., Amano, H. & Akasaki, I. (2000) IPAP Conf Ser, 1, 292.
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[38] Iwaya, M., Nakamura, R., Terao, S., Ukai, T., Kamiyama, S., Amano, H. & Akasaki, I. (2000) IPAP Conf. Ser., 1, 833. [39] Kamiyama, S., Iwaya, M., Hayashi, N., Takeuchi, T., Amano, H., Akasaki, I., Watanabe, S., Kaneko, Y. & Yamada, N. (2001) J. Cryst. Growth, 223, 83. [40] Kamiyama, S., Iwaya, M., Takanami, S., Terao, S., Miyazaki, A., Amano, H. & Akasaki, I. (2002) Phys. Stat. Sol. (a), 192, 296. [41] Mukai, T. & Nakamura, S. (1999) Jpn. J. Appl. Phys., 38, 5735. [42] Hirayama, H., Enomoto, Y., Kinoshita, A., Hirata, A. & Aoyagi, Y. (2000) Phys. Stat. Sol. (a), 180, 157. [43] Khan, M.A., Adivarahan, V., Zhang, J.P., Chen, C , Kuokstis, E., Chitnis, A., Shatalov, M., Yang, J.W. & Simin, G. (2001) Jpn. J. Appl. Phys., 40, L1308. [44] Iwaya, M., Takanami, S., Miyazaki, A., Watanabe, Y., Kamiyama, S., Amano, H. & Akasaki, I. (2003) Jpn. J. Appl. Phys., 42, 400.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 4
Technology of MOVPE Production Tools M. Dauelsberg^, E.J. Thrush'', B. Schineller^ and J. Kaeppeler^ ^AIXTRON AG, Kackertstr. 15-17, 52072 Aachen, Germany ^Thomas Swan Scientific Equipment, Anderson Road, Buckingway Business Park, Swavesey, Cambridge CB4 5FQ, UK
4.1. INTRODUCTION This chapter will describe the activities of the AIXTRON group of companies in the MOVPE of Ill-nitrides. AIXTRON is a pure supplier of equipment for the semiconductor market, and therefore, we will describe our activities to deliver the state-of-the-art MOVPE tools to the Ill-nitride market. The MOVPE of Ill-nitrides became important in the early 1990s when Akasaki [1] and Nakamura [2] first demonstrated nitride-based light-emitting diodes (LEDs). These results motivated a lot of research groups to embark on research into the MOVPE of Ill-nitrides. These groups often started with modified reactors, which were originally used for the growth of GaAs- or InP-based materials. The precursors used for the group III component when growing Ga(Al,In)N are mainly the same as used for the growth of GaAs- or InP-based materials. These are TMGa, TEGa, TMAl and TMIn. Regarding the group V precursor, NH3 was normally used for growing Ill-nitrides. A notable difference between this reagent and ASH3 and PH3 is the higher bond energies (-70.6-72.8 kcal/mol for AsHs, - 7 6 . 9 81.4 kcal/mol for PH3 and - 100-105.7 kcal/mol for NH3 [3]), which requires a higher growth temperature of about 1100°C for GaN. A detailed description of the thermal chemistry is made in Section 4.3. As the existing reactors were designed for maximum growth temperatures of about 850-900°C, modifications were required to enable the reactors to run at temperatures up to or above 1100°C. For the substrate holder (susceptor) to reach these temperatures, most reactors are equipped with a radio frequency (RF) heater or resistance heater. Most of the fundamental research was performed on these small homemade reactors. In the mid-1990s, a few groups were able to grow LED structures on these small systems and the first interest in larger scale reactors for the production of blue LEDs developed. At that time, production processes for growing the GaAlInP-based epilayers used for LEDs operating in the yellow to red spectral region were established on multi-wafer
E-mail address:
[email protected] (J. Kaeppeler).
39
40
Optoelectronic Devices: Ill-Nitrides
systems. These systems were not, however, able to grow GaN-based material because the maximum operation temperature was limited to 900°C. Another limitation concerned with the material for the wafer carrier (susceptor) was mainly the uncoated graphite. This could not be used in an NH3 containing ambient because NH3 or its decomposition products react with pure graphite at these elevated temperatures. The most common solution to this problem is to coat the graphite with SiC, which does not react, with NH3 at process temperatures, and therefore, protects the graphite against corrosion. Another important development which was addressed at this time concerned the provision of in situ monitoring of the wafer surface during growth. As there are still no commercial substrates available, which are lattice-matched, sapphire and SiC are the most commonly used substrates. In order to ameliorate the effects of the lattice mismatch between these substrates and GaN, a low-temperature nucleation layer is required [4]. As an aid to improving the growth control, especially during the transition between the growth of the low-temperature nucleation layer, which has a three-dimensional growth mode, and the epi-layer proper, which grows in a two-dimensional, step-flow, regime, in situ reflectance measurements have proved to be very useful. This means that optical access to the wafer surface is essential for MOVPE reactors. The current market requirements for production MOVPE machines are significantly changed from those of the late 1990s. Today, the market expects a system with high throughput and low cost of ownership (CoO) combined with high performance regarding the uniformity of layer properties such as thickness, wavelength, electro-luminescence intensity and doping level. This market also requires an up-scaling of the reactor to permit growth on larger wafer areas whilst at the same time improving the performance of the reactor. Computational modeling of nitride MOVPE processes and reactors is essential in the development of MOCVD equipment. The use of this technique improved the quality and reduced the time of the reactor development, and will, therefore, be explained here. The Planetary Reactor® and Close-Coupled Showerhead (CCS) reactor concepts will be described as these are the state-of-the-art production tools for GaN-based LED offered by the AIXTRON group of companies.
4.2. TYPES OF REACTORS 4,2,1 Horizontal Tube Reactors The horizontal reactor in its simplest form is a tube equipped with a heated wafer carrier through which the process gases flow, as shown in Figure 4.1. The concentration of the process gases will deplete from the gas inlet towards the gas outlet. This will cause a decrease in growth rate in the gas-flow direction. The most efficient means of compensating for this effect is to rotate the substrate, which will average the growth conditions in a radially symmetric manner. If the depletion curve can be tuned
Technology ofMOVPE Production Tools
41
Reactor wall / ^ ^
^.---''^ Susceptor
Gas Substrate
\
Reactor Figure 4.1. Schematic top view of a horizontal MOCVD reactor.
to a linear shape, this rotation will generate a flat, uniform layer thickness on the wafer. The rotation will also help to flatten the temperature profile of the substrate. Today, horizontal reactors are mainly used for the R&D of Ill-nitride layers and for the small-scale production of high-value device structures such as laser diodes. The horizontal reactor AIX 200/4RFS is optimized to the special requirements for this application. By using an inductively heated susceptor, substrate temperatures up to 1200°C can be reached. The susceptor utilizes a gas-driven rotation mechanism for the wafer platter (the so-called Gas Foil Rotation, GFR®). The group III and group V reagent gases are separately delivered to the substrate surface and guided over the heated substrate holder through a rectangular-shaped liner tube, as shown in Figure 4.2. The group III (metalorganics in N2 or/and H2) and the group V (NH3 in N2 or/and H2) components are kept separate until they reach the growth area above the substrate to avoid premature reaction between them. A stainless steel reactor with three optical ports allows optical
Group I
In-situ measurement tool (reflectance and temperature)
Group V
Figure 4.2. AIX 200/4 RFS reactor.
42
Optoelectronic Devices: Ill-Nitrides
access to the substrate surface for the use of in situ measurement tools such as a reflectometer or pyrometer. 4,2,2 Planetary Reactors 4,2,2,1 Concept, The concept of the planetary reactor is based on the horizontal tube reactor. In the horizontal reactor, the gas is flowing with a nearly constant velocity across the wafer. The depletion of the process gases in the gas-flow direction will cause a continuous reduction in growth rate. The deposition rate on the wafer is governed by the flow and diffusion of group III species, as shown in Figure 4.3. Although the depletion of reagents can be compensated for by rotation of the wafer, the process gases will not be utilized very efficiently if the reaction time between gaseous precursors and wafer is limited. A decreasing velocity would increase the potential reaction time between reagents in the gas phase and wafer surface. This would cause stronger depletion whilst increasing the utilization efficiency of the process gases. Now, the velocity could be decreased by increasing the cross-section of the flow channel of such a reactor. This could be realized by increasing the width of the flow channel across the wafer in the gas-flow direction. The rotation of the main planetary disk is not of fundamental importance for layer-growth quality; it is mainly used to average the heat flux from the heater to the substrate holder to guarantee a uniform circular temperature distribution. The top view of such a reactor would look like a piece of cake. The planetary reactor can be regarded as an aggregate of such reactor sections to form a complete circular shape. Frijlink developed the concept of the planetary reactor in the late 1980s [5]. The substrates placed on a platen rotate around the gas inlet at the center of the reactor. The gas inlet is separated into two levels. Through the top inlet group III process gases are injected whilst the lower inlet is used to inject group V precursor and its carrier gas into the reactor. A schematic view of the reactor is shown in Figure 4.4. The ceiling of the reactor flow channel is made of quartz and is heated by radiation from the IR- or RF-heated susceptor. The temperature of this ceiling is controlled by the varying ratio of the two gases comprising the gas mixture, which flows between the ceiling and the water-cooled reactor top. These two gases are chosen to have a markedly different thermal conductivity from each other, such that the adjustment of the composition of the mixture effectively regulates the transport of heat from the ceiling. In most cases, these gases are H2 and N2.
Transport by flow Group I
Group V
Diffusi in cross-flow direction I Diffusion Figure 4.3. Transport of growth limiting species.
I
Technology of MOVPE Production Tools
43
In the original reactor built by Frijlink, IR lamps heated the susceptor. As described in Section 4.1, GaN growth requires susceptor temperatures of about 1100°C. Due to this requirement for higher process temperatures, planetary reactors for Ill-nitride growth are equipped with an inductive RF-heater. 4,22,2 Up-scaling, The first planetary reactor designed for Ill-nitride growth, the AIX 2000HT, had a 6 X 2 in. configuration. A few years later, this configuration was established as the state-of-the-art production tool for Ill-nitride-based LEDs. However during the late 1990s the production market was calling for larger reactor loads, prompting the evolution to the next size which had a 11 X 2 in. configuration. During this evolution, computational modeling was used to specify the reactor geometry. The main changes required were a larger susceptor diameter, a modified reactor height and a larger RF-coil for heating the larger susceptor. The modeling also provided guidance in the adjustment of the process parameters such as flow of carrier and process gases needed to transfer the process from the 6 X 2 in. to the 1 1 x 2 in. platform. It has been shown that the larger configuration maintains, or even out-performs, the process characteristics of the smaller reactor.The next up-scaling to the 24 X 2 in. configuration (AIX 2600G3 HT) changed one more important parameter, the satellite size, which was increased to fit one 4-in. wafer or three 2-in. wafers on each of the eight satellites. This increased the growth length in the radial direction on the susceptor and required some additional parameter adjustment but
Carrier + NHo
Carrier + group III elements + dopant
Tliermostated quartz glass ceiling Injector
Growth rate on rotated wafer
Wafer on rotating satellite
Rotating inductively heated susceptor
radius Figure 4.4.
Schematic view of Planetary Reactor® concept.
44
Optoelectronic Devices: Ill-Nitrides
Figure 4.5.
AIX 2600G3 HT with 24 X 2-in. configuration.
the growth results following this tuning indicated that the process could again be transferred effectively to the larger configuration shown in Figure 4.5. 4,2.23 Growth Results, We will now discuss current developments and results relating to the growth of nitride semiconductors with a special focus on large-scale production. Here, the key issue is CoO, to which the main contributing factors are yield, precursor consumption, ratio of uptime to downtime, cycle time between runs, and the wafer area, which can be deposited on in a single run. All these topics must be addressed by the epitaxy tool manufacturer to support the customer in this challenging marketplace. Optoelectronic Devices and Structures. While the relatively mature optoelectronics sector is still focused on 2-in. processing capability, 4-in. sapphire wafers are becoming available in the market, making a switchover to 4-in. processing lines a commercially viable option in the near future. The epitaxy tool manufacturers such as AIXTRON must ensure smooth transitions from one wafer size to the other by making the processes scalable and transferable. The AIX 2600G3 HT system in its 24 X 2 in. configuration, which, as the world's largest epitaxy system, is also the workhorse of the optoelectronics industry, answers this issue by design. The susceptor of this reactor features eight Gas Foil Rotation™ recesses, each of which can hold disks for either three 2-in. wafers or for one 4-in. wafer. This allows the reactor to be operated in 24 X 2 or 8 X 4-in. configurations, and even mixed configurations using 2 and 4-in. wafers simultaneously are possible for evaluation purposes. Since the geometry of the process chamber is not changed, the process
Technology ofMOVPE Production Tools
45
conditions for both wafer sizes are identical and the change from 2 to 4-in. operation merely requires the exchange of the wafer disks, which can be done in a couple of minutes. When statistically evaluating the room temperature photoluminescence maps of all 24 wafers from the same run, a uniform distribution of the wafer properties, independent of their respective position on the susceptor, can be found. For instance, for an average wavelength of 475.4 nm with a standard deviation from wafer to wafer of just 1.11 nm, the on-wafer standard distribution of the wavelength was measured to be between 1.5 and 2.5 nm using a 3 mm edge exclusion. This performance is corroborated by additional data for a run in the green spectral range. The mean wavelength was at 525.3 nm with 1.7 nm standard deviation from wafer to wafer and on-wafer standard deviations in the order of 3 nm. The slightly higher variation in wavelength for these structures as compared with the first run is explained by the increased tendency of the InGaN quantum well material to undergo spinodal decomposition into In-rich clusters in a Ga-rich matrix. Energetically, these In-rich clusters form quantum-dot-like structures, which strongly affect the recombination efficiency and wavelength. In addition, the lattice mismatch between the Ga-rich matrix and the In-rich clusters gives rise to piezoelectric effects and spontaneous polarization, which also contribute to wavelength shifts and efficiencies. Such effects are more pronounced with the higher amount of In used in the green spectral range; hence, the higher sensitivity of the material to slight temperature variations as they naturally occur on the wafer surface. Reproducibility is one of the main factors that affects yield and CoO. Therefore, a stable epitaxy tool and process are prerequisites for mass production and the epitaxy tool manufacturer must address these issues while maintaining the tool's flexibility for different applications. Figure 4.6 shows the photoluminescence data from eight runs in the blue and green spectral ranges. The range of the emission wavelengths was measured to be ^^max-min = 2.4 nm for the blue and AAmax-min = 4.4 nm for the green spectral range. These results show that modern epitaxy systems produce predictably good results while offering the device manufacturers the flexibility to address their markets. As discussed earlier, the facile transfer of processes to larger wafer sizes has been established. Figure 4.7 shows the photoluminescence map of an LED structure grown on a 4-inch wafer under similar process conditions as discussed above. The slightly higher standard deviation of the wavelength is a consequence of greater inherent strain in the sapphire, which causes the edge of the wafer to bow, reducing the thermal contact to the substrate holder. This effect is currently being addressed by the wafer vendors and it is expected that they will find a solution soon. Electronic Device Structures. The high-power/high-temperature electronics device market is currently emerging from its research and development phase and is now attracting significant interest in the industrial mainstream. In contrast to
46
Optoelectronic Devices: Ill-Nitrides
3
4
5
Run number Figure 4.6.
Example for tool and process stability for eight runs at two different wavelength regimes.
the optoelectronics market, the electronic device industry utilizes processing lines with 4-in. capability. The uniform deposition of all materials commonly used in electronic devices, most notably doped and undoped AlGaN of differing compositions, can be seen as the cornerstone for efficient and cost-competitive production of transistors. Figure 4.8 shows a thickness map measured by white light interference for AIN grown on a 4-in. sapphire wafer. At a thickness of 450 nm, a standard deviation of just 0.025 nm Peak Lambda
nm 505.0 499.0 493.0 487.0 481.0 475.0 469.0 463.0 457.0 451.0 445.0 Avge : 471.4 Median: 471.1 Std Dev: 1.098 % (5.175)
Figure 4.7.
Photoluminescence mapping of an InGaN/GaN MQW structure grown on 4-in. sapphire under simmilar process conditions as discussed above.
Technology ofMOVPE Production Tools Thickness
47 pm |0.950 0.850 0.750
\
0.650
\ \
0.550
1
0.450
1
0.350
1 1
;3"v:
0.250 0.150
/
H0.050 •-0.050
Avge : 0.458 Median : 0.466 Std Dev: 5.492 % (0.025) Figure 4.8. Thickness mapping for AIN grown on 4-in. sapphire at a growth rate of 1 ixm/h.
was achieved. Most notably, the high growth rate of 1 jjum/h in this process shows that mass production with short cycle times is possible for the production of transistor structures. In addition, the growth of binary AIN material is widely seen as challenging. Possible pre-reactions between TMAl and NH3 in the gas phase, which result in the formation of particulates and effect low growth rates in some alternative reactor designs, make the careful engineering of reactors mandatory. 4,2,2,4 Future Developments, The ever-changing marketplace with its constant focus on CoO and better device performance is likely to keep the epitaxy tool manufacturers busy for years to come. Current and future challenges will lay in making the wafer throughput higher, not only by following the proven routes of expanding the reactor chambers, but also by reducing cycle times between runs, increasing heat-up and cool-down ramp rates and improving wafer uniformities to increase the usable area per run. In addition to that, the stability and longevity of reactor parts, reduced and plannable maintenance efforts and the reduction in the usage of source materials will be at the heart of future developments. In this way, the epitaxy tool manufacturers will stand firmly by the side of their customers, addressing the arising issues of constant market evolution. 4,2,3 Close-coupled Showerhead Reactors 4,2,3,1 Concept, The concept of the CCS reactor is based upon a mathematical analysis of fluid flow undertaken more than 40 years ago. In a treatment by Schlichting [6], which employed an analytical solution of the relevant Navier-Stokes equations to describe the flow streamlines, velocity distribution and boundary layer arising when
48
Optoelectronic Devices: Ill-Nitrides
a uniform flow of gas stalls against a perpendicular flat surface, it was shown that the boundary-layer thickness is independent of the distance from the stagnation point (i.e. the point at which the flow separates to pass around the object in the path of the flowing gas). The boundary layer is a notional layer of gas, adjacent to the solid surface, through which the velocity increases from zero at the surface to the free stream velocity. A diagrammatic representation of this situation is given in Figure 4.9. As the diffusion of growth precursors through this boundary layer, in the classical mass transfer limited regime commonly used for MOCVD, determines the growth rate and composition of higher alloys, its invariance with position on the susceptor implies that reactors of this geometry should inherently give good uniformity. It should be noted, however, that the analysis discussed earlier applies to an idealized situation where the susceptor is immersed in an infinite volume of gas, at a fixed temperature, which flows toward the susceptor with no other constraints. In practical reactors, there are generally a number of deviations from this ideal situation, which complicate the simple concept. One of the most important of these is a "wall drag" effect that causes the gases flowing through the deposition chamber to develop a parabolic velocity profile that increases progressively as the distance from the injection point to wafer is increased. Traditional designs that require the injected gases to expand into the deposition zone from a narrow entry point are also prone to complex "jetting", effects which can lead to recirculation cells at the gas injection point. Additionally, thermal buoyancy-driven recirculation cells, which arise from the change in density of the gas as it enters the hot reaction zone, can also degrade both the uniformity
Local horizontal flow vectors Figure 4.9.
Schematic diagram depicting streamlines, velocity profile and boundary layer for an idealized stagnation-point flow, rotating disk reactor (after H. Schlichting [6]).
Technology ofMOVPE Production Tools
49
and the interface quality of the structures grown. Finally, for the MOCVD growth of III-V compounds from group III metal alkyls and group V hydrides, the simple pyrolysis-based chemistry is complicated by a parasitic low-temperature reaction between these two types of reagent (the formation of addition compounds), which can undermine the control and chemical efficiency of the process and give rise to particulate contamination. A feature of the CCS reactor, shown diagrammatically in Figure 4.10 and as a photograph in Figure 4.11, is that it provides the means of minimizing these unwanted second-order effects such that the idealized behavior can be closely approximated to in a simple manner. This is done by introducing the reagents across the whole of the reaction zone from a multiplicity of separate injector tubes, embodied in a water-cooled showerhead, located very close to the growing wafers. The SIC coated graphite wafer platen is in the form of a short inverted cylinder, open at the bottom, which rotates about a fixed multi-zone spiral heater. The distribution of power to these zones can be adjusted within the control software to permit flat susceptor temperature profiles to be realized across the temperature range used for III-V epitaxy. The fact that the injection area is matched to that of the deposition zone mitigates against unwanted macroscopic jetting effects, whilst the close proximity of the injector to the growing wafers minimizes the scope for the development of the parabolic velocity profile referred to earlier. The proximity of the showerhead to the reaction zone also suppresses thermal buoyancy-driven instabilities, which tend to be exacerbated in reactors
Optical probes Showerhead water cooling Top plenum chamber
|«e^
Gas inlet bottom plenum chamber Three zone heater Thermocouple
t—^
Double 0-ring seal
Susceptor — Water cooled chamber Quartz liner
Exhaust
Figure 4.10.
Schematic diagram of 19 X 2-in. close-coupled showerhead reactor.
50
Optoelectronic Devices: Ill-Nitrides
Figure 4.11. Close-coupled showerhead reactor (19 X 2 in.; open for loading).
having a large volume above the hot susceptor. In the patented design used for the Thomas Swan showerhead, the tubes are fed from two separate plenum chambers and are arranged on two interleaved matrices such that efficient mixing of the gases can be effected right at the edge of the reaction zone whilst still allowing complete mixing prior to the point of pyrolysis. The latter assertion is supported by both in-house and independent [7] fluid dynamic modelling, which has indicated that, under typical operating conditions, the gases from the two plenums are fully mixed, and the individual jets from the injection tubes are fully dissipated, by the time they arrive at the wafer surface. This ability of the CCS design to effectively mix the gases at the last possible moment is particularly important for the growth of GaN-based materials as the adducts between ammonia (which is used as the group V precursor) and the group III alkyls are easily formed because ammonia is a relatively strong base. The reduced interaction afforded by this "late mixing" yields a growth process with a high chemical efficiency, which, together with the reactor's relative mechanical and operational simplicity, contributes to a low CoO.
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4.2.3.2 Scale-up, As discussed earlier the CCS arrangement intrinsically yields a uniform boundary layer thickness irrespective of position on the susceptor radius, which in turn provides the foundation for uniform deposition. A corollary to this argument is that the design should produce these desirable characteristics on any length scale, implying that there are no conceptual limitations to the realization of good uniformity, even for very large reactors of this type. Moreover, it can be argued that larger diameter reactors should have enhanced performance as any residual second-order perturbations of the gas flow caused by the proximity of the reactor wall, or rotation-induced re-circulation cells at the susceptor edge, should have a proportionately smaller effect as the reactor size is increased. This reasoning has been borne out by detailed fluid dynamic modelling (as discussed in Section 4.3), which provided the reassurance necessary to invest the considerable engineering effort required to increase the size from the original single 2-in. wafer variant to the current large-capacity multi-wafer reactors. Results from reactors ranging in capacity from 1 x 2 through 3 X 2 and 6 X 2 to 19 X 2-in. have shown, in fact, that it is easier to optimize the larger reactors for highly uniform, chemically efficient, deposition than is the case for their smaller counterparts, although all of the multi-wafer reactors have produced state-of-the-art material specifications, as discussed in Section 4.2.3.3. In addition to the more favorable gas flow pattern discussed earlier, another factor which makes the larger reactors easier to use is that thermal distinction between the separate zones of the multi-zone heater is more easily achieved as the size is increased. This implies that the susceptor temperature uniformity can be more easily controlled, which has a positive impact on the uniformity of parameters which are very temperature sensitive, such as the composition of InGaN and the growth and annealing of low-temperature nucleation layers on which most GaN-based structures are grown. 4.2.3.3 Growth Results GaN Template Growth in CCS Reactors. Using the proven "two-temperature" technique, which deposits GaN or AIN low-temperature nucleation layers prior to the growth of thick GaN epilayers at a higher temperature, specular GaN templates have been prepared on sapphire and silicon carbide substrates. Also, using a high-temperature AIN nucleation layer, GaN templates have been prepared on silicon. Typically, these exhibit a standard deviation in thickness below 2% across a 2-in. wafer, although the best-case values below 1% have been noted. Such uniformities have been achieved on 3 X 2, 6 X 2 and 19 X 2-in. reactors. The final surface morphologies of these layers (as indicated by atomic force microscopy) exhibit a "step-flow" pattern indicative of monolayer two-dimensional growth. These surfaces have RMS roughness values down to —0.13 nm over an area of 4 fxm^, as indicated by Figure 4.12a and b, which show the topologies of GaN template material grown on sapphire and silicon, respectively, in a 6 X 2-in. reactor. Two different regimes have been investigated for the growth of the high-temperature epilayers, one in which the isolated GaN crystallites, which result from the annealing
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Optoelectronic Devices: Ill-Nitrides
of the nucleation layer, coalesce quickly, and the other where a protracted period of threedimensional growth follows the growth and annealing of the nucleation layer. The rate at which the GaN coalesces, and the surface approaches, specular reflectivity, influences the ability to "grow out" misfit dislocations and this has a profound effect upon the conductivity of undoped material. GaN grown using conditions that promote rapid coalescence is found to be semi-insulating (up to 10^ fl/square), whereas GaN, grown in such a way that coalescence occurs gradually, is invariably conducting. Transmission electron microscopy (TEM) analysis of these materials has shown that the semi-insulating layers grown using the "rapid recovery" regime contain more edge-type dislocations than do the conducting layers grown using a "slow recovery" strategy. Real-time monitoring of the evolution of the surface morphology, using an in situ laser-based interferometer, has given considerable insight into, and afforded improved control of, the mechanisms responsible for these different growth regimes. Figure 4.13 shows the different interferograms that result when growth conditions are adjusted to produce templates which are (a) semi-insulating or (b) conducting. There are a number of strategies for managing the rate at which coalescence is approached. Bougrioua et al. [8] adjusted the growth rate, growth temperature and nucleation layer annealing time to achieve this end, whilst work at Cambridge University has used ammonia partial pressure during the annealing of the nucleation layer as the main controlling parameter. Higher partial pressures are found to promote a faster recovery of the reflectivity. It is important in terms of system flexibility that both types of template can be grown. Conductive templates are believed to have superior crystalline quality and are chosen for the buffer layers of device structures requiring ambi-polar current injection such as LEDs and lasers, whilst a high-resistivity buffer layer is mandatory to obtain good pinch-off characteristics for field effect transistors (PETS).
2.0|Lim
Figure 4.12. Atomic force microscopy (AFM) images of GaN on sapphire (a) and (b) silicon.
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2800
3800
4800
5800
53
6800
7800
Time (s) Figure 4,13. Laser interferograms taken whilst growing (a) semi-insulating, and (b) conductive GaN templates on sapphire.
Optoelectronic Structures Quantum Wells in CCS Reactors. Currently, the most commercially significant sector for MOCVD-grown GaN-based structures is that of LEDs. Consequently, we have devoted effort to the study of quantum wells that form the active region of such devices. We have noted that both InGaN/GaN and GaN/AlGaN quantum wells grown in a 6 X 2-in. system are characterized by abrupt interfaces as perceived by TEM (see Figure 4.14), and that their high resolution X-ray diffraction rocking curves exhibit both Pendelosung fringes and satellite peaks out to the eighth order, for 10 period multi-quantum well (MQW) structures [9]. Figure 4.15 shows results for InGaN/GaN structures and similar results are obtained for GaN/AlGaN quantum wells. Reciprocal space maps for both types of quantum well structures indicate that they are fully pseudomorphic when grown correctly. An example of such a map for an InGaN/GaN MQW structure is given in Figure 4.16. The technique used to construct this map employs the asymmetric (105) reflection and shows the spread both normal to (y-axis) and in the plane (jc-axis) of the layers, with the zero and + 1 order MQW satellite peaks straddling that of the bulk GaN peak. The precise alignment of the peaks on the x-axis indicates that the structures are fully strained. Similar results are obtained for GaN/AlGaN quantum well structures grown within the critical thickness constraints. To characterize the optical quality of InGaN/GaN, MQWS variable temperature photoluminescence (PL) measurements were made as a means of determining the internal quantum efficiency. For the best samples, high room temperature efficiencies up to 43%
Optoelectronic Devices: Ill-Nitrides
54
Figure 4.14.
Bright field cross-sectional TEM of InGaN/GaN MQWS.
e/2e(degrees) Figure 4.15. X-ray rocking curves of InGaN /GaN quantum wells.
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were obtained. In order to study the optical quality as a function of well composition (and therefore, emission wavelength), a series of InGaN/GaN single quantum wells were grown covering the wavelength range 370-570 nm (at 6 K). The indium content of the wells, which is a prime parameter in determining the emission wavelength, was controlled by varying the well and barrier growth temperatures and determined by X-ray diffraction measurements. At 6 K, the spectra of these samples were dominated by strong localized exciton emission, with attendant phonon replicas, across the whole of the wavelength range, as shown in Figure 4.17. The growth temperatures and indium contents of the quantum wells are also shown in this figure. The line-widths of the zero phonon lines are very narrow with the FWHM of the peak at 374 nm being 3.1 nm (28 meV), indicating quantum wells of very high quality. Further details are given in an earher publication [10]. Finally, the performance of our largest 19 X 2-in. system is exemplified by results from a growth campaign undertaken after its commissioning at a customer's site [11]. This work, aimed at establishing a capability for blue LED structures, was based upon a five- period InGaN/GaN MQW structure grown on an n-type silicon doped template, capped by a p-type magnesium doped layer. To determine the optical emission uniformity, PL mapping of the 19 X 2-in. wafers was undertaken using an Accent RPM 2000 system. The intra-wafer standard deviations of PL intensity and PL emission wavelength averaged 4.13% and 1.91 nm, respectively, within a 3 mm edge exclusion zone, whilst the corresponding inter-wafer standard deviations of the means of those parameters, from all the wafers, were 2.94% and 1.81 nm, the global average PL
Intensity measured on a logarithmic scale, interval between contours ~2.6x 3560
3580
3600
3620 3640 QX*10000(rlu)
3660
Figure 4.16. Reciprocal space map of InGaN/GaN MQWS.
3680
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Optoelectronic Devices: Ill-Nitrides Wavelength (nm) 1.2
700
600
500
TIO^C 730°C
1.0 H
1.8
Figure 4.17.
2.0
2.2
2.4
400 750°C
2.6 2.8 Energy (eV)
770°C
3.0
800°C
3.2
3.4
3.6
6 K PL of single quantum wells with different indium contents.
wavelength for this run being 459.0 nm. An estimate of doping uniformity was also obtained from sheet resistance measurements made on these structures using a contactless resistivity profiler. This data, which predominantly samples the conductivity of the Si-doped buffer layer, yields a standard deviation of 0.61% across the wafers and 0.5% between them, implying good growth temperature uniformity. Following commissioning, the PL wavelength data were collected from 22 consecutive runs, made to the same recipe, as a test of the system's reproducibility. This indicated that the standard deviation of the global average wavelength (of the 19 wafers) over the 22-run series was 1.18 nm. Electronic Structures Two-dimensional Electron Gas Structures Grown in CCS Reactors. Using highresistivity GaN buffer layers, as described in the section "GaN Template Growth in CCS Reactors", AlGaN/GaN high electron mobility transistor (HEMT) structures have been grown. The conducting channel in such devices is a two-dimensional electron gas (2DEG) at the AlGaN/GaN interface, arising from a combination of spontaneous and piezoelectric polarization at this interface. The transport properties of this 2DEG are a sensitive measure of interfacial perfection with the mobility (for a given sheet carrier concentration) being degraded if the interface is not abrupt and the AlGaN is crystallographically relaxed rather than fully pseudomorphic. X-ray diffraction studies of HEMT structures with AlGaN
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thicknesses up to ~ 40 nm thick and aluminium contents of up to ~ 30% have shown very good agreement between experimentally derived 6/26 rocking curves and simulations based upon perfect interfaces and zero relaxation in the AlGaN. Qualitatively, this implies that the structures are of high quality in these two respects. Additionally, XRD reciprocal space maps of such structures have indicated that the AlGaN is fully strained. Using such structures, state-of-the-art mobilities of greater than 1400 cm^ V~^ s~\ for a sheet carrier concentration ---10^^ cm~^, have been obtained on both sapphire and silicon carbide substrates using the CCS reactor.
4.3. COMPUTATIONAL MODELLING OF NITMDE MOVPE PROCESSES AND REACTORS 4.3,1 Introduction One of the challenges of multi-component MOVPE during the fabrication of modem electronic and optoelectronic devices based on nitride compound semiconductors lies in the accurate control of layer thickness and composition uniformity over large wafer surface areas and the control of heterostructure interface quality, while ensuring reproducibility, process reliability, high up time and low cycle times during this highly complex deposition process in an industrial volume production environment. Adding even more complexity to the above requirements, typical nitride MOVPE processes encompass a wide range of process conditions with frequent changes of operating pressure, growth temperature, carrier gas composition and gas flow rates throughout a single growth sequence. Modeling of nitride MOVPE processes has been used to gain insight into the fundamentals of the growth process itself [12, 13]. On the other hand, as MOVPE has evolved into a mass production technique, modelling has been of increasing value in supporting and guiding process development and equipment design [14]. Semiconductor equipment vendors routinely use computational modelling in order to improve reactor design and processes to shorten their development cycles and to cut down development and testing costs. The assessment of reactor design performance, even before the equipment is built and tested, is based on the prediction of flow dynamics, heat transfer, chemical species distribution and deposition profiles by computer simulations. Modelling has become an integral part of equipment and process development and is used at various stages of the design process, starting with the initial feasibility analysis of novel reactor concepts, the scaling of proven reactor types to larger wafer capacity and the design optimization of critical components, such as gas inlets and heaters. It has also provided guidance to process engineers in finding robust process regimes to achieve the required performance. It goes without saying that the consistent use of modelling provides the potential for significant cost savings.
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Optoelectronic Devices: Ill-Nitrides
4,3.2 Fluid Flow Dynamics^ Heat Transfer and Related Gas Phase Transport Phenomena Fluid flow in MOVPE reactors is characterized by incompressible mixed forced and natural convective flow. For basic flow analysis, dimensionless numbers are used, which arise from scaling the governing transport equations and characterize the behavior of MOVPE reactors [15]. The Reynolds number {Re) measures the ratio of flow momentum over diffusive momentum transport, i.e. viscous drag, and determines the size of momentum-driven return flow cells and vortices as well as the length of flow jets, but also the transition from laminar to turbulent flow. For circular tube flow, for instance, the onset of turbulent flow occurs at a critical value of Re ~ 2300. Under MOVPE conditions, the values of the Re number normally are rather low in the range from Re= 10 to 1000 and laminar flow is ensured. Nevertheless, in adverse cases, there may be momentum-driven vortices, which give rise to enhanced gas phase pre-reactions between precursor species or provoke memory effects. In the case of nitride MOVPE, the mean molecular weight and, hence, the density of the process gas mixtures tends to be higher (due to the required high amount of hydrides and the partial use of nitrogen as carrier) than for MOVPE of conventional III-V compound semiconductors, resulting in typically rather high Re numbers in the order of Re = 100-1000. As a consequence, usually extra care has to be taken with the design of gas inlets and process chambers in order to obtain satisfactory flow patterns. The Grashof and Rayleigh numbers serve to characterize the strength of natural convection. In MOVPE reactors, buoyancy-driven flows due to thermal gradients opposed to gravity are likely to occur. As these parameters vary as the cube of reactor height, tall vertical reactors are particularly prone to natural convection effects. Furthermore, they vary linearly with temperature gradient and as the square of density or pressure. The regimes used for the MOVPE of nitrides typically employ higher growth temperatures, higher density gas flows (composed of significant concentrations of ammonia and nitrogen), and quite often at higher operating pressures than are used for the (usually) entirely hydrogen-based regimes for the MOVPE of conventional III-V compound semiconductors. This regime presents greater challenges with respect to the control of process stability. Gas expansion caused by heating of the gas flow plays a major role in MOVPE reactors. Although gas flow in MOVPE reactors occurs as low Mach numbers (i.e. flow velocity is low compared with the speed of sound) and there are no compressibility effects, the temperature dependence of the gas density has to be accounted for by the ideal gas law. Other dimensionless numbers indicate the relative contribution of forced convection and diffusion to the mass transport of chemical species or to heat transfer (Peclet numbers). They can also be used to compare transport time scales with reaction times
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(Damkohler numbers), thus characterizing whether growth is transport Hmited or reaction rate Hmited. Ample Hterature is available on the transport phenomena occurring in MOVPE reactors and on the application of modeling gas phase transport in order to relate typical performance figures (growth rate, composition, uniformity, interface abruptness) to process conditions and operating parameters [16-20]. By way of illustration. Figure 4.18 shows the predicted GaN growth rate profiles for various gas flow rates in a production scale planetary reactor accommodating 24 X 2-in. substrates for simultaneous processing. Under normal operation, the substrate carrier disks with 3 X 2-in. wafers are rotated to average the layer properties over the wafer area. In the data presented in this figure, one of the disks has been clamped to obtain the underlying growth rate depletion profile. The results indicate the predictive accuracy obtained using transport and reaction modelling of MOVPE deposition of GaN thin layers and the practical use of reactor scale modelling to understand the effect of various process tuning parameters in MOVPE reactors. 4,3,3 Chemical Kinetics Predicting process behavior in a transport and reaction model of the nitride growth process occurring in a MOVPE reactor requires a knowledge of gas phase and surface reaction mechanisms to be incorporated into the physical model, including the reaction pathways of various gas phase compounds and their reaction rate constants.
carrier gas flow = 12.25 Sim
Experimental: Carrier flow rate • 12.25 Sim o 15.25 Sim o 18.25 sIm
0.12 0.14 0.16 0.18 distance from center (m)
0.22
Figure 4.18. Dependence of GaN growth rate profiles on hydrogen carrier gas flow rates for rotated and static wafer carrier disks. Growth temperature, T = 1030°C, operating pressure, p = 200 mbar, precursors NH3 and TMGa (experimental data by AIXTRON Material Research Laboratory, Aachen, Germany).
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Optoelectronic Devices: Ill-Nitrides
The thermal decomposition of most metalorganic source materials is well understood and involves sequential first-order pyrolytic reactions. Rate constants for each step were determined by kinetic decomposition experiments under conditions close to MOVPE operating conditions [21] and, more recently, by means of ab initio computational chemistry [22, 23]. Both approaches yield rather good agreement. The onset of thermal decomposition of TMGa, for instance, occurs at a temperature of 350-400°C by cracking the first Ga-CH3 bond with an activation energy of —59 kcal/mol. The thermal cracking of NH3 has been the subject of experimental studies in combustion chemistry resulting in the elucidation of the detailed kinetic mechanisms and the quantitative measurements of reaction rates [24]. Gas phase decomposition proceeds in a second-order reaction with a rather high activation energy of ~ 95 kcal/mol, with initial cracking at temperatures well above 800-900*^C and ammonia dissociation of only a few percent at typical growth temperatures of GaN epitaxial layers (1000-1100°C). Apparently, at MOVPE, the majority of NH3 is decomposed catalytically on the growing surface through dissociative adsorption in conjunction with adsorbed group-III compounds. The use of alternative nitrogen sources, such as hydrazine derivatives like unsymmetric dimethyl-hydrazine (UDMH), has been investigated too. Experimental decomposition studies indicate 50% cracking at 420°C, i.e. a decomposition temperature well matched to that of the metal organic group-III precursors [25]. For deposition of GaN, the formation of adducts between ammonia and group-III precursors through a Lewis acid-base interaction plays a crucial role in determining the concentration of reactive intermediates. A number of experimental and modeling studies have focused on the gas phase pre-reaction of NH3 and TMGa or TMAl [2,26-28]. According to Thon and Kuech [26], the formation of the initial adduct between NH3 and TMGa takes place at temperatures below 200°C. Subsequent methane elimination leads to (CH3)2Ga-NH2, which can react to form dimeric and trimeric compounds with Ga and N atoms forming a ring. At temperatures above 700°C, the abundance of dimeric and trimeric species tends to decline again owing to their thermal decomposition. The strength of the Lewis donor-acceptor bond itself is rather weak, unless subsequent alkane elimination takes place leading to the formation of more or less stable compounds with direct bonds between III- and V-atoms. The relative magnitude of adduct strength and the barrier to alkane elimination is crucial for the MOVPE process and depends on the participating III-V elements. Apparently, aluminum and nitrogen form the most stable compounds among the relevant group-III elements, which explains the high risk of particle formation during growth of AIN. Ab initio quantum chemical computations of thermochemical properties and reaction rate constants attract particular attention. Using such techniques, gas phase and surface mechanisms for the MOVPE of GaN and AlGaN have been successfully modelled, even though large and geometrically complex molecules are involved [22,23].
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4,3,4 Mathematical Model The mathematical model used for computational predictions of the MOVPE growth process is based on the continuum mechanical description offlow,heat transfer and multicomponent chemical species mass transfer, including the mathematical models for thermal radiation transfer, gas phase and surface chemical reactions and electromagnetic inductive heating. The continuum description is adequate since MOVPE reactors operate at sufficiently high pressures (10-1000 mbar) and large characteristic dimensions such that the Knudsen number, i.e. the ratio of the mean free path length over the characteristic dimensions of the flow domain, is below Kn
CpV'(puT) = V-(AVr)
VipuY,) = V | P A ( V F , + a , F , ^ ) j +/?„ p
/ = 1,...,A^
N 1=1
with p = density, u = velocity, p = pressure, p. = dynamic viscosity, Cp = heat capacity at constant pressure, T = temperature, A = heat conductivity, Yi = species mass fraction, Di = diffusion coefficient, a^ = thermodiffusion factor, M/ = molar mass, R = gas constant. For multi-component gas mixtures, as typically encountered during MOVPE, gas phase transport properties, such as viscosity, thermal conductivity and species diffusion coefficients, are temperature and mixture dependent. Most generally, they can be determined by kinetic gas theory (Chapman-Enscog theory), based on either experimentally obtained values or on estimated Lennard-Jones potential parameters for the single species and the application of appropriate mixing rules [30-32]. MOVPE growth exhibits a high sensitivity not only to local growth temperature and thermal uniformity on the substrate, but also to the thermal environment within the entire reaction chamber. For the purpose of predictive equipment, scale modelling the accurate calculation of temperatures is indispensable; hence, the modelling of thermal radiation in the MOVPE reactor and ambient is very important as it is the predominant mode of heat transfer. Some radiation models are based on ray tracing
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Optoelectronic Devices: Ill-Nitrides
or view factors and typically provide high spatial resolution but, on the other hand imply high computational effort. Another class of approaches, the so-called diffusive approximations, are based on the solution of the radiation transfer equation, as, e.g. the popular discrete ordinates method. A comprehensive review of radiation models is given in Ref. [33]. In practice, the choice of the radiation model usually involves a compromise between the degree of prediction accuracy and the computational effort. 43,5 Numerical Methods and Software Computational fluid dynamics (CFD) is the field of science dedicated to the development of numerical solution techniques for the above system of coupled partial differential equations. The most commonly used numerical technique for the regime of incompressible, viscous flow, including multi-component gas mixtures, is based on the finite-volume method. It consists of the discretization of the governing equations on structured or unstructured computational grids and the iterative solution of the resulting system of algebraic equations involving some pressure-correction scheme. For details on numerical techniques, refer to Refs. [34,35]. CFD has been a field of significant research and development over the past 20 years. Nowadays, flexible and robust multi-purpose commercial CFD packages for modelling flow and related multi-disciplinary physics are available as a result of those activities, quite a few of them with special focus towards applications in the semiconductor industry [36-38]. They differ mostly with respect to the variety of physical models they include. Combined with lower costs and higher performance of high-end PCs and Unix workstations, CFD-based modeling can be employed on a day-to-day basis without the need to use supercomputers other than for very advanced calculations.
4.4. IN SITU TECHNOLOGffiS The application of optical in situ technologies to the metal-organic chemical vapor deposition process enables the MOCVD engineer to directly observe the growth and facilitate process tuning. This chapter describes different in situ techniques of differing levels of complexity, which provide information about the growing film, including the determination of growth rate, surface quality, composition and doping levels. 4,4.1 Measurement of Layer Properties The most commonly used in situ measurement technique employs the evaluation of Fabry-Perot interference between a layer interface with differing indices of refraction and the growing surface, widely known as "in situ reflectivity measurement". The resultant
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oscillation of the reflectivity yields information about the growth rate, the interface and surface roughness and, by counting the number of oscillations, the total thickness of the growing layer. The in situ reflectivity measurement employs a light beam and detection at normal incidence to the wafer surface. The energy of the light is chosen to be below the bandgap of the growing layer, facilitating an ideally infinite penetration depth without any significant quenching of the signal due to absorption in the layer, allowing for the direct comparison of the layer quality across all stages of the growth. Applying basic rules of optics yields for the growth rate r: _ A^ _ AQ ^~ At ~ 2nsXAt' where AQ is the probe-light wavelength in vacuum, n^ is the refractive index of the semiconductor layer and At is the time between two maxima of the Fabry-Perot oscillations. In the case of the EpiTune II measurement tool, the probing light is generated by a 950 nm LED. The time difference At is determined by numerically fitting the recorded trace over several oscillations, thus improving the accuracy with which the growth rate can be determined. In addition to the information, which permits the determination of the growth rate, the reflectivity signal bears additional information about the layer, most notably the roughness of the interface with the largest difference in refractive index and the roughness of the growing surface. These properties modulate the amplitude of the FabryPerot oscillations. Figure 4.19 shows an example of an ideal Fabry-Perot interference trace (dotted line). It can be seen that the signal amplitude of this trace remains constant. In reality, however, imperfections of the lower interface and the growing surface will disturb the interference condition, and hence quench the signal. The amount of quenching can be taken as a measure of the interface and surface quality and is an important piece of information that assists the epitaxy expert in the optimization of the growth conditions. 4,4,2 Measurement of Surface Temperature Another important class of in situ tools facilitates the measurement of the surface temperature by emissivity corrected pyrometry. Stefan-Boltzmann's law yields for the radiation Ms of a perfect black body at temperature T:
M^ = Cs(-^]=
^
^Vioo/
5.67Wm"^K"^
^
' (-^] vioo/ -
Stefan-Boltzmann constant
Material which does not resemble a perfect black body, however, requires the modification of this law by the introduction of emissivity factor e, which yields
64
Optoelectronic Devices: Ill-Nitrides 30
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Time [s] Figure 4.19.
Schematic of an ideal Fabry-Perot interference trace (dotted), a quenched trace (bold) and its envelopes.
This emissivity factor is a material constant that has been evaluated for many common materials. In epitaxy, however, the growing layer and its emissivity factor are subject to constant change since emissivity and reflectivity of a surface are interconnected. Emissivity-corrected pyrometry (such as EpiTune II) utilises a single sensor head, which measures the reflectivity of the wafer surface as described earlier, calculates the emissivity and subsequently performs a pyrometric temperature measurement. This can be achieved by pulsing the probe light at frequencies of up to 20 Hz, making a quasisimultaneous reflectance, emissivity and temperature measurement possible. Figure 4.20 shows the experimentally obtained trace of reflectivity together with the traces representing the uncorrected and corrected pyrometric wafer temperature, as recorded during the epitaxy run used to produce a GaN layer. It can be seen that the pyrometrically measured wafer temperature is unstable, due to the changing emissivity of the surface, and oscillates with the same frequency as the reflectivity. By simultaneously measuring the reflectivity, the temperature measurement can be corrected to show the true temperature of the surface. From the physics of semiconductor growth, it becomes directly evident that most processes from dissociation to incorporation of species into the growing layer are highly temperature sensitive. In this context, the knowledge of the temperature on the wafer surface and the facility to accurately control it permit an increased level of reproducibility in modem
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1000
980
o
960-
o
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Q.
E 0
920
900 01:12:00
01:19:12
01:26:24
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growth time [hh:mm:ss] Figure 4.20.
Traces showing the on-line recorded reflectivity (lower trace), pyrometric wafer temperature and corrected wafer temperature (upper traces) for the growth of a thick GaN layer.
Figure 4.21. Cross-sectional three-dimensional view of the sensor head, reactor lid, viewport and susceptor with wafer discs.
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Optoelectronic Devices: Ill-Nitrides
epitaxy systems. In addition, a reliable measurement of the surface temperature allows for the correction of process parameters during the run, either manually or automatically. 4,4,3 Integration of In Situ Technologies into Modern Epitaxy Systems 4,4,3,1 Mechanical Integration, Since in situ technologies are add-ons to modem epitaxy systems, their integration into the tool must combine the strengths of the sensors without curtailing the flexibility and stability of the reactor. In addition, their adaptation to multi-wafer systems requires the correlation of the measurement signal with the wafer that is being monitored. Figure 4.21 shows the incorporation of a sensor head on top of an AIX 2xxxG3 reactor lid. The sensor remains outside the process chamber and probes the wafer through a viewport and a small hole in the reactor's quartz ceiling. This insures that the impact of the measurement set-up on the process chamber is minimal and the reactor's performance is not impaired. In addition, the slow rotation speeds of the susceptors in modem MOCVD systems allow for each measurement to be correlated to the individual wafer. m-^-i
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^1 |^^;S'i!^^'||i|f Figure 4.22. Screen-shot of the control interface of an AIX 2600G3 HT epitaxy system. The right-hand panel of the display shows how recorded system parameters such as flows and temperatures (lower graph) and in situ measurement data (upper graph) can be displayed and analyzed during the run.
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67
This method of incorporation can be adapted to virtually any kind of optical sensor head that utilises a normal incidence set-up, be it a reflectivity measurement (e.g. EpiRAS, EpiTune II) or pyrometry. 4.4,3.2 Software Integration. In the industrial as well as the research and development environment, the operators rely on a technically sound and seamless integration of each hardware component into the tool's control system. All information needs to be instantly accessible via the control interface of the system during the run. Figure 4.22 shows a screenshot of the user interface of an AIX 2600G3 HT reactor during a growth run. The right-hand side panels of the display show the reflectivity curves of the layer as well as additional information about the growth run. All information from in situ sensors taken on the individual wafers during the run is stored alongside the complete data-log of the system. Like this, information on individual wafers is retrievable and later on can be correlated to the system's performance.
REFERENCES [1] Akasaki, L, Amano, H., litoh, K., Sakai, H., Tanaka, T. & Manaba, K. (1992) Inst. Phys. Conf. Ser., 129, 851. [2] Nakamura, S., Mukai, T. & Senoh, M. (1994) AppL Phys. Lett., 64, 1687. [3] Simka, H., Willis, B.G., Lengyel, I. & Jensen, K.F. (1997) Prog. Cryst. Growth Charact., 35, 117. [4] Amano, H., Sawaki, N., Akasaki, I. & Toyoda, T. (1986) Appl. Phys. Lett., 48, 353. [5] Frijlink, P.M. (1988) A new versatile, large size MOVPE reactor. /. Cryst. Growth, 93, 207-215. [6] Schlichting, H. (1960) Boundary Layer Theory, McGraw Hill, New York. [7] Mihopoulos, T.G., Hummel, S.G. & Jensen, K.F. (1988) /. Cryst. Growth, 195, 725-732. [8] Bougrioua, Z., Moerman, L, Sharma, N., WalHs, R.H., Cheyns, J., Jacobs, K., Thrush, E.J., Considine, L., Beanland, R., Farvacque, J.L. & Humphreys, C.J. (2001) /. Cryst. Growth, 230, 573-578. [9] Thrush, E.J., Kappers, M.J., Dawson, P., Vickers, M.E., Barnard, J., Graham, D., Makaronidis, G., Rayment, F.D.G., Considine, L. & Humphreys, C.J. (2003) J.Cryst. Growth, 248, 518-522. [10] Thrush, E.J., Kappers, M.J., Dawson, P., Graham, D., Barnard, J.S., Vickers, M.E., Considine, L., MuUins, J.T. & Humphreys, C.J. (2002) Phys. Stat. Sol. (a), 192 (2), 354-359. [11] Paper 246 (2002). CS-lMax technical Digest. [12] Karpov, S.Yu., Talalaev, R.A., Makarov, Yu.N., Grandjean, N., Massies, J. & Damilano, B. (2000) Surf. ScL, 450, 191. [13] Mihopoulos, T.G., Gupta, V. & Jensen, K.F. (1998) /. Cryst. Growth, 195, 733. [14] Bland, S.W. (2002) /. Mater ScL: Mater Electron., 13, 679. [15] Jensen, K.F. (1989) /. Cryst. Growth, 98, 148.
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Devices:
Ill-Nitrides
[16] Bergunde, T., Dauelsberg, M., Kadinski, L., Makarov, Yu.N., Yuferev, V.S., Schmitz, D., Strauch, G. & Jurgensen, H. (1997) J. Cryst. Growth, 180, 660. [17] Dauelsberg, M., Kadinski, L., Makarov, Yu.N., Bergunde, T., Strauch, G. & Weyers, M. (2000) /. Cryst. Growth, 208, 85. [18] Kleijn, C.R. & Hoogendoom, C.J. (1991) Chem. Eng. Sci., 46, 321. [19] Biber, C.R., Wang, C.A. & Motakef, S. (1992) /. Cryst. Growth, 123, 545. [20] Joh, S. & Evans, G.H. (1997) Numerical Heat Transfer Part A, 31, 867. [21] Stringfellow, G.B. (1999) Organometallic Vapor-Phase Epitaxy, Academic Press, London. [22] Simka, H., Willis, B.G., Lengyel, I. & Jensen, K.F. (1997) Prog. Cryst. Growth Charact., 35, 117. [23] Sengupta, D. CFD Research Corp. Huntsville, AL, unpubUshed results, www.cfdrc.com. [24] Davidson, D.F., Kohse-Hoinghaus, K., Chang, A.Y. & Hanson, R.K. (1990) Int. J. Chem. Kinetics, 22, 513. [25] Lee, R.T. & Stringfellow, G.B. (1999) /. Electron. Mater, 28, 963. [26] Thon, A. & Kuech, T.F. (1996) Appl. Phys. Lett., 69, 55. [27] Mihopoulos, T., (1999). PhD Thesis, MIT. [28] Chen, C.H. (1996) J. Electron. Mater, 25, 1004. [29] Bird, R.B., Stewart, W.E. & Lightfoot, E.N. (1960) Transport Phenomena, Wiley, New York. [30] Kleijn, C.R. (1995) Chemical vapor deposition processes, in Computational Modeling in Semiconductor Processing, Ed. Meyyappan, M., Artech House, Boston, pp. 97-230. [31] Reid, R.C., Prausnitz, J.M. & Poling, B.E. (1987) The Properties of Gases and Liquids, McGraw-Hill, New York. [32] Hirschfelder, J.O., Curtis, C.F. & Bird, R.B. (1954) Molecular Theory of Gases and Liquids, Wiley, New York. [33] Modest, M.F. (1993) Radiative Heat Transfer, McGraw-Hill, New York. [34] Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow, Hemisphere, New York. [35] Ferziger, J.H. & Peric, M. (1996) Computational Methods for Fluid Dynamics, Springer, Berlin. [36] CFD-ACE + from CFD Research Corporation, www.cfdrc.com. [37] Fluent from Fluent Inc., www.fluent.com. [38] CFX from Ansys Inc., www.ansys.com/cfx/.
optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 5
MOCVD Growth of Group III Nitrides for High-power, High-frequency Applications M.A. di Forte-Poisson^'*, M. Magis^, M. Tordjmann^ and J. di Persio'' ^Thales Research & Technology, Domaine de Corbeville, 91404 Orsay Cedex, France ^Universite de Lille, LSPES-59655 Villeneuve d'Ascq, France
This chapter reports on the LP-MOCVD growth optimization of bulk GaN, GaAlN materials and GaAlN/GaN heterostructures grown on sapphire and silicon carbide substrates for MESFET and HEMT applications, and on the device performances obtained with these structures. High-purity GaN grown on sapphire and silicon carbide has been obtained, with carrier concentration lower than 10^^ cm~^. GaN/Al203 MESFETs based on such high-purity GaN buffer layers, have exhibited very promising static and microwave performances: high breakdown voltage ~ 200 V, ft = 12 GHz, /rnax = 25 GHz and CW output power in excess of 2.2 W/mm at 2 GHz. They have shown the best low-frequency noise (LFN) performances, with the lowest Hooge's parameter as compared to the values reported in the literature for different GaNbased FETs (HFETs and HEMTs). The incorporation of aluminum in the solid phase has been studied as a function of the growth parameters, and a parasitic reaction was clearly identified to occur in the gas phase between TMA and NH3, with a strong influence on the growth rate and the aluminum incorporation. The GaAlN bulk material appeared to be highly tensilely strained and electrically compensated for Al content higher than 20%. Plastic relaxation, associated with the generation of misfit dislocations and a strong decrease of the elastic strain, was observed in GaAlN alloy with 30% Al content, which well correlates with a critical thickness of 1000 A for this alloy composition. The thickness of the high bandgap layer of the GaAlN/GaN HEMT structures under study (Al content in the range 22-28.5%), grown on sapphire or SiC, is lower than the observed critical thickness, leading to a pseudomorphic growth which was confirmed by high-resolution X-ray diffraction (HR-XRD) and TEM. The critical impact of some growth parameters on the physical properties of the GaAlN/GaN epilayers grown on SiC has been identified and studied using HR-XRD, E-mail address:
[email protected]
69
70
Optoelectronic Devices: Ill-Nitrides
AFM, C-V and Eddy current probe measurements. The SiC substrate surface preparation (both ex situ and in situ) and the nucleation layer growth conditions (growth temperature, thickness, composition and strain) have been found to be key steps of the GaAlN/GaN/SiC growth process. SiC substrates from different suppHers have been evaluated and their influence on the physical properties of the GaAlN/GaN HEMT structures investigated. Static characteristics of the devices such as maximum drain current /^ss or pinch-off voltage have been correlated with the nucleation layer composition of the HEMT structure and the defect density of the SiC substrate. The devices' performances related to our first GaAlN/GaN HEMT structures grown on sapphire and silicon carbide have confirmed the high potentiality of GaN and related alloys for high-power microwave transistors. Load-pull measurements performed at 2 GHz on devices related to GaAlN/GaN/Al203 HEMT structures, have shown a remarkably high output power density (4.4 W/mm) and absolute power level (3.5 W for 1 mm devices). These power level results for devices on sapphire substrates measured on wafer, are in good agreement with the international state-of-the-art. Nevertheless, the thermal effects, which lead to a significant reduction of the power density with the increase of the transistor size, have been found to be more pronounced for devices on sapphire. In order to improve the thermal properties of HEMT's material, the growth process of GaAlN/GaN HEMTs was transferred onto silicon carbide substrates. Devices related to GaAlN/GaN/SiC HEMT structures have been measured at 10 GHz using a load-pull system. They exhibited a CW output power in excess of 4 W/mm for a gate length of 0.25 |xm.
5.1. INTRODUCTION Wide bandgap semiconductors, such as SiC and GaN, exhibit many attractive properties far beyond the capabilities of Si and GaAs: the unique combination of the wide bandgap, the high breakdown field (over 2 MV/cm), the high saturation velocity and the ability to form high-quality GaAlN/GaN heterostructures with good transport properties make them ideal candidates for high-power, high-frequency applications. GaAlN/GaN high electron mobility transistors (HEMTs) with high impressive power densities up to 11.2 W/mm at 10 GHz have been reported by Cornell [1], and recently up to 20 W/mm at 4 GHz by Cree Research [2]. HRL [3] has demonstrated a current gain cutoff frequency (/t) of 110 GHz. This rapid progress in the performance of microwave power transistors, as compared to results published in early 1998 (2 W/mm), has been obtained thanks to the use of SiC substrates instead of sapphire. Although the device performance benefits from the high-thermal conductivity and high-thermal stability of SiC, the lattice mismatch (—3.5%) and the thermal expansion
MOCVD Growth of Group III Nitrides
71
difference of SiC relative to GaN (—3.2%) produce a high density of threading dislocations in the GaAlN/GaN HEMT structures. These dislocations together with the defects present in the substrate affect the background doping of the GaN buffer layer and degrade the device performance. In this chapter, we report on a comparative study of the physical properties of GaAlN/ GaN HEMT structures grown, respectively, on sapphire and silicon carbide substrates. The critical steps of the MOCVD growth process of GaN on SiC (substrate surface preparation, nucleation layer composition and growth parameters) are described and their effects on the physical properties of the HEMT structures and the associated device performances are presented. The GaN growth optimization on sapphire for MESFET applications and the obtained devices performances are also reported. MESFET devices have been developed mainly to test the GaN material quality and the potentiality of this material for microwave applications.
5.2.
GaN MESFET DEVICES
5.2.1 Experimental Procedure The non-intentionally doped and silicon (Si) doped GaN layers were grown at low pressure (50 mb), in an AIXTRON RF reactor on sapphire substrates, using triethylgallium (TEG) or trimethylgalHum (TMG) and ammonia (NH3) as gallium and nitrogen precursors. The growth was performed using the popular two step procedure. First, a nucleation layer (GaN or AIN) was deposited at low temperatures (480-560°C). Then, the GaN layers were grown at high temperatures (1050-1150°C) at a growth rate of about 1.2 |jLm/h, with a V/III ratio of 1500. Hydrogen was used as the carrier gas. Several growth parameters were varied to optimize GaN films: growth temperature and thickness of the nucleation layer, growth temperature and growth rate of the high temperature deposited GaN epilayer, V/III ratio, substrate orientation and the insertion of a second low temperature deposited GaN layer to reduce etch pit density. The material quality of GaN layers was assessed by various characterization techniques such as Hall and C-V measurements, HR-XRD, low-temperature photoluminescence (LT-PL), transmission electron microscopy (TEM), and secondary ion mass spectroscopy (SIMS). Reflectivity was used in complement to photoluminescence owing to its sensitivity to intrinsic properties of nid GaN. 5.2.2 Results Non-intentionally doped GaN samples with characteristics close to the state-of-the-art were obtained using a GaN nucleation layer on c-axis sapphire substrates.
72
Optoelectronic Devices: Ill-Nitrides
The background concentration, which must be minimized to utilize GaN as a buffer layer for MESFET device [4] was found to be lower than 10^^ cm~^ under optimized growth conditions. These nid GaN samples showed full linewidths at half maximum (FWHM[ooo2]) in HR-XRD of about 250-300 arcsec and sharp band-edge emission lines of about 4 meV in LT-PL (10 K). LT-PL and reflectivity spectra of two highly resistive GaN samples (p, respectively, close to 10 and 50 fl cm), are shown in Figures 5.1 and 5.2, respectively. The reflectivity spectra exhibit three resolved resonances, due to excitons involving the Fg and the two Fj valence band holes, labeled A, B and C, respectively. The corresponding PL spectra display free exciton A and B transitions and the usual residual donor bound exciton line (DoX) observed in undoped GaN, which is 6-7 meV lower in energy than the A line. A shift of 6-7 meV between the excitonic transitions of the two samples is observed. This shift may be due to a residual strain in the GaN layer [5], whose level is strongly dependent on the growth conditions, nucleation and layer thickness. The more resistive GaN sample (p ~ 50 H cm), grown with the insertion of a second low temperature deposited GaN layer, appears to be less strained than the less resistive one (p ~ 10 n cm). Such a highly resistive GaN was used as a buffer layer for the GaN MESFET we have fabricated. N type doping of GaN has been achieved using silicon from silane. We have observed a linear variation of the silicon concentration incorporated with the increase of silane flow rate in the gas phase (Figure 5.3).
Reflectivity Photoluminescence
Figure 5.1. LT-PL and reflectivity spectra of highly resistive GaN (p = 10 O cm).
73
MOCVD Growth of Group III Nitrides " Reflectivity Pliotoluminescence p = 50 Q cm
Figure 5.2. LT-PL and reflectivity spectra of highly resistive GaN (p = 50 ft cm).
A good control of the carrier concentration was obtained in the range 5 X 10^^10^^ cm~^. Thickness and doping dispersion obtained on 2-in. GaN samples were less than 5%. No significant degradation of the GaN structural properties was observed with the incorporation of silicon. X-ray rocking curves revealed an increase of the FWHM from
6x10^^
0.0
1.0x10"^
2.0x10"^
3.0x10"^
4.0x10"®
5.0x10"®
SiH4 flow rate (mol/min) Figure 5.3. Hall carrier concentration of Si doped GaN as a function of silane flow rate.
74
Optoelectronic Devices: Ill-Nitrides
300 arcsec for 5 X 10^^ cm~^ doped GaN samples to 430 arcsec for highly doped GaN samples (~ 10^^ cm~^). The 10 K photoluminescence linewidth of the near band edge transition of these samples increased from 5 to 80 meV as silicon level was increased. This broadening can be attributed to the random distribution of donor impurities. The MESFET epilayer structure under study consisted of a 3.6 ixm insulating GaN buffer and a 0.2 luim Si-doped GaN (~2 X 10^^ cm~^) (Figure 5.4). Hall measurements have shown a room temperature mobility of 330 cm^fV s with a carrier density of 3.8 X 10^^ cm^. The fabrication process was a conventional mesa isolated process with chlorine RIE used for mesa definition. Ti/Al/Ni/Au was used for ohmic contact formation and Pt/Au for the gate metal. Devices were realized with gate lengths (Lg) of 2 and 0.3 luim (Figure 5.4). Figure 5.5 shows the output I-V characteristic of a device with L^ = 2 juum and sourcedrain separation of 5 ixm. The gate-drain breakdown voltage is up to 200 V. Small signal microwave characterization performed on device with Lg = 0.3 ixm yielded current-gain and power-gain cut-off frequencies (/x and/^ax) of 12 and 25 GHz respectively as shown in Figure 5.6a and b. For the Lg = 0.3 ixm devices, the peak saturation current achieved at VGS = +1 V was 330 mA/mm and a maximum extrinsic transconductance {g^) of 32 mS/mm was obtained. CW power measurements were performed at 2 GHz using a load-pull system. A record output power density [6] of 2.2 W/mm with an associated power added efficiency (PAE) of 25% was measured on 0.3 jxm X 100 jxm devices (Figure 5.7). GaN MESFET devices have also been investigated through LFN characterizations.
ptmi mAlM/Au
Seure«
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/
Channel GaN (2 ^.0^^ cm-^
Buffer ^ N - N X D
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pE dapphire 5ubs1ratB Figure 5.4.
GaN MESFET structure.
Dm in
2000;(
Z,ifm
75
MOCVD Growth of Group III Nitrides
Vds max = 100 V, Id = 80 mA/mm Figure 5.5.
Vbr = 200 V
Output I-V characteristic of the MESFET (Lg = 2 ixm, Lsd = 5 |xm).
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(a) Current gain versus frequency; (b) power gain versus frequency.
76
Optoelectronic Devices: Ill-Nitrides 2.2 W/mm
15
5 10 Output Power (dBm) Figure 5.7.
20
Power performance of a 0.3 |xm X 100 jjum GaN MESFET on sapphire at 2 GHz.
10^
10^ Frequency [Hz]
Figure 5.8.
Input referred equivalent noise voltage spectral density for GaN MESFETs.
11
MOCVD Growth of Group III Nitrides
Figure 5.8 reports the noise spectra of the equivalent input voltage spectral density ^v for GaN MESFET devices. We have observed that all the noise spectra exhibit a llf noise shape and that pronounced generation-recombination {g-r) bumps are absent. On the other hand, it can be observed that the noise spectra exhibit a pronounced dependence on VGS- The noise magnitude at frequencies above 1 kHz decreases with decreasing VGSIn order to better address the device quality, the investigated devices were compared in terms of their Hooge's parameter, defined as follows: «H ^Vsat/d
where Sy is defined in Figure 5.8, g^ is the transconductance, Vsat is the electron saturation velocity in the channel, I^ is the drain current, L^ff is the length of the saturated velocity channel beneath the gate, / is the frequency and q is the elementary charge. Figure 5.9 compares the Hooge's parameters obtained in the present work with the values reported in the Hterature for different GaN-based FET's (HFET and HEMT) [7-9]. Moreover, it is worth noticing that the GaN MESFET devices exhibit values of the Hooge's parameter comparable, or at least lower, to the values reported in Ref. [7] for other HFET devices.
3i
• HEMT
I
o o 21 +
HFET
E cz I—
a. 11 + o o X
HFET
MESFET [This work]
'.S; 1 1997
Figure 5.9.
1998
1999 Year
2000
2001
Comparison of the Hooge's parameter for different GaN-based FET technologies.
78
Optoelectronic Devices: III-Nitrides
5.3. GaAlN/GaN HEMT DEVICES 53,1 Sapphire Substrate 5.3.1.1 Experimental Procedure, GaAlN bulk material and GaAlN/GaN HEMT heterostructures with Al content varying from 12.5 to 29% were grown in a single wafer AIXTRON reactor, on sapphire substrates, using triethylgallium (TEG), trimethygallium (TMG), trimethylaluminum (TMAl) and ammonia (NH3) as group III and group V precursors, respectively. The incorporation of aluminum in the solid phase has been studied as a function of the group III element molar fraction, V/III ratio and growth temperature. A parasitic reaction was clearly identified to occur in the gas phase between TMAl and NH3, which has strong influence on the growth rate and the aluminum incorporation. As a matter of fact, these two parameters were found to decrease as the NH3 flow (V/III ratio) is increased, as seen in Figure 5.10, while their variation with the Al/Al -|- Ga molar fraction appeared to be non-linear. 5.3.1.2 Material Property Results, GaAlN bulk material grown on GaN appeared to be highly tensilely strained. The strain, checked by HR-XRD was found to increase with Al incorporation (a =13
GPa; JCAI = 12.5% => a= 2.82 GPa; JCAI = 29%).
Plastic relaxation, associated with the generation of misfit dislocations and a strong decrease of the tensile strain, was observed in GaAlN alloy with 30% Al content, which correlates well with a critical thickness of 1000 A for this alloy composition [10].
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MOCVD Growth of Group III Nitrides
79
N-type doping of GaAlN material has been studied as a function of Al content, using Si from silane as dopant. The material appeared to be electrically compensated for Al content higher than 20%. However, SIMS analysis performed on such samples revealed silicon incorporation up to 10^^ cm~^ even in highly compensated samples, associated with a low oxygen concentration ([O] ~ 5 X 10^^ cm~^). The observed compensation could be explained by the amphoteric behavior of silicon (N type -^ P type material) due to the high nitrogen vacancy concentration generated in GaAlN bulk material with high Al content (low anmionia flow during the growth), or by the presence of a deep level bound to Al. More investigation studies have to be done on this specific aspect. The physical properties of the GaAlN/GaN bulk material we have grown are summarized in Table 5.1. GaAlN/GaN HEMT heterostructures under study consisted of a 3 ixm insulating GaN buffer layer followed by 0.03 (jim undoped and Si doped GaAlN layer with Al content varying from 22 to 29%. The surface morphology was observed to be "mirror like" for all the heterostructures. This roughly indicates that the high bandgap layer thickness is lower than the critical thickness in the range of the alloy composition studied. The transport properties of such heterostructures have been studied at low temperatures (10-300 K) and at high temperatures (300-500 K). The variation of the hall mobility and sheet carrier density for one of these heterostructures (x^i ~ 20%) is illustrated in Figures 5.11 and 5.12. We observe a constant value of the Hall mobility from 100 to 10 K, which can be explained by the formation of a two-dimensional electron gas (2DEG) at the GaAlN/GaN interface of the HEMT heterostructure. Our analysis of undoped and doped HEMT structures revealed that the 2DEG sheet charge density is mainly due to the spontaneous and piezoelectric polarization, while the contribution of the introduction of Si doping into the GaAlN layer plays a secondary role in the formation of such 2DEG sheet charge density. Table 5.1. Physical properties of GaAlN bulk material Run number {R °) Al content XAL(%)
Strain a (MPa)
Sheet resistance
Rnm AEC791 AEC789 AEC792 AEC788 AEC790 AEC805
12.5 15.4 16 19 23 29
1.3 1.75 1.75 2.19 2.5 2.82
1150 1250 1500 2800 10,000 > 20,000
Carrier concentration Nd-Na (cm'^)
Hall carrier concentration
1.5X10^^ 7X10^^ 5 X 10^^ 5-7x10^^
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-
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Hall mobility fjL (300 K) (cm^A^ s)
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Optoelectronic Devices: Ill-Nitrides
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Temperature (K) Figure 5.11. Temperature dependence of Hall mobility for an GaAlN/GaN HEMT heterostructure.
In the temperature range of 300-500 K, the sheet carrier density appeared to be constant as seen in Figure 5.12, while a 50% reduction in the Hall mobility is observed in the same range of temperature. This behavior of the mobility, also observed in SiC material, will lead to a decrease in the current density and output power density of the associated HEMT device. This is the major reason for the decrease in the device current density with the gate periphery, as previously published. aec 603b 1E13
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100 300
350
400 450 Temperature (K)
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Figure 5.12. Temperature dependence of Hall mobility and sheet carrier density for a GaAlN/GaN HEMT heterostructure.
MOCVD Growth of Group III Nitrides Btructufe hemt
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Figure 5.13. X-ray rocking curves of a GaAlN/GaN HEMT heterostructure (experiment and simulation).
The high-mobility value obtained at low temperatures (/177 K = 3670 cvc^fW s) for the above-mentioned HEMT structure reveals a good quality of the GaAlN/GaN interface, in good agreement with the structural properties checked by HR-XRD and TEM measurements. Figure 5.13 shows a nice fit of the experimental and calculated X-ray rocking curves related to the mentioned GaAlN/GaN HEMT heterostructure. The main characteristics of the HEMT heterostructure extracted from this profile have been the following: thickness of each layer (woaAiN = 30 nm, WoaN = 3 ixm), Al content of the high-bandgap layer (x^i = 19%). The observation of fringes on the experimental spectrum, which suggests a good structural quality of the HEMT heterostructure, was confirmed at the atomic scale by TEM (Figure 5.14). The GaAlN/GaN interface is perfectly delineated, as observed in Figure 5.14, and 57 monolayers (5.18 A) can be counted in the whole thickness of the GaAlN layer which fit the expected 300 A already measured using X-ray.
AEC 603
GaAIN
(JiiN
Figure 5.14.
TEM cross section of a GaAlN/GaN HEMT structure.
Optoelectronic Devices: Ill-Nitrides
82 HEMT
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Figure 5.15, X-ray rocking curves of six GaAlN/GaN/Al203 HEMT structures.
A good reproducibility of the growth process is illustrated in Figure 5.15, which shows the X-ray rocking curves of six HEMT structures which have been grown with the same growth parameters and following the same structure design. A nice superimposition of the different figures is observed which fit with an Al content of 22.5%. The good electrical characteristics of such HEMT structures: room temperature mobility higher than 1000 cvc^/W s associated with a high sheet carrier density of 1.4 X 10^^ cm~^, and a low sheet resistance of about 500 H, have been confirmed by the high performance of the corresponding HEMT devices. A successful comparison of our HEMT structures' electrical data (/i, A^^, /?•) with the already pubUshed data is shown in Figure 5.16. 2000
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GaAlN/GaN HEMT carrier concentration versus mobility data.
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MOCVD Growth of Group III Nitrides
83
5,3,1.3 Device Results, Device processing has been performed using a conventional mesa isolated process with chlorine RIE (SiCl3, BCI3) for mesa definition. Either Ti/Al or Ti/Al/Ni/Au metallisations were used for ohmic contact formation and Pt/Au or Ir/Au for the gate metal. The devices were realized with gate lengths (Lg) of 0.5,0.3 and 0.15 juim. Typical ohmic contact resistances of 0.3-0.5 fit mm were obtained after RTA annealing of the metal alloys (850°C, 30 s) while gate contacts with an ideality factor lower than 2 and a Schottky barrier of about 0.8 eV have been achieved. The processed wafers have shown a good homogeneity within an edge exclusion of about 3-5 mm. The mapping of the device-related parameters such as the sheet resistivity of the active layer (Figure 5.17), the maximum saturation current /^ss, the pinch-off voltage Vp (Figure 5.17) and the transconductance g^ are in good agreement with the variation of the basic material properties {/JL, NS, XAI, etc.). For 0.5 juim X 100 |xm devices, we have obtained a typical g^ between 180 and 200 mS and an /^ss maximum of 0.85 A/mm at + 1 V. The bar chart given in Figure 5.18 depicts the main device results (/^ss, ,^m' ^p) of two processed 2-in. diameter GaAlN/GaN HEMT wafers, showing homogeneous data. This indicates stable processing conditions for both epitaxy and processing of the wafers. The small signal microwave performances of 0.5 ixm X 100 jjim devices from the above wafer (AEC837) are shown in Figure 5.19. They show a similar unilateral gain around 25 db at 2 GHz, current-gain and power-gain cut-off frequencies (fi and/j^ax)^ respectively, of 20 and 108 GHz. Load-pull measurements performed at 2 GHz on such wafers (AEC837 and AEC842) have shown remarkably high output power density and absolute power level for devices from wafer AEC837. The measurements have been performed on wafer without additional thermal coupling of the devices.
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Wafers
Figure 5.18.
Summary of device data such as ^^-max, /^^s, Vp from representative GaAlN/GaN 2-in. wafers in bar chart form.
Small devices (0.5 |xm X 100 luim) exhibited at 2 GHz a maximum output power density of 4.2 W/mm with a PAE of 45% as shown in Figure 5.20a. The scaling of output power and power density with device size is given in Figure 5.20b. The significant reduction of power density with increase in the transistor size is due to thermal effects. Nevertheless, the absolute power level of 3.2 W for 1 mm devices on sapphire substrates measured on wafer without efficient coupling to a heat sink is in good agreement with the international state-of-the-art. A summary of the microwave data (output power and PAE) before and after passivation are depicted in bar chart form in Figure 5.21a and b. The passivation increases both
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Small signal microwave properties of typical 0.5 |xm X 100 jxm devices from wafer AEC837.
MOCVD Growth of Group III Nitrides
-15 -10
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0
400
5
85
600
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Gate width [\\m)
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(a) Pout, PAE and gain versus pin for small devices (0.5 jxm X 100 iJim) at 2 GHz; (b) scaling of output power and power density with device size at 2 GHz.
microwave output power and PAE. However the degree of improvement depends on the individual wafer. High material quality GaAlN/GaN HEMT wafers have shown a minor influence on passivation (AEC837). In contrast, the data from wafers with somewhat lower quality (higher defect density) can be improved significantly by the passivation (AEC842).
B f f l g RF-power before passr^ation ir::..;.l RF-power final measurement
AEC 837 AEC 842 Wafers
^ • M PAE: before passivaljon P ^ ^ PAE: final meaBuremenl
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Wafers Figure 5.21. (a) Summary of representative microwave data (output power) at 2 GHz before and after passivation (0.5 |xm X 100 jxm devices); (b) summary of representative microwave data (PAE) at 2 GHz before and after passivation (0.5 jjim X 100 |xm devices).
86
Optoelectronic Devices: Ill-Nitrides
5,3,2 Silicon Carbide Substrate 5,3,2,1 Experimental Procedure, GaAlN/GaN heterostructures with 22% Al content were grown by MOVPE in a single wafer 200RF AIXTRON reactor on semi-insulating on-axis 4H-SiC substrates, using triethylgallium (TEG), trimethylaluminum (TMA), and ammonia (NH3) as group III and group V precursors. The growth has been performed at low pressure (50 mb), high temperature (1160°C), and the growth rate was roughly 0.5 |jLm/h for GaAlN and 1.2 juim/h for GaN. The GaAlN/GaN HEMT structures under study consisted of GaN or GaAlN nucleation layers, followed by a 1 ixm thick insulating GaN buffer layer, then a 27 nm Si doped GaAlN layer with 22% Al content, and finally a 3 nm thick undoped GaN cap layer. The transport properties of such heterostructures were studied as a function of temperature from 100 to 500 K. Hall mobihty about 1100 cm^A^ s at 300 K has been obtained, associated with a sheet carrier density of 1.2 X 10^^ cm~^. Since HEMT devices are expected to operate at high temperatures, there is considerable interest to study the influence of temperature on electron mobility. Such an influence can explain the limitation in power and efficiency of the HEMT devices at large drain bias. As shown in Figure 5.22, increasing temperature from room temperature to 500 K reduces the electron mobility by a factor of 2.5. Several growth parameters have been investigated, aiming at optimizing the material quality of the GaAlN/GaN HEMT structures, namely, the growth temperature, thickness and composition of the nucleation layer, and the SiC surface preparation. Various characterization techniques such as atomic force microscopy (AFM), TEM, HR-XRD,
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Sheet carrier density and hall mobiHty of a GaAlN/GaN HEMT structure as a function of temperature.
MOCVD Growth of Group III Nitrides
87
capacitance-voltage (C-V) and Eddy current probe measurements have been used again for this study. 5,3.2,2 Material Property Results, Due to the large lattice mismatch between GaN and SiC (Aa/a ~ 3.5%), the deposition of the first monolayers is a critical point of the MOCVD process of GaN on SiC. Three major steps in the GaAlN/GaN/SiC growth process have been identified and their impact on the physical properties of the HEMT structures clearly demonstrated [11]: • •
nucleation layer growth temperature, nucleation layer composition. substrate surface preparation.
5,3,3 GaN Nucleation Layer Our first approach of the GaAlN/GaN/SiC growth studies has been concerned with the optimization of HEMT structures based on GaN nucleation layers. The growth temperature of the first GaN monolayers has been identified to have a marked influence on the structural properties of the GaAlN/GaN/SiC HEMT structures. At low growth temperatures, HEMT structures with a ''mirror like" surface morphology are obtained, while a three-dimensional growth process is observed at higher growth temperatures. This observation has been confirmed by HR-XRD measurements. As clearly seen in Figure 5.23, the rocking curves related to GaAlN/GaN/SiC HEMT structures grown at two different GaN nucleation layer growth temperatures, namely 985 and 990°C, exhibit very different X-ray signatures. A good crystallographic quality of the HEMT structure
10^ SiC
GaN FWHIVi=105arcsec FWHM=150arcsec Q.
63
64
65
67
Omega/2Theta (°) Figure 5.23. X-ray rocking curves of two GaAlN/GaN HEMT structures, for two different nucleation layer growth temperatures.
88
Optoelectronic Devices: Ill-Nitrides
Figure 5.24.
TEM cross section of a GaN/SiC interface (low growth temperature GaN nucleation layer).
deposited at the lower GaN nucleation layer growth temperature is observed, evidenced by well-delineated peak satellites, up to the second order, of a superlattice structure implemented in the GaN buffer layer, which is indicative of sharp interfaces. TEM analysis revealed that GaN/SiC interfaces grown at low temperatures (980°C) are indeed sharp with steps originating from the substrate misorientation (Figure 5.24), while more ill-defined at higher growth temperatures. 5.3.4
Substrate Surface Preparation
We have observed that the SiC surface preparation is another key point of the GaAlN/GaN growth process on SiC, as illustrated below. AFM measurements performed on as-received substrates have confirmed the poor quality of the surface preparation realized by the substrate suppliers, as seen in Figure 5.25a. A "specific" surface preparation of SiC substrates by Novasic has allowed to obtain a very good surface morphology characterized by an RMS close to 0.7 A and steps at the atomic level (Figure 5.25b).
a) RMS = 6.9 A
b) RMS = 0.7 A
Figure 5.25.
Surface morphology of an "as-received" SiC substrate (a) and after a Novasic surface preparation; (b) 5 |xm X 5 |jLm surface area.
MOCVD Growth of Group III Nitrides
89
Moreover, correlated with this ex situ specific surface preparation by Novasic, we have observed that an in situ anneaUng of the SiC substrate at high temperatures (~ 1000°C) under hydrogen flow, has led to a real breakthrough of the crystalline quality of the GaAlN/GaN epilayers. A reduction of 50% of the GaN rocking curve FWHM (FWHM = 50 arcsec) has been measured as compared to the GaAlN/GaN epilayers grown on as-received substrates (FWHM = 1 0 0 arcsec). The SiC surface preparation also plays an important role on the electrical properties of such GaAlN/GaN HEMT structures. GaAlN/GaN HEMT structures grown on as-received SiC substrates have presented very high sheet resistances {Ru = 4000-15,000 d ) , very far from the targeted value of 500 fl obtained on SiC substrates with the specific surface preparation mentioned above. This evolution of the sheet resistance with the substrate surface preparation may be explained by a strong increase in the piezoelectric effect induced by strain or by the generation of deep traps due to the high density of defects at the GaN/SiC interface. Indeed, due to some surface kinetic aspects, the use of a GaN nucleation layer favors an island growth mode for the first monolayers on SiC. This growth mode would generate more tensile strain and defects in the GaN buffer layer. The substrate surface preparation could play, in this aspect, a catalyst role. This was confirmed by HR-XRD measurements. The GaN buffer lattice parameter (c) was found to be close to 5.158 A for the highly resistive HEMT structures as compared to the 5.1850 A for the unstrained GaN lattice. 5.3,5 GaAlN Nucleation Layers The strong influence of the substrate surface preparation and growth temperature on the growth of the first atomic layers on SiC makes the GaAlN/GaN/SiC growth process clearly non-reproducible using a GaN nucleation layer. In order to improve the reliability of the MOVPE process, we have investigated the growth of GaAlN/GaN/SiC HEMT structures with a GaAlN (Al content = 25%) based nucleation layer. In this case, the growth of the nucleation layer on SiC starts using a step flow mode, leading to a GaN buffer layer also grown in a step flow mode and so less tensilely strained in the HEMT structure. Indeed, the GaN buffer lattice parameter, checked by X-ray, was found to be close to 5.17 A in that case. As a rule, we found a clear improvement of the physical properties of the GaAlN/GaN HEMT structures, as compared to HEMT structures with GaN nucleation layers, with a good reproducibility from run to run. Due to less strain and less defects in the HEMT structures, the residual carrier level in the GaN buffer, checked by C- V measurements, was found to be a decade lower as depicted in Figure 5.26. Mapping of the sheet resistance and pinch-off voltage using C-V and Eddy current probe measurements performed on such GaAlN-based nucleation layer HEMT structures reveal a good homogeneity of these electrical characteristics on 2-in. wafers, as seen in Figure 5.27. Figure 5.28 shows an AFM image of the surface of such a layer and confirms a very good crystaUine quality of the GaAlN/GaN epilayers with a RMS close to 0.3 nm.
90
Optoelectronic Devices: Ill-Nitrides GaN nucleation layer
GaAIN nucleation layer
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Figure 5.26.
0.6 0.8 Depth (|im)
1
2 Depth (|im)
Capacitance-voltage depth profiles of two GaAlN/GaN HEMT wafers with GaN and GaAIN nucleation layers.
53,6 Device Results Devices related to GaAlN/GaN/SiC HEMT structures based on GaN and GaAIN nucleation layers have been fabricated using a conventional mesa isolated process with RIE for mesa definition. Ti/Al/Ni/Au was used for ohmic contact formation and Pt/Au for the gate metal. The devices were realized with gate length (Lg) of 0.5, 0.3 and 0.25 |xm. Under static measurements we found a maximum drain current /^ss around 1 A/mm and a pinch-off voltage of - 5 V for devices with a gate length of 0.5 juim and a GaN nucleation layer. Better static results have been obtained for devices with the same geometry but with GaAIN nucleation layer. As a matter of fact, an /^ss up to 1.5 A/mm has been recorded [12]. Devices related to HEMT wafers with GaN nucleation layers have been measured at 10 GHz using a load-pull system. They exhibited a CW output power in excess of 2.8 W/mm for a gate length of 0.5 luim, as shown in Figure 5.29.
Figure 5.27.
Sheet resistance and V pinch-ofiF mapping of a 2-in. GaAlN/GaN/SiC HEMt wafer.
MOCVD Growth of Group III Nitrides
Figure 5.28.
91
Surface morphology of a 2-in. GaAlN/GaN/SiC HEMT wafer: RMS = 0.3 nm.
At 2 GHz, we have obtained an absolute output power in excess of 6.5 W for 2 mm X 0.3 ^lm devices and a maximum output power density of 3.5 W/mm has been reached for 1 mm X 0.3 (xm devices. The scahng of the absolute output power and power density versus the gate width of the devices is given in Figure 5.30a and b. A comparison of our results with data from different wafer suppliers is made (Figure 5.30a and b).
5
Figure 5.29.
10 15 Input Power (dBm)
CW performance at 10 GHz of a 0.3 mm X 0.5 ^jim device measured under probes.
92
Optoelectronic Devices: Ill-Nitrides (a)
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(a) Scaling of the absolute power versus gate width measured at 2 GHz (Lg = 0.3 [xm). (b) Scaling of the power density versus gate width measured at 2 GHz (0.3 jxm).
The shorter gate of the devices (Lg = 0.3 |xm as compared to Lg = 0.5 U | Lm for the former device process) has led to significantly higher cut-off frequencies: /t increased from 20 to 35 GHz whereas /^ax is higher than 100 GHz.
93
MOCVD Growth of Group III Nitrides Vds = 30V and VQS = -ZVat 10GHz
-PoLrt[dBm] Gain[dB] ^PAE(%)
10 15 Pabs (dBm) Figure 5.31. Load-pull measurement at 10 GHz of a 0.3 mm X 0.25 ixm GaAlN/GaN/SiC HEMT device.
An improvement of the microwave performances has been observed for devices issued from HEMT wafers with GaAlN nucleation layer. CW on-wafer load-pull measurements have been performed at 10 GHz. For 0.3 mm X 0.25 ixm devices, a power density of 4 W/mm has been obtained with a PAE of 28% as shown in Figure 5.31.
5.4.
CONCLUSION
GaN MESFET structures and GaAlN/GaN HEMT structures have been grown on sapphire and silicon carbide by low-pressure MOVPE. The influence of some critical growth parameters on the physical properties of the device structures has been identified and their optimization has led to high-microwave performance devices such as CW output power up to 4 W/mm at 10 GHz for GaAlN/GaN HEMTs on SiC.
ACKNOWLEDGEMENTS The authors would like to thank C. Brylinki and J.-C. Jacquet for fruitful discussions and a careful reading of the manuscript, B. Grimbert, E. Morvan, M. Laurent, N. Caillas, V. Hoel and J. Wtirfl for device processing, E. Delos, D. Ducatteau, C. Gaquiere and J. Graffeuil for microwave and noise measurements, R. Aubry, N. Sarazin, M. Peschang, D. Lancefield, R. Seitz, E. Pereira, D. Theron and the Novasic Company for material characterization, S. Delage and J.-C. De Jaeger in charge of GaN project at TRT/IEMN common laboratory and D. Pons who launched the GaN program at TRT. The research work presented here has been supported by the French Ministry of Defence (DGA/STTC).
94
Optoelectronic
Devices:
Ill-Nitrides
REFERENCES [1] Shealy, J.R., Kaper, V., Tilak, V., Prunty, T., Smart, J.A., Green, B. & Eastman, L.F. (2002) An AlGaN/GaN high-electron-mobility transistor with an AIN sub-buffer layer. /. Condens. Matter Phys., 14, 3499-3509. [2] Hobgood, H.McD. (2003) Silicon carbide crystal and substrate technology: a survey of recent advances, ICSCRM2003, Proc, Lyon, p. 46. [3] Micovic, M., Nguyen, N.X., Janke, P., Wong, W.S., Hashimoto, P., McCray, L.M. & Nguyen, C. (2000) Electron. Lett., 36, 358. [4] di Forte-Poisson, M.A., Huet, F., Romann, A., Tordjman, M., Trassaert, S., Boudart, B., Theron, D., Seitz, R. & Pereira, E. (1999) LP-MOCVD growth of GaN MESFETs, Proceedings of the European Workshop on Metal Organic Vapor Phase Epitaxy VIII, Prague, p. 77. [5] Leroux, M., Beaumont, B., Grandjean, N., Massies, J. & Gibart, P., (1996) Characterization of near band edge optical transitions in undoped GaN/Sapphire, grown by MVPE, HVPE and GSMBE, Proceedings of MRS Fall Meeting, Boston 1996. [6] Trassaert, S. (2000) Realisation Technologique de transistors aeffet de champ dans les fiUeres InP et GaN pour amplification de puissance Hyperfrequence, Thase de doctorat de I'Universite des sciences et technologies de Lille, 4 Fevrier 2000. [7] Balandin, A., Cai, S., Li, R., Wang, K.L., Ramgopal, V. & Viswanathan, C.R. (1998) Flicker noise in GaN/AlGaN doped channel heterostructure field effect transistors. IEEE Electron. Dev. Lett., 19 (12), 475-477. [8] Balandin, A., Morozov, S.V., Cai, S., Li, R., Wang, K.L., Wijeratne, G. & Viswanathan, C.R. (1999) Low flicker-noise GaN/AlGaN heterostructure field-effect transistors for microwave communications. IEEE Trans. Microwave Theory Tech., 47 (8), 1413-1471. [9] Levinshtein, M.E., Rumyantsev, S.L., Gaska, R., Yang, J.W. & Shur, M.S. (1998) AlGaN/GaN high electron mobility field effect transistors with low 1// noise. Appl. Phys. Lett., 37 (8), 1089-1091. [10] di Forte-Poisson, M.A., Romann, A., Tordjman, M., Dessertenne, B., Cassette, S., Surrugue, M., Frapsauce, N., Adam, D., Delage, S.L., Boudart, B., Gaquiere, C , Vellas, N., Lancefield, D. & di Persio, J. (2001) LP-MOCVD growth of GaAlN on sapphire. Application to HEMT's devices. Proceedings of the European Workshop on Metal Organic Vapor Phase Epitaxy IX, Wrexham, p. 115. [11] di Forte-Poisson, M.-A., Romann, A., Tordjman, M., Magis, M., Di Persio, J., Jacques, Ch. & Vicente, P. (2003) LP-MOCVD growth of GaN on Silicon Carbide. /. Cryst. Growth, 248, 533-538. [12] di Forte-Poisson, M.-A., Magis, M., Tordjman, J., Aubry, R., Peschang, M., Delage, S.L., Di Persio, J., Grimbert, B., Hoel, V., Delos, E., Ducatteau, D. & Gaquiere, C. (2003) LP-MOCVD growth of GaAlN/GaN heterostructures on Silicon Carbide. Application to HEMT's devices. Proceedings of MRS Fall Meeting, Boston.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 6
Growth of Nitride Quantum Dots Hyun Jin Kim, Soon-Yong Kwon and Euijoon Yoon School of Materials Science and Engineering, Seoul National University, Seoul 151-742, South Korea
6.1. INTRODUCTION For the past few decades, low-dimensional quantum structures, such as quantum wells (QWs), quantum wires (QWRs), and quantum dots (QDs) have been attracting lots of interest due to their potential advantages compared with bulk materials (Figure 6.1). Among these, QDs are expected to be the most promising due to their unique electronic states, such as 5-function-like density of states, three-dimensional (3D) carrier confinement, etc. Due to their unique properties, the semiconductor laser with a QD active layer is expected to have ultra-low threshold current, reduced temperature sensitivity, narrower spectral line width, and high-modulation bandwidth, etc. [1,2]. Furthermore, the semiconductor photodetector with QDs are also expected to have the sensitivity for the normally incident light, enhanced photoexcited carrier lifetime, reduced dark current, and higher electric gain [3]. It was in 1982 that the concept of QDs was proposed for the first time as artificial atoms for semiconductor laser application by Arakawa and Sasaki [4]. Since then, there has been lots of research devoted to the realization of predicted potential advantages of QDs. However, it took about 10 years to realize the fabrication of the practical QD structures. In the 1990s, both selective growth and self-assembled growth technique without the formation of nonradiative defects were well developed. Particularly, the StranskiKrastanow (SK) growth mode was very successful for InGaAs/GaAs systems [5-7]. As a result, lasers, detectors for both inter-band and inter-subband transitions have been successfully demonstrated using the InGaAs/GaAs QDs [8-10]. From the late 1990s this material system has been extended to other material systems. Among those material systems, nitride semiconductors have received the most attention for applications to blue and ultraviolet (UV) light emitting devices, especially, due to the possibility of much bigger impact of QDs in GaN-based LDs [11]. In nitride semiconductors, the larger effective mass of electrons nic or the larger ratio of the effective mass of holes m^ to rric {mjm^), compared to GaAs-based semiconductors.
E-mail address:
[email protected] (E. Yoon).
95
96
Optoelectronic Devices: Ill-Nitrides Bulk
m
Quantum Film
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Quantum Wire
Quantum Dot
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Figure 6.1. Density of states in bulk material, quantum wells, quantum wires, and quantum dots.
results in an increase in the threshold current density of QW lasers: the threshold current density /th of GaN-based QW lasers is expected to be ~ 1 kA/cm^, whereas that of GaAsbased QW lasers to be ~ 100 A/cm^. On the other hand, it was suggested that, if QDs are used in the active region and the size of the QDs is small enough that the population of carriers in the higher subband can be ignored, the achievable threshold current /th in both GaAs-based and GaN-based LDs is almost the same, about 100 nA-1 mA, as shown in Figure 6.2. Therefore, with the use of QDs, the threshold current density is reduced by a factor of 100 in GaN-based lasers compared to GaAs-based lasers, suggesting that the impact of QDs is much bigger in GaN-based LDs than in GaAs-LDs. The promising aspect in the applications of the nitride QDs is also confirmed in the emission mechanism of the InGaN active layer. InGaN active layers for blue and green light emitting diodes (LEDs) are known to have excellent optical properties despite the presence of high-density defects. It is widely accepted that their high-luminescence efficiency is due to the carrier localization induced by the presence of compositional fluctuation and/or QD-like features usually observed in InGaN layers of sufficiently high In content [12]. Therefore, the introduction of QDs would also increase the luminescence efficiency in the system of high dislocation density and especially in material systems without compositional fluctuation such as low In content InGaN, AlGaN, etc. Since the late 1990s, several methods to form QDs using nitride semiconductors were suggested. They can be categorized into four methods: (1) using SK growth mode, (2) using "anti-surfactant", (3) using selective epitaxy, and (4) other novel methods. One of the most attractive methods for defect-free QD formation is the SK growth in lattice-mismatched semiconductor systems, widely used in the QD fabrication of other material systems, such as InGaAs/GaAs [5-9], InAs/InP [10,13], InP/GaAs [14,15],
Growth of Nitride Quantum Dots
97
Gan QW Lasers
(5
QD Lasers 4 6 m,, / m_ Figure 6.2.
8
10
Carrier density at transparency condition plotted as a function of the ratio of effective mass of holes to that of electrons for quantum well (QW) lasers and quantum dot (QD) lasers [11].
GaSb/GaAs [16], InSb/InP [17], SiGe/Si [18], ZnCdSe/ZnSe [19], etc. The schematic diagram of the SK growth mode is presented in Figure 6.3. In the SK growth mode, the mismatched epitaxy is initially accommodated by biaxial compression in a layer-bylayer (2D) growth region, traditionally called as "wetting layer". After the deposition of a few monolayers, the strain energy builds up. Then, the evolution to 3D islands becomes more favorable than the continued, strained planar growth. Such islands are referred to as self-assembled QDs (SAQDs).
Volmer-Wfeber mode
•••••••••••••H
••••••••••!
Figure 6.3. Schematic diagram of typical 3D growth mode (Volmer-Weber mode) and the StranskiKrastanow (SK) growth mode. A wetting layer between the substrate and the quantum dots is present in SK growth mode.
98
Optoelectronic Devices: Ill-Nitrides In contents of InGaN (%) 20 40 60 80
100
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Ei c
4
(Ai O
0)
c
0)
1^0 O
GaN
Q. (Q
4o
c o o
G)
I 2 QQ
InN 3.1
^
3.2
3.3 3.4 Lattice constant (A)
3.6
3.6
Figure 6.4. Bandgap energies of AIN, GaN, and InN vs their lattice constants. Ticks and labels in top axis and right axis show the variation in lattice mismatch of InGaN grown on GaN and that of GaN grown on AlGaN, respectively.
Nitride semiconductors can be epitaxially grown to form a strained heterostructure, which is indispensable for the SK growth mode. Figure 6.4 shows the lattice constants of AIN, GaN, and InN compared with their bandgap energies. As shown in Figure 6.4, the lattice mismatch between AlGaN and GaN ranges from 0 to 2.4%, and that between InGaN and GaN ranges from 0 to 11.1%, which is sufficiently large to have all growth modes (the strained 2D growth mode, the SK growth mode, and the relaxed 3D growth mode). By the proper combination of QD and substrate materials, the extent of strain in the film and subsequent QD growth behavior can be controlled. It is also worth noting that the large difference in their bandgap energies in Figure 6.4 (from 0.7 eV (InN) to 6.2 eV (AIN)) is also advantageous for the realization of heterostructure with large band-offsets, which would enhance the carrier localization efficiency of QDs. The nitride QDs were also demonstrated by using "anti-surfactant". The pretreatment of the growth surface by anti-surfactant, such as tetraethylsilane (TESi, Si(C2H5)4), were found to result in the 3D growth mode of the subsequent layer, even in the case with little lattice-mismatch. The presence of the wetting layer was not confirmed in the QDs grown by this method. Since this growth mode does not require lattice mismatch, the restriction in the choice of film/substrate combination can be somewhat relaxed.
Growth of Nitride Quantum Dots
99
The method using selective epitaxy attempted in the nitride QD formation is similar to the method of patterning QWs, generally used in other III-V compound semiconductors. In this case, at first, pyramidal structures are grown on a patterned substrate using selective epitaxy. Then, QDs are grown on top of those pyramidal structures. However, this method has similar advantages with the method of patterning QWs, such as (1) the possibility of almost arbitrary lateral shape, size, and position realization, (2) general compatibility with the modem ULSI technologies in the patterning process of this method. However, there are some drawbacks, such as defects or damages induced by etching process. Besides the techniques described above, other novel techniques were also attempted to fabricate the nitride QDs, such as the nitridation of metallic droplets [20-22], the surface passivation and/or pretreatment [23-25], the laser ablation [26], the ion implantation [27], the colloidal synthesis [28], etc., by several research groups. In this chapter, various techniques to form nitride QDs are reviewed, and the current status of nitride QD research is discussed. In particular, emphasis is put on three major growth techniques such as growth of strain-induced SK QDs, growth by anti-surfactant, and growth by selective epitaxy. Table 6.1 summarizes the three major techniques for nitride QD formation and material systems explored. Effects of various parameters in each growth techniques and changes in physical properties are reviewed. Finally, novel formation techniques are briefly reviewed.
Table 6.1. Summary of three major techniques to form nitride quantum dots Techniques SAQDs by SK growth mode
Organization
Authors
Growth
Material system
CEA-Grenoble
Daudin et al.
MBE
CNRS
Damilano et al.
MBE
University of Tokyo Seoul National University University of Montpellier II
Tachibana et al.
MOCVD
Kim et al.
MOCVD
GaN/AlN [29-31,37]; InGaN/GaN [35] GaN/AlN/Si [32]; InGaN/GaN [33,34,36] GaN/AlN/6H-SiC [38]; InGaN/GaN [39-41] In-rich InGaN/GaN [42,43]
Briot et al.
MOCVD
InN/GaN [45]
QDs using anti-surfactant
RIKEN
Tanaka et al.
MOCVD; MBE
GaN/AlGaN/6H-SiC [49-53]; InGaN/GaN/6H-SiC [54]
QDs by selective epitaxy
University of Tokyo University of Tokushima
Tachibana et al.
MOCVD
Wang et al.
MOCVD
InGaN/GaN [55]; GaN/AlGaN [56] InGaN/GaN [57,58]
100 6.2.
Optoelectronic Devices: Ill-Nitrides GROWTH OF STRAIN-INDUCED QUANTUM DOTS
6,2,1 Self-assembled Quantum Dots by MBE One of the most attractive methods to form defect free QDs is the SK growth in latticemismatched systems. The growth of SAQDs by the SK growth mode has been successfully demonstrated using both MBE and MOCVD. The GaN QD growth using SK growth mode was reported for the first time by Daudin et al. [29]. They monitored the changes in growth mode of GaN on AIN by reflection high-energy electron diffraction (RHEED). Their growth of (0001) AIN and GaN with wurtzite structure was carried out by MBE on (0001) sapphire substrates. Atomic nitrogen was produced by an RF plasma source. After nitridation of a sapphire substrate by exposing it to nitrogen plasma, a thin (about 15 ml) AIN buffer was deposited at a substrate temperature T^ of 500°C, followed by the growth of a 2-|ULm-thick GaN buffer and of a 200-nm-thick AIN layer at 650°C. AIN layer was fully relaxed with respect to the GaN buffer, judging from the changes in RHEED streak spacing. Subsequently, GaN epilayer was deposited on AIN and its relaxation was studied by RHEED. The growth behavior of GaN on AIN was rather different depending on substrate temperature, 7^, as shown in Figure 6.5. At 720''C, the Bragg spot intensity increased after deposition of 2 ml, which was attributed to 2D/3D growth mode transition. For further GaN deposition, the Bragg spot intensity remained constant, indicating a persistent 3D growth mode. In contrast, at 620°C, the indication of 2D/3D transition is hardly observed and the Bragg spot intensity decreased rapidly down to the value corresponding to the reflectivity of a smooth GaN surface, suggesting a fast recovery of 2D growth. On the other hand, at intermediate temperature ranges, for example, at 690°C, the increase in the Bragg spot intensity after the deposition of 2 ml GaN was followed by a rapid decrease after deposition of about 6 ml. This rapid decrease in intensity was found to be associated with the transition of streaky RHEED pattern to spotty pattern. By precise control of SK growth mode by RHEED observation, GaN QDs were obtained [29,30]. The image of a smooth AIN base layer prior to GaN deposition is shown in Figure 6.6(a). When about 4 ml GaN layers were deposited on the AIN surface, GaN QDs were formed as shown in Figure 6.6(b). They are typically 10 nm wide, 2 nm high and their density was about 5 X 10^^ cm~^. The size and density of QDs could be further controlled by using growth interruption. Figure 6.6(c) shows GaN QDs obtained at 710°C by depositing 2 ml GaN, followed by exposure to N plasma for 50 s. Clearly, the QD density was reduced (5 X 10^^ cm~^), however, their size became larger (25 nm wide and 5 nm high) than in the previous case, due to the coalescence process occurring under atomic nitrogen flux. Inclined RHEED streaks were observed in this case, indicating that pyramidal QDs with sixfold symmetry and (10-13) facets were formed after the coalescence.
Growth of Nitride Quantum Dots (a)
101
3 :
2.5 [•
•
•
Tg = 720°C
'•
3 1.5 3 0.5 0 ^-0.5
\ f
Pl-^. [[
1
U A ^ /i
-
Time (s)
:
)
2
4
6
8
\
10 •
(0
c 0
Q
10
15
25
Thickness (ML) Figure 6.5.
Change in in-plane lattice parameter (dotted line) and Bragg spot intensity (full line) as a function of the thickness of GaN on AIN [29].
The atmosphere during the growth interruption played an important role in the coalescence process. GaN QD formation at 700°C by depositing 3 ml GaN on AIN surface and subsequent growth interruption under either N plasma or under vacuum for 3 min at 700°C resulted in different surface morphology. Growth interruption under vacuum led to further coalescence process with sparse and larger QDs, as shown in Figure 6.7, presumably due to the increase in the mean-free-path of Ga on N-deficient surface.
102
Optoelectronic Devices: Ill-Nitrides
200 nm
200
nm Figure 6.6. (a) AFM observation of a smooth AIN surface, (b) GaN QDs formed by depositing 4 ml GaN on the AIN surface followed by cooling down under vacuum, (c) GaN QDs formed by depositing 2 ml GaN on the AIN surface followed by exposure to N plasma for 50 s [29].
Growth of Nitride Quantum Dots
103
Figure 6.7. 200 nm X 200 nm AFM images for GaN QDs grown on AIN at 700°C and experienced the growth interruption and cooling process (a) under N plasma flux, and (b) under vacuum [30].
The optical properties of the GaN SAQDs could be tailored by controlHng their sizes [31]. PL spectra at 2 K from "small dots" with a typical height of 2.3 nm (8 nm in diameter) and "large dots" with a typical height of 4.1 nm (17 nm in diameter) are compared in Figure 6.8. The PL peak from "small dots" is centered at 3.75 eV, nearly 0.3 eV blue shifted with respect to the GaN bandgap. On the other hand, that from "large dots" in the blue at 2.95 eV, i.e. 0.5 eV below the bulk GaN bandgap energy. This striking QD size effect is attributed to the quantum confined Stark effect caused by the presence of a huge piezoelectric field in the QDs along the c-axis. Estimated piezoelectric field present in these QDs was around 5.5 MV/cm, which is more than one order of magnitude larger than the piezoelectric field found in zinc-blende semiconductors for the same amount of strain. Due to this large value, piezoelectric field effects are dominating for QDs whose heights are larger than only 3 nm [31].
I I I—I I I I I—I I I—|—I—r—i—I I I I—|—r
hT=2K
2.4
Large dots
2.6 2.8
I I I—I—I I I I—I—pi
Small dots
3.0 3.2 3.4 3.6 Photon Energy (eV)
3.8 4.0
Figure 6.8. PL spectra (2 K) of small and large GaN QDs grown on AIN [31].
104
Optoelectronic Devices: Ill-Nitrides
T ^ mm
CD
1000
600
600
400
200
Wavefength (nm) Figure 6.9. Room temperature PL spectra from GaN QDs on A1N/Si(lll). (a), (b), and (c) correspond to a single plane of GaN QD layer with nominal thickness of 7, 10, and 12 ml, respectively, (d) is the PL spectrum from four-layer-stacked QDs, producing white light [32].
Damilano et al. reported the further red shift of PL emission from GaN QD samples of different QD sizes [32]. They could observe the intense room temperature PL emission from blue to even orange, depending on QD size. Corresponding PL spectra of blue, green, and orange QDs are shown in Figure 6.9. They also grew the stacked GaN QD sample containing four planes of QDs of properly chosen sizes to produce white light, as shown in Figure 6.9(d). MBE growth of InGaN QDs by SK growth mode was also reported. The soHd composition of InGaN, consequently the amount of lattice mismatch, controls its growth mode. Grandjean et al. studied the growth of In^Gai_;,N on GaN with RHEED [33]. It is evident that the critical thickness for 2D/3D transition decreased with increasing In composition in InGaN as shown in Figure 6.10, and that InGaN with high In composition would be favorable for the growth of SAQDs. It was found that only 3 ml could be grown layer-by-layer before islanding when In composition was greater than 0.3. When In composition was less than 0.12, the growth mode no longer underwent a strong 2D/3D transition (denoted by open squares), but rather a progressive roughening of the growth surface occurred, most likely due to insufficient driving force for 2D/3D morphological transition. By careful control of the SK growth mode, the successful growth of InGaN SAQDs on GaN by MBE was made by Damilano et al. [34]. The mean size of their typical QDs was
Growth of Nitride Quantum Dots
105
15
c10 o 2 Q Q
5h
CM
• . . . . - •
0 Figure 6.10.
10
20 30 40 In composition (%)
50
Critical thickness associated with the 2D/3D growth mode transition at various In composition for the growth strained InGaN on GaN at 600°C [33].
about 35 nm in diameter and 4 nm in height. The QD density was ~ 5 X 10^^ cm~^, which was greater than the dislocation density in the GaN base layer (~5 X 10^ cm~^). The In content in these QDs was 15% and the critical thickness was 4 - 5 ml. Adelmann et al. also reported the growth of InGaN SAQDs on GaN by MBE [35]. When In content of their QDs increased to 35%, the mean QD size was decreased to about 27 nm in diameter and 2.9 nm in height. The QD density was increased to ~ 9 X 10^^cm~^ and the critical thickness was decreased to 2 ml. The changes in QD size affected the PL emission wavelength. Damilano et al. also reported that the PL peak energy from their Ino.2Gao.8N/GaN QDs shifted from 3.03 to 2.51 eV with increasing QD size, as shown in Figure 6.11 [34,36]. Changes in PL emission wavelength were attributed to both a decrease in the carrier quantum confinement energy and an increase in the quantum confined Stark effect. The main parameter which determines the QD energy level for a given In composition is the QD height because of the strong built-in electric field along the c-axis and relatively large QD diameter. Gogneau et al. proposed the modified SK mode to grow GaN QDs on AIN by MBE [37]. The schematic diagram of this technique is presented in Figure 6.12. A GaN layer was grown under Ga-rich conditions with absorbed excess Ga bilayer on the growing surface. The resulting GaN epilayer was 2D and had a flat surface as examined by RHEED (Figure 6.12(a)). After the growth was stopped under Ga flux, the surface remained 2D. The RHEED pattern remains unchanged (Figure 6.12(b)). Under vacuum, however, the Ga film desorbed in a few seconds (Figure 6.12(c)), and the GaN layer transformed into facetted 3D surface. The RHEED pattern evidences this island formation by the presence of additional lines characteristic of facets (Figure 6.12(d)).
Optoelectronic Devices: Ill-Nitrides
106
-,
,
,
^
,
p—,
,
,
J
RcMDm temperature
,
,
,
y-
M\ 3.03 0V
J'2.85 eV
eV
A"'
t\ J.
2.51 eV
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
Photon energy (eV) Figure 6.11. Room temperature PL spectra of the InGaN/GaN QDs with different sizes. The PL peak energy of 3.03, 2.85, 2.71, and 2.51 eV correspond to the nominal thickness of 1, 1.5, 2, and 3 nm, respectively [36].
(c)
Ga
ftttt
(d)
Figure 6.12. Schematic diagram of the experimental procedure for the growth of GaN SAQDs by a modified SK growth mode. Ga desorption during growth interruption induces the SAQD formation [37].
Growth of Nitride Quantum Dots
107
(a)i
Figure 6.13. AFM images (1 |xm X 1 yun) of the high density GaN QDs grown on AIN by MBE at 750°C. The GaN coverages are (a) 2.8 ml, (b) 6 ml, (c) 10 ml, and (d) 13 ml [37].
They found that the formation of GaN QDs by this method was governed by GaN coverage. The resulting GaN QDs grown with different GaN coverages are shown in Figure 6.13. It was observed that the island density increased rapidly from the GaN coverage of 2.8-6 ml before saturation, and followed by a slow decrease. It also appears that the QD density can be controlled over about one order of magnitude
108
Optoelectronic Devices: Ill-Nitrides
(3 X 10 - 2 X 10^^ cm~^ range) for coverages varying from 2.8 to 6 ml. In comparison, the density of GaN QDs grown by SK mode is already 5 X 10^^ cm~^ for a coverage of only 4 ml and saturates at around this value [30,31]- Therefore, the slight modification of growth process in MBE gave us process flexibility to control QD density as well as size.
6,2,2 Self-assembled Quantum Dots by MOCVD The growth of SAQDs using MOCVD was also reported by several groups. Miyamura et al. reported the growth of GaN SAQDs on AIN surface by MOCVD [38]. They grew a 110-nm-thick AIN layer on a (0001) 6H-SiC substrate at 1180°C with an NH3 flow rate of 2.0 slm. After the AIN layer was grown, the growth temperature was reduced to 960-990°C to grow GaN QDs, relatively lower than the typical GaN growth temperature. The growth temperature and V/III ratio were quite important parameters for the formation of GaN QDs. These parameters affected the migration and/or evaporation of Ga atoms on the GaN surface, leading to surface diffusion to form the 3D nanostructures. The flow rate of NH3 must be reduced to 3 seem (corresponding V/III ratio of 30) during the successful growth of GaN QDs to induce SAQD formation.
(a)
3.4 ML
(b)
5.8 ML 5.0 nm
2.5 nm
0.0 nm
9.2 ML
200 nm Figure 6.14.
AFM images (500 nm X 500 nm) of GaN QDs by MOCVD. The GaN coverages are (a) 3.4, (b) 5.8, (c) 6.9, and (d) 9.2 ml, respectively [38].
Growth of Nitride Quantum Dots
109
A typical morphology of GaN QDs grown on AIN by MOCVD is shown in Figure 6.14. The growth temperature was 965°C under the V/III ratio of 26. The initial GaN surface exhibited a typical 2D growth mode, as shown in Figure 6.14(a). However, as GaN coverage increased more than 4 ml, 2D/3D growth mode transition began with the formation of QDs by SK mode. The average diameter and height of the QDs were 20 and 2 nm, respectively, by AFM measurement. The density of the QDs could be increased to 5 X 10^^ cm~^ by optimizing the growth temperature and the GaN coverage. PL studies on the GaN QDs revealed the existence of the wetting layer, suggesting that the QDs were surely grown by SK growth mode. Figure 6.15 shows the PL spectra of AINcapped GaN samples at room temperature. The sample of Figure 6.15(a) is grown under GaN deposition of 4 ml, and it may contain the wetting layer and no QDs, as shown in Figure 6.14(a). The samples in Figure 6.15(b) and (c) both contain QDs evolved by increasing the equivalent thickness of GaN deposition more than 4 ml. QDs in Figure 6.15(b) and (c) were of different sizes controlled by V/III ratio and growth temperature. Figure 6.15(b) and (c) shows different intense peaks at around 4.1 and 3.5 eV, respectively. These peaks originate from the QD structure and are consistent with their average sizes. However, these three samples exhibit the same PL peak around 4.7 eV,
1
•
1
•
1.0
^
1 < Q D s (c)
1 • 1 > 1 Q D s (b) W L (a)
'
1
'
1 1-
Peak energy Sample (a): 4.77 eV Sample (b): 4.18 eV Sample (c): 3.59 eV
0.8
M
FWHM Sample (a): 240 meV Sample (b): 480 meV Sample (c): 580 meV
CO
S
0.6
c _i
S
1 /
by A r F excimejr I ^^5cited er(193nm)atRT
0-4
03
E o 2
0.2
0.0
A —
\
1
1
Gan bulk ...
1
2.5
1
1
3.0
1
1
3.5
1
1
4.0
1
1
1
4.5
1
5.0
1
1
5.5
1
i
6.0
Photon Energy [eV] Figure 6.15.
Room temperature PL spectra of GaN QDs grown on AIN by MOCVD [38].
no
Figure 6.16.
Optoelectronic Devices: Ill-Nitrides
AFM images of (a) a GaN buffer layer, and InGaN SAQDs formed on GaN by the deposition of (b) 6.4 ml and (c) 19.1 ml [39].
which is the wetting layer peak, because QD samples grown by SK growth mode would have the wetting layer of almost the same thickness. The growth of InGaN QD on GaN using MOCVD was also reported by Tachibana et al. [39]. They grew 30 nm of a GaN nucleation layer at 500°C and a thick GaN buffer layer at 1075°C on (0001) sapphire substrate. After the growth of the thick GaN buffer layer, growth temperature was reduced to grow InGaN QDs. V/III ratio during InGaN QD growth was kept at about 7000, which was much higher than 30 used in the case of GaN QDs, presumably due to the increased lattice mismatch in InGaN/GaN QDs. The morphologies of the resulting InGaN QD layers with different coverages are shown in Figure 6.16. As InGaN coverage was increased, the density of QDs increased. The In content of the InGaN QDs was estimated as about 25%. The typical InGaN QDs were 19.5 nm wide and 4.5 nm high. The density of typical InGaN QDs was estimated as 6 x 1 0 ^ cm~^, relatively lower than the density of the GaN QDs on AIN addressed above. They further grew a stacked InGaN QD structure and investigated its optical properties [40]. The room temperature PL spectra from the InGaN QD structures with different
Growth of Nitride Quantum Dots
111
sjngle-sheet 3-stacked — 10-stacked HO'Cd 20 mW RT
'c CD
c
x10
2.0 Figure 6.17.
2.6 3.0 Energy [eV]
3.5
PL spectra at room temperature from (a) a single-layer InGaN QDs, (b) three-layer stacked InGaN QDs, and (c) 10-layer stacked InGaN QDs [40].
number of stacks are shown in Figure 6.17. Stacking of InGaN QDs resulted in an increase in QD density as well as integrated PL intensity. The PL intensity from the three-layer stacked InGaN QDs is about 40 times higher than that from the single-layer QDs. Moreover, the PL intensity from 10-layer stacked InGaN QDs is about 180 times higher than that from the single-layer QDs. In general, the integrated intensity is proportional to the number of stacks, and it is quite likely that the structural quality of InGaN QDs improved as stacking continued. They also grew a laser structure using this 10-layer stacked InGaN QDs [40,41]. The active layer was sandwiched by the Alo.07Crao.93N cladding layers. The cavity facet was fabricated by reactive ion etching (RIE). The laser structure was characterized at room temperature under optical excitation, and the stimulated emission could be observed as shown in Figure 6.18. Above the threshold excitation power, the width of emission peak
en 'c ID
. RT
^ ro
3^ (0
s
-(c)/=1.8/,,
1 1 Jlk
1 1
x1
nm
1
(a) n o r m a l _ E L — ^ ' ^ ' ^ ' ' - - ^ ^ ^
I
JKO.1
^0 "co
E LU
3<35
Figure 6.18.
400 405 Wavelength (nn1)
41
(a) PL spectrum at room temperature under low-power excitation. Stimulated emission spectra at (b) 1.44 and (c) 1.84 [41].
112
Optoelectronic Devices: Ill-Nitrides
became as narrow as 0.1 nm (resolution limit), and the emission intensity was dramatically increased. The estimated carrier concentration at the threshold suggested that the lateral confinement of carriers in the stacked InGaN QDs at room temperature was not enough. Further improvement in the QD growth is necessary to obtain reduced QD lateral size and highly uniform QD size distribution and to achieve lower threshold carrier density. In most cases, the In compositions of reported InGaN QDs were limited to below 50%, possibly due to the difficulty of In incorporation into InGaN. However, the growth of In-rich InGaN QDs on GaN would be more favorable for SAQD formation via SK growth mode by increasing lattice mismatch. The growth of In-rich InGaN QDs was reported by Kim et al. [42,43]. They adopted a rather low growth temperature to obtain In-rich InGaN layer compared with the growth temperature of typical InGaN QWs to suppress the In evaporation. The In content of the InGaN QD was precisely estimated by electron probe microanalysis and it ranged around 70-80%. The AFM images of the In-rich InGaN QDs is shown in Figure 6.19. The temperature decrease from 730 to 640°C resulted in drastic changes in surface morphologies and the formation of QDs. The average diameter, height and density of the In-rich InGaN QDs were estimated as about 66 nm, 1.2 nm, and 5.5 X 10^ cm~^, respectively. The low aspect ratio of In-rich InGaN QDs is attributed to the high volatiUty of InN and the high lattice mismatch as high as 11% for pure InN with respect to GaN. Optical properties of the In-rich InGaN QDs were investigated by PL. Figure 6.20 shows 12 K PL spectra of the QDs grown at different input TMIn flow rate and growth time. Emission wavelength from In-rich InGaN QDs could be controlled by slight adjustment of growth conditions. As growth time and input TMIn flow rate decreased, emission peaks showed blue shift to even near-UV emission at 380 nm. PL emission from
Figure 6.19.
AFM image (4 jxm X 4 fxm) of InGaN SAQDs grown on GaN by MOCVD at (a) 730°C, and (b) 640°C [42,43].
Growth of Nitride Quantum Dots
1 d cc 3^ 1 c ; e
:
113
1
1
1 ^-(°) fh-""'^—/^'^
II
/^
„.IU 2lfi^^^22':r^^ 360
400
440
J 480
520
Wavelength (nm) Figure 6.20. PL spectra (12 K) of In-rich InGaN SAQD (a) grown at a standard condition (640°C, input TMIn flow rate 10 fxmol/min, growth time 5 s), (b) grown with less input TMIn flow rate (640°C, input TMIn flow rate 4 fjimol/min, growth time 5 s), (c) grown with shorter growth time (640°C, input TMIn flow rate, 10 |jLmol/min, growth time, 2 s) [42,43].
the QDs could also be observed at room temperature and their thermal stability was found to be much better than In-rich InGaN/GaN QW samples. It strongly suggests that carrier confinement in In-rich InGaN QD sample was enhanced by the introduction of QD structure. The peak emission wavelengths from In-rich InGaN QDs ranged from 380 to 430 nm, corresponding to much higher photon energy than the expected bandgap energy of In-rich InGaN. Large blue shift was also observed from the In-rich InGaN/GaN single QW and it was attributed to the large band-offsets, small effective mass, and very small height of In-rich InGaN QDs [44]. It is believed that the similar mechanism is responsible for the large blue shift in In-rich InGaN QDs and theoretical analysis is currently under way to fully understand the origins. Growth of InN QDs on GaN by MOCVD was demonstrated by Briot et al. [45]. It was found that the growth temperature and V/III ratio were the key process parameters to obtain high quality InN QDs due to the extreme volatility of InN. QD density could be controlled by growth temperature, V/III ratio, and growth time. The size of typical InN QDs grown at 550°C and a V/III ratio of 30,000 for 45 s were 25-35 nm in diameter and 2.7-5.6 nm in height, producing a fairly flat QD due to high surface diffusion under their growth conditions. 6,2,3 Stacking of Self-assembled Quantum Dots In general, QDs do not cover the whole area of surface. If QDs are used in the active layer, the volume fraction of QDs is much smaller than that of QWs, and the absolute luminescence intensity from the QD active layer is low. Therefore, stacking of QDs is indispensable for the device fabrication by increasing the total active volume responsible for carrier recombination process. Formation of highly uniform QDs is a prerequisite for
114
Optoelectronic Devices: Ill-Nitrides
Figure 6.21. HRTEM image of a stacked GaN QDs grown at 720°C. AIN spacer layers were used between GaN QDs. Vertical correlation is clearly seen [30].
successful stacking. Otherwise, QD stacking itself generates defects and it renders QD obsolete for device applications. Widmann et al. reported the stacking of GaN QDs separated by an AIN spacer by MBE [31]. By HRTEM, they could observe the vertical correlation between the GaN dots, depending on the thickness of the AIN spacer layer. Whereas no vertical correlation was found for an AIN spacer thickness of 20 nm, such correlation was present for an AIN spacer thickness of 8 nm, as shown in Figure 6.21. The GaN 2D wetting layer, about 2 ml thick, was clearly seen. It is worth noting that the lateral spacing between adjacent QDs is about 3.5 times larger than the thickness of the AIN spacer, in good agreement with the theoretical estimation by Tersoff et al. [46]. The vertical correlation was attributed to the merging of the strain fields resulting from close-spaced islands, leading to the nucleation of a single island above them when depositing the next layer. The alignment of QDs is also affected by the presence of threading dislocations, as shown in the far left column of QDs in Figure 6.21 [31,47]. It is likely that combined strain field from both the underlying QDs and the threading dislocations would affect the vertical correlation of QDs.
Growth of Nitride Quantum Dots
115
I
500
250
[nm]
Figure 6.22. AFM images of the surface morphology of (a) single-layer, (b) three-layer, and (c) 10-layer stacked InGaN QDs [40].
Stacking of self-assembled InGaN QDs using MOCVD was also reported by Tachibana et al. [48]. The surface morphologies of stacked InGaN QDs at various number of stack layers with 5 nm spacer layer are shown in Figure 6.22. The integrated PL intensity increased with the number of QD stacks, as shown in Figure 6.17, and lasing by optical pumping from this stacked InGaN QDs was reported.
6.3. GROWTH OF QUANTUM DOTS BY ANTI-SURFACTANT At the early stage of the nitride QD research, the fabrication of QD structures was tried using anti-surfactant. Use of anti-surfactant could realize the QD growth regardless of strain in the film which was necessary for the formation of SAQDs by SK growth mode. Tanaka et al. reported the growth of GaN QD for the first time, with the help of Si as an anti-surfactant [49]. They grew the GaN QDs on a Si-face of (0001) 6H-SiC substrate by MOCVD. After depositing an 1.5-nm-thick AIN buffer layer, a 0.6-|xm-thick Al;cGai_;,N
116
Optoelectronic Devices: Ill-Nitrides
layer was grown, with the Al content x was varying in the range of 0.07-0.2 by changing the gas flow ratio. TESi was then supplied to the Al_^Gai_;,N surface, followed by a short supply (5 s) of TMGa and NH3 gases for the growth of GaN QDs. Their growth temperature was varied in the range of 1060-1100°C. Typical morphology of their GaN QDs grown on Alo.2Gao.8N surface with Si antisurfactant is shown in Figure 6.23(a) and (b). The hexagon-shaped GaN QDs, with an average width of about 40 nm and a height of about 6 nm was uniformly distributed on the AlGaN surface. The QD density of this sample was around 3 X 10^ cm~^. In Figure 6.23(b), the detailed shape of GaN QDs was clearly observed. In contrast, a step flow growth of GaN on the AlGaN surface was observed without introducing TESi, as can
Figure 6.23. (a) Plan-view and (b) bird's eye view of a typical GaN QD formed on AlGaN surface using TESi as an anti-surfactant, (c) The GaN surface morphology without the use of TESi shows a step flow growth mode [49].
Growth of Nitride Quantum Dots
111
be seen in Figure 6.23(c). No QDs were observed in this case. The lattice mismatch between Alo.2Gao.8N and GaN was too small (—0.18%) to induce the SK growth mode. GaN QDs were only obtained when the AlGaN surface was exposed to the TESi gas flow before the GaN deposition procedure. However, the presence of a wetting layer was not confirmed in Figure 6.23, which is the unique feature of the SK growth mode. The GaN QD growth on the anti-surfactant exposed AlGaN surface is more or less Volmer-Weber growth, or 3D island growth. TESi dose was found to play an important role in QD formation. To find out the precise mechanism of Si anti-surfactant, the GaN samples grown with various TESi doses of 0,3.2, 4.8, 8.1, and 32 nmol were investigated [50]. As the input dose of TESi increased, a morphological transition from 2D to 3D was observed. A clear step and terrace feature (2D) prior to TESi exposure, as seen in Figure 6.24(a), was transformed to a 3D-like structure in Figure 6.24(e). From these features, they proposed a model of "masking by the Si-N bondings" to explain this morphological transition induced by TESi, which is schematically shown in Figure 6.25(a)-(c). Figure 6.25(a)-(c) corresponds to 0 nmol (2D), 2.2-4.8 nmol (quasi2D), and 8.1 nmol (quasi-3D) cases, respectively. With the supply of TESi, Si-N bonds on top of the Ga(Al) dangling bonds of the Al;cGai__^N surface would be formed. The Ga(Al) atoms at the surface could also be replaced with Si atoms. These changes in the surface structure and chemistry by the Si supply should energetically and kinetically affect the
Figure 6.24.
Effects of TESi dose on the GaN surface morphology [50].
Optoelectronic Devices: Ill-Nitrides
118 (a) 2D striictyre ^^^
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^^iiif
A(GaN(0001) surface Figure 6.25. Schematic diagram of the model explaining the structural transitions observed by AFM. (a), (b), and (c) correspond to 0, 2.2 to 4.8, and 8.1 nmol cases, respectively, (d) A plan-view diagram of (c) to illustrate the GaN nucleation sites affected by Si-N bonding, (e) A possible surface potential energy diagram across the region along the line A - B in (d) [50].
GaN nucleation process, resulting in morphological transition. Such an area caused by the nano-scale modification of the surface may act as a nano-scale mask where GaN deposition is suppressed. It may also create a kinetic energy barrier for adatom diffusion. Tanaka et al. thought that GaN deposition would be suppressed at this place (see the masking territory in Figure 6.25(d) and (e)). Figure 6.25(e) illustrates a possible surface potential energy diagram in their model across the region along the line denoted "n" in Figure 6.25(d). The potential gradient (chemical potential) induced by Si-N bonds would lead the migration of adatom to the potential-minima regions, and the deposition of
Growth of Nitride Quantum Dots
119
1 1 1 1 1 I I • • I'P I I I I I I I I 1 I
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3.40 3,45 3.50 3.55 3.60 3.65 Photon energy (eV) Figure 6.26.
PL spectra of GaN QDs with three different sizes [51].
GaN would occur preferentially at those places. The large amount of holes observed in Figure 6.24(b) and (c) would correspond to the area of nano-scale masking. Therefore, as the masking area increased, the surface structure with both 2D and 3D characteristics would appear, and eventually the whole surface would be composed of 3D structures [50]. They also investigated optical properties of these GaN QDs. Figure 6.26 shows the 80 K PL spectra of the GaN QD samples of different sizes [51]. The different QD sizes are obtained by changing the deposition time of GaN while keeping the substrate temperature constant. The PL emission energy was observed to shift to higher energy with decreasing QD size. This effect was supposed to be a combination of a blue shift from the confinement-induced shift of the electronic levels and a red-shift from the piezoelectric field-induced quantum-confined Stark effect. An LD structure with these GaN QDs was prepared and optical pumping experiment was made [52]. GaN QDs, with an average size of about 10 nm width, 1 - 2 nm height, and a density of about 10^^ cm~^ were used in this experiment. Their LD structure is schematically shown in Figure 6.27. Stimulated emission was clearly observed at 21 K from the GaN QD LD structure under high excitation pump power density, as shown in Figure 6.28. At the pump power density of 0.78 MW/cm^, a sharp peak centered at 3.49 eV appeared. The FWHM was about 10 meV. The emission peak showed a red-shift of about 50 meV from the spontaneous emission peak observed at 77 K. Recently, the GaN QDs formed by this technique was used for the active layer of UV LED [53]. The room temperature UV emission at 360 nm was reported by current injection. This is the first report on the device application by current injection. The growth of InGaN QDs using TESi anti-surfactant was also reported by Hirayama et al. [54] In order to achieve a surface suitable for the growth of InGaN QDs, a "twolayered buffer" was used: 100 nm-thick Alo.12Gao.88N layer (topmost) and 300-nm-thick Alo.24Gao.76N layer deposited at HOOT on a 6H-SiC substrate. Prior to the InGaN
120
Optoelectronic Devices: Ill-Nitrides N| Met
>^k23^%77^ ciliickling Jpyer ^bjO«G%9^N barrieriiiyef OaN quantum doii ^^.i2*^'*o.8s'^ byrri^r layer A^O^QSO.IWN cladding lnycr
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The schematic diagram of a GaN QD laser structure with AlGaN barrier layers [52].
growth, a small amount of Si anti-surfactant modifying the surface properties was deposited at 1120°C, which is similar to that of the TESi pretreatment for GaN QD growth. Then, InGaN growth was performed at around 800°C. This resulted in a 3D nano-scale island growth. They found that the QD density was controllable in the range of cm by increasing the TESi dose. Similar trend was also reported in the growth of GaN QDs. A typical morphology of the InGaN QDs with an approximate density of 10^ ^ cm~^ obtained by this technique is shown in Figure 6.29. The average size and thickness of QDs are about 10 and 5 nm, respectively. Room temperature PL emissions from InGaN QDs grown with Si anti-surfactant were observed as shown in Figure 6.30 [54]. In this experiment, all InGaN QDs were
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Growth of Nitride Quantum Dots
121
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A typical A I ^ image of InGaN QDs grown on the AlGaN surface by using anti-surfactant [54].
grown with the same TESi dose. The PL peak energy position was controlled by changing the growth temperature, resulting in changes of In mole fraction of InGaN QDs. For comparison, InGaN QW structure with an estimated thickness of 5 nm was grown without TESi exposure on the AlGaN surface. It was found that the PL emission of the InGaN QD samples was several times stronger than that of the QW structure. This result strongly suggests that the increased luminescence efficiency is caused by the additional carrier confinement. From the calculation with PL peak positions in Figure 6.30, the In contents of InGaN QDs grown at 770, 800, 830, and 850°C were estimated as 52, 38, 25, and 22%, respectively. However, this calculation seemed to be based on the old value of InN bandgap energy of 1.9 eV; accordingly. In composition would be modified.
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Figure 6.30.
Room temperature PL spectra of InGaN QDs grown on AlGaN at various temperatures [54].
122
Optoelectronic Devices: Ill-Nitrides
6.4. GROWTH OF QUANTUM DOTS BY SELECTIVE EPITAXY The aim of this method is to control the position, size and density of the QDs by high-resolution patterning techniques. With the help of the recent improvement of lithography techniques, it is expected that the position control and the uniformity of the QDs would be greatly enhanced by this technique; however, QD density obtainable by this technique is far lower than by either SK growth method or anti-surfactant growth method. Tachibana et al. reported the growth of InGaN QD structures by selective MOCVD on a Si02/GaN/sapphire substrate patterned by conventional photolithography [55]. At first, they grew a 2-|jLm-thick GaN layer on a (0001) sapphire substrate. Then, 40 nm of Si02 was deposited on the GaN layer by sputtering and the Si02 layer was patterned by conventional photolithography and a buffered HF solution. The pattern was grid-like, with 4 |xm period and square openings of 2 jxm side length. Selective growth of GaN was then performed and uniform hexagonal GaN pyramids were realized, as shown in Figure 6.31(b) and (c). Then, the growth of three periods of InGaN/GaN MQWs was
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Growth of Nitride Quantum Dots
123
followed on the hexagonal GaN pyramids. The schematic diagram of this structure is illustrated in Figure 6.31(a). The lateral size of InGaN QDs formed at the apex of GaN pyramids was no more than 30 nm, estimated from the curvature of the apex of pyramid in Figure 6.31(c). PL spectra were measured at room temperature. With the emission peak at 3.4 eV from the GaN bulk layer, a very broad peak (the FWHM is 290 meV) was also observed at 2.88 eV (430 nm), as shown in Figure 6.32. To identify the regions giving the PL emission at 430 nm, micro-PL intensity images were recorded at room temperature. Figure 6.33(a) shows an image consisting mainly of reflected light. Hexagonal shapes can be seen very clearly. Figure 6.33(b) shows a micro-PL intensity image of PL of wavelength around 430 nm. The same area was observed in Figure 6.33(b) as in Figure 6.33(a). It is evident that the detected light was from the InGaN QD structure on the apex of pyramids, not from the GaN bulk. They also reported the successful growth of GaN/AlGaN QD structures on a Si02/GaN/sapphire substrate patterned using the similar technique with that of InGaN QDs [48,56]. QD density of these dots was less than 10^ cm~^ due to the resolution limitation imposed by photolithography. Wang et al. demonstrated the formation of higher density InGaN QDs by selective growth on Si-patterned GaN epilayer/GaN buffer layer/(0001) sapphire substrate with the improved patterning technique [57,58]. The Si mask was patterned by a partial removal of Si mask by 30keV Ga^ focused ion-beam (FIB) irradiation and subsequent photoassisted wet (PAW) etching of remaining Si mask with a solution of 3KOH:H202. If the window is patterned only by FIB, the damage of the GaN underlayer is inevitable.
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Energy (eV) Figure 6.32. PL spectrum of the selectively grown InGaN QDs at room temperature [55].
Optoelectronic Devices: Ill-Nitrides
124
Figure 6.33.
(a) Optical microscope image of selectively grown InGaN QDs, (b) micro-PL image at a wavelength of 430 nm [55].
mainly due to the highly energetic Ga"^ atoms penetrating the residual Si layer during FIB process. The growth of GaN pyramids and InGaN/GaN MQWs was followed. The schematic diagram of this procedure is shown in Figure 6.34. The typical top-view scanning electron microscope (SEM) image of an InGaN QD sample is shown in Figure 6.35(a). There are 25 QD structures in each luim square area (2.5 X 10^ cm~^) and they looked uniformly arranged. An AFM image of the InGaN QD array in Figure 6.35(b), however, showed that the dimensions of each QD were not completely uniform due to the fluctuations in the window size by this patterning technique.
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Schematic diagram of FIB/PAW process used for the fabrication of InGaN/GaN QDs [58].
125
Growth of Nitride Quantum Dots
Figure 6.35.
(a) A typical top-view SEM image of selectively grown InGaN QDs. Diameter of the FIB windows was 80 nm; (b) 3D AFM image of the same QDs [58].
The CL spectrum measured at 80 K from the InGaN QD sample is shown in Figure 6.36. In this measurement, the electron beam was focused on an area covering 25 QDs. A clear blue shift of about 240 meV could be observed when compared with the emission from a reference InGaN QW sample. This value corresponds to an InGaN QD with a diameter of ~ 3 nm. The FWHM of the emission peak from QD was 48 meV, whereas that of the emission peak from QW was 84 meV. This result shows that the size fluctuation of QDs was suppressed to a certain extent by their technique.
6.5. NOVEL TECHNIQUES FOR QUANTUM DOT GROWTH Oliver et al. reported the InGaN QD growth on a GaN/sapphire substrate by MOCVD [20]. They had grown two InGaN epilayers under identical conditions, and then annealed
InOsN/GaN ODs T=SOK FWHM =48 nitV
3.29
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3.37
Energy («V) Figure 6.36.
Cathodoluminescence spectrum measured at 80 K from selectively grown InGaN QDs. The inset shows a PL spectrum obtained for a reference InGaN MQW sample [57].
126
Figure 6.37.
Optoelectronic Devices: Ill-Nitrides
AFM images (1.8 fxin X 1.8 |xm) of InGaN epilayers on GaN after (a) annealing under NH3 for 30 s, (b) annealing under N2 for 30 s [20].
the two samples at 700°C for 30 s after the growth under different conditions: under NH3 flow or under N2 flow. The anneal under N2 flow changed the surface morphology significantly as shown in Figure 6.37(b). Small nanostructures with a density of 5 X 10^^ cm~^, and an average height of 0.93 nm could be found along with many small pits in the wetting layer. They observed very sharp emission peaks with typical linewidth of —700 ixeV at 4.2 K by micro-PL experiments. Their time-resolved PL studies on the sample revealed that excitons have lifetimes around 2 ns at 4.2 K. They suggested that pits in Figure 6.37(b) were created by the decomposition of In-rich regions in InGaN epilayer (formed by spinodal decomposition), which appeared to be unstable in a nitrogen atmosphere. The nanostructures observed in Figure 6.37(b) might be very small In droplets, also formed due to decomposition, since they found that these structures could be removed by the HC1:3H20 etchant. These In droplets would then react with ammonia, before or during the growth of the capping layer, and this would result in the formation of InGaN QDs, possibly by some interdiffusion with the GaN capping layer [20]. Similar methods using the nitridation of metallic droplets were also reported by other research groups. Kawasaki et al. demonstrated the GaN QDs formed on an AlGaN/SiC substrate by MBE using Ga droplets [21]. At first, they deposited the Ga droplets on the substrate surface by supplying Ga at 300°C. Then, the sample was annealed under NH3 gas flow for 10 min in order to nitridate the Ga droplets. Figure 6.38(a) shows the SEM image of QDs obtained by this technique at a nitridation temperature of 600°C. The histogram of the QD diameter in Figure 6.38(b) shows that the GaN QDs formed were between 4 and 15 nm in diameter with an average diameter of approximately 9 nm. The QD density was greater than 3 X 10^^ cm~^. Hu et al. also reported the growth of QDs by MOCVD using the formation of Ga liquid droplet and nitridation process [22]. The fabrication of InGaN QDs by surface pretreatment using TMIn was reported by Zhang et al. [23]. TMIn pre-treatment with only TMIn and NH3 input flow was made just before the growth of InGaN well layer. The typical microstructure of InGaN QDs formed
Growth of Nitride Quantum Dots
:••'
12
14
111
16
Figure 6.38. (a) SEM image of GaN QDs formed by Ga droplet formation and subsequent nitridation at 600°C. (b) Histogram of the GaN QDs with mean diameter of 9 nm, and standard deviation of 2 nm [21].
(a)
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Figure 6.39. Cross section HRTEM images of InGaN SQW (a) with and (b) without TMIn pretreatment. Arrows point to the low-barrier/well interfaces [23].
128
Optoelectronic Devices: Ill-Nitrides (b)
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3.2
3.4
(a) The AFM surface morphology of InGaN QDs from by TMIn pretreatment, (b) comparison of PL spectra of InGaN QDs and homogeneous InGaN film [24].
in QW with TMIn pre-treatment was shown in Figure 6.39(a). Obvious contrasts, originating from In-rich regions in the low-In composition matrix, can be clearly seen along the lower-barrier/well interface. The average dimension of the contrast was as small as ~ 4 nm in width and 1.5 nm in height. The microstructure of the SQW without the TMIn treatment is shown in Figure 6.39(b) for comparison. Both the lower- and upperbarrier/well interfaces are quite sharp without obvious contrast, indicating that the growth mode was 2D throughout the growth of SQW structure without TMIn pre-treatment. The surface passivation method was also attempted to form InGaN QDs on GaN by Chen et al. [24,25]. High-temperature grown GaN surface was passivated by air exposure for 24 h and it was reloaded for the growth of a low temperature GaN layer at 550°C. It was found that the surface of the low temperature GaN layer had nano-scale roughness. They suggested that the surface passivation would increase the energy barrier for the hopping of the atoms, resulting in a decrease in the surface diffusion length. Subsequently, the growth of InGaN QDs was followed at 800°C. Figure 6.40(a) shows the image of InGaN QD structure grown on the passivated GaN surface. The average size of InGaN QDs was measured as 80 nm in diameter and 5 nm in height. The density of QDs was estimated as 5X 10'^ cm . PL spectrum of InGaN QDs was shown in Figure 6.40(b), compared with that of homogeneous InGaN thin films grown without surface passivation. 6.6. CONCLUSIONS So far, we have reviewed the various methods to form nitride QDs. They were classified into four methods: (1) using SK growth mode, (2) using "anti-surfactant", (3) using selective
Growth of Nitride Quantum Dots
129
epitaxy, and (4) other novel techniques. Growth of GaN/AlGaN, InN/GaN, InGaN/GaN QDs by MBE or MOCVD reported in the Hterature was reviewed. The first paper on the growth of nitride QDs appeared in 1996 and the number of publications and researchers are relatively small compared to III-V QDs. Nitride QD research is still in the developmental stage, however, considering the strong potential of nitride QDs in device applications, especially in LDs, UV-LEDs, etc., the interest from both academia and industry in nitride QDs increases very rapidly and the future of nitride QDs seems very promising.
REFERENCES [1] Bimberg, D., Grundmann, M. & Ledentsov, N.N. (1999) Quantum dot heterostructures, Wiley, New York. [2] Tatebayashi, J., Hatori, N., Kakuma, H., Ebe, H., Sudo, H., Kuramata, A., Nakata, Y., Sugawara, M. & Arakawa, Y. (2003) Electron. Lett., 39, 1130. [3] Phillips, J., Kamath, K., Zhou, X., Chervela, N. & Bhattacharya, P. (1997) Appl. Phys. Lett., 71, 2079. [4] Arakawa, Y. & Sasaki, H. (1982) Appl. Phys. Lett., 40, 939. [5] Xie, Q., Kobayashi, N.P., Ramachandran, T.R., Kalburge, A., Chen, P. & Madhukar, A. (1996) J. Vac. Sci. Technol, B, 14, 2203. [6] Lubyshev, D.I., Gonzalez-Borrer, P.P., Mareg, E., Jr., Petitprez, E., La Scala, N., Jr. & Basmaji, P. (1996) Appl. Phys. Lett., 68, 205. [7] Heinrichsdorff, F., Krost, A., Grundmann, M., Bimberg, D., Bertram, P., Christen, J., Kosogov, A. & Werner, P. (1997) /. Cryst. Growth, 170, 568. [8] Allen, C.Ni., Poole, P.J., Marshall, P., Eraser, J., Raymond, S. & Fafard, S. (2002) Appl. Phys. Lett., 80, 3629. [9] Finkman, E., Maimon, S., Immer, V., Bahir, G., Schacham, S.E., Gauthier-Lafaye, O., Herriot, S., Julien, F.H., Gendry, M. & Brault, J. (2000) Physica E, 1, 139. [10] Borgstrom, M., Bryllert, T., Sass, T., Bustafon, B., Wemersson, L.-E., Seifert, W. & Samuelson, L. (2001) Appl. Phys. Lett., 78, 3232. [11] Arakawa, Y. (2001) Phys. Stat. Sol. (a), 188, 37. [12] Chichibu, S., Azuhata, T., Sota, T. & Nakamura, S. (1996) Appl. Phys. Lett., 69, 4188. [13] Yoon, S., Moon, Y., Lee, T.-W., Yoon, E. & Kim, Y.D. (1999) Appl. Phys. Lett., 74, 2029. [14] Sopanen, M., Lipsanen, H. & Ahopelto, J. (1995) Appl. Phys. Lett., 65, 1662. [15] Marchand, H., Desjardins, P., Guillon, S., Paultre, J.-E., Bougrioua, Z., Yip, Y.-F. & Masut, R.A. (1997) Appl. Phys. Lett., 71, 527. [16] Chidley, E.T.R., Haywood, S.K., Mallard, R.E., Mason, N.J., Nicholas, R.J., Walker, P.J. & Warburton, R.J. (1989) Appl. Phys. Lett., 54, 1241. [17] Ferrer, J.C, Peiro, F., Comet, A., Morante, J.R., Uztmeier, T., Armelles, G. & Briones, F. (1996) Appl. Phys. Lett., 69, 3887. [18] Eaglesham, D.J. & Cerullo, M. (1990) Phys. Rev. Lett., 64, 1943. [19] Lowisch, M., Rabe, M., Stegemann, B., Henneberger, F., Grundmann, M., Turck, V. & Bimberg, D. (1996) Phys. Rev. B, 54, R11074. [20] Oliver, R.A., Briggs, G.A.D., Kappers, M.J., Humphreys, C.J., Yasin, S., Rice, J.H., Smith, J.D. & Taylor, R.A. (2003) Appl. Phys. Lett., 83, 755.
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Ill-Nitrides
[21] Kawasaki, K., Yamazaki, D., Kinoshita, A., Hirayama, H., Tsutsui, K. & Aoyagi, Y. (2001) AppL Phys. Lett., 79, 2243. [22] Hu, C.-W., Bell, A., Fonce, F.A., Smith, D.A. & Tsong, I.S.T. (2002) Appl. Phys. Lett., 81, 3236. [23] Zhang, J., Hao, M., Li, P. & Chua, S.J. (2002) Appl. Phys. Lett., 80, 485. [24] Chen, Z., Lu, D., Yuan, H., Han, P., Liu, X., Li, Y., Wang, X., Lu, Y. & Wang, Z. (2002) J. Cryst. Growth, 235, 188. [25] Huang, J.S., Chen, Z., Luo, X.D., Xu, Z.Y. & Ge, W.K. (2004) /. Cryst. Growth, 260, 13. [26] Goodwin, T.J., Leppert, V.J. & Risbud, S.H. (1997) Appl. Phys. Lett., 70, 3122. [27] Borsella, E., Garcia, M.A., Mattei, G., Maurizio, C. & Mazzoldi, P. (2001) J. Appl. Phys., 90, 4467. [28] Mii, O.I., Ahrenkiel, S.P., Bertram, D. & Nozik, A.J. (1999) Appl. Phys. Lett., 75, 478. [29] Daudin, B., Widmann, F., Feuillet, G., Samson, Y., Arlery, M. & Rouviere, J.L. (1997) Phys. Rev. B, 56, R7069. [30] Widmann, F., Daudin, B., Feuillet, G., Samson, Y., Rouviere, J.L. & Pelekanos, N. (1998) J. Appl. Phys., 83, 7618. [31] Widmann, F., Simon, J., Daudin, B., Feulliet, G., Rouviere, J.L., Pelekanos, N.T. & Fishman, G. (1998) Phys. Rev. B, 58, R15989. [32] Damilano, B., Grandjean, N., Semond, F., Massies, J. & Leroux, M. (1999) Appl. Phys. Lett., 75, 962. [33] Grandjean, N. & Massies, J. (1998) Appl Phys. Lett., 72, 1078. [34] Damilano, B., Grandjean, N., Dalmasso, S. & Massies, J. (1999) Appl. Phys. Lett., IS, 3751. [35] Adelmann, C , Simon, J., Feuillet, G., Pelekanos, N.T., Daudin, B. & Fishman, G. (2000) A/?/?/. Phys. Lett., 76, 1570. [36] Damilano, B., Vezian, S., Grandjean, N. & Massies, J. (1999) Jpn. J. Appl. Phys., 38, L1357. [37] Gogneau, N., Jalabert, D., Monroy, E., Shibata, T., Tanaka, M. & Daudin, B. (2003) /. Appl. Phys., 94, 2254. [38] Miyamura, M., Tachibana, K. & Arakawa, Y. (2002) Appl. Phys. Lett., 80, 3937. [39] Tachibana, K., Someya, T. & Arakawa, Y. (1999) Appl Phys. Lett., 74, 383. [40] Tachibana, K., Someya, T. & Arakawa, Y. (1999) Phys. Stat. Sol (a), 176, 629. [41] Tachibana, K., Someya, T., Arakawa, Y., Werner, R. & Forchel, A. (1999) Appl Phys. Lett., 75, 2605. [42] Kim, H.J., Na, H., Kwon, S.-Y., Kim, Y.-W. & Yoon, E. (2003) The Fifth International Conference on Nitride Semiconductors (ICNS-5), May 25-30, Nara, Japan. [43] Kim, H.J., Na, H., Kwon, S.-Y., Seo, H.-C, Kim, H.J., Shin, Y., Lee, K.-H., Kim, D.H., Oh, H.J., Yoon, S., Sone, C , Park, Y. & Yoon, E. (2004) J. Cryst. Growth, 269, 95. [44] Kim, H.J., Na, H., Kwon, S.-Y., Seo, H.-C, Kim, H.J., Shin, Y., Lee, G.-H., Kim, Y.-W., Yoon, S., Oh, H.J., Sone, C , Park, Y., Cho, Y.-H., Sun, Y. & Yoon, E. (2003) Phys. Stat. Sol (c), 0, 2834. [45] Briot, O., Maleyre, B. & Ruffenach, S. (2003) Appl Phys. Lett., 83, 2919. [46] Tersoff, J., Teichert, C. & Lagally, M.G. (1996) Phys. Rev. Lett., 76, 1675. [47] Louviere, J.L., Simon, J., Pelekanos, N., Daudin, B. & Feuillet, G. (1999) Appl Phys. Lett., 15, 2632. [48] Tachibana, K., Someya, T., Ishida, S. & Arakawa, Y. (2001) Phys. Stat. Sol (b), 228, 187. [49] Tanaka, S., Iwai, S. & Aoyagi, Y. (1996) Appl Phys. Lett., 69, 4096. [50] Tanaka, S., Suemune, L, Ramvall, P. & Aoyagi, Y. (1999) Phys. Stat. Sol (b), 216, 431. [51] Ramvall, P., Tanaka, S., Nomura, S., Riblet, P. & Aoyagi, Y. (1999) Appl Phys. Lett., 73,1104.
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[52] Tanaka, S., Hirayama, H., Aoyagi, Y., Narukawa, Y., Kawakami, Y., Fujita, S. & Fujita, S. (1997) AppL Phys. Lett., 71, 1299. [53] Tanaka, S., Lee, J.S., Ramvall, P. & Okagawa, H. (2003) Jpn. J. Appl Phys., 42, L885. [54] Hirayama, H., Tanaka, S., Ramvall, P. & Aoyagi, Y. (1998) Appl. Phys. Lett., 72, 1736. [55] Tachibana, K., Someya, T., Ishida, S. & Arakawa, Y. (2000) Appl. Phys. Lett., 76, 3212. [56] Tachibana, K., Someya, T., Ishida, S. & Arakawa, Y. (2002) /. Cryst. Growth, 237-239, 1312-1315. [57] Wang, J., Nozaki, M., Lachab, M., Ishikawa, Y., Fareed, Q., Wang, T., Hao, M. & Sakai, S. (1999) Appl. Phys. Lett., 75, 950. [58] Lachab, M., Nozaki, M., Wang, J., Ishikawa, Y., Fareed, Q., Wang, T., Nishikawa, T., Nishino, K. & Sakai, S. (2000) /. Appl. Phys., 87, 1374.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 7
AIN Epitaxial Layers for UV Photonics H.X. Jiang and J.Y. Lin Department of Physics, Kansas State University, Manhattan, KS 66506-2601, USA
7.1.
INTRODUCTION
Ill-nitride wide bandgap semiconductors have been widely recognized as technologically important materials. Photonic devices based on Ill-nitrides offer many benefits including UV/blue/green emission (allowing chem-bio-agents detection and higher optical storage density), large band offsets of InN/GaN/AlN heterostructures (allowing novel quantum well device design), and inherently high emission efficiencies. These unique features may allow the creation of optoelectronic and photonic devices with unprecedented properties and functions. The research activities on Al;,Gai_;,N (3.4 < E^ < 6.2 eV) with high AIN mole fractions and devices operating in the ultraviolet (UV) spectral regions are still in their embryonic state. Achieving device quality Al-rich AlGaN with high conductivities and high quantum efficiencies remains as one of the foremost challenges for the nitride community. AIN and Al-rich AlGaN alloys, covering wavelengths from 300 to 200 nm, are ideal materials for the development of chip-scale UV light sources/sensors, because AlGaN is the only ultra-wide-bandgap semiconductor system in which the bandgap can be easily engineered through the use of alloying and heterostructure design. Efficient solid-state UV light sources/sensors are crucial in many fields of research and development. For instance, protein fluorescence is generally excited by UV light; monitoring changes of intrinsic fluorescence in a protein can provide important information on its structural changes [1]. Thus, the availability of chip-scale UV light sources is expected to open up new opportunities for medical research and health care. Solid-state UV light sources also have applications in water purification, equipment/personnel decontamination, and white light generation [2]. There is an urgent need to develop new approaches to further improve material quality with reduced dislocation density and unintentional impurities and improved surface morphologies in Al-rich AlGaN alloys, which would enhance the doping efficiency and device performance. AIN is an end point of the AlGaN alloy system. A full understanding of the AlGaN alloy system (particularly Al-rich AlGaN alloys) could not be achieved before the binary AIN
E-mail address:
[email protected] (H.X. Jiang).
133
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Optoelectronic Devices: Ill-Nitrides
material is well understood. Moreover, AIN is unique due to the fact that no other semiconductors possess such a large direct bandgap as well as the ability of bandgap engineering through the use of heterostructures. In spite of the recognition of the importance of AIN, many of its fundamental optical emission properties are not well known in the past due to the lack of high-quality materials as well as technical difficulties involved for the deep UV (down to 200 nm) optical measurements. Rapid progress has been made recently in the epitaxial growth and understanding of the basic physical properties, as well as the device applications of AIN epilayers. This chapter aims at providing a brief summary on these recent advances with emphasis on the fundamental optical properties, basic impurity parameters, and conductivity control of AIN and AlGaN epitaxial films with high Al contents. In Section 7.2, we discuss epitaxial growth and characterization techniques to identify high quality films; such as atomic force microscopy (AFM) for studying the surface morphology and SIMS for probing unintentional impurities such as oxygen. In Section 7.3, we present recent advances in understanding the fundamental optical properties of AIN. The detailed band structure near the F-point of wurtzite (WZ) AIN is presented. The unique band structure of AIN, i.e. the negative crystal-field splitting, affects profoundly the optical properties of AlGaN alloys, in particular of Al-rich AlGaN alloys. One of the immediate consequences is that the dominant band-edge emission in GaN (AIN) is with polarization of E L c {E\\c). Accordingly, the emission intensity in Al-rich Al^cGai-^^N alloys decrease with increasing x for epilayers grown on the c-plane sapphire. The recombination dynamics of the bound exciton (I2) and free exciton (FX) transitions in AIN epilayers were probed by deep UV time-resolved photoluminescence (PL). The PL decay lifetimes were found to be around 80 ps for the bound exciton and 50 ps for the free exciton at 10 K in AIN epilayers, which are slightly shorter than those in GaN. This is a direct consequence of the large energy bandgap of AIN. The extrapolated radiative decay lifetimes in AIN epilayers increases with temperature according to T^'^ between 100 and 200 K and are affected by the free-exciton dissociation at temperatures above 200 K, following the same trend as in GaN. From the low-temperature (10 K) emission spectra, the temperature dependence of the recombination lifetime, and the PL emission intensity activation energy, the binding energies of the donor bound excitons and free excitons in AIN were deduced to be around 16 and 80 meV, respectively. The observed large freeexciton binding energy implies that excitons in AIN are extremely robust entities that would survive well above the room temperature. Impurity transitions involving nitrogen vacancies generated during ion implantation and Al vacancies and/or complexes in as-grown layers have been studied. The results indicate that VAI and/or V A I - O N complexes are deep acceptors with an energy level of 2.59 eV above the valence band of AIN, which is directly correlated with the reduced conductivities in Al-rich AlGaN and AIN and is thus detrimental to optoelectronic devices using AIN and AlGaN epilayers. The experimentally determined nitrogen vacancy energy level is around
AIN Epitaxial Layers for UV Photonics
135
260 meV. As a consequence of the large activation energy (0.26 eV) as well as high formation energy, VN in AIN cannot contribute significantly to the n-type conductivity. With recent advances in epitaxial growth, conductive n-type Al-rich Al^^Gai-^cN alloys with high Al contents (x > 0.7) have been obtained. Section 7.4 summarizes recent advances in the conductivity control of AlGaN alloys of high Al contents and AIN and understanding of impurity parameters in these materials. A room temperature n-type resistivity as low as 0.0075 H cm with an electron concentration of 3.3 X 10^^ cm~^ and mobility of 25 crn^fV s has been obtained for Alo.7Gao.3N. The resistivity was observed to increase by almost one order of magnitude as the Al content was increased by about 8%, due to the deepening of the Si donor level with increasing x. Transport measurements have indicated that n-type conduction in pure AIN can be achieved. It was found that heavy doping is needed to bring down the donor activation energy and achieve higher conductivities in Al-rich AlGaN alloys. Mg acceptor ionization energy in Al^^Grai-jcN alloys as a function of x has also been measured, from which a binding energy of 0.51 eV for Mg acceptor in AIN was determined. Although Mg acceptors are an effective mass state in this ultra-large-bandgap semiconductor, as a consequence of this large acceptor binding energy of 0.51 eV, only a very small fraction (about 10~^) of Mg dopants can be activated at room temperature in Mg-doped AIN, implying that it is extremely difficult to achieve p-type AIN by Mg doping. Section 7.5 discusses applications of AIN epitaxial layers. These include the insertion of AIN epilayers in UV and deep UV emitters, serving as active layers or dislocation filters. Since a high quality AIN epilayer is UV transparent all the way down to 200 nm and can be grown with superior surface morphology over an AlGaN alloy, it is an ideal template for the subsequent UV photonic device structure growth. Applications of AIN epilayers for other types of active device applications such as for surface acoustic wave (SAW) and electron emission devices are also discussed. In Section 7.6, we present concluding remarks with focuses on future prospects and remaining challenges.
7.2. EPITAXIAL GROWTH AND CHARACTERIZATION
AIN epilayers have been grown by MOCVD, MBE, RF reactive sputtering, and pulsed laser ablation on different substrates (sapphire, SiC, Si, diamond, and AIN bulk crystals) [3-42]. In general, it is much more difficult to obtain high-quality AIN epilayers than GaN epilayers. This is because the growth of high-quality AIN requires much higher temperature and lower V/III ratio. Moreover, achieving conductive Al;cGai_;,N alloys with high Al contents is very challenging due to several well-known mechanisms: (i) an increase in the ionization energy of the dopants and (ii) an enhanced compensation of native defects (cation vacancy and cation vacancy-oxygen complex) with an increase in
136
Optoelectronic Devices: Ill-Nitrides
the alloy composition [43,44]. For MOCVD growth of AIN and Al-rich AlGaN alloys, the metal organic sources used are typically trimethylgallium (TMGa) for Ga and trimethylaluminum (TMAl) for Al. Mg and Si are the common choice as acceptor and donor impurities, respectively. For Mg-doping of AlGaN and AIN, bis-cyclopentadienylmagnesium (Cp2Mg) can be transported into the growth chamber with ammonia during growth. The gas sources are blue ammonia (NH3) for nitrogen and Saline (SiH4) for Si doping and the doping levels can be controlled by the flow rates. There are several methods to confirm the targeted Al contents in Al;fGai_;^-N alloys, including energy dispersive X-ray (EDX) microanalysis. X-ray diffraction (XRD) measurement, secondary ion mass spectroscopy (SIMS) measurement, and optical measurements such as the PL spectral peak position of the band-edge transition. For high Al content Al^cGrai-^cN alloys, the targeted Si- and Mg-dopant concentrations can be verified by SIMS measurements (by Charles Evans & Associates). Determining the quality of the Ill-nitride materials is key to improving the manufacturing process. Unlike many other Ill-nitride compounds, however, measuring the optical and electrical properties of AIN has been a challenge because the material is a good insulator, which renders some standard characterization methods, such as Hall measurement, useless. On the other hand, XRD measurements can provide information about crystalline quality; it provides, however, very little information about electrical and optical qualities of AIN epilayers. As shown in Figure 7.1, the full width at half maximum (FWHM) of the XRD rocking curve of the (0002) reflection peak of AIN epilayers grown on sapphire by the authors' group can be as narrow as 50 arcsec, which is smaller than that 80000 -
KSU-A897 70000 - AIN/sapphire
(002) Rocking Curve
60000 50000 B
40000 -
c
5
FWHM = 50"
30000 20000 -
1 1 J v_
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1
1
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1
1
1
18.4
1
18.6
1
1
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e (deg) Figure 7.1. XRD rocking curve of the (0002) reflection peak of AIN epilayers grown on sapphire by the authors' group at Kansas State University and the XRD measurement was performed by Air Force Research Laboratory, Sensors Directorate, Hanscom AFB (M.L. Nakarmi, Ph.D. Thesis, in preparation).
AIN Epitaxial Layers for UV Photonics
137
of the same reflection peak in GaN epilayers grown on sapphire and is also comparable or even smaller than the best value reported for AIN grown on 6H-SiC (68 arcsec) [12]. However, the value is two times larger than that reported for thin AIN single crystalline platelets (25 arcsec) [36] and five times larger than that of AIN bulk crystals [27]. It is established now that the out-of-plane structural features in Ill-nitrides, e.g. the symmetric (0002) XRD peak in AIN, cannot be used to correlate the material quality and the optical and electrical properties [13,14]. This was attributed to the fact that in Ill-nitrides the edge dislocations only distort the asymmetric planes and induce no significant distortion on the symmetric planes. Thus, there is only a strong correspondence between the in-plane structural order and the electrical and optical properties of Ill-nitrides. For optoelectronic device applications based on AIN and high Al content AlGaN alloys, it is essential to characterize their optical and optoelectronic properties directly. It has been clearly demonstrated in the past that the optical characterization techniques, especially time-resolved optical studies, which provide the temporal characteristics of carrier recombination, together with spectra information are indeed a powerful method for determining the optical processes or transition mechanisms involved because different optical transitions have different dynamical behaviors. The dynamics of injected carriers involved in optical processes is determined by the sample crystalline quality, purity, alloy composition, and quantum well interface properties in different materials and device structures. More importantly, the dynamics of various optical transitions can provide important information regarding excitation and energy transformation processes and recombination lifetimes of injected carriers, which are strongly correlated with quantities such as the quantum efficiency and optical gain. Recently, a deep UV laser spectroscopy system has been developed in author's laboratory (Figure 7.2) which allows one to make picosecond time-resolved PL measurements of AIN and thus, to effectively characterize, and thereby improve the material's quality. The deep UV picosecond time-resolved laser spectroscopy system consists of a frequency quadrupled 100 fs Ti:sapphire laser with an excitation photon energy set around 6.28 eV (with a 76 MHz repetition rate and a 3 mW average power), a monochromator (1.3 m), and a streak camera with a detection capability ranging from 185-800 nm and a time resolution of 2ps. Because only high-quality semiconductor materials emit predominantly exciton PL, the identification of excitonic spectra reveals the optical quality of the sample. The effectiveness of PL spectroscopy measurement is illustrated in Figure 7.3(a), where the room temperature PL spectra for two selective AIN epilayers (KSU A-767 and KSU A-1080) grown under different growth conditions are shown, which contain different oxygen impurity concentrations. The oxygen and carbon impurity profiles as measured by SIMS are shown in Figure 7.3(b) for sample KSU A-1080. Comparing the PL spectra of the two samples, it can be seen that the optical quality or
Optoelectronic Devices: Ill-Nitrides
138 MCP-PMT Single Photon Counting ~30ps
Monochromator (186-800 nm)
Monochromator (800-1700 nm)
H >^ ^ ^
MCP-PMT Single Photon Counting ~30 ps
InGaAs Detector
195 nm (10 mW) 200 fs
Figure 7.2. The femto-second deep UV time-resolved photoluminescence measurement system at Kansas State University. The system is integrated with a near-field scanning optical microscopy and is specifically designed for high Al content AlGaN and AlInGaN alloys, covering the band-band emission in pure AIN. Capabilities include: 2 ps time resolution, 50 nm spatial resolution (SNOM/AFM), 190 nm < A < 1700 nm.
(b)10^^
(a) 8 6-1
4J
AIN (KSU A-767) ©2=1x1020 cm-3
A
300 K
5.98 eV
1
2
£ 8
Jw AIN (KSU A-1080) O2=2x10i7cm-3
I 5.98 eV:
6 4 2
(x10)
0 4 E(eV)
5
^10^ E E o 6 ^o^^ o O
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0.5 1.0 Depth (|um)
1.5
Figure 7.3. (a) Room temperature PL spectra measured for selective AIN epilayers grown under different conditions. The oxygen concentrations are also indicated, (b) Oxygen and carbon impurity profiles in sample KSU-A1080, as probed by SIMS (performed by Charles Evans & Associate) (M.L. Nakarmi, Ph.D Thesis, in preparation).
AIN Epitaxial Layers for UV Photonics
139
the intensity ratio of the band-edge to the deep-level impurity transitions depends strongly on the growth conditions. Furthermore, Figure 7.3(a) shows that the PL emission intensity ratio of the band-edge transition line near 5.97(±0.01) eV to the impurity transition line near 3.40 eV is directly correlated with the oxygen impurity concentration. In the better-optimized AIN epilayer (KSU A-1080) with a lower oxygen impurity concentration, the emission intensity of the impurity transition is two orders of magnitude lower than that of the band-edge transition at room temperature, indicating a significant improvement in material quality. Figure 7.4 compares the PL spectra of AIN and GaN epilayers covering a broad spectral range from 2.2 to 6.2 eV for AIN and 1.8 to 3.6 eV for GaN [34]. It is interesting to note that although the 10 K band-edge emission intensity is about one order of magnitude lower in AIN than in GaN, the room temperature emission intensities are comparable for both compounds. This impHes that it is possible to obtain AIN that displays less thermal quenching and fewer problems resulting from impurities, dislocations and nonradiative recombination channels than GaN, particularly at elevated temperatures. This points to the great potential of AIN for many device applications, because it is already well known that the detrimental effect of dislocations/impurities in GaN is much less severe than in other III-V and II-VI semiconductors. For optimized epilayers grown by MOCVD, the surface morphology of AIN is comparable to those of GaN. This is illustrated in Figure 7.5, where scanning electron (b) 0.4
(a) 12T=10K AIN, KSUA-742
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8-1
1
4-1
T = 300 K AIN, KSU A-742
6.033 eVj
5.960 eV
4.36 eV 2.94 eV
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2.0
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Figure 7.4. PL spectra of AIN and GaN epilayers measured at (a) 10 K and (b) 300 K, which cover broad spectral ranges to include both the band-edge and deep-level impurity transitions (after Ref. [34]).
140
Optoelectronic Devices: Ill-Nitrides Layer structures
Layer structures
AI2O3 KSU567.GaN
A\fi^ KSUA841-AIN
Figure 7.5. Scanning electron microscopy images of AIN and GaN epilayers showing that the surface morphology of AIN epilayer is as smooth as that of GaN epilayer (M.L. Nakarmi, Ph.D. Thesis, in preparation).
microscopy (SEM) images for both GaN and AIN epilayer surfaces are shown. The typical AFM root mean square surface roughness of GaN and AIN in a 10 |xm X 10 |jLm scan area is about 0.8 nm. For undoped AIN epilayers, the emission intensity of the band-edge emission is, in general, correlated with the surface morphology.
7.3. OPTICAL PROPERTIES OF AIN 7,3.1 Band Structure of Wurtzite AIN Besides important practical applications, AIN is also a unique semiconductor compound for fundamental studies. In contrast to all the other II-VI and III-V binary semiconductors, AIN in the zinc-blende (ZB) structure has a larger bandgap than that in the WZ structure [45]. AIN is also the only WZ semiconductor compound that has been predicted to have a negative crystal field splitting at the top of valence band [46-48]. Confirmation of these predictions are important because the negative crystal field splitting can lead to unusual optical properties of AIN than other WZ semiconductors such as GaN [49]. Our knowledge concerning the band structure and optical properties of AIN is still very limited as compared to GaN. For example, the detailed band structure parameters near the F-point of AIN are less understood. The bandgap was determined in the past only by optical absorption, reflectance, and transmission measurements with energy values scattered around 6.1-6.3 eV at liquid helium temperatures [50]. Due to poor optical quality of AIN in the past, the band structure parameters, including the effective masses of electrons and holes as well as the character and splitting at the valence band-edge and
AIN Epitaxial Layers for UV Photonics
141
the associated fundamental optical transitions including the band-to-band and excitonic transitions have not been well investigated. It is, therefore, of fundamental and technological importance to fill in the unknowns for AIN. With recent new progresses in the growth of AIN epilayers, the properties of the fundamental optical transitions in AIN can be studied. By comparing the experimental results with first-principles calculations, a coherent picture for the band structure parameters of WZ AIN near the T-point has been obtained [51]. The results reveal significant differences between AIN and GaN in their band-structure parameters, and hence, their fundamental optical properties. The results also explained the puzzling discrepancy in energy bandgap values of AIN obtained previously by different methods [50]. Figure 7.6(a) shows typical temperature dependent band-edge PL emission spectra for AIN. In obtaining the PL spectra shown in Figure 7.6(a), the laser excitation beam was directed to the sample at an angle of ~ 50° with respect to the c-axis of the sample (or the crystal growth direction). At 10 K, two emission lines at 6.033 and 6.017 eV are resolved. Based on time-resolved and temperature-dependent PL studies, as well as their light polarization dependence (discussed below), these emissions are attributed to the free A-exciton (FX) and its associated neutral donor bound (I2) exciton transitions, respectively. As the temperature increases, the relative intensity of the I2 transition peak at 6.017 eV decreases, while that of the FX transition at 6.033 eV increases, which
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Figure 7.6. (a) PL spectra of AIN epilayer measured at different temperatures between 10 and 300 K. An additional weak emission line indicated as hv^^^-21.0 that becomes visible at room temperature is due to the Raman scattering of the excitation laser line with two longitudinal optical phonons (2L0). (b) The Arrhenius plot of PL intensity [ln(4ini) vs. 1/7] for AIN epilayer. The solid line is the least squares fit of data to Eq. (7.1), from which a free exciton binding energy of 80 meV is obtained (after Ref. [51]).
142
Optoelectronic Devices: Ill-Nitrides
resembles the behavior of I2 and FX seen in GaN [49,52]. This is expected because the donor-bound excitons dissociate at higher temperatures into FX and neutral donors D^, (D^X ^ FX + D^). Figure 7.6(b) shows the Arrhenius plot of the PL intensity of the FX transition line at 6.033 eV. The solid line in Figure 7.6(b) is the least squares fit of the measured data to the equation below, which describes the thermal dissociation (activation) of free excitons: / e m i m = /o[l + C e ( - ^ « ^ ^ ^ V ^
(7.1)
where IQ^\{T) and /Q are, respectively, the PL intensities at a finite temperature Tand 0 K, while EQ is the activation energy, i.e. the free exciton binding energy E^^, in AIN. A binding energy of EQ = 80 meV is obtained from the fitting, which agrees with the value determined from the temperature dependence of the FX decay lifetime [53]. The energy gap at 10 K is thus 6.033 eV + 0.080 eV = 6.11(±0.01) eV. To gain the insights of the detailed band structure parameters near the F-point, firstprinciple band structure calculation have been performed for WZ AIN at the experimental lattice constants. The local density approximation (LDA) as implemented by the allelectron, relativistic, WIEN2k code has been used [54]. The calculated band structure together with the measured bandgap and exciton binding energy are shown in Figure 7.7(a). Compared with the band structure of GaN shown in Figure 7.7(b) [49], the most significant difference is the negative crystal-field splitting ACF ( - 2 1 9 meV) in AIN instead of a positive value (+38 meV) in GaN. This is because AIN, being more ionic, has a much smaller c/a ratio (1.601 vs. 1.626 for GaN) and a much larger u parameter (0.3819 vs. 0.3768 for GaN). Here, M is a dimensionless cell-internal coordinate that distinguishes the two nearest-neighbor anion-cation bond lengths in WZ structure. For an ideal WZ structure with c/a = (8/3)^^^ and u = 0.375 the two bond lengths are equal. Neglecting this effect in calculations can lead to large errors. This larger structural distortion in AIN also explains why WZ AIN has a smaller bandgap than ZB AIN, whereas for all the other binary semiconductors the opposite trend exists [55]. There are many important consequences of this large negative AQF in AIN. First, the order of the valence bands in AIN is different from that of GaN. The valence bands, given in increasing order of their transition energies, are Fvvbm (A), Tg^ (B), Fyy (C) for AIN, whereas in GaN the order is Fpvbm, Tvy, Tjy [49]. Because of the large energy separation between the top most valence band and the second and third valence bands (Figure 7.7), fundamental optical transitions near the F-point, as well as the transport properties of the free holes in AIN, are predominantly determined by the top Fvvbm band instead of the top r9vbm band in GaN. Secondly, the optical properties of AIN differ significantly from GaN. Table 7.1 lists the calculated square of the dipole transition matrix elements / = \{il/y\p\il/c)\ between the conduction state and the three valence states at F of WZ AIN for lights polarized parallel (||) and perpendicular (±) to the c-axis. For an arbitrary light polarization, the matrix element 1(6) = cos^^/(£'||c) + sin^^/(£' _L c), where E denotes
143
AIN Epitaxial Layers for UV Photonics (a)
Band Structure of Wurzite AIN
(b) Band Structure of Wurzite GaN
6.3 6.2 6.1
\ v
r
CBM E^= 80 meV
6.0
ES=E^=20meV
6.11 e V
>
Eg= 3.504 eV
^7vbm
VBM
/^lU
r
|, AE^3=6meV
meV
-0.2
AE^^= 37 meV
-0.3 \y
13 meV
-0.4 -0.5 Figure 7.7. (a) Calculated band structure of wurtzite AIN near the T-point. At k = 0, the top of the valence band is split by crystal field and spin orbit coupling into the r7vbm (A), Tgv (B), and T ^ (C) states. The sign 1 (II) denotes the direction perpendicular (parallel) to the c-axis of the AIN epilayer. The A band exciton binding energy is denoted as £^ [51]. (b) Calculated band structure of wurtzite GaN near the F-point. At A; = 0, the top of the valence band is split by crystal field and spin orbit coupling into the FQvbm (A), T^^ (B), and Fvv (C) states. The A band exciton binding energy is denoted as E^ (after Ref. [49]).
the electric field component of the light and 6 is the angle between E and the c-axes. Our results show that the recombination between the conduction band electrons and the holes in the top most valence state (XiYhm or A) is almost prohibited for E L c, whereas the recombination between the conduction band electrons and holes in the (r9v or B) and (Fvv or C) valence bands are almost forbidden for E\\c, as is shown schematically in Figure 7.8(a). This is in sharp contrast to GaN in which the theoretical and experimental results have shown that the recombination between the conduction band electrons and the holes in the top most valence band (FQvbm oi* A) is almost prohibited for E\\c [49,56]. To further confirm this unusual band structure in AIN, the polarization dependence of the A-exciton and donor-bound exciton emission lines has been measured in AIN Table 7.1. Calculated square of the dipole transition matrix elements / (in a.u.) of WZ AIN for light polarized parallel (||) and perpendicular ( ± ) to the c-axis (after Ref. [51]) Transition
/ (^Ik)
I{E
1 7c *"*• 1 7vbm
0.4580 0 0.0007
0.0004 0.2315 0.2310
Fvc ^ F9v
Lc)
144
Optoelectronic Devices: Ill-Nitrides (a) AIN: r-Poin1t
GaN: r-Point ^7c
6.34 eV
6.32 eV
3.547 eV
6.11 eV
3.510| eV
'r
A
E//C B n
E l C ^7
B
'' E±c
(b)
3.504 eV
— r.
E//C
T=10K, A-742 AIN/Sapphire 6.033 eV
(D°. X ) ElC
GaN/Sapphire]
i
3
E 4-1
6.00
E(eV)
6.04
•
, E // c
3.42 3.44 3.46 3.48 3.50 3.52 3.54
E(eV)
Figure 7.8. (a) The selection rules for the optical transitions at the F-point in AIN and GaN. The sign ± (||) denotes the direction perpendicular (parallel) to the c-axis of the epilayers. (a) Measured polarization dependence of the A-exciton emission spectra in AIN and the donor-bound exciton in GaN (after Ref. 151]).
and GaN, respectively. To do so, a polarizer was placed in front of the entrance slit of the monochromator, so that the PL emission with either E ± c or E\\c was collected. Figure 7.8(b) presents a comparison of the emission spectra of an AIN epilayer obtained for £" _L c and E\\c for AIN and GaN. It conclusively demonstrates that the free A-exciton and the associated bound-exciton transitions in AIN (GaN) are almost prohibited for £ 1 c (£"1^), consistent with the theoretical calculation. It is interesting to note that the PL spectral peak position shift between the £ .L c and E\\c components, as expected for the free electron-hole transition, is not observed in Figure 7.8(b). This is primarily due to the fact that the exact selection rule only applies to the free-hole transition at F = 0, without considering the excitonic effect. The transition is not totally forbidden under the influence of the excitonic effect [57]. Instead, one expects the forbidden transition appears at the same energy position as the allowed
AIN Epitaxial Layers for UV Photonics
145
transition, but with weaker emission intensity [57], Moreover, strain effect and substrate misorientation can also relax the selection rule. The understanding of the AIN band structure can be used to explain nicely some puzzling experimental data for AIN, such as the strong dependence of the measured bandgap on the details of the experiments. The c-axis of nitride films grown epitaxially is always parallel to the crystal growth direction. In many optical measurements such as absorption, transmission, and reflectance, the propagation direction k of the excitation light is generally parallel to the c-axis and the light is, thus, polarized perpendicular to the c-axis, E ± c (the so called a polarization). As illustrated in Figure 7.8(a), the transition between the Fjc and the top valence band rvvbm. which determines the minimum energy gap of AIN, is not active for E ± c. Therefore, this type of optical measurement cannot obtain the true fundamental bandgap of AIN. Instead, it measures the energy gap between the conduction band and the B (or C) valence band because these transitions are active for a polarization. This explains why larger bandgaps, about 6.3 eV, were reported in earlier measurements [50], whereas the value of 6.11 ± 0.01 eV is obtained by PL. This is in contrast to the case for GaN epilayers, in which the emission to the topmost valence band is allowed for a polarization [49,56]. Thus, different optical measurements would generally yield the same bandgap value in GaN [50]. The absorption coefficients for GaN and AIN were calculated for two different light polarization directions, E ± c and E\\c. The results are shown in Figure 7.9, which clearly show that optical measurements with polarization orientation of E ± c, would reveal for (a) 5
1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 y i 1 1 '
(b)
' y
AIN
-
_
_
^ l l /
/«!
-
-
"1^1 1 1 1 i - < < i 1 1. 1 . 1 . 1 . . .
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
6.1
6.2
6.3
6.4
6.5
6.6
1 . . 1
6.7
6.8
Energy (eV) Figure 7.9.
Calculated absorption coefficients a^ and a^ of AIN for light polarization E 1 c and E\\c (after Ref. [51]).
Optoelectronic Devices: Ill-Nitrides
146
AIN an apparent energy gap of Eg + AAB ~ 6.3 eV that is about 0.2 eV larger than the minimum energy gap. 7,3,2 Unique Polarization Properties ofAlGaN Alloys and AIN The unusual valence band structure of AIN gives rise to unique optical properties of AlGaN alloys and their associated UV emitters. Several studies have been carried out to explore the polarization properties of AlGaN alloys and AIN [26,30,58]. Figure 7.10 shows the low temperature (10 K) PL spectra for Al_;cCrai-;,N alloys (0 < x < 1). The experimental measurement geometry is depicted in the inset of Figure 7.10, where the PL emission with either E\\c or E 1 c polarization orientation can be collected using a polarizer in front of the monochromator. The dotted (solid) lines indicate the band-edge emission spectra collected with the polarization of £" ± c (E\\c). Several features are evident: (a) the emission peak position increases with increasing x for both polarization components and (b) the PL emission intensity, /pL, decreases with increasing jc for £^ _L c polarization component. The PL emission component evolves from E ± c being dominant for GaN to E\\c for AIN. Once again, the PL spectral peak position shift between the £" _L c and E\\c components (of about 0.21 eV), as expected for the free electron-hole transition, is not observed due to the excitonic effect [57]. The bowing parameter for AlGaN alloys can be obtained by fitting data with the equation Eg(x) = (1 - A:)£'g(GaN) +x£'g(AlN) - bx(l — x), where h denotes the bowing 10-
T=10K x=0
QI
/laser
AlxGa-, XN/AI2O3
monochromator polarizer
8H
E±c E//c
x=0.5 E
x=0.7
x=1
3.0
3.5
4.0
4.5 5.0 E(eV)
5.5
J
6.0
6.5
Figure 7.10. Low temperature (10 K) PL spectra of Al;fGai_;^N alloys of varying JC, for from jc = 0 to 1. The experimental geometry was depicted in the inset, where the electrical field of PL emission (£") can be selected either parallel (||) or perpendicular ( ± ) to the c-axis (after Ref. [58]).
AIN Epitaxial Layers for UV Photonics
147
parameter. The bowing parameter determined from Figure 7.10 is Z? = 0.86 eV, which is within the range of reported values [59-61]. By analyzing extant data, it was suggested that the intrinsic bandgap bowing parameter for AlGaN alloys is ^ = +0.62(±0.45) eV [60]. A correlation was found between the measured bandgaps and the methods used for epitaxial growth of the Al^Gai-^^N: directly nucleated or buffered growths of Al;,Gai-;cN initiated on sapphire at temperatures T > 800°C usually lead to stronger apparent bowing (Z?>+1.3eV); while growths initiated using low-temperature buffers on sapphire, followed by high-temperature growth, lead to weaker bowing (^ < +1.3 eV) [60]. The degree of polarization (P) is defined by P = (Ij_ - I\\)/(Ij_ + /||), where /^ and /|| are the integrated PL intensities for the polarization components of £^ -L c and E\\c, respectively. Figure 7.11(a) plots P as a function of x. P decreases almost linearly with increasing jc, and P = 0 3.tx = 0.25. The representative band structures near the F-point of Al;,Gai_^N alloys are depicted in Figure 7.11(b) for (a) x = 0, (b) x = 0.25, and (c) x= 1. The conduction bands have Fy symmetry in both AIN and GaN. Compared with the band structure of GaN, the most significant difference in AIN is the negative crystalfield splitting AQF (-219 meV) compared with a positive value (+38 meV) in GaN, as
(a) 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Al content (x)
Figure 7.11. (a) The degree of polarization P vs. x in Al^^Gai-^cN alloys, (b) The band structure of wurtzite Al;,Gai_;,N near the F-point for jc = 0, 0.25, and jc = 1 (after Ref. [58]).
148
Optoelectronic Devices: Ill-Nitrides
discussed in Section 7.3.1. Because of this large negative ZICF in AIN, the order of the valence bands in AIN is different from that in GaN. The top valence band has T^ (Fy) symmetry in GaN (AIN) because of the positive (negative) ZicF- Therefore, light emission due to the recombination between the conduction band electrons and the holes in the top valence band is polarized with £'||c in AIN, which is opposite to that in GaN (£• _L c). This unique band structure of AIN affects acutely the optical properties of AlGaN alloys, in particular of Al-rich AlGaN alloys. When Al content is increased from X = 0 to 0.25, the valence band with T^ symmetry evolves as the lowest valence band (C-band) in GaN to the topmost valence band (A-band) in Al;,Gai_;,N alloys {x > 0.25). At X = 0.25, three valence bands become degenerated at the F-point and the degree of polarization P becomes zero. Thus, the experimentally observed x dependence of the polarization degree shown in Figure 7.11(a) is a direct consequence of the band structure evolution with x. Figure 7.12(a) shows the FWHM of PL emission spectra of Al;,-Gai_;^;N alloys with different x measured at 10 K. The variation of the FWHM with x follows the general trend of the previous theoretical prediction [62-64], i.e. it increases as a function of x, but decreases as x further increases from jc = 0.7 to 1. Figure 7.12(b) shows the variation of the integrated PL emission intensity of Al;,Gai_;,N alloys with the Al content, Ipi vs. x, measured at 10 K for both polarization orientations of £" .L c and E\\c. The emission intensity of the £ ± c component decreases with increasing x, while /pL of the E\\c component is almost independent of x except for GaN. It is well documented that, the overall PL emission intensity decreases with increasing x in Al^Gai_;^N alloys [51,63]. (a)
100^
T=10K AI,Gai.,N:
80
0)
E, 60 J •
1 40S 20 0-
(b)
•
•
•
• •
"•
1 I
'
•
1
11
8
.-^ d "1 E
•
6 4.
X
• E_Lc • X
0)
X •
X
X
•
•
X E//C X
; J
2 •
c
n. U T 0.0
1
0.2
04^
0.6
0.8
1
Al content (x) Figure 7.12. (a) The full width at half maxima (FWHM) of PL vs. x in A^Gai-^^N alloys at 10 K. (b) PL emission intensities for E L c and E\\c vs. x in AljcGai__^N alloys measured at 10 K (after Ref. [58]).
AIN Epitaxial Layers for UV Photonics
149
The efficiency of UV light emitting diodes (LEDs) using Al^^Gai-jcN alloys as active layers is also known to decrease with increasing emission wavelength. The results shown in Figure 7.12(b) suggest that the unique optical property of AlGaN alloys is partly responsible for the low emission efficiency in AlGaN alloys and related UV LEDs, i.e. the emission intensity of the E\\c component decreases with increasing x. The fact that the emission intensity of the E\\c component is almost independent of x seems to preclude the dislocations and nonradiative centers being the dominant cause for the reduced emission efficiency in Al;^Gai __^N alloys with increasing x. In terms of implications of this unique polarization property on device applications, the most significant effects include (i) the power output of LEDs decreases and (ii) the light guiding for edge-emitting laser diodes (LDs) with a predominantly TM mode enhances with an increase of the Al content if AlGaN alloys are being used as active layers, due to the negative crystal-field induced unique polarization property of AlGaN alloys. It is well known in conventional LEDs that the extraction efficiency is only about 5% from each side due to internal reflection. The light can only escape from the top and bottom surfaces when it is within a cone of about 6^ ~ 20°, where 9^ is the critical angle of total internal reflection. For all types of existing LEDs from near infrared to blue color, emitted photons in this cone are able to escape since the polarization of emitted light is mainly perpendicular to the crystal axis within this cone (E 1 c) [65]. However, for UV LEDs using Al^Gai-;,N as active layers (x > 0.25), the most dominant emission will be photons with polarization parallel to the c-axis iE\\c), which implies that UV photons can no longer be extracted easily from the escaping cone. Figure 7.13(a) illustrates schematically this situation for UV LEDs using Al;cGai_;cN alloys as active layers, which shows that only photons polarized perpendicular to the c-axis (E 1 c) can be extracted from the escaping cone (^c ~ 20°). However, the E ± c polarization component is prohibited in the escape cone. We thus emphasize that finding methods for enhancing the light extraction is more critical in UV LEDs with Al;cCrai_;cN active layers than in blue/green LEDs with InGaN/GaN active layers. Techniques for extracting light of transverse propagation such as |x-LEDs [66], photonic crystals [67,68] and other methods are not only recommended, but also necessary for future high-power short wavelength nitride UV emitters. For edge-emitting LDs based on AlGaN alloys, since light cannot leak out from the top and bottom layers due to their unique polarization property, the guiding effect of light is thus enhanced. Figure 7.13(b) shows the schematic diagram of LDs with Al^^Gai-j^N alloys as active layers. The transverse electric (TE) mode is usually the dominant laser emission in all other semiconductor LDs, where the electric field of the mode is parallel to the layer interfaces. However, for LDs with Al_^Gai_;cN as active layers (x > 0.25), the transverse magnetic (TM) mode should be the dominant laser emission, in which the magnetic field is parallel to the layer interfaces.
150
Optoelectronic Devices: Ill-Nitrides (a)
AixGa^,xN(x>oj2g^ LED with AIGaN as active layer
(b)
I / / /
/
AlyGai.yN(y>x) AlxGai.xN(x;>0^ AlyGai.yN(y>x) LD with AIGaN as active layer
Figure 7.13. (a) Schematic diagram of UV LEDs with Al^Gai -j,N alloys as active layers. The light escape cone is about dc ^ 20°, within which any photons extracted are nearly polarized perpendicular to the c-axis. (b) Schematic diagram of LDs with Al;,Gai _^N alloys as active layers. In contrast with other semiconductor LDs with TE being the dominant mode, the TM mode is expected to be the dominant mode in AIGaN UV LDs (after Ref. [58]).
7.3.3 Exciton Recombination Dynamics in AIN The recombination dynamics associated with the fundamental optical transitions in AIN are unknown due to the lack of high quality materials as well as technical difficulties involved for the deep UV (down to 200 nm) time-resolved PL measurements in the past. The availability of AIN epilayers with high optical quality as well as the deep UV picosecond time-resolved PL system opens the possibility to probe the recombination dynamics associated with fundamental optical transitions in AIN. Recently, deep UV picosecond time-resolved PL spectroscopy has been employed to study the recombination dynamics of the donor-bound exciton (I2) and free exciton (FX) transitions [53]. Figure 7.14(a) shows the low-temperature (10 K) PL spectrum for an AIN epilayer, in which the dominant emission line at 6.015 eV is due to the neutral donor-bound-exciton recombination (D^X) or I2. A second emission line at the higher energy side around 6.031 eV is also clearly resolved, which is attributed to free-exciton transition (FX). The I2 and free exciton emission peak positions shown in Figure 7.14(a) are 2 meV different from the PL spectra shown in Figure 7.6(a). This is quite common for Ill-nitride epilayers as
AIN Epitaxial Layers for UV Photonics (a)
(b)
1.5
AIN epilayer KSU1767
151 | i/"\
<
6.015 e V /
T=10K 5.92
5.96
6.00
6.04
E(eV)
6.08
6.12
5.90
yl6.031 eV
(y y
5.95
6.00
X_(FX) 6.05
6.10
E(eV)
Figure 7.14. (a) Low-temperature (10 K) CW PL spectrum of an AIN epilayer grown on sapphire, in which the donor-bound exciton recombination is a dominant transition line at low temperatures, (b) PL spectra measured at different temperatures for an AIN epilayer. The arrows indicate the PL spectral peak positions of the bound exciton (I2) and free exciton (FX) transition lines. The spectra are vertically shifted for a better illustration. (after Ref. [53]).
the magnitude of strain usually varies from sample to sample. The emission spectral line shape resembles those of GaN epilayers in which both free- and bound-excitons emission lines were present [49,52]. The separation between the two peaks is around 16 meV, which corresponds to the binding energy of I2, E^^, in AIN epilayer. The temperature evolution of the time-integrated PL spectra is shown in Figure 7.14(b). Other than the larger separation energy between the I2 and FX emission lines seen in AIN than in GaN (16 vs. 6 meV), the temperature variation of the PL spectra of AIN shown here is very similar to that of GaN epilayers [69,70]. The thermal activation energy of the donor-bound-exciton obtained by measuring the temperature-dependent bound exciton emission intensity in the lowtemperature region agrees with the value of 16 meV obtained from the spectroscopy measurement. This value is about 2.5 times larger than in GaN (^bx = ^-^ meV) [49,52, 71-73]. This enhanced binding energy of the donor bound exciton in AIN is attributed to the fact that the free exciton binding energy, E^, in AIN is larger than that in GaN due to the larger effective masses of electrons and holes in AIN. The temporal responses of the h and FX recombination lines were measured at their respective spectral peak positions at 10 K as displayed in Figure 7.15(a). The decay lifetimes were found to be around 80 ps for I2 and 50 ps for FX transition at T = 10 K. The bound exciton lifetime in AIN is slightly shorter than the approximately 100 ps reported for GaN epilayers [49,52,71]. Values ranging from 50 to 350 ps for the lifetime of free excitons in GaN epilayers depending on the purity and crystalline quality
Optoelectronic Devices: Ill-Nitrides
152 (a)
Qj^.^
T = 1 0 K , AINepilayers Tj - 8 0 ps, l2(E=6.015 eV)
=-
0-L Tpx~50 ps, FX(E=6.031 eV)
0.2
0.4
Time (ns)
0.6
100
150
T(K)
Figure 7.15. (a) Temporal responses of PL emissions measured at 10 K at the bound exciton and free exciton spectral peak positions in an AIN epilayer. (b) Top: emission energy dependence of the decay lifetime of the bound exciton and free exciton transition hnes in an AIN epilayer measured at 10 K. The time-integrated emission spectrum is also included. Bottom: temperature dependence of the recombination lifetime of the bound and free excitons measured at their respective spectral peak positions (after Ref. [53]).
of the materials have been reported [49,52,71]. In semiconductors, the radiative recombination rate of fundamental optical transitions increases quadratically with the bandgap, r^ocE^, while the nonradiative recombination rate decreases exponentially with an increase of the bandgap [74,75]. This means that the estimated ratio of the exciton hfetime in AIN to GaN would be roughly (3.4 eV/6.1 eV)^ « 0.3. Thus, it is believed that the observed low-temperature free exciton lifetime of 50 ps is predominantly the radiative recombination lifetime in AIN. Figure 7.15(b) plots the decay lifetime (jeff) of the I2 transition line as a function of the emission energy (£'emi) measured at T = 10 ^ and the temperature dependence of the recombination lifetime of the I2 and FX transitions measured at their respective spectral peak positions. The decay lifetime decreases monotonically from 102 ps at £" = 6.004 eV to 78 ps at £ = 6.027 eV. Similar behaviors have been observed for the I2 and Ii (acceptor bound exciton) transition lines in GaN epilayers [76,77], which was attributed to the existence of a distribution of the binding energy of the bound exciton. The measured decay lifetime of the FX transition is almost independent of ^emi- Decay lifetimes of both the I2 and FX transitions decrease with increasing temperature; however, the FX decay lifetime decreases slower than the I2 transition, which corroborates the results shown in Figure 7.14(b)—the bound exciton dissociates first into a neutral donor and a free exciton with increasing temperature.
AIN Epitaxial Layers for UV Photonics
153
The radiative recombination lifetime of free excitons, Tj-ad, can be obtained from the measured decay lifetimes (r^ff) and quantum efficiency, rj = /enii(r)//enii(0), with the assumption that the radiative recombination is the dominant process at low temperature, where /emi(^) and /emi(O) are the PL emission intensities at temperature T and 0 K, respectively. The radiative lifetime (Tj-ad) can be obtained from the following equation [78]: 'T'rad = Teff/T?.
(7.2)
By taking /emi(O) "^ 4mi(10 K), the temperature dependence of Tj-ad for AIN epilayers has been obtained for T > 100 K, as shown in Figure 7.16. From Figure 7.14(b), the process of the bound exciton dissociation into FX transition affects the measured decay lifetime and quantum efficiency largely at 7 < 100 K. As shown in Figure 7.16, r^ad increases with T according to T^^^ in the temperature range of 100 < T < 200 K for AIN, a well-known feature of free excitons or free carriers in semiconductors [79]. A similar behavior has been observed in GaN between 50 and 100 K [78]. The temperature range for the relation '^rad ^ T^^^ to hold in AIN is higher than in GaN, which is attributed to a larger binding energy of the bound exciton in AIN. At temperatures above 200 K, the measured decay lifetime of FX transition is affected by the dissociation of free excitons. However, the FX transition is usually the dominant transition at room temperature in AIN. The observed temperature dependence of Tj-ad shown in Figure 7.16 corresponds very well to a theory based on free exciton dissociation (solid line) [78], from which a free
3UU] Ex = 80 meV
200-
/
[
100. /
•
•
•
/•.••' -p3/2
O)
o
1
50 yy
AIN epilayer
yy' 100
(FX) 150
200
300
log(T) (K) Figure 7.16.
Temperature dependence of the radiative decay lifetime of free excitons in AIN. The solid line is the fit based on a theory of free exciton dissociation in Ref. [78] (after Ref. [53]).
Optoelectronic Devices: Ill-Nitrides
154
exciton binding energy of E^ = 80 meV is deduced for AIN. This value also agrees fairly well with the thermal activation energy of the free exciton obtained by measuring the temperature-dependent free exciton emission intensity at higher temperatures, i.e. the slope of the InC/gmi) vs. 1/7 plots shown in Figure 7.6(b). We believe this value represents the largest free exciton binding energy ever observed in semiconductors and implies that the excitons are highly robust in AIN, which could have a great significance upon deep UV photonic device applications based on AIN. The effects of Si doping on the donor-bound exciton recombination dynamics in AIN epilayers have been investigated. Doping-induced PL emission linewidth broadening, enhanced nonradiative decay rate, and bandgap renormalization have been observed [80]. Figure 7.17(a) shows the low-temperature (10 K) PL spectra for a set of Si-doped AIN epilayers grown under identical conditions with different Si dopant concentrations, Nsi, in which the dominant emission peak is due to the donor-bound exciton or I2 transition. The top panel of Figure 7.17(b) shows that the I2 emission intensity decreases continuously with increasing A^si- This implies an increased defect density as well as a reduced materials quality with an increase of A^si- This fact contrasts the results obtained for GaN and AlGaN, in which Si-doping in general improves the material quality and the PL emission
(a)
6 6.024 eV
4
FWHM= 16.8 meV
2
(b)
I T=10K, Si-AIN
/
3-
""i.^.,,^^^^
E
0 6.015 e v i
4
FWHM= 17.3 m e V ^ /
2
T = 1 0 K , Si-AIN
Nsr4x10i7cm-3
Z)
%
20
X
18
6.000 eVi
<
FWHM= ; ia4meV,'
\ \
16 6.02
5.991 eV i FWHM= / 20.0 meVr"' 90
5.95
^
\
6.00 E
6.00 data
\
5.98 6.05 (eV)
6.10
6. 15
fit: AEp=-KxNsi^^^
5.96 10
10^ ,-3^
Nsi(cm-^)
Figure 7.17. (a) Low-temperature (10 K) PL spectra of the band-edge transitions in Si-doped AIN with different Si-doping concentrations, Nsi. (b) The integrated PL intensity, full width at half maximum (FWHM), and the PL energy peak position of the I2 emission line, Ep, as functions of Nsi in Si-doped AIN epilayers and the solid line is the least squares fit of data with Eq. (7.4) (after Ref. [80]).
AIN Epitaxial Layers for UV Photonics
155
intensity [81-83]. AFM studies also reveal that the surface roughness increases with increasing A^si^ varying from 0.7 nm for A^si = 0 to 6 nm for A^si = 1-5 X 10^^ cm"^, indicating a reduced material quality with increasing A^si ^^^ corroborating the PL results. The FWHM of the h transition line can be described by a model that accounts for the emission line width broadening due to local potential fluctuations induced by random distributions of doping impurities [81,82], FWHM = Eo-\- a ^ A ^
(7.3)
where EQ is the FWHM at A^si = 0, a, a constant depending on materials, and r^, the Debye and Thomas-Fermi screening radius for nondegenerate and degenerate doping concentrations, respectively. The solid line in the middle panel in Figure 7.17(b) is the least squares fit of data with Eq. (7.3). The fitted value of £"0 is 15.1 meV, which is in excellent agreement with the FWHM (15.5 meV) of the I2 transition in undoped AIN shown in Figure 7.14(a). Silicon doping also induces bandgap renormalization. The bottom panel of Figure 7.17(b) shows that the spectral energy peak position (^p) of the I2 emission line decreases (i.e. is red-shifted) with an increase of A^si ^^ Si-doped AIN epilayers. Bandgap renormalization is usually due to free carrier screening and is written as A£'p = —Kn^^^, where AE^ is the reduction of the bandgap, n is the electron concentration, and K is a. proportionality constant depending on materials [84-86]. However, no free electrons were found in these samples since all of our AIN epilayers studied here exhibit high resistivity. The bandgap reduction in this case is presumably due to the screening of ionized impurities. In such a context, AE^ is assumed to be proportional to A^si for compensated materials, A£p = -KN'^^
(7.4)
The dotted line in the bottom panel of Figure 7.17(b) is the least squares fit of data with Eq. (7.4) and clearly shows the effect of doping-induced bandgap renormalization in Si-doped AIN epilayers. The PL temporal responses of AIN epilayers with different Si doping levels have been measured at their respective spectral peak positions and the results are shown in Figure 7.18(a). Figure 7.18(b) shows that the PL decay lifetime, r, decreases linearly with increasing A^si- ^^ Figure 7.18(b), the solid line is a linear fit of the experimental data. The fitted value of r = 82 ps at A^si = 0 is also in excellent agreement with the decay lifetime (80 ps) of the I2 transition in undoped AIN shown in Figure 7.15(a). It was believed that the linear decrease of PL decay lifetime with A^si is associated with an increased nonradiative recombination rate with increasing A^si^ which corroborates the PL intensity decreasing with A^si shown in Figure 7.17.
156
Optoelectronic Devices: Ill-Nitrides (a)
2 T=10K Si-doped AIN
0 -2H _a) _4
-8-]
A
Nqi=4.0x10^^cm-2 ^Si' Nsi=1.5x10^Scm-
-10
0.0
0.1
0.2
0.3
Time (ns)
0.5
1.0 Nsj(x10^Scm-3)
Figure 7.18. (a) Temporal responses of the I2 recombination line in Si-doped AIN epilayers with different A^si measured at their respective spectral peak positions, (b) PL decay lifetime as a function of A^si- The solid line is a linear fit of the experimental data (after Ref. [80]).
7,3.4 Optical Properties of Nitrogen and Aluminum Vacancy Complexes in AIN Epilayers As-grown GaN is usually n-type; however, as-grown AIN is highly resistive and n-type conductivity is very difficult to obtain. For many years, it was believed that nitrogen vacancies (V^) were the cause of the high background n-type conductivity in unintentionally doped GaN [87]. First principle calculations indicate that the isolated nitrogen vacancy in GaN has large formation energy and can be excluded as the source of n-type conductivity [88]. Nitrogen vacancies have been observed in electron-irradiated GaN epilayers and is well understood now; however, little is known about V^ in AIN. Previous theoretical investigation revealed that V^ in AIN is a GaN epilayers and the energy level of V^ in GaN was determined to be around 25 meV [89]. This is close to
AIN Epitaxial Layers for UV Photonics
157
a value of 30 meV obtained from a tight-binding calculation [90] and seems to be consistent with the value obtained from the effective-mass theory without central-cell correction [91]. More recent positron annihilation experiments show that Ga vacancies are the dominant acceptors in n-typc GaN [92]. Furthermore, the Ga vacancy concentration was observed to be equal to the total acceptor density determined by the temperature-dependent Hall experiments. The depth profile of Ga vacancies is similar to that of O, suggesting that the Ga vacancies formed during the growth are bound to defect complexes with the oxygen impurities [92]. While the properties of V^ in GaN are relatively well understood now, Httle is known about V^ in AIN. A previous theoretical investigation showed that VN is a shallow donor with an activation energy of about 300 meV [90]. A recent calculation indicated that as-grown AIN epilayers do not contain V^ because of the high formation energy of V^ [93]. While deep levels offer preferential recombination routes, they are frequently nonradiative and thus inimical to photonic devices. It is known that in GaN, high dose ion-implantation induces nitrogen vacancies that cannot be recovered completely by thermal annealing [94]. Co, Mn, and Cr ions were implanted into AIN epilayers at an energy of 250 keV and with a fixed dose of 3 X 10^^ cm~^ [95,96]. The ion-implanted AIN epilayers were then thermally annealed in nitrogen ambient at various temperatures up to 1325°C for 15 min. Structural characterization was done through high-resolution XRD measurements. FWHM of XRD rocking curve of (0002) peak of the as-grown AIN epilayers was around 400 arcsec, which increased by about 30% for Co-implanted AIN epilayers, but the peak position did not change. Figure 7.19 compares the low temperature (10 K) PL spectra of as-grown and Co-, Mn-, and Cr- implanted AIN epilayers [96]. The arrows indicate the peak positions of the spectra. The as-grown epilayer exhibits a strong band-edge emission line at 6.05 eV and its longitudinal optical (LO) phonon repHcas at 5.94 eV (ILO) and 5.83 eV (2L0). For the ion implanted AIN, the band-edge transition at 6.05 eV is absent, which could not be recovered by thermal annealing in nitrogen ambient up to 1325°C [95]. However, a new emission line with a peak position at 5.87 eV is evident. The spectral peak position and the intensity of the new peak suggest that point defect recombination centers were created during ion-implantation. Furthermore, PL spectra of Co-, Mn- and Cr-implanted samples were identical independent of the implanted species, which also suggests that the 5.87 eV emission line is not related with the implanted ions, but to the nitrogen vacancies (VN) created during ion-implantation [95]. It was believed that ions with energy 250 keV only displace nitrogen atoms to generate nitrogen vacancies (VN) in AIN. Antisites and N intersitials (Ni) are energetically less favorable due to the large lattice mismatch in the covalent radii of Al and N. The 5.87 eV emission line was attributed to the band-toimpurity transition, involving electrons bound to V^ and free holes [96]. Because of the high formation energy of V^ in AIN [93], VN ^nd hence the V^ related optical transition is absent in as-grown AIN epilayers.
Optoelectronic Devices: Ill-Nitrides
158
12 8
4-1
6.055 eV T=10K A-838, Undoped-AIN 5.943 eV: 5.831 eV ,
JL ^ *
< (x200)
^y* —-i«w^
0 2
Co-AIN
1-1 5.5
(x200)
/K .—^ 5.6
5.7
5.8
5.9
6.0
6.1
6.2
6.3
E(eV) Figure 7.19. PL spectra of as-grown AIN and Cr, Mn and Co-implanted AIN epilayers measured at 10 K. For the ion-implanted AIN epilayers, the band-edge transition at 6.05 eV disappears and a new emission hne is observed at 5.89 eV (after Ref. [95]).
Time-resolved PL was employed to measure the recombination lifetime of the VN related emission line at 5.87 eV in the Co-implanted sample. The measurement reveals that the decay kinetics was a single exponential with a very short decay time constant (<20ps), which precludes the possibility for a donor-acceptor-pair (DAP) transition. Fast decay lifetime indicates that it is a band-to-impurity type rather than a DAP type transition. For the band-to-impurity transitions, the decay rate is proportional to the total impurity (defect) concentration. The results thus indicate that the concentration of nitrogen vacancies generated by ion implantation is quite high, which is consistent with the absence of the band-edge transitions (6.05 eV) in ion-implanted samples. Since the Al vacancy (VAI) is believed to be a deep acceptor with an energy level larger than 2 eV [90], the possibility of V^i being involved in the 5.87 eV PL emission can also be precluded. Figure 7.20(a) shows the temperature dependence of the 5.87 eV emission line in the Co-implanted AIN measured from 10 to 250 K. The peak position changes slightly with temperature and in fact depicts a week blue shift with increasing temperature in the range from 10 to 180 K. This further supports the assignment that the 5.87 eV emission line is a band-to-impurity transition, since the spectral peak position of this type of emission is
AIN Epitaxial Layers for UV Photonics (a) T=250 K T=200 K
159
(b)
AIN:Co
AIN: Co 5.90 eV 1
"E
=^ 1 Eo=0.26 eV
fitted by Ln[le^i/lo]=-Ln[1+ce
5.8
5.9
6.0
0.004
0.005
0.006
0.007
1/T(1/K)
E(eV)
Figure 7.20. (a) PL spectra of Co-implanted AIN epilayer measured from 10 to 250 K. (b) The Arrhenius plot of the integrated PL emission intensity at 5.87 eV in the temperature range between 170 and 250 K. The solid line is the least squares fit of data with Eq. (7.1). The fitted value of activation energy (£"0) is also indicated (after Ref. [96]).
expected to follow the temperature variation of the bandgap with an initial blue shift before thermal energy for impurity ionization is reached. Above 170 K, the integrated PL intensity (/jnt) of the 5.87 eV emission line decreases with temperature rapidly and diminishes completely above 250 K, which is predominantly due to the thermal activation process of V^, •V^+e"
(7.5)
where EQ is the thermal activation energy. Figure 7.20(b) is the Arrhenius plot of the PL intensity of the 5.87 eV emission line for the temperature range between 170 and 250 K. The soHd line is the least squares fit of the data with Eq. (7.1). The fitted value of the activation energy EQ is 260 meV, which agrees quite well with the theoretically calculated 300 meV energy level of V^ [90]. Since V^ emission line is located at 5.87 eV with an energy level of 260 meV, the bandgap of AIN can be deduced to be 5.87 eV + 0.26 eV = 6.13 eV, which agrees well with a previous determination of 6.11 eV [53]. This, in turn, also supports the interpretation that the emission line at 5.87 eV in ion implanted AIN is due to a band-to-impurity transition involving V^. The results suggest that nitrogen vacancies in AIN cannot contribute significantly to the n-type conductivity, as a consequence of the large activation energy (0.26 eV) as well as high formation energy. In GaN, the well-known yellow line (YL) with emission energy at around 2.15 eV is often present [43,44,97-99]. The transition mechanism of the YL in GaN is still under debate; however, recent results point towards the donor-to-acceptor pair (DAP) transition
160
Optoelectronic Devices: Ill-Nitrides
between a shallow donor and a deep acceptor related with Ga vacancy (Vca) or Ga vacancy and oxygen complex (Vca-ON) in GaN [44,92,100-106]. The YL intensity in GaN was observed to increase with increasing oxygen, Si, and Vca concentrations [92,103-106]. The formation energy of Al vacancy decreases with increasing Al content in AlGaN, and becomes very low with a triple negative charge state in AIN (Vif) [43,44,102]. Although impurity transitions in AIN are much less studied, a broad violet line (VL) at 3.40 eV was commonly observed and the involvement of Al vacancy (VAI) ^nd oxygen (ON) complexes (VAI-ON) has been suggested [44,107]. Needless to say, the presence of a strong VL is detrimental to optoelectronic devices using AIN and AlGaN epilayers with high Al contents, similar to the effect of YL on GaN. The room temperature PL spectra for selective AIN epilayers are shown in Figure 7.3. A VL emission line at 3.40 eV is the dominant transition in sample KSU-A767 with an oxygen concentration of 1 X 10^^ cm~^, while it almost disappears in sample KSU-A1080 with a much lower oxygen concentration o f 2 x lO^^cm"^, which indicates that the VL is directly correlated with oxygen impurities in AIN. The decay lifetime of the 3.40 eV emission line measured at 10 K was longer than 1 |JLS, which precludes the possibility for a band-to-impurity type transition that has a recombination lifetime in the order of 1 ns [108,109]. The broad emission band of VL also indicates that it is a DAP type transition [44]. From the temperature evolution of the time-integrated PL emission intensity of the 3.40 eV line, a thermal activation energy EQ = 60 meV is obtained. This suggests that the 3.40 eV emission line is a DAP transition involving a deep acceptor and a shallow donor (with an ionization energy of around 60 meV). The chemical origin of the shallow donor involved in VL in AIN might be related with Si or O impurities, while the deep acceptor involved is most likely the VAI-ON complex as previously suggested [43,102]. The concentration of Al vacancies depends on Fermi level and impurity concentration [43,44, 102]. It is known that impurity incorporation can enhance the formation of Al vacancies during the crystal growth to form energetically stable VAI oi* ^AI complexes [92,101,102]. Thus the VAI-ON impurity complex, which bears analogy to the Voa-ON impurity complex involved in YL in GaN, is the most favorable candidate for the origin of the VL in AIN or AlGaN with high Al contents. However, VAI-SIAI or other types of VAI complexes as an origin of the deep acceptor are also possible, although their formation energies are larger than that of VAI or VAI-ON complex in AIN.
7.4. IMPURITY PARAMETERS AND CONDUCTIVITY CONTROL IN HIGH Al-CONTENT AlGaN AND AIN
7,4,1 Si Donors and N-type AlGaN and AIN Highly conductive n-type and p-type Al;cGai-;,N alloys with high Al contents {x > 0.6) are needed for the realization of high-performance practical deep UV optoelectronic
AIN Epitaxial Layers for UV Photonics
161
devices. Achieving conductive Al^^Gai-^^N alloys with high Al content is very challenging due to an increase in the ionization energy of the dopants and an enhanced compensation of native defects (cation vacancy and cation vacancy-oxygen complex) with an increase in the alloy composition [43,44]. Oxygen solubility in AIN is high and oxygen-free AIN crystals and surfaces are not easy to obtain. However, it is necessary to control the oxygen concentration before an efficiency doping can be implemented. Progress has been made over the past many years in terms of conductivity control in the high Al-content AlGaN alloys. N-type conduction in high Al-content Al^^Gai-^cN (x > 0.5) has been obtained by Si-doping by several groups by both MOCVD and MBE growth [110-113]. More recently, using In-Si co-doping, n-type Alo.65Grao.35N epilayers have been achieved with an electron concentration of 2.5 X 10^^ cm~^ and mobility of 22 cvc^fN s corresponding to a resistivity of 0.011 fl cm [114]. Most recently, the authors' group has achieved highly conductive n-type Alo.7Gao.3N epilayers (with a resistivity p = 0.0075 /2 cm) by heavy doping with silicon atoms (A^si = 3.5 X 10^^ cm"^) [115]. It was observed that a minimum silicon doping level of 10^^ cm~^ is necessary for achieving high conductivities in AlGaN alloys with high Al contents [116,117]. On the other hand, pure AIN was usually referred to as a ceramic material due to its very large bandgap, poor crystalline quality, and highly insulating nature and was considered useful as a semiconductor only when alloyed with GaN or used as buffer and spacer layers in nitride structures and devices. However, recent advances on epitaxial growth have shown that it is possible to control the conductivity of AIN by Si doping [116,117]. Figure 7.21(a) shows the typical Hall measurement results for an Alo.7Gao.3N alloy sample with a Si dopant concentration A^si = 3.5 X 10^^ cm~^ in the temperature range from 70 to 600 K. The temperature variations of the free electron concentration and mobility are typical for a semiconductor in which the electron transport is dominated by the ionized impurity scattering at low temperatures and by polar optical phonon scattering at higher temperatures. Compared with GaN in which the maximum mobility appeared around 100 K [118], the temperature for the maximum mobility in n-type Alo.7Gao.3N is much higher due to increased ionization energy of Si donors. In Figure 7.21(b), the temperature variations of the resistivity of Alo.7Gao.3N alloys with different Si-dopant concentrations are presented. The topmost curve is for the sample with the lowest dopant concentration (A^si = 1-5 X 10^^ cm~^), in which a clear thermal activation process is observed. However, this thermal activation behavior becomes less evident as the Si-doping level increases. The sample reaches a lowest resistivity at A^si ~ 3.5 X 10^^ cm~^, beyond which the resistivity increases with further increase in dopant concentration. This could be due to the self-compensation effect or scattering from heavily doped impurity atoms. This trend is more obvious from Figure 7.22(a), which shows the dopant concentration dependence of the room temperature resistivity. The variation of the Si donor activation energy EQ in Alo.7Gao.3N alloy as a function of the Si dopant concentration is presented in Figure 7.22(b), where the values of EQ were obtained from
162
Optoelectronic Devices: Ill-Nitrides
(a) _ 0.9E o
a
-|—'—r
0.8-^
(b)0.05KSU-A1496 n-AloyGao.sN Ne;=3.5x10^^cm-3H
• Nsi=1.5x10^9cm-3 o Nsi=2.0x10^9cm-3" A Nsi=2.5x10^9cm-3
0.04-
O Nsi=3.0x10^9cm-3 • Nsi=3.5x10^9cm-3+ Nsi=4.0x10^9cm-3
•••
0.7-
a 0.034.0-
3.0-
Si 0.02* o oo o
25• •• 20-
0.01 * * * * • • • • • • •
15-
1 — I — I — I — I
100 200 300 400 500 600 700
0
T(K)
-r -r -r
100 200 300 400 500 600 700 T(K)
Figure 7.21. (a) (From top to the bottom): variations of resistivity p, electron concentration n, and electron mobility /x with temperature for n-Alo.7Gao.3N with Si-dopant concentration N^i = 3.5 X 10^^ cm~^). (b) Temperature dependent resistivity of an n-Alo.7Gao.3N with varying Si doping levels from 1.5 X 10^^ to 4.0 X 10*^ cm~^ (after Ref. [115]).
the Arrhenius plots of the resistivity data. The inset of Figure 7.22(b) illustrates an example of an Arrhenius plot of the resistivity for Nsj = 3.5 X 10^^ cm~^. The solid line in the inset is the least squares fit of data with p = po/[l + C txp(-Eo/kT)]
(7.6)
where EQ is the donor activation energy, k is Boltzmann constant, and C is a fitting constant, from which a value £^0 of ^^ ^^^ was obtained for Si donor in Alo.7Gao.3N alloy at a dopant level of A^si = 3.5 X 10^^ cm~^. There is a clear trend that £"0 decreases with an increase in the Si-doping level. This is due to the bandgap renormalization effect [119,120], and it can be described by the following equation: Eo = Eo(0) - K(Nsi) 1/3
(7.7)
where K is the renormalization constant, £"0(0) is the extrapolated activation energy at Nsi = 0. In Figure 7.22(b), the solid line represents the least squares fit of EQ with Eq. (7.7). £'o(A^si = 0) was deduced to be 55 meV. A simple calculation shows that the binding energy of a shallow donor in Alo.7Gao.3N alloys is about 60 meV using a linear relation for the parameters between GaN (e = 9.5 and ml/rriQ = 0.2) and AIN (e = 8.5 and ml/m^ = 0.4), which is consistent with the experimental observation. K was obtained as 0.65 X 10~^ meV cm, which is also consistent with a value (2.1 X 10~^ meV cm)
AIN Epitaxial Layers for UV Photonics (a) 0.035 n
' — 1 — 1 — 1 — 1 — 1 — 11 — 1 — 1 — 1 — 1 — 1 — 1 —
163
(b) 35
n-Alo.7Gao.3N • 0.030 -
T=300K
•
0.025 E o a 0.020-
•
a^ > 0.015-co
-
> CD
-
'(/)
E
0
a:
•
0.010-
•
0.005 0 000 - ' 1 1 .0 1.5
•
'1
•
-
1 — 1 — 1 — 1' — 1 — ' — 1 — ' — 1 — ' —
2.0 2.5
3.0 3.5
Nsi(10^9cm-3)
4.0 4.
2 3 Nsi(10^9cm-3)
Figure 7.22. (a) Room temperature resistivity as a function of the Si dopant concentration, A^si • (t>) The Si donor activation energy in Alo.7Gao.3N as a function of dopant concentration, A^si- Filled circles are measured values and solid line is the least-squares fit with the bandgap renormalization effect of Eq. (7.7). The inset is an Arrehenius plot of resistivity of n-Alo.7Gao.3N with A^si = 3.5 X 10^^ cm~^. Filled circles are the measurement result; solid line is the least squares fit of data with Eq. (7.1). The fitted activation energy is 23 meV (after Ref. [115]).
suggested for GaN [121,122]. The resistivity results shown in Figure 7.22(b) suggest that heavy doping is needed to achieve highly conductive Al;cGai_;cN alloys with high x for device applications. Another interesting parameter one could obtain from Eq. (7.7) is the maximum Si-doping level required to bring EQ down to zero (metallic behavior). Using the fitting results, this doping level can be extrapolated to be about 2 X 10^^ cm~^. However, the resistivity data shown in Figure 7.22 indicate that heavy doping could induce degradation of material quality and impurity compensation. Thus, an optimal doping scheme has to be employed in obtaining highly conductive Al;cGai-;cN alloys with high x. The attainment of highly conductive Al^^Gai-^^N alloys with high Al contents made the measurement of the Si donor parameters in Al^^Gai-^^-N alloys as a function of the Al content in high x end possible [116,117]. Figure 7.23(a) presents the room temperature Hall measurement results of n-Al^cGai-^^N (x > 0.7), showing the Al content (x) dependent resistivity, electron concentration, and electron mobility, respectively. This set of samples were grown on sapphire substrates by MOCVD with a thickness of about 1 iJim. A 0.5 (xm AIN epilayer was first deposited on (0001) sapphire substrate with a low temperature buffer, followed by the growth of Si-doped Al;,Gai_;,N epilayer [117]. The Si dopant concentration (Nsi) was 3.5 X 10^^ cm~^ in all samples as guided by the result shown in Figure 7.22(a). The dopant concentration, A^si^ for selective samples was
Optoelectronic Devices: Ill-Nitrides
164
^) 1
(a) E o
UU- -
1
I
I
1
'
1
•
1
'
1
•
1
J
75-
a
•
> b^ 5 0 O UJ
• 25-
•
^ o
0.03-
^
0.02
Q.
r
0.01- V
(3 4
0- — ' — 1 — ^
85
90
Al Content (%)
95
100
•
n-AI^Gai
A
-
x= 0.77
8 12 16 1000/T(K-^)
-
T—'—1—'—1—'—1—'—1—•—
65 70 75 80 85 90 95 100 Al Content (%)
Figure 7.23. (a) Room temperature Hall measurement results of n-Al;,Gai -J>i (x > 0.7). The top, middle and bottom sections of (a) show the resistivity, electron concentration, and electron mobihty as functions of the Al content (x), respectively; lines are guide to the eye. For all samples, the silicon dopant concentration was 3.5 X 10^^ cm~^. (b) Si donor activation energy as a function of the Al content, x. The inset shows the fitting result for Alo.77Gao.23N, and an activation energy of 41 meV was obtained (after Ref. [117]).
determined by SIMS measurements. The resistivity increases with the Al content (x) rapidly and the dependence can be described by the following empirical equation: p(Al^Gai_^N) = p(AlN) X IQ-^^-^^^^-^^
(7.8)
from which one can deduce that the resistivity of n-Al;,.Gai_;^N (x > 0.7) increases by about one order of magnitude when Al content, jc, is increased by about 8%. This rapid increase in resistivity with x is predominantly due to an increase in donor ionization energy. The temperature-dependent resistivity results for n-Al;,Gai_;,N (x > 0.7) in the temperature range from 70 to 620 K have been measured. At the fixed Si dopant concentration of3.5X lO^^cm"^, a strong temperature dependence is seen for samples with high Al content (x > 0.8). Weaker temperature dependence is observed for samples with lower Al contents (x < 0.8), which indicates the trend of moving towards the metallic behavior due to heavy Si doping. The Al content dependence of the Si donor ionization energy (£"0) is depicted in Figure 7.23(b), which clearly shows that EQ increases linearly with an increase in the Al content. The inset of Figure 7.23(b) illustrates an Arrhenius plot of the resistivity data for Alo.77Gao.23N, where a value of 41 meV for the Si donor activation energy (£"0) was obtained in this alloy sample. This deepening of £"0 is due to the fact that with an increase
AIN Epitaxial Layers for UV Photonics
165
in the Al content in AlGaN alloys, the bandgap and electron effective mass increase, while the dielectric constant and bandgap renormalization effect decrease. For pure AIN, an estimated value ofEo of about 120 meV is obtained by extrapolating the experimental data shown in Figure 7.23. Taniyasu et al. estimated that the donor ionization energy in heavily doped AIN is about 85 meV [116]. It is believed that, for optimized materials, the predominant cause for the rapid increase in resistivity of Al-rich Al^^Gai-^^N alloys with x is the deepening of the Si donor energy level. These recent experimental results indicate that we can achieve measurable n-type conductivity in pure AIN. The effect of persistent photoconductivity has been observed in Si-doped AIN grown by MBE, suggesting that Si may undergo a DX-like metastability [111]. However, more recent results seem to suggest that silicon impurities act more like an effective mass state [116,117], in agreement with a previous theoretical prediction [102]. These discrepancies may be accounted for by the fact that the concentrations of oxygen impurities and Al vacancies (VAI) or VAI complexes have been significantly reduced in highly conductive AlGaN alloys grown recendy by MOCVD and MBE. By further optimizing the growth condition and hence minimizing the effects of impurity compensation, it is possible to further improve the conductivity of pure AIN by heavy doping. 7,4,2 Mg Acceptors in AlGaN and AIN Understating the electrical properties of Mg-doped AlxGai-xN alloy is critical for further improving the p-type conductivity and hence the performance of optoelectronic devices based on these materials. Several groups have reported MOCVD growth and electrical properties of Mg-doped Al;cGai_;cN alloys with low Al contents [123-126]. The authors' group has achieved p-type conduction in Al;cGai-;cN epilayers for x up to 0.27 [127]. Mg doping in AIN has also been attempted. However, all as-grown and post growth annealed Mg-doped layers were highly resistive, although SIMS measurements revealed that Mgdopant concentration was about 7 X 10^^ cm~^ in Mg-doped AIN epilayers [127]. Figure 7.24(a) shows PL spectra measured at different temperatures for Mg-doped AIN epilayers. The low temperature (10 K) PL spectrum of an undoped AIN epilayer grown under identical conditions is also included for comparison. The band-edge transition at 6.06 eV is the dominant transition in undoped AIN epilayers, which is at a slightly higher energy position than those shown in Figures 7.6 and 7.14. Two broad emission lines with much lower emission intensities related with deep-level impurities at about 2.94 and 4.40 eV are also observable in undoped AIN at 10 K. Mg-doped AIN exhibits two dominant emission lines at 4.70 and 5.54 eV at 10 K, which are absent in undoped AIN and are thus attributed to Mg impurity related transitions. The spectral peak positions of these emission lines suggest that they are either band-to-impurity or DAP transitions. However, the slow component of the recombination lifetimes of both emission lines measured at 10 K are about 1 |JLS (not shown), which precludes the possibility for the band-to-impurity
166
Optoelectronic Devices: Ill-Nitrides (a) AIN: Mg
4
^
3
KSU-A1081
KSUA-1081 •
T=300K
(b)
....JxlO)
AIN: Mg Ep=5.54 eV Eo=60 eV
E _a)
(x10) _l
1 .-. ^ ^ - v i(x10) '
1 J fitted by Ln[l3jlo]=-Ln[1+ce-^o/kT]
0.00 2.0T
^.5.54 eV^
0.02
0.04
0.06
0.08
0.10
.
.
•
.
•
0.12
Ep=4.70 eV Eo=0.50 eV
•••^.^
\ / ^ 6.02 eV 4.70 e V N - / \ I
(180
6.06 eV
(x100)
T=10K, Undoped
^^
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.1 E(eV)
1.0 0.003
0.004
0.005
0.006
1/T(1/K)
Figure 7.24. (a) PL spectra measured at different temperatures for Mg-doped AIN epilayers. The low temperature (10 K) spectrum of an undoped AIN epilayer is also included for comparison. The arrows indicate the PL spectral peak positions, (b) The Arrhenius plots [ln(/emi) vs. 1/T] for two emission Unes in Mg-doped AIN: (a) 4.70 eV at r < 150 K and (b) 5.54 eV at T > 150 K. The solid Unes are the least squares fits of data with Eq. (7.1). The fitted activation energies (iE^o) ^ ^ indicated in the figure (after Ref. [127]).
type transitions which are known to have a recombination lifetime in the order of 1 ns in nitrides [128]. Figure 7.24(b) shows the Arrhenius plots of the PL intensities of the 5.54 and 4.70 eV emission lines in Mg-doped AIN measured in the temperature regions T < 150 and > 150 K, respectively. The solid lines are the least squares fit of data with the thermal activation behavior described by Eq. (7.1). The fitted activation energy £"0 (= 60 meV) for the 5.54 eV emission line again suggests that the 5.54 eV emission line is a DAP transition involving a Mg acceptor and a shallow donor (with an ionization energy of 60 meV). Although the ionization energy of the shallow donor involved in the optical transition is in agreement with a value estimated for substitutional shallow donors in AIN by the effective mass theory by taking an electron effective mass of m* = 0.33mo [129,130], the chemical nature of the donor impurity involved is not clear. Possible candidates are Si and O impurities. The monotonic decrease of the 5.54 eV emission intensity with increasing temperature shown in Figure 7.24(a) is due to the thermal dissociation of the shallow donors involved. By neglecting the Coulomb interaction between the ionized donors and acceptors {-e^/sr with r being the distance between the ionized donor and acceptor and s being the static dielectric constant), a value of Ep, = 0.52 eV for the Mg acceptor binding energy in AIN is deduced from E;, ^ E^ - 5.54 eV - 0.06 eV with £„ = 6.12 eV at 10 K [53].
AIN Epitaxial Layers for UV Photonics
167
The 4.70 eV emission line was assigned to a DAP transition involving a deep-level donor and Mg acceptor. Due to the competing recombination channel at 5.54 eV at low temperatures, the thermal activation process of the 4.70 eV emission line is more complicated than that of the 5.54 eV line. However, the Mg impurity level Ep^ can also be obtained simply from the Arrhenius plot of the 4.70 eV PL intensity for T > 150 K, above which the 5.54 eV emission hne is no longer present. Based on the PL spectral peak position of the 4.70 eV line, it can be concluded that the energy level of the donor involved is deeper than that of the Mg impurities. Thus, the thermal activation behavior of the 4.70 eV hne is a direct measure of the activation of Mg impurities. A value of EQ = 0.50 eV is obtained from Figure 7.24(b) for the 4.70 eV emission hne, which corroborates quite well with the Mg acceptor binding energy of 0.52 eV deduced from the Arrhenius plot of the 5.54 eV hne. Therefore, the Mg acceptor level in AIN is about 0.51(± 0.01) eV above the valence band. Again by neglecting the Coulomb interaction between the ionized donors and acceptors, the binding energy of the deep-level donor (E^) involved in the 4.70 eV transition can be calculated from E^^ ^ E^ - 4 JO eV - 0.5 eV « 0.90 eV. Based on the results shown in Figure 7.24, the energy diagram for the impurity levels in AIN can be constructed, as shown in Figure 7.25. The upper limit of Mg^ level in AIN is estimated to be about 0.97 eV if we assume that the Mg^ level is lined up within the bandgaps of GaN and AIN near the interface of a AlN/GaN heterojunction [131,132]. The conduction band offset parameter is assumed to be 70% for the GaN/AIN heterostructure and EA is 0.17 eV for Mg acceptors in GaN [125,133,134]. The lower limit of the Mg^ energy level in AIN is determined by the effective mass theory with values scattered
0.90 eV
T
1.81 eV
\ shallow donor 0.06-0.12 eV
CB
deep donorT 4.70 eV 5_54ev6.11eV 3.50 eV 0.17 eV • ^ -
0.80 eV (30 %) GaN
0.97 eV
MgO (calculated)
_
I Mg°(exp). 0.51 eV 1 AIN
0.421 eVt O.aOieV '
•
*_
VB
Figure 7.25. Energy diagram showing the impurity levels, including Mg acceptor level, in AIN. The upper limit of Mg acceptor level in AIN is estimated to be about 0.97 eV by lining up its energy levels within the bandgaps of GaN and AIN near the interface of an AlN/GaN heterojunction. The shaded region shows Ej^ predicted by the effective mass theory with uncertainty due to scattered values of the reported hole effective masses (after Ref. [127]).
168
Optoelectronic Devices: Ill-Nitrides
between 0.42 and 0.80 eV, as indicated by the shaded region in Figure 7.25, due to the uncertainty in the hole effective mass in AIN [135,136]. The experimental value of £A = 0.51 eV is close to the lower limit values obtained by the effective mass theory. By using the experimentally determined value of Ep^ = 0.51 eV and the high frequency dielectric constant of s(oo) = 4.6 [136,137], an average hole effective mass m^ of about 0.8mo in AIN is estimated, which agrees well with several calculation results [130,138]. The value of ml in GaN is determined to be about 0.46mo by using m}} = 2.03mo and m^ = 0.33mo [139]. The larger ml in AIN suggests a smaller hole mobility in AIN than in GaN. Figure 7.26 presents the determined Mg acceptor ionization energy in AIN and in Al;^Gai_;,N as a function of the Al content x. The dotted line is the linear extrapolation of data from Al^^Gai-^^N alloy with low Al content. The solid line is to guide the eyes by including the value for Mg-doped AIN. It is clear that the activation energy increases with the bandgap, as predicted by the effective mass theory. With the value of Mg acceptor ionization energy being determined for AIN, the issue regarding the possibility of achieving p-type AIN with Mg doping can be addressesed. As a consequence of the large value of Ej^ = 0.51 eV, only a very small fraction (e~^^^^^ = g-0.51/0.025 _ 2Q-9^ of the Mg dopants can contribute free holes for conduction at room
(a) 1.0
(b) 10^ AlxGa-i.xN: Mg
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AlxGa-i.xN: Mg guide to the eyes
16
D Hal-effect data
0.8
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0.2
0.4 0.6 0.8 Al content (x)
1.0
10^ 0.0
0.2
0.4 0.6 Al content (x)
0.8
1.0
Figure 7.26. (a) Mg acceptor activation energy in Mg-doped Al^Gai-;cN as a function of the Al content (x). Closed squares are data from AI^GSLI-XN of low Al contest as determined from Hall measurements, whereas the filled triangle is the data for AIN obtained from Figure 7.24(b). The dotted line is the linear extrapolation of data from Al;,Gai_;,N of low Al contest to x = 1 and the solid line is a guide to the eyes, (b) Calculated hole concentration (p) and resistivity (p) of Mg-doped Al^^Gai -J
AIN Epitaxial Layers for UV Photonics
169
temperature in Mg-doped AIN. This prevents the determination of any free hole concentrations by conventional measurements (such as Hall effect and capacitancevoltage). Based on the values of the Mg acceptor activation energies in Al^cGai-^cN shown in Figure 7.26(a), the hole concentration (p) and resistivity (p) of Mg-doped Al^^Gai-^cN as functions of the Al content x can be calculated and the result is shown in Figure 7.26(b). For a Mg dopant concentration (N^) of 10^^ cm~^ and a hole mobility (fi^) of 1 or 10 cvci'N s, the resistivity of Mg-doped AIN, p = (pfi^ey^, is estimated to be as high as p = 3 Mil cm with a free hole concentration of ;? = 2 X 10^^ cm~^ and a mobility of /Xh = 10 cm^A^ s. This implies that it is extremely difficult to achieve p-type AIN by Mg doping. It is also interesting to point out that the binding energy of Mg acceptor (0.51 eV) is comparable to that of C acceptor (0.50 eV) in C-doped AIN [140], indicating that p-type AIN is also very difficult to achieve by C doping. It was previously reported that low resistivity AIN epilayers could be achieved by C doping with a C fraction as high as 14% of AIN [141,142]. However, it is believed that C can no longer be treated as dopants in that case because such high C concentrations should instead form AlCN alloys with undetermined optical qualities.
7.5. AIN EPILAYERS FOR DEVICE APPLICATIONS 7,5,1 AIN Epilayer as a Template The benefits of inserting an AIN epitaxial layer as a template for the growth of subsequent Ill-nitride device structures have been demonstrated in several experiments [143,144]. Shibata et al. have shown that the FWHM of the XRD rocking curve of GaN grown on sapphire substrate with a low-temperature GaN (LT-GaN) buffer layers was 216 and 466 arcs for (0004) and (2024) reflections, respectively. However, the FWHM of GaN grown on an AlN/sapphire template exhibited low values of 61 and 232 arcs for (0004) and (2024) reflections, respectively [143]. Furthermore, smooth surface morphology, no pit termination with clear step formation, was observed in n-GaN grown on AlN/sapphire template as probed by AFM. The threading dislocation density of GaN grown on AIN/ sapphire templates was as low as 5 X 10^ cm~^ as probed by transmission electron microscopy measurements. Compared with the n-GaN grown directly on sapphire using a low temperature GaN buffer, cathodoluminescence measurements revealed a 50-60% reduction in dark spot density in n-GaN grown on AlN/sapphire template, indicating that the n-GaN epilayers grown on AlN/sapphire templates comprise lower dislocation density compared with the GaN grown directly on sapphire using LT-GaN buffer [143]. InGaN multiple-quantum-well LEDs were also grown on an AlN/sapphire template by MOCVD [144]. It was found that the FWHM of XRD rocking curves in GaN (0004) oy-lB scan mode were about 82.8 and 231.6 arcsec for the LEDs grown on an AlN/sapphire template and on sapphire, respectively. The results indicated that the LED structure on
170
Optoelectronic Devices: Ill-Nitrides
the AlN/sapphire template shows a better crystalline quality and more perfect interfaces than the one on sapphire using a LT-GaN buffer layer, which was due to the small mismatch in the lattice constant and the thermal expansion coefficient between the template and the GaN-based epilayers. Furthermore, the thermal stability of the LED grown on AlN/sapphire template was demonstrated to be superior to the LEDs deposited directly on sapphire substrate. As illustrated in Figure 7.27, the output power at 200 mA decreased by 7.3% for LEDs on the AlN/sapphire template upon increasing temperature from 25 to 95°C, while that for the LED on sapphire decreased by 23.9%. The peak external quantum efficiency decreased from 0.23 to 0.22% and from 0.15 to 0.10% for the LEDs on the AlN/sapphire template and on sapphire, respectively. The EL spectrum peak (a)
mu
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Current (m A) Figure 7.27. Temperature dependence of light output power (a) and external quantum efficiency (b) vs. current of LEDs grown directly on sapphire and on the AlN/sapphire template (after Ref. [144]).
AIN Epitaxial Layers for UV Photonics
111
at 20 mA shifted to lower energy by 17.2 meV for the LED on the AlN/sapphire template upon increasing temperature, while that for the LED on sapphire shifted by 32.7 meV. The results clearly demonstrated that the LED on the AlN/sapphire template exhibited a higher output power and a better thermal stability with respect to the conventional LED on sapphire using a low-temperature GaN buffer layer, which is due to the low threading dislocation density in the active layer and the high thermal conductivity of AIN layer [144]. Recently, several groups have successfully demonstrated the operation of deep UV emitters based on AlGaN alloys grown on AlN/sapphire template [145-149]. By employing a 350 nm thick high-temperature AIN epilayer together with a 30 period Alo.85Gao.15N/AlN (50 A/50 A) superlattice topped with a 50 nm AIN compliance layer as a dislocation filter, as illustrated in Figure 7.28, the growth of a very short wavelength AlGaN-based single quantum well UV LED structure with peak emission at 267 nm has been successfully carried out [147]. An output power of 4.5 mW in pulsed operation mode and 165 |ULW in CW operation mode was achieved for an array of four LEDs in parallel. These results demonstrated that high quality AIN epilayer template is indispensable in achieving Ill-nitride deep UV LEDs with high performance. So far, active devices based on AIN p - n junctions have not yet been attempted since p-type doping of AlGaN with high Al content has been very difficult. However, a very interesting work on n-AlN/p-diamond heterojunction diodes was carried out at the Walter Schottky Institute [37]. Si-doped wurzite (0001) AIN epilayer was grown on (100) naturally boron-doped diamond (p-type) substrates by plasma-induced MBE [38]. The surprisingly good structural quality of the AIN film was assessed by high resolution XRD. The fabricated p - n heterojunction diodes show clear diode characteristics with rectifying ratios between 10^ and 10"^ at low voltages. Under forward bias, an intense light emission in the blue (2.7 eV) and UV (4.8 eV) was obtained. Although the origin of the Hght
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| 1000 1060 1100 1160
Growth T(^C) Figure 7.28.
Layer structure of a 280 nm UV LED using AIN epilayer as a template (after Ref. [147]).
172
Optoelectronic Devices: Ill-Nitrides
emission was unclear, both the UV and the blue light emission were only detected under forward bias of the diode, pointing to an electron-hole recombination process through the interface. The presence of defects at the heterojunction interface should also allow tunneling-assisted emission processes, which was also suggested by the diode ideality factor of 3. The authors believe that many fabrication steps for n-AlN/p-diamond heterojunction diodes can be improved, such as growth parameters, AIN and diamond doping levels, contacts and device technology, etc. [38]. The work opens up interesting perspectives for future optoelectronic devices operating in the deep UV spectral region. 7.5.2 AIN for Surface Acoustic Wave Devices The increase in the operation frequencies of wireless communication systems has stimulated the research and development of high-frequency, low-cost, microelectronic filters with standard technological processes. SAW filters implemented on conventional piezoelectric materials (such as quartz or lithium niobate) are widely used in consumer electronics, in which frequency control is required. The resonance frequency of a SAW device is determined by the equation/ = Vph/A, where/is the resonance frequency, Vph is the phase velocity of the SAW, and A is the wavelength [150]. The wavelength A is primarily defined by the pitch of the interdigital transducer (IDT). From a materials point of view, there exist three main methods for increasing the frequency of operation of the SAW device [41]. In the first instance, high-velocity waves, such as leaky SAW, have been employed and materials such as LiTaOs and LiNbOs have shown high-phase-velocity waves ranging between 6000 and 7000 m/s [41]. In the second instance, materials, such as lithium tetraborate (Li2B407), the SAW velocity of which is 6780 m/s, have been developed [41]. Finally, improved SAW filter performance can also be achieved by using the layered structures of piezoelectric thin films grown on highvelocity substrates. For instance, zinc oxide (ZnO) on sapphire [151,152] and AIN on sapphire [153,154] have been developed, obtaining high velocities of 5500 and 6700 m/s, respectively. Thin piezoelectric film technology that enables one to choose the proper film/ substrate combination. AI2O3 nonpiezoelectric substrates and high-quality AIN piezoelectric films are ideal candidates for the realization of high-frequency [42,155-161] temperature-compensated [162,163], low-cost SAW filters due to their high SAW velocities and opposite temperature coefficients. More recently, the layered structure of AIN on diamond has been developed to take advantage of the high acoustic velocity as well as the high thermal conductivity of diamond [41]. Caliendo has characterized the acoustic and thermal properties of SAW delay lines, implemented on AIN thin and thick films sputtered on AI2O3 substrates at low temperature [42]. SAW delay lines working at frequencies up to 2.4 GHz were fabricated on poly crystalline AI2O3/AIN structures using only a simple optical lithography at 7.5 |ULm. Experimental electromechanical coupling factor and phase velocities of SAWs propagating along x- and ^-propagation directions, for different AIN film thickness to
173
AIN Epitaxial Layers for UV Photonics 5750-j
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0.0 0.2 04 06 08 10 1.2 1.4 1.6 1.8 20 2.2 h/X Figure 7.29. Theoretical dispersion curve (phase velocity vs. h/X) and experimental phase velocities (dots) for SAWs propagating along x- and y-axes of z-cut AI2O3/AIN structures. The theoretical curve takes into account only the interdigital transducer (IDT) electrical loading (Ref. [42]).
SAW wavelength (A) ratio (h/X), were estimated and were found to be in good agreement with the theoretical values relative to SAWs propagating in single-crystal AIN films on AI2O3 substrates. Figure 7.29 shows the theoretical dispersion curve (phase velocity vs. h/X) and experimental phase velocities (dots) for SAWs propagating along x- and j-axes of z-cut AI2O3/AIN structures. The theoretical curve takes into account only the IDT electrical loading. The opposite temperature coefficient of delay (TCD) of AI2O3 and AIN can allow the realization of temperature-compensated (temperature coefficient of frequency (TCF) = 0 ppm/°C) acoustic devices at a specific film thickness. For this purpose, the author measured the first-order TCF of AIN/AI2O3 structures for different h/X values. The TCF compensated point was found to be around h/X = 1.116 (/o = 2.39 GHz) with the estimated value of TCF equal to 0.5 ppm/°C. The experimental data confirm that AIN poly crystalline films have a negative TCD ( = - TCF); this value is asymptotically reached upon increasing h/X. In particular, TCD is equal to -23.45 ppm/°C for h/X = 1.86. These data provide the feasibility to achieve temperature-compensated SAW devices with proper AIN film thickness [42]. 7,5,3 AlN'based Field Emission Devices AIN is a promising material for field emitters because electrons in materials with nearly zero electron affinity can be easily extracted from the surface to vacuum [164]. The reported value ranges from negative to 0.25 eV [165,166]. High-performance electron field emitters have applications in vacuum microelectronic devices, such as field emission
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Optoelectronic Devices: Ill-Nitrides
displays (FEDs) and high-frequency micro-vacuum tubes. However, for AIN, the reported field emission current is too low, and the turn-on electric field is too high for the device application. The reason for the low-field emission current and high turn-on electric field is probably that the electron concentration in the undoped AIN samples is so low that the electrons necessary for field emission cannot be efficiently supplied to the surface [164]. Recently, Taniyasu et al. of NTT have not only demonstrated n-type conduction in AIN epilayers by Si doping [116], but also studied the field emission properties of Si-doped AIN by using a diode (sample-anode) configuration in an ultrahigh vacuum chamber [164]. They found that heavy Si doping is very effective in improving the field emission properties of AIN. As the Si doping concentration increases, the turn-on voltage decreases, and, consequently, the field emission current increases greatly. For a Si doping concentration, [Si], of 1 X 10^^ cm~^, the largest current density was as high as 220 mA/cm^. In addition, the field emission current was extremely stable; the fluctuation in field emission current over time was only 3%. The authors believe that there are three factors that contribute to the field emission properties of the heavily Si-doped AIN with [Si] ~ 10^^ cm~^. The first is the formation of a Si impurity band below the conduction band [116]. The electrons necessary for field emission are effectively supplied to the surface through this impurity band. The second is nearly zero electron affinity. Because the Si impurity band is around 86 meV below the conduction band in heavily doped AIN, the energy barrier for electrons in the Si impurity band is still low enough for the field emission. The third process is field enhancement due to sharp ridges induced by Si doping, whose top has a radius of curvature in the nanometer range [116]. The sharp ridge formation decreases the effective energy barrier of field emission and thereby enhances field emission efficiency. The authors estimated that the ridge effect decreases the energy barrier by 1.5 eV. Thus, Si-doped AIN is a very promising material for field emitters. More impressively, they have achieved a triode-type FED using heavily Si-doped AIN. Their FED has a vertical triode structure consisting of the heavily Si-doped AIN, mesh grid, and phosphor coated anode screen as shown in Figure 7.30(a). The heavily Si-doped AIN was set on the cathode electrode. The mesh grid was separated from the AIN surface by a glass spacer and acted as an extraction electrode. The field-emitted electrons were accelerated by the anode voltage. The electrons that pass through the Al thin layer excited the phosphor. The luminescence emitted from the phosphor was observed through the glass. After the FED fabrication, the air was evacuated from inside the FED and the vacuum pressure was kept at 7 X 10~^ Pa. Figure 7.30(b) shows photographs of the FED (a) before and (b) during operation. Green luminescence was emitted from the center of the phosphor screen. The luminescence area on the phosphor screen is almost the same as the opening area of the mesh grid. Uniform and bright luminescence was observed over the entire field emission area. The brightness increased as the field emission current IQ was increased. They obtained the brightness of 300 cd/m^ at VQ = 2.3 kV, Vj^ = S kV, and IQ = 16 jjuA. The authors believe that this
AIN Epitaxial Layers for UV Photonics
175
Figure 7.30. (a) Schematic diagram of the field emission display structure using the heavily Si-doped AIN. The device has a vertical triode structure consisting of the Si-doped AIN field emitter, mesh grid, and phosphor-coated anode screen, (b) The photographs of the FED (a) before and (b) during operation at VQ = 2.3 kV and FA = 8 kV. The green luminescence with the brightness of 300 cd/m^ is emitted from the center of the phosphor screen and scattered light is observed from the surrounding area (Ref. [164]).
brightness is high enough for display appHcation. The authors have also confirmed the stability of the field emission current and the luminescence properties in an actual FED, which originates from the high physical and chemical stability of the AIN surface due to the strong Al-N bond strength [164].
7.6. CONCLUDING REMARKS As a semiconductor material, AIN is about 10 years behind GaN in terms of its property control, basic understanding, and potential applications for optoelectronic devices. However, as of this writing, rapid progress has been made in epitaxial growth of AIN. The crystalline quality, surface morphology, optical quality, and the ability for conductivity control have improved significantly. By employing AIN epilayer as a template, UV LEDs with emission wavelengths shorter than 340 nm and milliwatts output power under CW operation have been achieved [145-149]. These recent results demonstrate that AIN materials are very promising for deep UV photonic device applications. However, methods for improved material qualities as well as conductivity control still need to be further explored. The use of AIN bulk single crystals as substrates are expected to reduce crystal defect densities due to its better lattice constant, and thermal expansion coefficient matches over other substrates. Thus epitaxial growth
176
Optoelectronic Devices: Ill-Nitrides
conditions for AIN epilayers and the subsequent UV emitter device structures on AIN bulk substrates have to be optimized. Due to the rapid evolution in material quality, basic properties of AIN remain to be probed for different structures (e.g. heteroepitaxial vs. homoepitaxial layers and epitaxial layers vs. bulk crystals) to gain insight into the fundamental values. These include the fundamental band structure parameters, effective electron and holes masses, dielectric constants recombination dynamics associated with the fundamental optical transitions, mechanisms of the impurity/defects (or defect complexes) related optical transitions, and n- and p-type impurity parameters. Properties of native defects and their effects on doping issues must be continuously investigated. The fundamental limit and hence the feasibility for achieving p-type doping needs to be continuously assessed. We envision that device quality conductive n-type AIN epilayers will be available within 2 - 3 years. This will enable the fabrication of active deep UV solid-state photonic devices down to 200 nm, which will open up many important and new applications. Furthermore, conductive AIN will be the first active dielectric material in which the index of refraction can be controlled by applying electric field or by carrier injection. This could bring out unforeseen properties and applications. Active devices in the wavelength scale have not been explored in deep UV wavelength regime. Nano-photonics involves photonic structures and devices with sizes comparable with the wavelengths of the light they manipulate (A/n), where n is the index of refraction, which is typically in the range of 50-200 nm for deep UV nitride devices. As the lateral size approaches the emission photon wavelength scale, quantum nature of light is expected to play an important role. Fundamental issues including the size effects (and surface effects) on the carrier dynamics in submicron and nano-cavities must be fully explored. Recent work has shown that both the surface recombination velocities in asgrown Ill-nitride epilayers and etched sidewalls are one order of magnitude lower than the corresponding values in GaAs [167,168]. This together with other unique features of Ill-nitrides makes them very attractive for the study of nano-photonic structures and devices. It would be very interesting to study the effects of artificially built-in photonic crystals and microcavities on the recombination processes of AIN based materials and devices. Ill-nitride photonic crystals are expected to possess special functionalities in the visible and UV spectral regions. It is our belief that Ill-nitride micro- and nano-photonics structures and devices will open many more important applications and is a burgeoning field with outstanding potentials. As we move toward deep UV wavelength (or ultra-wide-bandgap) regime, we have entered a virgin territory in the field of semiconductors. We are challenged in all fronts by this new class of semiconductor materials, ranging from material growth, characterization techniques, understanding new phenomena, to invention of new devices. Though the light emitted by AlGaN alloys dims with an increase of Al composition due to the diminishing ability of human eyes for seeing deep UV photons, we believe that the future
AIN Epitaxial Layers for UV Photonics
111
prospects of AlGaN-based materials and devices are bright because of the unique features of AIN that have already been revealed. AIN and AlGaN alloys are likely to become parts of solutions of a wide variety of problems ranging from improved efficient lighting for energy savings, national security, entertainment, medical and health care and information technology.
ACKNOWLEDGEMENTS We are indebted to the contributions from our group members: M.L. Nakarmi, K.B. Nam, J.Li, K.H. Kim, J. Shakya, N. Nepal, Z.Y. Fan, T. Oder, S.X. Jin, and K. Zhu. We gratefully acknowledge the theory input and collaboration of Dr. S.-H. Wei's group at NREL. The authors' research program at Kansas State University is supported by grants from ARO, NSF, DOE, and DARPA.
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Lakowicz, J.R. (1999) Principles of Fluorescence Spectroscopy, 2^^ Edition. Bergh, Craford, G., Duggal, A. & Haitz, R. (2001) Phys. Today, December, 42. Yoshida, S., Misawa, S. & Itoh, A. (1975) Appl Phys. Lett., 26, 461. O'clock, G.D., Jr. & Duffy, M.T. (1973) Appl. Phys. Lett., 23, 55. Khan, M.A., Kuznia, J.N., Skogman, R.A., Olson, D.T., Millan, M.M. & Choyke, W.J. (1992) Appl. Phys. Lett., 61, 2539. Militello, M.C., Gaarenstroom, S.W. & Simko, S.J. (1992) Surf. Sci. Spectra, 1, 3. Chourasia, A.R., Chopra, D.R. & Hatwar, T.K. (1992) Surf. Sci. Spectra, 1, 75. Saxler, A., Kung, P., Sun, C.J., Bigan, E. & Razeghi, M. (1994) Appl. Phys. Lett., 64, 339. Okano, H., Tanaka, N., Takahashi, Y., Tanaka, T., Shibata, K. & Nakano, S. (1994) Appl. Phys. Lett., 64, 166. Meng, W.J., Sell, J.A., Perry, T.A., Rehn, L.E. & Baldo, P.M. (1994) J. Appl. Phys., 75, 3446. Vispute, R.D., Narayan, J., Wu, H. & Jagannadham, K. (1995) J. Appl. Phys., 77, 4724. Chaudhuri, J., Thokala, R., Edgar, J.H. & Sywe, B.S. (1995) /. Appl. Phys., 77, 6263. Keying, B., Wu, X.H., Keller, S., Li, Y., Kapolnek, D., Keller, B.P., DenBaars, S.P. & Speck, J.S. (1996) Appl. Phys. Lett., 68, 643. Zhu, Q., Botchkarev, A., Kim, W., Aktas, 6., Salvador, A., Sverdlov, B., Morkog, H., Tsen, S.-C.Y. & Smith, D.J. (1996) Appl. Phys. Lett., 68, 1141. Dovidenko, K., Oktyabrsky, S., Narayan, J. & Razeghi, M. (1996) /. Appl. Phys., 79, 2439. Johnson, M.A.L., Fujita, S., Rowland, W.H., Jr., Bowers, K.A., Hughes, W.C., He, Y.W., ElMasry, N.A., Cook, J.W., Jr. & Schetzina, J.F. (1996) /. Vac. Sci. Technol. B, 14, 2349. Hossain, F.R.B., Tang, X., Wongchotigul, K. & Spenser, M.G. (1996) Proc. SPIE, 1%11, 42. Zettering, M., Ostling, M., Wongchotigul, K., Spencer, M.G., Tang, X., Harris, C.I., Ordell, N. & Wong, S.S. (1997) /. Appl. Phys., 82, 2990. Malengreau, F., Vermeersch, M., Hagege, S., Sporken, R., Lange, M.D. & Caudano, R. (1997) /. Mater Res., 12, 175.
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optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 8
Properties of III-V Nitrides Substrates and Homoepitaxial Layers Jaime A. Freitas Jr. Naval Research Laboratory, Electronic Science and Technology Division, Electronic Materials Branch, Washington, DC 20375, USA
8.1. INTRODUCTION The unique combination of extreme values of fundamental physical and chemical properties rank the III-V nitride semiconductor system as one of the most promising material systems for the fabrication of a variety of optical and electronic devices capable of performing at extreme conditions of power, frequency, temperature, and in harsh environments. Despite the remarkable improvement in the quality of thin heteroepitaxial GaN and AIN films achieved in the last decade, their properties are still seriously limiting the performance of devices demanding higher material yields, e.g. laser diodes and highfrequency/power devices. The high growth temperature usually required to produce these wide bandgap materials exacerbates fundamental material problems such as residual stress, difference in thermal expansion coefficient, low energy defect formation, and impurity incorporation. In addition, doping activation and self-compensation are difficult to control at the typically high deposition temperatures. Overcoming these limitations will require the use of native substrates to grow electronic grade homoepitaxial layers. Nominally unintentional doped (UID) heteroepitaxial GaN films, deposited commonly on sapphire or SiC, are partially compensated and have room temperature net free-electron concentrations typically between ~ 5 X 10^^ and ~ 1 X 10^^ electrons/cm^. These films can be doped with Mg to reproducibly achieve p-type conductivity with concentration in the lower 10^^ holes/cm^ range [1]. The control of the conductivity type led to the fabrication and commercialization of a number of optical devices, despite the high concentration of dislocations (typically between 10^ and 10^^ cm~^), the limitation on the hole concentration, and the lack of identification and further reduction of the background donor concentration. A number of models were suggested to explain the large background concentration of free-electrons observed in UID heteroepitaxial GaN films. Previous
E-mail address:
[email protected] (J.A. Freitas, Jr.).
185
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Optoelectronic Devices: Ill-Nitrides
calculations have indicated that the nitrogen vacancy (Ny) could behave as the active shallow donor in GaN [2]. Basically, a Ny would form a void surrounded by four Ga atoms contributing with three electrons, from which two of them will reconstruct leaving a single electron available for conduction. However, more recent first-principles calculation results have shown that the formation energy of Ny is too high to allow the incorporation of such a high concentration of donors during the growth [3]. Detailed electronic transport studies of electron irradiated samples showed conclusively that the binding energy of Ny donor is considerably higher than that observed for shallow donors in UID films [4]. Although impurities such as oxygen and silicon have been considered as the potential pervasive shallow donors in GaN, only recently detailed experimental work had identified the chemical nature of the these donors [5]. Despite the considerable progress accomplished lately for the growth of bulk AIN, large area bulk AIN is not fully developed and commercialized yet. Previously, low-temperature (amorphous) and high-temperature (polycrystalline) thin (< 1000 A) AIN films were employed mostly as intermediated layers (nucleation/buffer layers) for GaN heteroepitaxial growth on sapphire and SiC, respectively [6-9]. Increasing interest on optical devices operating at deep-UV wavelength range has motivated the material scientists to grow high-quality AIN heteroepitaxial layers [10-12]. AIN has been deposited by both MOC VD and MBE techniques, and more recently by hydride vapor phase epitaxy (HVPE) [13-15]. Surface preparation and structural properties of heteroepitaxial AIN have been investigated in detail [16,17]. Plan view and cross-sectional TEM studies verified that the dislocation density of these heteroepitaxial layers are typically between ~ 1 X 10^ and 2 X 10^^ cm~^, which are close to the values commonly observed in heteroepitaxial GaN films [18]. Typically, UID AIN films are insulators. Research on carbon doping of AIN indicates that p-type conductivity with hole mobility of 60 cm^fV s was achieved for a doping level of ~ 10^^ cm~^ [19]. n-Type conductivity has been reported for Si-doped AIN films with electron concentration of about 1 X 10^^ cm~^ [20]. Attempts to increase the free-electron concentration resulted in lower net carrier concentration, which suggests that self-compensation is dominant at high doping levels. The potential difficulties on controlling the electrical properties of AIN substrates may indicate that this material will be more suitable for passive applications such as substrates for optical devices and highfrequency devices based on ternary or quaternary alloys with high Al content. Considering that AIN has the same crystallographic structure as GaN, it may be an adequate substrate option to replace sapphire and/or SiC for heteroepitaxial growth. As summarized in Table 8.1, except for the lower thermal conductivity value as compared to SiC, AIN seems to be a foreigner substrate of choice for GaN epitaxial growth. This chapter will review the status of growth of bulk and thick freestanding (FS) III-V nitride substrates and their structural, optical, and electronic properties, and their potential application as substrates for epitaxial growth.
Properties of III- V Nitrides Substrates and Homoepitaxial Layers
187
Table 8.1. Comparison between some properties of GaN and commonly used substrates Material Parameter
GaN
AIN
AI2O3
Si
6H-SiC
ZnO
Aa/fl (%)
0 1.7 [22] 2.1 [23] 3.1 [30]
-2.4 2.85 [24]
- 1 6 [21] 0.25 [25]
- 1 7 . 6 [21] 1.56 [26]
-1.9 0.54 [29]
3.48 [31]
5.0 [25]
2.616 [32]
-3.5 4.9 [27] 3.9 [28] 4.46 [33]
K (W/cm K)
4.75 [34]
8.2. GROWTH OF III-NITRIDE SUBSTRATES The III-V nitrides or Ill-nitrides semiconductors crystallize in the wurtzite structure and cubic structures such as zinc blende (sphalerite) or rock salt. The thermodynamically stable structures are wurtzite for bulk AIN, GaN, and InN and zinc blende for BN. The rock salt structure is stable only at elevated pressures [35-37]. The cubic zinc blende phase of GaN and InN are metastable and have been realized only in thin heteroepitaxial layers deposited on highly mismatched substrates (OOl)-oriented, e.g. GaAs, InAs, MgO, Si, and p-SiC [38-43]. Ill-nitrides cannot be grown from the stoichiometric melts by well-established techniques such as Czochralski or Bridgman because of the extremely high melting temperatures and very high decomposition pressures for nitrogen, as indicated in Table 8.2. Therefore, crystal growers across the world have modified or adapted different methods requiring lower temperatures and pressures to grow Ill-nitride semiconductors. 8.2.1 Growth of Bulk and Thick-film GaN There are several techniques under development for producing bulk GaN crystals including vapor phase transport, growth from supercritical fluids, and growth from flux [49-53]. However, only high-pressure-high-temperature (High nitrogen Pressure Solution technique, HPS) and HVPE methods have produced large area substrates, which will be discussed in detail in this chapter. Unseeded GaN hexagonal platelets or needles (the latter formed at higher supersaturation conditions) have been grown by the HPS method from gallium melts saturated Table 8.2. Melting conditions for Ill-nitrides semiconductors Material AIN GaN InN
T (K), theory
PN^ (kbar)
~ 3500 [44] - 2 8 0 0 [46] - 2 2 0 0 [44,45]
0.2 [45] 45 [47,48] 60 [45]
188
Optoelectronic Devices: Ill-Nitrides
with 1 at.% nitrogen at temperatures up to 1700°C and nitrogen pressures of 20kbar [54-56]. The supersaturation in the growth solution is achieved by the application of a temperature gradient of 2-20°C/cm along the axis of the crucible. The nitrogen dissolves at the hotter end of the crucible and the GaN crystallizes at the cooler end. For a typical process duration of 150-200 h relatively thin (—300 |xm thick) hexagonal platelets are grown with a rate of <0.1 mm/h, in the{ 1010} directions (perpendicular to c-axis), with maximum lateral dimensions up to 10 mm X 14 mm. The mechanism hindering the lateral growth of the platelets after 150-200 h can be related to changes in the mass transport mechanisms in the solution due to the presence of the crystal [57]. The (0002) XRD rocking curve full width at half maximum (FWHM) of these crystals are typically between 30 and 40 arcsec showing the presence of low angle (1-3 arcmin) boundaries separating grains of 0.5-2 mm in size [58]. High-resolution transmission electron microscopy studies indicate that threading dislocations commonly observed in heteroepitaxial GaN films are not detected in the HPS bulk GaN. Planar defects such as stacking faults and dislocation loops are present in large concentrations on the crystal basal plane, mostly at the rough side of the crystal (the initial growth surface, where the density can be as high as 10^ cm~^), but their concentrations reduce drastically with increasing film thickness [59]. Growth of crack free UID GaN films with thickness ranging from 100 to 300 |xm on two-inch c-plane sapphire substrates using the HVPE technique have been reported by a number of research groups [60-62]. The substrates are placed on a 1030°C horizontal susceptor in a hot-wall HVPE reactor. Ga metal and HCl are pre-reacted to form GaCl gas, which is transported by nitrogen carrier gas to the hot growth-zone where it reacts with NH3 and deposits GaN on the (0001) sapphire substrate. For a V/III ratio from 20 to 35, a growth rate between 30 and 100 |xm/h can be reproducibly achieved. These thick layers can be removed from the sapphire substrates by laser-assisted lift-off (248 nm line of KrF laser, with 20 ns pulse width and 50 Hz pulse rate). A laser beam energy density of 0.2-0.3 J/cm^ was enough to release the nitrogen from the film forming a thin layer of liquid Ga at the film/substrate interface. To prevent fractures induced by the wafer bowing during the laser lift-off process, the GaN/sapphire templates were kept hot at a temperature below the decomposition temperature [60]. The growth surfaces of the FS GaN templates are extremely rough with large number of hillocks, and so they are inadequate for homoepitaxial growth. Flat, smooth surfaces are obtained after mechanical polishing, which introduces subsurface damage extending up to 4000 A below the surface. The polished growth surfaces (Ga-face) are reactive ion etched (RIE) to remove the damage [61]. Efficient chemical-mechanical polishing process of the growth surface is still in development. GaN (0002) XRD reflections obtained from the FS-UID HVPE-GaN wafers were measured at both surfaces (growth and interface) and with different wafer orientations for beam widths of 500 and 100 |xm in order to establish the source of the rocking curves broadening. The reflection intensities versus angle of the sample scanned with the 500 [xm
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
189
beam at the growth surface and the interface, measured with two orientations rotated 90° around the c-axis in reference to the cleavage plane, resulted in asymmetric lines with FWHM values between 633 and 721 arcsec, clearly showing multi-components contribution [63]. Note that these values are nearly identical, indicating that they are independent of the surface and orientation of the wafer. Measurements performed with 100 |jLm beam width results in sharp symmetric lines with 56 and 162 arcsec for the front and back surfaces, respectively, as shown in Figure 8.1 [63]. From the difference in the horizontal scales used in the plots, we conclude that the irregular broadening observed with the larger beam is due mostly to the larger number of imperfections seen by the beam. The range of angular variations and mosaicity is effectively limited to within the region of a single grain, such that the observed broadening in this case characterizes the mosaicity within the grain. The dislocation density of these substrates is typically < 10^ cm~^ [61]. Thick HVPE GaN substrates have also been realized on GaAs (111) using a two-step growth process, which basically is accomplished by depositing a low temperature 50 nm thick GaN buffer layers prior to the growth of the high-temperature film deposited at 1000°C. These GaN films can be easily removed from the substrates by selective etching. Films with 100 iJim of thickness have typical X-ray rocking curve FWHM of 4.7 min and dislocation density of < 10'^ cm~^ [64]. A number of techniques have been modified to use seeds in the attempt to increase crystal growth rate. HPS grown GaN platelets have been successfully used as substrates for subsequent re-growth in the c-axis ((0001)) direction by HPS and HVPE methods [65]. 1.2
1.0
"T
1
\
1
1
J—I \
1
\
1
p
"1~~^—I
I
I
I
I
I
I
GAN FS-HVPE Sample#2
2 0.6
0.4 h
Front
0.2 h 0
,i^^^^^^*^^
-600 -500 -400 -300 -200 -100 0
100 200 300 400 500 600
Relative Crystal Angle (arc-sec) Figure 8.1. X-ray rocking curves measured with 100 jxm beam width. Note the large difference on the FWHM between the spectrum acquired in the growth surface and the interface side of the FS-HVPE GaN substrate (after Ref. [63]).
190
Optoelectronic Devices: Ill-Nitrides
Growth rates of about 10 and 50 ixm/h were achieved on the Ga-polar (0001) face of the substrates using HPS and HVPE techniques, respectively. Samples grown by both methods resulted in substrates with fewer than 100 dislocations/cm^. Recently, recrystallization of GaN powder using FS-HVPE substrates seeds have been accomplished by using powder precursors mixed with molten inorganic salt-fluxes at high-pressure and high-temperature conditions [66]. Samples of 15 mm X 18 mm size with dislocation densities lower than 100 cm~^ were produced. Another approach to synthesize larger GaN samples employed the fast growth rate characteristic (over 100 juum/h) of the HVPE technique and selected FS-HVPE substrate, to realize GaN boules longer than 3 nmi in length. Wafers cut from these boules typically show (0004) X-ray rocking curve FWHM of 38 arcsec and dislocation density less than 10"^ cm~^ [67]. 8.2,2 Growth of Bulk and Thick-film AIN Bulk AIN crystals have been produced by sublimation, vaporization, and solution routes [68]. The nitrogen vapor pressure over AIN is six orders of magnitude lower than over GaN, which makes it possible to grow bulk crystals at atmospheric or subatmospheric pressure [69]. Due to the excessively high melting point, estimated over 2800°C, AIN cannot be grown from the melt. AIN has been successfully grown by sublimation, but the high reactivity of aluminum gas at high sublimation temperatures (typically around 2000°C) cause problems with regards to AIN purity and crucible stability [70-72]. The largest crystal dimensions previously reported was of 470 mm^ [72,73]. In this technique, the AIN precursor, prepared by direct reaction of aluminum powder and nitrogen at 1850°C, was sealed in a tungsten crucible and an unseeded multi-grain crystal grew at the rate of 0.3 mm/h at 2250°C in a nitrogen atmosphere. Samples produced by sublimationrecondensation technique are continuously improving. Boules of 15 mm diameter, grown at a 0.99 mm/h rate, are easily reproduced. These boules contain grains exceeding 1 cm, which typically show X-ray rocking curves with FWHM of around 100 arcsec or less and dislocation density less than 10"^ cm"^ [74-76]. Recently, crystals with X-ray rocking curve of FWHM less than 10 arcsec and dislocation densities of 800-1000 cm~^ have been fabricated [77]. Bulk growth techniques that minimize the effects associated with container reactions and impurity inclusions are highly desirable. Bulk AIN crystals with centimeter-sized areas have been fabricated using RF energy, oscillating at frequencies between 450 kHz and 4 MHz at power levels up to 100 kW, to directly heat the precursor kept at pressures over 100 atm to prevent decomposition. Crystals with X-ray rocking curve with FWHM of 27 arcsec have been produced [78]. Polycrystalline AIN boules of 1.25-in. diameter with centimeter-sized crystals have also been fabricated by vapor phase technique in a RF heated reactor, under a 600 Torr nitrogen atmosphere, in the temperature range between 2000 and 2400°C. Growth rate of 0.3 mm/h was achieved under these conditions [79]. Large boules of AIN crystals, with 25 mm diameter and 15 nmi in length, have been
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
191
fabricated by physical vapor transport technique using AIN powder and N2 gas as precursors, in the temperature range between 2100 and 2250°C and pressure between 200 and SOOTorr [80]. Microprobe analyses indicate that these crystals are free of residual impurities such as carbon and oxygen. X-ray rocking curve studies show a single line with FHHM value of 0.08°. Large area, ranging from 0.5 to 1.75 in. diameter, thick (0001) AIN films have been deposited on Si and/or SiC substrates by HVPE technique, and chemically removed from the substrates [81]. These FS films were used as seeds to grow AIN boules of few millimeters of thickness. Wafers of 200-500 ijum of thickness were sliced from the boules. After lapping and polishing, selected wafers were used again as seeds for the growth cycle to improve the boules crystalline quality. The typical value of the X-ray rocking curve FWHM of the (0002) reflection is of 700 arcsec, using a wide (10 mm X 1 mm) X-ray beam [82]. Spontaneous nucleated AIN crystals can also be grown from the single precursor A1C13-NH3. This process requires several successive steps, namely, the synthesis of A1C13-NH3, the evaporation and transport to a reaction chamber and the decomposition and growth of single crystal AIN. The dry A1C13-NH3 is obtained by a sequence of few processing steps. Initially, dry AICI3 is produced after heating pure Al powder in dry HCl flow. The AICI3 is saturated with ammonia at 150°C to form a polyammoniate polycrystalline powder with composition AlCl3-(1.5-2.5NH3). The polyammoniate is slowly heated in He flux at 417-420°C to distill the white monoammoniate powder. The distilled A1C13-NH3 precursor powder is placed in the cold zone of a two-zone quartz tube reactor. The temperature of the evaporator is increased up to 300-320°C to produce A1C13-NH3 vapor subsequently transported by hydrogen or helium carrier gas to the hotter zone to decompose the A1C13-NH3 and grow the AIN crystals. AIN platelets with hexagonal cross-section (up to ~4naLm^ and 150 juim thick) are spontaneously nucleated on graphite or quartz substrates in the temperature range between 1300 and 1400°C. A detailed discussion of the growth technique has been reported elsewhere [83]. The AIN (0002) XRD reflections obtained from various samples fabricated from monoammoniate, using a beam width of 500 |xm, show symmetric lines with FWHM between 36 and 54 arcsec. Figure 8.2 shows an XRD line with FWHM of 36 arcsec measured on one hexagonal platelet with an area of about 3 mm^ [84]. The small FWHM value and the high intensity of the single-line indicate the high single-crystalline quality of this sample.
8.3.
STRUCTURAL PROPERTIES OF III-NITRIDES SUBSTRATES
The lattice parameters of semiconductors are affected by factors such as stoichiometry, excess of free-carriers, high concentration of point and extended defects, external stresses
192
Optoelectronic Devices: Ill-Nitrides 10.0 [ AIN (decomposition) Sample#2 7.5
CO
O
^5.0 36 arc-sec
2.5
-300
-200
-100
0
100
200
300
Relative Crystal Angle (arc-sec) Figure 8.2.
Room temperature first-order polarized Raman scattering spectra of a ~ 167 iJim thick FS-HVPE GaN substrate (after Ref. [84]).
(e.g. heteroepitaxial layers), etc. Therefore, Ill-nitride lattice parameters are still not completely determined. Lattice parameters values acquired from samples fabricated by different techniques are listed in Table 8.3, illustrating the effects of the material quality on its lattice parameter values. Ideal wurtzite structure is characterized by lattice parameter ratio (c/a) and w-parameter value (u = bic, where b is the bond-length in the c-direction) of 1.633 and 0.375, respectively [91]. The deviation from this ideal arrangement occurs with changing of da ratio and/or the M-parameter. Although deviations from the ideal arrangement are often observed in the wurtzite structure, the correlation between the da and the M-parameter is kept: if da decreases, than the u value increases in such a way that the four tetrahedral distances remain nearly constant and the tetrahedral angles are distorted [92]. Compounds characterized by larger departure from the ideal da ratio show greater differences in Table 8.3. Lattice parameter of wurtzite AIN and GaN fabricated by different techniques Crystal (description) AIN (bulk) AIN (powder) AIN (on SiC) GaN (homoepitaxial layer on bulk GaN:Mg) GaN (bulk, 5 X 10^^ electrons/cm^) GaN (powder) GaN (on sapphire)
a{k)
^(A)
Reference
3.1106 3.1130 3.110 3.1885 3.1890 3.1893, 3.190 3.1892
4.9795 4.9816 4.980 5.1850 5.1864 5.1851, 5.190 5.1850
[85] [86] [87] [87] [88] [86,89] [90]
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
193
Table 8.4. Structural parameters of potential GaN substrates Material AIN GaN ZnO
c/a
u
.601 [93] .627 [93] .6024 [91]
0.385 [91] 0.377 [91] 0.345 [91]
the electronegativities [92,93]. Only wurtzite structures with c/a ratio lower than the ideal value of 1.633 are stable. These structural parameters for GaN, and AIN and ZnO, potential substrates for GaN epitaxial grown, are listed in Table 8.4. Note that the w-parameter for GaN is very close to its ideal value, while AIN is above and ZnO is below this value. The Ill-nitrides commonly have their faces perpendicular to the c-axis. These faces are polar with either nitrogen or gallium termination. There has been a considerable controversy in regards the identification of GaN face polarities [94,95]. Presently, there is a common agreement that the nitrogen-terminated face is chemically active, whereas the gallium-terminated face is inert. Therefore, the face polarity can be easily identified by selective chemical etching techniques [96]. The hexagonal (2H) phase of GaN and AIN (wurtzite structure belonging to the space group C^^ or P6^mc) has two molecules per unit cell. Group theory predicts eight zonecenter optical modes, namely lAi(TO), lAi(LO), 25i, l£:i(TO), 1J&I(LO), and 2^2. The two BY modes are optically inactive, but all of the six allowed modes have been observed by Raman spectroscopy [97,98]. The first order Raman scattering (RS) spectra of a FS-HVPE GaN sample measured at room temperature for different sample orientations and light polarizations are represented in Figure 8.3. Using sample orientation and polarization selection rules for the incident and scattered light we measured the first order Raman spectra with the Z{X,XY)Z, Y{Z,XZ)Y, and Y{X,XZ)Y symmetries, as represented in Figure 8.2 by Porto's notation [99]. The Raman shift for the allowed modes Ai(TO), £i(TO), El, Ai(LO) and £i(LO) are 534, 559, 569,734, and 740 cm~\ respectively. Analyses of the peak positions and linewidths of the observed first order phonons confirm the good crystalline quality and lower biaxial stress of the wurzite FS-HVPE GaN substrates [63]. RS spectra of a number of GaN samples fabricated by HPS method also show most of the optical phonons expected for the 2H-GaN polytype. However, due to the high background concentration of free-electrons in these samples, the Ai(LO) mode is replaced by a new mode resulting from the interaction between the Ai(LO) with the conduction electron plasmons [100]. High-quality AIN crystals fabricated by thermodecomposition of aluminum chloride monoammoniate, was used to study the first order RS spectra of AIN. Figure 8.4 shows the Raman spectra measured at two different sample orientations and light polarizations. The Raman fines for the allowed modes Ai(TO), £:i(TO), El, Ai(LO) and £i(LO) are
194
Optoelectronic Devices: IILNitrides
GaN FS-HVPE Sample#2
'^exc =514.5 nm
I A^(LO) o
10^'
10^" 300
400
500
600
700
800
900
Raman Shift (cm''')
Figure 8.3. XRD reflection of the c-plane AIN fabricated from monoammoniate precursor (sample#2) measured with beam width of 500 jjim (after Ref. [63]).
observed at 608.5, 667.2, 655.1, 888.9, and 909.6 cm~ , respectively. The peak positions and relatively small linewidths of the phonon lines indicate that this low-temperature growth process can fabricate low defect and stress-free crystals. A complete discussion of the RS study will be presented elsewhere [101].
8.4.
OPTICAL AND ELECTRONIC PROPERTIES OF III-NITRIDE SUBSTRATES
Wurzite GaN has the conduction band minimum at the center of the Brillouin zone (F-point, k = 0), and has a r7-symmetry with a quantum number J^ = 1/2. The valence band of 2H-GaN has its maximum also at the F-point, which results in a direct fundamental bandgap. As result of the crystal-field (4cr) and spin-orbit {A^Q) coupling, the top of the valence band splits into three sub-bands with symmetries Fg, F-j^^^^^^, and F'^IQ^^J.^ which are traditionally labeled A, B, and C, respectively [102-108]. There is a considerable disagreement on the value of the fundamental bandgap due to residual strain within the individual samples, which causes a considerable large variation in the value of A^rIn addition, uncertainty in the Rydberg value to be added to the exciton energy increases the uncertainty of the fundamental bandgap energy. Assuming the thick HVPE GaN is stress-free and using a Rydberg value of 24 ± 3 meV the low-temperature bandgap of 2H-GaN has been estimated to be 3.499 ± 6 eV [109].
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
195
zouu X(Z,YZ)X 2000- AIN decomposition 2 +2 Sample#2 ^2 o 1500O Ai(TO) 2 1000-
Ei(TO)
1\ Jli
Ei(LO)
1
500-
p i
'^
NlMyi«ii.i»<(l>ifrtl^***^
n ^lf<)w^*|*»w*^<Ml»^>wn|<^*f»W•^l'«|'>"*''*'**l^<>W'"'V*^#'^ 200 300 400 500 600 700 800 900 7000_
6000-
1 o ^
5000 -
>^
1
E2|
Z(Y,XY)Z AIN decomposition Sample#2
^
4000-
3000-
0)
1
20001000-
Ai(LO)
E2^ 1
>
L
,,.A-
— 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1 — 1
02()0 300 400 500 600 700 800 900 Raman Shift [c;m-i]
Figure 8.4. Room temperature polarized Raman spectra of bulk AIN grown by thermodecomposition of AICI3NH3. The letters inside the parentheses represent the incident and the scattered light polarization, while the letters outside of the brackets represent the direction of the incident and scattered light (after Ref. [101]).
Reported calculations of AIN generally agree that the A^^ is negative and promotes the ^7upper band to higher energy than the Tg band. However, there is a considerable disagreement with regard to the calculated values for effective masses (m* between 0.27 and 0.35mo, and m^ between 1.54 and 1.62mo), crystal field, and spin-orbit splitting [103,107,110]. There is also a considerable discrepancy in the measured values of the dielectric constant of AIN [111,112]. However, we can estabUsh lower and upper bound values for the free-exciton energy of 37 and 70 meV, respectively. Thus, assuming that the bandgap at low temperature is 6.12 eV, we expect to observe excitons in the spectral range between 6.05 and 6.08 eV [84,113]. 8.4.1 Bulk and Thick-film GaN Bulk GaN crystals grown by HPS method are typically n-type and degenerate, with temperature-independent carrier concentration and mobilities typically between
196
Optoelectronic Devices: Ill-Nitrides
10^^-10^^ cm"^ and 30-90 cm^A^ s, respectively [100]. This result is consistent with the strong LO-phonon/conduction electron-plasmons couphng mode observed in the Raman spectra [100]. Oxygen is assumed to be the shallow donor responsible for the observed high concentration of free-electron [114]. The low-temperature PL spectra of such samples typically show an intense broad band with peak around 2.25 eV and a weelc and relatively broad bandedge emission near 3.5 eV [115]. The large shift of the edge emission results from the large concentration of free carriers causing the semiconductor-metal transition, or the so-called Bumstein-Moss effect [116,117]. Unintentionally doped thick FS-HVPE GaN films are also typically n-type, but with much lower background free-electron concentration than HPS bulk GaN. Detailed electrical transport experiments yield a room temperature carrier mobility of 1245 cm^A^s and a carrier concentration of 6.7 X 10^^ cm~^ for an acceptor concentration of 1.7 X 10^^ cm"^ [118]. Assuming an ideahstic reduction of two orders of magnitude of the background donors and acceptors, to keep the same compensation level, the maximum mobility at room temperature is expected to reach 1350 cm^fV s [118]. Low-temperature PL spectra of similar UID FS-HVPE GaN films typically show intense recombination emission lines associated with annihilation of excitons bound to neutral donors (X-D^) and their phonon replicas (nLO-XD^). Also commonly observed are weak zero-phonon lines from shallow-donor/shallow-acceptor pairs (DAP) recombination and their phonon replicas (nLO-DAP). Broad luminescence bands observed below 3.0 eV are discussed elsewhere [119]. Figure 8.5 shows the PL spectra of a ~12|jLm thick heteroepitaxial film (sample#l) from reactor 1 and a ~ 150 [xm thick FS film (sample#2) from reactor 2. The spectrum of sample#2 shows, in the 3.52-3.46 eV region, emission lines related to the excited state of the free-exciton A (FX^), the ground state of the freeexciton B (FXB), the ground state of the free-exciton A (FXj^), and the dominant exciton bound to a neutral donor (X-D^). Around 3.45 eV we detect the so-called two-electron satellite (2ES) spectrum resulting from the recombination processes in which the neutral donors are left in an excited state after the exciton annihilation. Note that for energies below 3.42 eV we observe the one-phonon replicas of all features listed above. The PL spectrum of sample#l, dotted line, shows most of the features observed in the spectrum of sample#2. However, these features are broader and smeared, and shifted to higher energy due to inhomogeneous broadening and compressive strain, respectively, caused mostly by the substrate [120]. Figure 8.6 shows four PL spectra of sample#2 measured with higher resolution (bandpass < 100 fieV) at 5 K under several laser excitation intensities, as indicated in the figure. The dominant features in all spectra are emissions associated with the recombination of ground-state excitons bound to neutral donors (often designated I2, or X-D^) centered around 3.4714(2) eV (all energy values are corrected for index refraction of air). The dominant peak is composed of three peaks at 3.4714(4), 3.4718(9), and 3.4722(8) eV (average values obtained from a number of measurements), assigned to A excitons bound to different neutral donors [121]. To identify the chemical nature of these
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
10^
105
197
GaN FS-HVPE Sample#2 6K
o CD
104
^ w
103
5^
102
10^
10°
3.34
3.38
3.42 3.46 Energy (eV)
3.50
3.54
Figure 8.5. PL spectra (6 K) of a —12 ijum heteroepitaxial film (sample#l) and of a —150 |xm thick freestanding film (sample#2). The presence of a variety of sharp excitonic lines in this spectral region indicates the high crystalline quality of both samples (after Ref. [120]).
3.465 3.470 3.475 3.480 3.485 Energy (eV) Figure 8.6. High-resolution and low-temperature PL spectra of the sample#2 in Figure 8.3 measured with different laser power densities. The line assignments are discussed in the text (after Ref. [121]).
198
Optoelectronic Devices: Ill-Nitrides
three background donors, high-resolution IR absorption and high sensitivity SIMS measurements were carried out on the same set of samples characterized by high resolution PL spectroscopy [122]. Figure 8.7 shows the low-temperature IR absorption spectra for sample#l (dotted line) and sample#2 (continuous line). The shallowest and not fully compensated donor, Nl, is dominant in sample#l, while the deepest observed donor, N2, is present at higher concentrations in sample#2. A third shallow donor, N3, is observed only in sample#2. Assigning the dominant spectral lines to ls-2p transitions, the values 30.19 ± 0.1, 33.21 ± 0.1, and 31.23 ± 0.1 meV are obtained for the ground state binding energies of donors Nl, N2, and N3, respectively [122]. The 0.3 meV shift of the peak positions of Nl and N2 in sample#l to higher energy as compared with sample#2 results from the biaxial strain in the heteroepitaxial sample#l. High sensitivity SIMS measurements were performed to identify the atomic nature of these donors. Special concern was dedicated to the SIMS impurity background and references for each tested impurity. C, CI, H, O, Si, and S impurity levels were measured. The detected concentrations of O and Si are ~ 2.4 X 10^^ and ~ 1.2 X 10^^ cm~^ for sample#l (heteroepitaxial layer), and ~ 2.1 X 10^^ and ~ 3.7 X 10^^ cm~^ for sample#2, respectively. The concentration of O in both samples is about the same, while sample#l has about 34 times more Si than sample#2.
0.6 FS-HVPE GaN Sample#2
18
20
22 24 26 Energy (meV)
28
30
Figure 8.7. FTIR transmission spectra of sample#l and sample#2. Note the change in the relative intensity of the Hnes Nl and N2. The unidentify transition at 19.3 meV, marked with "?" has been assigned to widely separated pairs or triads (after Ref. [122]).
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
199
The integrated absorption coefficients (IAC) for donors Nl and N2 are, respectively, 10,177 and 1918 for sample#l and 302 and 1931 for sample#2. It is important to point out that the IAC for N2 is about the same for both samples, while the Nl IAC is approximately 34 times larger for sample#l than sample#2. These results, since none of the other investigated impurities tested by SIMS are consistent with the IR results, indicate that the shallow donors Nl and N2 observed in our HVPE samples are Si and O, respectively [122]. Assuming a similar lAC for N3 (D?), a concentration of 2.1 X lO^'^cm"^ is obtained. This extremely small value confirms the high sensitivity of FTIR spectroscopy to detect background impurities. The three PL lines at 3.4714(4), 3.4718(9), and 3.4722(8) eV, represented in Figure 8.6, based on the FTIR and SIMS results, are assigned to A excitons bound to O, D?, and Si neutral donors, respectively. This identification is consistent with the linear dependence between exciton binding energies and impurity binding energies, which follows the empirical Haynes rule with linear coefficient of 0.214 [120,123]. In addition, the Si and oxygen impurity binding energies measured from the 2ES spectra are in excellent agreement with the IR binding energy values [124]. Although n-type bulk substrates are convenient for optical devices fabrication, semiinsulating (SI) substrates are most desirable for high-frequency devices fabrication. Material scientists have employed different approaches, adequate for each growth techniques, to reduce the background carrier concentration by controlling the growth conditions and/or doping with impurities to provide the necessary concentration of compensating centers. Degenerated HPS bulk GaN substrates, doped during the growth with Mg, show increasing resistance with increasing doping concentration. For concentrations between 10^^ and 10^^ cm~^ resistance was observed to be as high as 10^ fl at about 600 K [125]. Infrared transmission measurements performed in such samples show no free-carrier absorption and improved optical properties. Nominally undoped FS-HVPE GaN, which are also typically n-type with background carrier concentration < 1 X 10^^ cm~^, can be grown SI by using intentionally introduced transition metal impurities during the growth to compensate the residual donors. Iron concentration lower than 1 X 10^^ cm~^ are sufficient to compensate unintentionally incorporated impurity and native defects. The resistivity of such samples measured at 250°C was 3 X 10^ fl cm and at room temperature was estimated as 2 X 10^ fl cm [126]. Zn doping, with concentration ranging between 10^^ and 10^^ cm~^, was also successfully employed to grown SI GaN films with resistivity 10^^ n cm at 300 K and 10^ fl cm at 500 K [127]. 8.4.2 Bulk and Thick-film AIN Despite the large concentration of residual oxygen in AIN grown by sublimationrecondensation, typically between 3 X 10^^ to 1 X 10^^ cm~^, it is still SI at room
200
Optoelectronic Devices: Ill-Nitrides AIN sublimation 5K
5 keV, 3 \xA
Energy (eV) Figure 8.8. CL spectrum (5 K) of an a-plane AIN sample fabricated by sublimation-recondensation technique. The nature of NBE and the two broad emission bands are discussed in the text (after Ref. [130]).
temperature. This is due to the fact that most of the oxygen is not incorporated as a substitutional shallow donor, but as impurity forming complexes with point and extended defects, which are located deep in the gap and behaving as compensating centers [128, 129]. AIN wafers grown by HVPE show a typical resistivity exceeding 10^ H cm at room temperature and 10^ fl cm at 500 K [82]. Figure 8.8 shows the low-temperature cathodoluminescence (CL) spectrum from 2.0 eV to approximately 6.2 eV of the a-face AIN sample OOG of Ref. [130], which has a considerable low oxygen content. In addition to an intense sharp emission near-bandedge (NBE) around 6.0 eV, two broad and featureless bands with peaks near 3.5 eV (VB) and 4.4 eV (UVB) are also observed, which have been previously associated with oxygen impurities [128,129]. The high-resolution CL spectrum of the sample represented in Figure 8.8 is highlighted in Figure 8.9. The continuous line represents the best fit to the experimental data, represented by the open circles, using Lorentzian line shapes. The intensity and the sharpness of the lines attest to the high crystalline quality of the sample. Thermoionization studies of the recombination processes in the spectral range represented in Figure 8.9 strongly suggests that the most intense line at 6.010 eV is associated with the annihilation of FXA bound to a shallow neutral impurity with an exciton binding energy of about 15 meV [130]. The Hues at 6.026 and 6.041 eV are observed up to 150 K, which may be related to the annihilation of free excitons [130]. Figure 8.10 shows the low-temperature CL spectra of sample#2, grown by thermodecomposition of aluminum chloride monoammoniate, in the spectral range between 2.0 and 6.2 eV. The spectrum measured with a 0.5 (A e-beam current shows two
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
201
350
5.98
Figure 8.9.
6.00
6.02 Energy (eV)
6.04
6.06
High-resolution CL spectra of the sublimation AIN sample represented in Figure 8.8. The assignments of the NBE lines are discussed in the text (after Ref. [130]).
broad overlapping bands with peaks at 3.6 and 4.3 eV. Note the similarity of all these spectral features with that observed in the CL spectrum of the sublimation sample. The spectra measured with 1.0 and 5.0 |JLA currents show an additional band at 5.3 eV, whose origin is not understood [84]. Figure 8.11 shows the high resolution CL spectrum in
10"^ AIN (decomposition)
^m
sample#2
O 10^
3.0
3.5
4.0 4.5 Energy (eV)
5.0
Figure 8.10. Low-temperature CL of a c-plane AIN (sample#2) measured at three different electron beam currents. The spectra between 2.0 and 4.1 eV were corrected with a calibrated light source to removed instrumental response (after Ref. [84]).
202
Optoelectronic Devices: Ill-Nitrides lU
i
1
'
1
'——
1
'
r
'
1 —^
1
• AIN decomposition «- 10^ r sample#2 ; 5keV, 2|iA
•
3
M
^o 102 -
'
5K 40K 60K 80 K 90K
°
c
IF' ft*
0
\
• 1 = -
:
u4
^ 10^ _l O
E
. ^^\.ij
-
jfen'-^
.
|R^/\*\ A ' y ° \ ^ °o
t^° °o \ HE
10°
do a,
1
5.96
,
\
5.98
._
1
.
1
6.00 6.02 Energy (eV)
1
1
6.04
.
'
1
" ^ ^ ^
6.06
6.08
Figure 8.11. High-resolution CL spectra of sample#2 measured at different temperatures. The assignments of the NBE hnes are presented in the text (after Ref. [84]).
the NBE spectral region measured at various temperatures of the thermodecomposition sample. The spectra show the expected systematic reduction of the CL intensity upon increasing temperature from 5 to 90 K. Note that the intensity of the line at 6.0089 eV reduces at a faster rate than that of the lines at 6.0250 and 6.0363 eV. This behavior is commonly observed in recombination processes involving complexes, such as excitons bound to neutral impurities, where one of the components (i.e. the exciton) has lower binding energy. Based on this observation and the similarity of these spectra with that of GaN, the line at 6.0089 eV is assigned to a recombination process associated with the annihilation of exciton bound to a shallow neutral impurity (probably a donor, XD^, due to the small energy value), while the lines at 6.0250 and 6.0363 eV are assigned to recombination processes associated with the annihilation of FX. The value of the FX binding energy to the shallow donor is given by the slope, Ex/kT, of the exponential quenching curve at the highest temperatures (i.e. 17.76 meV), and it is consistent with the 16.10 meV separation between the XD^ and FXA lines [84]. The asymmetry at the lower energy side of the XD^ line may indicate the presence of an additional line at 6.0058 meV, resolved assuming Lorentzian line shapes in the spectral fitting, which may be associated to a second shallow donor. The major difference of the lowest temperature spectrum of Figure 8.11 as compared with the spectrum in Figure 8.9 is the relative intensity of the three major bands. This observation suggests a pervasive character of the shallow donors associated with the NBE emission bands in bulk AIN. Therefore, a more systematic study is required to access the intrinsic material properties.
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
203
CL measurements performed in samples fabricated by RF assisted vapor phase technique and HVPE show the same spectral features observed in the CL spectra of samples grown by sublimation and thermodecomposition. This observation strongly supports the idea of pervasive impurities incorporation in AIN independent of the growth technique [79,82].
8.5. OPTICAL AND ELECTRONIC PROPERTIES OF HOMOEPITAXIAL III-NITRIDE FILMS
The viability of improved quality bulk and thick FS films of GaN and AIN substrates open the possibility to fabricate high-quality device grade homoepitaxial layers and ternary and quaternary epitaxial alloy layers for the fabrication of high-performance and high-yield devices. 8,5.1 Homoepitaxial GaN Films Epitaxial films have been deposited on bulk HPS GaN substrates by MBE, using surface cracked ammonia as nitrogen precursor, and MOCVD methods [131,132]. Detailed lowtemperature PL and reflectance measurements were performed on the MOCVD film to identify the nature of the lines observed in the NBE spectral region [132]. The lines assigned to the recombination process involving excitons bound to shallow donors have FWHM of about 100 |xeV, indicating the high crystalline quality of the homoepitaxial layer. X-ray diffraction experiment performed on similar structures indicates that the homoepitaxial film has lower lattice parameter c than the substrate, which typically has room temperature free-carrier concentration in excess of 5 X 10^^ cm~^ [133]. UID and Si-doped (< 1 X 10^^ electrons/cm^) homoepitaxial layers were deposited on FS-HVPE GaN substrates with nominal surface roughness of about 5 nm by low-pressure OMCVD. Films with thicknesses of about 5 |xm are characterized by growth surface roughness of about 0.2 nm RMS and reduced thread dislocation density, as compared with the substrate [134]. The full-gray line spectra of Figure 8.12 marked as HOMO-UID, measured on the UID homoepitaxial film, shows a reduction of the total intensity of the neutral donor-bound exciton related emissions and a relative decrease in the intensity of the free-exciton line. The lower energy side of the neutral donor-bound exciton emission band is also reduced, suggesting that the dominant donor is at the highest energy side of this band. This is consistent with the reduction in the concentration of the neutral background in the UID homoepitaxial layer. The PL spectrum of this Si-doped layer is characterized by a larger increase in the high-energy side of the neutral donor-bound excitons indicating that Si is in fact the shallower donor in GaN [134]. These results further strengthen the identifications of O and Si proposed in Refs. [117,118].
204
Optoelectronic Devices: Ill-Nitrides
Homo-layers: unintentional doped (UID) 33%Si doped
3.460 3.465 3.470 3.475 3.480 3.485 3.490
Energy (eV) Figure 8.12. High-resolution PL spectra of tow MOCVD films, an UID and a Si-doped GaN, deposited on FS-HVPE substrates. The assignments of the lines associated with excitonic recombination processes are discussed in the text (after Ref. [134]).
8,5,2 Homoepitaxial AIN Films UID homoepitaxial films deposited by MOCVD on high-quality AIN substrates misaligned 10° from the c-axis, with a nominal thickness of 0.5 |xm, have been investigated by variable-temperature high-resolution CL spectroscopy. The NBE CL spectrum measured at 5 K, represented in Figure 8.13, show six individual lines assigned
5.98
6.00 6.02 Energy (eV)
6.04
Figure 8.13. High-resolution CL spectra of a MOCVD AIN film deposited on a sublimation AIN substrate. The details of the line assignments are presented in the text (after Ref. [135]).
Properties of III-V Nitrides Substrates and Homoepitaxial Layers
205
to recombination processes involving the annihilation of free-excitons and excitons bound to neutral donor and acceptor impurities. These assignments rely on detailed thermal quenching studies [130]. These lines are considerably narrower than those previously observed in the substrate, which indicates the higher structural and optical properties of the homoepitaxial layer [135]. UID homoepitaxial HVPE films of about 2 fim have also been successfully deposited on wafers grown by HVPE. The increased ratio of the intensity of NBE emission lines to the intensity of the deep emission bands of the homoepitaxial layer in comparison with the ratio of these bands in the HVPE substrates strongly suggests the improved quality of the homoepitaxial layers [80].
8.6.
CLOSING REMARKS
A number of techniques have been used to evaluate the morphological, structural, optical and electronic properties of bulk and thick FS-HVPE films of AIN and GaN grown by a number of techniques for substrates application. Similar studies carried out on homoepitaxial layers deposited on some of these substrates indicate that films with improved structural, optical, and electrical properties could be realized. However, epitaxial-ready surface is still an important issue to be addressed in detail. Chemicalmechanical polishing and reactive ion etching has been used to achieve epitaxial ready surface with 0.3-0.5 nm RMS of roughness, but these processes have not been fully developed yet [67,77,136-139]. The well-estabhshed technology for the fabrication of LEDs on sapphire and SiC ensures that these substrates will remain as the substrate of choice for the foreseeable future. Therefore, bulk or quasi-bulk Ill-nitride substrate may play a role in the fabrication of devices that require high power density and low leakage current such as LD and high-frequency and/or high-power devices. The limited size of the Ill-nitride substrates and their present high commercial cost are serious limiting factors for a generalized use of these substrates for the fabrication of optical and electronic devices. Presently, an increasing numbers of R&D institutions are seeking commercialization of AIN and GaN substrates grown by a variety of techniques. It is expected that in the longterm, after a few growth techniques and associated processes are fully developed, the cost will drop and high-quality substrates will be available, as realized in other semiconductor material systems.
ACKNOWLEDGEMENTS
This work was in part supported by ONR contracts N0001401WR20178 and N0001401WR20015 (Dr C.E.C. Wood). Dr S.K. Lee, Dr D.D. Koleske, Dr L.M. Ivanova,
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Dr L J . Schowalter, and Prof. G.A. Slack are gratefully acknowledged for providing the samples. I am thankful to Dr E.R. Glaser and Dr B. Feigelson for helpful discussions.
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[80] Singh, N.B., Berghamns, A., Zang, H., Wait, T., Clarke, R.C., Zingaro, J. & Golombeck, J.C. (2003) /. Cryst. Growth, 250, 107. [81] Nikolaev, A., Nikina, I., Zubrilov, A., Mynbaeva, M., Melnik, Yu. & Dmitriev, V. (2000) MRS Internet J. Nitride Semicond., 595, W651. [82] Melnik, Yu., Soukhoveev, V., Ivantsov, V., Sizov, V., Pechnikov, A., Tsvetkov, K., Kovalenkov, O., Dimitriev, V., Nikolaev, A., Kuznetsov, N., Silveira, E. & Freitas, J.A., Jr. (2003) / Phys. Stat. Sol. (a), 200, 22. [83] Pletyushkin, A.A. & Slavina, N.G. (1968) hvestyiya Akademii Nauk SSSR Neorg. Mater., 4, 893. [84] Freitas, J.A., Jr., Braga, G.C.B., Silveira, E., Tischler, J.G. & Fatemi, M. (2003) Appl. Phys. Lett., 83, 2564. [85] Tanaka, M., Nakahata, S., Sogabe, K., Nakata, H. & Tabioka, M. (1997) Jpn. J. Appl. Phys., 36, L1062. [86] Angerer, H., Brunner, D., Freudenberg, F., Ambacher, O., Stutzmann, M., Hopler, R., Metzger, T., Bom, E., DoUinger, G., Berggmaier, A., Karsch, S. & Komer, H.-J. (1997) Appl. Phys. Lett., 71, 1504. [87] Leszczynski, M., Suski, T., Domagala, J. & Prystawko, P. (1999) Gallium Nitride and Related Semiconductors, EMIS Datareviews Series No. 23, Eds. Edgar, J. H., Strite, S., Akasaki, L, Amano, H. & Wetzel, C , INSPEC, lEE, Lodon, pp. 6. [88] Leszczynski, M., Teisseyre, H., Suski, T., Grzegory, I., Bockowski, M., Jun, J., Porowski, S., Pakula, K., Baranowski, J.M., Foxon, C.T. & Cheng, T.S. (1996) Appl. Phys. Lett., 69, 73. [89] Shintami, A. & Minagawa, S. (1994) /. Cryst. Growth, 22, 1. [90] Detchprohm, T., Hiramatsu, K., Itoh, K. & Akasaki, I. (1992) Jpn. J. Appl. Phys., 31, L1454. [91] Wyckoff, R.W.G. (1965) Crystal Structures, 1, Wiley, New York, pp. 111-113. [92] Schulz, H. & Thiemann, K.H. (1977) Solid State Commun., 23, 815. [93] Jeffrey, G.A., Parry, G.S. & IVlozzi, R.L. (1956) / Chem. Phys., 25, 1024. [94] Ponce, F.A., Bour, D.P., Young, W.T., Suanders, M. & Steeds, J.W. (1996) Appl. Phys. Lett., 69, 337. [95] Liliental-Weber, Z., Kisielowski, C , Ruvimov, S., Grzegory, L, Bockowski, M., Jun, J. & Porowski, S. (1996) /. Electron. Mater, 25, 1545. [96] Weyher, J.L., MuUer, S., Grzegory, I. & Porowski, S. (1997) J. Cryst. Growth, 182, 17. [97] Freitas, J.A., Jr. & Khan, M.A. (1994) Mater Res. Soc, 339, 547. [98] Bergman, L., Dutta, M. & Nemanich, R.J. (2000) Raman Scattering in Materials Science. Springer Series in Materials Science, vol. 42, Eds. Weber, W.H. & Merlin, R., p. 273. [99] Porto, S.P.S. (1969) in Light Scattering Spectra of Solids, Ed. Wright, G.B., Springer-Verlag, New York, pp. 1. [100] Perlin, P., Camassel, J., Knap, W., Talercio, T., Chervin, J.C, Suski, T., Grzegory, I. & Porowski, S. (1995) Appl. Phys. Lett., 67, 2524. [101] Tischler, J., Freitas, J.A., Jr. (2004) Appl. Phys. Lett., 85 (11). [102] Gil, B., Briot, O. & Aulombard, R.L. (1995) Phys. Rev. B, 52, R17028. [103] Suzuki, M., Uenoyama, T. & Yanase, A. (1995) Phys. Rev. B, 52, 8132. [104] Shikanai, A., Azuhata, T., Sota, T., Chichibu, S., Kuramata, A., Horino, K. & Nakamura, S. (1997) 7. Appl. Phys., 81, 417. [105] Volm, D., Oettinger, K., Streibl, T., Kovalev, D., Ben-Chorin, M., Diener, J. & Meyer, B.K. (1996) Phys. Rev. B, 53, 16543. [106] Chichibu, S., Azuhata, T., Sota, T., Amano, H. & Akasaki, I. (1997) Appl. Phys. Lett., 70, 2085.
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[107] Kim, K., Lambrecht, W.R., Segall, B. & van Schilfgaarde, M. (1997) Phys. Rev. B, 56, 7363. [108] Chuang, S.L. & Chang, C.S. (1996) Phys. Rev. B, 54, 2491. [109] Gil, B. & Leroux, M. (1999) Gallium Nitride and Related Semiconductors, EMIS Datareviews Series No. 23, Eds. Edgar, J. H., Strite, S., Akasaki, I., Amano, H. & Wetzel, C , INSPEC, lEE, Lodon, p. 65. [110] Wei, S.-H. & Zunger, A. (1996) Appl. Phys. Lett., 69, 2719. [ I l l ] Collins, A.T., Lightowlers, E.C. & Dean, P.J. (1967) Phys. Rev., 158, 833. [112] Jones, D.J., French, R.H., Mullejans, H., Loughin, S., Domeich, A.D. & Carcia, P.P. (1999) J. Mater Res., 14, 4337. [113] Shishkin, Y., Davity, R.P., Choyke, W.J., Yun, P., King, T. & Morkog, H. (2001) Phys. Stat. Sol. (a), 188, 591. [114] Wetzel, C , Suski, T., Ager, J.W., IE, Weber, E.R., Haller, E.E., Fisher, S., Meyer, B., Molnar, R. & Perlin, P. (1997) Phys. Rev. Lett., 78, 3923. [115] Perlin, P., Suski, T., Leszczynski, M. & Teisseyre, H. (1997) Optoelectronic Properties of Semiconductors and Superlattice. GaN and Related Materials, vol. 2, Ed. Pearton, S.J., Gordon & Breach, London, p. 315. [116] Bumstein, E. (1954) Phys. Rev., 93, 632. [117] Moss, T.S. (1954) Proc. Phys. Soc. (London), B76, 775. [118] Look, D.C. & Sizelove, J.R. (2001) App/. Phys. Lett., 19, 1133. [119] Freitas, J.A., Jr., Nam, O.H., Davis, R.F., Saparin, G.V. & Obyden, S.K. (1998) Appl. Phys. Lett., 72, 2990. [120] Freitas, J.A., Jr., Braga, G.C.B., Moore, W.J., Lee, S.K., Lee, K.Y., Song, I.J., Molnar, R.J. & Van Lierde, P. (2001) Phys. Stat. Sol., 188, 457. [121] Freitas, J.A., Jr., Moore, W.J., Shanabrook, B.V., Braga, G.C.B., Lee, S.K., Park, S.S. & Han, J.Y. (2002) Phys. Rev. B, 66, A#233311. [122] Moore, W.J., Freitas, J.A., Jr., Braga, G.C.B., Molnar, R.J., Lee, S.K., Lee, K.Y. & Song, I.J. (2001) Appl. Phys. Lett., 79, 2570. [123] Haynes, J.R. (1960) Phys. Rev. Lett., 4, 361. [124] Moore, W.J., Freitas, J.A., Jr., Lee, S.K., Park, S.S. & Han, J.Y. (2002) Phys. Rev. B, 65, 81201. [125] Staszewska, L., Suski, T., Grzegory, I., Porowski, S., Perlin, P., Robertson, J.L., Contreras, S., Wasik, D., Witowski, A., Cote, D. & Clerjaud, B. (1999) Phys. Stat. Sol. (b), 216, 567. [126] Vaudo, R.P., Xu, X., Salant, A., Malcame, J. & Brandes, G. (2003) Phys. Stat. Sol. (a), 200, 18. [127] Kuznetsov, N.I., Nikolaev, A.E., Zubrilov, A.S., Melnik, Yu.V. & Dmitriev, V.A. (1999) Appl. Phys. Lett., 75, 3138. [128] Slack, G.A., Schowalter, L.J., MorelU, D. & Freitas, J.A., Jr. (2002) /. Cryst. Growth, 246, 287. [129] Youngman, R.A. & Harris, J.H. (1990) /. Am. Ceram. Soc, 73, 3238. [130] Silveira, E., Freitas, J.A., Jr., Slack, G.A. & Schowalter, L.J. (2003) Phys. Stat. Sol. (c), 0, 2618. [131] Mayer, M., Pelzmann, A., Kamp, M., Ebling, K.J., Teisseyre, H., Nowak, G., Leszczynski, M., Grzegory, L, Porowski, S. & Karczewski, G. (1997) Jpn. J. Appl. Phys., 36, L1634. [132] Kormitzer, K., Ebner, T., Tonke, K., Sauer, R., Kirchner, C , Schwegler, V., Kamp, M., Leszczynski, M., Grzegory, I. & Porowski, S. (1999) Phys. Rev. B, 60, 1471.
Properties of III-V Nitrides Substrates and Homoepitaxial
Layers
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[133] Leszczynski, M., Prystawko, P. & Porowski, S. (1999) Gallium Nitride and Related Semiconductors, EMIS Datareviews Series No. 23, Eds. Edgar, J. H., Strite, S., Akasaki, I., Amano, H. & Wetzel, C , INSPEC, TEE, Lodon, pp. 391. [134] Freitas, J.A., Jr., Moore, W.J., Shanabrook, B.V., Braga, G.C.B., Lee, S.K., Park, S.S., Han, J.Y. & Koleske, D.D. (2002) /. Cryst. Growth, 246, 307. [135] Silveira, E., Freitas, J.A., Jr., Kneissl, M., Treat, D.W., Johnson, N.M., Slack, G.A. & Schowalter, L.J. (2004) Appl Phys. Lett., 84, 3501. [136] Weyher, J.L., Mueler, S., Grzegory, L & Porowski, S. (1997) J. Cryst. Growth, 182, 18. [137] Myers, T.H., VanMil, B.L., Holbert, L.J., Peng, C.Y., Stinespring, CD., Alam, J., Freitas, J.A., Jr., Dmitriev, V.A., Pechnikov, A., Shapovalova, Y. & Ivantsov, V. (2002) /. Cryst. Growth, 246, 244. [138] Lee, K. & Auth, K. (2001) Jpn. J. Appl. Phys., 40, L13. [139] Schauler, M., Eberhard, F., Kirchner, C , Schwegler, V., Pelzmann, A., Kamp, M., Ebeling, K.J., Bertram, F., Riemann, T., Christen, J., Prystawko, P., Leszczynski, M., Grzegory, I. & Porowski, S. {1999) Appl. Phys. Lett., 74, 1123.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 9
Ill-nitride Ultraviolet Light Emitting Sources Alireza Yasan and Manijeh Razeghi Center for Quantum Devices, Department of Electrical and Computer Engineering, Northwestern University, Cook Room 4051, 2220 Campus Drive, Evanston, IL 60208-3129, USA
9.1.
INTRODUCTION
Research on Ill-nitrides started some 80 years ago when the first AIN was synthesized from metallic aluminum [1]. After that, GaN and its family have been grown with various methods and after several breakthroughs, finally blue/violet LEDs were demonstrated. Following the commercialization of blue laser diodes, the interest shifted towards shorter wavelength light emitters, i.e. UV LEDs and laser diodes. From the standpoint of device structure, UV light emitters resemble well-known blue/violet LEDs, i.e. double heterostructure or quantum well (QW) active layer structure. A blue/ violet LED structure can be modified for UV emission by simply decreasing the indium content in the In^cGai-^cN active layer. The minimum wavelength that can be achieved using ternary InGaN active layers is ~ 365 nm. For shorter wavelengths, ternary AlGaN should be used instead of InGaN. To date, a number of groups have demonstrated UV LEDs [2-10] and LDs [11,12] and the quest for high-power devices still continues. Due to the high density of dislocations and doping difficulties, realization of highefficiency UV light emitters is more challenging than that of blue/violet light emitters. In this chapter, we briefly review the growth, processing, and characterization of ultraviolet light emitters based on the Ill-nitride material system, with more emphasis on deep UV LEDs (A < 280 nm), due to the challenges involved. Figure 9.1 presents a timeline of the evolution of Ill-nitride materials and related light-emitting devices.
9.2. THE NEED FOR UV LIGHT EMITTERS There are numerous applications for ultraviolet light emitters. A 360 nm UV laser would cause a fivefold increase in information storage in compact discs. This is due to the inverse relationship between the areal packing and the square of the wavelength.
E-mail address:
[email protected] (A. Yasan).
213
Optoelectronic Devices: Ill-Nitrides
214 Synthesis of AIN from metallic Al
1928
Synthesis of GaN powder (and later on InlN)
1932
Single crystal GaN by HVPE, vapor transport C VD & MBE
h=>
1969
GaNbyMDCVD
1971
= >
1971
Introduction of lowtemperature buffer
First p-type GaN by LEEBI of GaN:Mg
1983
1989
1991
Commercialization of blue lasers (400 nm, 5mW,40mA,5V)
UV laser diodes @ 375 nm (2 mW, 45 mA,4.5V)
AlGaNUVLEDs® 280 nm
Short-wavd ength AlGaN-basedUV laser diodes
1999
2002
2002
Riture
10,000 hrs lifetime RTCWInGaN violet LD
1997
First p-n GaN blue LED
P-type GaN by thermal annealing
First GaN LED (MIS structure, no p-type)
= >
1992
First CWInGaNbased blue-violet LD
1996
Figure 9.1. Timeline of the evolution of IE-nitride materials and related optoelectronic devices.
High-efficiency low-cost white lighting is another major application of UV LEDs that can have an impact on the market in near future. There are three common methods for generation of white light: one method is to combine red, green, and blue (RGB) colors in order to achieve white color. Although this method can be very efficient and allows for a very good color rendering, some problems such as color mixing and existence of the yellow-green gap are yet to be overcome. Another way of generating white light is to use blue color together with yellow phosphorus. This method is simple and exhibits good color rendering. However, it is limited on efficiency due to phosphorus conversion efficiency and self-absorption. In addition, multi-phosphor versions are needed to improve color rendering. The third and last approach is to use UV LED pumped RGB phosphors. In this case, white light is determined by phosphors only (tolerant to LED variation), excellent color rendering is possible, and it is easy to manufacture. This type of white LEDs is expected to take over the market because they offer superior color reproducibility. Another important apphcation of UV LEDs is detection of biochemical agents. Certain agents fluoresce when illuminated by an UV excitation source. The fluorescent light from these agents can then be sensed in order to determine the existence of these particular agents. Non-line-of-sight (NLOS) communication is another application of UV light sources. There is a need for a secure means to send messages in a battlefield using low-power communication systems, a requirement that cannot be met with conventional RF radios. Covert communication is made possible by UV sources that exploit the solar blind region located at 280 nm and below. In this region of the spectrum the terrestrial solar flux is negligible; this very low background can be used for NLOS communications over distances
Ill-nitride Ultraviolet Light Emitting Sources
215
up to 250 m. The strong extinction coefficient (high scattering, high absorption) of the signal in the UV makes it difficult to detect these emissions from a distance. The success of such a portable UV frequency communicator unit depends on the availability of a compact, powerful and energy-efficient UV optical source. In addition to all these, some other potential applications such as water purification, UV photolithography, in situ activation of drugs through optical stimulus, and laser surgery exist for Ill-nitride based UV light sources.
9.3. BASIC STRUCTURE OF III-NITRIDE BASED UV LEDs
A basic structure of a UV LED is shown in Figure 9.2. The active region of the UV LEDs could be composed of low In-content InGaN, GaN, AlGaN, or quaternary AlInGaN layers. This LED structure is of a "double heterostructure" type, meaning that the active layer is sandwiched between two materials with wider bandgaps (Figure 9.3). Double heterostructures are popular structures because (1) carriers are confined in the active region by the heterojunction potential barriers on both sides; (2) optical field is confined within the active region by the abrupt reduction of the refractive index outside the active region. p-GaN contact layer p-AIGaN (or superlattice) (Confinement layer) Active region (Single or multiple quantum well) n-AIGaN (or superlattice) (Confinement layer) n+-(AI)GaN contact layer
(A\)GaH buffer layer Low-temperature AIN/GaN nucleation layer (0001) Sapphire
Figure 9.2. Typical structure of a UV LED on c-plane sapphire.
216
Optoelectronic Devices: Ill-Nitrides
^ |/^^/'^>' h\) ^ 1 n-AlxGa-|.xN
p-AlxGai.xN (x>y)
AlyGa^.yN Figure 9.3. A schematic band diagram of an Al;fGai_vN/AlvGai-vN double heterostructure. r is the recombination time.
Addition of an intermediate bandgap "separate confinement" layer surrounding the active layer (resulting in a single or multiple-QW active region) can help confine the carriers inside a narrow QW layer (Figure 9.4). In this case, the electric field (photons) is confined by the outer step and the electrons are confined by the barriers in the active region. 9.3.1 Growth of UV LED Structures 9.3.1.1 Low-temperature AIN Buffer. Due to the large difference between the lattice parameters of AlInGaN alloys and sapphire, it is practically impossible to grow highquality epilayers directly on top of sapphire. To address this problem, a low-temperature GaN or AIN layer is generally grown on top of the sapphire substrate to initiate nucleation [13]. The purpose of the low-temperature buffer layer is to optimize the transition between the sapphire substrate and subsequent high-temperature epilayers. This creates a dislocated interface between the low-temperature buffer layer and the sapphire substrate. However, the following high-temperature layers will be of high quality and do not have to follow the surface arrangement of the sapphire substrate. A theoretical model has been suggested for the epitaxial relation between AIN and sapphire [14]. This model is shown in Figure 9.5. Since the (00.1) surface of sapphire is oxygen-terminated, each Al atom will be placed between three oxygen atoms, meaning that the first atomic plane will have the same structure as sapphire. The N atoms from NH3 combine with Al ions to form a tetrahedron with oxygen. The chemical bonds will then gradually change their nature from ionic to covalent. Lattice mismatch can be calculated (a)
_ (b)
—u— n Figure 9.4.
^jiJLrLr ^irLTLTL
Bandgap profile of (a) single quantum well, and (b) multiple quantum well separate confinement double heterostructures.
Ill-nitride Ultraviolet Light Emitting Sources
217
[1001 Eight times N-N distance of AIN
[1101 'AiA Figure 9.5.
Cross section view of the interfacial atomic structure model of AIN on (00.1) AI2O3 showing the formation of an edge-type dislocation.
from the change of Al-Al atomic distances between AIN and AI2O3 and will be about 13%, meaning that roughly every nine Al-Al atomic distance in sapphire corresponds to eight Al-Al atomic distance in AIN: ^
(^AIN - ^sapphireVV^ ^ «sapphire/>^
"
3 . 1 1 2 " 2.747
13.2%
(9.1)
^.747
Figure 9.6 shows a lattice image of an AIN buffer layer grown on top of sapphire substrate. This image clearly shows the 9:8 relationship predicted by theory. It should be noted that a misfit dislocation appears at termination of each atomic plane.
'mmmw Hi...........
If I
m
••ii}:.y,t,y,iY-ii'.-,in\
,,, Figure 9.6.
_ nm.
Lattice image of the AlN/sapphire interface.
Optoelectronic Devices: Ill-Nitrides
218
9.3.1.2 Growth of Crack-free AlGaN Layers. One of the most important aspects of the growth of Ill-nitrides is the difference in lattice parameters and thermal expansion coefficients of the AlInGaN compounds. For example, the difference between the lattice constants of AlGaN and GaN results in biaxial strain in the top AlGaN layer which together with the difference in the thermal expansion coefficients, which shows up upon cooling down the growth chamber, can eventually form cracks in the epilayers. For Al;^:Gai__^N on GaN, the in-plane stress is of "tensile" type, because the lattice parameter of Al;,Gai -^ is smaller than that of GaN. In most of the semiconductor material systems, this stress can be relieved through generation of misfit dislocations, if the thickness of the layer under tensile stress exceeds a "critical thickness". Below this critical thickness, the top layer will grow "pseudomorphically", i.e. its in-plane lattice constant will assume that of GaN. Figure 9.7 shows the structure of an epilayer under biaxial tensile strain, either pseudomorphic or relaxed. Of peculiar properties of Ill-nitrides, one is the absence of an effective slip system [15], which makes it difficult for dislocations to generate and glide. Brittle relaxation happens due to the fact that it is not possible to nucleate misfit dislocations by the MatthewsBlakeslee mechanism in [0001]-oriented Ill-nitrides [16]. The Matthews-Blakeslee theory describes the introduction of a misfit segment by the binding of pre-existing dislocations. It also explains the nucleation and gUde of dislocations from the surface. However, for hexagonal Ill-nitirdes, these glide systems have not been observed. Consequently, the plastic relaxation of AlGaN layers directly grown on GaN templates occurs through cracking [17]. In order to avoid cracking, the magnitude of tensile strain should be reduced to near zero. This can be achieved through the insertion of an underlying layer that adds a "compressive" strain component such that it cancels out the tensile strain component. It has been reported that AlyGai-;^:N with x > 0.4 grown on sapphire is under biaxial compression [18]. Therefore, growth of AlGaN on Al;»;Gai-;^N with x > 0.4 results in a layer that is compressively strained below its critical thickness. This leads to an increased critical thickness of the top Al^^Gai-^cN layer that will eventually delay
(a)
^ _ ^ _ ^ ^
nffl Figure 9.7.
(b) 1 1 1
^W\
Structure of an epilayer under biaxial tensile strain: (a) pseudomorphic and (b) relaxed with misfit dislocations.
Ill-nitride Ultraviolet Light Emitting Sources
219
cracking of the material. A similar approach has been employed to AlGaN/GaN heterostmctures. Amano et al. employed low-temperature AIN interlayers between GaN and AlGaN for dislocation filtering [19]. They later combined this approach with substrate patterning to obtain crack-free AlGaN layers on GaN [20]. AIN interlayers have also been employed for the growth of thick crack-free AlGaN/GaN distributed Bragg reflectors (DBRs) [21,22]. Similarly, crack-free AlGaN on GaN layers have been successfully grown on Si substrates using AIN interlayers [23]. Strain relief has also been achieved using AlGaN/AlN [24] or AlGaN/GaN superlattices (SLs) [25]. SLs are known to help relieve the strain, caused by the large lattice mismatch between sapphire and Ill-nitrides as well as among the AlInGaN family itself [26,27]. Al^^Gai-^.N/AIN SLs can also be used for dislocation filtering purposes [28].
9,3,1.3 Doping of High Al-content Al^Gaj -^N layers n-Type Doping. Si is the common n-type dopant for the Ill-nitride material system. However, while Si-doping of GaN is not much of an issue, doping of high Al-content AlGaN films seems to be more challenging. At high aluminum concentrations, the electrical conductivity of Si-doped Al^^Gai -J>^ layers is very low which makes these layers not suitable for optoelectronic devices. Impurities, dislocations, and native defects can form compensation sites with acceptor-like character leading to reduced n-type conductivity of AlGaN:Si. Oxygen, for instance, can behave as a deep acceptor when it becomes a DX center [29,30]. Carbon also has been speculated to act as an acceptor [31]. Cation vacancies are another acceptor-like compensating sources whose formation energy decreases with increasing Al composition [32]. For instance, Wagener et al. [33] found two mid-gap states arising from the third and second ionization states of the aluminum vacancy that could be responsible for the compensation mechanism. In addition to all these, dislocations may also introduce acceptor-like centers through dangling bonds along the dislocation line [34]. Deepening of the Si impurity level as a function of Al composition is another plausible argument as to why the electrical conductivity decreases [35]. Therefore, either the presence of compensation centers, or the deepening of Si level, or a combination of both could be responsible for the increase in the resistivity of Si-doped, high Al-content Al_^Gai_;,N layers. Adding a small amount of indium to the Si-doped AlGaN epilayers has been shown to be beneficial. A few groups have reported Si-In co-doping of high Al-content AlGaN layers resulting in high carrier concentrations and low resistivities [36,37]. There are a number of hypotheses as to why indium increases the conductivity of Si-doped AlGaN layers. Addition of indium into ternary AlGaN layers results in the reduction of defect density. This improvement in the structural quality can result in higher conductivity through suppression of the dislocation-induced compensation sites. It has also been speculated that indium may counteract the incorporation of defects
220
Optoelectronic Devices: Ill-Nitrides
responsible for self-compensation of high Al-content AlGaN layers, such as DX centers and cation vacancies [38]. Indium may occupy the cation vacancies (Vm sites) to inhibit the acceptor formation. p-Type Doping. p-Type doping of GaN and its ternary alloys is one of the most challenging tasks pertaining to the growth of Ill-nitride materials. The most common p-type dopant is magnesium (Mg), however, Mg doping without post-growth treatment still results in a compensated material. Amano et al. [39] achieved the first p-type doping by performing a post-growth low-energy electron beam irradiation (LEEBI). Two years after this breakthrough, it was found that thermal annealing of the Mg-doped GaN layer under N2 could also yield a p-type layer. The annealing temperature is in the range of 800-1000°C. Annealing under NH3, on the other hand, resulted in a compensated material. Therefore, it was concluded that hydrogen is the compensating agent. In fact, it is suggested that hydrogen passivates Mg [40], and therefore, post-growth treatment is necessary in order to break the H-Mg bonds and liberate the acceptors. Magnesium can be considered as a "deep acceptor" since the acceptor level in Mg-doped AlGaN layers lies hundreds of meV above the valence band. The energy difference between the valence band and the acceptor level is called the "activation energy" of the acceptor, which for Mg in AlGaN system increases with increasing Al composition. Figure 9.8 shows the Mg activation energy as a function of Al composition, up to 20% [41] (data collected from Refs. [42-46]). For AlNiMg, an activation energy of 510 meV has been measured which means that only a very tiny fraction of the Mg dopants (10~^) contribute free holes at room temperature [47].
320 ^
300
1
_
1
^
1
1
> I 280 > 260 ki
g 240 LU
c 220
0
^
Figure 9.8.
1—
-
-
zy^ 5 •• v ^ y
-
_ -
x ^ i
H
1. Tanakaef. a/.
200
^> _ 0 180 < 1* 160 140 ion
1
X
2. Saxler ef. a/. 3. Suzuki e^ a/. 4. Yasan ef. a/.
4
5. Kozodoy et. al. —1
5
1
1
i_
1
10 15 Al Composition (%)
1
1
20
-
1
25
Activation energy of Mg in AlvGai-;fN as a function of Al mole fraction (data collected from Refs. [42-46]).
Ill-nitride Ultraviolet Light Emitting Sources
111
One way to tackle the problem of p-type doping is to take advantage of the spontaneous and piezoelectric polarization in AlGaN/GaN heterostmctures. Ill-nitrides normally have a wurtzite structure, which is the structure with the highest symmetry compatible with the existence of spontaneous polarization. Furthermore, the piezoelectric coefficients for wurtzite GaN-based materials are about one order of magnitude higher than that of other zinc-blende III-V and II-VI semiconductors. These two effects combine to build a huge electric field, on the order of a few MV/cm. This large polarization field creates a periodic saw-tooth variation in the band structure which results in a periodic lowering of the acceptor level below the Fermi level, thus increasing the fraction of ionized acceptors [48]. Total polarization charge can be calculated as total
(9.2)
piezoelectric "•" •'spontaneous polarization
where ^piezoelectric "
^Lattice mismatch + ^Thermal strain — ^ [ ^ 3 1 + ( C i 3 / C 3 3 ) ^ 3 3 ] 8 ; ^
(9.3)
By substituting the values for piezoelectric (e^i and ^33) and elastic (C13 and C33) constants [49], the in-plane strain (e^) [50] and the spontaneous polarization [51] in Eq. (9.3), the following expression was obtained for the total polarization charge. For Al;cCrai_;^N, the constants were calculated by linear interpolation between AIN and GaN: Ap
_
^ • t tnfp] —
pW
-t total total
_
pi
-t 1total
/
0.16jc^ + 16.59x-h 42.14 \ \ 2.46JC2 - 133.23X + 1291.54 /
(CW)
(9.4)
where P\total and ^p btotal are the total polarization charge in the wells and barriers, respectively. Figure 9.9 shows the plot of the total polarization charge as a function of Al
Q
5e+13
CD JC
o •o
I- Eo
1e+13
ii
5e+12
_CD X3 O Q.
Ql
Figure 9.9. Total polarization induced charge density in Al^^Gai -^^N/GaN heterostmctures as a function of Al composition {x%).
222
Optoelectronic Devices: Ill-Nitrides
composition. A maximum sheet concentration of 6 X 10^^ cm~^ is expected for an AIN/ GaN heterostnicture. It is worth noting that the effect of dislocations on strain was neglected in this calculation. Virtually every UV LED structure reported in the literature utilizes p-GaN/p-AlGaN heterostnicture capping configuration to aid in the formation of ohmic contacts.
9.4. GaN/InGaN UV LEDs (365 < A < 400 nm) Low indium-composition In^^Gai-^N layers can constitute the active layers of UV LEDs with peak emission wavelengths down to ~ 365 nm. The InGaN UV LED structure resembles that of an InGaN blue/violet LED [52], with less indium in the active region. A typical InGaN UV LED on sapphire consists of a low-temperature GaN buffer layer, a thick (1-3 |xm) undoped GaN layer, an n-type GaN layer, n-type AlGaN (or SL) confinement layer, a low-indium composition InGaN-based active region (usually GaN/ InGaN single or multiple-QW structure), a p-type AlGaN (or SL) confinement layer, and finally a p-GaN layer as a contact layer. InGaN-based LEDs have been shown to be very efficient despite the large number of dislocations arising from the large lattice mismatch between GaN and sapphire. This has been attributed to the presence of localized states (band-tail states) due to indium mole fluctuation and/or layer thickness variation [53,54]. The carriers are believed to be captured by these localized states and then radiatively recombine before being captured by non-radiative recombination centers formed by the large number of dislocations [55]. Therefore, it can be said that the non-radiative recombination centers are bypassed by these localized states. In fact, it has been shown that reduction of dislocations by means of lateral epitaxial overgrowth (LEO) does not help enhance the output power of blue LEDs when compared to the same structure grown on sapphire [56]. Logically, the depth of these localized states should increase as the indium mole fraction increases, since there will be more indium fluctuation for high indium-content In_;,Gai-;,N layers. For InGaN UV LEDs with low indium compositions (shallow wells), the depth of localized states will be smaller; therefore, some of the carriers may leak out and get captured by non-radiative recombination centers resulting in a reduced efficiency of these devices compared to blue LEDs. Defect reduction techniques such as LEO and substrate patterning have been shown to be effective in the enhancement of the efficiency of InGaN UV LEDs [57,58].
9.5. (Al)GaN/(Al)InGaN UV LDs (360 < A < 400 nm) The structure of GaN/InGaN UV LDs is similar to that of InGaN blue/violet LDs [52] with a reduced indium composition in the active layers of the device (zero in the case
Ill-nitride Ultraviolet Light Emitting Sources
223
of GaN QW). The minimum achievable wavelength using GaN in the QW of the laser diode structure is about 365 nm [59]. To further reduce the emission wavelength, aluminum needs to be added to the QW. There are very few reports regarding UV laser diodes based on AlGaN or AlInGaN QWs, and even those have utilized low aluminum compositions which resulted in emission wavelengths limited to about 360 nm [60,61]. All these structures are grown on GaN or LEO-GaN template layers on sapphire. The aluminum composition in the cladding and waveguide layers should be increased when increasing the Al% in the active region. This will eventually lead to cracking of the laser structure grown on GaN, because the total thickness of the structure will exceed the critical thickness. The threshold current density of nitride LDs increases rapidly with increasing Al composition, due to lower material quality, difficulties in doping, and increased strain in the AlGaN layers grown on GaN base layers. For example, it has been reported [61] that the threshold current density increases from 3.2 kA/cm^ for 366 nm LDs to 5.5 kA/cm^ for 364 nm LDs to around 15 kA/cm^ for 355 nm LDs, showing an increase of more than one order of magnitude in threshold current density by reducing the lasing wavelength by only 11 nm. This exemplifies the great difficulty experienced in the growth of shorter wavelength laser diodes.
9.6. SHORT-WAVELENGTH UV LEDs (X < 365 nm) For emission at wavelengths shorter than 365 nm, ternary Al^^Gai-^^N or quaternary Alj^In^Gaj-^-^N with low indium composition replace the In^cGai-^^N active layer material. Depending on where to collect the light from, there are two possible configurations for LEDs: top-emission LEDs can be grown on GaN buffer layers over sapphire or SiC. On the contrary, for back-emission devices, no GaN layer can be used prior to the growth of the LED structure, because GaN has a bandgap of 3.4 eV which absorbs photons of wavelengths of 364 nm and below. Back-emission devices have an advantage over the top-emission devices in a sense that sapphire is transparent to the emitted UV light, while for top-emission LEDs, the p-GaN cap layer and the semitransparent p-type ohmic metal contact considerably absorb the UV light leading to a reduced efficiency of the LED. It is worth noting that SiC cannot be used as a substrate for back-emission short-wavelength UV LEDs because it has a bandgap energy of ~ 2.9 eV and absorbs the UV light. 9,6.1 Top-emission AlGaN UV LEDs As outlined earlier, one of the important issues pertaining to top-emission LEDs is the light absorption in the top p-GaN contact layer as well as the semi-transparent metal contact. Optical losses in these two layers are shown separately in Figure 9.10 [62]. Only 70% of the light is transmitted through the semi-transparent contact layer at 400 nm and this value
224
Optoelectronic Devices: Ill-Nitrides (a) 90 h
after annealing - • before annealing
80 70 60 1-
50 I40 30
Annealing condition: 500°C/10 mins
200
200
250 300 350 Wavelength (nm)
250
300
350
400
400
Wavelength (nm) Figure 9.10.
(a) Optical transmission of the semi-transparent Ni/Au ohmic contact before and after annealing (b) optical transmission of a 50 nm-thick GaN grown on AIN buffer.
decreases as the wavelength decreases (~60% at 340 nm and 50% at 280 nm). In addition, the p-GaN contact layer on the top absorbs the light markedly above its bandgap. Figure 9.10(b) shows the optical transmission graph of a 50-nm-thick GaN layer grown on top of an AIN buffer layer. These two losses combine for a considerable reduction in the extraction efficiency of top-emission UV LEDs. Despite these problems, top-emission UV LEDs with peak emission wavelengths as short as 280 nm have been demonstrated [63]. One advantage of top-emission LEDs is the high quality of the GaN buffer layer and n-type GaN contact layer, which allows for the growth of UV LED structures with rather low density of dislocations. However, due to the aforementioned problems, usually the extraction efficiency of top-emission short wavelength LEDs is very low.
Ill-nitride Ultraviolet Light Emitting Sources
225
9.6.1.1 UV LEDs (340 nm) Grown on GaN Substrate. Native substrates such as GaN are of great interest because they possess low dislocation densities and are lattice matched to epitaxial GaN. In addition, they dissipate heat more effectively due to their large thermal conductivity, which is about five times higher than that of sapphire. The only problem that has prevented GaN substrates from being the substrates of choice is the complicated growth techniques, which have made them expensive and luxurious substrates at the present time. Growth of laser diodes on GaN substrates is simpler than the growth on other substrates, because there will no longer be a need for time-consuming processes such as LEO [64-67], pendeo-epitaxy [68], or substrate patterning [69-71] to reduce the dislocation density of the subsequent epitaxial layers. Characteristics of UV LEDs grown on free-standing GaN substrates were investigated by fabricating 340 nm MQW UV LED structures on sapphire and GaN substrates and comparing their properties [72]. The complete UV LED structure is given in the inset of Figure 9.11. The 1-V characteristics of the devices is also shown in this figure. The turnon voltage of both devices is ~ 4 Volts. However, the LED grown on GaN substrate shows a sharper turn-on with a differential resistance of 13 fl. The same LED structure grown on sapphire gives a value of 40 fl for differential resistance. This indicates that the LED grown on GaN substrate has higher material quality than that of sapphire, due to lower defect density. In Figure 9.12, we compare the output power of the device grown on GaN substrate with the one grown on sapphire in pulsed injection mode. An enhancement of more than one order of magnitude has been achieved for the LED grown on GaN substrate due to higher \
"
•
1
••"
•
1
p-GaN contact layer
100
P-AI0.25Ga0.75N/AI0.2Ga0.8N SL 80 5 X AllnGaN/AllnGaN MQW
1
60 -
n-Alo 25Gao 75N/AI0 2Gao QN SL
c 0)
1
O
/
n-GaN On (00.1) sapphire or GaN substrate
40
^ 1
/
^
1
20
on sapphire
J
/
/
^
/
^
1
0 - 1
1
•
L
0
1.
1
2 Voltage (V)
4
•-
i.
,
1
_,
Figure 9.11. I-V characteristics of 340 nm UV LED grown on GaN substrate (solid line) and on sapphire (dashed line); inset shows complete structure of the devices.
226
Optoelectronic Devices: Ill-Nitrides
A on GaN substrate • on sapphire
% o Q_
100 200 300 Injection Current (mA) Figure 9.12.
Comparison between output power of the 340-nm LED grown on GaN substrate (triangles) and on sapphire (squares) in pulsed injection mode (duty cycle = 1%).
material quality. The slope efficiency for the LED grown on GaN substrate is one order of magnitude higher. In addition, GaN substrate provides better heat dissipation, as for the LED grown on sapphire, power saturates at a current of higher than 120 mA in continuous-wave (cw) injection mode due to heating inside the device. However, for the LED grown on GaN substrate, the output power in cw injection mode does not saturate for the injection currents up to 350 mA. This is understandable by the fact that the thermal conductivity of GaN is about five times higher than that of sapphire. Shown in Figure 9.13, in semi-log scale, is the output power vs. injection current of these two devices in cw injection mode. The maximum output power for the LED grown on GaN substrate is more than 20 times higher than the LED grown on sapphire. To summarize this experiment, the UV LED grown on GaN substrate shows about 65% reduction in the differential resistance and more than one order of magnitude increase in the output power compared with the LED grown on sapphire. Due to a better heat dissipation, the output power of the device does not saturate for currents up to 350 mA in cw mode for the LED grown on GaN substrate (almost three times as high as the LED grown on sapphire). High-power UV LEDs can, therefore, be grown on GaN substrates due to their low defect density. For example, 10 mW of cw output power has been extracted out of 352 nm UV LEDs grown on GaN substrates and the LED efficiency has been shown to be an order of magnitude higher than the same structure grown on conventional substrates [73].
Ill-nitride Ultraviolet Light Emitting Sources
111
0
o Q_
A on GaN substrate • on sapphire
100
200 300 Injection Current (mA)
400
Figure 9.13. Comparison of output powers of the 340-nm LED grown on GaN substrate (triangles) and on sapphire (squares) in cw mode.
9.6.2 Back-emission AlGaN UV LEDs As described eariier, top-emission UV LEDs suffer from optical absorption losses mainly in the p-GaN contact layer and the semi-transparent metal contact. These losses can be avoided if the emitted light is collected from the backside of the sapphire substrate. In this type of structure, no GaN layer can be deposited prior to the LED growth, because GaN absorbs photons with energies higher than 3.4 eV (wavelengths below 364 nm). Therefore, an Al;cGai_;cN buffer layer has to be used instead of GaN with x selected such that this layer is transparent at the emission wavelength. 9,6,2.1 Growth, Processing, and Characterization of UV LEDs (X = 280 nm). In this section, we discuss growth, processing, and characterization of a typical back-emission UV LED with a peak emission at 280 nm. Growth was carried out in a low-pressure horizontal-flow MOCVD reactor on double-side polished c-plane sapphire. The precursors were trimethylgallium (TMGa), trymethylaluminum (TMAl), trimethyhndium (TMIn), ammonia (NH3), silane (SiH4), and bis(cyclopentadienyl)magnesium (Cp2Mg) as sources for gallium, aluminum, indium, nitrogen, silicon, and magnesium, respectively. Deposition began with a 20 nm low-temperature AIN buffer layer grown at ~700°C followed by a 350-nm-thick high-temperature AIN layer and a 30-period Alo.85Gao.15N/AIN (50 A/50 A) SL topped with a 50 nm AIN compliance layer. These layers collectively comprise a high-quality template for the growth of UV LED structure. This template is not only transparent to wavelengths longer than 230 nm, but also keeps the top layers under compressive strain to
Optoelectronic Devices: Ill-Nitrides
228
avoid cracking of the material. As pointed out before, the SL structure can be used for strain relief as well as dislocation filtering. On top of this template, 0.8 U | Lm of highly conductive Si-In co-doped Alo.5Gao.5N was deposited forming the n-type contact layer. Hall effect measurement of this layer shows the resistivity, mobility, and carrier concentration to be 0.04 ft cm, 55 cm^fV s, and 3.1 X 10^^ cm~^, respectively. The Si-In co-doping scheme was used in order to increase the electrical conductivity of this high Al-content AlGaN layers. A 100-nmthick n-Alo.45Gao.45N layer was then grown as confinement layer. The high Al mole fractions of the previous layers are chosen for transparency at 280 nm, so as to allow back-emission. The active region consisted of a 10 nm Alo.4Gao.6N barrier, after which a 5 nm Alo.36Gao.64N (QW) was grown, ending with a second 5 nm Alo.4Gao.6N barrier. The asymmetric design of the active region is intended to compensate for the lower mobility of holes compared to electrons. This allows more of the injected electrons to recombine in the QW, which in turn increases the efficiency of the LED. A 10 nm Alo.6Gao.4N current blocking layer was then deposited to help prevent overflow of electrons out of the active region. The structure was then completed with a 50-nm-thick p-Alo.45Gao.55N layer followed by a 50-nm-thick p-GaN contact layer. After the growth, the sample was examined with both an optical and a scanning electron microscope and was found to be crack-free. A cross section of the device structure including the ohmic contacts is shown in Figure 9.14. Ti/Au
Thin Ni/Au
-p-Alo.6Gao.4N SQW Active layer
ii^-Ai(|jGao.5H
t
Figure 9.14.
Aro.85Gao.isN/AINSL
Structure of the 280 nm UV LED including the metal contacts.
Ill-nitride Ultraviolet Light Emitting Sources
229
Au-Sn Solder bumps
iSliiiiiiiiiis^^ Indium die attach
Figure 9.15. Schematic of a flip-chip bonded LED.
Standard photolithography and dry etching techniques were utiHzed to fabricate the devices. Square mesas, 300 fjim X 300 |xm, were etched down to the n-type contact layer. A thin Ni/Au layer was used for the p-type ohmic contact while Ti/Al was used to form the n-type ohmic contact. A thick Ti/Au layer was deposited on top of the ohmic contacts for bonding purposes. The devices were then packaged for power measurement. The LED wafer was diced into arrays of five devices before bonding to thermally conducting AIN submounts, via Au-Sn solder bumps. The diced die was bonded, epi-down, to the submount using thermo-compressive bonding. The back of the submounted LED was then bonded to a copper heatsink using indium. Figure 9.15 shows a schematic cross section of a flip-chip bonded LED die. An image of the submounted die is shown in Figure 9.16. This image shows five diodes with a common n-type metal contact surrounding the mesas. The square on the top right comer is the n-type contact pad. Figure 9.17 shows the I-V characteristics of this UV LED exhibiting a turn-on voltage of ~ 4.5 V with a series resistance of 25 fl. The turn-on voltage is around the expected value obtained from the bandgap of the QW layer. In order to calculate the series resistance, the ideal diode equation was utilized: dV nkT (9.5) --I = RJ^ d/ q where R^ is the series resistance and n is the ideality factor of the diode. Therefore, the slope of the (dV/d/)-/ vs. / curve determines the series resistance while the interception with the y-Sixis will yield the ideality factor. Figure 9.18 shows this plot for this UV LED. The slope of the curve at higher currents is the series resistance of the diode, which is-15-25 a
Optoelectronic Devices: Ill-Nitrides
230 W^^^'f
Figure 9.16.
Optical micrograph of a flip-chip bonded UV LED die.
In addition to the series resistance, we modeled the ideality factor in order to gain insight into the conduction mechanisms. Under low current injection, the effect of series resistance is negligible; thus, the ideality factor of the diode can be calculated. The inset of Figure 9.19 shows the low current regime of the / - V curve in log scale; the ideality factor is calculated by fitting the linear part of the curve with Eq. (9.6), which yields an ideality
ou -
Von-4.5V
25-
/
Rg = 25 Q ^
/
20-
1 c
15-
O
10-
/
50-
1
'
1
'
1
2
'
1
4
'
1
'
1
'
10
Voltage (V) Figure 9.17.
I-V characteristics of the 280 nm UV LED showing a turn-on at —4.5 V and a series resistance of 25 O.
Ill-nitride Ultraviolet Light Emitting Sources
.
Hav/ai; Linear fit
2.5-
> ^-•o -
231
2.01.51.0-
Rs = 18.6 Q Y=18.64*x+1.81734
0.5-
R2 =0.86539 0.0-J
1
10
Figure 9.18.
'
15 l(mA)
1
'
1
'
25
20
30
Extraction of series resistance from the ideal diode equation. Effect of the non-ideal ohmic contact(s) is also highlighted on the graph.
factor of n = 5.3 for this diode: (9.6)
/f oc exp
\nKT )
Eq. (9.6) arises from the combination of the equations for diffusion current (Eq. (9.7)) and recombination current (Eq. (9.8)), the two currents that usually dominate
1010^ <
10-
]
n = 1(Diff.)
j
;* n = 2(Rec.)
1
''
- exp (qV/nkT)
/
0)
J \ 1
10- J
1
•" ' ^.'/ *'
.'; / •'/
/
n = 5.3 (Tunneling)
/
10-
1
0
Figure 9.19.
1
2 Voltage (V)
3
'
4
Low current regime of the diode I-V curve in log scale. The linear fit of this data gives an ideality factor of 5.3. Slopes for ideality factors of 1 and 2 are displayed for comparison.
232
Optoelectronic Devices: Ill-Nitrides
the diode current.
^diff
^rec
y Tp A^D
\kT J
^ 2^ m ; , h A ^ , n i e x p ( ^ )
(9.8)
In Eqs. (9.7) and (9.8), /jiff is the diffusion current, Dp is the hole diffusion coefficient, r^ is the hole lifetime, n^ is the intrinsic carrier concentration, A^^ is the donor concentration, /^ec is the recombination current, W is the depletion region width, cr is the conductivity, Vth is the thermal velocity, and A^t is the density of traps. Combining Eqs. (9.7) and (9.8) into a single empirical equation yields Eq. (9.6), where n, the ideality factor, has a value between 1 and 2. If n is closer to 1, then diffusion current dominates, however, if n is closer to 2, recombination current dominates. Figure 9.19 displays the corresponding slopes for the cases of n = 1 (diffusion) and n = 2 (recombination). However, the value of n = 5.3 falls outside of this expected range, suggesting that an additional process makes a significant contribution to the conduction mechanism. This non-ideal behavior has been attributed to tunneling conduction in Ill-nitrides. For InGaN/ AlGaN heterostructures, it has been proposed that holes tunnel into empty acceptor impurity bands and vacant valence band-tails [74]. Moreover, for 285 nm UV LEDs, it has been speculated that high-energy electrons from the active layer are able to tunnel into the p-type barrier layers [75]. Similarly, a temperature-dependent study on 280 nm UV LED structures indicated possible leakage of carriers out of the QW (see Section 9.6.2.2 for details) [76]. Non-ideal ohmic contacts could also be responsible for anomalously big ideality factor values. Figure 9.20(a) shows the room temperature EL spectra of the LED at various current injection levels. The dominant peak occurs at ~ 280 nm with a full width at half maximum of ~ 10 nm. A very small defect-related peak with a very low integrated intensity is also observed in the spectra at A = 320 nm, which becomes even less significant as the current increases. The ratio of the primary peak to the secondary peak, the "primary-to-stray light ratio", is plotted in Figure 9.20(b) as a function of current with the semi-log EL spectra shown as an inset. Output power of the device was measured inside a calibrated integrating sphere. Figure 9.21 shows the output power of the flip-chip bonded device in pulsed operation mode (pulse width of 200 ns, frequency of 200 Hz). A high value of 1.8 mW at a current of 400 mA was achieved for the bonded LED. The P-I curve deviates from a linear relationship at higher currents due to heating inside the device. The cw power is substantially lower than the pulsed power which shows that removal of the generated heat is one of the major problems that needs to be addressed.
Ill-nitride Ultraviolet Light Emitting Sources
233
(a)
250
300
350
400
450
500
Wavelength (nm) (b)
30
I 25 B) 20
I 10H
20
Figure 9.20.
40
80 60 Current (mA)
100
(a) EL spectra of the 280 nm UV LED at various injection currents at room temperature and (b) the ratio of primary to stray light; inset shows the EL spectra in semi-log scale.
One way to reduce the heating at high operation currents is to distribute the current, and therefore, heat, among an array of parallel diodes. In this case, due to current distribution, there will be less heat generated in each diode. The output power of the array of four diodes reaches 6.5 mW at an injection current of 880 mA in pulsed mode, while the cw output power is 310 juiW at 390 mA. Figure 9.22 compares the pulsed output power of an array of four diodes in parallel with that of the single diode. At an injected current of 400 mA, the output powers of the single diode and the array are 1.8 and 3.9 mW, respectively, with the array reaching a high power of 6.5 mW at 880 mA. The curve for the diode array gives an initial slope efficiency of 14.7 |xW/mA, which falls off to 4.8 |xW/mA at higher current, meaning
234
Optoelectronic Devices: Ill-Nitrides 2.0 Pulsed, RT
1.8 J\ (200 nsec/ 200 Hz) 1-6 1— O — CW, RT X = 280 nm Single Diode
1.4
^
^y
^
v Vv-v
§ 1.2 E
V
r 0.8 1.0 H
§
CL
0.6 0.4-j
0.2 J
.^
P'
y
7
0.0 ^ 5oo ^
-O-O-O'O-O-O-O-O-O-O-O 400
200 300 Current (mA)
100
Figure 9.21. Power vs. current for a single 280 nm UV LED in pulsed and cw mode.
that even for the array, heating is detrimental at high injection currents. The inset of this figure displays P-I curves measured under cw operation for both a single diode and an array of four diodes. At 300 mA, output powers of 100 and 270 |xW were measured for the single device and the array, respectively. Figure 9.23 shows the comparison between external quantum efficiencies (EQE) of the array and the single diode. Basically, EQE reflects the efficiency of the LED in converting the electrical input energy in the form of electrons to the optical output
- Array
7
-Single
6H
RT, Pulsed
/
I 3 CL
2-1
1-1 0
/ • / ^oooo'
—•— Array _ 2 5 0 —o— Single 3 2 0 0 RT, CW 0) 150 _o-0-0-0-0-0
5o^
o4^
100
^ 0
200
400 600 Current (mA)
200 300 Current (niA)
800
400
1000
Figure 9.22. Comparison of output powers of the single diode and the array in pulsed and cw mode (inset).
Ill-nitride Ultraviolet Light Emitting Sources
235
0.00% 200
400 600 Current (mA)
800
1000
Figure 9.23. Comparison of EQEs of the single diode and the array in pulsed and cw mode (inset).
energy in the form of photons:
Ilq
(9.9)
where P^ut is the optical output power and / is the injection current. Under pulsed current operation, the single device reaches a peak EQE value of 0.24% at a current of 40 mA while the array reaches 0.26% at a higher current. The array reaches its peak efficiency at a later current because the current is spread across a larger area. However, after this peak value, the array EQE drops at a slower rate than the single device because, as discussed earlier, there is less localized device heating. Similarly, the continuous wave EQE of the array reaches a higher value and stays relatively constant as compared to the continuous wave EQE of the single device. The continuous wave EQE curves reach peak values of 0.012 and 0.022% for the single device and the array, respectively. 9.6,2.2 Non-radiative Centers in Short-wavelength UV LEDs. Although tremendous progress has been made in this field, the efficiency of short-wavelength UV LEDs is still much lower than their blue/violet counterparts. There are a few factors involved in the reduction of UV LED efficiency at shorter wavelengths. One of the problems is the insufficient electrical conductivity of doped AlGaN layers with high Al composition. Especially, low p-type doping limits the carrier injection into the active region. Low doping levels also make realization of ohmic contacts problematic. Another problem with high Al-content AlGaN layers is the increased number of defects. Dislocations are a source of radiative or non-radiative recombination centers which detract from the efficiency of LEDs. Temperature-dependent PL measurements can give us some insight into the recombination mechanisms. A 280 nm UV LED structure was used in this study. PL spectra
236
Optoelectronic Devices: Ill-Nitrides
1+Aexp{-E^/KJ)
E^=activation energy of first non-radiative channel Eg=activation energy of second non-radiative channel
10
20 30 1000/T(1/K)
40
50
60
Figure 9.24. Arrhenius plot of integrated PL intensity (triangles), fitted curves assuming only one non-radiative recombination process (dashed and dotted lines), and fitted curve taking into account both non-radiative recombination processes (solid line).
were measured over a temperature range of 20-300 K using the 244 nm line of a frequency-doubled Argon ion laser. In Figure 9.24, an Arrhenius plot of the normalized integrated PL intensity over the temperature range of study is presented. Thermal quenching of the integrated PL intensity due to activation of non-radiative channels can be observed for temperatures higher than ~ 50 K. The following expression is generally used for the calculation of the activation energy (f^) in thermally activated processes: I(T) =
/o
l-\-Acxp(-E^/K^T)
(9.10)
where I(T) is the temperature-dependent integrated PL intensity, /Q is the integrated PL intensity at low temperatures, K^ is the Boltzmann's constant, and A is a rate constant. However, this expression alone does not provide a good fit to the experimental data (dotted line). This suggests that a second non-radiative pathway exists [77], that is active in addition to the main non-radiative recombination channel. Assuming two dominant processes, Eq. (9.10) can be modified as follows: I(T) =
1 + A Qxpi-Ej^/K^T) + B Qxp(-E^/K^T)
(9.11)
where E^ is the activation energy for the second non-radiative channel. This expression provides a very good fit to our experimental data (solid line) with the activation energies being Ej^ ~ 50 meV and E^ ^ 1 meV for the first and second non-radiative channels, respectively. The contribution from each non-radiative channel is shown individually in
Ill-nitride Ultraviolet Light Emitting Sources
237
Figure 9.21 by a dotted line for the first and a dashed line for the second non-radiative channel. From this plot it appears that the first channel dominates at higher temperatures since it provides a better fit at temperatures above 100 K, while the second non-radiative channel is more significant at lower temperatures. The origin of the first non-radiative recombination channel could be partially related to the overflow of carriers out of the confining potential. For an Alo.4Gao.6N/Alo.36Gao.64N QW one gets a conduction band offset of ~ 75 meV [78]. Since this value is in the same order as £'A, it is reasonable to explain this non-radiative behavior by thermal emission of the carriers out of the QW. It is expected that by increasing the depth of the QW, this non-radiative pathway will become less significant. Dislocations in Ill-nitrides also play a significant role in radiative or non-radiative recombination processes. To estimate the number of dislocations, the etch pit density was measured using hot H3PO4. This revealed ~ 10^^ etch pits per cm^ for this sample, more than one order of magnitude higher than that of a typical GaN sample. This correlates with the calculated pre-factor A in Eq (9.11) being about an order of magnitude higher than that of a typical GaN sample. This pre-factor is directly related to the density of non-radiative centers [77]. Therefore, it can be concluded that high dislocation density is one of the major factors in having a large value of A and thus a pronounced quenching effect in this sample. The origin of the second non-radiative channel is not known yet, however, due to its low activation energy, we believe it is due to thermal quenching of bound excitons. Due to the complexity of the structure, it is not feasible to determine what kind of bound exciton is dominant in this process. 9.6,23 Effects of Self-heating and Current Crowding on the Performance of Shortwavelength UV LEDs, Self-heating of the LEDs is another reason as to why the efficiency of the LEDs is low, especially under cw operation. Due to the low thermal conductivity of sapphire {a = 0.3 W/cm K), the generated heat cannot be extracted from the backside of the substrate. Therefore, as explained earlier, flip-chip bonding is generally used in order to transfer the heat out of the epi-side to a thermally conducting submount such as AIN with a thermal conductivity of — 2 W/cm K. This helps alleviate the self-heating effect to some extent. However, any residual heat still reduces the efficiency, as seen by the decline of the power at high injection currents, in both pulsed and cw operation. A study on 324 nm UV LEDs has shown that at a cw injection current of 50 mA, the device temperature rises to about 70°C [79]. A thermal impedance of 190°C/W has been calculated for these LEDs. Heating inside the diode causes the emission spectrum to shift to longer wavelengths. In addition, the FWHM of the spectrum increases due to thermal broadening. In Figure 9.25, the EL spectra of a 280 nm UV LED, under 100 and 300 mA of cw injection currents, have been plotted. As a result of the increased injection current, the spectrum has redshifted by approximately 8 nm, and it is broadened by ~ 3.5 nm, a 35% increase. This shows that despite the flip-chip packaging, there still exists a considerable residual heating inside the LED. The temperature inside the LED under 300 mA of cw
Optoelectronic Devices: Ill-Nitrides
238
• 300 mA •100 mA W=289nm /^X
d CTJ
W = 281 nm FWHM = 10 nm
^V) c "c B
•
/ / / / // / / / / /— / 1
265
Figure 9.25.
FWHM = 13.5nm
1—
280
\
\
\ \
\
v. 1
\^ ^
1
295 Wavelength (nm)
1
1
1 —
310
EL spectra of a UV LED structure under 100 mA (dashed) and 300 mA (solid) of cw injection current.
current is approximated to be in the range of 500-600°C. Reducing the total resistance of the LEDs should result in a lower thermal resistance. Figure 9.26 shows the near field image of a UV LED under 80 mA of cw current. It can be seen that most of the light is coming from the periphery of the mesa. This has been attributed to current crowding due to low lateral conductivity of n-type AlGaN conduction layer. This effect causes the LED temperature to rise around the periphery more than it does in the center. Increasing the lateral conductivity of the n-type contact layer should yield a more uniform emission, and therefore, a more uniform heat distribution.
Figure 9.26. Near-field image of a UV LED under 80 mA of DC current.
Ill-nitride Ultraviolet Light Emitting Sources
239
n-contact
Figure 9.27.
Simplified schematic of an AlGaN UV LED along with the equivalent circuit for the calculation of current spreading length.
In a square-shaped mesa, a major portion of the current flows within a current spreading length, Ls, of the n-contact. This suggests that LEDs with dimensions larger than L^ do not necessarily emit more light than smaller LEDs, because the current never flows beyond the spreading length. Based on a model given in Ref. [80], we calculate the current spreading length in the 280 nm UV LED structure we discussed before. Figure 9.27 shows a simplified schematic of the LED structure along with the equivalent circuit used for modeling the current spreading length. In this circuit, R^ represents the sum of the resistance of p-type AlGaN cladding and p-contact, R^ is the resistance of n-type AlGaN cladding layer, and Vj is the voltage drop across the junction. Assuming that the junction voltage under forward bias and the voltage drop across the p-type series resistance (R^) are much larger than kT/e, the following expression is obtained for the current density, J(x): / W = /(0)exp(-
Pn
(9.12)
where J(0) is the saturation current density, p^ ^^^ Pp ^^^ the resistivities of the n-type cladding layer and p-type cladding layer, respectively, and p^ is the specific contact resistivity of the p-type ohmic contact. The current spreading length, L^, is defined as the length where the current density has dropped to l/e of its value at the edge of the mesa (/(Ls)//(0) = 1/e): ^ ^
I (Pc + Pp^p)^n Pn
The parameters used in this calculation are t^ = 800 nm ^p = 100 nm
(9.13)
240
Optoelectronic Devices: Ill-Nitrides
Pn = 0.02 fl cm p^ = 5.4 X 10"^ XI cm^ Pp = l/(^A^Ai^p) = 1/(1-6 X 10"^^ X 10^^ X 5) = 125 11 cm Note that the values of A^^ ^^^ Mp ^re not measured directly and they are merely an estimation of the carrier density and mobility in high Al-content AlGaN layers. This gives a value of ~ 52 ixm for the current spreading length, in agreement with what was measured based on the near-field emission pattern. According to Eq. (9.13), in order to increase the current spreading length, one must do one or more of the following: •
•
• •
increase the resistance of the p-type cladding layer. This is not desirable because it leads to a big voltage drop across the p-type cladding layer and also detracts from the LED efficiency by decreasing the number of injected holes into the active region; increase the resistivity of the p-type ohmic contact. Again this is not desirable due to the increased voltage drop across the metal/semiconductor interface delaying the turn-on of the diode; increase the thickness of the n-type cladding layer; reduce the resistance of the n-type cladding layer.
The last two options are more viable solutions. In Figure 9.28 we have plotted the current spreading length as a function of the resistivity of the n-type cladding layer and its thickness. It can be seen that in order for the current to be uniformly distributed (Ls = 150 |ULm), either the resistivity should be an order of magnitude lower, which is not 250
200,
5.0
7.5
tn (l^m)
10.0
1E-3
0.01 Pn ( ^ cm)
Figure 9.28. Current spreading length as a function of thickness of the n-cladding layer (left) and its resistivity (right). Dashed lines correspond to a current spreading length of 150 jjim for a uniform current injection throughout the entire 300 \xm X 300 jxm mesa.
Ill-nitride Ultraviolet Light Emitting Sources
241
achievable at this point, or the thickness should be —7.5 fjim, which will not only take a long time to grow but will also result in the cracking of the epilayer. Therefore, as an alternative to the current crowding problem, different mesa geometries can be used such that every point on the mesa is about a current spreading length away from the edges. For example, multi-finger geometries can be used in order to homogenize the heat distribution and at the same time decrease the differential resistance. This is especially helpful at high currents, when these types of geometries have been shown to be more useful by delaying the roll-off current (the current at which the output power saturates) [81]. We have investigated different mesa geometries with extended perimeters and captured their emission pattern using a CCD camera. Figure 9.29 shows the UV Hght emission pattern of different mesa geometries under ~ 100 mA of cw injected current. As can be seen, the regular square-shaped mesas suffer from the light non-uniformity the most.
Figure 9.29. Near field images of 280 nm UV LEDs with different mesa geometries under 100 mA of cw current, (a) shows the 300 X 300 \Lm square mesa along with multifinger geometries, including 4,6, and 8 fingers; (b) shows other designs that exhibit more uniform light emission patterns than square geometry.
Optoelectronic Devices: Ill-Nitrides
242
Square 4 Fingers 6 Fingers 8 Fingers
200 Current (mA) Figure 9.30.
400
Wall-plug efficiency of 280 nm UV LEDs with different mesa geometries.
The light uniformity improves for multi-finger mesas as the number of fingers increases from four to eight. In Figure 9.30 we have plotted the wall-plug efficiency of some of these LEDs under cw current injection. The efficiencies of the LEDs are almost equal at low currents. However, at higher currents the LEDs with larger perimeters possess higher efficiencies. For instance, the eight-finger LED has the highest power at a current of 300 mA, due to the fact that the finger widths for this mesa geometry are less than or equal to the current spreading length, which was estimated to be approximately 50 |ULm. 9.6.2.4. Deep UVLEDs (A = 265 nm). Growth of short wavelength UV LEDs becomes more challenging as we move towards shorter wavelengths. This is due to deteriorated material quality and pronounced problem of doping of high Al-content Al;,Gai_;,N layers. Apart from the increased molar fraction of Al in Al^Gai-^N layers, the structure of a 265 nm UV LED resembles that of a 280 nm LED. A cross section of the device structure is shown in Figure 9.31. Figure 9.32 shows the / - V characteristics of the 265 nm UV LED exhibiting a turn-on voltage of ~ 5.5 V with a series resistance of 72 fi. The turn-on is sluggish due to the high resistivity of the n- and p-type layers arising from the difficulty of doping of Al^cGai-^^N at high Al mole fractions. Figure 9.33 shows the room temperature EL spectra of the LED at various current injection levels. The dominant peak occurs at 265 nm with a full width at half maximum of — 9.5 nm. A very small defect-related peak with a very low integrated intensity is also observed in the spectra centered at A = 310 nm, which saturates rapidly as the current increases.
lU-nitride Ultraviolet Light Emitting Sources
243
n^-AlogglnoogGao^N
AlpggGao.isN/AIN SL
Sapphire (00.1) Figure 9.31. Structure of a 265 nm UV LED.
Power measurement was performed using a calibrated integrating sphere. Figure 9.34 shows the output power of the flip-chip bonded device in pulsed operation mode (pulse width of 200 ns, frequency of 200 Hz). A high value of 2.4 mW at a current of only 360 mA was achieved for the bonded LED. The optical power at a pulsed current of 50 mA is as high as 0.5 mW. The P-I curve deviates slightly from a linear relationship at higher currents due to heating inside the device. For the same reason, the slope efficiency decreases from 12.8 jjiW/mA at low injection currents to 4.3 ixW/mA at higher injection currents. For an array of four diodes in parallel, the slope efficiency increased from 4.3 to
Rs=72 Q
15-
1
Turn-on ~ 5.5 V
/
< 10-
/
1—
O
/
^
^
n —
1
—
-2
'
—
1
—
0
'
—
1
2
—
1
—
1
^ —
I
—
1
4 6 Voltage (V)
—
'
—
1
8
—
"
—
1
—
10
•
—
12
Figure 9.32. l-V characteristics of the 265 nm UV LED showing a series resistance of 72 H .
244
Optoelectronic Devices: Ill-Nitrides
60mA 40nnA ----- 20mA Room Temp.
210 240 270 300 330 360 390 420 450 480 Wavelength (nm) Figure 9.33. EL spectra of the 265 nm UV LED at various injection currents.
7.4 jjiW/mA and the output power increased from 2.4 to 3.5 mW at an injection current of 400 mA. The output power for this packaged array reached a value as high as 5.3 mW at a pulsed injection current of 700 mA. Figure 9.35 shows the output power of the LED under cw current injection. The P-I curve starts to deviate from a linear trend at 100 mA and the power saturates at a current of
Pulsed, RT
p-o-
X - 265 nm • Single
P'O^
7.4 |iW/mA
4.3 j^W/mA
200
400 Current (mA)
600
Figure 9.34. Output power vs. current for the 265 nm UV LEDs under pulsed injection current for single diode (triangles) and an array of four diodes (circles). Also shown in the figure are the slope efficiencies at low and high injection currents.
Ill-nitride Ultraviolet Light Emitting Sources
100 150 200 Current (mA)
245
250
Figure 9.35. Output power vs. current for the 265 nm UV LED under continuous-wave injection current, for a single diode (triangles) and an array of four diodes (circles). Also shown in the figure is the slope efficiency of the LED prior to roll-off.
— 150 mA where it reaches a maximum power of 90 |xW. The slope efficiency of the cw power vs. current is much lower than that of the pulsed power, even at low currents. This figure also shows the cw output power of an array of four diodes in parallel. The slope efficiency has improved by 20% compared to the single diode case and power does not roll-off until —250 mA when the power reaches a value of 170 |JLW. The EQE (r/ext) of the LED is plotted in Figure 9.36. In pulsed mode, T7ext reaches its maximum of —0.23% at a current of 40 mA, corresponding to a current density of — 44 Aleve?. The value of r}^^^ starts to decrease with increasing current at a current of 50 mA due to the generated heat. By further improving the material quality, hence
0
0.05
X UJ
100
200 Current (mA)
300
400
Figure 9.36. External quantum efficiency of the 265 nm UV LED in pulsed and cw operation mode.
246
Optoelectronic
Devices:
Ill-Nitrides
reducing non-radiative recombination centers, higher efficiencies would be achievable. The value of 17^x1 is much lower under cw injection current and begins to decrease after reaching a maximum value of 0.03%. This again results from excessive heating of the device and will be improved by further optimization of the packaging technology.
ACKNOWLEDGEMENTS The authors of this chapter gratefully acknowledge the contribution of R. McClintock, K. Mayes, S.R. Darvish, and P. Kung of the center for quantum devices, department of electrical and computer engineering. Northwestern university, Evanston, IL. They would also like to thank Dr Dravid and Dr Zheng of the material science and engineering department for providing them with the TEM image.
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[72] Yasan, A., McClintock, R., Mayes, K., Darvish, S.R., Zhang, H., Kung, P., Razeghi, M., Lee, S.K. & Han, J.Y. (2002) Appl Phys, Lett, 81, 2151. [73] Nishida, T., Saito, H. & Kobayashi, N. (2001) Appl. Phys. Lett., 1% 711. [74] Casey, H.C., Jr., Muth, J., Krishnankutty, S. & Zavada, J.M. {1996) Appl Phys. Lett., 68, 2867. [75] Chitnis, A., Pachipulusu, R., Mandavilli, V., Shatalov, M., Konkstis, E., Zhang, J.P., Adivarahan, V., Wu, S., Simin, G. & Asif Khan, M. (2002) Appl Phys. Lett., 81, 2938. [76] Yasan, A., McClintock, R., Mayes, K., Kim, D.H., Kung, P. & Razeghi, M. {200'i)Appl Phys. Lett., 83, 4083. [77] Leroux, M., Grandjean, N., Beaumont, B., Nataf, G., Semond, F., Massies, J. & Gibart, P. (1999) /. Appl Phys., 86, 3721. [78] For the calculation of band offsets, we assumed a bowing parameter of 1 and a conduction band offset equal to75% of the bandgap difference. [79] Chitnis, A., Sun, J., Mandavilli, V., Pachipulusu, R., Wu, S., Gaevski, M., Adivarahan, V., Zhang, J.P., Asif Khan, M., Sarua, A. & Kuball, M (2002) Appl Phys. Lett., 81, 3491. [80] Guo, X. & Schubert, E.F. (2001) /. Appl Phys., 90, 4191. [81] Chitnis, A., Adivarahan, V., Shatalov, M., Zhang, J., Gaevski, M., Shuhai, W., Pachipulusu, R., Sun, J., Simin, K., Simin, G., Yang, J. & Asif Khan, M. (2002) Jpn. J. Appl Phys., 3B, L320 Part 2.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 10
Ill-nitride UV Photoconductors Ryan McClintock and Manijeh Razeghi Department of Electrical and Computer Engineering, Center for Quantum Devices, Northwestern University, Cook Room 4051, 2220 Campus Drive, Evanston, IL 60208-3129, USA
10.1.
INTRODUCTION
10.1.1 The Solar Ultraviolet Spectrum The majority of the solar radiation that reaches the earth lies close to the visible region of the spectrum. The intensity falls off from there slowly into the infrared and more quickly into the ultraviolet (UV) with the spectrum resembling that of a typical blackbody source with a temperature of approximately 5800 K. This solar spectral irradiance is shown in Figure 10.1; the data is taken from Ref. [1]. UV light is defined as hght having a lesser wavelength of about 400 nm, but longer than that of X-rays; however, very little light with a wavelength shorter than 280 nm actually reaches the earth's surface due to atmospheric absorption by the ozone layer. More generally the UV spectrum consists of three major regions: UV A covering wavelengths in the range of 400-315 nm, UV B covering 315-280, and UV C, 200-280 nm [2]. AlGaN-based Ill-nitride photodetectors are well poised to cover these three regions: ranging from binary GaN with a direct band gap of 3.4 eV (365 nm), to binary AIN with a band gap of 6.2 eV (200 nm). Latter in this chapter this versatility is demonstrated for both photoconductors and p - i - n photodiodes in Figures 10.2 and 10.8, respectively. Recently as the growth of high Al composition AlGaN has matured, interest has focused on detectors operating in the solar-blind region of the UV spectrum. The solar-blind region corresponds to the strong atmospheric absorption of solar UV in the range of 240-290 nm. This creates a natural low background window for detection of man-made UV sources. 10.1.2 UV Photodetector Applications The development of UV photodetectors has been driven by numerous applications in the defence, commercial, and scientific arenas. These include, for example, covert space-tospace communications, secure non-line-of-sight communications, early missile threat
E-mail address:
[email protected] (R. McClintock).
251
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Optoelectronic Devices: Ill-Nitrides
0.00 250 500 750 1000 1250 1500 1750 2000 Wavelength (nm) Figure 10.1. Solar spectral irradiance as seen from space. On earth absorption by atmospheric ozone strongly attenuates wavelengths less than 280 nm thus creating a solar-bhnd window.
detection, UV spectroscopy, chemical and biological threat detection, flame detection and monitoring, UV environmental monitoring, and UV astronomy [3-5]. In addition to ozone, many other organic and inorganic compounds have absorption lines or florescence lines in the UV region of the spectrum. If a number of different cut-off wavelength UV photodetectors are used, it is possible to determine the presence of individual spectral lines and attempt to identify the presence of specific chemicals. This potential for compact solid-state florescence spectroscopy is one of the most interesting applications. In the past few years, technological and scientific advances in high Al composition AlGaN and AlN-based semiconductor materials have led to a renewed interest in UV photodetectors, especially solar-blind photodetectors. Because of the low natural background in the solar-blind region (290-240 nm), detectors operating in this range allow for a number of unique applications. Heat sources such as flames, jet engines, or missile plumes emit Hght in this portion of the spectrum. The mihtary is interested in developing ground and air-based solar-blind sensors to detect the unique signature of an active missile plume, and provide early warning and potentially allow for missile tracking and ultimately interception [6,7]. The military is also interested in secure non-line-of-sight communications which would require both solar-blind emitters and detectors, and take advantage of atmospheric scattering and attenuation to provide a means of secure shortrange communication. Commercial applications in the solar-blind region include monitoring of atmospheric ozone concentrations, and high-temperature flame sensors for industrial combustion monitoring.
Ill-nitride UV Photoconductors
253
10.1,3 UV Detection Technologies For many decades, the detection of UV light has been accomplished using photomultiplier tubes. These enjoy a high sensitivity to UV photons while being insensitive or "blind" to photons with wavelengths longer than the detector cut-off wavelength. However, they are fragile vacuum tube devices that require bulky high-voltage power sources to operate. This inherent complexity also makes them relatively expensive. A solid-state alternative to PMTs are siUcon-based photodetectors [8]. However, Si-based devices are not as robust as AlGaN-based photodetectors, and they have considerable sensitivity to photons in the visible and infrared spectral regions in addition to the UV portion of the spectmm. The out-of-band response is conmionly addressed by the use of filters, such as a Woods glass optical filter. However, these filters increase the size and weight of the device, and reduce the overall quantum efficiency of the system. Other semiconductor materials besides Si have also been proposed by researchers with more or less the same success, including Ge, GaAs, and SiC; this is done in the hope of realizing an efficient solid-state UV photodetector which would enjoy the visible-blindness of a photomultiplier tube. It is only in the second half of the 1990s that wide bandgap Ill-nitride semiconductors, and AljcGai -xN in particular, have begun to emerge as the most promising material systems for such a device, thanks to their exceptional material properties [8]. 10.2.
DEVELOPMENT OF UV PHOTODETECTORS
The development of Ill-nitride-based UV photodetectors began in the early 1990s. The initial research work focused on GaN, and was primarily an offshoot from the technological advances resulting from the drive to develop high quality GaN material for blue light emitting diodes and lasers. The few photodetectors, which were demonstrated at the time, were simple GaN photoconductors and Schottky photodiodes. During the second half of the 1990s wide band gap GaN had established itself as a promising material for UV detectors, and soon Al^^Gai -J<1 was being investigated for the development of detectors operating over the entire 200-400 nm range. By the late 1990s and early 2000s, Alj<:Gai_;cN had reached a certain level of maturity, and back-illuminated photodetectors were being investigated for potential solar and visible-blind UV imaging applications. A review of the early stages of development of GaN and Al^cGrai-jcN-based UV photodetectors has been done in Ref. [8]. Since then, several research groups have investigated different types of detectors based on these materials, including photoconductors [9,10], Schottky metal-semiconductor-metal (MSM) detectors [17-21] Schottky barrier photodiodes [18,19] p - i - n photodiodes [24,28-37] avalanche photodiodes [38,39]. A nice table comparing the performance characteristics of these different types of detectors can be found in the last page of Ref. [7]. More recently, research has been geared toward achieving shorter cut-off wavelengths and has especially been focused on developing detectors operating in the strategic
254
Optoelectronic Devices: Ill-Nitrides
solar-blind window. This push for shorter wavelength has required the use of higher Al content compounds, and has introduced many technological challenges related to the growth and processing of this wide bandgap material. There has also been interest in the realization of back-illuminated devices [49,54] which can then be hybridized to a silicon readout integrated circuit to create Ill-nitride based focal plane arrays (FPA) for imaging in the UV [62-70]. 10,2.1 Photoconductors Photoconductive UV detectors were the first to be demonstrated, as they are generally the simplest detectors to grow and fabricate. They consist of a slab of semiconductor material with two ohmic contacts. After GaN, the first Al^^Gai-^^^N photoconductive detectors covering the complete range of Al concentrations (0 < JC < 1) were rapidly reported [9]. Single undoped epilayers with thicknesses 0.5 — 1.5 |xm were grown on basal plane sapphire substrates by MOCVD and the metal contacts were Ti/Au. The photoconductors exhibited sharp cut-off wavelengths from 365 to 200 nm as shown in Figure 10.2. Specifically, the peak responsivity for x = 0.34 (^cutoff ^ 285 nm) is about 0.6 AAV. This was the first proof that Al^^-Gai-^^N materials were suitable for solar-blind detector applications. The detectivity of these photoconductors at a modulating frequency of 14 Hz reaches 5.5 X 10^ and 3.3 X 10^ cm Hz^^^AV for GaN and Alo.75Gao.25N, respectively. Moreover, the effective carrier lifetime derived from frequency-dependent responsivity measurements have been estimated to be in the range of 6-36 ms [10]. However, recently, interest in photoconductor has subsided due to the inability to fully resolve the issue of persistent photoconductivity. Persistent photoconductivity in ni-nitrides has been observed in both GaN and AlGaN-based photodetectors based on AI^Ga^.^N
200
250
300 Wavelength (nm)
350
400
Figure 10.2. Photoconductors exhibiting sharp cut-off wavelengths covering the entire M^GSLI -J>i compositional range: from GaN (365 nm) to AIN (200 nm). The inset shows a simplified photoconductor structure.
Ill-nitride UV Photoconductors
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undoped, and both p-type and n-type photoconductors [11-15]. The increased conduction persists long after the photo-excitation is removed, and the effect can easily last for up to several hours. This makes the responsivity of the photoconductor a complex function of the time the sample has been illuminated, or kept in the dark. Persistent photoconductivity is commonly attributed to defects and dislocations in the material. It is proposed that charges accumulate at the surfaces of the photoconductor and around bulk dislocations. These space charge regions then modulate the effective conduction cross section of the photoconductor. Both the persistent photoconductivity and the gain dependence on optical power have been modeled by considering this lightinduced band bending due to related defects [16]. 10,2.2 Schottky Metal-Semiconductor-Metal Detectors Schottky MSM photodetectors are also relatively simple photodetectors to realize. They generally consist of a single epitaxial layer with two interdigitated Schottky metal contacts deposited on the surface, this creates two back-to-back rectifying junctions. Electron-hole pairs are generated when photons are absorbed near the depletion regions formed at these Schottky junctions. The geometry of a typical interdigitated finger device is shown in Figure 10.3. In the case of GaN and Al^^Gai-^pN materials, these devices are arguably simpler to fabricate because there is no need to highly dope the material and achieve ohmic contacts. MSM detectors exhibit all of the desirable attributes of a practical photodetector, such as high gain, low dark current, high speed, large bandwidth and high sensitivity. However, these devices require an applied bias to operate, and their performance characteristics are
V '.'. 1
'• I' ^' :
'! \\'f.
]• '''It
Figure 10.3. The geometry of a typical interdigitated finger MSM device with a length of 150 ixm a finger width of 2 |xm and a pitch of 10 |xm.
256
Optoelectronic Devices: Ill-Nitrides
dependant on this applied bias, as it changes the volume of the depletion region. The device performance also depends on geometry, e.g. the spacing and length of the interdigitated fingers, and the thickness of the active epilayer. GaN-based Schottky MSM devices were extensively studied [17]. Response time of MSM devices are typically less than 10 ns; this is limited primarily by the RC time constant of the measurement apparatus, for MSM detectors fabricated on 1 |xm thick undoped GaN films on sapphire and operated at 1 V bias. Typical dark currents are only ~ 2 nA at a bias of 5 V, while the noise power spectral density remains below 10"^^ A^/Hz, the minimum commercially measurable level, up to about 5 V. There have also been reports of similar detectors with different layer thicknesses and finger geometry which exhibited external quantum efficiencies of up to about 50% with applied bias in the range of 5-20 V and without internal gain [18]. These devices also show a very low dark currents, as low as 800 fA at a bias of 10 V. Schottky-based MSM UV detectors were also demonstrated on LEO grown GaN films on sapphire [19]. A typical spectral response from such a detector is shown in Figure 10.4. A three orders of magnitude sharp cut-off at the band edge of GaN is observed. The high responsivity obtained is indicative of the presence of internal gain in these devices. Recently, research has focused more on realizing shorter wavelengths, in particular solar-blind, MSM detectors. For example, using an Alo.4Gao.6N epilayer on sapphire, an external quantum efficiency as high as 49% (responsivity 107 mAAV) at a 90 V bias has been reported for an MSM detector with peak responsivity wavelength of 272 nm. The detectivity was estimated at 3.3 X 10^^ cm Hz^^^AV for a 500 Hz bandwidth and 37 V bias [20]. Such devices were operated under front-illumination, i.e. the incident light was reaching them from the epilayer side with the interdigitated metal contacts, as shown in Figure 10.3.
200
300
400
500
600
Wavelength (nm) Figure 10.4. A typical spectral response of a Schottky-based MSM photodetector.
Ill-nitride UV Photoconductors
257
More recently, back-illuminated solar-blind MSM detectors have been reported in an effort to move the technology toward FPAs in which the epilayer (front) side of the device will be connected to the readout circuitry [21]. In the case of these MSM detectors, backillumination has the advantage of avoiding the blockage of incident photons by the interdigitated metal contacts, thus enhancing the quantum efficiency. However, because the depletion region (the active region) of the device is located at the epilayer/metal interface (front), the incident photons have to first traverse the substrate and most of the Al^Gai-^^N epilayer before reaching the active region. This can be partially circumvented by utilizing a heterostructure in which a larger bandgap epilayer (e.g. Al;cGai-;(;N) is first grown on the substrate before the active Al^Gai_3;N layer with x> y. Such types of devices have been reported with external quantum efficiencies of ~ 50% (responsivity 110 mAAV) at a peak response wavelength of 262 nm, for a bias higher than 12 V. The dark current was lower than 20 fA for a bias < 100 V. Schottky MSM detectors hold a great promise for the realization of commercial solarblind detectors. However, the need to apply a bias, which can be significant when high concentrations of Al are used in solar-blind devices, needs to be addressed for commercial system applications. In addition, the fabrication of FPAs for imaging seems to favor the use of p - i - n based structures. 10.2.3 Schottky Barrier Photodiodes Schottky barrier photodiodes have received much less attention than other types of photodetectors [22], solar-blind Al^Gai_;,N Shottky photodiodes were not demonstrated until the year 2000 [23], mainly because of the very rapid interest and progress in Schottky MSM detectors. Schottky barrier photodetectors consist of a layer of semiconductor with two different contacts, one ohmic and one rectifying. Electron-hole pairs are generated when photons are absorbed near the depletion region formed at the Schottky junction. This leads to a development of photo voltage across the two contacts. The typical spectral response of a Schottky barrier photodetector is shown in Figure 10.5, with the corresponding device structure shown in the inset. A peak responsivity of 70 mAAV was realized at 272 nm, without applied bias, corresponding to an external quantum efficiency of 32%. Schottky barrier detectors exhibit good solarblindness; this example shows a four orders of magnitude rejection ratio between the peak response and visible wavelengths. 10.2.4 p-i-n Photodiodes Most of the recent research work on UV and especially solar-blind detectors has been focused on realizing p - i - n photodiodes. Figure 10.6 shows the typical structure of an Al^Gai_;cN photodiode. To date, all p - i - n photodiodes are oriented such that the n-type layer is closer to the substrate; mainly because the quality of n-type Al^^Grai _^N is typically superior to that of p-type Al;,Gai_;,N.
Optoelectronic Devices: Ill-Nitrides
258
Spectral Responsivity ""3
10-'' r
NiMu
^^.^^
3000 A
1
AIGaN
1 jam AIGaN: Si
1
^°1r
•t
10-3
Ti/Au
1
•j
5000AGaN:Si 2 urn GaN: Si
r
\
c
1 10-^ r
1
Sappiiire
(0
Device Structure
\
1
(D
a: 10-5
r
10-6
r
\ .
.
200
. 300
.
•j _i 400
J W^ —-1 L I —_3 600 500
Wavelength (nm) Figure 10.5. The typical spectral response of a Schottky barrier photodetector. The corresponding device structure is shown in the inset.
The interest in p - i - n photodiode UV detectors is driven by their intrinsic advantages: (i) a very low dark current due to large potential barrier, (ii) high speed of operation, (iii) a high impedance suitable for FPA readout circuitry, (iv) a direct control of the quantum efficiency and speed through the control thickness of the intrinsic layer, and (v) the device can operate under low bias. There are two modes of operation for photodiodes: photovoltaic (operation under no bias) and photoconductive (operation under reverse bias). Under the reverse bias, the depletion layer is quite wide and the device exhibits a very low dark current corresponding to the reverse saturation current. The mode of
Ni/Au ^000AAIGaN:Mg| 2000 A AIGaN 1 /im AIGaN:Si
Ti/Au
2.5 jum GaN:Si
Sapphire Side view
Top view
Figure 10.6. The typical structure of a front-illuminated AlxGai_;cN-based p - i - n photodiode.
Ill-nitride UV Photoconductors
259
operation is chosen based on the desired application; in the photovoltaic mode, the dark current is at the lowest, while in the photoconductive mode the device exhibits a faster response. The first report of photovoltaic effects in GaN p - n junctions was published in 1995 [24], in which a simple partial modeling of the spectral response allowed determining the hole diffusion length in n-type GaN to be 1000 A [24]. A similar modeling of the spectral responsivity of GaN p - i - n photodiodes using a calculation for the quantum efficiency later led to an electron diffusion length in p-type GaN of 880 A [23]. Analytical modeling of the responsivity of a GaN p - i - n photodetector is a relatively simple problem because many of the material parameters are relatively well known (e.g. mh, me, Dh, etc.). Because of this it is relatively easy to obtain a good fit to experimental data as shown in Figure 10.7. Fitting the data can be used to determine the minority carrier diffusion lengths and lifetimes. These parameters are critical to device performance; a larger minority electron diffusion length ensures highly efficient absorbance of the incident light by the intrinsic region resulting in a higher quantum efficiency. Using analytical modeling of GaN p - i - n photodetectors has lead to the first experimental determinations of the minority carrier diffusion length in p-GaN [25,26]. A wide range of Al^Gai_^N p - i - n photodiodes have been demonstrated, most of which are front-illuminated [27-34]. Devices, which are going to be operated only under front illumination, are generally designed as an AlGaN p - i - n structure on a rather thick ( > 2 |xm) GaN template layer on sapphire substrate. The use of this GaN layer helps prevent the defects at the substrate/epilayer interface from reaching the active layers of the device. The p - i - n structure can either be a homostructure or a heterostructure. A thin (50 ~ 100 A) p-type GaN layer is sometimes incorporated above the p - i - n structure in order to increase the collection of photogenerated carriers, and improve the contact 0.25
0.20
\
r
experimental theoretical fit
0.15 0
0.10k
250
300
350
400
Wavelength (nm) Figure 10.7. The spectral responsivity of the GaN p - i - n photodiode and the theoretical fit.
260
Optoelectronic Devices: Ill-Nitrides
resistance: this is because p-type GaN is easier to dope than p-type AlGaN, and thus is often much more conductive. The spectral response of a set of front-illuminated Al^^Gai-^N p - i - n photodiodes with different Al compositions is shown in Figure 10.8. By tailoring the Al content in the active region from 0 to 70%, the peak responsivity wavelength can be tuned from 364 to 232 nm. This shows that both solar-blind and visible-blind (insensitive to visible light and longer wavelengths) p - i - n photodiodes can successfully be achieved using Al;cGai_;cN materials. External quantum efficiencies as high as 70% (responsivity 0.2 AAV) at a peak responsivity wavelength of 362 nm, without applied bias, are shown. Solar and visible-blindness in the range of 4 - 6 orders of magnitude are also common. The external quantum efficiency of these devices has been progressively increasing, thanks to optimization of the device structure through a combination of experimental and theoretical work. These devices exhibited an l/f noise mechanism and a detectivity as high as 6.4 X lO^^cmHz^^^AV. The concept of back-illuminated devices had first been reported in this material system in 1998 for GaN photodiodes [35], for which the purpose then was to enhance the quantum efficiency by avoiding absorption of photons in the p-type GaN top layer. To do so, an n-type Alo.28Gao.72N layer was first grown on the sapphire substrate, before depositing the i- and p-type GaN layers. Because this ternary layer has a larger bandgap energy than GaN, it is transparent to the photon wavelengths that were being detected. Since then, the growing need for solar-blind FPAs made from Al^^-Gai-^^N materials has driven the development of back-illuminated p - i - n photodiodes [27,36-38]. The realization of back-illuminated AlGaN p - i - n photodiodes was then new in
200
300 400 500 Wavelength (nm)
600
Figure 10.8. The spectral response of a set of front-illuminated Al^^Gai -^'N p - i - n photodiodes with various Al compositions. The line at the top indicates the theoretical maximum for a p - i - n photodetector corresponding to a quantum efficiency of one.
Ill-nitride UV Photoconductors
261
the Ill-nitride research community, and required a new device structure and necessitated new approaches to growth and fabrication. Although sapphire is transparent across the entire AlGaN compositional range, no thick GaN layers can be used prior to growing the p - i - n structure because any low Al composition layers will strongly absorb the incident light if their bandgap energy is smaller than that of the photodetector active region. Building off of the first backilluminated heterostructure GaN p - i - n photodiodes, AlGaN-based devices use a similar p - i - n heterostructure, as shown in Figure 10.9; the bottom layers have a higher Al content and thus larger bandgap than the intrinsic and p-type AlGaN layers. Indeed, this way, the photons of interest with a wavelength near the desired peak responsivity wavelength are able to reach the depletion region with minimal absorption by the thick bottom n-type AlGaN layer. Such a p - i - n structure, therefore, acts as a bandpass filter. To minimize stress between the heterostructure layers, as well as piezoelectric effects, the Al content is sometimes graded at the interfaces. It is also important to remember that such a structure designed for back-illumination, depending on the p-(Al)GaN contact layer and metal contact geometry, can actually be operated both under front- and back-illumination. Once back-illuminated AlGaN photodetectors started to become established, research began to concentrate on the development of back-illuminated photodetectors operation in the solar-blind region. For solar-blind photodetectors, the typical Al concentrations in the bottom n-type are in the range 60-64%, while they are 37-40% in the i- and p-type layers. A typical spectral response curve for an AlGaN solar-blind detector designed for backillumination is shown in Figure 10.10; in this figure the bandpass behavior of the device can be clearly observed when operated under back-illumination [27]. External quantum efficiencies of 60% (responsivity 135 mAAV) have been reported for unbiased photodiodes exhibiting a peak responsivity at 280 nm [49]. Dark currents as low as 5 nA/cm^ at a bias of - 10 V and a detectivity between 4.2 X 10^^ and 5.3 X 10^^ cm Hz^^^AV at 0 V have also been reported [37].
Ni/Au 1000 A AlGaN :Mg 2000 A AlGaN
Ti/Au
AIGaN:Si
Sapphire Figure 10.9. The structure and band diagram of a back-illuminated p - i - n photodetector.
262
Optoelectronic Devices: Ill-Nitrides
0.011
Front-illumination Back-illumination
I 1E-3p'
c
1E-6 200
250
300
350
400
450
500
550
600
Wavelength (nm) Figure 10.10. Typical photoresponse of a back-illuminated solar-blind photodetector.
The optimal structure of back-illuminated solar-blind p - i - n photodiodes is not yet fully established. For example, facing difficulties in obtaining high-quality p-type Al;,Gai-;^.N, a few researchers have designed a so-called inverted heterostructure photodiode in which no p-type Al;,.Gai_;».N layer is needed but only a p-type GaN layer is used instead [36]. In this structure, a wide bandgap intrinsic active layer is placed between narrower bandgap p- and n-type contact layer. For dual illumination devices, the top contact layer must be chosen thin enough to allow most of the incident light to pass through. While at the same time the doping level must be sufficiently high to allow ohmic contacts. In addition, the band offset between the active layer and adjacent contact layers must be sufficient to block the diffusion of photoexcited carriers from contact layers to the active layer. It should be noted that for the back-illuminated device, the n-type contact layer should be an AlGaN layer with higher Al concentration than the active layer to minimize the light absorption by this layer. 10.2,5 Avalanche Photodiodes The rapid progress in the development of GaN and Al;,Gai_;,N based UV photodiodes has naturally paved the way for research work on avalanche photodiodes. To date, there are only few reports of such devices; they consisted primarily of GaN p-i-n"^ photodiodes grown by MOCVD [39], or GaN ir-i-n"^ grown by hydride vapor phase epitaxy (HVPE) in which the TT doping was achieved using Zn [40]. An avalanche gain of 23 was reported at a reverse bias of - 1 0 5 V for the device grown by MOCVD, corresponding to an electric field of ---4 MV/cm. Both linear gain and photon counting modes were observed from the device grown by HVPE. A linear gain of 10 was obtained at - 90 V.
Ill-nitride UV Photoconductors
263
In spite of these successes, the presence of microplasmas in these devices remains an issue. Furthermore, the realization of avalanche photodiodes with shorter cut-off wavelengths, sufficient to reach the solar-blind region, will undoubtedly be challenging as the doping of Al^^Gai-^^N becomes more difficult with increasing Al content. However, if successful, these devices may one day rival the high sensitivity performance of photomultiplier tubes.
10.3. IMPORTANT PHOTODETECTOR PARAMETERS 103,1 General Photodetector Parameters One of the most important photodetector parameters is responsivity; it is a measure of the opto-electric conversion of a photodetector. Responsivity (H) is defined as the photocurrent, in amps, per unit of incident optical power, in watts. It depends upon the number of electron hole pairs generated per incident photon (the quantum efficiency (w)), the wavelength of the incident photons, and the gain, if any, of the photodetector (g). The responsivity is given by the following equation:
where h is Planck's constant, c is the speed of light, and q is the electron charge. The quantum efficiency, 17, in the above equation is the external quantum efficiency. It is also possible to estimate an internal quantum efficiency (rji) for the active region by removing the photon losses associated with reflection and incomplete absorption within the photodetector: r^ = T,i(l - R)(l - e-"^),
(10.2)
where in the above equation R is the optical reflectivity, a is the absorption coefficient of the photodetector, and d is the effective thickness of the absorbing region. Noise equivalent power (NEP) is another parameter commonly used to characterize photodetectors. Essentially, the NEP represents the minimum detectable signal; it is defined as the incident light power necessary to obtain a unity signal to noise ratio in the photodetector signal, and is given by NEP=^^,
(10.3)
where ^ is the responsivity of the photodetector, and i^ is the total noise current. The noise current and its constituent elements are discussed in more detail in Section 10.3.2. NEP is also used in the calculation of detectivity (D*), another common figure of merit for many different types of photodetectors. It characterizes the signal-to-noise
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Optoelectronic Devices: Ill-Nitrides
performance of the device, and is defined as
where Aopt is the optical area of the detector. The detectivity of infrared photodetectors is usually limited not by the detector, but rather by the presence of naturally occurring infrared background radiation. However, in the case of UV, the background falls off very quickly with decreasing wavelength, and is essentially non-existent at wavelengths below 280 nm; Ill-nitride UV photodetectors are usually Hmited by internally generated noise [41]. For a more detailed treatment of these basic photodetector parameters see Chapter 13 of Ref. [42], or Chapter 14 of Ref. [43]. 10.3.2 Basic Noise Analysis Theory The noise response of a detector is an important parameter to understand in detail because it ultimately limits the maximum detectivity of a UV photodetector. Understanding the basic concept of noise and the common origins and types of noise can be useful in the characterization and development of high quality UV photodetectors. Although, typically devices made from wide band gap material will have a low noise level. This section provides a general overview of noise analysis theory. The total noise power generated in a photodetector is given by p„ = (/2>i?L (a),
(10.5)
where /?L is the load resistance and /„ is the noise current. The total noise current representation consists of contributions from many noise sources, but these can be simplified into the three most dominate sources of noise currents: 1// noise (jitter noise), shot noise (generation-recombination noise), and Johnson noise (thermal noise): < 0 =
+
(10.6)
Analysis of the noise power spectrum combined with a basic understanding of the three dominate noise sources can be useful in understanding the operation of UV photodetectors. Noise analysis can often identify the limiting factor for the operation of a particular detector. For 1/f noise, the noise power is calculated as the area under the noise power spectral density curve in the bandwidth range of interest, (BW). The 1/f noise contribution is represented as follows:
<4> = 1^ S,(f)df = 1^ S^ifW + j ^ S„(f)Af,
(10.7)
Ill-nitride UV Photoconductors
( 4 ) = ^0 + ^0 j ^ y d/ = ^oCln BW + 1),
265
(10.8)
although it is also common to just neglect the noise frequencies below 1 Hz and measure the area under the noise power spectral density graph directly. The IIf noise dominates at low frequency (less than 1 kHz). At intermediate frequencies shot noise generally dominates. The shot noise can be estimated by <4ot) = lehBW.
(10.9)
where e is the electron charge. This is also called generation-recombination noise because it describes the effects of generation and recombination centers created by the impurities or lattice defects in the material. The rates depend on the individual nature of the center, its predominant state of charge carriers, and the position of the level within the band gap. The spectral density of Johnson noise is constant, essentially white noise. It is associated with the finite resistance of the device, R, and is due to the random thermal motion of charge carriers in the semiconductor crystal, not to be confused with the fluctuation of the total number of charge carriers. The Johnson noise current can be written as <.r> = ^
,
(10.10)
where R^^^ is the parallel combination of the junction resistance, the external load resistance, and the input resistance of the amplifier. It is usually dominant at high frequencies due to the inversely proportional qualities of the other sources of noise to frequency. However, because Johnson noise is inversely proportional to R, and the resistance of these wide band gap Ill-nitride devices is usually very large, it follows that the Johnson noise does not usually play a significant role in the noise behavior except in special circumstances. 10,3.3 Noise Analysis in GaNp-i-n Photodiodes In attempts to measure the noise level of high Al content Al^cGai -^^N photodetectors, the noise level usually falls well below the resolution of the measurement system. Therefore, we start with an investigation of the noise response of GaN p - i - n devices, as they have a smaller bandgap, and thus their noise is more measurable than that of devices made from AlGaN. The noise in the GaN-based detectors is still traditionally lower than in other III-V semiconductors due to its significantly higher resistance and wider bandgap. In fact, the noise of these devices is still not easily measured except under applied bias: most low noise measurement systems are limited to about 100 fA noise current. The actual photovoltaic (zero bias) noise has to be extrapolated from a series of higher voltage measurements.
266
Optoelectronic Devices: Ill-Nitrides
-5 0 Bias Voltage (V) Figure 10.11. The dark current of GaN p - i - n photodetector at different applied biases.
It is possible that the device is Umited by shot noise. Shot noise can be calculated from the dark current: the I-V curve, in the absence of illumination, for a typical GaN p - i - n device is shown in Figure 10.11. Based on this IV curve, the expected shot noise values of the device at various reverse bias levels are calculated in Table 10.1. The key to this extrapolation is the variation of the dark current with reverse bias. The noise power density of a typical GaN p - i - n detector, at different voltage biases, is measured using a FFT Spectral Analyzer; the data is shown in Figure 10.12. However, the expected values for shot noise in this device are much less than the minimum noise shown in this graph, thus ruling out the shot noise contribution to the noise in these devices. Johnson noise can also be ruled out as an important noise contribution due to the fact that Johnson noise is characterized as white noise, however, this response shows a strong frequency dependence. Based upon analysis of the noise spectrum we can determine that 1// noise dominates; this is the noise behavior that would be expected for a typical Ill-nitride detector operating at low frequencies. In this case the noise power spectral density S^, satisfies the following empirical relationship: '^n =
^0^
(10.11)
(A'/HZ),
Table 10.1. Dark current and shot noise levels for various reverse bias voltage values Bias voltage (V) -5 -6 -7 -8 -9 -10
Dark current (nA) 1.13 2.63 6.15 10.57 20.94 40.00
Shot noise level (A^/Hz) 3.6 X 8.4 X 2.0 X 3.4 X 6.7 X 1.3 X
10"^^ 10"^^ 10~^^ 10~^^ 10~^^ 10"^^
Ill-nitride UV Photoconductors
267
Frequency (Hz) Figure 10.12. The noise power spectral density of a GaN p - i - n photodetector.
where 4 is the dark current,/is the frequency, and SQ and y are fitting parameters. The best fits usually occur with y ~ 1, and the noise parameter SQ should be independent of biasing. Using this equation, the noise power spectral density shown in Figure 10.12 is fit for each of the different biases. These fitting parameters can then be extrapolated back to zero bias and a NEP and detectivity can be estimated. 10.3A Noise Analysis in AlGaNp-i-n Photodiodes The flicker (1//) noise dominates at low to intermediate frequencies, however, at frequencies above 1 kHz, its effects are significantly diminished: usually shot noise begins to dominate; however, with small area AlGaN photodiodes, as in the case of a FPA, the dark current can be so small that shot noise is still insignificant. In high resistance, high Al composition, small area, photovoltaic devices with low leakage currents, Johnson noise becomes the significant source of noise. With high Al composition photodetectors the contribution from thermal noise (Johnson noise) becomes larger than the background radiation. This means that the detectivity of the photodetector is thermal limited. In this case the detectivity can be expressed as follows: Dr
-m
(10.12)
where RQ is the resistance at zero-bias, A is the area of the photodetector, and M is the responsivity. This establishes a maximum detectivity if the photodetector frequency and leakage current are such that neither 1// noise or shot noise are significant [42,44]. In this case the detectivity can be estimated by measuring the photodetector's responsivity and zero-bias resistance, the temperature and area should already be known. Measurement of the responsivity is relatively straightforward; however, Ill-nitride photodetector resistances are usually so high that they cannot be directly measured. This again introduces the need for extrapolation in order to determine the detectivity.
268
Optoelectronic Devices: Ill-Nitrides
However, a method of extrapolating the zero-bias resistance has been proposed by Campbell et al. [45]. After the removal of any instrument-induced offsets exponential fits made to both the forward and reverse bias curves. The forward and reverse bias fits can then be combined to form a single equation for the low current behavior of the diode: / = a(e^^-l) + c(e^^-l), where a and b, and c and d are the exponential fitting parameters from the reverse and the forward bias fits, respectively. The value ofR^ can then be estimated by taking the inverse of the derivative at zero [45]:
JL - _^
, Ro=-r^(10.13) v=o ab + cd This method of exponential fitting provides a good estimate of the zero-bias resistance of an AlGaN photodetector when direct measurement is precluded by instrument noise. The stability of this fit is also found to be better than polynomial fits [45].
10.4. GROWTH, PROCESSING AND MEASUREMENT OF BACK-ILLUMINATED p-i-n PHOTODETECTORS 10,4,1 Introduction In the previous sections we have briefly discussed the common types of Ill-nitride photodetectors, and have provided some basic background on the operational and noise principles of these devices. In this section we take the special case of back-illuminated p - i - n photodetectors, and look in depth at the device structure and its growth, the processing steps and procedures, and provide an overview of the basic measurement of these devices. Back-illuminated detectors operating in the solar-blind region are of special interest, however, they are among the most difficult to grow and fabricate. The solar-blind region corresponds to the strong atmospheric absorption of solar UV in the narrow range of 240-290 nm. The AlGaN material system has a wide direct bandgap and is ideally suited to detection of UV light in the solar-blind range (A < 285 nm), however, this wavelength region requires Al compositions of around 50%. The AlGaN material system suffers from several key problems: large dislocation densities, low doping n-type and p-type efficiency (i.e. conductivity), and lattice and thermal expansion mismatches leading to cracking of the material. All of these problems are exacerbated by the increased aluminum compositions necessary in back-illuminated solar-blind photodetectors. In this section we outline some of these difficulties and the special techniques used to overcome some of these limitations.
269
Ill-nitride UV Photoconductors
10.4.2 Material Growth and Characterization Growth is carried out in a horizontal flow low-pressure metal-organic chemical vapor deposition reactor (AIXTRON 200/4-HT). Double side poHshed basal plane (00.1) sapphire is chosen because it is the only well-established substrate that is UV transparent at the wavelengths of interest; it needs to be double side polished to minimize reflection at substrate since the light will be entering the device through this back surface. The nucleation of the growth begins with the deposition of a thin 200 A low-temperature AIN buffer layer. It is also possible to use an AlGaN buffer with a sufficiently high Al composition to avoid absorption, however, even a thin GaN buffer will absorb an appreciable quality of the incident light and significantly reduce the efficiency of the photodetector. On top of this nucleation layer, 350 nm of high-quality AIN was grown at a temperature of ~ 1 lOO^C. This is followed by a 30-period Alo.87Gao.13N/AlN (50 A/50 A) dislocation-filtering strain-relief superlattice [46]. Atomic force microscopy of this template, as shown in Figure 10.13, reveals aflatsurface with well-ordered atomic steps and an RMS roughness of only 1.3 A for a 5 fxm X 5 ixm scan size. X-ray diffraction reveals narrow full width at half maximums (FWHMs) for both the AIN and AlGaN/AlN superlattice: 61 and 62 arcsec, respectively, for the symmetric (00.2) peaks; and, 260 and 270 arcsec, respectively, for the asymmetric (10.5) peaks. Similar AlGaN/AIN superlattices have been instrumental in the realization of back emission UV light emitting diodes operating in the same solar-blind range [47,48]. 5.00
3«0 nm
1
1.5 nm
2.50
0»0 nm
Figure 10.13. AFM image showing the surface of the high-quahty AlGaN/AlN SL template, 3 nm data scale. The RMS roughness for the 5 mm square scan shown is 1.3 A.
270
Optoelectronic Devices: Ill-Nitrides
Before transitioning into the device structure, a second high-temperature AIN layer is grown, 50 nm thick. In this case lateral conduction is achieved through the use of an 800 nm Alo.5Gao.5N silicon-indium co-doped layer. In order to maximize the lateral current conduction, and thus collection of photo-generated carriers, the conduction layer should ideally be as thick as possible. The limiting factor of conduction layer thickness is generally the cracking of subsequent growth, and depends on material quality; thus the emphasis put on high-quality of the buffer and template layers. The addition of indium to the growth of the conduction layer helps improve the conductivity of the Si-doped material, but can have a negative impact on the morphology. Without indium at first, by careful optimization of the SiH4 flow, and the use of the highquality dislocation filtering superlattice template described above, Alo.5Gao.5N:Si had a tolerable carrier concentration of/i I X l O c m " and a mobility of /x ~ 40 cm^A^ s. The addition of ~ 25 fimol/min of TMIn yields a carrier concentration of n 5 X 10^^ cm~^ and mobility of /A ~ 60 cm^fV s, corresponding to an electrical conductivity approximately five times higher than conventional singly-doped AlGaN of the same aluminum composition [49]. A number of groups have also reported similar success doping high Al content AlGaN using Si-In co-doping [50,51]. In order to facilitate indium incorporation and improve the conductivity of the material, they tend to grow the AlGaN:Si-In at a much reduced growth temperature. This can yield good results for the conduction of the layer, however, two problems can easily arise with low-temperature growth: first the low-temperature growth results in poorer morphology which then adversely affects the quality of the subsequent epilayers' growth; and secondly, the resistivity of the low-temperature AlGaN: Si-In layer, while initially low, has a tendency to increase after the subsequent high-temperature device regrowth, possibly due to desorbtion of a large part of the indium from the codoped material. There is a trade-ofif involved but we have found the optimum temperature to be a relatively high temperature of ~ 1100°C for the growth of the conduction layer. Indium also serves several other beneficial purposes, the most important to the growth of solar-blind photodetectors is that it helps further relieve some of the strain in the layer [52], and thus allows for the growth of a thicker crack-free Alo.5Gao.5N: Si-In conduction layer, while still realizing a completely crack-free device structure. Before the conduction layer and template can be used to grow an active region, it is necessary to confirm the UV transparency at the wavelengths of interest. UV transmission measurement involves using a xenon light source, a monochromator, and a calibrated UV enhanced Si photodetector. First measuring the intensity of the lamp as a function of wavelength, using a synchronous detection scheme, produces a baseline. Then the asgrown template and conduction layer are placed in front of the lamp. Optical transmission of a typical conduction layer is shown in Figure 10.14; it shows a sharp cut-off, and welldefined fringes owing to the high-quality of the material and smooth surface of material grown as described abov^e. In addition the absorbance squared can be calculated; this data
111
Ill-nitride UV Photoconductors 5|— - Absorbance'^2 " Linear Fit
1h
Absorbtion Cutoff 4.76 eV 260 nm
< 3.5
4.0
250
4.5 / Energy (eV)
5.0
300 350 Wavelength (nnn)
5.5
400
Figure 10.14. Optical transmission and absorbance squared of the Alo.sGao.sNiSiiln conduction layer grown on a high-quality AlN/AlGaN SL template. The conduction layer shows a sharp cut-off owning to the excellent material quality, and with the absorption edge occurring at 260 nm.
is also plotted in Figure 10.14. By performing a linear fit an absorption edge of 260 nm is calculated. The template will absorb light with a wavelength shorter than this, and we will see a second cut-off in the detector response. Thus creating the traditional bandpass like response spectra typical of back-illuminated photodetectors. On top of this highly conductive layer the p - i - n photodiode structure consisting of 100 nm n-type Alo.45Gao.55N:Si followed by 200 nm undoped Alo.36Gao.64N and 50 nm p-type Alo.36Gao.64N:Mg is grown. In order to help in the formation of ohmic contacts, it is common to cap the structure with a thin highly doped p-GaN layer. The complete structure is shown in Figure 10.15. Inspection of the material after growth reveals a smooth surface with no signs of cracking. P-type doping is an on going problem in Ill-nitrides, and the doping of the p-GaN and p-AlGaN are especially important to the operation of the photodetector. If the material is not sufficiently well doped the formation of a p-type ohmic contact becomes difficult. Nonohmic p-type contacts can lead to a significant negative photoresponse arising out to 364 nm from Schottky barrier photodetector like behavior of the contact. This behavior has been reported elsewhere in the literature, and attributed to the non-ohmic nature of p-type contacts [49,53]. The presence of a negative photoresponse subtracts from the overall efficiency of the device and decreases the device's degree of solar-blindness.
272
Optoelectronic Devices: Ill-Nitrides Ti/Au
Thin Ni/Au
Back-Illumination Figure 10.15.
Schematic cross-section showing the structure of a back-illuminated solar-blind photodetector.
A typical photoresponse for a solar-blind back-illuminated photodetector with a negative photoresponse is shown in Figure 10.16. In order to maximize the out-of-band rejection ratio, the photoresponse from the Schottky needs to be minimized. Optimization of the doping in order to remove the negative response is discussed in Ref. [54]; through careful optimization, in that reference, much improved devices could be
280 320 360 Wavelength (nm)
400
Figure 10.16. Responsivity vs. wavelength for a back-illuminated p - i - n photodiode, showing a significant negative photoresponse.
Ill-nitride UV Photoconductors
273
600 h Various CpgMg flows 400 200
Over Doped — o — Reduced doping — • — Optimized doping
0 3
o
-200 -400 -600 -10
-5
10 Voltage (v)
Figure 10.17. I-V curves for several dijfferent Cp2Mg flows used to optimize the p-type layers. The structure and measurement geometry are shown in the lower right-hand corner.
realized. Optimization is difficult because direct attempts to characterize the Alo.36Gao.64N:Mg layer by Hall effect measurements reveal that the material is highly-resistive (measurement limited). Thus, in order to optimize the material it is proposed to use the transfer length method (TLM) to study the I-V characteristics, specific contact resistivities, and sheet resistances as a function of doping. To examine the quality of the p-type material a series of test structures is grown. These begin with the same high-quality superlattice template grown on sapphire, as previously described. Then 100 nm of Alo.36Gao.64N:Mg is deposited, and in order to help in the formation of ohmic contacts, this layer is then capped with the same highly doped thin pGaN layer, as in the photodetector structure. This test structure is shown in the inset of Figure 10.17. The contact resistivities can then be extrapolated from TLM measurements, and the insight provided can be used to optimize the AlGaN. 10.4.3 p-i-n Photodetector Processing In order to fabricate the material into diodes, the samples are first annealed at 1000°C for 30 s, under N2 ambience, to activate the magnesium in the p-type layers. Then 30 A Ni/30 A Au is deposited on top of the mesa, and annealed under ambient air at 500°C for 10 min, to form p-type ohmic contacts. The devices are lithographically patterned into 1 mm X 1 mm square mesas and etched using electron cyclotron resonance etching. A 300 A Ti/1800 A Al ring contact is then deposited around the mesa, and is then annealed under nitrogen to form an ohmic n-type contact to the Alo.sGao.sNrSi-In conduction layer. Finally a 400 A Ti/1200 A Au bonding pad is deposited on top of the mesa to facilitate wire bonding of the device.
274
Optoelectronic Devices: Ill-Nitrides
Additional post processing of the device is also worth considering, although not implemented for these devices. The electrical properties of the device can be improved by passivation of the surface. However, there has been less investigation of passivation of high Al composition p - i - n photodetectors; the majority of the work focuses on Schottky barrier photodetectors and MSMs. Both Si3N4 and Si02 have been implemented [55,56], and their performance characteristics have been compared [57]. In surveying the literature the overwhelming preference seems to be for Si02 passivation. Si02 also has the advantage of having much higher transmission in the solar-blind region, thus a Si02-passivated device can optimally be used for both front and back-illumination. Additionally an anti-reflection coating can be applied to the back of the sapphire substrate to reduce reflection at the surface and thus improve the external quantum efficiency of the device. However, to date very few groups seem to have actually implemented anti-reflection coating on their devices, and the majority of publications make a point of saying "without anti-reflection coating." In the case presented here, no post processing of the device was implemented. 10,4.4 Photodetector Measurement and Discussion The processed devices are mounted to a copper block with a hole in the center to facilitate handling, provide pads for wire bonding of the device, and allow illumination of the sample for back-illuminated responsivity measurement. Working with back-illuminated devices can become a challenge because of the increased complexity involved in packing and handling these devices. The current-voltage (/-V) parameters of the device are measured using a low noise probe station and a semiconductor parameter analyzer. A typical I-V curve is shown in Figure 10.18. From the / - y curve it is possible to determine the device turn-on and estimate the series resistance by plotting /(dV/d/) vs. current and taking a linear fit in the high current regime
3
o
Voltage (V) Figure 10.18. I-V curve of a typical back-illuminated photodiode in semi-log scale.
IILnitride UV Photoconductors
115
as discussed in Ref. [58]. In this case a turn-on of 6.8 V, and a series resistance of 202 fl are estimated. The leakage is determined by applying 5 V of reverse bias to a dark junction, and measuring the current; in this case the leakage was 230 ixA/cm^. In addition, the ideality factor can be modeled in order to gain insight into the conduction mechanisms operating in the photodetectors. Under low current injection, the effects of series resistance become negligible; thus, the ideality factor of the diode can be extracted. Figure 10.19 shows the natural log of the current, in the low current regime for a typical device. The ideality factor is calculated by fitting the linear part of the curve with the following equation:
this yields an ideality factor of n = 2.89 for this diode. This equation arises from the combination of the equations for diffusion current and recombination current, the two currents that usually dominate in the diode current. The ideality factor is expected to have a value between 1 and 2. Whereas if n is closer to 1, then diffusion current dominates, however, if n is closer to 2, recombination current dominates. However, a value of n = 2.89 falls well outside of this expected range, suggesting that an additional process makes a significant contribution to conduction. The most probable explanation for the non-ideality of this device is the weak Schottky-like nature of the p-contact creating a second diode in series with the p - i - n junction. The photoresponse is measured using a high intensity xenon lamp and monochromator, calibrated with a reference calibrated UV-enhanced silicon photodetector, such as Newport model number 818-UV. The photoresponse under back-illumination for a typical device is shown in Figure 10.20. The spectral response drops four orders of magnitude from the peak into the near-UV region, and no negative photoresponse occurs.
"-T—'—I—'—I—»—I—«—I—'—I—'—I—'—I—'
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Voltage (V) Figure 10.19. Natural log of current versus voltage data. The low current regime is modeled and an ideality factor of 2.89 is extracted.
276
Optoelectronic Devices: Ill-Nitrides 70
102
60
Un-Biased External Q.E. 68% @ 280 nm
50
10°^
40 10-''
30
10-2
20
10-2 Un-Biased Peak Responsivity 150mA/W@280nm
10
220 240 260 280 300 320 340 360 380 Wavelength (nm)
0 250
260
270 280 290 Wavelength (nm)
300
Figure 10.20. Responsivity vs. wavelength for a typical photodiode, showing a peak responsivity of 150 mAAV at a wavelength of 280 nm, and no negative photoresponse. This peak responsivity corresponds to an external quantum efficiency of 68%. The inset shows the external quantum efficiency of the device in linear scale.
The photoresponse curve never changes sign, at any point, in contrast to the photoresponse of the unoptimized diode that was shown in Figure 10.16. This device shows an unbiased peak responsivity of 150 mAAV at 280 nm, with a FWHM of 12 nm; this responsivity corresponds to a high-value of 68% for the external quantum efficiency of the device. Under a - 5 V bias (measurement set-up limited) the responsivity increases to 169 mAAV, corresponding to an external quantum efficiency of 74% [54]. In summary, we overviewed the growth and processing of high efficiency AlGaN-based back-illuminated solar-blind p - i - n photodetectors. High-quality AIN and AlGaN/AlN superlattice layers and a high-lateral-conductivity n-type AlGaN:Si-In co-doped layer are discussed as a means of improving the device. In addition optimization of the p-AlGaN layer in order to eliminate the out-of-band negative photoresponse is discussed.
10.5.
FOCAL PLANE ARRAYS
10.5.1 Introduction to Focal Plane Array Technology There is a considerable increase in complexity in going from single pixel large area photodetectors to developing cameras based on FPAs. The many thousands of pixels in FPAs require some sort of multiplexer technology to interface them with the image creation electronics. In a very small array the pixels can be individually wire bonded to a neighboring image processing circuit; however, in larger arrays it becomes necessary to use flip chip technology to hybridize the FPA to a Si readout integrated circuit (ROIC), shown in Figure 10.21. The ROIC contains a sample and holds unit cell for each individual pixel: in the case of detection of low background UV signals with high impedance Ill-nitride photovoltaic pixels, this is traditionally a capacitive transimpedance input amplifier (CTIA) unit cell. This cell uses a transimpedance amplifier with capacitive
111
Ill-nitride UV Photoconductors Reset In Solder bumps
Cint Detector
/Vt x^ Figure 10.21.
A schematic cross section of a Ill-nitride FPA flip-chip bonded to a Si ROIC. On the right is a simpHfied schematic of a typical CITA unit cell as used in a ROIC.
feedback to integrate the photocurrent [59]: a simplified schematic of a CTIA unit cell is shown in Figure 10.21. The ROIC also contains multiplexer electronics to sequentially read out the various rows and columns of the array. Depending on the application, the ROIC may contain more sophisticated image processing electronics: this varies from the simplest ROICs that just output the raw pixel data, to more complex designs that allow programmatic control of gain and integration, and output NTSC compatible video [60]. Hybridization with a ROIC requires that the photodetector be illuminated through the substrate so that the epitaxial side can be indium bump bonded directly to the ROIC. As discussed earlier, back-illumination introduces a number of complications for Ill-nitride photodetectors; most of these problems arise from the need for high Al content in the template and conduction layers in order to provide UV transparency. The photodetector pixels are generally in the order of 30 [xm^ with only 5 fxm between adjacent pixels, and there are tens of thousands of these pixels, all spanning an area of about 1 cm^. Fabrication of FPAs requires a consistently high level of uniformity over a large area. It is also necessary to obtain good current spreading to allow current collection from the center of the array. Hybridization also introduces its own host of problems: it requires additional processing to passivate the detectors, open a window, and deposit In bumps on each of the mesas as well as the ROIC itself. In addition a specialized flip-chip bonding tool is necessary to allow proper registration of the FPA and the ROIC, and to form a mechanically and electrically robust bond across the entirety of the array. Despite these difficulties, a number of groups have been successful in reporting GaN and AlGaN based FPAs [61,62,64-70]. 10,5,2 Development of UV Focal Plane Arrays Linear arrays of Ill-nitride photodetectors were reported as early as 1996; an example is the linear array of 16 photoconductors on GaN using MSM structures reported by Huang et al. [61]. By 1997, the first two-dimensional arrays were reported. However, the array dimensions were still too small to be of practical application for UV imaging; for example, a simple 8 x 8 GaN Schottky photodiode array was barely able to record the image of two parallel lines [62]. The first practical 256 X 256 UV imaging camera was demonstrated in
278
Optoelectronic Devices: Ill-Nitrides
1999 by the NASA/Goddard Space Flight Center [63]. This camera consisted of an array of 65,532 (30 fxm X 30 iJim) photoconductive GaN UV detector elements In bump bonded to a Si read-out intergraded circuit. The FPA assembly was integrated with driver electronics and a computer so as to create a complete imaging system. This camera was capable of taking pictures with complex two-dimensional geometry. Building a camera based of photoconductive detector elements is easier than using photovoltaic elements; a photoconductive array can take advantage of the potentially high photoconductive gain to realize a much larger responsivity than is possible with p - i - n photovoltaic detector elements. A GaN p - i - n photodetector, assuming 100% external quantum efficiency, has a maximum theoretical responsivity of 0.270 AAV, whereas the photoconductive pixels in the array described above had an estimated responsivity of 690 AAV [63]. However, photovoltaic detectors generally have the advantage of much faster response times than photoconductors; for example, the photoconductive array had an estimated response time of 0.2-1.0 ms [63], whereas a similar p - i - n photodiode array has as estimated response time of 1 -100 ns [64]. This allows for much faster frame rates, limited only by the integration time necessary to obtain an adequate signal. Unlike photoconductors, photodiodes can operate without an applied bias; operation of these photodetectors without bias significantly reduces the noise levels, and allows for much higher detectivities. The first successful demonstration of a UV digital camera based on GaN/AlGaN heterostructure p - i - n photodetector elements was also reported in 1999 [65]. The pixels of this array had an estimated responsivity of 0.2 AAV from 365 to 320 nm. This visiblebUnd camera was capable of imaging a simple alphanumeric scene composed of a brass gobo backlit by a Hg(Ar) pencil lamp. In a second publication an attempt was made to image human likenesses [66], however, the 32 X 32 resolution of this first camera limits the usefulness. Since then, other groups have reported 32 X 32 arrays of p - i - n photodetectors [67]; in addition larger 128 X 128 [64] and 320 X 256 [68] visible-blind p - i - n based cameras have been demonstrated. These later generation visible-blind cameras show good uniformity and are capable of capturing a high level of detail;
(a)
^ 1 Figure 10.22. (a) Visible image and (b) 320 X 256 UV FPA image of the Engineering Graduate Research Center in the North Carolina State University campus. [Figure reproduced with permission from Ref. [68]].
Ill-nitride UV Photoconductors
279
Figure 10.22 shows a sample 320 X 256 image taken by researchers at North Carolina State University [68]. Successes in the development of GaN-based UV FPAs, and single pixel AlGaN photodetectors, especially back-illuminated devices, have recently lead to the realization of FPAs based on AlGaN absorption layers [69,70]. However, to date, very few truly solarblind cameras have been realized. Lamarre et al. [70], in addition to reporting several longer wavelength cameras, also reported that in 2001 BAE systems successfully processed a wafer provided by Cree Inc. [71] to create a 265-285 nm solar-bHnd camera based on an Alo.44Gao.56N absorption layer. However, they only provide statistics on the uniformity and pixel operation, and they do not publish any images from this first reported AlGaN-based solar-blind camera. A year later North Carolina State University reported a solar-blind camera and published an image of several geometric shapes, shown in Figure 10.23 [68]; however, the quahty of the image shown reveals that there is a great deal of improvement necessary before Ill-nitride solar-blind cameras can be commercialized. (a)
Figure 10.23. (a) Visible image and (b) UV image taken with a 320 X 256 solar-blind UV FPA. [Figure reproduced with permission from Ref. [68]].
280
Optoelectronic
Devices:
Ill-Nitrides
ACKNOWLEDGEMENTS The authors of this chapter gratefully acknowledge the contribution of A. Yasan, K. Mayes, S.R. Darvish, and P. Kung of the center for quantum devices, Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL.
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[49] McClintock, R., Yasan, A., Mayes, K., Shiell, D., Darvish, S.R., Kung P., Razeghi, M., (2004) High quantum efficiency AlGaN solar-blind p - i - n photodiodes, Appl Phys. Lett, 84, 1248-1250. [50] Cantu, P., Keller, S., Mishra, U. & DenBaars, S. (2003) Metalorganic chemical vapor deposition of highly conductive Alo.65Gao.35N films. Appl Phys. Lett, 82, 3683-3685. [51] Adivarahan, V., Simin, G., Tamulaitis, G., Srinivasan, R., Yang, J., Khan, A., Shur, M. & Gaska, R. (2001) Indium-silicon co-doping of high-aluminum-content AlGaN for solar blind photodetectors. Appl Phys. Lett, 79, 1903-1905. [52] Yamaguchi, S., Kariya, M., Nitta, S., Amano, H. & Akasaki, I. (2000) Strain reUef by In-doping and its effect on the surface and on the interface structures in (Al)GaN on sapphire grown by metalorganic vapor-phase epitaxy. Appl Surf. Set, 159/160, 414-420. [53] Collins, C , Chowdhury, U., Wong, M., Yang, B., Beck, A., Dupuis, R. & Campbell, J. (2002) Improved solar-blind detectivity using an Al^^Gai-^^N heterojunction p - i - n photodiode. Appl Phys. Lett, 80, 3754-3756. [54] McClintock, R., Yasan, A., Mayes, K., Shiell, D., Darvish, S.R., Kung, P., Razeghi, M., (2004) High quantum efficiency solar-blind photodetectors, Proc SPIE, 5359, 434-444. [55] Biyikh, N., Kimukin, I., Kartalogl, T., Aytur, O. & Ozbay, E. (2003) High-speed solar-blind AlGaN-based metal-semiconductor-metal photodetectors. Phys. Stat Sol (c), 0 (7), 2314-2317. [56] Adivarahan, V., Simin, G., Yang, J.W., Lunev, A., Asif Khan, M., Pala, N., Shur, M. & Gaska, R. (2000) Si02 -passivated lateral-geometry GaN transparent Schottky-barrier detectors. Appl Phys. Lett, 11 (6), 863-865. [57] Monroy, E., Calle, P., Pau, J.L., Munoz, E., Verdu, M., Sanchez, F.J., Montojo, M.T., Omnes, P., Bougrioua, Z., Moerman, I. & San Andres, E. (2001) Effect of dielectric layers on the performance of AlGaN-based UV Schottk photodiodes. Phys. Stat Sol (a), 188 (1), 307-310. [58] Collins, C , Li, T., Beck, A., Dupuis, R., Campbell, J., Carrano, J., Schurman, M. & Ferguson, I. (1999) Improved device performance using a semi-transparent p-contact AlGaN/GaN heterojunction positive-intrinsic-negative photodiode. Appl Phys. Lett, 75, 2138-2140. [59] Vampola, J.L. (1993) in Readout Electronics for Infrared Sensors, The Infrared and ElectroOptical Systems Handbook, vol. 3, Ed. Rogatto, W.D., Infrared Information Analysis Center/ SPIE Optical Engineering Press, Michigan, USA, Washington, DC, Chapter 5; Executive editors: Accetta, J.S., Shumaker, J.L. [60] ISC9809 320 X 256 low background ROIC, Indego Systems, Inc., http://www.indigosystems. com/product/roic_9809.html, 2003. [61] Huang, Z.C, Chen, J.C., Mott, D.B. & Shu, P.K. (1996) High performance GaN linear array. Electron. Lett, 32 (14), 1324-1325. [62] Lim, B.W., Gangopadhyay, S., Wang, J.W., Osinsky, A., Chen, Q., Anwar, M.Z. & Khan, M.A. (1997) 8 x 8 GaN Schottky barrier photodiode array for visible-blind imaging. Electron. Lett, 33 (7), 633-634. [63] Ted, Z.C.H., David, B.M. & Anh, La. (1999) Development of 256 X 256 GaN ultraviolet imaging arrays. Proc. SPIE, 3764, 254-260. [64] Brown, J.D., Boney, J., Matthews, J., Srinivasan, P. & Schetzina, J.F. (2000) UV-specific (320-365 nm) digital camera based on a 128 X 128 focal plane array of GaN/AlGaN p - i - n photodiodes. MRS Internet J. Nitride Semicond. Res., 5 (6). [65] Brown, J.D., Yu, Z., Matthews, J., Harney, S., Boney, J., Schetzina, J.F., Benson, J.D., Dang, K.W., Terrill, C , Nohava, T., Yang, W. & Krishnankutty, S. (1999) Visible-blind UV digital
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camera based on a 32 X 32 array of GaN/AlGaN p - i - n photodiodes. MRS Internet J. Nitride Semicond. Res., 4 (9). Brown, J.D., Matthews, J., Harney, S., Boney, J., Schetzina, J.F., Benson, J.D., Dang, K.V., Nohava, T., Yang, W. & Krishnankutty, S. (1999) High-sensitivity visible-bHnd AlGaN photodiodes and photodiode arrays. MRS Internet J. Nitride Semicond. Res., 5S1 (W1.9) From Symposium W, Gallium Nitride and Related Alloys at the Fall meeting of the Material Research Society. Yang, B., Heng, K., Li, T., ColHns, C.J., Wang, S., Dupuis, R.D., Campbell, J.C., Schurman, M.J. & Ferguson, I.T. (2000) 32 32 ultraviolet Al Ga N/GaN p - i - n photodetector array. Quantum Electron. Lett., 36 (11), 1229-1231. Long, J.P., Varadaraajan, S., Matthews, J. & Schetzina, J.F. (2002) UV detectors and focal plane array imagers based on AlGaN p - i - n photodiodes. Opto-Electron. Rev., 10 (4), 251-260. Lamarre, P., Hairston, A., Tobin, S., Wong, K.K., Taylor, M.F., Sood, A.K., Reine, M.B., Schurman, M.J., Ferguson, I.T., Singh, R. & Eddy, C.R., Jr. (2001) Mater Res. Soc. Symp. Proc, 639, GIO.9.1. Lamarre, P., Hairston, A., Tobin, S.P., Wong, K.K., Sood, A.K., Reine, M.B., Pophristic, M., Birkham, R., Ferguson, LT., Singh, R., Eddy, C.R., Jr., Chowdhury, U., Wong, M.M., Dupuis, R.D., Kozodoy, P. & Tarsa, E.J. (2001) AlGaN UV focal plane arrays. Phys. Stat. Sol. (a), 188 (1), 289-292. Tarsa, E.J., Kozodoy, P., Ibbetson, J., Keller, B.P., Parish, G. & Mishra, U. (2000) Solar-blind AlGaN-based inverted heterostructure photodiodes. Appl. Phys. Lett., 11 (3), 316-318.
optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 11
Quaternary InAlGaN-based UV LEDs Hideki Hirayama The Institute of Physical and Chemical Research (RIKEN), 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan
In order to realize 250-350 nm-band deep ultraviolet (UV) emitters using group Ill-nitride materials, it is necessary to obtain high-efficiency UV emission and hole conductivity for wide-bandgap (In)AlGaN. Use of the In-segregation effect, which has already been used for InGaN blue emitting devices, is quite effective for achieving highefficiency deep UV emission. We have demonstrated high-efficiency UV emission by introducing several percent of In into AlGaN in the wavelength range between 300 and 360 nm at room temperature (RT) using the In-segregation effect. Emission fluctuations in the submicron region due to In-segregation were clearly observed for quaternary InAlGaN epitaxial layers. An internal quantum efficiency as high as 15% was estimated for a quaternary InAlGaN-based single quantum well (SQW) at around 350 nm at RT. Such high-efficiency UV emission can even be obtained on high threading-dislocation density buffers. In addition, suitable hole conductivity was obtained for high Al content (>53%) Mg-doped AlGaN by using an alternating gas flow growth technique in metal-organic vapor phase epitaxy (MOVPE). We used these techniques to fabricate 310-nm-band deep UV light-emitting diodes (LEDs) with quaternary InAlGaN active regions. We achieved sub-milliwatt output power under RT pulsed operation for 308-314 nm LEDs. We also demonstrated a high output power of 7.4 mW from a 352 nm quaternary InAlGaN-based LED fabricated on a GaN substrate under RT CW operation.
11.1. INTRODUCTION AlGaN or InAlGaN alloys are attracting much attention as candidate materials for reahzing deep-ultraviolet (UV) LEDs or LDs. Figure 11.1 shows the relationship between the direct transition bandgap energy and the lattice constant of the wurtzite (WZ) InAlGaN material system and the lasing wavelengths of gas lasers. The direct transition emission of AlGaN can be adjusted between 6.2 eV (AIN) and 3.4 eV (GaN). The wide emission range
E-mail address: [email protected] (H. Hirayama).
285
286
Optoelectronic Devices: Ill-Nitrides i93nm Wavelength ArF
257nnn • Ar-SHG
325nm He-Cd
200nm
6.0
248nm KrF
308nm xeCI
300nm r
400nm
Excimer Lasers 500nm
rr
Developing Area for UV-LEDs orLDs
5.0
ir-
> 4.0
iS 3.0
GaN
Q.
(0 U> "D C
CD 2.0
700nm I
Wavelength of Ga^Lasers 1.5jum
1.0K
InN
3.0 ^4.0 Lattice Const. (A) Figure 11.1.
Relationship between the direct transition energy bandgap and the lattice constant of wurtzite (WZ) InAlGaN material and the lasing wavelengths of gas lasers.
in the UV of (In)AlGaN covers the lasing wavelengths of various gas or solid-state UV lasers, including XeCl (308 nm) or KrF (248 nm) excimer lasers, N2 lasers (337 nm) and He-Cd (325 nm) or Ar-SHG (257 nm) lasers, as shown in Figure 11.1. Figure 11.2 illustrates some applications for high-efficiency semiconductor UV light sources with wavelengths between 250 and 350 nm. There are many appHcations for high-efficiency UV LEDs or LDs, i.e. long-lifetime white lighting, high-density optical storage, medical fields or biochemical processes and the purification of the environment. They are also useful for household air cleaners or sterilization systems, automobile exhaust purifiers, UV sensing systems, etc. Fluorescent lamps could be replaced by long-lifetime white lamps excited with UV LED arrays if low-cost, efficient UV LEDs could be achieved. To obtain high absorption efficiency of the phosphor used in white lighting, a wavelength below 350 nm is required. Efficient UV lights have also recently attracted considerable attention for the purification of the environment, i.e. the purification of river water, industrial waste water or atmospheric gases. It has been pointed out that an efficient 320-340 nm UV fight source is required for the photocatalytic decomposition of refractory pollutants (dioxin, PCB or NO^, gas, etc.) with titanium oxide (Ti02).
Quaternary InAlGaN-based UV LEDs
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Applications of UV Light
White Lighting hOOOLEDs : 100W
|f
#4 White
High-Efficiency 30-40% '-°"9 J-ifetime:
HigH)ensity Memory DeepUV Laser Diode |(250-300nm)|
DVD Recorder using UV-Laser
Take place of fluorescent lamp U V L E D Array
U V D V D Disl<
Medical Rdd
Titanium^ Oxide
•Discrimination of Cancer Position •Sterilization • U V Laser Treatments
Siiort Waveiength->-Hrgh Densitv
J { Purified l^rf' Water)
Industrial Pollutants
Dioxin, PCB, U V L E D A r r a y etc. ."^Br-.Uunm
Another Applications:
(Water and Air Purfficafion) Rivem. Oceans. Lakes The atmosphere
• Automobile exiiaust • UV Sensors (NOx gas ) Purifier • Chemical or Biochemical Industries • Household Air Cleaner
Figure 11.2. Applications of UV LEDs or LDs with emission wavelengths of 250-350 nm.
In order to obtain high-intensity UV emission at a shorter wavelength than can be realized by InGaN, the development of AlGaN or quaternary InAlGaN-based UV emitters is necessary. Research into AlGaN-based UV LEDs was initiated by several research groups between 1996-1998. UV LEDs with wavelengths between 330 and 355 nm [1-3] have been reported using AlGaN-based structures. However, their output power was still low, due to a number of technical problems. Recently, high-power near-UV LEDs at a wavelength of 365 nm have been realized by Nichia, who use InGaN in the emitting regions [4]. External quantum efficiencies (EQE) as high as 30% have already been achieved for near-UV LEDs using InGaN. On the other hand, it is still difficult to obtain high EQE for wavelengths below 360 nm. There are several reports of 300-365 nm UV LEDs using AlGaN QWs [5-8] or InAlGaN QWs [9-12]. The maximum EQE for a 351 nm LED using an AlGaN QW fabricated on a GaN substrate was reported to be approximately 1% [5]. Recently, deep-UV LEDs with wavelengths shorter than 300 nm have been developed, i.e. 250 nm[13],267 nm[14],278 nm[15],280 nm[16], 285 nm [17] and 292 nm [18] using AlGaN-based QWs. The values of EQE obtained from 250-350 nm LEDs are still below 0.1% under CW operation. The realization of high-efficiency deep UV LEDs with wavelengths below 360 nm is still challenging because of some major problems in producing AlGaN-based UV emitters, i.e. the difficulty in obtaining efficient UV emission from AlGaN QWs at room
288
Optoelectronic Devices: Ill-Nitrides
temperature (RT) and the difficulty of injecting holes through high-Al-content AlGaN. A reduction in threading dislocation density (TDD) is necessary in order to obtain efficient UV emission from AlGaN-based structures. However, reducing the TDD of AIN or highAl-content AlGaN is still difficult to achieve. The use of quaternary InAlGaN emitting layers is considered to be quite effective for the realization of high-efficiency UV LEDs or LDs using group III nitrides due to the efficient emission they exhibit at wavelengths shorter than 360 nm, which is attributed to Insegregation effects [19,20]. We proposed the use of the emission from a localized electronhole pair in the In-segregation region in quaternary InAlGaN for the purpose of obtaining RT bright UV emission [21]. It has been reported that the quantum-dot-like region [22] formed by In-segregation in InGaN QWs is very effective for the suppression of nonradiative recombination and that an InGaN QW exhibits efficient emission at RT [23,24]. A similar effect to that obtained in InGaN QWs is expected for quaternary InAlGaN. Due to this effect, quaternary InAlGaN is very promising for use as the active layer of 300350 nm-band LDs or LEDs. We have demonstrated that the intensity of the 320-340 nm UV photoluminescence (PL) from quaternary InAlGaN is as strong as that of the 430 nm blue emission from InGaN at RT [19]. We have already demonstrated high-efficiency UV emission from quaternary QWs of InviAlyiGai_;,i_^,iN/In;,2A1^2Gai_;,2->^2N in the wavelength range between 300 and 350 nm at RT [20] and efficient 340 nm-band InAlGaN-based LEDs on SiC substrates [9,25]. The most important advantage of the use of quaternary InAlGaN is that high-efficiency deep-UV emission is obtained, even for a layer grown on buffer with high TDD. The emission intensity of AlGaN epitaxial layers is very sensitive to TDD. Therefore, UV devices using AlGaN-based active regions need to be fabricated on low TDD buffer-layers or substrates. On the other hand, quaternary InAlGaN UV LEDs show high-efficiency operation, even when fabricated on high TDD buffer layers grown on sapphire substrates. The use of InAlGaN quaternary as the emitting region is considered to be particularly useful for deep-UV LEDs, since reducing the TDD is still difficult for high Al-content AlGaN. In this chapter, we describe techniques for the realization of high-efficiency 300350 nm-band UV LEDs. In Section 11.2, we describe the growth and optical properties of high-Al-content Al;,Gai_;,N for application to deep-UV emitters. The growth conditions for high-quality Al_;,Gai_;cN are investigated and a single peak spectrum from high-Alcontent Al_;^Gai-;,N (Al content up to 80%) is observed emitting from near the band-edge. Intense UV emission around 230-280 nm is demonstrated from Al^^Gai-^^N/Al^Gap^N multi-quantum wells (MQWs) with wide-bandgap AlGaN barriers. The intensity of the deep-UV emission from AlGaN-based MQWs is shown to be as high as that of the blue emission from InGaN-based QWs at 77 K. However, the 200 nm-band UV emission from AlGaN-based QWs at RT is much weaker than the blue emission from InGaN. In Section 11.3, we describe the growth and the optical properties of quaternary In;^Al^Gai_;,_^N to obtain intense UV emission at RT by using the In-segregation effect.
Quaternary InAlGaN-based UV LEDs
289
We reveal that efficient emission is obtained from lnx\P^yiGdii-x\-y\^l^^x2^^y2^^\-x2-y:^ QWs in the wavelength range between 290 and 380 nm at RT. The UV emission from quaternary InAlGaN is shown to be as strong as the blue emission from InGaN at RT. For the realization of deep-UV LEDs, it is also necessary to achieve high-Al-content p-type AlGaN. In Section 11.4, we describe an alternating gas flow growth technique for producing high-Al-content p-type AlGaN. We reveal that the use of an alternating gas flow is quite effective for obtaining high-Al-content AlGaN with high crystalline quality. We observed hole conductivity in Mg-doped AlGaN with Al compositions as high as 53% that was grown using the alternating gas flow method. In Section 11.5, we describe UV LEDs with InAlGaN emitting regions. We demonstrated sub-milliwatt output power under RT pulsed operation from 308-314 nm quaternary InAlGaN-based LEDs fabricated on sapphire substrates. We also fabricated quaternary InAlGaN QW LEDs on GaN substrates in order to eliminate the effects of TDD. We demonstrate an output power of 7.4 mW at a wavelength of 352 nm under RT CW operation. We also demonstrate the highest EQE ever obtained for 350 nm-band UV LEDs with top emission geometry. From these results, the advantage of using the quaternary InAlGaN for 300-350 nm-band UV-emitting devices is confirmed.
11.2. GROWTH AND OPTICAL PROPERTIES OF Al^Gai_^N In this section, we describe how we investigated the basic growth conditions and optical properties of AlGaN as a first step in developing quaternary InAlGaN with efficient UV emission at RT. We demonstrate efficient UV PL at wavelengths ranging from 230-280 nm from Al^Gai-^NCAlNyAl^^Gai^N MQWs grown on SiC by MOVPE [26,27]. We systematically investigated the PL intensity of AlGaN-based MQWs with widebandgap AlGaN barriers as functions of both the QW thickness and the Al content of the barriers [28,29]. The efficiency of the deep-UV emission from AlGaN-based QWs is shown to be as high as that of the blue emission from InGaN-based QWs at 77 K. The samples were grown at 76 Torr on the Si-face of an on-axis 6H-SiC (0001) substrate, using a conventional horizontal-type MOVPE system. Ammonia (NH3), trimethylaluminum (TMAl) and trimethylgallium (TMGa) were used as precursors, with H2 as the carrier gas. N2 gas was supplied independently by a separate line in order to control the gas flow. Typical gas flows were 2 standard liters per minute (SLM), 2 and 0.5 SLM for NH3, H2 and N2, respectively. The molar fluxes of TMGa and TMAl for the growth of Al;,Gai_;,N (x = 0.11-1) were 38-3.8 and 2.6-45 |ULmol/min, respectively. Under these conditions, the growth rates of Alo.11Gao.89N, Alo.40Gao.60N and AIN were approximately 2.4, 1.0 and 0.4 luim/h, respectively. The substrate temperature during the growth of the Al;,Gai_;,N, as measured using a thermocouple located at the substrate susceptor, was approximately 1140,1170 and 1200°C for Al contents (JC) of 10-40,40-80
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Optoelectronic Devices: Ill-Nitrides
and 80-100%, respectively. All of the samples were undoped. The molar fraction x of Al in the Al^^-Gai-^^N alloy was determined by four-crystal X-ray diffraction (XRD) measurements. We investigated the optical properties of the Al;,Gai_;cN alloy over the entire AIN compositional range, i.e. GaN to AIN. Figure 11.3 shows the spectra and full-width at half maximum (FWHM) of the PL emission observed from the Al;cGai-;cN alloy over the entire AIN compositional range at 77 K. We observed a single-peaked PL spectrum from near the band-edge over the entire Al compositional range. The yellow emission around 500-550 nm was negligible, even for high-Al-content AlGaN. The phonon-replica peaks seen at the low-energy side of each spectrum for Al contents of 0.11-0.53 confirms the high crystalline quality of the AlGaN. Typical values of FWHM of the PL spectrum at 77 K were approximately 20, 65 and 100 meV for Al contents of 10-20, 35-60 and 70-95%, respectively. We observed PL emission from AIN (208 nm) from near the band edge. Figure 11.4 shows the PL spectra of high-Al-content Al;,Gai_;cN (where x is greater than 80%) measured at 77 K. We observed that the PL emission of AIN is significantly
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Quaternary InAlGaN-based UV LEDs
291
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enhanced by incorporating 5-10% of GaN into AIN. We hypothesize that the Al crystalline quality is greatly improved by introducing a small amount of Ga, which we characterized by XRD measurements. We then fabricated four series of AlGaN MQW samples, consisting of Al^Gai-^^N barriers with different Al contents. Table 11.1 summarizes the structure and the thickness of the buffer, barrier and well layers and the PL peak wavelength range of each series of AlGaN MQWs. Figure 11.5 shows an example of the schematic layer structure of an AIN/ AlGaN five-layer MQW sample (sample series (a) in Table 11.1). In order to achieve a flat surface suitable for the growth of AlGaN QWs, an approximately 250-400-nm-thick
Table 11.1. Structure and thickness of the buffer, barrier and quantum-well layers, displayed with the PL peakwavelength range of each series of AlGaN MQWs Sample series
Structure
Buffer
Barrier
(thickness, nm)
(thickness, nm)
Well (thickness, nm)
Peak wavelength (nm)
(a)
5-MQW
AIN (250)
AIN (5)
Alo.i8Gao.82 N (1.2-3.3)
229-285
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238-288
(c)
on 6 H - S i C 5-MQW
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Alo.7Gao.3N (5)
Alo.12Gao.88 N (1.4-2.7)
255-303
(d)
on 6 H - S i C 5-MQW
Alo.53Gao.47N (400)
Alo.53Gao.47N (5)
Alo.iiGao.89 N (1.4-3.4)
272-343
on 6 H - S i C
292
Optoelectronic Devices: Ill-Nitrides AIN(AIGaN) Capping Layer(20nnn) | \ AIGaNWell(1.2-3.3nm) /AIN(AIGaN) Barrier (5nm) 5-Layer MQW AIN(AIGaN) Buffer Layer (300nm)
Figure 11.5. Schematic layer structure of the fabricated AlN/Alo.i8Gao.82N MQW sample.
AlN(AlGaN) buffer layer was deposited, followed by a very thin AIN layer on a SiC wafer. We confirmed a step-flow-grown surface by atomic force microscopy (AFM) for each series of samples. The TDD of the AlGaN buffer was approximately 1 X 10^^ cm~^ [30]. As the next step, a five-layer MQW consisting of 1.2-3.4 nm-thick Al;,-Gai_;,N wells (jc = 0.11-0.18) and 5-nm-thick Al.Gap^N barriers (> = 0.53-1) and a 10-nm-thick Al3;Gat^,N cap {y = 0.53-1) were grown. The well and barrier thicknesses were simply estimated from the growth rate of the bulk AlGaN or AIN. Figure 11.6 shows PL spectra of (a) AlN/Alo.i8Crao.82N, (b) Alo.80Gao.20N/Alo.i8Gao.82N (c) Alo.70Gao.30N/Alo.12Gao.88N and (d) Alo.53Gao.47N/Alo.12Gao.88N five-layer MQWs for various well thicknesses. The samples were excited at 77 K using a Xe-lamp light source (215 nm) for sample series (a) and (b), a Xe-lamp light source (227 nm) for sample series (c) and an Ar-SHG laser (257 nm) for sample series (d). The excitation power densities with the Xe-lamp source and the Ar-SHG laser were approximately 20 W/cm^ and 5 kW/cm^, respectively. We obtained a single-peaked intense PL emission from every MQW. No yellow emission was observed from any of the samples. The most efficient emission was obtained at wavelengths of 234, 245, 255 and 282 nm for sample series (a), (b), (c) and (d), respectively. The optimum value for the well thickness was approximately 1.5 nm for each series of samples. The PL spectra of bulk Alo.80Gao.20N and bulk Alo.53Gao.47N (thickness approximately 400 nm) are also shown in Figure 11.6(b) and (d), respectively, as references. The PL intensity of the MQWs was 20-30 times larger than that of the bulk AlGaN, due to a quantized confinement effect. A quantized energy level shift can be clearly observed, as seen in Figure 11.6(a)-(d). The PL peak energies for different well thicknesses agree well with the calculated levels of the quantized energies, taking into account the piezoelectric field applied in the QW regions. The values of the piezoelectric field in the well regions, as estimated from the positions of the measured quantized levels, are more than 2 MV/cm, as already pointed out by Bemardini et al. [31]. The PL intensity depends heavily on the well thickness. A rapid reduction in the PL intensity with increasing well thickness was seen for each series of samples. The reason for this is considered to be a reduction of the radiative
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recombination probability due to the large piezoelectric field in the well [32]. The reduction of the emission intensity when the well is thinner than 1.5 nm may be due to an increase in non-radiative recombination on the hetero-interfaces. Figure 11.7 shows a comparison of PL intensities among sample series (a)-(d) for optimized QW thicknesses, all measured at 77 K. The samples were all excited with a Xelamp light source (215 nm) under the same excitation conditions. We found that the most efficient emission was obtained at around 245 nm for AlGaN-QW systems grown on SiC and that the optimum Al content for the AlGaN barrier was approximately 80%. The PL intensity of a QW is thought to be strongly dependent on the buffer layer conditions, because the hetero-interfaces of the QWs are very sensitive to the stress and flatness of the buffer surface. We presume that an Alo.80Gao.20N buffer grown on SiC yields the most suitable surface for the growth of AlGaN-based QWs under our growth conditions. More efficient emission is expected from AlN/AlGaN QWs by introducing a small amount (5%) of GaN into the AIN buffer and barriers in order to improve the crystalline quality of the AIN. Figure 11.8 shows a comparison of the PL intensity among AlGaN, GaN and InGaNbased QWs with optimized QW structures, as measured at 77 K. All of the samples were excited with a Xe-lamp light source (215 nm) under the same excitation conditions.
(a)AIN/Alo.,8GaN (W=1.5nm) (b) Alo.8Gao.2N / Alo.i8Gao.82N (W=1.6nm) (c) Alo7Gao.3N /Alo.i2Gao.88N (W=1.5nm) (d) Alo.53Gao.47N / Alo.11Gao.89N (W=1.7nm)
1
\
AlxGai.xN/AlyGai.yN 5-layer MQW
Excited with Xe-lamp Measured at 77K.
3
(d)
220
240
260 Wavelength (nm)
280
300
Figure 11.7. Comparison of PL intensity at 77 K between AlGaN 5-layer MQWs with different Al contents in the AlGaN barriers.
Quaternary InAlGaN-based UV LEDs
295
(1) AIN/Alo.i8Gao.82N-5MQW (2)Alo.iiGao.89N/GaN-5MQW (3)lno.o2Gao.98N/lno.2Gao.8N-SQW
\ Measured at 77K
"E 3
11
(1)
1
_ ^ c (1)
-
(3)
1
1
:'l LL 1 Iv. (2)
J
200
250
A
300
350
400
450
500
Wavelength (nm) Figure 11.8. Comparison of PL intensity at 77 K between AlGaN-, GaN- and InGaN-based QWs with optimized QW structures.
We found that the PL intensity of the 234 nm emission from an AlN/Alo.i8Gao.82N MQW is as strong as that of the 420 nm emission from an Ino.02Gao.98N/Ino.20Crao.80N single (S)QW, and is much stronger than that from an Alo.12Gao.88N/GaN MQW at 77 K. This result indicates that the AlGaN-based QW structure is grown with atomically flat heterointerfaces, even when the Al content of the AlGaN barrier is very high. However, the emissions from the AlGaN and GaN-based QWs at RT are much weaker compared with the emissions from InGaN-based QWs. The emission from InGaN-based QWs [23,24] is even efficient at RT, due to high ratio of radiative recombination from localized carriers in the Insegregation regions. These In-segregation effects can also be applicable to InAlGaN-based QWs. The emission of AlGaN-based QWs may be significantly increased by the incorporation of a small amount of In at RT. Also, by reducing the TDD on the AlGaN buffer [30], the emission intensity of the AlGaN-based QWs at RT may be greatly increased. In summary, in this section we have demonstrated single-peaked PL spectra from near the band-edge of Al_;cGai__^N over the entire Al compositional range. We systematically investigated the PL intensity of Al;,Gai_;cN(AlN)/Al3;Gai3;N MQWs with wide-bandgap AlGaN barriers as functions of the QW thickness and the Al content of the barriers. Singlepeaked efficient PL emission was obtained between 282 and 234 nm at 77 K by changing the Al content of the Al^^Gai-^^N barriers from 53 to 100%. The efficiency of the deep-UV
296
Optoelectronic Devices: Ill-Nitrides
emission from AlGaN-based QWs was as high as that of the blue emission from InGaNbased QWs at 77 K.
11.3. G R O W T H AND CHARACTERIZATION OF QUATERNARY In;,Al3,Gai_^_3,N FOR UV EMITTERS The emissions from AlGaN-based structures were found to be very efficient at low temperatures, as described in Section 11.2, but were weak at RT. Therefore, AlGaN-based structures are difficult to use as emitters in high-efficiency UV devices. We proposed the use of In-segregation in quaternary InAlGaN for the purpose of obtaining RT bright UV emission [21]. It has been reported that the emission from localized carriers in the Insegregation region in InGaN QWs is very efficient, with the suppression of non-radiative recombination [23,24]. The In-segregated region will be less effective for confining electron-hole pairs at higher temperatures. The strong emission from InGaN in comparison with that from AlGaN is considered to be due to that the carriers captured into the In-rich region recombine radiatively before being trapped in non-radiative centers generated by defects. A similar effect to that obtained in InGaN QWs is expected for quaternary InAlGaN. Due to this effect, quaternary InAlGaN is very promising for use as the active layer of 300-350 nm-band LDs or LEDs. Quaternary InAlGaN has previously been used for the fabrication of unstrained QW systems grown on GaN or AlGaN buffer layers, rather than for the fabrication of UV emitters. In this case, the possible emission wavelength range of the QWs is around 370-380 nm in order to satisfy the lattice-matched conditions. On the other hand, we intend to use quaternary InAlGaN for the reahzation of much shorter wavelength (250-350 nm-band) UV LEDs or LDs. In this section, we reveal systematic conditions for the growth of quaternary In;cAl3;Gai_;^_^N emitting in the 300 nm-band using MOCVD, and demonstrate the optical properties of In;,Al3;Gai_;,_yN-based bulk material and QWs. We reveal that UV emission is considerably enhanced by the In-segregation effect upon introducing 2 - 5 % of In into the AlGaN. Indium incorporation in quaternary In^^Al-^Gai-^^-jN is markedly enhanced with increasing Al content when using a relatively high growth temperature (830-850°C), resulting in an efficient RT UV emission [19]. We demonstrate intense RT emission in the wavelength range between 290 and 380 nm from quaternary In^^Al^Gai-^c-jN-based MQWs [20]. The samples were grown on the Si-face of on-axis 6H-SiC(0001) substrates by MOVPE. Layer structures consisting of In^^Gai-^^N or quaternary In^^Al^Gai-^c-jN were grown on an approximately 400-nm-thick Al^^Gai-^^N {x = 0.12-0.4) buffer layer to achieve a flat surface that was suitable for the QW layer and to reduce the TDD [30]. The precursors and the growth conditions used for AlGaN growth were the same as those mentioned in Section 11.2. Trimethylindium di-isopropylamine-adduct
Quaternary InAlGaN-hased UV LEDs
297
([(CH3)3]In(i-C3H7)2NH; TMI-adduct) was used as the indium source. The growth conditions for quaternary InAlGaN were based on the InGaN growth condition. Typical gas flows used for In(Al)GaN were 2 and 1.5 SLM for NH3 and N2, respectively. The molar fluxes of TMGa, TMAl and TMI-adduct for the growth of In^^Gai-^cN or quaternary In;,Al^Gai_;,_^N were 1.5, 0.13-0.78 and 30 fxmol/min, respectively. Typical growth temperatures for the In^^Gai-^^N and quaternary In^Al^Gai-^^-jN were 750-780 and 800-870°C, respectively. Under these conditions, the typical growth rates of the In;^Gai-;,N and of the In^^Al^^Gai-^^-jN quaternary were 0.1 and 0.12 (xm/hour, respectively. The optical properties of the InGaN and the quaternary InAlGaN films were investigated by PL measurements with excitation from an Ar-SHG laser (257.3 nm). The excitation power density was approximately 5 kW/cm^. First, we fabricated undoped In_^Al3;Gai_;c-3;N films on 400-nm-thick Alo.12Gao.88N buffer layers. Figure 11.9 shows the PL spectra of 120-nm-thick quaternary In^cAl^Gai-^c-yN for various TMAl flow rates measured at 77 K. The PL spectrum of 120-nm-thick InGaN is also shown for reference. All samples were grown at 830°C, which is approximately 50-80°C higher than the growth temperatures used for In^^Gai-^^N (x ~ 0.2-0.4). As observed in Figure 11.9, the emission from InGaN grown at 830°C is weak because of the small amount of In incorporation (approximately 2%) due to the relatively high growth temperature for InGaN. On the other hand, the emission is markedly enhanced by increasing the TMAl flow rate. This emission enhancement is due to an increase in the In-content in the quaternary In^Al3;Gai-;c-3;N, which is markedly increased
T iHxAlyGa-i.x.yN
TMAl Flow= 0.26|i mol/min m I
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/
ro
0.52|i mol/min
0.13|i mol/min
0.78|i mol /min I
300
320
0|i mol/min (lno.02Gao.98N)
340 Wavelength (nm)
360
380
Figure 11.9. PL spectra of 120-nm-thick Ino.02Gao.98N and quaternary In;(;Al3;Gai-;c-^N for various TMAl flow rates grown at 830°C, measured at 77 K.
298
Optoelectronic Devices: Ill-Nitrides
with increasing molar flux of Al. The In-content (JC) of the In^^-Gai-^^N was 2.2% and the In and Al contents (JC) and (y) of the quaternary In;^Al^Gai_;^:_3;N for a TMAl flow rate of 0.26 ijumol/min were 4.8 and 34%, respectively, as measured by Rutherford backscattering spectrometry (RBS). The tendencies of the growth conditions obtained in our quaternary InAlGaN growth agree well with the analytical deposition diagrams that have been calculated for the MOVPE-growth of quaternary InAlGaN by Koukitu et al., based on a thermodynamic analysis [33]. The emission intensity of Ino.05Alo.34Gao.6iN at 77 K and RT was as strong as that of Ino.2Gao.8N with the same film thickness. The marked enhancement in the emission intensity in quaternary InAlGaN is considered to be mainly due to the effect of In-segregation, which was already observed for the InGaN alloy. Figure 11.10(a)-(d) show w-lS scan profiles (0002) of the XRD rocking curves measured using a four-crystal XRD measurement system that were obtained for the I1io.022Gao.978N and quaternary In;^AlyGai_;,_^N samples with various TMAl flow rates that were used for the PL measurements in Figure 11.9. The peaks at around 0 = 17.85 and 17.4° that appear in each profile correspond to the diffractions from the 6H-SiC(0001) substrate and the Alo.12Gao.88N buffer layer, respectively. As is observed in Figure 11.10(a)-(d), the quaternary In^Al,.Gai_;,_-,,N peak shifts from 6= 17.3 to 17.7° with increasing TMAl flow-rate between 0 and 0.78 |xmol/min. Typical values of the FWHM of the XRD locking curves for the In_;,Al^Gai_;^-_^N quaternary were approximately 200 s, which were almost the same values obtained for Ino.022Gao.978N. Figure 11.11 shows the PL spectra of 120-nm-thick quaternary In^^Al^Gai-^^-^N for various In-flow rates measured at 77 K. The PL spectrum of 120-nm-thick Alo.2Gao.8N is also shown for reference. All of the samples were also grown at 830°C. The In-contents (x) in the quaternary In^^Al^Gai-^^-.^N were approximately 2 and 5% for TMI-adduct flow rates of 3 and 30 juimol/min, respectively, as determined by RBS measurements. The small emission peak at around 342 nm in each spectrum is the emission from the Alo.12Gao.88N buffer layers. The emission from the reference Alo.2Gao.8N film is weak because the layer is thin. We found that the emission intensity of AlGaN is markedly enhanced by incorporating approximately 2 - 5 % of In. We hypothesize that this is mainly due to a marked reduction in non-radiative recombination due to the effects of In-segregation, as shown later. We can observe several emission peaks in the spectrum obtained for a TMIadduct flow of 3 |jLmol/min, which are considered to be due to compositional phase separation in the quaternary In;^Al^.Gai_;,-_3;N. Moreover, the crystalline quality is improved by incorporating In into the AlGaN; this is confirmed by XRD measurements. Figure 11.12 shows a cathode luminescence (CL) image from 600-nm-thick Ino.034Alo.121Gao.845N layer measured at around 110 K. The CL image was measured at around the peak energy of the spectrum (355 nm). Emission fluctuations in the sub-micron region were clearly observed in the CL image. The emission fluctuation is considered to be due to carrier localization in the In-segregation area. We obtained similar CL images for quaternary In^^Al^Gai-^^-^N with different In and Al compositions emitting at
Quaternary InAlGaN-based UV LEDs
(a) =i -
CD
1
1
E
''^0.022^%978N
A
i^A JI i 1
-^ h
Ihi'Mf
(b) =
iM
1
A
E TMAI:
2^
=
J/
.llllf
=
1
Id I
1
1
\
1
A /\ /
V \ . \
3i H
=
/ /
~ 11 1
k\
\
\\
J iiliiiiUiii
,
=
1 \
\\
J
= E
V/ M
J \
=
\Till III 1 IF
(d) EI "c
-
J
1
F
=
1 1 1
Jl
- ln0.05AI0.34Ga0.61N
=
1
/
II
.1
S
z
\ i .M ,kj
/A y /
>> "w c (1)
E
1
/ \ \1
//
E TMAI: 3 x i 1 0.26|Li mol/ (D = min
_c
1
/\
^^ CO
(c)
'
11
^ ~ 0.13^1 mol/ CD E mm c 0 _c
3
lluilil
1
^^ (0 3
299
3
= TMAI: g. 0.78|imol/
A /
\
=J
'
= 1 lllllllff 17
A^kJ
17.5
\
^
18
6 (degree) Figure 11.10. co-Id scan profiles (0002) of the X-ray diffraction (XRD) rocking curves obtained for Ino.022Gao.978N and quaternary In;,.Al3;Gai_;,_^N with various TMAI flow rates measured by the four-crystal XRD measurement system.
300
Optoelectronic Devices: Ill-Nitrides 10^
— I
1
1
1
r
InxAlyGa^.x.yN
- 1 — I — I — I — I — I — I —
30|Lt mol/min ('no.05A'o.34G%6iN)
CO
TMI-adduct Flow=3|i mol/ -2 10^ - min CO
(D
Oji mol/min (Alo.2Gao.8N)
10^ 10°
Figure 11.11.
300 350 Wavelength (nm)
400
PL spectra of 120-iim-thick Alo.2Gao.8N and quaternary In;,AlyGai_;,_yN for various TMI-adduct flow rates grown at 830°C, measured at 77 K.
315-370 nm. The CL images obtained for quaternary InAlGaN films were very similar to those obtained for InGaN films. Figure 11.13 shows the PL spectra measured at RT of Ino.22Gao.78N and quaternary In^Al^Gai-;,-^N with different In and Al compositions (JC = 1.3-4.4, y = 12.0-31.2%).
1|am Figure 11.12. Cathode luminescence (CL) image from 600-nm-thick Ino.034Alo.121Gao.845N quaternary measured at around 110 K.
Quaternary InAlGaN-based UV LEDs (a) (b) (c) (d) 1
1
1
1
301
lno.22Gao.78N lno.044Alo.120Gao.836N lno.034Alo.121Gao.845N lno.020Alo.275Gao.705N
1 1
1
1
1
1 1
1—r-i
Measured atRT
1 1 1
1
1
1
1
1
(a)
n(cl)
(c)
3
CD
(e) 1 1
1 >v^ - K 1^1
300
>>,! i V l
1 J*-U
350
^
1
400 Wavelength (nm)
1
1
1
450
Figure 11.13. PL spectra of Ino.iiGao.ygN and quaternary In Al-^Gai-^^-yN with different In and Al compositions (jc = 1.3-4.4, y = 12.0-31.2%) measured at RT.
We used the optimized growth temperature and TMAl flow rate to obtain the maximum PL intensity for each emission wavelength in the growth of both the InGaN and quaternary InAlGaN layers. The growth temperatures of the InGaN or quaternary InAlGaN used for samples (a)-(e) in Figure 11.13 were 770, 790, 810, 830 and 870°C, respectively. We found that the appropriate growth temperature for quaternary InAlGaN is higher than that for InGaN by 4 0 - 100°C in order to obtain intense 300 nm-band UV PL. The required growth temperature becomes higher as the emission wavelength becomes shorter for quaternary InAlGaN. We obtained intense PL emission from quaternary InAlGaN in the wavelength range between 315 and 370 nm at RT. The PL intensity of the UV emission from quaternary InAlGaN was as large as that of the blue emission from InGaN at RT. These results indicate that quaternary InAlGaN is very promising for use as the active layer of QWs for 300-360 nm-band UV LDs or bright LEDs. We then fabricated InAlGaN-based QWs on SiC. We fabricated six series of In(Al)GaN-based QWs with various well thicknesses. The structure of the QWs, the compositional wavelengths of the quaternary InAlGaN and the InGaN used for the wells and barriers, the optimized well thicknesses for obtaining intense PL, and the emission wavelength range of intense P are summarized in Table 11.2. Figure 11.14 shows
302
Optoelectronic Devices: Ill-Nitrides
Table 11.2. Structures, compositional wavelengths of the InAlGaN and InGaN used for the wells and barriers, the optimized well thicknesses, and wavelength range of intense emmission of each series of QWs Sample series
(a) (b) (c) (d) (e) (f)
QW-Structure (well/barrier)
InAlGaN/InAlGaN-BMQW InAlGaN/InAlGaN-SMQW InAlGaN/InAlGaN-SMQW InAlGaN/InAlGaN-SQW InGaN/InAlGaN-3MQW InGaN/InGaN-SQW
Compositional wavelength (nm) Well
Barrier
308 340 364 362 408 430
270 300 310 345 334 370
Optimized well thickness (nm)
Wavelength range of intense emission (nm)
2.1 1.4 2.1 1.5 (3.3) 2.8
290-313 318-338 325-355 358-375 370-395 405-448
an example of the schematic layer structure of an InAlGaN MQW fabricated on a SiC substrate (which corresponds to series (b) in Table 11.2 and Figure 11.15(b)). The structure consists of a 400-nm-thick Alo.15Gao.85N buffer layer grown on SiC, a 50-nm-thick Ino.02Alo.60Gao.38N buffer region with a thin (approximately 3 nm) Ino.05Alo.34Grao.6iN strain reduction layer, a Ino.05Alo.34Gao.6iN/Ino.02Alo.60Gao.38N three-layer MQW and a 20-nm-thick Ino.02Alo.60Gao.38N cap. The barrier thickness was fixed at 7 nm. The QW thickness was changed from 0.7-3.5 nm. All of the layers were undoped. Figure 11.15 shows PL spectra of (a) Ino.03Alo.50Gao.47N/Ino.01Alo.60Gao.39N three-layer MQWs, (b) Ino.05Alo.34Gao.6iN/Ino.02Alo.60Gao.38N three-layer MQWs, (c) Ino.o6Alo.o8Gao.86N/Ino.o2Alo.52Gao.46N three-layer MQWs, (d) Ino.06Alo.09Gao.85N/Ino.03Alo.i8Gao.79N SQWs, (e) Ino.15Gao.85N/Ino.02Alo.15Gao.83N three-layer MQWs, and (f) Ino.20Gao.80N/Ino.02Gao.98N SQWs for various well thicknesses. All samples were excited at RT with Ar-SHG laser (257 nm). In order to make a strict comparison of the PL intensity between the samples, the excitation power of the Ar-SHG laser were stabiUzed to maintain the same value. We obtained
lno.02Alo.60Gao.38N Cap(20nm) 3-Layer MQW lno.05Alo.34Gao.6iN Well(0.7-3.5nm) /lno.o2Alo.6oGao.38NBarrier(7nm) 'no.05Alo.34Gao.6iN Strain Reducer(4nm) lno.o2Alo.6oGao.38N(30nm) Alo.i5Gao85N Buffer(400nm) SiC(0001)Subs. Figure 11.14.
Schematic of the layer structure of an Ino.05Alo.34Gao.6iN/Ino.02Alo.60Gao.38N three-layer MQW grown on a SiC wafer.
303
Quaternary InAlGaN-based UV LEDs I I I I I I I
(a)
(d)
T
lno.O6Alo.09Gao.85N/ 'noo3Alo.i8Gao.79N SQW
'no.03Alo.50Gao.47N/ IRQ OIAIQ eo^ao 39N
3MQW 1.5nm
Well Thickness 2.1nm
Well Thickness 2.8nm Measured atRT 2t )0 (b)
^
"c 3 -Q
S-
:^
300
350
250 (c)
'E
/1 «V/
/
3.5nm
1 1 1 1 1
1 111111111111 1
. .. , \l 1
1.4nm
r^ i
r J ^ 1 1 1 1—wf
300
Well Thickness 2.8nm 2.2nm 1.7nm 1.1 nm
500
250 (f)
Well Thickness 2.8nm
iA^4.2nrTi
0.9nm
250
'no.15Gao.85N/ "ln0.02AI0.15Ga0.83N 3MQW
Ino.oeA'o.osGao.seN/ ''^0.02Alo.52Gao 46N 3MQW
\ y — 3.5nm
C
I I I I I I I I I I I
0
Measured
500
250 (e)
/ V^^~/ ^*^^ 1 1 1 T w i t ^M i r t ^ ^ i ; ; i > H - 1 1 1 1 1 1 1 1 1 300 350 400 450 500
2.1nm
_l Q.
5C
1111111111111111 1 \ 'rio.05Alo.34Gao.6iN/ \ ''^o.02Alo.6oGao.38N 3MQW _ 1A'\ 2.1nm 1.4nm 1 1 I Well Thickness fi / 2.8nm
0.7nm Ij Q.
450
1 1 1 1 1 11
C
_J
400
0.8nm
4.8nm
_
c
Measured at RT
icJaha-_L 1 1 1 1 1 1 1 1 1
350
400
Wavelength X (nm)
450
500
250
300
350
400
450
500
Wavelength X (nm)
Figure 11.15. PL spectra of various types of Iii;,iAl^iGai-;,i-yiN/In;,2Al3;2Gai-^2-y2N and Ino.20Gao.80N/Ino.02Gao.98N QWs for various well thicknesses measured at RT. The In and Al contents xl and yl of the In^i Al3;iGai_;,i_yiN active layer, and x2 and y2 of the Injc2Al3;2Gai_;c2-y2N barrier layer were changed in the range of xl : 3-6%, yl : 8-50%, x2 : 1-3% and y2 : 15-60%, respectively.
a single-peak intense PL emission from every MQWs at RT. The most efficient emission was obtained at the wavelengths of 300,318,338,357,395 and 428 nm for sample series (a), (b), (c), (d), (e) and (f), respectively. The optimum value for the well thickness was 1.5-3 nm. The PL intensity of the MQWs was more than ten times larger than that of the bulk InAlGaN, due to a quantized confinement effect. A quantized energy level shift can be clearly seen, as seen in Figs. 15(a)-(f). For QW sample series (e), the strong PL was not obtained for thin (around 2 nm) quantum well. The reason for this is that the crystalline quahty of quaternary InAlGaN barrier for (e) was not sufficiently high, as discussed later.
Optoelectronic Devices: Ill-Nitrides
304 '
'
•
'
!
•
(02.1 nm
Measured atRT
' ' ' 1 ' ' ' ' 1'
n2.8nm
(d)1.5nm
3
^ ^ ^CO
-
0
^
(b) 1
1.4nm 1 (a) 1.4nm
I (d)2.8nm
j
I
-
V \ (e) /
A \ ^^ /
_l
Q.
A \^^ 1 ilu
250
,
300
350 400 Wavelength (nm)
h 1 1 1^^
450
Figure 11.16. Comparison of PL emission intensity between the 300 nm-band UV emission obtained from quaternary InAlGaN-based QWs and the blue emission obtained from an InGaN-based QW.
Figure 11.16 shows a comparison at RT between the UV emission spectra obtained from quaternary InAlGaN QWs and a blue emission spectrum obtained from an InGaN QW. The spectrum (a)-(f) in Figure 11.16 corresponds to series (a)-(f) in Table 11.2. We found that the intensity of the 320-360 nm UV emission from quaternary InAlGaN QWs is as strong as that of the blue emission from InGaN QWs at RT. The emission intensity at RT is weak for wavelengths below 300 nm. This is because a higher growth temperature was used to maintain high crystalline quality of quaternary InAlGaN with high Al content, and thus the incorporation of In into the InAlGaN quaternary was reduced due to the high growth temperature. The emission intensities for wavelengths around 370-400 nm were also not strong in comparison with the 320 nm-band emission. This is thought to be caused by degradation of the crystalline quality of quaternary InAlGaN due to the use of a low growth temperature, which is required to increase In-incorporation into the quaternary. Figure 11.17 shows the temperature dependences of the PL intensity of an Ino.05Alo.34Gao.6iN/Ino.02Alo.60Gao.38N three-layer MQW, an Ino.20Gao.80N/ Ino.02Gao.98N SQW, a GaN/Alo.i5Gao.85N five-layer MQW and an Alo.12Gao.88N/ Alo.53Gao.47N five-layer MQW with optimized QW thicknesses. The PL intensity of each sample is normalized to the PL intensity obtained at 20 K. As seen in Figure 11.17, the temperature dependence of the PL emission for InAlGaN-based QWs was greatly improved in comparison with that of GaN- or AlGaN-based QWs. The PL intensity of InAlGaN- and InGaN-based QWs was 1-2 orders of magnitude higher than that of GaNor AlGaN-based QWs at RT. The RT emission efficiency of the QWs was considered to be markedly improved due to the increase in radiative recombination caused by the localized electron-hole pairs in the In-segregation region, as indicated by CL measurements. Figure 11.18 shows the temperature dependence of the PL intensity and the PL spectra for various QW thicknesses of InAlGaN-based SQWs grown on SiC. The emission peak
Quaternary InAlGaN-based UV LEDs
305
10"^
10^ 13
A. 102 _• 'no.05Aio.34Gao.6iN/ 'no.02Alo.60Gao.38N -3MQW(320nm)
10^
~ZA
O lno.2Gao.8N/'no.o2Gao.98N -SQW(420nm) ~ A AI0.11Ga0.89N/AI0.53Ga0.47N -5MQW(280nm) A
10°
_A_
GaN/Alo.i2Gao.88N -5MQW(350nm) 100
200
300
Temperature (K) Figure 11.17. Temperature dependences of PL intensity of an Ino.05Alo.34Gao.6iN/Ino.02Alo.60Gao.38N 3-layer MQW, an Ino.20Gao.80N/Ino.02Gao.98N SQW, a GaN/Alo.i5Gao.85N 5-layer MQW and an Alo.12Gao.88N/Alo.53Gao.47N 5-layer MQW with optimized QW thicknesses.
wavelengths of the SQW samples were tuned at around 350 nm. The internal quantum efficiency was estimated from the ratio of the PL intensity measured at low temperatures (10 K) and at RT. The estimated value of the internal quantum efficiency was approximately 15% at RT. The TDD measured by a high-resolution scanning electron microscope (HR-SEM) [30] on an InAlGaN epitaxial layer on SiC was as high as 1 X lO^^cm"^. On AlGaN buffer layers with such a high density of threading dislocations, the internal quantum efficiency of AlGaN or GaN-based QWs is quite low. This high estimated internal quantum efficiency for InAlGaN-based QWs is thought to be due to In-segregation effects. To sunmiarize this section, we demonstrated intense UV emission at RT from quaternary In;,Al3;Gai_;c-3;N alloys grown by MOVPE in the wavelength range between 315-370 nm. We found that the UV emission is considerably enhanced by the Insegregation effect upon introducing 2 - 5 % of In into the AlGaN. The incorporation of In into quaternary In;cAl3;Gai_;,_^N is markedly enhanced by increasing the Al content when using a relatively high growth temperature (830-850°C), resulting in efficient RT UV emission. Maximum emission efficiency was obtained at around 330-360 nm from the fabricated quaternary In^Al^Gai_^_^N (where x = 2.0-3.4, y = 12-28%). The intensity of the 330 nm emission from quaternary Ino.034Alo.12Gao.85N was as strong as that of
306
Optoelectronic Devices: Ill-Nitrides
InAIGaN/lnAIGaN -SQW (Well Width: 1.5nm)
i2 'E
"S c J)
0.1
320
0.01
340 360 380 V\favelength(nm)
400
J_ 100 200 Temperature T(K)
300
Figure 11.18. Temperature dependence of PL intensity and PL spectra for various QW thicknesses of quaternary InAlGaN SQWs grown on SiC with wavelengths of around 350 nm.
the 430 nm emission from Ino.22Gao.78N at RT. We clearly observed In-segregation on a submicron scale from CL images of quaternary InAlGaN films. We also demonstrated intense UV emission at RT in the wavelength range between 290 and 380 nm for In^i(Alyi)Gai_;,i-^,iN/In;f2Aly2Gai_;^.2-^2N MQWs. The temperature dependence of the PL emission for InAlGaN-based QWs was greatly improved in comparison with that of GaNor AlGaN-based QWs. These results indicate that quaternary InAlGaN is very promising for use as the active layer of 300-350 nm-band UV LDs or bright LEDs.
11.4. HIGH-Al-CONTENT p-TYPE Al^Gai_^N GROWN USING AN ALTERNATING GAS FLOW TECHNIQUE The achievement of high-quality p-type Ill-nitrides is one of the key requirements for realizing the high-performance operation of nitride-based LEDs, LDs or high-speed, highpower transistors. In particular, for UV LEDs operating in the wavelength range below 350 nm, the requirement for a sufficiently high hole concentration in p-type AlGaN is important for suppressing electron overflow and for obtaining high injection efficiency. The highest possible limit of the Al content for Mg-doped Al;^-Gai-;cN is approximately 30% in order to obtain the desired hole conductivity. Recently, considerable research has been performed to realize high hole conductivity in Ill-nitride materials, i.e. the use of SLs [34-37], Mg-doped InGaN [38] or quaternary InAlGaN [39] or co-doping in GaN or AlGaN [40].
Quaternary InAlGaN-based UV LEDs
307
It is difficult to obtain a sufficiently high hole concentration in p-type AlGaN with a high Al content. The main reason for this is that the energy level of the Mg-acceptor is deep for high-Al-content AlGaN, and thus the activated hole concentration is quite small. In order to obtain hole conductivity, heavy Mg-doping of as high as 10^^ cm~^ is required. Such a heavily Mg-doped AlGaN easily becomes n-type, due to an increase in the number of vacancies or defects in the crystal. Therefore, in order to obtain adequate hole conductivity for high-Al-content p-type AlGaN, the identification of growth conditions for obtaining high crystalline quality AlGaN for even heavy Mg-doping is necessary. In this section, an alternating gas flow growth technique is introduced for the growth of high-Al-content p-type AlGaN. The crystalline quality of high-Al-content p-type AlGaN is considered to be remarkably improved due to enhanced migration of the precursors when using the alternating gas flow sequence. Moreover, by using alternating gas supply, the vapor reactions between NH3 and TMAl or NH3 and the Mg-source are considered to be significantly suppressed in front of the graphite susceptor. The crystalline quality of high-Al-content AlGaN is considered to be drastically improved by the suppression of these gas-phase reactions. The Mg-doped samples were fabricated at 76 Torr on sapphire substrates by MOVPE. The growth conditions for undoped Al^^Gai-^cN were the same as those used in the previous sections. Bis-ethylcyclopentadienylmagnesium (BECp2Mg) was used as a source of Mg, with H2 and N2 as the carrier gases. The molar flux of BECp2Mg for the growth of the Mg-doped GaN or AlGaN layers was approximately 15 (xmol/min. The growth temperature for Mg-doped-AlGaN using the alternating gas flow method was 1100°C. We first investigated the electrical properties of Mg-doped bulk GaN with a thickness of 600 nm grown on a SiC wafer. The hole concentration of an Mg-doped GaN layer measured after an annealing process was 0.5-1 X 10^^ cm~^, as obtained by Hall-effect measurements. The gas flow sequence used for the supply of NH3, TMGa, TMAl and BECp2Mg is shown in Figure 11.19. Ammonia gas and group III gases, i.e. TMGa, TMAl, BECp2Mg, were introduced alternately into the MOCVD reactor. We flowed a small amount of ammonia continuously using an additional line to suppress the desorption of nitrogen. We deduced the suppression of the vapor-phase reactions from the fact that the AlGaN growth rate became approximately twice as high when we used the alternating gas supply. Figure 11.20 shows the PL spectra of high-Al-content undoped AlGaN measured at 77 K with and without the use of the alternating gas flow sequence. As seen in Figure 11.20, we observed a reduction in the FWHM and an intensity enhancement of the PL spectrum by growing with the alternating gas flow sequence. We then tried to evaluate the hole conductivity of high-Al-content Mg-doped AlGaN by using Hall-effect measurements. The sample layer structure used for the Hall-effect measurement is shown in Figure 11.21. The layer structure consists of a low-temperature (LT)-AIN layer grown on a sapphire substrate, a 1.6-|jLm-thick undoped Alo.6Gao.4N buffer
308
Optoelectronic Devices: Ill-Nitrides
N2 TMGa+TMAI+BECP2 Mg NHS
NHS
TMGa
TMAI
BECP2Mg
2sec
2sec
Figure 11.19. Gas flow sequence of the supply of NH3, TMGa, TMAI and BECp2Mg used for the growth of high-Al-content Mg-doped AlGaN.
layer, a 0.4-(xm-thick Mg-doped Al;,Gai_;,N (jc = 0.46-0.53) layer grown with the alternating gas flow sequence and a 30-nm-thick Mg-doped GaN contact layer. Figure 11.22 shows the temperature dependence of the hole concentration (as measured by the van der Pauw method) observed for a Mg-doped Alo.46Gao.54N sample grown with alternating gas flow. We observed p-type character for Mg-doped AlGaN for Al contents ranging from 0.46 to 0.53. The effect of the alternating gasflowon p-type doping was revealed by the fact that the Mg-doped sample grown with usual continuous gas flow showed n-type character. The effective hole activation energy of the Mg-acceptors was obtained as 75 meV from Figure 11.22. Such a shaUow energy level of Mg-acceptors is thought to be obtained because it includes the effect of the two-dimensional hole-gases accumulated in the interface between the Mg-doped GaN contact layer and the Mg-doped AlGaN layer. In sunmiary of this section, we described an alternating gas flow growth technique in order to obtain sufficiently high hole density for high-Al-content p-type AlGaN. By growing with alternating gas flow, we achieved hole conductivity in Mg-doped
Quaternary InAlGaN-based UV LEDs
309
Alternating Gas Flow Alo.5Gao.5N FWHM=61.5meV
Normal Gas Flow FWHM=67meV
77K-PL 270
280 290 Wavelength (nm)
±.
300
310
Figure 11.20. PL spectra of high-Al-content undoped AlGaN measured at 77 K with and without using the alternating gas flow sequence.
Mg-doped GaN Contact Layer (30nm)
AlGaN Buffer (Al=0.6)1.6|ann
LT-AIN Sapphire Sub.
Figure 11.21.
Schematic of the sample structure of an Mg-doped AlGaN layer grown using the alternating gas flow method that was used for Hall-effect measurements.
310
Optoelectronic Devices: Ill-Nitrides Temperature (°C) 500 300 200
100
1—\—r
'
\
'
r
Alternating Gas Flow Mg-doped AIGaN (Al=46%)
10 19
ooa 0 - 0 (
^ - oo Ea=75meV
o O 10^ For Continuous Flow n-type character was shown.
o X
10^
_L
I
2 3 1000/T(1/K)
Figure 11.22. Temperature dependence of hole concentration measured by the van der Pauw method as observed for an Mg-doped Alo.46Gao.54N sample grown with alternating gas flow.
AIGaN with Al contents between 46 and 53%. On the other hand, we could not obtain p-type character for high-Al-content Mg-doped AIGaN grown with a conventional continuous gas flow regime. These results indicate that the alternating gas flow growth method is advantageous for obtaining high-Al-content p-AIGaN. 11.5. InAlGaN-BASED UV-LEDs 11,5.1 AIGaN and InAlGaN-based UV-LEDs on SiC In this section, we describe AIGaN and InAlGaN-based UV LEDs emitting at wavelengths around 340 nm that were fabricated using the techniques mentioned in the previous sections. We demonstrate high-intensity UV LEDs using quaternary InAlGaN as the active region for wavelengths around 340 nm [41,42]. A comparison of electroluminescence (EL) is made between InAlGaN, AIGaN and GaN LEDs fabricated on SiC substrates that emit between 340 and 360 nm [25,42]. Figure 11.23 shows (a) the schematic structure and (b) the current injection spectra for various current densities of the fabricated quaternary InAlGaN UV LED. The LED structures were grown on 6H-SiC substrates. The structure consisted of a Si-doped Alo.25Crao.75N buffer layer (50 nm), an Si-doped Alo.17Gao.83N layer (600 nm), an undoped quaternary Ino.05Alo.34Gao.6iN active layer (80 nm), an Mg-doped Alo.igGao.gzN layer (600 nm) and an Mg-doped GaN capping layer (60 nm). The samples were annealed at
Quaternary InAlGaN-based UV LEDs 1
(b) (a)
1
1
InAIGaN-LED Ni/Au
ft
p~-200
p-GaN:Mg(60nm)
S "E^ '•''^0.05Alo.34^%61^
Active Layer (80nm)
3
'SiC(0001)Sub.
r cw ^ "1
|L--175 1 11 Current
^ ^ ^
-
Density
0)
|n-Alo.25Gao.75N:Si| (50nm)
311
/125(A/cm2)
c 0
^
_l
LU
— Ni/Au
ill
J
300
/75
\
350 400 450 Wavelength (nm)
Figure 11.23. (a) Schematic structure and (b) current injection spectra measured under RT CW operation of a quaternary InAlGaN UV LED fabricated on a SiC substrate with an emission wavelength of 345 nm.
800°C in an N2 gas flow for 30 min in order to activate the Mg acceptors. The Mg incorporation in the Mg-doped Alo.i8Gao.82N layer was approximately 1.0 X 10^^ cm~^, as determined by secondary ion mass spectroscopy (SIMS) measurements. The hole and electron concentrations in the Mg-doped Alo.i8Gao.82N layer and in both the Si-doped Alo.25Gao.75N and the Alo.15Gao.85N layers were approximately 2 X 10^^ and 1 X 10 cm~^, respectively, as obtained from Hall-effect measurements. Ni/Au electrodes were used for both the p-type surface and the n-type SiC substrate. The diameter of the p-side electrode was approximately 0.6 mm. The emission spectra were measured under RT CW operation. The injection current density was changed within the range 0-200 A/cm^. We obtained single-peaked bright emission with a wavelength of 345 nm from the quaternary InAlGaN LEDs. We did not observe any deep-level emissions, such as emission from Mg-acceptor levels, nor 550nm-band yellow emission. In addition, there was neither a significant wavelength shift nor any output power saturation with increasing injection current in the current density range between 0-200 A/cm^. The UV output power of the LED was not high because of absorption losses through the p-GaN cap layer and the Ni/Au p-electrode. A high output power is expected if the structure could be optimized to extract UV Hght. Figure 11.23 shows (a) the emission spectra and (b) the emission intensities as a function of injection current density of UV LEDs with quaternary Ino.05Alo.34Gao.6iN,
312
Optoelectronic Devices: Ill-Nitrides 1
(a)
1
I
1
••
InAIGaN-LED
1
(b)
••
]
RT
cw 1
-
^
11
'E
1 1
Density:
'E 3
InAIGaN-LED
\ 1
LU
\ /
GaN-LED
340 360 380 400 Wavelength (nm)
/
-J LU
"/-/V :
320
^
c
1 AIGaN-LED
0)
/ _
Current 175A/cm2 _
CO c
— 1
1
420
/
GaN-LED
\
0
^
AIGaN-LED y
50 100 150 200 Current Density (A/cm^)
Figure 11.24. Comparison of (a) emission spectra and (b) emission intensities as a function of injection current density among UV LEDs with quaternary Ino.05Alo.34Gao.6iN, Alo.i8Gao.82N and GaN active regions.
Alo.i8Gao.82N and GaN as the active regions, all measured under RT CW operation. The layer structures of the AlGaN and GaN LEDs were the same as that used for the quaternary InAlGaN LED, except for the active region. As is evident from Figure 11.24(a) and (b), the UV emission intensity from the quaternary InAlGaN LED was more than one order of magnitude larger than that from the AlGaN or GaN LEDs. The TDD of an AlGaN buffer on SiC was approximately 1 X 10^^ cm~^ [30]. Therefore, the use of quaternary InAlGaN as a UV emitting region is advantageous, particularly in the case where it is fabricated on a high TDD buffer. In summary of this section, we fabricated UV-LEDs on SiC substrates using a quaternary InAlGaN active region and achieved bright 345 nm emission under RT CW operation. The UV intensity from quaternary InAlGaN LEDs was more than one order of magnitude higher than that obtained from AlGaN or GaN LEDs. From these results, we revealed that the use of quaternary InAlGaN as the emitting regions of UV emitters is advantageous in comparison with AlGaN or GaN, particularly when they are fabricated on wafers with high TDD buffer layers. 11,5,2 310 nm-band InAlGaN LEDs on Sapphire We fabricated InAlGaN-based 310nm-band UV LEDs with high-Al-content p-type AlGaN on sapphire substrates [43]. Figure 11.25 shows the schematic LED structure. The layer structure consists of a LT-AIN layer, a 1.6-|jLm-thick Si-doped Al^^Gai-^^N {x = 0.47) buffer layer, an approximately 60-nm-thick undoped In^AXyGdii-x-y^ emitting
Quaternary InAlGaN-based UV LEDs
313
Pd/Au Electrode GaN;MgCap Ni/Au Alo.53G%47N;Mg (300nm) IrixAlyGai.x.yN Emitting Layer n-Alo.47Gao.53N; Si Buffer (1.6|Lim) LT-AIN UV Output
Figure 11.25. Schematic structure of a quaternary InAlGaN UV LED fabricated on a sapphire substrate with an emission wavelength of around 310 nm.
layer, a 300-nm-thick Mg-doped Al;,Gai_;,N {x = 0.53) layer and a 30-nm-thick Mgdoped GaN contact layer. We employed a high-Al-content (greater than 50%) for the ptype AlGaN in order to suppress electron overflow adequately. If a lower-Al-content pAlGaN layer was used, the LED intensity was weak, since the electron injection efficiency into the QW was low due to electron overflow. For the growth of Mg-doped AlGaN, an alternating gas flow sequence was used, as mentioned in the previous section. We fabricated two types of LEDs with different emission wavelengths, i.e. 308 and 314 nm, i.e. the compositional wavelengths of the quaternary InAlGaN emitting-layers of the LEDs were tuned to 308 and 314 nm. The In and Al components of the quaternary InAlGaN emitting regions were approximately 0.02 and 0.46, and 0.02 and 0.42, respectively, for emission wavelengths of 308 and 314 nm. The UV emission could be extracted from the backside of the sapphire substrate through the n-Alo.47Gao.53N layer below the InAlGaN emitting layer, as shown in Figure 11.25. The samples were annealed at 830°C in a nitrogen atmosphere for 40 min in order to activate the Mg-acceptors. Ni/ Au electrodes were used for both the n-type and the p-type electrodes. The diameter of the Ni/Au p-type electrode was 500 (xm. Figure 26(a) and (b) shows the EL spectra of the UV LEDs with 308 and 314 nm InAlGaN emitting layers, respectively, as obtained for various injection currents measured under pulsed current injection at RT. We obtained single-peaked emission for both the 308 and 314 nm LEDs. The emission peak was confirmed to originate from the quaternary InAlGaN emitting layer, since the EL peak was just matched to the PL peak. The output power radiated into the backside of the LED was measured using a 10 X 10-mm Si photodetector located behind the LED sample. The maximum output power was 0.4 mW for
314
Optoelectronic Devices: Ill-Nitrides (a)
(b) InAIGaN-LED (:^=308nm) Measured atRT
CD
1
' 1
InAIGaN-LED "| (;i=314nm)
"E
sec)
300 400 Wavelength (nm)
'
h ^ 260mA J (Output Power Measured =0.8mW) atRT Pulsed / 200mA (5 \- (20KHZ, V 1 /150mA 10|isec)[ r| c 0 //100mA
^ 130mA (Output Power =0.4mW)
Pulsed _(20KHz, 5|LI
1
500
. ILJ 300 400 Wavelength (nm)
500
Figure 11.26. Electroluminescence (EL) spectra of InAlGaN UV LEDs with emission wavelengths at (a) 308 and (b) 314 nm for various injection currents measured under RT pulsed operation.
308 nm emission at an injection current of 130 mA, and 0.8 mW for 314 nm emission at an injection current of 260 mA. The external quantum efficiency (EQE) was approximately 0.08% for both LEDs at around maximum output power. The reason for the low efficiency of the LEDs is thought to be the use of bulk InAlGaN for the emitting region. Much higher efficiency might be obtained by using quaternary InAlGaN-based QWs as the active region. 11,5.3 350 nm-band High-power InAlGaN QW LEDs on GaN Substrates In this section, we demonstrated high-efficiency 350 nm-band UV LEDs fabricated using quaternary InAlGaN MQWs as the emitting region. GaN substrates were used in order to eliminate the effects of threading dislocations. The maximum UV output power obtained was as high as 7.4 mW under RT CW operation. The maximum EQE was 1.1% with an injection current of 50 mA, which is the highest EQE ever obtained for 350 nm-band UV LEDs with top-emission geometry [44]. Reduction of the TDD is of considerable importance for suppressing non-radiative recombination and leakage current, especially for an AlGaN-based UV emitter. A low-TDD AlGaN buffer fabricated on a GaN substrate is useful for achieving highefficiency UV LEDs [5] or LDs [45]. GaN substrates have been developed by Sumitomo Electric Industries, Ltd [46] Also, high-efficiency UV LEDs have already been fabricated on low-TDD AlGaN buffer layers using various techniques [47,48]. The advantage of using a quaternary InAlGaN emitter is that high-efficiency UV emission can be obtained due to In-segregation effects, as discussed in the previous sections. The combination of quaternary InAlGaN active layers and low-TDD buffers is
Quaternary InAlGaN-based UV LEDs
315
therefore considered to be most effective in realizing 300-360-nm-band high-efficiency UV emitters [49]. In this sub-section, we fabricated quaternary InAlGaN-based UV LEDs on GaN substrates in order to eliminate the effects of threading dislocations. The structures were grown at 76 Torr on GaN substrates by MOVPE. GaN substrates were produced by hydride vapor phase epitaxy by Sumitomo Electric Industries, Ltd [46]. The dislocation density of the GaN substrates was less than 1 X 10^ cm~^. The detailed growth conditions used for the growth of the AlGaN and the quaternary InAlGaN are indicated in the previous sections. Figure 11.27 shows a schematic of the typical structure of a UV LED fabricated on a GaN substrate and the pattern of the top emission. The structure consists of a 90-nm-thick Si-doped GaN layer deposited directly onto a GaN substrate, an approximately 50-nm-thick undoped Ino.04Gao.96N layer, a 30-nm-thick Si-doped Alo.i8Gao.82N buffer layer, a 35-nm-thick undoped quaternary Ino.05Alo.24Gao.71N buffer layer, an undoped Ino.02Alo.09Grao.89N/Ino.02Alo.22Grao.76N two-layer MQW active region, a 25-nm-thick undoped Alo.27Gao.73N electron-blocking layer and an Mg-doped 4-nm-thick Alo.24Grao.76N/4-nm-thick Alo.17Gao.83N super lattice (SL). The thicknesses of the well and barrier layers of the MQW were approximately 2.5 and 15 nm, respectively. The compositions of the In and Al incorporated in the quaternary InAlGaN were estimated
Ni/Au Electrode(Semi-transparent) Alo.24Gao.76N/ Alo.i7G%83N;MgSLs Alo.27Gao.73N Electron Blocking Layer lno.02Alo.09Gao.89N Well/ lnoo2Alo22Gao76N Barrier -2MQW lno.05Alo.24Gao.71N Alo.i8Gao.82N;Si lno.04Gao.96N GaN;Si Ti/AI Electrode Figure 11.27.
Schematic structure of a quaternary InAlGaN-based UV LED fabricated on a GaN substrate and the pattern of the top emission.
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Optoelectronic Devices: Ill-Nitrides
from RBS measurements. We fabricated two types of LEDs, i.e. with p-AlGaN/AlGaN SLs and with a bulk p-Alo.i8Gao.82N layer. The total thickness of the p-AlGaN layer was 66 nm in both cases. A 50-nm-thick InGaN layer was inserted just above the Si-doped GaN layer in order to suppress cracks. The samples were annealed at 830°C in a nitrogen atmosphere at 760 Torr for 50 min in order to activate the Mg acceptors. Then, a Ni/Au semi-transparent electrode and a Ti/Al electrode were formed on the p-side surface and on the GaN substrate, respectively. The size of the p-electrode was 400 X 400 |xm. The UV output power was detected from the p-side through the Ni/Au semi-transparent electrode. We formed the p-electrode directly on the p-AlGaN layer to reduce the absorption loss. Figure 11.28 shows (a) high-resolution scanning electron microscope (HR-SEM) and (b) CL images of a quaternary InAlGaN MQW layer grown on a GaN substrate. We can see a small pit and a dark spot, the origins of which are in the threading dislocation.
Figure 11.28. (a) High-resolution scanning electron microscope (HR-SEM) and (b) cathode luminescence (CL) images observed on a quaternary InAlGaN MQW layer grown on a GaN substrate.
Quaternary InAlGaN-based UV LEDs
317
shown in Figure 28(a) and (b), respectively. The TDD can be evaluated from the pit density observed on the In(Al)GaN epitaxial layers grown on the GaN or AlGaN layers [30]. From Figure 11.28(a) we can estimate that the TDD in the MQW region is less than 1 X 10^ cm~^. Emission fluctuations can also be clearly seen in the CL image, which are due to In-segregation and are considered to contribute towards the highefficiency emission. We have already observed In-segregation in quaternary InAlGaN deposited on a high TDD (> 10^^ cm"^) AlGaN buffer [19]. Confirmation that In-segregation is even obtained in dislocation-free quaternary InAlGaN is found in Figure 11.28(b). Figure 11.29 shows the I-V curve and Figure 11.30 shows the EL spectrum under RT CW operation of a UV LED fabricated on a GaN substrate. The applied voltage was 4.4 V for an injection current of 100 mA. Single-peaked emission was observed under RT CW operation. The emission wavelengths of an LED with a p-AlGaN/ AlGaN SL and with a bulk p-AlGaN layer were 351.7 and 352.2 nm, respectively. The typical value of the FWHM of the EL emission was 9 nm. Figure 11.31 shows the I-L characteristics of UV LEDs fabricated with p-AlGaN/ AlGaN SLs and with a bulk p-AlGaN layer under RT CW operation. The maximum UV output power was 7.4 mW for an injection current of 400 mA. The output power was 1.9 mW at an injection current of 100 mA, which is higher than the value of 1.5 mW that has been reported for a 351 nm AlGaN QW LED on a GaN substrate [5]. The wavelength shift of the emission peak due to sample heating was within 0.5 nm, even at a high current
100
I
'
\
'
\
InAIGaN-MQW UV-LED
80
^=352nm
<
60 Measured at RT CW
O
40
20
0
I 1
i I 2
J
L^U
\
3 4 Voltage (V)
\
\
5
L_
6
Figure 11.29. I-V curve of a quaternary InAlGaN-based UV LED on a GaN substrate.
318
Optoelectronic Devices: Ill-Nitrides '
1
\
'
1
'
InAIGaN-MQW UV-LED
'E
l=100mA FWHM=9nm
(0
c
" 1 I / \ 300
Measured at RT CW 400 500 Wavelength (nm)
" 600
Figure 11.30. Electroluminescence (EL) spectrum of a quaternary InAlGaN-based UV LED on a GaN substrate.
injection of 400 mA, indicating that the thermal conductivity of the GaN substrate is sufficiently high. Figure 11.32 shows the EQE of the LEDs with the p-AlGaN/AlGaN SLs and with a bulk p-AlGaN layer under RT CW operation. The maximum EQE obtained for an InAlGaN QW LED with a p-AlGaN SL was 1.1% at an injection current of 50 mA, which is the highest EQE ever obtained for a 350 nm-band UV LED with top-emission geometry.
>.=351.7nm U
O 4
p-AIGaN SLs
?i=352.2nm bulk p-AIGaN
Measured at RT CW J \ \ \ 200 300
L 400
Current (mA) Figure 11.31.
I-L characteristics of InAlGaN-based UV LEDs fabricated on GaN substrates with p-AlGaN/AlGaN SLs and with a bulk p-AlGaN layer under RT CW operation.
Quaternary InAlGaN-based UV LEDs
^
319
1
c 0 o LJJ
:>i=352.2nm bulk p-AIGaN
0.5 h
X LJJ
Measured at RT CW 100
200
300
Current (mA) Figure 11.32. External quantum efficiency (EQE) of InAlGaN-based UV LEDs fabricated on GaN substrates with p-AlGaN/AlGaN SLs and with a bulk p-AlGaN layer under RT CW operation.
This value is higher than that obtained for a 351 nm AlGaN QW LED fabricated on a GaN substrate [5]. From these results, the advantages of the use of quaternary InAlGaN in 350 nm-band UV emitters were revealed for the first time. The UV output will be further more increased by extracting the UV output from the bottom-side by removing the GaN substrate or by using a sapphire substrate. In summary of this section, we demonstrated 352 nm high-efficiency UV LEDs using quaternary InAlGaN MQW emitting regions fabricated on GaN substrates. The maximum UV output power obtained was as high as 7.4 mW under RT CW operation. The maximum EQE was 1.1% with an injection current of 50 mA, which is the highest EQE ever obtained for 350 nm-band UV LEDs with top-emission geometry. From these results, the advantages of the use of quaternary InAlGaN in 350 nm-band UV emitters was revealed for the first time. 11.6. CONCLUSIONS We have described techniques for the realization of high-efficiency 300-350 nm-band UV LEDs. We revealed that it is quite effective to use the In-segregation effect in quaternary InAlGaN to achieve high-efficiency 300 nm-band UV emission. We have demonstrated high-efficiency UV emission by introducing several percent of In into the AlGaN in the wavelength range between 300 and 360 nm at RT while making advantage of the In-segregation effect. An internal quantum efficiency as high as 15% was estimated from a quaternary InAlGaN-based SQW at around 350 nm at RT. Such a high-efficiency UV emission can even be obtained on high TDD buffer layers. We also revealed that
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an alternating gas flow growth technique is useful for obtaining high-Al-content p-type AlGaN. Using these techniques, we fabricated 310 nm-band UV LEDs with quaternary InAlGaN active regions. We achieved sub-milliwatt output power under RT pulsed operation for 3 0 8 - 3 1 4 nm LEDs. We also demonstrated the high output power of 7.4 mW from a 352 nm quaternary InAlGaN-based LED fabricated on GaN substrate under RT CW operation.
ACKNOWLEDGEMENTS I would like to thank Prof. Yoshinobu Aoyagi of Tokyo Institute of Technology (TIT) for a lot of supports and useful discussions. I would like to acknowledge Dr. Takao Nakamura, Mr. Katsushi Akita and Mr. Takashi Kyono of Sumitomo Electric Industries (SEI) Ltd. for a lot of experimental supports to fabricate and evaluate UV LEDs on GaN substrate. I also wish to thank Dr. Koji Ishibashi, the chief scientist of Advanced Devices Laboratory of RIKEN, for many supports to perform this research.
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Ill-Nitrides
[38] Kumakura, K., Makimoto, T. & Kobayashi, N. (2000) Jpn. J. Appl Phys., 39, L195 Part 2. [39] Hirayama, H., Enomoto, Y., Kinoshita, A., Hirata, A. & Aoyagi, Y. (2001) GaN and related alloys. Mater. Res. Soc, 693, 295-300. [40] Iwai, S., Hirayama, H. & Aoyagi, Y. (2002) Mater Res. Soc. Symp. Proc, 719, 3-9. [41] Kinoshita, A., Hirayama, H., Ainoya, M., Yamabi, T., Hirata, A. & Aoyagi, Y. (2001) GaN and related alloys. Mater Res. Soc, 693, 671-676. [42] Hirayama, H., Kinoshita, A., Ainoya, M., Yamanaka, T., Hirata, A. & Aoyagi, Y. (2001) Institute of Physics (lOP) Conference Series, No. 170, pp. 195-200 (Chapter 2). [43] Hirayama, H. & Aoyagi, Y. (2003) The Fifth International Conference on Nitride Semiconductors (ICNS-5), Th-P3.098, Nara, Japan. [44] Hirayama, H., Akita, K., Kyono, T., Nakamura, T. & Ishibashi, K. (2004) Jpn. J. Appl. Phys., Part 2, 43 (lOA). [45] Nagahama, S., Yanamoto, T., Sano, M. & Mukai, T. (2001) Jpn. J. Appl. Phys., 40 (8A), L785-L787. Part2. [46] Motoki, K., Okahisa, T., Matsumoto, N., Matsushima, M., Kimura, H., Kasai, H., Takemoto, K., Uematsu, K., Hirano, T., Nakayama, M., Nakahata, S., Ueno, M., Hara, D., Kumagai, Y., Koukitsu, A. & Seki, H. (2001) Jpn. J. Appl. Phys., Part 2, 40 (2B), L140-L143. [47] Nishida, T., Kobayashi, N. & Ban, T. (2003) Appl. Phys. Lett., 82 (1), 1-3. [48] Iwaya, M., Takanami, S., Miyazaki, A., Kawashima, T., lida, K., Kamiyama, S., Amano, H. & Akasaki, I. (2003) Phys. Stat. Sol. (a), 200, 110; (2003) Jpn. J. Appl. Phys. Part 1, 42 (2A), 400-403. [49] Akita, K., Nakamura, T. & Hirayama, H. (2004) The 5th International Symposium on Blue Laser and Light Emitting Diodes (ISBLLED2004), All-4, Korea.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 12
Design and Fabrication of GaN High Power Rectifiers K.H. Ba^k^ Y. Irokawa'', F. Ren^ S.J. Pearton", S.S. Park^ and S.K. Lee" ^Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611, USA Toyota Central Research and Development Laboratories, Inc., Nagakute, Aichi 480-1192, Japan ^Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA ^Samsung Advanced Institute of Technology, Suwon 440-600, South Korea
GaN power Schottky diodes have numerous advantages over more conventional Si rectifiers, achieving a maximum electric field breakdown strength over 10 times larger and on-state resistance (/?ON) approximately 400 times lower at a given voltage. These characteristics have made GaN devices attractive for hybrid electric vehicles and power conditioning in large industrial motors. In particular, Schottky rectifiers are attractive because of their fast switching speed, which is important for improving the efficiency of inductive motor controllers and power supplies. Both GaN and SiC power Schottky diodes have demonstrated shorter turn-on delays than comparable Si devices. In this chapter we review the design and fabrication of GaN power rectifiers.
12.1. INTRODUCTION There is a strong interest in the development of ultra high power inverter modules based on GaN and other wide-bandgap semiconductors [1-5]. These would have application in pulsed power for avionics and electric ships, in solid-state drivers for heavy electric motors and in advanced power management and control electronics. Schottky rectifiers are key elements of inverter modules because of their high switching speeds and low switching losses. While excellent reverse blocking voltages (VB) have been achieved in lateral GaN rectifiers (Vg up to —9.7 kV), these devices have limited utility because of their low on-state current [6,7]. Recently a number of reports have appeared on vertical geometry GaN rectifiers fabricated on free-standing substrates [8-10]. These have shown excellent forward current characteristics, with total currents > 1.7 A for 7 mm diameter
E-mail address: [email protected] (S.J. Pearton).
323
324
Optoelectronic Devices: Ill-Nitrides
devices and low forward turn-on voltages (Vp ~ 18 V). The reverse breakdown voltages in these structures are still limited by avalanche breakdown at defects and/or surfaces. The rapid progress in improving both defect density and purity of these free-standing substrates makes them the most promising approach for achieving both high V^ and on-state currents [11,12], in comparison to methods such as metal organic chemical vapor deposition (MOVCD) of lightly doped stand-off layers [5,13-16]. A simple model for avalanche breakdown in GaN resulting from impact ionization produces the relation [3] VB - 1.98X10^^A^"^^ where A^ is the doping concentration in the GaN. Currently, all GaN rectifiers show performance limited by the presence of defects and by breakdown initiated in the depletion region near the electrode comers. In SiC rectifiers, a wide variety of edge termination methods have been employed to smooth out the electric field distribution around the rectifying contact periphery, including mesas [17], high-resistivity layers created by ion implantation [18,19], field plates [20,21] and guard rings [22]. The situation is far less developed for GaN, with just a few reports of combined guard rings/ field-plate termination [8,9,23]. While SiC has been workhorse in the research area of high power devices, GaN has been dominant in the commercialization of light emitting devices and limited in the application of high power rectifiers due to the lack of freestanding substrates. The recent success of growing GaN freestanding wafers by hydride vapor phase epitaxy (HVPE) technology has geared up the power devices applications of GaN, especially high power rectifiers. In this chapter, the status of GaN high power rectifiers will be presented.
12.2. BACKGROUND In this review section, the theoretical calculations are given for reverse breakdown voltage and on-state resistance. Most parameters for GaN are extracted from epilayer GaN, and not from bulk GaN due to the lack of data. 12,2,1 Temperature Dependence ofBandgap (i) GaN EJQW)
= 3.475 - 9.39 X 10"^ 3.396 + 9 .39xlO"'^f
r + 772 300^ 300 + 772
r + 772
Design and Fabrication of GaN High Power Rectifiers
325
3.55 3.50 >- • • •
3-45
•
•
GaN
^
Eg = 3.396-^.5x10"^(T~-300)
3.40
^
|
/
I3.35 CD
D)
1
3.30
CG CD
3.25
I
4H-SiC
1 1
3.20 3.15 3.10 1
_i
100
200
1
_J
1
300
1
1
400
1
1—J
500
600
Temperature (K) Figure 12.1. Temperature dependence of GaN and 6H-SiC bandgap as a function of temperature. Dotted lines represent the linear fit mainly between 200 and 400 K [1].
For a linear fit between 200 and 400 K, £g(eV) = 3.463 - 5.3 X 10"^(r - 300), as shown in Figure 12.1. (ii) 6H-SiC £ (eV) = 3.19 - 3.3 X lO'^^Cr - 300) 72.2.2 Effective Density of States The effective density-of-states is derived by the following equation for most semiconductors, and determined by the effective masses of carriers and temperature. .3/2
NciT) = 2
h^
)
* \ 3/2 ,
2.50945 X 10 19
N^iT) = 2 ( ^ ^ ^ ) ' " = 2.50945 X lO'^
Uo/
V300^
Uo/ v3oo;
N^{T) = 2.3 X 10'^(r/300)3'^ ml = 0.20TOO for wurztite GaN; N^{T) = 4.6 X lO^' (^/300)3'^ ml = 1.50mo for wurztite GaN [2].
326
GaN 6H-SiC
Optoelectronic Devices: Ill-Nitrides N, (cm~^)
A^v (cm 0
2.3 X 10^^ 1.66 X 10'^
4.6 X 10' 3.29 X 10^'
12,2,3 Intrinsic Carrier Concentration The intrinsic carrier concentration n^ is described by the following equations, where A^c is the density of states in the conduction band, A^^ the density of states in the valence band, and £'g is temperature-dependent bandgap. ^i(r)-V^VcA^exp(-^) n;(T)= l.QSxlO^^r^^^exp^
20488.6
f
)
for GaN
n^(300) = 2.25 X 10~^^ cm"^ for GaN, n,(300) = 1.6 X 10"^ cm"^ for 6H-SiC. This small intrinsic carrier concentration at room temperature for wide bandgap semiconductors (Figure 12.2) causes the numerical underflow errors when calculating minority carrier concentration due to np =
n[.
3.0 3.5 Temperature (1000/K)
4.0
Figure 12.2. Intrinsic carrier concentration in SiC and GaN as a function of temperature [3].
Design and Fabrication of GaN High Power Rectifiers
327
12,2,4 Incomplete Ionization of Impurity Atoms Acceptor dopants for GaN are not fully ionized even at high temperatures. This incomplete ionization of impurities can be expressed by the following equation using Fermi-Dirac statistics with impurity ionization levels and degeneracy factors for the conduction and valence bands. N^ =
Nl =
E, - E,, = kTlni^^^,
£fn -E, = ^ ^ l n ( ^ )
= 0.016 for Si, A^A = 0.175 for Mg. In Medici™, the incomplete ionization of impurities is selected by specifying the FERMIDIRAC and INCOMPLE parameters on the MODELS statement. And the band degeneracy is given by the impurity dependent parameter GB. The donor and acceptor impurity activation energies are incorporated by the parameter EBO in the IMPURITY statement. Medici can provide for the doping and temperature dependence of the impurity activation energies. For very high doping concentrations such as more than 1.0 X 10^^ cm~^, the transition from incomplete ionization to complete ionization happens. Medici will take the complete ionization if the parameter HIGH.DOP is specified on the MODELS statement. The complete ionization will be assumed above for impurity concentration greater than HDT.MAX. A£D
12,2,5 Mobility Model (1) Analytical mobility model. (Temperature and concentration dependent mobility model)
,
Carriers Electrons Holes
Mrnaxl of\f\ ]
'V300
^n
A^max (Cm^/V S)
Mmin ( c m ^ A ^ S)
A^ref ( c m - ' )
a
P
7
1000 170
55 30
2 X 10^^ 3 X 10^^
-2.0 -5.0
-3.8 -3.7
1.0 2.0
328
Optoelectronic Devices: Ill-Nitrides
1000 ^•~»-,^
*\
o
— , , . s^ tiectron \
Hole 100 :
\\
! \
\
- s'.
I "~~~1
i
l\.________ i 1—1—1 1 1 m
1E15
1
I
1 1 1 1 iii
1E16
1
1E17
1
1 1 1 1
III
I
l_L 1 1
1E18
1.LI
1E19
1
1
1 1 1
III
1E20
Carrier concentration (cm~^) Figure 12.3. Low-field mobility of electrons and holes as a function of doping concentration in GaN at room temperature [4],
(2) Field dependent mobility model. Mn(^) =
M'n i/A
[-m']
BET AN = 2.0 BETAP - 1.0 for GaN 2.7 X 10^
Figure 12.3 is the low field mobility at 300 K as a function of doping concentration. 12.2,6 Generation and Recombination (1) Shockley-Read-Hall (SRH) lifetime. The SRH recombination-generation rate RSRK is given by ^SRH
pn — n{ rJn + n{) + T^ip + n,)
Design and Fabrication of GaN High Power Rectifiers
329
where the Hfetimes T^ and Tp of electrons and holes, respectively, are dependent upon the doping level, as described by the Scharfetter relation
1+ The lifetimes for GaN are observed in the order of 1 -100 ns. The following relation is often used for Si and is also used for GaN. '^nO = 5TpO
(2) Auger recombination ^Au = (^pP + C^n){np - nl) Auger recombination constants Q = 1 X 10"^^, Cp = 1 X 10"^^ cm^/s for GaN. Carriers
T„,p (s)
iVf"
7ns
Q p (cm'/s)
Electrons Holes
1 X 10"^ 1 X 10"^
5 X 10^^ 5 X 10^^
1 1
1 X 10~^° 1 X 10"^^
12,2,7 Reverse Breakdown Voltage The phenomenon of reverse breakdown is explained by avalanche multiplication, which involves impact ionization between host atoms and high-energy carriers. When a highenergy hole or electron under high electric field impacts an electron in the valence band, it will produce a new electron-hole pair (EHP). This newly generated EHP will cause other collisions and multiply carriers very rapidly. Avalanche breakdown is defined to occur in theory when ap exp
(an - a^)dx dx > 1
a^ — aQ exp
( ^ )
where Wj^ is the depletion width, a^ and a^ are the ionization rates of electrons and holes. Oguzman [32] and Kolnik [33] calculated the hole-initiated and electron-initiated ionization rate of electron and hole, respectively, for both wurtzite and zinc blende GaN. Figure 12.4 represents the calculated impact ionization coefficients as a function of inverse electric field for electrons and holes in wurtzite GaN and 6H-SiC [34-36]. GaN = 8.85xl0^exp[-^:^^]
(cm-^) [2]
330
Optoelectronic Devices: Ill-Nitrides
10^E-' E 0)
CD N
GaN electron & hole • Power-law fit for GaN 6H-SiC electron 6H-SiC hole • Power-law fit for 6H-SiC
Q.
E 10^ ^
- J
10° 2.5x10-'^
I
S.OxlO-"^
GaN
""-.^
I
\
S.SxIO"^
4.0x10"^
4.5x10-"^
S.OxlO""^
Inverse electric field (V/cm)"'' Figure 12.4. Calculated impact ionization coefficients as a function of inverse electric field for electrons and holes in wurtzite GaN and 4H-SiC [32,33].
6H-SiC an = 1.66 X lO^exp
/
-
1.273 X 10^ \
1 4^10
ap = 5.18 X 10^ exp( - —^
(cm-')
) (cm"^) [34]
To calculate the integrals of impact ionization without the aid of computer is timeconsuming and almost impossible. Thus, a power-law approximation can make the calculation easier in Fulop's form [36]; a^^^ = AE^ GaN (Fulop's form) a^^^ = A£" = 9.1 X m~^'E' [36] 6H-SiC (Fulop's form) a^^^ = AE"" = 4.55 X 10"^^£^ [37]
Design and Fabrication of GaN High Power Rectifiers
331
Simplified breakdown condition is expressed by the following ionization integral. rV
Jo
aeff dx = 1
Therefore, the depletion layer width at breakdown for GaN is
The critical electric field (Figure 12.5) can be calculated by ID Poisson's equation (dE/dx = qN^/sso) and obtained through numerical substitutions. d^V _ _ d ^ _ dx^ dx ,1/8
'
U
/
o
680 /
qN^ SSQ \l/7
X'^
\AWj
If Poisson's equation is solved with the voltage and electric field relationship, the breakdown voltage for non-punchthrough junction case is given by (Figure 12.6) ^Vpp = 2.87 X lO^^A^B ^^"^
7x10^
[ 6x10^ h
E
GaN^/^
5x10® TJ
^ a> o 4x10® o Q) h o
^
iC=
s
3x10®
o 2x10®
^,.^^\\-^\Z
f ^ t-"^
1x10® 1E15
^
L
1E16
1
J.
1
l-,_J-„U,iJL.
1E17
1E18
Doping concentration (cm"^) Figure 12.5. The critical electric field for 6H-SiC and wurtzite GaN as a function of doping concentration.
332
Optoelectronic Devices: Ill-Nitrides
F 10^
F ^^^^"^^'^^-^^^' --..^^^^GaN 10^
f
I
eHJsic ^^^^^^^^^^^^^^
^
^
^
102
10^ 1E15
1
—
1
1
1
1
1
•
I
1
1E16
1
1E17
•
1
i
1
l_LJ
1E18
Doping concentration (cm~^) Figure 12.6. The reverse breakdown voltage of non-punch through junction for 6H-SiC and wurtzite GaN as a function of doping concentration.
Each the depletion layer width, the critical electric field, and the breakdown voltage for 6H-SiC is given by
»'-(i)'"(^r=^-^x'»'"•"
In the case of punchthrough junction diode, the breakdown voltage is given by BVpT = E^WTTT PT
-
2eeo
Figure 12.7 is a plot of theoretical breakdown voltage of GaN punchthrough diode as a function of doping concentration and drift region thickness. It can be seen that 3 fim epilayer with doping concentration of 10^^ cm~^ gives more than 900 V of breakdown voltage. The actual experimental value of breakdown voltage is far from these theoretical predictions. The material imperfection such as the vertically threading dislocations leads to premature breakdown. Therefore, the edge termination technique should be developed for GaN to prevent the early breakdown, and the crystal quality should be advanced to improve the GaN device performance.
Design and Fabrication of GaN High Power Rectifiers
1E15
1E16
333
1E17
Doping concentration (cm"'^) Figure 12.7. The reverse breakdown voltage of punch through junction for GaN as a function of doping concentration and drift region thickness.
12,2,8 On-state Resistance The specific on-state resistance of unipolar diode is a sum of the drift region resistance, the contact resistance and the substrate resistance. R.diode
^drift + ^siib + ^(
The specific on-state resistance of drift region is given by R
= r
^
_
^D
where /x is the low-field mobility {^i = 1000 cm^/Vs for GaN), N^ is the doping concentration of drift region and W^ is the drift region thickness. The on-state resistance of drift region for GaN can be expressed by the reverse breakdown voltage and given by R^^ = 2.4 X 10" ^^^y^-^ (Ct cm^) as shown in Figures 12.8 and 12.9. For 6H-SiC R^^ = 1.45 X lO'^^^y^-^ ( a cm^)
334
Optoelectronic Devices: Ill-Nitrides 0.030
—-—— ———-
0.025 £ ^
r
0.020
i
c
I
0.015
/
GaN
(D
S 0.010 - - - -
-—
•
-
—
-
—
^^^
"
c
o 0.005
-..-.••^•-n,
„ „ — •
1
'—
2000
4000
6000
8000
10000
Reverse breakdown voltage (V) Figure 12.8. The specific on-state resistance for GaN Schottky diode as a function of breakdown voltage.
1 r : £ ?
/
• ,. ,.^AIGaN-UF AIGaN-UF GaN-UF/
Si /^ 0.1 IT
a
AIGaN-UF. GaN-UF /^
'-
c
•
CO
/ GaN-Calte(Dh /
\
3 (A C
o o
1E-3
'
/
1
102
1.
A / /
GaN-UF
""7
1E-4
/
6H-SiCy^ / GaN
GaN-UT
^/^ , _ ^ ' ' GaN-UF
/
GaN-UF/
/
/•
2? 0 . 0 1 ^
1
/
GaN Schottky rectifiers
1
I I — I I I ,
/
I
n
10^
„ 1
1
il
1
In, 1
1
10"^
Reverse breakdown voltage (V) Figure 12.9. The specific on-state resistance for Si, 6H-SiC, and GaN diode as a function of breakdown voltage.
Design and Fabrication of GaN High Power Rectifiers
335
Hybrid Electric Vehicle - Puris Regenerative brake equipment
-^^r?'""'"'"*'^^^^^^"-.'
Niclcel-metai-hycfride battery
Engine MMa0^'
^S ^iiiiiiBittil
]§Wf^^] 1
Fuel Tanl<
Transmission
liii^WiiB
Figure 12.10. Toyota Prius hybrid electric vehicle.
while for Si RON = 5.91 X 10~^BV^^ (ft cm^) These properties make GaN Schottky diode rectifiers attractive for power distribution in hybrid electric vehicles such as the Toyota Prius (Figures 12.10-12.12) where a 1000 V, 500 kA/cm^ at 1.4 V GaN diode and 850 V, 500 A/cm^ at 1.6 V GaN MISFET are needed for the inverter unit. Metal overlap
Dielectric film
30^m
Figure 12.11.
Bulk GaN Nd=1x10^6 cm'^
Power distribution unit in hybrid electric automobile.
336
Optoelectronic Devices: Ill-Nitrides
10 15 20 25 Metal overlap (jurx]) Figure 12.12. Sales figures foe electric and hybrid electric vehicles.
12.3. EDGE TERMINATION DESIGN 12,3,1
Field Plate Termination
The structure at the top of Figure 12.13 was used as our standard for simulation and is based on the available free-standing GaN bulk substrates, which currently have a doping density of ~ 10^^ cm~^. While their thickness is —200 iJim, the depletion depth is limited by the background doping and we used a thickness of 30 jxm in the simulations. The parameters we investigated in this study were the dielectric material, its thickness
1600 1500
-
S) 1400
-
> 1300
-
^
c
o 1200 •D
Q) 1100 1000 900
-
10 jjxw metal overlap 1-^"
,
1
,
0.0
0.2
0.4
I
0.6
.
I
.
0.8
I
1.0
Oxide Thickness (/im) Figure 12.13. Schematic of simulated bulk GaN rectifier structure.
Design and Fabrication of GaN High Power Rectifiers
337
5^m M
1.0/xm ^
w
W^9smr^^ •^>+ 2.5/im N
.
:N+
1.0 ;um
Figure 12.14. Effect of metal overlap distance in VB for rectifiers with 0.7 [xm thick Si02 field plate.
and the extent of metal overlap onto the field plate. The simulations were carried out using the MEDICI™ code. The back n-ohmic contact resistance was assumed to be 10~^ il cm^, which is consistent with our past experimental data, and an interface state density of 5 X 10^^ eV~^ cm~^ was assumed for the dielectric/GaN interface. Once again, this is based on our past experimental results. After designing the particular basic structure, a mesh of nodes is created to allow the solutions to the transport equations to be obtained. The program includes SRH and Auger recombination, an incomplete ionization model and an average of the available high-field saturation and avalanche models. We assumed a conduction band density of states of 2.6 X 10^^ cm~^ for the n-type GaN, a surface recombination velocity of 10^ cm/s and SRH Ufetime of 1 ns. The maximum electric field in an unterminated rectifier occurs directly under the comer of the Schottky contact and emphasizes that avalanche breakdown is more likely to initiate at that location. The breakdown voltage was 980 V. Figure 12.14 shows the calculated breakdown voltages obtained for a 0.7 ixm thick Si02 field plate on top of the rectifier, as a function of the extent of the overlap of the Schottky contact onto the Si02. Note that the Vg values increase rapidly for metal overlaps up to — lOjjLm, with a maximum increase of —63% in breakdown voltage relative to the unterminated device. Beyond an overlap of 10 ixm, there is no further improvement in breakdown voltage from this given thickness of Si02 field plate. We believe, this
Optoelectronic Devices: Ill-Nitrides
338
is due to the fact that the lateral spread of the depletion layer becomes comparable to the depth of this layer, so that extending thefieldplate into undepleted regions does not affect the breakdown behavior. The effect of Si02 thickness at a given metal overlap distance of 10 juim is shown in Figure 12.15. There is an almost linear increase in VB with increasing oxide thickness up to 0.7 juim. At thicknesses > 1 luim, the simulations showed that the electric field inside the oxide began to increase. One must, therefore, choose a thickness such that the field strength inside the oxide does not exceed its breakdown strength. The fact that very thick oxide layers do not lead to an improvement in V^ is an advantage from a practical viewpoint because such layers would require very long deposition times and introduce problems such as stress. Other dielectrics that have demonstrated reasonably low interface state densities on GaN include AIN, MgO and SC2O3. Si02 produces the highest breakdown voltage rectifiers for these conditions because of its large bandgap and low dielectric constant. However, in real devices it should be considered that reliability is of utmost importance and it is not necessarily the case that Si02 would be the best choice with this consideration in mind. For example, SC2O3 appears to produce the most effective passivation of surface states on GaN/AlGaN heterostructure field effect transistors [28]. Obviously, much more work needs to be done to establish experimentally the relative tradeoff between V^ and long-term device stability. The main findings of this simulation study can be summarized as follows: (a) the use of an optimized Si02 field plate edge termination can increase the reverse breakdown voltage of bulk GaN rectifiers by up to a factor of two compared to unterminated devices; 1300
5 1200
^m
O)
^
•^^^
1100
1 1000 0
ro 900 GO
CD
a: §
800
\^^^^ •
700 600 1
I
1
1
1
1
1
1
1
2 3 P-ring Spacing (^m) Figure 12.15. Effect of Si02 thickness on VB for rectifiers with 10 jjim metal overlap.
Design and Fabrication of GaN High Power Rectifiers
339
(b) the dielectric material, thickness and ramp angle all influence the resulting VB of the rectifier by determining where the maximum field strength occurs in the device structure. The key aspect in designing the field plate edge termination is to shift the region of the high field region away from the periphery of the rectifying contact. 12,3,2 Junction termination Figure 12.16 shows a schematic of a rectifier employing planar junction termination with a dielectric field plate. The breakdown point is extended beyond the contact periphery by this approach. Simply using the planar junction without the field plate increases VB to 760 V, while the addition of the Si02 field plate increases it up to 1110 V. Important design parameters influencing VB are the length of the metal overlap and the Si02 thickness. For a given value of the plate length, the Si02 thickness must be optimized in order to balance the electric field peaks at the junction and plate edges as reported previously for GaN [38]. Another alternative for edge terminations is the use of equipotential p"^ guard rings. As the bias in the main junction increases, the space charge region extends until it reaches the guard ring. The potential of the guard ring is given by 1/2
/2eNj,Ws2V^\
+
•"FFR
2s
where A^^ is the acceptor concentration, s the GaN permitivity, W^ the field ring spacing and VA the applied Schottky bias on the Schottky contact. As the bias is further increased. 3000 Single JTE
• >
2500 [--
0) D)
B "o >
2000
c
o
1500
-
•
1 p-rina
•D
2 p-rings
• —-^—•
CO 0
1000
Planar junction with the field plate
(D • . ^ - — ^ - ^ "
a:
Planar Junction
500 1
1
1
1
2
1
1
1
3
1
1
.
1
4
Edge Termination Method Figure 12.16.
Schematic of rectifier with planar junction termination and Si02 field plate (top) or with planar junction termination and one p^ guard ring (bottom).
340
Optoelectronic Devices: Ill-Nitrides
this potential increases, tracking the value of the equipotential line from the main junction [22]. At a given bias, the potential of the ring is equal to that of the highest potential around it and lower than the value on the main junction. The net effect is to reduce field crowding near the junction curvature [22]. In our case of one p-guard ring with additional planar junction termination, the calculated VB is 1180 V which is a slight improvement over the planar junction termination with the field plate. Figure 12.17 shows the effect of guard-ring spacing on the calculated Vg. In our geometry, the maximum V^ is obtained for a spacing of --^ 3 |xm. The benefits of the field spreading are lost at either very small or large spacing. The use of additional guard rings is also beneficial. For example, using two rings, separated by 2 and 3 juim, respectively, was found to increase V^ to 1458 V. The JTE method extends the high-doped side of the main junction by a connected region of lower doping level. The net effect is once again to spread the field lines and avoid premature breakdown. A key design parameter is obviously the doping concentration in the JTE region. In our case, a doping concentration of 4 X 10^^ cm~^ produced a V^ value of 2720 V. The value of VB was strongly peaked for a JTE doping around 4 X 10^^ cm~^, although VB values above 2000 V are achieved for a reasonable range of concentrations. Finally Figure 12.18 provides summary of the VB values calculated for the different edge termination methods. The single JTE approach provides an almost 5-fold increase relative to an unterminated rectifier and points out the clear necessity to employ one or more methods in order to maximize the blocking voltage even for GaN rectifiers.
2
3
Forward Bias (V) Figure 12.17, Effect of guard ring spacing on VB •
Design and Fabrication of GaN High Power Rectifiers
10^
^
341
GaN p+-n-n+ diode 5 jam thick drift
10-1
(0 c (D
I
10-3
o SRH+AUGER+incomplete Auger+incomplete
1x10-5 [•
SRH+AUGER
10-
2
3 4 Forward bias (V)
5
Figure 12.18. Comparison of VB values for GaN rectifiers employing different edge termination methods.
For GaN power rectifiers to mature into a manufacturable technology, attention must be paid to the design and implementation of edge termination methods that maximize the reverse breakdown voltage. Our current study shows that the JTE produces the highest blocking voltages for vertical bulk GaN rectifiers, although the VB values are highly sensitive to the doping in the JTE region. Guard-rings, field plates and planar junction were also examined in increasing VB over the value in unterminated rectifiers.
12.4. COMPARISON OF SCHOTTKY AND p-n JUNCTION DIODES The minority carrier concentration in GaN p - n junction is extremely small in the order of 10"^^ cm "^ for ND = 10^^ cm ^ at room temperature because the intrinsic carrier -10 concentration is about 10~^^ cm np = n^ 12.4,1 Reverse Bias Ideally, the reverse current density /R can be calculated by the generation current in the space charge region and the diffusion current due to the generation close to the space charge region.
342
Optoelectronic Devices: Ill-Nitrides
Tg is the appropriate generation lifetime in the space charge region, Tp is the minority carrier hfetime of hole in the n-region. The generation current is in the order of 10~^^ A/cm~^ for the GaN p-n~-n"^ diode at room temperature with a breakdown voltage of 1530 V. The diffusion current is in the order of 10~^^ A/cm~^ and diffusion current contribution is negligible. Those large leakage currents arise from the surface leakage, defects in epilayer and junction, and tunneling. 12.4.2 Forward Bias If a forward bias is applied, the built-in voltage must be exceeded, before a substantial current can flow:
"-f-m Vbi^ 3.178 V for GaN p-n"-n"^ diode (N^N^ = 10'^^ cm~^); V^^ = 2.119 W for 6H-SiC p - n " - n + diode (A^^A^A = 1 0 - 3 4 cm~^) The forward current density Jp ^t low forward voltage Vp is determined by a current contribution due to recombination in the space charge region and by a diffusion contribution due to recombination close to the space charge region.
Figures 12.19-12.21 compare forward I-V (including temperature dependence) for GaN p - n and Schottky diodes.
12.5. HIGH BREAKDOWN LATERAL DIODES For laterally depleting devices, the structure consisted of ~ 3 mm of resistive (10^ n/D) GaN. To form ohmic contacts, Si"^ was implanted at 5 X 10^"^ cm~^, 50 keV into the contact region and activated by annealing at 150°C for 10 s under N2. The Ohmic and rectifying contact metallization was the same as described above. Three different edge termination techniques were investigated for the planar diode: (1) Use of a p-guard ring formed by Mg"^ implantation at the edge of the Schottky barrier metal. In these diodes the rectifying contact diameter was held constant at 124 |ULm, while the distance of the edge of this contact from the edge of the ohmic contact was 30 |jLm in all cases. (2) Use of p-floating field rings of width 5 mm to extend the depletion boundary along the surface of the Si02 dielectric, which reduces the electric field crowding at the edge
Design and Fabrication of GaN High Power Rectifiers
343
lO^i-
/ 102 r E
/
r t
10°
'
i'
r
3
o
/
/
/ /
/
/sOOK
423'K 1
/ 1x10- r
/
; J
0
1
1
/
>
J i
/
^
/
^
/
/
/
/
10-2 r :
/ /
573 K / 1
S
/ /
1
' i
ocnonKy aioue
I
1 I
p-A7 diod6
J 1 \
/ 1
2
I
3
.
I
.
4
Forward bias (V) Figure 12.19. The forward l-V characteristics of 5 |jLm n region Schottky diode.
of this boundary. In these structures a 10 luim wide p-guard ring was used, and one to three floating field rings employed. (3) Use of junction barrier controlled Schottky (JBS) rectifiers, i.e. a Schottky rectifier structure with a p - n junction grid integrated into its drift region. In all of the edge-terminated devices the Schottky barrier metal was extended over an oxide layer at the edge to further minimize field crowding, and the guard and field rings formed by Mg"^ implantation and 1100°C anneahng.
0.2 o -£ 0.0 t
o -0.2 -4000
-2000 Voltage (V)
Figure 12.20. The forward 1-V characteristics of p^-n-n"*" diode.
344
Optoelectronic Devices: Ill-Nitrides
10 20 Guard Ring Width (jim) Figure 12.21. The temperature-dependent forward I-V characteristics of p"''-n-n^ diode.
Figure 12.22 shows the influence of guard ring width on V^ at 25°C. Without any edge termination, V^ is —2300 V for these diodes. The forward turn-on voltage was 15-50 V, with a best on-resistance of 0.8 fl cm^. The figure-of-merit (VQ)^/RQ^ was 6.8 MW/cm^. As the guard-ring width was increased, we observed a monotonic increase in VB^ reaching a value of —3100 V for 30 fxm wide rings. The figure-of-merit was 1535 MW/cm^ under these conditions. The reverse leakage current of the diodes was still in the nA range at voltages up to 90 of the breakdown value. Figure 12.23 shows the variation of VRB with Al percentage in the AlGaN active layers of the rectifiers. In this case we are using the VRB values from diodes without any edge termination or surface passivation. The calculated bandgaps as a function of Al composition are also shown, and were obtained from the relation Egix)
>
= ^g,GaN(l - X)-^ ^g,AlNA^ - ^A<1 -
X)
5000
Percentage of Al in AlxGa^.xN (%) Figure 12.22. Current-Voltage characteristics of GaN power rectifiers with p-guard for edge terminations (top), and effect of p-guard ring on the reverse breakdown voltage of GaN power rectifiers (bottom).
Design and Fabrication of GaN High Power Rectifiers
345
5000
4000
3000 H
2000 H
• GaN (edge terminated) • Alo.25Gao.25N (unterminated)
1000
50
100
150
200
Temperature (°C) Figure 12,23. Variation of VRB ^^ Al^Gai_;^N rectifiers without edge termination, as a function of Al concentration. The bandgaps for the AlGaN alloys are also shown.
where x is the AIN mole fraction and b is the bowing parameter with value 0.96 eV [19]. Note that VRB does not increase in linear fashion with bandgap. In a simple theory, VRB should increase as (E^)^-^, but it has been empirically established that factors such as impact ionization coefficients and other transport parameters need to be considered and that consideration of E^ alone is not sufficient to explain measured VRB behavior. The fact that VRB increases less rapidly with E^ at higher AIN mole fractions may indicate increasing concentrations of defects that influence the critical field for breakdown. Figure 12.24 shows the variation of VRB with temperature. The data can be represented by a relation of the form
VRB = VRBo[i + i8(r-ro)] where /3 = -6.00 ± 4 V/K for both types of rectifiers. However, in Schottky and p - i - n rectifiers we have fabricated on more conducting GaN, with VRB values in the 400-500 V range, the values were consistently around — 0.34 V/K. Therefore, in present state-of-theart GaN rectifiers, the temperature coefficient of VRB appears to be a function of the magnitude of VRB- Regardless of the origin of this effect, it is clearly a disadvantage for GaN. While SiC is reported to have a positive temperature coefficient for VRB there are
Optoelectronic Devices: Ill-Nitrides
346 1.4 1.2
500 Aim X 500'/im GalSI Schottky diode
[ 1.0 <0.8 0.6 O
h
0.4
0.2 1
^^^^^^^-^^
i
1
0.0 1
0
1
i
2
1
1
•
3 4 5 Bias voltage (V)
i
•
6
i
•
7
i
•
8
Figure 12.24. Temperature dependence of VRB for GaN and AlGaN rectifiers.
reports of rectifiers that display negative j8 values. One may speculate that particular defects present may dominate the sign and magnitude of j8, and it will be interesting to fabricate GaN rectifiers on bulk or quasibulk substrates with defect densities far lower than in heteroepitaxial material. 12.6. BULK DIODE ARRAYS A drawback of Schottky rectifiers fabricated on both conventional homoepitaxial (AI2O3) and free-standing GaN films is a strong dependence of reverse breakdown voltage, VB^ on device contact diameter [8]. In defect-free material, V^ is related to the maximum electric field at breakdown, ^ j ^ and the depletion depth at breakdown, W^, through [3] Vn
EMWM
However, in the presence of defects such as screw dislocations, nanopipes, or voids it has been demonstrated that temperature breakdown occurs in both GaN and SiC [8,16,17]. For example, in Pt Schottky diodes fabricated on free-standing GaN, we have previously reported a decrease in Vg from 160 V for 75 jxm diameter to ~ 6 V for 7 mm diameter devices [8]. In order to overcome this degradation in reverse bias performance when fabricating, we demonstrate in this paper a method for interconnecting the output of many (~ 130) smaller diodes (500 X 500 ixm^) to produce very high total forward current.
Design and Fabrication of GaN High Power Rectifiers
347
Similar parallel connection has been used to achieve high total forward current in SiC devices [15]. The diode arrays were fabricated in 1 cm^, 200 juim thick, free-standing GaN substrate grown by HVPE on c-plane AI2O3. The GaN films were subsequently removed from the sapphire by laser heating [18]. Full-area back contacts of Ti/Al/Pt/Au were deposited by e-beam evaporation and annealed at 850°C for 30 s to minimize contact resistance. Edge termination utihzed Si02 (1500 A) field plate and e-beam deposited Pt/Au Schottky contacts with 500 X 500 juim^ dimensions. To achieve parallel connection of the diode array, SiN_^ (2500 A) was deposited all over the wafer as an isolation and opened with 100 U | Lm diameter as current paths for each Schottky metal pad. Metal was further deposited with Ti/Au for adhesion and seed layers and Au was electroplated to a thickness of 3 U | Lm on both front and back of the rectifiers. A schematic of a completed device is shown in Figure 12.25. Prior to the interconnection of all the rectifiers, the current-voltage (I-V) characteristics at 25°C were recorded, and fit to the relation for thermionic emission
Electroplated Au (3 ^im)
Ti/Au Nitride (2500A)
P Pt/Au
Oxide (1500A)
Free-standing GaN (200 fjxn)
Ti/Au Electroplated Au (3 /xm)
Figure 12.25. Forward I-V
characteristic from single 500 X 500 ixm^ GaN Schottky rectifier (top) and schematic of free-standing GaN rectifier structure.
Optoelectronic Devices: Ill-Nitrides
348 over a barrier
(
e<j>^,\
Jp = A*T expl
( eV
where / is the current density, A*, Richardson's constant for n-GaN, T, the absolute temperature, e, the electronic charge, ^ , the barrier height, k, Boltzmann's constant, n, the ideality factor and V, the applied voltage. From the data, 0^ was obtained as 1.08 eV and n= 1.4. The forward turn-on voltage, Vp, for a Schottky rectifier is given by Vp = ^
l n ( - ^ ) + «*B + «ON-/F
where /?ON is the on-state resistance. Defining Vp ^s the bias at which the forward current density is 100 A/cm^, Vp was found to be 2.2 V and /?ON was 8 mXl cm^ for an individual device. With the thick plated metal on the rectifiers, the forward I-V characteristics in Figure 12.25 for a single 500 X 500 luim^ device showed a slight increase in Vp to ~ 3 V. This might result from current spreading in the structure. The forward DC current at 7 V was 1.2 A for the single device. The highest reported forward current from a GaN rectifier in 1.6 A under pulsed (10% duty cycle) conditions [20]. To connect the output of all of the individual devices, we clamped both sides of the array to Cu disks using a press-packed arrangement and measure the DC I-V
180 r
160
140
Free-standing GaN Schottky diode array
[email protected]?V
• /
r
120
7^ 100
I
80
O
60
'
40 20 0 -20l
[
1
j
1
1
i
2
1
i
3
1
1
4
i
. 1 . . 1 .. i.
5
6
1
.
7
Bias voltage (V) Figure 12.26. Total forward l-V characteristic from rectifier array.
Design and Fabrication of GaN High Power Rectifiers
349
characteristics at 25°C using Tektronix 371B curve tracer. Figure 12.26 shows a typical I-V characteristic, with output currents of 24 A at 3 V and 161 A at 7.12 V. The latter value corresponds to a total on-state resistance of 44 mfl cm^. The on/off ratio was ~ 8 X 10^ at 5 V / - 100 V for this rectifier array at 25°C. The currents demonstrated with the bulk rectifier array show the promise of this technology for even the most demanding applications, such as utility power switching [21] and power distribution in next-generation naval vessels [22,23]. A simple calculation indicates that VB values in excess of 16 kV are achievable on free-standing GaN substrates of thickness > 50 [xm provided the carrier concentration is < 5 X 10^^ cm~^, so that both high forward currents and high reverse breakdown voltages should be possible with this approach. 12.7.
CONCLUSIONS
In summary, the size and geometry dependence of GaN Schottky rectifiers on both sapphire and quasi-bulk substrates has been investigated. The reverse breakdown voltage increases dramatically as contact size is decreased and is also much larger for vertically depleting devices. The low on-state resistances produce high figure-of-merits for the rectifiers and show their potential for applications involving high power electronic control systems [24-38]. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8]
[9] [10] [11] [12]
Heydt, G.T. & Skromme, B.J. (1998) Mater. Res. Soc. Symp. Proc, 483, 3. Brown, E.R. (1998) Solid State Electrochem., 43, 1918. Trivedi, M. & Shenai, K. (1999) /. Appl. Phys., 85, 6889. Pearton, S.J., Ren, F., Zhang, A.P. & Lee, K.P. (2000) Mater. Sci. Eng., R30, 55. Bandic, Z.Z., Bridger, D.M., Piquette, E.G., McGill, T.C., Vaudo, R.P., Phanse, V.M. & Redwing, J.M. (1999) Appl. Phys. Lett., 74, 1266. Zhang, A.P., Johnson, J.W., Ren, F., Han, J., Polyakov, A.J., Smirnov, N.B., Govorkov, A.V., Redwing, J.M., Lee, K.P. & Pearton, S.J. (2001) Appl Phys. Lett., 78, 823. Zhang, A.P., Dang, G., Ren, F., Han, J., Polyakov, A.Y., Smirnov, N.B., Govorkov, A.V., Redwing, J.M., Cao, X.A. & Pearton, S.J. (2000) Appl. Phys. Lett., 76, 1767. Johnson, J.W., LaRoche, J.R., Ren, F., Gila, B.P., Overberg, M.E., Abemathy, C.R., Chyi, J.I., Chuo, C.C., Nee, T.E., Lee, CM., Lee, K.P., Park, S.S., Park, J.I. & Pearton, S.J. (2001) Solid State Electrochem., 45, 405. Johnson, J.W., Zhang, A.P., Luo, W.B., Ren, F., Pearton, S.J., Park, S.S., Park, Y.J. & Chyi, J.I. (2002) IEEE Trans. Electron. Devices, 49, 32. Johnson, J.W., Luo, B., Ren, F., Palmer, D., Pearton, S.J., Park, S.S. & Park, Y.J. (2002) Solid State Electron., 46, 911. Park, S.S., Park, l.W. & Choh, S.H. (2000) Jpn. J. Appl. Phys., 39, LI 141. Morkoc, H. (2001) Mater Sci. Eng., R33, 135.
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Devices:
Ill-Nitrides
[13] Zhang, A.P., Dang, G.T., Ren, F., Cho, H., Lee, K.P., Pearton, SJ., Chti, J.-L, Nee, T.E. & Chuo, C.C. (1999) Solid State Electron., 44, 619. [14] Ren, F., Zhang, A.P., Dang, G., Cao, X.A., Cho, H., Pearton, SJ., Chyi, J.I., Lee, CM. & Chuo, C.C. (1999) Solid State Electron., 44, 619. [15] Zhu, T.G., Lambert, D.J., Shelton, B.S., Wong, M.M., Chowdhurg, V. & Dupuis, R.D. (2000) Appl. Phys. Lett., 11, 2918. [16] Shelton, B.S., Zhu, T.G., Lambert, D.J. & Dupis, R.D. (2001) IEEE Trans. Electron. Devices, 48, 1498. [17] Neudeck, P.G., Larkin, D.J., Rowell, A. & Matus, L.G. (1994) Appl. Phys. Lett., 64, 1386. [18] Morisette, D.T., Cooper, J.A., Jr., Melloch, M.R., Doing, G.M., Shenoy, P.M., Zakari, M. & Gladish, J. (2001) Trans. IEEE Electron. Devices, 48, 349. [19] Itoh, A., Kimoto, T. & Matsunami, H. (1996) Electron. IEEE Devices Lett., 17, 139. [20] Saxena, V., Su, J.N. & Steckl, A.J. (1999) IEEE Trans. Electron. Devices, 46, 456. [21] Tarplee, M.C., Madangarli, V.P., Zhang, Q. & Sudarshan, T.S. (2001) IEEE Trans. Electron. Devices, 48, 2659. [22] Dyakonova, N.V., Ivanov, P.A., Koglov, V.A., Levinshtein, M.E., Palmour, J.W., Pumyantsev, S.L. & Singh, R. (1999) IEEE Trans. Electron. Devices, 46, 2188. [23] Zhang, A.P., Dang, G., Cao, X.A., Cho, H., Ren, F., Han, J., Chyi, J.-L, Lee, CM., Nee, T.E., Chuo, C.C, Chi, G.C, Chu, S.N.G., Wilson, R.G. & Pearton, S.J. (2000) MRS Internet Nitride J. Semicond. Res., 551, W11.67. [24] Mehandru, R., Gila, B.P., Kim, J., Johnson, J.W., Lee, K.P., Luo, B., Onstine, A.H., Abemathy, C.R., Pearton, S.J. & Ren, F. (2002) Electrochem. Solid State Lett., 5, G51. [25] Hong, M., Ng, H.M., Kwo, J., Kortran, A.R., Baillargeon, J.N., Chu, S.N.G., Mannaerts, J.P., Cho, A.Y., Ren, F., Abemathy, CR. & Pearton, S.J., (2000) Presented at the 197th Electrochemical Society Meeting, May 2000, Toronto, Canada. [26] Luo, B., Johnson, J.W., Kim, J., Mehandru, R., Ren, F., Gila, B., Onstine, A.H., Abemathy, C.R., Pearton, S.J., Baca, A.G., Briggs, R.D., Shul, R.J., Monier, C & Han, J. (2002) Appl. Phys. Lett., 80,1661. [27] Brezeane, G., Fernandez, J., Millan, J., Rebello, J., Badila, M. & Dilimot, G. (1998) Mater Sci. Forum, 264-268, 941. [28] Teisseyre, H., Perlin, P., Suski, T., Grzegory, I., Porowski, S., Jun, J., Pietraszko, A. & Moustakas, T.D. (1994) J. Appl. Phys., 76, 2429. [29] Levinshtein, M.E., Rumyantsev, S.L. & Shur, M.S. (2001) Properties of Advanced Semiconductor Materials, Wiley Interscience, New York. [30] Kolessar, R., Nee, H.-P. (2001) APEC 2001, Sixteenth Annual IEEE, vol. 2. [31] Mnatsakanov, T.T., Dmitriev, M., Bathova, L., Osinsty, A. & De Huth, L. (2003) Solid State Electron., 47, 2498. [32] Oguzman, I.H., Bellotti, E., Brennan, K.F., Kolnik, J., Wang, R. & Ruden, P.P. (1997) J. Appl. Phys., 81, 12. [33] Ruff, M., Mitlehner, H. & Helbig, R. (1994) IEEE Trans. Electron. Devices, 41, 1040. [34] Trivedi, M. & Shenai, K. (1999) J. Appl. Phys., 85, 6889. [35] Kolnik, J., Oguzman, H., Brennan, K.F., Wang, R. & Ruden, P.P. (1997) /. Appl. Phys., 81, 2. [36] Fulop, W. (1967) Solid State Electron., 10, 39. [37] He, J., Wang, Y., Zhang, X., Xi, X., Chan, M., Huang, R. & Hu, C (2002) IEEE Trans. Electron. Devices, 49, 933. [38] Ren, F. & Zolper, J.C (2003) Wide Energy Bandgap Electronic Device, World Scientific, Singapore, p. 125.
Optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 13
GaN Negative Dififerential Resistance Components with Terahertz Operation Capability: From Fundamentals to Devices Dimitris Pavlidis Department of Electrical Engineering and Computer Science, The University of Michigan, 1301 Beal Ave., Ann Arbor, MI 48109-2122, USA and Department of High-Frequency Electronics, Technische Universitdt Darmstadt, Mercksta^e 25, D-64823 Darmstadt, Germany
13.1.
INTRODUCTION
Negative differential resistance (NDR) devices are solid-state components based on the NDR principle, providing a solution for low-cost, low noise, and high power microwave radiation sources. Such devices are extensively used in intrusion alarms, microwave test instruments, and automotive collision avoidance systems. Currently, these devices are fabricated on GaAs and InP, which are III-V, direct bandgap semiconductor materials exhibiting NDR. Although the devices based on these materials have proven to be reliable, they are limited in power and operation frequencies due to fundamental material features related to the bandstructure and transport properties. For higher frequency and high power applications like military radar, high-speed communications, and possibly biological agent detection, it is necessary to explore other semiconductor materials. One such material that is being investigated for these applications of NDR devices is GaN. GaN is a wide-bandgap semiconductor material whose velocity-field characteristics are expected to present NDR. The advantages of using GaN over GaAs and InP, in terms of increased power handling capability and higher operation frequency, are directly related to its larger intervalley energy gap and higher peak and saturation velocities. Although in GaN, further confirmation is needed regarding the presence of a transferred-electron effect (which causes NDR) and the processing technology of GaN is in its early stages, it has a lot of potential and thus is worth investigating.
E-mail address: [email protected] (D. Pavlidis).
351
352 13.2.
Optoelectronic Devices: Ill-Nitrides PRINCIPLES OF OPERATION OF NDR DEVICES
NDR devices operate on the principles of the Gunn effect although, as explained later other mechanisms may also play a role in the presence of NDR in GaN-based devices. The generalized Gunn effect describes the mechanism of electron transfer leading to a negative differential conductivity (resistance) in a homogeneous, bulk semiconductor material [1]. These devices are unipolar, two terminal devices. The semiconductor materials that exhibit the Gunn effect must be direct bandgap materials that have more than one valley in the conduction band and the effective mass and the density of states in the upper valley(s) must be higher than those in the main valley. The typical velocity-field characteristics of a bulk material exhibiting the Gunn effect are shown in Figure 13.1a. The main valley of the conduction band is where the electrons initially reside with little or no external electric field applied as shown in Figure 13.1b. If the external field is increased to a value above a threshold field. Figure 13.1c, many of the electrons acquire enough energy to be scattered ("transferred") into the upper satellite valley. Since the effective mass in the upper satellite valley is larger than in the main valley, the mobility, and the average drift velocity of the electrons is reduced. The mobility is given by er m*
f^
(13.1)
where r is the relaxation time and m* is the effective mass in a semiconductor material. The differential mobility, defined as, /JL^ = dv/dE, becomes negative when the electric field is above the threshold value as this can be seen in Figure 13.1a. This leads to the NDR.
(b)
ik
(a) ^pk
/^J\.
^saf /
1
^th
J,
• £
£<e,y
^'sat
(c) e
-• k
(d) £
\J -> k
-• k Cfh < e < e«;
e >£^,
Figure 13.1. (a) Generalized velocity-field characteristics of a transferred electron device, (b)-(d) Simplified energy-band diagram for a direct two-valley semiconductor showing electron transfer.
GaN Negative Differential Resistance Components
353
As the field is continually increased beyond the saturation field. Figure 13.Id, the drift velocity of the electrons saturates. To see how microwave frequencies can be produced from a bulk semiconductor material exhibiting the transferred electron effect as described above, further analysis is needed in the region of negative differential mobility, which is between the threshold field and the velocity saturation field in Figure 13.1a. A sample of bulk semiconductor material biased in the negative differential mobility region, (under uniform doping concentration and uniform electric field) is thermodynamically unstable. In an attempt to establish a steady state, an energetically more favorable state is reached if, instead of having a homogeneous distribution of charge over the sample length, the charges split up into space charge regions [1]. Any existing space charge inhomogeneity, Q{x,t), traveling at a velocity, v, will follow an exponential law given in Eq. (13.2) that can be derived from Maxwell's equations [2]: Q(x, t) = Q(x - vt, 0)exp^- - J
(13.2)
T is the energy relaxation time given by
where N^ is the doping concentration and fi^ is the differential mobility. From Eq. (13.2) it is clear that at low electric fields, when fi^ > 0, the charge inhomogeneity decays with r = r^, the dielectric relaxation time. At electric fields above the threshold value, when in^ < 0, the charge inhomogeneity can grow. The growth factor is given by
(V)(T)
S,V
where / is the device length and v is the electron velocity. Equivalently, NDI > T T ^
(13.5)
If the growth factor given by Eq. (13.5) exceeds the threshold level, then the charge inhomogeneity reaches a significant level and grows into a dipole domain. From Eq. (13.5) it is clear that the design of NDR devices lies in choosing the device length, /, and the doping concentration, A^^. One would want to choose / as small as possible to minimize the electron transit time from cathode to anode and Nj^ as large as possible to satisfy Eq. (13.5). However, there is a lower limit in choosing the device length, called the "dead space layer". The dead space layer arises, due to the fact that the scattering of electrons into the upper satellite valley occurs over a finite distance. It is well known that using a method of hot electron injection can reduce the dead-space layer and enhance the performance of
354
Optoelectronic Devices: Ill-Nitrides
NDR devices [3]. Furthermore, to avoid the formation of static domains at the anode, Nj) should not exceed the critical doping concentration given by A^CRiT =
(13.6)
^xFj^/q
In Eq. (13.6), Fj^ is the threshold electric field. Eqs. (13.5) and (13.6) are central to the design of NDR devices. From the above discussion, since the charge is inhomogeneous in the negative differential mobility region, the electric field distribution over the sample length is also inhomogeneous. A typical electric field distribution in a NDR device is shown in Figure 13.2a. It can be seen from Figure 13.2a that there is a region of high electric field surrounded by a region of low electric field. The corresponding charge distribution is shown in Figure 13.2b. In Figure 13.2 the accumulation of charge in the region where the electric field is increasing is a result of significant decrease in mobility caused by scattering of electrons into the upper valley. In the region of the sample where the electric field is decreasing, the electrons accumulated in the upper valley lose energy and scatter back into the lower valley of the conduction band. When this happens, a depletion region is created. The accumulation and the depletion regions together form the dipole domain. The dipole domain forms near the cathode and propagates along the length of the device to the anode as shown in Figure 13.3. When the domain reaches the anode it collapses and a new domain is formed at the cathode. The process of domain build-up, propagation, and extinction is repeated.
(a) ^ 4 eh
->x
(b) A/A
-•X
Figure 13.2. (a) Electric field profile for a dipole domain, (b) Carrier concentration for a dipole domain.
355
GaN Negative Differential Resistance Components
Figure 13.3. Schematic representation of electric field and charge inhomogeneity in a NDR device.
In this way, transit-time current oscillations are produced in the external circuit which have a fundamental frequency given by
/ = - = T
L
VD
L
(13.7)
where, v^ is the electron drift velocity and L is the length of the active region of the device. The fundamental frequencies of these devices can be well within the microwave region for velocities on the order of 10^ cm/s and sample lengths in the micron range making them suitable for microwave signal sources.
13.3. TRANSPORT PROPERTIES OF GaN GaN is becoming the material of choice for high temperature and high-speed semiconductor devices due to the very large bandgap and large peak electron velocity in the material. It is important to understand the basic material properties of GaN in order to evaluate the advantages of using GaN in the NDR signal generators. The study of the fundamental properties of bulk GaN material through simulations indicates that this material exhibits a transferred-electron effect. Many simulations have been done using Monte Carlo techniques to study in detail the basic transport properties in the GaN material. It is well known that GaN crystallizes in both zinc-blende and wurtzite (the commonly used phase for experimental device development) structures with slightly different material properties and substantially different band structures. Studies of the material properties of both wurtzite and zinc-blende GaN have been done using numerical simulations. Kolnik et al. [4] have done calculations of the drift velocity versus electric field dependencies based on the ensemble Monte Carlo simulations. These results are shown in Figure 13.4. These simulation results show that GaN exhibits negative differential mobility. Various possibilities are suggested for the nature of the NDR effect, including the electron intervalley transfer and the inflection of the central valley. Although further confirmation is needed on the nature of the NDR, Gunn domain instability is expected according to
Optoelectronic Devices: Ill-Nitrides
356
r~ 2h
4
V
^"^^^
f l y
5' ••-zinc blende QaN o-wuitzita GaN • ^ M
0
100
200
300
400
500
Electric field [kV/cm] Figure 13.4. Calculated steady state electron drift velocity in bulk GaN as a function of applied electric field along the (100) direction in the zinc-blende phase and within the basal plane along the (1010) direction in the wurtzite phase. (After Ref. [4]).
the simulated velocity-field characteristics, making this material very promising in applications based on the Gunn effect. Other simulations of GaN properties such as the electron transit time have also been done using Monte Carlo techniques. The electron transit time, the time it takes for electrons to travel across the active region of the device, is fundamental in determining the frequency of operation of the device. The result of the Monte Carlo simulation done by Foutz et al. [5] comparing the electron transit time, for GaN and GaAs, is shown in Figure 13.5. From Figure 13.5, it is obvious that the electron transit time in GaN is much lower than in GaAs. This is due to the fact that the velocity of electrons is higher in GaN than in GaAs. Furthermore, characterization of GaN grown by plasma-assisted molecular beam epitaxy on (0001) sapphire was done by Moustakas et al. [6]. Transport properties for a large number of GaN samples, grown with a different nitridation and GaN buffer conditions, were investigated by Hall effect measurements [6]. The obtained dependence of electron mobility as a function of free carrier concentration at room temperature is shown in Figure 13.6. In Figure 13.6 the bell shape of the curves is believed to be due to scattering by charged threading dislocations combined with ionized impurity scattering. At very high carrier concentrations, the dislocations are screened out and impurity scattering becomes the dominant mechanism. Moustakas et al. [6] also studied the vertical and lateral transport in the GaN films grown by plasma assisted MBE on sapphire. They found that the vertical
GaN Negative Differential Resistance Components
357
6-1
GaN (Zincblende) 0.0
—I 0.2
1 1 0.4 0.6 Distance (micron)
r— 0.8
1.0
Figure 13.5. Electron transit time as a function of distance. The field strengths chosen minimize the transit time across 1 |xm. The applied fields are 5 kV/cm for GaAs and 150 kV/cm for wurtzite GaN and 120 kV/cm for zincblende GaN. (After Ref. [5]).
1000
iiiii
1 1 1 iiiiii
1 Ill
1 N„,,=5x10^cm-^:
' 0,.
I
> ^l
2 N„„=2x10^»cm-^:
T N<,is,.=7x10^<'cm-^
100
% • \
o ; 10 10"
'•
-••••0
— 1 — i _ i 1iiiii
10"
1 1 1
'0 1 1 ml
-
1 1—1 1 1 1 Mil
1... 1-1 11 tiJ
10" 10" 10" N„-N^ (cm')
1 1 1 1 iiiiJ
10'"
1—i_i_i-Liii.
10''
Figure 13.6. Electron mobility versus net carrier concentration for n-GaN films. (After Ref. [6]).
358
Optoelectronic Devices: Ill-Nitrides
Table 13.1. Material properties of GaAs and GaN Material (kV/cm) GaAs GaN
3.5 150
^SAT
^PEAK
M-NDR
/NDR
(MV/cm)
(cm/s)
(cm/s)
(V/cm^/s)
(V/cm^/s)
(GHz)
0.4 2
0.6 X 10^ 2X10^
1.5X10^ 2.9 X 10^
8000 280
2500 50
109 740
mobility offilmswith carrier concentration of 8 X 10^^ cm~^ is about, 950 CVCL'IW S, which is close to the theoretical value predicted by Monte Carlo simulations. The lateral mobility for the same films is about, 200 cm^fV s. The dislocations significantly reduce the lateral mobility but since the experimental and theoretical values for vertical mobility are close, it is possible to conclude that dislocations do not limit the mobility in the vertical direction. This leads to the conclusion that GaN NDR devices with vertical geometry are expected to be less limited by fundamental effects such as defects which impede ideal operation of lateral devices such as FETs, HEMTSs. The basic material properties of GaAs and GaN (from Monte Carlo simulations) are compared in Table 13.1. The results from the transit time simulation imply that GaN NDR devices should have higher operation frequencies than GaAs devices, since the operation frequency is directly proportional to the transit time which in its turn is related to carrier velocity. It is also important to study the transport properties as a function of temperature, in order to determine the device performance over the temperature ranges expected in applications. Anwar et al. performed theoretical studies of zinc-blende GaN using Monte Carlo simulations of the low field mobiUty and the drift velocity as a function of temperature [7]. The scattering mechanisms considered in the simulation, include acoustic phonon, optical phonon, intervalley, alloy, ionized impurity, and piezoelectric scattering. Figure 13.7 illustrates the temperature dependence of the scattering mechanisms. It is obvious from Figure 13.7 that for the low field case, the relative importance of ionized impurity and acoustic phonon scattering decrease with increasing temperature, while polar optical phonon scattering becomes the dominant scattering mechanism above 200 K. For the high field case, polar optical phonon scattering is dominant for temperatures below 150 K. As the temperature increases, non-equivalent phonon scattering, which is caused by the scattering of electrons from the central valley to the upper conduction valleys and vice versa, is dominant. The scattering mechanisms of Figure 13.7 form the basis for the transport properties. In Figure 13.8 the simulated low field mobility is plotted as a function of temperature for various doping concentrations. It can be seen from Figure 13.8 that by increasing the doping concentration, the peak in the low field mobility decreases. This is attributed to ionized impurity scattering. Also, as
GaN Negative Differential Resistance Components E
1.0
-•—•— -•--•—
(0
0.8
o
E e (0
359
Polar optical phonon Acoustic phonon Equivalent phonon Non-equivalent phonon
0.6
GaN
0,4
High field
0.2
o o 4) (0
0.8
oa
0.6
E
Low field
0.4
> OS
1
0.2 0.0 0.0
100.0 200.0
300.0
400,0
500.0
Temperature (K) Figure 13.7. Most probable scattering mechanisms as a function of temperature in zinc-blende GaN for high fields and low fields. (After Ref. [7]).
800.0 h
600.0 h
I
400.0 h
- * - Nd=10^^crn"^ Experiment
200.0 h -L 0.0
100.0
J_
_L
J-
200.0
300.0
400.0
500.0
Temperature (K) Figure 13.8. Mobility of zinc-blende GaN for various temperatures. (After Ref. [7]).
360
Optoelectronic Devices: Ill-Nitrides
the temperature is increased, the low field mobility is decreased significantly. The decrease in low field mobility at high temperatures can be explained by considering the dominant scattering mechanisms. From Figure 13.7 it is clear that polar optical phonon scattering is dominant at low fields and high temperatures resulting in the degradation of mobility. In Figure 13.9 the simulated electron drift velocity is plotted as a function of electric field with temperature as a parameter. While the peak velocity increases significantly with decreasing temperature the saturation velocity is less dependent on temperature. Based on the above results it is expected that diode operation will be limited more for higher doping designs and higher temperature of operation. When a high electric field F > Fj^, is applied to bulk GaN, electrons experience a negative differential mobility /X-NDR [8]- Under these conditions, a non-uniformity of electron concentration would grow at a rate 1/TDDR. TDDR is known as the differential dielectric relaxation time and is calculated using expression (13.8) TDDR = ^
^
(13.8)
where A^ is the electron concentration, s is the dielectric constant, and ^UNDR is the peak negative differential mobility. It is recognized that domain growth lasts for at least 3 X TQDR [9] and, thus, the operation frequency of NDR devices can be limited by the active layer doping. The dependence of frequency capabilities on A^ for GaN and GaAs was calculated using the material parameters of Table 13.1. The material parameters used are summarized again in Table 13.2 together with the TNDR values and the parameters for Zb GaN. The negative differential mobility in GaAs is larger than in GaN and, therefore, for low-doped devices, growth of electron domains occurs faster in GaAs than in GaN.
3.0
'
' —•'
1
'
r
I «
P
'•^
1
1
1
GaN 2.0
> Q
'
-t- ^ -•-
r r 0.0
W
0.0
,
1
100.0
1
T=100K TS300K T=500K
_ L ,
200.0
1
1
300.0
1
400.0
J
500.0
Electric field (kV/cm) Figure 13.9. Drift velocity as a function of electric field for undoped, zinc-blende GaN for various temperatures. (After Ref. [7]).
GaN Negative Differential Resistance Components
361
Table 13.2. Semiconductor material parameters of GaAs and GaN Material
FxH
(KV/cm) GaAs WzGaN ZbGaN
3.5 150 80
M-NDR
^SAT
^PEAK
(MV/cm)
(cm/s)
(cm/s)
(V/cm^/s)
(V/cm^/s)
0.4 2 1.2
0.6 X 10^ 2X10^ 1.7X10^
1.5 X 10^^ 2.9 X 10^ 3.5 X 10^
8000 280 730
-2500 -50 -220
%DR ( p s )
9.4 1.4 0.25
However, as A^ is increased, TDDR is reduced, and the frequency capability improves until it reaches the NDR relaxation frequency/NDR discussed in Section 13.2. Since/N^R^ < f§^ the frequency capability of GaN-based devices improves for higher A^ without being limited by /NDR as in case of GaAs. This leads to GaN NDR operation that exceeds the GaAs limit of 105 GHz for GaN doping levels above 5 X 10^^ cm~l (A^ X L) criteria for the possibility of Gunn domain instability are based on the fact that the domain growth rate 1/TDDR should be higher than the transit frequency /x = VPEAK^^A (N and L indicate the electron density and length of the semiconductor in which the Gunn effect may be present): {N^L^) > (NDo - ^^^^55AK
(13.9)
where Np^ is the doping and L^ is the thickness of the active layer and the factor 3 accounts for the domain growth time as explained earlier. The critical values of (NL) product for GaN and GaAs were calculated using Eq. (13.9) and the material parameters of Table 13.1, and the results are summarized in Table 13.3. The results show that, due to a higher peak velocity and a smaller negative mobility, (NL)Q for GaN is 10-100 times larger than for GaAs. However, if A^A exceeds the critical doping concentration A^CRIT^ static domains can be formed inside the active layer [9]. Formation of parasitic static domains results in a decrease of output power and may lead to an early breakdown. Values of critical doping concentration A^CRIT calculated using Eq. (13.10) for cases of GaN and GaAs are also listed in Table 13.3. A^CRiT = ^ ^ (13.10) q Due to the large difference in threshold electricfields,A^CRIT in GaN is much higher than in GaAs and, thus, the active region in GaN diodes can be doped significantly higher Table 13.3. (NL)o products and critical doping levels for GaN and GaAs Material (NL)o (cm-2)
GaAs
ZbGaN
WzGaN
0.1 X 10^^ 3.4 X 10^^
2.5 X 10^^ 1.2X10^^
8.2 X 10^^ 4.3 X 10^^
362
Optoelectronic Devices: Ill-Nitrides Cathode GaN 0.1 urn
Active layer GaN n-type 10^ ^cm-^
Anode 0.1 M^m n-type lO^^on"^
Bias
Figure 13.10. The schematics of the GaN NDR diode oscillator.
(^ 10^^ cm ^) than in GaAs designs (- 10 cm ). The latter is a very important result in terms of feasibility of GaN-based NDR diodes since the availability of low-doped GaN material (A^^ < 5 X 10^^ cm~^) is still limited. Higher doping of active layers in GaN NDR diodes also leads to reduction of TD^R in this material, helping to increase its frequency capability. A typical GaN NDR diode designed to operate at ~ 100 GHz had an n-type active layer with thickness L^ of 3 luim and doping A^^ of 1 X 10^^ cm~^. The active layer was sandwiched between anode and cathode layers and their corresponding ohmic contacts. Both contact layers were 0.1 |xm-thick and doped at 1 X 10^^ cm~^. The diameter of the diode D was selected to be 50 |xm. A final three-dimensional model of GaN NDR diode oscillator is shown in Figure 13.10 together with the bias supply and a parallel LCR circuit used to represent the resonant cavity.
13.4. GaN NDR DEVICE SIMULATION Based on the theoretical calculations for the design of NDR devices given by Eqs. (13.5)(13.7), a GaN NDR oscillator was designed. A schematic of the device design is presented in Figure 13.10 connected to an LCR resonant cavity. The radius of the diode is 10 [xm with a 3 |jLm long active layer. The active layer is n-type GaN, doped at 1 X 10^^ cm~^. The ohmic contacts to the diode are made using 0.1 |JLm thick, highly doped n^ GaN material with a doping level of 1 X 10^^ cm~^. Based on the material and design parameters, the device with an active layer length of 3 luim is expected to operate at 100 GHz and the device with an active layer of 5 juim is expected to work at 60 GHz. The values of the resistor (/?), inductor (L), and capacitor (C) values are chosen so that the natural frequency of the resonant cavity is at the operating frequency of the diode. The structure of Figure 13.10 was simulated using the device simulator MEDICL The models used for the simulations include the analytical mobility model which takes into account the concentration and temperature dependent empirical mobility, field dependent mobility model, energy balance model, electron/hole energy relaxation time, impact
GaN Negative Differential Resistance Components
363
ionization model and negative differential mobility model. Since MEDICI did not internally have the data for GaN at the time the simulations were performed, and further confidence regarding material parameters was felt to be necessary with in-house performed experiments, a material data file had to be created using the material parameters for Wz GaN selected from Ref. [4] and from various pubHcations [5-6] on GaN material studies including the field dependent mobility model based on the v-F characteristics calculated by Monte Carlo simulations by Kolnik et al. [4]. Fitting of device characteristics as reported in publications or developed in-house has helped in adjusting the material values to more realistic conditions. Comparisons of simulated performance with experimental characteristics of GaN-based MESFETs and PIN diodes were made to enable validation of the selected parameters. Further details on the adopted approach are presented elsewhere [10]. A low-field electron mobility of juin = 280 and 60 CTCI'N S were assumed for wurtzite (Wz) GaN doped at A^ = 5 X 10^^ and 1 X 10^^ cm~^ respectively [11]. The value of electron lifetime Tn = 7 ns and hole lifetime Tp = 0.1 ns used in the simulations was based on the experimental data measured by an electron-beam-induced current method [12]. Coefficients for calculating impact-ionization rates in GaN were obtained by fitting to the theoretical predictions presented in Ref. [13] and verified by comparing simulation results with experimental breakdown voltages reported for GaN PIN diodes [14]. Models for field dependence of electron mobility in GaN were based on the v-F characteristics calculated by Monte-Carlo simulations [4,15]. Velocity-field characteristics, evaluated in these studies, demonstrated a bulk NDR effect in the high-field region due to the intervalley transfer. However, the threshold field for intervalley transfer and consequent appearance of NDR in GaN was much larger than in conventional semiconductors such as GaAs. An increase of the threshold field is caused by a larger separation between the satellite and central valleys in Wz GaN where AE is —2.1 eV compared to AJE" ~ 0.3 eV for GaAs. The analytical expression (Eq. (13.11)) for v - F characteristics in GaAs [16] was used in the simulations
v(F) = fjiF
^ ^ ^^™/
(13.11)
UTH/ This was fitted to the results of Ref. [15] in order to obtain the v - F dependence of GaN, which manifests a higher peak velocity VPEAK (^ X 10^ versus 1.5 X 10^ cm/s), increased saturation velocity VSAT (2 X 10^ versus 0.6 X 10^ cm/s), and much larger threshold field F^H (150 versus 3.5 KV/cm) compared with GaAs. At the same time, the GaN low-field mobility of 280 cm^A^ s and peak negative differential mobility /XNDR = max(-dv/dF) of 50 cm^A^ s are lower than the GaAs values of 8000 and 2500 cm^fV s, respectively.
364
Optoelectronic Devices: Ill-Nitrides
According to recent studies of GaN band structure, the T-valley inflection point, at which the group electron velocity is maximal, was found to be located below the lowest satellite valley in both Zb (zinc-blende) [17] and Wz GaN [18]. Although further studies are necessary to confirm this, it is possible that the reduction of electron drift velocity in the r valley caused by carriers becoming energetic enough to approach the inflection point can lead to bulk NDR. This contrasts other semiconductors, where intervalley transfer or impact ionization are initiated at a lower field than the inflection-point NDR [19]. Quantum devices employing superlattice structures to reduce the threshold field of inflection-based NDR mechanisms were first proposed by Esaki [20] and their feasibility has since been confirmed [21]. The reported v-F characteristics of Zb GaN calculated using Monte Carlo simulations were based on a band structure containing the /"-valley inflection point, and the results indicated that NDR was indeed caused primarily by the dispersion of the electron drift velocity in the Tvalley [17]. The inflection-based NDR manifested a threshold field Fjn of 80 KV/cm and peak velocity VPEAK of 3.8 X 10^ cm/s compared with FXH = 110 KV/cm and VpEAK = 2.7 X 10^ cm/s calculated in [4] for intervalley-transfer-based NDR. However, by far a more important consequence of the inflection-based NDR is the elimination of the intervalley-transfer relaxation time from the time required for NDR formation and, thus, a possibility of significantly increased frequency capability for GaN inflection-based NDR diodes. Frequency-independent v-F characteristics can be used to describe electron transport in the presence of time-varying electric field as long as the frequency of operation/ is much lower than the NDR relaxation frequency/NDR defined by expression (13.12) /
i
(13.12)
where TER is the energy-relaxation time and TET is the intervalley relaxation time. TER can be estimated as the time it takes to accelerate electrons to the threshold energy A^" [19] V2meffA£ ^ER = -—^
(13.13)
The energy-relaxation time of 0.15 ps calculated for Wz GaN was 10 times smaller than the GaAs value of 1.5 ps. The intervalley-transfer relaxation time r^j was evaluated from the results of Monte Carlo studies of ballistic transport [22]. By extrapolating reconstructed r^j(F) curves to the point of threshold field F = Fj^, electron intervalley transfer times T^J of 7.7 and 1.2 ps were found for GaAs and GaN, respectively. Based on the results of this straightforward analysis, the NDR relaxation frequency/NDR of GaAs was found to be —105 GHz in an excellent agreement with experimental and theoretical results [19]. The frequency capability of GaN-based NDR devices was found superior to that of GaAs Gunn diodes as indicated by the GaN NDR relaxation frequency
GaN Negative Differential Resistance Components
365
/NDR of ^ 700 GHz for case of intervalley-transfer-based NDR and ~ 4 THz for the case of inflection-based NDR (with TEJ = 0 ps). Since the equation and the frequency-response of v - F characteristics in GaN is not yet well determined, both intervalley-transfer-based NDR of Wz GaN and inflection-based NDR of Zb GaN were considered in order to account for uncertainty in published v-F characteristics. Important material parameters for Wz GaN, Zb GaN, and GaAs were summarized in Table 13.2. GaN offers higher peak and saturation velocities than GaAs, which lead to reduced transit time and increased frequency of operation. The threshold and breakdown fields are also larger in GaN, which allow operation at a higher bias and lead to increased output power. Increased frequency response of high-energy electrons in GaN is attributed directly to higher electrical strength of this material compared with GaAs. THz capability, predicted for GaN devices operating on the inflection-based NDR, is possible due to exceptionally high frequency response of electrons to the variations of the band structure as suggested in Ref. [21]. A few of the important material parameters used in the simulation such as bandgap energy (Eg), energy separation betweeii valleys (A£g), threshold electric field (£'th), peak velocity (VPEAK)' saturation velocity (v^at) and the negative differential mobility (/^NDR) are shown in Table 13.4. Once the material parameters and mobility models were defined in MEDICI, the large signal steady state and transient characteristics were simulated for devices with active layer lengths of 3 and 5 |xm. The simulated large signal velocity-field characteristics of the device are shown in Figure 13.11. From these results, a bias point was chosen on the velocity-field curve to be twice the critical field to ensure that the device operates in the negative differential mobility region. In Figure 13.11, the velocity-field characteristics show a peak velocity at 150 kV/cm and a saturation velocity at 2 X 10^ cm/s as expected. The critical voltage for the onset of NDR can be calculated easily from knowing the critical electric field. For the design with L = 3 and L = 5 |xm the critical voltage is 45 and 75 V, respectively. The simulation results for the transient characteristics, voltage versus time and current versus time, for the device with active layer length of 3 and 5 |xm, are shown in Figure 13.12a and b. In order to achieve convergence, the voltage
Table 13.4. Material parameters for Wz GaN (at 300 K) used in the simulations ^g A£g Fth
3.39 eV 2.1 eV 150kV/cm
/ANDR
5 0 CVCL'fW S
VpEAK
3 X 10^ c m ^ / s
v,at
2 X lO"^ cm^/s
366
Optoelectronic Devices: Ill-Nitrides GaN Gunn Diode Vglocity^ Field Characteristics
x10
4
8 Electric Field (V/cm)
8 X10"
Figure 13.11. Simulated velocity-field characteristics for a GaN Gunn diode designed for L = 3 jjim and L = 5 |jLm. Also shown, is the bias point which has a value of twice the critical electric field.
GeN Ginn Diode Transient CharacterlsUcsforL=Suni
GaNGifin DiodeTrBn6ien(ChareeterlrtinforL=auni j
j
1
1
1
:
:
:
:
:
:
.y/-"^
i
i
i
i
0.1
0.2
0.3
0.4
0.5
-\
:
..,^A"';
:
5 40
^^^] 0.1
0.2
0.3
0.4
O.S
0.6
0.7
a8
0.9
1
i 0.6
i
i 0.9
0.7
1 X10-'
<
i.sh
- yr~^rmm•Mfmiim
-r'"^^^^?^^^io..v:v:MWWfiy»^.
11
•
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
'
0.1
•
0.2
.
'
:
0.3
•
•
0.4
-
.
0.5 "r»ne(8)
i
1
i
1
0.6
0.7
0.6
0.9
1 _.o-»
Figure 13.12. Simulated transient characteristics of current and voltage for a diode design with (a) L = 3 [xm; (b) L = 5 |xm.
GaN Negative Differential Resistance Components
367
applied to the anode was ramped up to the value of the bias voltage over a time period of 0.5 ns. Recall that the bias voltage for the design with L = 3 and L = 5 juum was 90 and 150 V, (twice the critical voltage) respectively. The results in Figure 13.12 confirm the expected oscillations in current and voltage for a GaN Gunn diode. It is also important to notice from Figure 13.12 that the maximum DC current flowing in the device is —1.4 A. Since the current is determined by the cross sectional area of the device and not by the length, the maximum DC current is the same for both designs. For the 3 |jLm device the resulting DC power is ~ 126 W. Similarly, the design with L= 5 |xm generates an average DC power of 210 W. It is obvious that the longer device will generate more power due to the larger bias voltage needed for sustained oscillations. Furthermore, one can see that the peak-to-peak amplitude of the voltage oscillations is larger for the design with L = 3 luim whereas the peak-to-peak amplitude of the current oscillations is smaller compared to the design with L = 5 ixm. A possible explanation for this can be provided by considering the electric field in the device. The dynamics of the electric field are shown in Figure 13.13 for both 3 and 5 luum designs. From Figure 13.13, it can be seen that the electric field in the device is not uniformly distributed. The simulation results show that while the electric field grows it also propagates in time and disappears at the anode so that the total voltage in the device (integral under the electric field curve) remains the same. Since the voltage is the integral of the electric field distribution, one can
X 10'
G a N O u n n Diode D y n a m i c Electric Field for L—3um
eg- 10
i » •
1^ 1
S •s
. • ^ . ^ ^ ^ ^ ,
'
-
-
, - - ^
- I
•^"i^T'S^ "^^
^^^^^J'K.X^
, X 10^
-
1.5
2
G a N G u n n Diode D y n a m i c Electric Fieici for L = 5 u m
E
1 " 2.S Distance Cum)
Figure 13.13. Simulated dynamics of the electric field showing a non-uniform distribution from the cathode to the anode for devices w i t h L = 3 andL = 5 |xm.
368
Optoelectronic Devices: Ill-Nitrides
see that the area under the curves of the electric field for the L = 5 |xm does not change much and hence the voltage amplitude is small. To explain the differences in the peak-to-peak amplitude of the current oscillations, one must consider the dynamics of the electron concentration in the device for at least one period of oscillations. Typical domain formation time is given by Eq. (13.8). Since the doping concentration is also the same for both designs, it is obvious from Eq. (13.8) that the growth rate of the electron concentration is the same for both designs. Next, consider the drift velocity of the domains, which is the same for any device design since it is a basic material property. Given these conditions, it is obvious that in the case of a longer active layer, the peak of the electron concentration will be larger by the time it reaches the anode, since it has more time to grow. Therefore, the amplitude of the current oscillations measured at the anode should be larger. This behavior can also be analyzed by considering the dynamics of the dipole domains inside the active layer. The dynamics of the electron concentration were also simulated in MEDICI and the result is shown in Figure 13.14 for the design with a 3 and 5 ixm active layer. Each of the curves in Figure 13.14 was captured in time steps of 1 ps during the time period of sustained oscillations. Figure 13.14 clearly shows the growth and propagation of the dipole domain as well as their termination at the anode. Notice that the initial growth of the dipole domain does not start exactly at the cathode, but is initiated at about 0.6 jxm. It is a well-known effect that the initial growth of the dipole domains takes place beyond a certain distance from the cathode, which is called the dead
G a N G u m Dtode Dynamic Electron Concentration fior L=3unn
E 5
1 peMn»
1
k^^JL^j^yi^
2.5 Distance Cum)
Figure 13.14. Simulated dynamics of the electron concentration from the cathode to anode for devices with L= 3 and L = 5 |xm.
GaN Negative Differential Resistance Components
369
space layer. This is because the carriers need to acquire enough energy to transfer into the upper valley where they accumulate (growth of domains) due to a negative differential mobility. In Figure 13.14, comparing the dynamics of the electron concentration for the design with L = 3 fxm and the design with L= 5 \Lm, it can be said that the amplitude of the electron concentration is larger for any given distance from the anode for the design with a 5 fxm active layer, and therefore, the amplitude of the current oscillations is larger. Another point to make concerning the dynamics of the electric field and the dynamics of the electron concentration is that in the regions where the electric field is increasing, there is an accumulation of electrons shown by the growth in the peak of the electron concentration. In the regions of decreasing electric field there is a depletion of electrons shown by the downward peak in the electron concentration. This is because the electric field and the electron concentration are directly related through Maxwell's equation, which says that the change in electron concentration is proportional to the change in electric field
From the simulation results above several important performance metrics can be calculated in order to design the optimal GaN Gunn diode. For practical applications of GaN Gunn diodes, it is important to evaluate the frequency of operation and the power efficiency of the device. The data obtained from the transient simulations was subjected to Fourier analysis and the resulting frequency spectrum is shown in Figure 13.15. Figure 13.15 shows that the operating frequency for the design with L = ?> and L = 5 |jLm is about 110 and 75 GHz, respectively. As expected, the operating frequency for the shorter diode is larger since the operating frequency is inversely proportional to the length of the active layer. However, the ratio of the frequencies is not exactly the same as the ratio of the lengths. This is due to boundary effects as will be discussed later. Using the data obtained from the simulations, the power efficiency for the two designs was calculated. Table 13.5 shows the peak-to-peak RF voltage/current and the DC voltage/ current as well as the calculated power efficiency. From Table 13.5 it is seen that the RF power efficiency is higher for the design with a shorter active layer. This is because the DC power is greatly reduced since the operating voltage of the shorter diode is reduced. The relation between device length and power efficiency is complicated and the trend cannot be easily predicted by studying just two designs. More work is required on this topic to be able to conclude which design gives a higher power efficiency. Although, in general it can be concluded that the power efficiency is quite low for these devices. From the basic theory of Gunn diodes, it could be expected that the percent decrease in the length of the active layer results in the same percent increase in the operating frequency of the device. It is also expected that the power efficiency should be higher for devices with
370
Optoelectronic Devices: Ill-Nitrides Frequency Spectrum for GaN Gunn Diode 500
1
1
1
1
450 ^
400
^
350
g
300
—
1
L=3um L=5um
—
at
^ ^
--ft-i
250
—
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200
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to
I 150 o °-
i ; ; i
100
—_ -—^
50
50
60
^:
y\
i
""•""'V"""; 1 ^"^ 80 90
70
— —^^
100
110
1 — \
130
120
\ — ^
140
150
Frequeny (GHz) Figure 13.15.
Frequency spectrum for GaN Gunn diode design with L = 3 and L = 5 jjim.
longer active layers. However, this classical theory alone cannot be used to describe the behavior of very short diodes like the designs analyzed above. For very short diodes with active layer length less than a few microns, the boundary effects determine the performance of the device. For example, take the distribution of the electric field and the electron concentration in the active layer. According to the classical theory, the electric field distribution and the dipole domains should represent the distribution shown in Figure 13.3. In Figure 13.3, the electric field has a Gaussian distribution and the electron concentration forms a full dipole domain with regions of accumulation and depletion as it propagates in the active layer. Comparing the predicted distribution to the simulated distributions of electric field and electron concentration from Figures 13.13 and 13.14, there is a big difference. The simulated distribution of the electric field shows only half of a Gaussian profile. Similarly, the distribution of electron concentration does not show full accumulation and depletion regions. The domains terminate at the anode before they have a chance to grow fully. Due to these kinds of effects, the performance of very short diodes will vary from what is described
Table 13.5. Rf and DC power for the GaN NDR device with active layer length L == 3 and L = 5 |jLm VPEAK ( V )
L = 3 um
7
L= 5 um
4.5
/PEAK
(mA)
230 320
VDC
(V)
/DC
(A)
(PRF/PDC)
X 100
90
1.4
1.3
150
1.4
0.67
(%)
GaN Negative Differential Resistance Components
371
by the classical theory. The operating frequency is not simply given by the domain drift velocity divided by the length of the active layer, but will also depend on the precise boundaries of the structure, which is why the ratios of the frequencies for the two designs was not the same as the ratios of their lengths as discussed previously. The impact of the biasing voltage on the frequency, output power, and efficiency was investigated using the same Wz GaN NDR diode oscillator (Figure 13.16). The frequency of oscillations decreased steadily from 98 to 83 GHz as the bias was increased from 55 to 125 V in agreement with the experimental trends observed for GaAs Gunn diodes [23]. The output power increased steeply once the applied bias exceeded V^R' ^^^ saturated for VD > ^VCR. A slow decrease for V^ > 3ycR is attributed to an ensuing mismatch between the large-signal impedance of the GaN NDR diode and the terminating impedance ZL. The conversion efficiency was maximal for V^ = 2ycR and this bias was employed for performing comparative studies of various GaN NDR diode oscillators. The power and frequency capabilities of GaN NDR diodes were compared with that of GaAs Gunn diodes by simulating the performance of the corresponding oscillators while modifying the thickness L^ and the doping A^^ of the active layer in these devices. The nominal GaAs Gunn diode had the same dimensions as the nominal GaN NDR diode: L^ = 3 jxm and D = 50 fxm, but the doping was reduced to 3 X 10^^ cm~^ in order to satisfy the design condition A^A < ^CRIT (Table 13.3). This design of GaAs Gunn diode was analogous to the published descriptions of Ka-band Gunn diodes in Ref. [24]. The bias y^ for both GaN- and GaAs-based devices was selected to be twice the critical bias VCR ^^^^ for nominal designs, was 90 and 2.1 V, respectively. Designs of LCR circuits for GaN (L = 17.5 pH, C = 0.1 pF, R = 50 (1 and GaAs (L = 25 pH,
100 a
80
c
60 Output Power 'B
40
4 r^
CD
•a 20 Efficiency
i t i ^ I 40
60
80
100
i
h^
i l-j^^ 120
140
Voltage [V] Figure 13.16. A variation of the output power, frequency, and efficiency of GaN NDR diode oscillator.
372
Optoelectronic
Devices:
Ill-Nitrides
40
14^GaN —f5(um
E 30 00 -o
I
/CN
-2/im.J
ZibGaN
20
CL
(iaAs 3
o
10 5;um~
3^m 20
40
60 80 Frequency [GHz]
100
Figure 13.17. The power-frequency diagram for the GAN NDR diode and GaAs Gunn diode oscillator for the devices with an active layer width between 2 and 5 fjim.
C = 0.45 pF, /? = 50 O) were optimized to provide maximum output power when used with devices of nominal designs. The results of the study conducted by varying the thickness of the active layer are shown in Figure 13.17. All devices demonstrated expected trends of increasing the oscillation frequency and decreasing the output power when the thickness of the active layers was reduced. Reduction of output power for GaN NDR diodes with thicker than 3 jxm active layers was due to an increasing mismatch with the resonant cavity. An even more significant degradation was observed for GaAs Gunn diodes and special care was taken in that case to re-optimize ZL for devices with thicker active layers. The frequency-power tradeoff of GaAs Gunn diodes was restored by proper choice of ZL and only the reoptimized results are shown in Figure 13.17. The simulations were conducted for the NDR diodes made of both Wz and Zb phases of GaN in order to account for uncertainty in published v-F characteristics. The simulations showed that the overall characteristics of GaN-based NDR diodes outperform those of GaAs Gunn diodes in terms of output power and frequency of oscillations independent of the specific v-F characteristics used to model material properties of GaN. Thus, given the same thickness of the active layer, the operation frequency of GaN NDR diodes ( 6 5 - 9 5 GHz) was approximately twice that of GaAs Gunn diodes ( 2 7 - 4 0 GHz), while given the same device area, the maximum output power of GaN NDR diodes was ~ 3 5 dBm compared with ~ 10 dBm for GaAs Gunn diodes. The power-frequency capability of GaN NDR diodes was also studied as a function of the doping of the active layer. When A^^ was increased from 5 X 10^^ to 5 X 10^^ cm~^ the oscillation frequency was increased from 85 to 120 GHz due to reduced differential dielectric relaxation time in higher-doped devices.
GaN Negative Differential Resistance Components
373
Overall, when compared with GaAs Gunn diodes, GaN NDR diodes showed a significant improvement in terms of output power density and frequency. These results are supported by similar conclusions drawn with the help of the microwave signal generator figure-of-merit Pf^Z = /^B ^PEAK/4, which measures the maximum output power (P) delivered from an oscillator to a matched impedance (Z) at a frequency (/) [19]. Based on the considered material properties, Pf^Z for GaN is 50-100 times that of GaAs, indicating a strong potential of GaN for microwave signal generation. Based on the simulation results obtained thus far, a few conclusions can now be made regarding the design of GaN NDR devices. The simulation results show that a shorter active layer offers an advantage in terms of operating frequency. Although it was not possible to make a definite conclusion about the effect of device length on power efficiency, the power efficiency is in the order of few percent for devices with active layer length in the order of a few microns. Moreover, the shorter active layer device will generate less power, which is a big advantage in reducing the effects of self-heating on device performance. With this in mind, one needs to determine the smallest possible active layer. The lower limit on the length of the active layer is actually set by the fundamental operation of the device. To explain this, consider the formation of domains. The domains form when the carriers have enough energy to transfer from the lower valley to the upper valley. In a constant electric field there is a finite distance needed to obtain enough energy for the transfer process to take place. This finite distance, called the dead space layer, is the determining factor for the minimum length of the active layer. To reduce the length of the dead space layer, and hence further reduce the length of the active layer, it has been proposed to introduce a heterojunction at the cathode. The purpose of the heterojunction is that carriers will travel from a large bandgap material to a smaller bandgap material. In this way the carriers will be initially launched with a very high energy so as to reduce or eliminate the dead space region. The effect of the launcher layer is known in GaAs devices and is being investigated for GaN devices as well.
13.5.
OTHER NDR DEVICE APPROACHES AND FUNDAMENTAL STUDIES
Various studies have shown that doped Esaki-Tsu superlattices exhibit negative differential conductance; the negative differential conductance is a consequence of Bragg reflection of miniband electrons, which are accelerated by an electric field [25]. Undoped superlattices can show photoexcited damped current oscillations. Recently, it was observed that a doped semiconductor superlattice with negative differential conductance showed self-sustained current oscillations. The oscillation frequency of 6 GHz was most likely caused by traveling charge density domains due to the negative differential conductance. A connection between Bragg reflection of band electrons and the occurrence of dipole domains has been discussed earlier. A millimeter wave oscillator
374
Optoelectronic Devices: Ill-Nitrides
1
2
voltage (V) Figure 13.18. (a) High frequency circuit and (b) current-voltage characteristic of the superlattice.
based on self-sustained current oscillations in a superlattice was reported [25]. The superlattice was operated at room temperature. The superlattice structure, grown by molecular beam epitaxy on a n^ GaAs substrate, consisted of 100 periods of GaAs wells (3.45 nm thick) and AlAs barriers (0.96 nm thick) doped with silicon (10^^ cm~^). The superlattice was embedded between graded layers of gradual composition and doping level to avoid abrupt heterojunctions. A n^ GaAs cap layer was provided for the formation of ohmic contacts. Mesa diodes (Figure 13.18) with area 64 and 10,000 fim^ were formed using Au-Ge-Ni ohmic contacts. Using a highfrequency (HF) probe needle (picoprobe 67A) both mesas were connected with a 50 V coaxial cable for transmission of both the direct current and HF current. The mesa with the smaller area acted as an active element responsible for the nonlinear current-voltage characteristic and the generation of the HF currents, while the large-area mesa served via the substrate as an electrical connection to the backside of the small-area superlattice, thus allowing a planar design of the superlattice oscillator as shown in
GaN Negative Differential Resistance Components
375
Figure 13.18. Direct and HF currents were separated from each other by a bias tee with inductive and capacitive resistance. The direct current was delivered by a voltage source. The HF fields were monitored using a spectrum analyzer (Tektronix 2782). The current-voltage characteristic (Figure 13.18b) shows regions of negative differential conductance, with current jumps, which give evidence for dynamical processes in the current flow. From the peak current (40 mA) and the mesa area we find a peak current density of 60 kA/cm^ and a peak drift velocity of 4 X 10^ cm/s. This value is consistent with the propagation of electrons in the lowest miniband, for which we estimated, with a Kronig-Penney model, a width of 74 meV. Attention should also be given to Ill-Nitrides as possible material system suitable for SL terahertz sources. GaN-based materials possess sufficient high-frequency properties to deliver high power in the MMW and SMMW regions and are expected to enable compact, reliable, high-power amplifier systems, capable of operating in harsh environments and temperatures with no need for cooling systems. The submillimeter sources may benefit from the advanteges of the GaN material family. The traveling dipole domain oscillation frequency in group-III Nitride SLs has been calculated [26]. The estimations show that THz-range oscillations are possible using this material system. A combination of the material properties suitable for high-temperature electronic and photonic devices and SL nonlinear effects—all this could make GaN material family a promising candidate for the new type of applications—terahertz-range electromagnetic generation. Resonant tunneling diodes (RTD) based on GaN/AlGaN heterojunctions should in principle show high values of peak/valley ratio due to the large conduction band discontinuities between GaN and AlGaN. Moreover, such structures have been studied to be used in quantum cascade lasers for near infrared emission. However, polarization fields can mask such benefits and make the design of RTD quite complicated. An atomistic point of view was applied to describe current flowing in GaNbased RTD and investigate polarization issues [27]. The sp^d^s* tight-binding (TB) model and a transfer matrix approach were used to describe the proper scattering states of the RTD system. The TB model allows us to describe the whole Brillouin zone of the semiconductors and relax all the envelope function approximations usually made for treating tunneling problems in RTDs. It was observed that the effect of the polarization fields is to shift the transmission coefficient peaks while keeping a very high PVR. An optically detected time-of-flight technique with femtosecond resolution that monitors the change in the electroabsorption due to charge transport in a p - i - n diode was employed by Wraback et al. and showed how it may be used to determine the electron transit time and velocity-field characteristic in GaN at room temperature [28]. A measurement of the high-field transient electron velocity overshoot was performed using a semi-transparent p-contact AlGaN/GaN heterojunction p - i - n diode. Further experiments by the same group employed an AlGaN/GaN diode rather than a ring p-contact to avoid
Optoelectronic Devices: Ill-Nitrides
376
o
^
7
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^avg ^theory
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5 o
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o
-
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o
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2 •
•
1 0
, 100
_1
1
200
1
1
300
1
1
1
1
400
500
600
Electric Field (kV/cm) Figure 13.19. Experimental and theoretical electron velocities as a function of field. Circles: peak transient velocity; squares: average velocity; line: full zone calculation of steady-state velocity in the c-direction [After [29]].
current crowding and non-uniform fields and thus obtaining a more accurate picture of the effects taking place [29]. The latter allowed in fact demonstration of steady state and average velocities in closer agreement with theoretical data. This study is very relevant to NDR effects in GaN since it provides further insight into its presence in this material. The experimentally determined electron velocity shown in Figure 13.19 was obtained from the transit time based on theoretical expectations. The steady-state velocity-field characteristic derived from an IVLonte Carlo ElVIC calculation including a full Brillouin zone band structure is shown in Figure 13.19 for comparison with the measurements. The theoretical results are in qualitative agreement with the data. A peak transient electron velocity of 7.25 X 10^ cm/s within the first 200 fs after photoexcitation has been observed at a field of 320kV/cm. At higher fields, the measurement of the peak velocity is limited by the 80 fs duration of the pulses, but the increase in transit time with increasing field suggests the onset of NDR. Theoretical Monte Carlo calculations incorporating a GaN full-zone band structure show that although the peak steady-state velocity occurs at ~ 200 kV/cm, the ensuing NDR region of the velocity-field curve is not initially associated with intervalley transfer, as the majority of electrons do not attain sufficient energy to effect this transfer until they are subjected to much higher fields (>325 kV/cm). Insight into this behavior can be gleaned from the band nonparabolicity deduced from the constant energy surfaces in the F valley, which shows that the effective mass in the c-direction can be viewed as becoming larger at high ^-values. This larger effective mass may play a role in velocity overshoot by reducing the velocity and momentum relaxation time at high A:-values in the r valley.
GaN Negative Differential Resistance Components
377
It has been suggested theoretically that for semiconductors in which the energy difference between the F valley minimum and that of the lowest satellite valley in the conduction band is large, electron-polar optical phonon scattering acting in a nonparabolic F valley alone can yield NDR. As mentioned earlier GaN, may be such a material. Electrons traveling in such a band may experience, in addition to NDR, a deceleration that leads to transient velocity overshoot without intervalley scattering. While transient velocity overshoot is observed in the c-direction at fields as low as 130 kV/cm, theoretical Monte Carlo calculations employing a full band structure indicate that at electric fields below 300 kV/cm, this velocity overshoot is associated primarily not with intervalley transfer, but with band nonparabolicity in the F valley, characterized by the onset of a negative electron effective mass at an energy well below that required for intervalley scattering [30]. Calculations of transport in the basal plane suggest that a similar velocity overshoot is not expected in this case until much higher fields — 175 kV/cm are reached. Figure 13.20 shows the temporal evolution of the electron velocity for transport in the c-direction computed from Monte Carlo simulations incorporating the full band structure at four fields corresponding approximately to the experimental data [30]. The calculations show an onset of velocity overshoot at 125 kV/ cm in the c-direction (F~A), as compared to 175 kV/cm for the F-M (basal plane) direction inset, and a peak transient velocity that becomes larger and shifts to earlier times as the field increases. The significance of this full band Monte Carlo calculation is
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175kV/cm 225 kV/cm
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150kV/cm(r-A) 150kV/cm(r-M) 175kV/cm(r-M)
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0 1.
2
0
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2 1
3
Time (ps) Figure 13.20. Full band Monte Carlo calculation of the temporal evolution of the electron velocity in the cdirection for four representative electric fields. Inset: comparison of calculated transient electron velocity for cdirection {F-A) and basal plane (F-M) transport [After [30]].
378
Optoelectronic Devices: III-Nitrides
underscored by the fact that multivalley analytical Monte Carlo studies of GaN predict velocity overshoot and NDR primarily due to intervalley scattering. Since the steady-state velocity for transport in the c-direction decreases at fields larger than 180 kV/cm, the NDR calculated for the 180-300 kV/cm range is primarily associated not with intervalley transfer, but with nonparabolicity in the F valley. These results may have a dramatic effect on the design of high-power, high-frequency electronics and avalanche photodiodes, NDR devices. Based on the previous discussion, lateral high-frequency electronic devices such as HFETs could benefit by operating with transport in the c-direction, for which both the transient and steady-state electron velocity are higher, while vertical devices such as avalanche photodiodes may improve with transport in the basal plane, for which intervalley transfer leading to impact ionization is more likely and the existence of a negative effective mass does not preclude diode breakdown. GaN NDR devices are for the above-mentioned reasons explored in both the c- and (2-direction since traditional NDR by intervalley transfer may be possible in the (2-direction while c-direction NDR operation may or may not be feasible by nonparabolicity effects depending on the energy of states available and the current associated with such a mechanism.
13.6. FABRICATION As it was previously discussed, theoretical and experimental studies show that the dislocations in the film significantly limit the lateral mobility in GaN films, whereas the vertical mobility was hardly affected. Based on this consideration, NDR devices should be designed and fabricated as vertical structures. However, other considerations related to basal plane transport features may dictate a lateral GaN NDR diode design. A schematic of a vertical NDR structure is shown in Figure 13.21. As shown in Figure 13.21, the device structure is quite simple consisting of a thin layer of highly doped n^ GaN on top for making the anode contact via an airbridge, followed by
air-bridge
Buffer layer
Substrate (Si, SiC, or Sapphire) Figure 13.21.
A schematic of a vertical NDR structure.
GaN Negative Differential Resistance Components
379
a thick layer of n~ GaN beneath for the active layer and beneath this is another layer of n^ GaN for making the cathode contact. The GaN material is grown on a substrate of silicon, silicon-carbide or sapphire with a buffer layer technology to lattice match the GaN material to the substrate. The general technology used to fabricate the above structure mainly involves anisotropic etching of the material using a series of masks and can be accomplished in about 5-6 masks, which is relatively inexpensive compared to other device fabrication. Etching of GaN material can be done using a dry etching technique such as reactive ion etching (RIE) or inductively coupled plasma etching (ICP) or a wet etching technique such as photo-electrochemical etching (PEC). The best etching method, in terms of etch rate, selectivity and post etch surface quality (which is a determining factor for the contact resistance), is still being investigated since the processing technology for GaN is still under development. There are two kinds of technologies that can be used to fabricate vertical NDR devices, the on-wafer and stand-alone technologies, which are selected based on the type of testing and application that follows. A schematic of the on-wafer technology is shown in Fi gure 13.22. The basic fabrication steps for the on-wafer technology starts with the isolation etch in order to electrically separate each device on the wafer. The next step is the mesa etch which defines the placement of the ohmic contacts. Of course, following the mesa etch is the actual deposition of the metal for the anode and cathode ohmic
NDR Diode Technology Top n+ layer
Substrate
Active ri-layer ^ Isolation etch: Discrete device| Bottom separation ' ri+ layer Anode metal
> Mesa etch: Diodes structure definition Cathode metal
^ Metal Deposition: Ohmic contacts
^ Au-Plating: Air Bridges
On-wafer NDR diode
Figure 13.22. On-wafer technology for GaN NDR device.
380
Optoelectronic Devices: Ill-Nitrides Beam leads Anode metaj Cathode metal
Active region Figure 13.23. Stand-alone technology for GaN NDR device.
contacts. Finally the transmission lines, i.e. coplanar waveguide lines and airbridges are defined and electroplated for on-wafer, high-frequency testing. For mounting the devices on an integrated heat sink and testing in a microwave cavity, it is necessary to use the stand-alone technology. Like the on-wafer technology, the standalone technology also requires the isolation and mesa etch as the first two steps. Next it is necessary to create a via hole from the back side and electroplate the anode and cathode contacts. Finally, the substrate is completely removed and individual devices are released. The stand-alone technology is shown by a schematic in Figure 13.23. In the solid-state electronics laboratory at the University of Michigan, GaN NDR devices have been fabricated using the on-wafer technology. The fabricated devices have an active layer, which is 30 |jLm in diameter and has a thickness of 4 jjim. An SEM picture of such a device is shown in Figure 13.24. A device with such a large diameter and relatively thick active layer, as in Figure 13.24, is capable of high current values leading to improved power performance and also facilitates high-frequency testing. On the other hand, such large devices impose several
-
"'^'-^^^^^r:::,-
Au-plated air-bridge
Isolation
Diode mesa
Air-bridge pillar Anode metal
Cathode pad i-plated cathode metal Figure 13.24. SEM photo of a GaN NDR device fabricated at the University of Michigan using the on-wafer technology. The device has an active layer with a diameter of 30 [xm and thickness of 4 iJim.
381
GaN Negative Differential Resistance Components Isolation Au-plated air-bridge
Air-bridge pillar Au-plated cathode metal Figure 13.25.
SEM photo of a GaN NDR device fabricated at the University of Michigan. The device has an active layer with a diameter of 10 juim and thickness of 0.5 |JLm.
difficulties. The large amount of current flowing in the device, combined with the thick active layer and low thermal conductivity of GaN, all contribute to self-heating effects, which severely limit the operation of the devices. To reduce thermal effects, smaller geometry diodes were designed and fabricated. The diameter was reduced from 30-50 to 8-20 fxm and the thickness of the active region was reduced from 4 - 6 to 0.5 ixm. An SEM photo of such a device is shown in Figure 13.25. | Lm In the ideal case, the expected power dissipation would be 25 times smaller in a 10 U diameter device compared to a device with 50 jxm diameter. The experimentally observed power dissipation for devices with active layer thickness of 0.5 ixm and doping of 1 X lO^^cm""^ is about 4 - 5 W for devices with a diameter of 50 iJim ( 7 = 15 V, / = 330 mA) and about 1-2 W for devices with 10 iJim diameter (V = 15 V, / = 130 mA). Besides reducing the size of the device it is also necessary to package the device in an integrated heat sink in order to overcome self-heating effects. For on-wafer technology the integrated heat sink becomes the substrate.
Device'
Heat flow
Heat sink
Heat sink with high thermal conductance Figure 13.26.
Device Heat sink
^
Heat flow
h Heat sink with low thermal conductance
Schematic showing the heat flow for a device mounted on a good heat sink and one mounted on a poor heat sink.
382
Optoelectronic Devices: Ill-Nitrides Table 13.6. Thermal conductivity of possible substrate for GaN Substrate
Thermal conductivity (W/cm K)
Sapphire Silicon Silicon carbide
0.32 1.48 3
Figure 13.26 shows a schematic of heat flow from a device mounted on a good heat sink and one mounted on a poor heat sink while Table 13.6 compares the thermal conductivity of possible substrates for GaN. It is obvious that the stand-alone technology is expected to offer definite advantages. Thermal simulations have been performed based on various designs and technology approaches and are currently implemented in device demonstrations. It is obvious from Table 13.6 that the best substrate for thermal dissipation is silicon carbide. However, since SiC is quite expensive, silicon substrates are a good alternative. Moreover, silicon substrates can be easily thinned down to about 100 |JLm by using a lapping tool to further improve heat dissipation. Substrates of this type have already been employed for GaN NDR devices at the author's laboratory and further work is in progress. For stand-alone devices, heat dissipation can be facilitated by the combination of very thin electroplating of the anode/cathode contacts and then mounting these devices on diamond heat sinks.
13.7. TESTING The general testing set-up involves a high-power pulse generator to apply the DC bias to the device in the NDR region of the current-voltage characteristics, which can be
Q
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spectrum analyzer |j
1 n
\i ,
1
Out
Pulse Gen erator ^
Current Drobe
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r7r\ I \'
CaVI (y
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Biasing terminal
Output terminal
Figure 13.27. Block diagram of the testing set-up used for a device mounted in a microwave cavity.
GaN Negative Differential Resistance Components
383
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•
50-
//
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• •
0-
1
1
10 V(V)
15
20
Figure 13.28. I-V characteristics of a GaN NDR device fabricated using the University of Michigan process.
measured using a current probe and viewing the results on an oscillosocpe. The microwave oscillations generated by the NDR device mounted in a microwave cavity, can be viewed on a spectrum analyzer. A block diagram of the testing set-up is shown in Figure 13.27. The GaN devices that were fabricated at the University of Michigan (with 10 fxm radius and 0.5 iJim active layer thickness), were tested for DC characteristics then mounted in a microwave cavity for high-frequency testing. The current-voltage characteristics are shown in Figure 13.28. The onset of NDR for this device was observed around 15 V. The device burned around 17 V due to excessive power generation and poor heat dissipation. High-frequency testing for these devices is performed in a cavity as previously mentioned. A co-axial cavity in the range of 10-20 GHz and a waveguide cavity in the range of 35-50 GHz, shown in Figsure 13.29 and 13.30, are being used for microwave testing of the devices fabricated at the University of Michigan.
RF output thru, coaxial connection
Anode connection ring
/ ^ ^ ^
IX'] bias connection
Futier
Diode package
Cathode connection using wire bond
Figure 13.29. Photographs of a co-axial cavity (10-20 GHz) used for microwave testing of GaN NDR devices at the University of Michigan.
Optoelectronic Devices: Ill-Nitrides
384 DC bias thm SMA connector
\
Back short used for tuning
RF output signal thru, waveguide connection
DC bias post connected to SMA
Mounted diode
Figure 13.30. Photographs of a mm-wave waveguide cavity used for microwave testing of GaN NDR devices at the University of Michigan.
Testing the devices in the cavity are under way. But first, the self-heating issue needs to be resolved because, as seen in the current-voltage characteristics, the device bums making it difficult to bias it well into the NDR regime. Once the self-heating problem is resolved, it will be more likely to see high-frequency oscillations from the cavity testing.
13.8. SUMMARY The material properties of GaN such as large bandgap and small electron transit time, brings new possibilities not within reach of the traditional semiconductors such as Si and GaAs. The most important advantages of GaN NDR devices are high-frequency operation, with possibility in the THz range, and high output power. The theoretical studies of the fundamental properties of GaN show that NDR is possible in this material. Technological developments for the growth and processing of GaN are underway. Currently, the biggest challenge with GaN NDR devices lies in finding appropriate heat sink to dissipate the heat generated. The work completed so far on GaN NDR diodes shows very promising results for high-power and very high frequency applications extending to the THz regime.
ACKNOWLEDGEMENTS The work reviewed in this paper would not have been possible without the invaluable contributions by Dr E. Alekseev, A. Manasson, G. Eadara, K. Mutamba and O. Yilmazoglu who performed extensive theoretical and experimental studies on GaN-based NDR devices. Thanks are also due to S. Hubbard and W. Sutton for device processing, Dr J. East for mm-wave packaging and testing help, Dr K. Tomizawa for theoretical considerations and Dr M. Wraback for helpful comments. The support and continuous encouragement
GaN Negative Differential Resistance Components
385
by Drs C. Wood, J. Zolper, E. Martinez and H. Dietrich is greatly acknowledged. Work supported by ONR (Contract No. N00014-92-J-1552 and Contract No. N 0 0 0 1 4 - 0 M 0902) and DARPA/ONR (Contract No. N00014-99-1-0513).
REFERENCES [1] [2] [3] [4]
[5] [6]
[7]
[8] [9] [10] [11] [12]
[13]
[14] [15] [16] [17] [18] [19]
Bosch, B. (1975) Gunn Effect Electronics, Wiley, New York. Sze, S.M. (1998) Modem Semiconductor Device Physics, Wiley, New York. Sze, S.M. (1969) Physics of Semiconductor Devices, Wiley, New York. Kolnik, J., Oguzman, I.H., Brennan, K.F., Wang, R., Ruden, P.P. & Wang, Y. (1995) Electronic transport studies of bulk zinc-blende and wurtzite phases of GaN based on ensemble Monte Carlo calculation including a full zone band structure. /. Appl. Phys., 78 (2), 1033-1038. Foutz, B.E., Eastman, L.F., Bhapkar, U.V. & Shur, M.S. (1997) Comparison of high field electron transport in GaN and GaAs. Appl Phys. Lett., 70 (21), 2849-2851. Moustakas, T.D., Iliopoulos, E., Sampath, A.V., Ng, H.M., Doppalapudi, D., Misra, M., Korakakis, D. & Singh, R. (2001) Growth and device apphcations of Ill-nitrides by MBE. /. Cryst. Growth, 227-228, 13-20. Anwar, A.F.M., Wu, S. & Webster, R.T. (2001) Temperature dependent transport properties in GaN, Al;(;Gai_;,N, and In;(-Gai-;,N semiconductors. IEEE Trans. Electron. Dev., 48 (3), 567-572. Alekseev, E. & Pavhdis, D. (2000) Large-signal microwave performance of GaN-based NDR diode oscillators. Solid State Electron., 44, 941-947. Shur, M. (1987) GaAs Devices and Circuits, Plenum Press, New York. Alekseev, E. & Pavhdis, D. (2000) DC and high-frequency performance of AlGaN/GaN heterojunction bipolar transistors. Solid State Electron., 44, 245-252. Mohammad, S.N. & Morco^, H. (1996) Progress and prospects of group-Ill nitride semiconductors. Prog. Quantum Electron., 20 (5/6), 361-525. Bandic, Z.Z., Bridger, P.M., Piquette, E.C, Beach, R.A., Phanse, V.M., Vaudo, R.P., Redwing, J. & McGill, T.C. (1998) Nitride based high power devices: transport properties, linear defects, and goals. 1998 MRS Symp. Proc, 512, 27-32. Kolnik, J., Oguzman, LH., Brennan, K.F., Wang, R., Ruden, P.P. & Wang, Y. (1997) Monte Carlo calculation of electron initiated impact ionization in bulk zinc blende and wurtzite GaN. J. Appl Phys., 81 (2), 726-733. Dmitriev, V.A., Kuznetsov, N.I., Irvine, K.G. & Carter Jr., C.H. (1996) Electric breakdown in nitride PN junctions. MRS Symp. Proc, 395, 909-912. Bhapkar, U.D. & Shur, M.S. (1997) Monte Carlo calculation of velocity-field characteristics of wurtzite GaN. /. Appl Phys., 82 (4), 1649-1655. Medici, Two-dimensional Device Simulation Program, Version 2.3, User's Manual, February 1997, Technology Modeling Associates, CA. Krishnamurthy S., Schilfgaarde, M.V., Sher, A. & Chen, A.B. (1997) Bandstructure effect on high-field transport in GaN and GaAlN. Appl Phys. Lett., 71 (14), 1999-2001. Chen, A.B., Private communications (see also Ref. [17]). Sze, S.M. (1998) Active Microwave Diodes, in Modem Semiconductor Devices Physics, Eds. Eisele, H. & Haddad, G.I., Wiley, Northwood, MA.
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Ill-Nitrides
[20] Esaki, L. & Tsu, R. (1970) Superlattice and negative differential conductivity in semiconductors. IBM J. R&D, 14 (1), 61-65. [21] Schomburg, E., Grenzer, J., Hofbeck, K., Blomerer, T., Winnerl, S., Brandl, S., Ignatov, A.A., Renk, K.F., Pavelev, D.G., Koschurinov, Yu., Ustinov, V., Zhukov, A., Kovsch, A., Ivanov, S. & Koplev, P.S. (1998) Millimeter wave generation with a quasi planar superlattice electronic device. Solid State Electron., 42 (7/8), 1495-1498. [22] Foutz, B.E., Eastman, L.F., Bhapkar, U.V. & Shur, M.S. (1997) Comparison of high field electron transport in GaN and GaAs. Appl Phys. Lett., 70 (21), 2849-2851. [23] Haydl, W.H. (1983) Fundamental and harmonic operation of millimeter wave Gunn diodes. IEEE Trans. Microwave Theory Tech., 31 (11), 879-889. [24] Ruttan, T.G. (1974) High-Frequency Gunn Oscillators. IEEE Trans. Microwave Theory Tech., February, 142-144. [25] Schomburg, E., Brandl, S., Hofbeck, K., Blomeier, T., Grenzer, J., Ignatov, A.A., Renk, K.F., Pavel'ev, D.G., Koschurinov, Yu., Ustinov, V., Zhukov, A., Kovsch, A., Ivanov, S. & Kop'ev, P.S. (1998) Generation of millimeter waves with a GaAs/AlAs superlattice oscillator. Appl. Phys. Lett., 72 (12), 1498-1500. [26] Litvinov, V.I., Manasson, V.A. & Sadovnik, L.S. (2000) GaN-hased Terahertz Source, Proc. SPIE, 4111, Terahertz and Gigahertz Electronics and Photonics II, pp. 116-123. [27] Sacconi, F., Di Carlo, A. & Lugli, P. (2002) Modelling of GaN-based resonant tunneling diodes influence of polarization fields. Phys. Stat. Sol. (a), 190 (1), 295-299. [28] Wraback, M., Shen, H., Bellotti, E., Carrano, J.C, Collins, C.J., Campbell, J.C, Dupuis, R.D., Schurman, M.J. & Ferguson, LA (2001) Femtosecond Studies of High-Field Transient Electron Transport in GaN, in State-of-the-Art-Program on Compound Semiconductors (SOTAPOCS XXXV). Electrochemical Society Proceedings 2001-20,103, Eds. Chang, P.C, Chu, S.N.G. & Buckley, D.N. [29] Wraback, M., Shen, H., Rudin, S. & Bellotti, E. (2002) Experimental and theoretical studies of transient electron velocity overshoot in GaN. Phys. Stat. Sol., B234, 810. [30] Wraback, M., Shen, H., Rudin, S., Bellotti, E., Goano, M., Carrano, J.C, Collins, C.J., Campbell, J.C. & Dupuis, R.D. (2003) Direction-dependent band nonparabolicity effects on high-field transient electron transport in GaN. Appl. Phys. Lett., 82 (21), 3674-3676.
Optoelectronic Devices: Ill-Nitride M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 14
Ferromagnetism in GaN and Related Materials SJ. Pearton^, C.R. Abernathy^, G.T. Thaler% R.M, Frazier^, Y.D. Park*' and J.M. Zavada"" 'Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611, USA ^CSCMR and School of Physics, Seoul National University, Seoul 151-747, South Korea US Army Research Office, RTF, Triangle Park, NC 27709, USA
Recent results on achieving ferromagnetism in transition metal-doped GaN, AIN and related materials are discussed. While current generations of semiconductor electronic and photonic devices utilize the charge on electrons and holes in order to perform their specific functionality such as signal processing or light emission, the field of semiconductor spintronics seeks to exploit the spin of charge carriers in new generations of transistors, lasers and integrated magnetic sensors. There is strong potential for new classes of ultralow power, high-speed memory, logic and photonic devices. The utility of such devices depends on the availability of materials with practical magnetic ordering temperatures and most theories predict that the Curie temperature will be a strong function of bandgap. We discuss the current state-of-the-art in producing ferromagnetism in GaN and related materials, exhibiting room temperature ferromagnetism, the origins of the magnetism and its potential applications. 14.1. INTRODUCTION The emerging field of semiconductor spin transfer electronics (spintronics) seeks to exploit the spin of charge carriers in semiconductors. It is widely expected that new functionalities for electronics and photonics can be derived if the injection, transfer and detection of carrier spin can be controlled above room temperature. Among this new class of devices are magnetic devices with gain, spin transistors operating at very low powers for mobile applications that rely on batteries, optical emitters with encoded information through their polarized light output, fast non-volatile semiconductor memory and integrated magnetic/electronic/photonic devices ("electromagnetism-on-a-chip"). Since the magnetic properties of ferromagnetic semiconductors are a function of carrier concentration in the material in many cases, then it will be possible to have electrically or
E-mail address: [email protected] (S.J. Pearton).
387
388
Optoelectronic Devices: Ill-Nitride
optically controlled magnetism through field-gating of transistor structures or optical excitation to alter the carrier density. A number of recent reviews have covered the topics of spin injection, coherence length and magnetic properties of material systems such as and the general areas of spin injection from metals into semiconductors and applications of the spintronic phenomena [1-4]. Although there have been recent reports of successful and efficient spin injection from a metal to a semiconductor even at room temperature by ballistic transport (i.e. Schottky barriers and tunneling), the realization of functional spintronic devices requires materials with ferromagnetic ordering at operational temperatures compatible with existing semiconductor materials.
14.2. POTENTIAL SEMICONDUCTOR MATERIALS FOR SPINTRONICS
There are two major criteria for selecting the most promising materials for semiconductor spintronics. First, the ferromagnetism should be retained to practical temperatures (i.e. > 300 K) [5-8]. Second, it would be a major advantage if there were already an existing technology base for the material in other applications. Most of the works in the past have focused on (Ga,Mn)As and (In,Mn)As. There are indeed major markets for their host materials in infrared light-emitting diodes (LEDs) and lasers and high-speed digital electronics (GaAs) and magnetic sensors (InAs). In samples carefully grown single-phase by Molecular Beam Epitaxy (MBE), the highest Curie temperatures reported are -- 110 K for (Ga,Mn)As and ~ 35 K for (In,Mn)As as one of the most effective methods for investigating spin-polarized transport is by monitoring the polarized electroluminescence output from a quantum-well (QW) LED into which the spin current is injected. Quantum selection rules relating the initial carrier spin polarization and the subsequent polarized optical output can provide a quantitative measure of the injection efficiency. There are a number of essential requirements for achieving practical spintronic devices in addition to the efficient electrical injection of spin-polarized carriers. These include the ability to transport the carriers with high transmission efficiency within the host semiconductor or conducting oxide, the ability to detect or collect the spin-polarized carriers and to be able to control the transport through external means such as biasing of a gate contact on a transistor structure. We focus on a particular and emerging aspect of spintronics, namely, recent developments in achieving practical magnetic ordering temperatures in technologically useful semiconductors [5-10]. While the progress in synthesizing and controlling the magnetic properties of Ill-arsenide semiconductors has been astounding, the reported Curie temperatures are too low to have significant practical impact. Other materials for which room temperature ferromagnetism has been reported include (Cd,Mn)GeP2 [6], (Zn,Mn)GeP2 [7], ZnSnAs2 [8], (Zn,Co)0 [9] and (Co,Ti)02 [10]. Some of these chalcopyrites and wide bandgap oxides have interesting optical
Ferromagnetism in GaN and Related Materials
389
properties, but they lack a technology and experience base as large as that of most semiconductors. The key breakthrough that focused attention on wide bandgap semiconductors as being the most promising for achieving practical ordering temperatures was the theoretical work of Dietl et al. [11]. They predicted that cubic GaN doped with ~ 5 at.% of Mn and containing a high concentration of holes (3.5 X 10^^ cm~^) should exhibit a Curie temperature exceeding room temperature. In the period following the appearance of this work, there has been tremendous progress on both the realization of high-quality (Ga,Mn)N epitaxial layers and on the theory of ferromagnetism in these so-called dilute magnetic semiconductors (DMS). The term DMS refers to the fact that some fraction of the atoms in a non-magnetic semiconductor like GaN is replaced by magnetic ions. A key, unanswered question is whether the resulting material is indeed an alloy of (Ga,Mn)N or whether it remains as GaN with clusters, precipitates or second phases that are responsible for the observed magnetic properties [12]. Table 14.1 summarized recent work in realizing room temperature ferromagnetism.
Table 14.1. Compilation of semiconductors showing room temperature ferromagnetism Material
Bandgap of host (eV)
Cdi-;cMn;,GeP2 (Ga,Mn)N (Ga,Mn)N (Ga,Mn)N (Ga,Cr)N
1.72 3.4 3.4 3.4 3.4
(ZnO):Co
3.1-3.6
(Al,Cr)N
6.2
(Ga,Mn)P:C
2.2
(Zni_,Mn,)GeP2
1.83-2.8
(ZnMn)GeP2 ZnSnAs2 ZnSiGeN2 SiC
<2.8 0.65 3.52 3.2
''Extrapolated from measurements up to ~ 750 K.
Comments
Solid-phase reaction of evap. Mn Mn incorporated by diffusion Mn incorporated during MBE; n-type Mn incorporated during MBE Cr incorporated during MBE or bulk growth Co incorporated during PLD; ~ 15% Co Cr incorporated during MBE, sputtering or implantation Mn incorporated by implant or MBE; p - 10^° cm"^ Sealed ampoule growth; insulating; 5.6% Mn Mn incorporated by diffusion Bulk growth Mn-implanted epi Mn or Fe implantation
Ordering temperature (K)
Reference
>300 228-370 >300 940^ >400
[7] [22] [29] [25] [34]
>300
[9]
>300
[52,53,81]
>330
[68]
312
[6]
350 329 -300 -300 (by hysteresis)
[7] [8] [48] [31,32]
390
Optoelectronic Devices: Ill-Nitride
14.3. MECHANISMS OF FERROMAGNETISM Two basic approaches to understanding the magnetic properties of DMSs have emerged. The first class of approaches is based on mean-field theory. The theories that fall into this general model implicitly assume that the DMS is a more-or-less random alloy, e.g. (Ga,Mn)N, in which Mn substitutes for one of the lattice constituents. The second class of approaches suggests that the magnetic atoms form small (a few atoms) clusters that produce the observed ferromagnetism [12]. A difficulty in experimentally verifying the mechanism responsible for the observed magnetic properties is that depending on the growth conditions employed for growing the DMS material, it is likely that one could readily produce samples that span the entire spectrum of possibilities from single-phase random alloys to nanoclusters of the magnetic atoms to precipitates and second phase formation. Therefore, it is necessary to decide on a case-by-case basis which mechanism is applicable. This can only be achieved by a careful correlation of the measured magnetic properties with materials analysis methods that are capable of detecting other phases or precipitates. If, for example, the magnetic behavior of the DMS is characteristic of that of a known ferromagnetic second phase (such as MnGa or Mn4N in (Ga,Mn)N), then clearly the mean field models are not applicable. To date, most experimental reports concerning room temperature ferromagnetism in DMS employ X-ray diffraction (XRD), selected-area diffraction patterns, transmission electron microscopy (TEM), photoemission or X-ray absorption (including extended X-ray absorption fine structure, EXAFS, as discussed later) to determine whether the magnetic atoms are substituting for one of the lattice constituents to form an alloy. Given the level of dilution of the magnetic atoms, it is often very difficult to categorically determine the origin of the ferromagnetism. Indirect means such as SQUID magnetometer measurements to exclude any ferromagnetic inter-metallic compounds as the source of magnetic signals and even the presence of what is called the anomalous or extraordinary Hall effect, that have been widely used to verify a single-phase system, may be by itself insufficient to characterize a DMS material. The mean field approach basically assumes that the ferromagnetism occurs through interactions between the local moments of the Mn atoms, which are mediated by free holes in the material. The spin-spin coupling is also assumed to be a long-range interaction, allowing use of a mean-field approximation [13-20]. In its basic form, this model employs a virtual-crystal approximation to calculate the effective spin-density due to the Mn ion distribution. The direct Mn-Mn interactions are antiferromagnetic so that the Curie temperature, TQ, for a given material with a specific Mn concentration and hole density (derived from Mn acceptors and/or intentional shallow level acceptor doping), is determined by a competition between the ferromagnetic and anti-ferromagnetic interactions. Numerous refinements of this approach have appeared recently, taking into account the effects of positional disorder [16,17], indirect exchange interactions [18], spatial inhomogeneities and free-carrier spin polarization [19,20]. Figure 14.1 shows
Ferromagnetism in GaN and Related Materials Group IV III-As lll-P lll-N
400
^
| # GaCrN _ GaMnN
^"RAcaCrN
D Ill-Sb D Oxides # Experiment, others
300
CL
391
^^^"^^GaMnN
I
0)
A
I-
2
Experiment, UF
PAIR
200
E 0 •^ 1 0 0 InAs 01— 0.0
GaSb 0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Semiconductor Band Gap (eV) Figure 14.1. Predicted Curie temperatures as a function of bandgap, along with some experimental results.
a compilation of the predicted TQ values, together with some experimental results. In the subsequent period after appearance of the Dietl et al. [11] paper, remarkable progress has been made on the realization of materials with TQ values at or above room temperature. While most of the theoretical work for DMS materials has focused on the use of Mn as the magnetic dopant, there has also been some progress on identifying other transition metal atoms that may be effective. Figure 14.2 summarizes the two main theoretical approaches
Scenario 1: Delocalized holes form a Fermi liquid. Coulomb effects are approximated. Effective medium theory. (Dietl, Konig/SchlJemann/yacDonald, ...)
Scenario 2: Holes form an almost localized tight-binding band. Fluctuation effects due to randomness and hole-hole correlations are approximated. Site i
Site I
Sitej
(Berciu/Bhatt, Kaminski/Das Sarma, Dagotto, ...)
Figure 14.2. Schematic of theoretical approaches for ferromagnetism mechanisms in dilute magnetic semiconductors. The top figure represents the mean field approach and the bottom the bound magnetic polaron approach.
392
Optoelectronic Devices: Ill-Nitride
to understanding the ferromagnetism. In the mean-field theories, the Mn ions are considered to be embedded in a high concentration of free carriers that mediate the coupHng between the Mn ions. In the bound magnetic polaron (BMP) models, the carrier concentration is much less than the Mn density and BMPs form consisting of carriers localized around large clusters of Mn. As the temperature is lowered, the diameter of the BMPs increases and eventually overlaps at the Curie temperature.
14.4. (Ga,Mn)N In epitaxial GaN layers grown on sapphire substrates and then subjected to solid state diffusion of Mn at temperatures from 250-800°C for various periods, clear signatures of room temperature ferromagnetism were observed [21,22]. Anomalous Hall effect was observed at 323 K. The Curie temperature was found to be in the range 220-370 K, depending on the diffusion conditions. The use of ion implantation to introduce the Mn produced lower magnetic ordering temperatures [23,24]. In (Ga,Mn)N films grown by MBE at temperatures between 580-720°C with Mn contents of 6-9 at.%, magnetization (M) versus magnetic field {H) curves showed clear hysteresis at 300 K, with coercivities of 52-85 Oe and residual magnetizations of 0.08-0.77 emu/g at this temperature. An estimated TQ of 940 K was reported, using a mean field approximation to analyze the experimental data [25]. Note that while the electrical properties of the samples were not measured, they were almost certainly n-type [26-28]. As we discussed above, it is difficult to obtain high Curie temperatures in n-type DMS materials according to the mean-field theories and this is something that needs to be addressed in future refinements of these theories. The 940 K result is now considered to be most likely due to MnGa or Mn4N inclusions and not to single-phase (Ga,Mn)N. Room temperature ferromagnetism in single-phase n-type (Ga,Mn)N grown by MBE has also been reported by Thaler et al. [29], as shown in Figure 14.3. In general, no second phases are found for Mn levels below ~ 10% for growth temperatures of ~750°C. The (Ga,Mn)N retains n-type conductivity under these conditions. In that case, strenuous efforts were made to exclude any possible contribution from the sample holder in the superconducting quantum interference device (SQUID) magnetometer or other spurious effects. It is also worthwhile to point out that for the studies of (Ga,Mn)N showing ferromagnetic ordering by magnetization measurements, a number of materials characterization techniques did not show the presence of any second ferromagnetic phases within detectable limits. In addition, the values of the measured coercivities are relatively small. If indeed there were undetectable amounts of nano-sized clusters, due to geometrical effects, the expected fields at which these clusters would switch magnetically would be expected to be much larger than what has been observed. In accordance with most of the theoretical predictions, magnetotransport data showed the anomalous Hall
Ferromagnetism in GaN and Related Materials (a) _ t'_l "1 1I'1 "1 IM1 "j i I, T' ; |1"T 'J • _: 10 L
10
lU
393
I I I I I I I I I I I [J
(b)
H = 1 kOei
L../: ^
MO
(D
-10 r .
' T = 300K^ _L_L I I I I I I
~i 1 1 1 1 1 1 1 1 1 1 1 1 1 i~
-40 -20 0 20 H (kOe)
0
40
•- 1 1 1 1 1 1 1 1 1 1 1 1 1 • • 1 1 11
(c) 60
100 200 T(K)
1 1 1 1 1 1 1 1 1 I iisf-^
- 3 % ^ ^ ^
7
300
T
30 0 -30
: Sapphire Substrate^ -^
f•—
•—•jjiflir
:
y^^^ T = 300 K
-60 i-H^i
-30
1 1 1 1 1 1 1 1 1 1 1 11 11 1 11 11 1 1 1 1 1
-20-10
0
10
20
i i.-l
1 4
30
H (kOe) Figure 14.3. (a) B - H from MBE grown (Ga,Mn)N with 9.4 at.% Mn (filled circles) and from sapphire substrate (open circles), (b) M - T of (Ga,Mn)N, (c) B - H from (Ga,Mn)N as a function of Mn concentration.
effect, negative magnetoresistance and magnetic resistance at temperatures that were dependent on the Mn concentration. For example, in films with very low (< 1%) or very high (—9%) Mn concentrations, the Curie temperatures were between 10-25 K. An example is shown in Figure 14.3 for an n-type (Ga,Mn)N sample with Mn ~ 7%. The sheet resistance shows negative magnetoresistance below 150 K, with the anomalous Hall coefficient disappearing below 25 K. When the Mn concentration was decreased to 3 at.%, the (Ga,Mn)N showed the highest degree of ordering per Mn atom. Figure 14.3(a) shows hysteresis present at 300 K, while the magnetization as a function of temperature is shown in Figure 14.3(b). Data from samples with different Mn concentrations is shown in Figure 14.3(c) and indicates ferromagnetic coupling, leading to a lower moment per Mn. Data from field-cooled (FC) and zero field-cooled (ZFC) conditions was further suggestive of room temperature magnetization. The significance of these results is that there are many advantages from a device viewpoint to having n-type ferromagnetic semiconductors. EXAFS measurements have been performed on (Ga,Mn)N samples grown by MBE on sapphire at temperatures of 400-650°C with Mn concentrations of ~ 7 X 10^^ cm~^ (i.e. slightly over 2 at.%) [30]. Most of the Mn substituted for Ga on substitutional lattice positions. In the samples grown at 650°C, < 1 at.% of the total amount of Mn was found to be present as Mn clusters. However, at lower growth temperatures (400°C), the amount
394
Optoelectronic Devices: Ill-Nitride
of Mn that could be present as clusters increased up to ~36at.% of the total Mn incorporated. The ionic state of the substitutional Mn was found to be primarily Mn(2), so that these impurities act as acceptors when substituting for the Ga with valence three. However, when the electrical properties of these samples were measured, they were found to be resistive [29]. This result emphasizes how much more needs to be understood concerning the effects of compensation and unintentional doping of (Ga,Mn)N, since the EXAFS data indicated the samples should have shown very high p-type conductivity due to incorporation of Mn acceptors. However, there are still strong variations in the reported magnetic behavior, with some films exhibiting only paramagnetism and even those with ferromagnetism showing a wide range of apparent Curie temperatures (T^c) [31-40]. In particular, the origin of this ferromagnetism is not clear. Current hypotheses include a mean-field model (based on the Ruderman-Kittel-Kasuya-Yoshida, RKKY interaction) in which the ferromagnetism results from carrier mediation by delocalized or weakly localized holes in p-type material or various types of small clusters of the Mn such as Mn^^N. Given that the Mn^"^^^ "^ acceptor level is deep (~ Ey -h 1.8 eV), it is not expected that free-carrier mediated magnetism is significant but tightly bound carriers could play a role. The first class of approaches based on mean-field theory which originates in the original model of Zener magnetism [41-43]. The theories that fall into this general model implicitly assume that the DMS is a more-or-less random alloy, e.g. (Ga,Mn)N, in which Mn substitutes for one of the lattice constituents. The second class of approaches suggests that the magnetic atoms form small (a few atoms) clusters that produce the observed ferromagnetism. A difficulty in experimentally verifying the mechanism responsible for the observed magnetic properties is that depending on the growth conditions employed for growing the DMS material, it is likely that one could readily produce samples that span the entire spectrum of possibilities from single-phase random alloys to nanoclusters of the magnetic atoms to precipitates and second phase formation. Therefore, it is necessary to decide on a case-by-case basis which mechanism is applicable. This can only be achieved by a careful correlation of the measured magnetic properties with materials analysis methods that are capable of detecting other phases or precipitates. If, for example, the magnetic behavior of the DMS is characteristic of that of a known ferromagnetic second phase (such as MnGa or Mn4N in (Ga,Mn)N[44]), then clearly the mean field models are not applicable. There is clearly a need to examine the properties of (Ga,Mn)N with and without second phases, at least as detected by common analysis methods such as XRD. The magnetic properties of (Ga,Mn)N with a broad range of Mn concentrations(5 or 50 at.%) and which exhibited either one phase or multiple phases were examined. The first sample had a Mn concentration of ~ 5 at.% as determined by both Auger Electron Spectroscopy and Rutherford backscattering. The growth conditions (temperature, rate and V/III ratio) were optimized to produce single-phase material. The second sample also had a Mn concentration of ~ 5 at.%, but was grown under conditions where
Ferromagnetism in GaN and Related Materials
395
10^ A: GaN B: AI2O3 10^
C: Ga^Mn,
I 10^
(0
102
10^
10°
J_
30
35
40 26 (degrees)
45
50
Figure 14.4. XRD scans from (Ga,Mn)N with either 5 at.% Mn (optimized growth, sample 1), 5 at.9 Mn (unoptimized growth, sample 2) or 50 at.% Mn (sample 3).
we observe second phases. The third sample had a Mn concentration of ~ 50 at.% and was designed to contain large concentrations of second phases. Figure 14.4 shows the resulting XRD powder scans from the three samples. Secondphase peaks are observed for the unoptimized 5 at.% Mn sample and the 50 at.% sample. In the optimized 5 at.% Mn material, only peaks due to hexagonal c-axis aligned GaN and GaMn were observed. In separate experiments we have observed a linear variation in (Ga,Mn)N lattice constant with Mn concentration provided the material does not develop secondary phases. The only second phases observed in the unoptimized or high Mn concentration samples are Ga^^Mn^. Within this family of compounds, most are reported to be ferromagnetic in bulk form, namely, Mn2Ga {TQ = 690 K); MusGa (TQ = 743 K); MnsGag (^c - 210 K) and MnGa (TQ > 300 K). We have not observed Mn4N or other Mn;,N^ phases under our growth conditions. In growth of (Ga,Mn)N by MBE using a single precursor of [Et2Ga(N3)NH2CH3],the dominant second phase was MusGaN (Tc ~ 2 0 0 K ) [26]. All of the samples exhibited hysteresis in 300 K magnetization versus field loops (Figure 14.5), with coercivities in the range of 100 G. A more instructive measurement is that of the temperature dependence of the FC and ZFC magnetization, performed in Quantum Design SQUID magnetometer. As shown in Figure 14.6 (top), the single-phase (Ga,Mn)N is ferromagnetic to > 300 K as evidenced by the separation in FC and ZFC curves. By sharp contrast, the x = 0.5 sample shows behavior typical of a spin glass at < 100 K (Figure 14.6 center), while the multi-phase x = 0.05 material shows behavior
396
Optoelectronic Devices: Ill-Nitride 1
8x10-^- 5% Mn Single phase 4x10"^-
''*
300 K 1
0m
4x10-6-8x10-6-
'V
1t
r i
1
-1000— '
1 -500
'
0 H (Gauss)
1
1
500
1000
8x10-6 50% Mn Multi-phase 4x10-6
1
300 K
J
-4x10-6 41
1
,\ 'ii'"
Mr
1
-1000
i
-500
1
0 H (Gauss)
1
1
1—'
500
1000
0 500 H (Gauss)
1000
5% Mn Multi-phase 1x10"^ 300 K (D
hi
E o E
1*
..:::• -1x10-4 -1000
-500
Figure 14.5. Hysteresis loops (300 K) for (Ga,Mn)N with 5 at.% Mn (optimized growth) at top, 50 at.% Mn (at center) or 5 at.% Mn (unoptimized growth) at bottom.
Ferromagnetism in GaN and Related Materials -4.0x10-^
397
5% Mn Single Phase
•
F 0
"c -8.0x10-^ 0
E o E o
"O)
Q
-1.2x10-^
c
FC
•
CO
'BeBBDBnSBiioa°Dngpnc:
ZFC
-1.6x10-5
100 200 Temperature (K)
300
6.0x10-5 .
^
4.0x10-5
^^fflfflfflf
50% Mn Multi-phase
a ffl FC
_ I
ZFC , • ' • • • •
o o 2.0x10-
•Q
0.0
"lilHHHHHIBaBH 1
1
— 1 ,
1 ..
1
_i
100 200 Temperature (K)
..J
300
5.0x10-5 5% Mn Multi-phase
CD
c
r c
4.5x10-5
ffl H
0
E o E
I
D
ZFC
•
s
FC ffl
4.0x10-5
•
• • • • i•••
s^ •
•
3.5x10-5 1
ffl
1
I
100
•• .
•••• I
.
200
•••
I
300
Temperature (K) Figure 14.6. Temperature dependence of FC (top curve in each case) and ZFC (bottom curve in each case) magnetic moment for (Ga,Mn)N with 5 at.% Mn(optimized growth) at top, 50 at.% Mn at center or 5 at.% Mn (unoptimized growth) at bottom.
398
Optoelectronic Devices: Ill-Nitride
consistent with the presence of at least two ferromagnetic phases (Figure 14.6, bottom). Note that the 50% sample still exhibits a loop at 300 K, indicating a small difference in FC and ZFC magnetization at this temperature. All of this behavior is consistent with the XRD data. In summary, (Ga,Mn)N with 5 at.% Mn, grown by MBE under optimum conditions, shows no detectable second phases in XRD spectra and exhibits ferromagnetism to > 300 K. In material known to have second phases, the magnetization versus temperature behavior shows either a spin-glass type transition or cusps corresponding to the presence of multiple phases. While a number of groups have reported room temperature ferromagnetism in GaN doped with Mn or Cr [31,32,34,35], there has been Uttle investigation of the electrical and optical properties of the material. The carrier-induced ferromagnetism model requires hole-induced interactions between the spins of the substitutional transition metal ions. However, the few reports of the position of Mn in the GaN bandgap find it to be very deep, ^v + 1-4 eV, where it would be an ineffective acceptor dopant [45-47]. In addition, most of the data reported for GaMnN indicate it is either insulating or n-type. The resistivity of GaMnN grown by MBE has been examined using both Schottky diode and transmission line method (TLM) measurements and optical absorption spectra from GaMnN films as a function of Mn concentration. Features at £'c — 1.9 eV are found in the absorption spectra, corresponding to transitions from Mn to the conduction band. However, this state does not control the Fermi level position in the GaMnN and the material remains high-resistivity n-type with a thermal activation energy of ~ 0.1 eV. The results have interesting indications for both the existing theoretical models for DMSs and for the potential technological uses of GaMnN. Figure 14.7 (top) shows the low bias / - V characteristics at 25°C from the GaMnN/GaN device structure. The results are consistent with the GaMnN having a high resistance and the characteristic is approximately linear over this voltage range. The resistivity of this layer can be obtained from the relation p = RA/W where R is the total measured resistance of the GaMnN layer of thickness W between the top contact of area A and the ohmic contacts. For W = 0.3 luum, this translates to p= 3.1 X 10^ H cm. Even at higher biases, the I-V characteristic is dominated by the high resistance of the GaMnN (Figure 14.7, bottom). From TLM ohmic metal patterns placed directly on the GaMnN layer, we were able to measure the temperature dependence of the sheet resistivity. Figure 14.8 shows an Arrhenius plot of this data, corrected for the temperature dependence of the mobility contribution to the sheet resistivity. Over a broad range of temperature, the sheet resistivity varies as Ps = Pso Qxp(-EJkT)
Ferromagnetism in GaN and Related Materials
399
6.0x10-^ Schottky contact 80 |jm Current-Voltage
4.0x10"^ 2.0x10-^ h 0.0
-2.0x10-^
Resistivity=3.7x10^ Qcm
-4.0x10-^ -6.0x10-^
-10
0 Bias (V)
10
3.0x10-5 2.5x10-5 2.0x10-5 .-v
<, c
1.5x10-5
13
1.0x10-5
0)
o 5.0x10-^ 0.0 -5.0x10-^
200
300
Bias (V) Figure 14.7. Low bias I-V characteristics at 25°C from Schottky diode GaMnN/GaN structure (top) and forward I-V plots from several diodes at highest bias (bottom).
where E^ = 0.ll ± 0.02 eV. This represents the activation energy of the defects or impurities controlHng the n-type conductivity of the GaMnN. These results are consistent with the absorption data. Figure 14.9 shows the spectral dependence of absorption coefficient for GaMnN as a function of Mn concentration. The introduction of Mn produced an absorption band with a threshold near 1.9 eV which has been previously ascribed to transitions from Mn acceptors to the conduction band. We do not observe the band with a threshold near 1.4 eV corresponding to the transition from
400
Optoelectronic Devices: Ill-Nitride 24.6 24.4 24.2 ^
MBE grown GaMnN Ohmic contact (Ti/AI/Pt/Au) Annealed at 700 C, 30 s, N2
24.0
•lo 23.8 Q.
E =0.1eV
23.6 23.4 23.2 23.0 1.6
2.0
2.4
3.2
2.8
1000/T(K-'') Figure 14.8, Arrhenius plot of sheet resistivity of GaMnN layer, adjusted for the temperature dependence of mobility. The resulting activation energy is —0.1 eV.
the valence band to the Mn acceptor, which is a strong evidence for the sample being n-type with the Fermi level in the upper level of the bandgap. Thus, even though there is a very high concentration of Mn acceptors in the GaMnN, these do not control the electrical properties of the materials. One possibility for the 0.1 eV donors are nitrogen vacancies. Recent experiments on photoluminescence (PL), optical absorption and photocapacitance spectra from Mn-doped layers grown by metalorganic chemical vapor deposition
1
Z.UXIU"
E
1.6x10^
0) 0
1.2x10^
lE
8 c q
'
1
'
1
GaMnN
/
••^^''iP
,
/
"
1
10% Mn / 5% Mn / 3%Mn
//
//''
^
/ 0 % Mn
8.0x10"^
"Q.
0
<
4.0x10"^ p - j * * * " ^ ^ •*«.»-.
,
, ,
3 4 Photon energy (eV) Figure 14.9. Optical absorption spectra from GaMnN layer as a function of Mn concentration.
Ferromagnetism in GaN and Related Materials
401
(MOCVD) suggest that Mn forms in GaN a deep acceptor level near £'Y + 1.4 eV [48 - 51 ]. However, Mn-implanted and annealed GaN films with Curie temperatures close to room temperature do not show the semi-insulating behavior expected in such a case. Therefore, some other defect centers must also be formed in high concentration and contribute to conduction mechanisms in implanted films. Apart from Mn, it is also expected that other transition metal dopants can produce ferromagnetic behavior in GaN. The GaN layers into which the Mn and the Co ions were implanted were grown by MOCVD on sapphire. The GaN was not intentionally doped and was 6 luum thick. Mn ions with energy of 250 keV were implanted at 350°C for two doses, 3 X 10^^ and 4 X 10^^ cm~^. The high temperatures during implantation prevented the material from amorphization. The incorporation depth of the Mn ions was close to 0.2 |xm and the peak volume concentration of the Mn in the implanted region was close to 3 at.% (dose of 3 X 10^^ cm~^) and 4% (dose of 4 X 10^^ cm"^). The Co ions were implanted at 300 keV, also at 350°C. The implantation dose was 4 X 10^^ cm~^, the incorporation depth was about 0.2 |xm and the peak volume concentration in the implanted region was about 4 at.%. All implanted samples were annealed at 700°C for 5 min in a N2 atmosphere to remove the radiation damage. The optical transmission spectrum taken for the control sample (Figure 14.10) showed a sharp edge near 3.4 eV, and a dense pattern of interference fringes without any measurable absorption in the below-bandedge region. In contrast, the two Mn-implanted samples showed a strong absorption near 1.8 eV, i.e. close to the optical threshold for the transition from the E^^ -\-lA eV Mn acceptor level to the conduction band edge. For the Co-implanted sample the absorption edge was slightly red-shifted to 1.7 eV, indicating the presence of a deep level, about 0.1 eV deeper than the Mn acceptor. In both types of samples an 100 Control 80 60 1.7eV(Co) •l.8eV(Mn)
40
20-1 2.7 eV (Mn and Co) 300 350 400 450 500 550 600 650 700 750 800 Wavelength (nm) Figure 14.10. Optical transmission spectra at 300 K for the control sample, the 4 X 10^^ cm~^ Mn-implanted sample and the 4 X 10^^ cm~^ Co-implanted sample.
402
Optoelectronic Devices: Ill-Nitride
additional band with the threshold near 2.7-2.8 eV was present. The optical transition involved could be the same as giving rise to the blue luminescence band in MCL spectra. Typical 90 K MCL spectra taken on the control GaN at low and high excitation intensities show the h donor bound exciton line near 3.45 eV, the defect band near 3.4 eV, the donor-acceptor pairs series in the 3.1-3.3 eV range, the blue band near 2.95 eV and a very weak yellow luminescence band peaked near 2.3 eV. In implanted samples the MCL intensity was much lower than in the control GaN, due to the radiation damage defects not being completely annealed at the annealing temperature of 700°C. It should be noted that we could not detect in MCL spectra any of the bands directly attributable to the Mn or Co acceptors. One would expect to see a band near 2 eV corresponding to the transition from the conduction band to the Mn acceptor level and indeed we observed such a transition in GaMnN samples grown by MBE. We believe that in the implanted samples the observation of such a band is effectively precluded by the presence of the strong shoulder of yellow luminescence and by the overall low luminescence efficiency. Capacitance-voltage measurements on the unimplanted GaN gave an electron concentration of 2 X 10^^ cm~^ and the intercept value in the 1/C^(y) plot of 0.7 V which is standard for Au Schottky diodes prepared on undoped n-GaN films grown by MOCVD. The frequency and temperature dependence of capacitance was very shght. The behavior of the implanted samples was much more complicated. The capacitance at low frequencies was considerably higher than at high frequencies. At temperatures near 400 K the capacitance versus frequency curves showed well-defined low-frequency and high-frequency plateaus. At low frequencies the measured thickness of the space charge region was lower than 0.2 |jLm (i.e. the space charge region boundary was moving within the implanted region). The roll-off frequency in the low-frequency range decreased with decreased measurement temperature in a similar manner for all implanted samples and application of the standard admittance spectroscopy analysis to the shift in frequency with temperature yielded an activation energy of 0.45-0.5 eV. The 1/C^(y) plots were linear for all three implanted samples, the apparent concentration deduced from the slope increasing from 6 X 10^^-8 X 10^^ cm~^ for the Mn-implanted samples to 4.2 X 10^^ cm~^ for the Co-implanted sample. Thus at these low frequencies the C-V curves are determined by the uncompensated portion of the deep electron trap concentration with level near EQ - 0.5 eV. These are most likely the traps responsible for the strong blue band in the MCL spectra and for the absorption band near 3 eV in Figure 14.10 (the total concentration of these deep traps could be much higher than the value deduced from C-V measurements since the latter relate to the uncompensated portion of the total density). It should be noted that no such centers were introduced in n-GaN upon implantation of protons and it seems reasonable to associate the observed centers with complexes of radiation defects with the transition metal acceptors.
Ferromagnetism in GaN and Related Materials
403
The apparent thickness of the depleted region deduced from the value of high-frequency capacitance was close to 1 |xm. Everything looks as though there is a region about 1 |jLm thick adjacent to the implanted region having high density of deep centers that cannot respond to the probing frequency in C-V measurements so that the entire region behaves as a dielectric layer at high frequencies. At low temperatures, however, the high-frequency \IC^{V) plots become linear with the apparent slope giving the apparent electron concentration of 1 X 10^^ cm~^ (i.e. still considerably lower than in the initial unimplanted sample (2 X 10^^ cm~^). The most obvious explanation is that as the temperature goes down the electrons in the damaged region freeze out so that the space charge region extends right down to the thickness of 1 (xm corresponding to the total thickness of the damaged region. This produces the appearance of measurable slope in high-frequency C-V curves at low temperatures. However, the region probed still contains a certain number of defects as suggested by the reduced electron concentration and also from DLTS results discussed in Section 14.5. Arrhenius plots of sheet resistance of the Mn-implanted (3 X 10^^ cm~^) GaN clearly showed more than one defect level present, producing a non-linear plot. The slopes at the two extremes of the plot corresponded to activation energies of 0.85 and 0.11 eV. Figure 14.11 presents typical DLTS spectra taken on the control GaN with electrical pulse injection (positive signal, electron traps) and optical pulse injection with the light of a D lamp source and the negative sign corresponds to the capacitance decreasing with time during the transient (minority traps). The set of electron and hole traps observed is typical for undoped MOCVD grown GaN. In Figure 14.12 we compare the DLTS spectra for the electron traps in the control sample and the 3 X 10^^ cm~^ Mn-implanted sample. The Mn implantation greatly increases the density of the EQ - 0.25 eV electron traps and EQ — 0.7 eV electron traps
0.2 g CO
0.85 eV
0.6 eV
0.4 0.25 eV
0.0 -0.2 -0.4 50
0.9 eV
0.3 eV 100
150
200
250
300
350
400
Temperature ( K) Figure 14.11. DLTS spectra taken on control sample with electrical pulse injection (the positive curve) and the optical pulse injection (the negative curve).
404
Optoelectronic Devices: Ill-Nitride
Mn3x10^^
0.7 eV 7\
CO
0.25 eV
c CO
50
100
150
200
250
300
350
400
Temperature (K) Figure 14.12. DLTS spectra of the control sample at - 1 V with + 1 V forward pulse (solid curve), of the 3X lO'^cm"^ Mn-implanted sample taken with reverse bias of - 1 V and forward bias of + 1 V (short dashed curve) and of the same sample measured with reverse bias of - 3 V and forward bias of - 1 V (dashed curve).
known to be related to point defects introduced, e.g. during proton implantation into n-GaN. Moreover, the magnitude of the signal taken with reverse bias of - 1 V and forward bias of 1 V in the implanted sample was much higher than that taken with reverse bias of — 3 V and the forward bias pulse of — 1 V. We attribute the difference to the fact that in the former case the space charge boundary during the injection pulse is pushed deeper into the damaged region where the density of deep radiation defects is higher. In Figure 14.13 we compare the DLTS spectra of the Mn-implanted and the Co-implanted
Co 4x10^6
Control
50
100
150
200
250
300
350
400
Temperature (K) Figure 14.13. DLTS spectra of the Mn-implanted (dashed curve) and the Co-implanted (solid curve) samples.
Ferromagnetism in GaN and Related Materials
405
samples taken under the same conditions. It can be seen that the concentration of radiation defects in the Co-implanted sample is considerably higher most likely due to the higher initial density of the radiation defects in the region implanted with Co, Co being heavier than Mn. Our previous studies of the proton-implanted n-GaN samples have shown that the EQ — 0.7 eV radiation defects are very efficient lifetime killers which explains the extremely low photosensitivity of the Mn and Co-implanted samples and the very low MCL intensity observed in these samples (the low photosignal and MCL signal was observed even with electron beam excitation with the beam energy of 25 kV when the excitation region penetrated much deeper than the projected Mn or Co ions range of 0.2 |xm, but not deeper than the thicker damaged region). The spectra taken with optical injection were very instructive. In Figure 14.14 we show the optical DLTS spectra measured on the 3 X 10^^ cm~^ Mn-implanted sample when the deuterium lamp UV source and the tungsten lamp visible light source were used. It can be seen that with the strongly absorbed UV light of the deuterium lamp, the spectrum was dominated by electron traps with energy of 0.28 eV and an overlapping feature produced by the 0.35 and 0.5 eV electron traps. With the slightly absorbed visible light of the tungsten lamp the dominant features were the hole traps near Ey + 0.2, E^ + 0.35 and Ey -h 0.43 eV. The results in the figure refer to the Mn-implanted sample but the only difference with the Co-implanted sample was the absence of the 0.35 eV electron trap peak in the D-lamp-excited spectrum. The difference might be due to the different penetration depth of the D lamp light and the W lamp light. In the first case electrons and holes are generated mainly in the near-surface implanted region where a very high density of Mn or Co acceptors exist. The holes are effectively trapped by these acceptors and are disposed of
0.28 eV 0.35 eV
200
Figure 14.14.
0.5 eV
250 T(K)
Optical DLTS spectra taken on the 3 X 10^^ cm~^ Mn-implanted sample with the D lamp excitation and the W lamp excitation.
406
Optoelectronic Devices: Ill-Nitride
by some very slightly activated process such as hopping via acceptor states with subsequent tunneling at the Schottky diode. Thus only electron traps are left to be observed in the capacitance transients and among them the 0.5 eV trap is most likely the one dominating the low frequency C-V characteristics and producing the blue MCL band. For the weakly absorbed W lamp light generation mainly occurs within the broader damaged region not containing the Mn or the Co acceptors. In this case hole traps other than Mn or Co are free to capture holes and thus become visible in the capacitance transients. We have shown that Mn implantation into GaN gives rise to a strong absorption with the threshold near 1.8 eV which is close enough to the band observed in MOCVD grown GaMnN samples in which Mn was shown to produce an acceptor level near Ey -\-\A eV. The optical threshold for the Co-implanted sample was about 0.1 eV lower implying that the Co acceptor level could be slightly deeper than the Mn level. This would be in line with general observations on the depth of the transition metals in III-V materials as a function of the d-shell filling: it has been noted that the higher the filling the deeper the level so that, in GaAs, the Mn acceptor is at £^v + 0.1eV and the Co acceptor is at £'v + 0.16eV, although for the wider bandgap GaP both dopants produce acceptor levels near Ey + 0.4 eV. In addition to the deep Mn and Co acceptors we also see in the implanted region a very high density of electron traps with the level near EQ — 0.5 eV. These traps seem to be closely related to the very prominent blue MCL band different from the blue band in the unimplanted sample. We tentatively associate these traps with formation of complexes between the Mn or Co acceptors and some native defects such as nitrogen vacancies. The fact that room temperature ferromagnetism can be achieved in n-type GaMnN is contrary to the main mean field models, but is attractive from a technological viewpoint since most devices require either n-type material (i.e. field-effect transistors) or both n- and p-type material (i.e. bipolar transistors and optical emitters). Further optimization of the growth conditions will be needed to reduce the unintentional donor concentration to the point where p-type GaMnN can be produced. Other reports have also recently appeared on the magnetic properties of GaN doped with other transition metal impurities [31,32,34,35,48-51]. For initially p-type samples directly implanted with either Fe or Ni, ferromagnetism was observed at temperatures of ~ 200 and 50 K, respectively. (Ga,Fe)N films grown by MBE showed Curie temperatures of < 100 K, with EXAFS data showing that the majority of the Fe was substitutional on Ga sites [29]. (Ga,Cr)N layers grown in a similar fashion at 700°C on sapphire substrates showed single-phase behavior, clear hysteresis and saturation of magnetization at 300 K and a Curie temperature exceeding 400 K [51]. A key requirement for successful realization of spin-based devices is an understanding of the transport properties within the DMS, since carriers need to be injected from contacts and cross heterointerfaces in order to be collected. Some potential early demonstration
Ferromagnetism in GaN and Related Materials
407
devices include spin LEDs, in which injection and recombination of spin-polarized carriers could lead to polarized light emission, and spin transistors in which electron field gating can be used to control the carrier-induced ferromagnetism. Most GaN is still grown heteroepitaxially on lattice-mismatched substrates such as sapphire, and therefore, contains high concentrations (usually > 5 X 10^ cm~^ as measured by TEM) of threading dislocations and other extended defects. Numerous reports have demonstrated the deleterious effect of charged dislocations on the transverse carrier mobility in GaN. However, vertical devices are much less degraded by the repulsive band bending around dislocations and the directional dependence of the scattering due to the these dislocations because of the greater average distance between defects in this geometry. This has been confirmed by an investigation of vertical and lateral transport in n-GaN films, which showed vertical electron mobilities of ~950 cvci'fW s compared to lateral mobilities of 150 - 200 cm^A^ s. Hall measurements showed (Ga, Mn)N electron mobilities in the range of 102 crn^fV s at 373 K to 116 cm^A^ s at 298 K. We believe these values are close to the true mobility in the (Ga,Mn)N, since measurements made on the GaN prior to Mn implantation showed much higher electron mobilities of ~ 600 cm^fV s at 298 K and thus if most of the current was flowing in the buffer layer, we expect to measure an effective mobility closer to this value. This latter value of 600 cvci'lW s is similar to that reported for high quality n-type GaN. To obtain the vertical mobilities, temperature dependent I-V measurements were performed in the Schottky diode structures. The I-V characteristics on (Ga,Mn)N diodes measured from 298 ~ 373 K are shown in Figure 14.15. The barrier heights (<^) extracted from the forward part of the / - V characteristics for both these and the diodes without Mn were obtained, with values ranging from 0.91 eV at 298 K to 0.88 eV at 373 K for the (Ga,Mn)N. In contrast, the measured barrier height on Pt/GaN diodes was 1.08 eV, as reported in Ref. [26]. The saturation current density, J^, can be represented as T
Js=A
4**^2
/
4*Q\
rexp^--j
where A** is the Richardson's constant for (Ga, Mn)N, T is the absolute measurement temperature and k is Boltzmann's constant. This can also be written in the form 1/2 ^
=h.v4^]'"Hp(^) where NQ is the effective density of states in the conduction band, JHYEKT is the electron mobility in the perpendicular direction, e is the electron charge, y^i is the built-in voltage, 8 is the dielectric constant and A^^ is the doping density in the (Ga,Mn)N. The vertical values are factors of —3-8 higher at a given temperature than the lateral mobilities
408
Optoelectronic Devices: Ill-Nitride
o
10 -10 -2
Measured at 25 C^ Measured at 50 C Measured at 75 C Measured at 100°C Bias (V)
Figure 14.15. I-V characteristics as a function of temperature from n-(Ga,Mn)N Schottky diodes.
obtained from the Hall data. If the active area of the diodes is less than the geometric area then the effective vertical mobilities will be even higher than calculated here. To give a visual representation of why the lateral mobility is more degraded by threading scattering is the vertical mobility. Figure 14.16 shows a cross-sectional TEM micrograph of the (Ga, Mn)N/GaN structure. Threading dislocations originating from the GaN/Al203 interface can reach the surface, and therefore, electrons traveling laterally through the structure encounter scattering from all of these defects. In contrast, for vertical surface , GaMnN
Figure 14.16. TEM cross-section of (Ga,Mn)N layer formed in GaN by high dose Mn implantation.
Ferromagnetism in GaN and Related Materials
409
transport, there is a relatively large fraction of undefective material through which electrons can pass with undegraded mobility. The defects remaining in the (Ga,Mn)N are mostly loops, which have only a second-order effect on the electrical properties, as reported previously for implanted GaAs. To place the experimental data in context, Figure 14.17 shows these results along with the calculated electron drift mobility of undoped GaN in both lateral and vertical directions and the individual components from the scattering processes (acoustic, polar phonon, and piezoelectric) present. While no quantitative conclusions may be drawn, it is clear that the vertical and lateral mobilities are of comparable magnitude to those in material with minimal scattering. In the existing (Ga,Mn)N the vertical electron mobility is relatively unaffected by charged dislocation scattering and gives an indication of the values that it will be possible to achieve for lateral electron mobilities in material synthesized on low-defect GaN such as free-standing quasi-substrates. In summary, the effect of dislocation scattering on electron mobihty in (Ga,Mn)N has been examined through a comparison of vertical and lateral transport properties. The vertical electron mobilities are found to be a factor of 3-8 higher than the corresponding lateral mobilities at the same temperature. (Ga,Mn)N-based spintronics devices with vertical geometries will be at an advantage relative to lateral devices. 10*
"»
E
'
•—«—r-r-|
1 1 t
1
1
'
1
—1
1
1
j
\
L
\ r
^
acoustic
polar phonon
H
\
10^ t
t-
•d j
F
]
L ^VERT
>
r
^LAT
- ^ ^ ^ piezoelectric
10^ t
^•^^^-.^H.^^WS,^^
t
\
^'"•'"^^Ov ^
[• r
^ VVx>\ ^
GaMnN
L
p
1
J
^•N.
°XN\
[• h
1.1
J
H
V.
X\\
^LAT
F
10^
•«• •*..^*».
D
• 10'
1 i J
^j H
aD ^
......i
1
.
J
1
I
1
1 1 1
1
100 Temperature (K)
H
11 1
1
1
1000
Figure 14.17. Theoretical drift mobilities in pure GaN, along with contribution from the various scattering processes present and the experimentally determined vertical and lateral mobilities for n-(Ga,Mn)N.
Optoelectronic Devices: Ill-Nitride
410
One of the possible applications of DMS is in the so-called spin field effect transistor (Spin FET) in which electric field gating is used to control the carrier-induced ferromagnetism. This has already been demonstrated in metal-insulator-semiconductor (MIS) structures based in (In,Mn)As at 10 K. Therefore, it is necessary to understand the properties of rectifying contacts on (Ga,Mn)N as a first step towards realizing practical spintronics switches. Figure 14.18 shows the forward I-V characteristics from the Pt Schottky diodes as a function of measurement temperature. The forward current increases with increasing temperature. The saturation currents /§ at each temperature (T) were extracted from the relation
=4^4(^))} °'^ ' >=^"'^^ where V is the applied voltage, R^ the series resistance, e is the electronic charge and n is the ideality factor. The extracted values in terms of saturation current density /§ were 4.28 X 10"^ A/cm^ n=l.2l at 298 K, 6.60 X 10"^ A/cm^ n = 1.17 at 323 K, 1.08 X 10"^ A/cm^ n = 1.16 at 348 K, and 8.42 X 10"^ A/cm^, at 373 K. In the latter case, we could not determine an accurate value of n. The saturation current can also be represented as T exp
h=AA' 10-
10-
I
^
'
I
'
I
'
\
r
kT
) ,-o-o,-o-o-q
y
o
Figure 14.18. Forward I-V-T
^
/^
100 |im diameter
characteristics from 100 jxin diameter Pt contacts on n-(Ga,Mn)N.
Ferromagnetism in GaN and Related Materials
411
where A** is the Richardson's constant for (Ga,Mn)N, A the diode area and (/)B is the Schottky barrier height. The theoretical value of A** for n-GaN is 24 A/cm^ ¥? [15], but is not known for (Ga,Mn)N because the electron effective mass has not been determined. From the / - V - T characteristics, we extracted a value for A** of 91.2 AJcvc? K^, but there is a large uncertainty (~ ± 60%) in this due to narrow range of measuremental temperatures from which we had to extrapolate to obtain the estimated Richardson's constant. For comparison, a similar analysis for Pt/n-GaN Schottky diodes reported values of 64.7-73.2 for A**. From the measured I-V characteristics at each temperature we were able to extract the (/)B values, as shown in Figure 14.19. The barrier height at 25°C was 0.82 ± 0.04 eV, which compares to a value of 1.08 eV for Pt on n-GaN determined from I-V characteristics [14,16]. We have not yet determined the bandgap of (Ga,Mn)N but preliminary data suggest it is smaller than GaN and this is consistent with the smaller barrier height for Pt on (Ga,Mn)N. It should also be noted that in the early stage of developing a new materials system it is common to have a wide range of values reported for barrier heights due to the presence of surface defects, interfacial layers and material inhomogeneities. The barrier height was also extracted from the activation energy plots in the measured I-V-T data and the saturation current at each temperature. Figure 14.20 shows the plot of ln(/s/Ar^) versus inverse temperature, yielding a barrier height of 0.91 ± 0.06 eV which is consistent with the value at 25°C derived from the forward I-V characteristics. 1
u.»u
0.85
'
1
1
'
-\
_ •
CD CQ
1
r 11
0.75
'
'
^
1
0.80
CD
1
~~
— - 1'
11
-
-
0.70 Pt/n-(Ga, Mn)N n=3.5x10^^cm-3
1
0.65
1
300
,
1
1
320
340
,
1
,
360
1
380
Temperature (K) Figure 14.19. Barrier height extracted from forward I-V characteristics at different temperatures.
Optoelectronic Devices: Ill-Nitride
412
Figure 14.21 shows the reverse I-V characteristics from the diodes as a function of temperature. The reverse leakage depends on both bias and temperature. From a moderately doped sample of the type studied here, we would expect thermionic emission to be the dominant leakage current mechanism. According to image-force barrier height lowering, this leakage current density, / L can be written as -/s exp
m
where A(/)B is the image-force barrier height lowering, given by eE^
. 1/2
V 4178^
where E^, is the electric field strength at the metal/semiconductor interface and ss is the permittivity. The experimental dependence of 7L ^^ bias and temperature is stronger than predicted from this last equation. The large bandgap of (Ga,Mn)N makes the intrinsic carrier concentration in a depletion region very small, suggesting that contributions to the reverse leakage from generation in the depletion region are small. Therefore, the additional leakage must originate in contributions from other mechanisms such as thermionic field emission or surface leakage.
-20
Pt/n-(Ga, Mn)N 0.91+-0.06eV
-30 0.0026
JL
0.0028
0.0030
0.0032
0.0034
1/T(K-^) Figure 14.20. Arrhenius plot of Is^AT^ used to extract barrier height of Pt on n-(Ga,Mn)N.
Ferromagnetism in GaN and Related Materials
413
0.00
^q(j(jijtjmmMummMm -0.02
-0.04
o
-0.06
-0.08
-5
-4
-3
z -2
jP
100 |am diameter 75°C 50°C 25°C -1
0
Bias (V) Figure 14.21. Reverse I-V-T
characteristics from 100 ixm diameter Pt contacts on n-(Ga,Mn)N.
In summary Pt contacts on n-(Ga,Mn)N show rectifying behavior with a barrier height at 25°C of 0.8-0.9 eV, depending on which analysis method is employed. This is a useful first step in making gated spin FET structures based on this DMS.
14.5. AIN AIN plays an important role in many areas of solid-state devices [52-67], including thin film phosphors, nitride-based MIS heterostructure transistors, thin-film gas sensors, acoustic wave resonators, UV LEDs, distributed Bragg reflectors, heat spreaders and heterojunction diodes. AIN may also be promising in the emerging field of spintronics, due to its predicted high Curie temperature {TQ) when doped with particular transition metals. Room temperature ferromagnetism has been reported for Cr-doped AIN thin films deposited by reactive sputtering [52] or MBE [53]. Ion implantation provides a versatile and convenient method for introducing transition metals into semiconductors for examination of their effects on the structural and magnetic properties of the resulting material [68]. AIN is an ideal host in this regard, since Kucheyev et al. [69] reported that single crystal epilayers of AIN grown on sapphire substrates did not become amorphous even at LN2 temperatures for high doses of keV heavy ions such as Au. In addition, very high quality AIN on sapphire has recently been reported by several groups [70,71], providing well-characterized material in which to examine the properties of transition
414
Optoelectronic Devices: Ill-Nitride
metals. The fabrication of ferromagnetic AIN would create a wider range of possible all semiconductor spin-dependent devices. For example, ferromagnetic AlMnN could be used as a magnetic barrier in a tunnel junction where it would serve as a spin filter. The predicted Curie temperature of AlMnN is greater than 300 K and recently a Curie temperature of more than 340 K has been observed for AlN:Cr [52,53]. Growth of the films was carried out by gas-source MBE. Solid A1(7N) and Mn(7N) sources were heated in standard effusion cells. Gaseous nitrogen was supplied by an Oxford RF plasma head. All films were grown on (0001) oriented sapphire substrates, indium mounted to Mo blocks. AlMnN and AIN films were grown at a temperature of 780°C, as indicated by the substrate heater thermocouple. Sapphire substrates were first nitridated for 30min at a substrate temperature of 1000°C under 1.1 SCCM nitrogen (chamber pressure = 1.9 X 10~^ Torr). Nucleation at 575°C for 10 min and a 30 min buffer layer at 950T followed nitridation, both under 1.1 SCCM nitrogen. Both AIN and AlMnN films were grown with a substrate temperature of 780°C and an Al effusion cell temperature of 1150°C. The Mn cell temperature was varied from 635 to 658°C. The growth rate of the AIN was 0.2 |xm/h and the growth rate of the AlMnN films was 0.16 ixm/h. In situ reflection high energy electron diffraction (RHEED) was used to monitor films during growth. AIN demonstrated 2D growth and AlMnN films demonstrated 2D/3D growth. AlMnN grown with an Mn cell temperature of 635°C was found to be single phase. The AlMnN with Ty^^ = 658°C formed AlMn as detected by powder XRD. A Mn cell temperature of 650°C was found to be the upper limit of single-phase AlMnN under previously mentioned growth conditions. For comparison, a layer of Mn4N was also grown on sapphire. The lattice constant was found to decrease as the Mn cell temperature increased for single-phase material. A similar pattern was observed for single-phase GaMnN films grown in the same system under different conditions. GaN implanted with Mn has been reported to exhibit substitutional or near substitutional incorporation. It is expected that the incorporation of interstitial Mn should either increase or have no effect on the lattice constant. The observation of a decrease in the lattice constant of the AlMnN films suggests that the Mn occupies a substitutional site. This is further confirmed by Hall analysis, which showed pure AIN to be highly resistive as expected and material containing an AlMn second phase to be highly conductive n-type. In contrast, single-phase AlMnN was found to be p-type. If Mn incorporates substitutionally, one would expect by analogy with its behavior in other III-V materials that it would behave as a deep acceptor. The observation of p-type behavior fits this explanation. Magnetic remanence and coercivity indicating hysteresis was observed in ternary AlMnN films at 10,100, and 300 K. Measurements over 300 K were not possible due to limitations in the magnetometer. Saturation magnetization was found to decrease at 300 K compared to 100 K for AlMnN grown at T^in = 650°C. The values of temperature dependent saturation magnetization of AlMnN are shown in Figure 14.22. This data indicates an approaching TQ
Ferromagnetism in GaN and Related Materials 1.0x10"^ n
1
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1
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1
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415 '
r
8.0x10-^H
6.0x10-^H CD N
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4.0x10-® -AIMnN, TMn = 650
c
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^
2.0x10^
"m C O
0.050
100
150
200
"T"
T"
250
300
Temperature (K) Figure 14.22. Saturation magnetization versus temperature for single-phase AlMnN grown at 650°C. Saturation magnetization was extracted from SQUID hysteresis loops.
for this material. However, hysteresis persisted to 300 K, demonstrating soft ferromagnetism at room temperature. Figure 14.23 depicts the field dependence of magnetization for AlMnN and AINfilms.Pure AIN grown under the same conditions as AlMnN demonstrated paramagnetic behavior. This indicates that ferromagnetism arises with the addition of Mn. The diamagnetic background due to the sapphire substrate was subtracted from the raw data and the subsequent corrected data was used for analysis. The magnetization was not normalized to the Mn concentration due to the difficulty in calculation of the precise amount of Mn in the films. Perpendicular measurements were found to have lower values for saturation magnetization in AlMnN films. The hysteresis observed in the AlMnN is believed to arise from the inclusion of Mn into the AIN lattice. Clusters of second phases, undetectable by methods mentioned above, are not thought to be the cause of ferromagnetism observed at 300 K. This is supported by magnetic analysis of material containing the most likely cluster phases, AlMn and Mn4N. Magnetization as a function of temperature for AIN, single-phase AlMnN, AlMnN with an AlMn phase present, and Mn4N show substantially different behavior, as shown in Figure 14.24. The reason for the low T paramagnetic behavior seen in AIN and AlMnN films is still unknown. The M versus T of Mn4N clearly indicates ferromagnetic behavior, and the formation of clusters has been proposed as the cause of hysteresis in some ferromagnetic III-V materials. However, the formation of Mn4N clusters does not
416
Optoelectronic Devices: Ill-Nitride 2.0x10-5
1
1.5x10-5
1
•
I
-
I
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1
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AIMnN,TMn=650
TT
Il
1.0x10-5
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^
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ji
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-2.0x10-5
J
-1000
-500
0 H(Oe)
500
.
1
1000
Figure 14.23. Magnetization versus applied field for single-phase AlMnN.
influence the magnetization above 250 K, since clearly the magnetization drops to zero at that temperature. Also, the magnetization versus temperature indicates that the formation of AlMn clusters is not the cause of the ferromagnetism observed, evidenced by the order of magnitude difference between the values of magnetization over 150 K. Hence, the incorporation of Mn into the AIN lattice forming the ferromagnetic ternary AlMnN is most likely the reason for the observed hysteresis. In conclusion, room temperature ferromagnetism has been observed in AlMnN grown by gas-source MBE. The lattice constant decreased with increasing Mn cell temperature for single-phase material, indicating constant site occupation, probably substitutional. Hysteresis in M versus H at room temperature was observed in single-phase material and the magnetization as a function of temperature suggests ferromagnetism caused by AlMnN, not clusters. Ferromagnetism has also been observed in transition metal-implanted films. Implantation of Cr~^, Co"^ or Mn"^ ions was carried out at an energy of 250 keV (corresponding to a projected range of ~ 1500 A in each case) and a fixed dose of 3 X 10^^ cm~^. As a rough guide, the peak transition metal concentrations, located at the projected range, are ~ 3 at.% in the AIN. After implantation, the samples were annealed at 950°C, 2 min under flowing N2. PL measurements were carried out with a quadrupled Ti: sapphire laser as an excitation source together with a streak camera, providing an excitation power of ~ 3 mW at 196 nm [72].
Ferromagnetism in GaN and Related Materials
— ' — 1 — ' — I — ' — I — ' — I —
1.5x10"
1.0x10-
i ' 5.0x10-^1
All
—•— single phase AIMnN ~^e- AIMnN/AIMn -B-AIN - Mn,N
— AIMnN »-AIMnN/AIMn »-AIN
v;v-vvA \/X/\ A \ A
• ^ } A ^
0.0 50
100
150
200
Temperature (K)
250
/ 300
50
100
150
200
250
300
Temperature (K)
Figure 14.24. Magnetization versus temperature for AIN, AIMnN, Mn4N and AIMnN/AlMn. The magnetic signal is determined by subtracting the zero field-cooled trace from the field-cooled curve.
PL spectra taken at 10 K of the AIN implanted with Cr, Mn or Co after annealing at 950°C for 2 min looked basically identical in each case, even without annealing. The unimplanted AIN showed strong band-edge emission at ~ 6.05 eV and two broad emission bands related with deep level impurities at —3.0 and 4.40 eV each of which had peak intensity of ~ 1% of the band-edge emission intensity. The Cr-, Mn- and Co-implanted AIN showed an absence of band-edge emission, which suggests that the point defect recombination centers created during implantation are stable against annealing at 950°C. Well-defined hysteresis was present in the Co-implanted AIN, with a coercive field of ~ 160 Oe at 300 K and 230 Oe at 10 K. The diamagnetic contributions from the substrate have been subtracted out of the data. At 300 K, the saturation moment, MQ = glJi^S, where g is the degeneracy factor, [x^, the Bohr magnetron and 5, the total number of spins, was calculated to be ~ 0.65/xg for Cr. This value is lower than the theoretical value of 3/>IB expected for a half-filled d-band of Cr, if all of the Cr ions were participating in the ferromagnetic signal. Disorder effects due to implantation-induced change may contribute to creating a distribution of exchange couplings that favor antiferromagnetism and reduce the effective magnetism. Similar data is shown in Figure 14.25 for the Co-implanted AIN. Once again there is hysteresis present at 300 K, with a coercive field of ~ 1750 Oe at 300 K and 240 Oe at 100 K and a calculated saturation moment of 0.52/XB for Co. The FC and ZFC magnetization versus temperature are shown at the bottom of the figure. In this case the differences extend to —100 K. Figure 14.26 (top) shows magnetization versus field at 100 K for Mn-implanted AIN. This was the highest temperature for which clear hysteresis could be obtained. The coercive field was —220 Oe at both 100 and 10 K. The FC and ZFC phases are almost coincident at an applied field of 500 Oe, as shown at the bottom of the figure and consistent
418
Optoelectronic Devices: Ill-Nitride
with lower overall magnitude of the magnetization. The calculated saturation moment was for Mn at 100 K, compared to the theoretical value of four. The main 6-26 XRD peaks of the Cr or Mn-implanted samples after 950°C annealing correspond to the expected A1N(0002) and (0004) lines and AI2O3 (0002),(0006) and (0012) substrate peaks and the broad peak at 2^ = 20° is due to short-range disorder from the implantation process and was not observed on the as-grown films. No peaks due to the half-metallic ferromagnetic Cr02 phase were detected in the Cr-implanted sample and other potential second phases which could form, such as Cr, CrN [73-75], Cr2N and Al^^-Cr^;) were not detected and in any case are not ferromagnetic at the temperatures used in these experiments. Similarly, in the case of Co implantation, metaUic Co has a Curie temperature of 1382 K and CO;,N phases are all Pauli ferromagnetic. Finally, for Mn implantation, metallic Mn is antiferromagnetic while Mn;cN is ferromagnetic with a Curie O.IT^LB
AIN:Co 3%
1.0x10-^
1^ 5.0x10-6-1
..!!'S .\\
300 K
ii
0.0 c -5.0x10-®-^ -1.0x10-5-1
iiU''^
-1000
1000 H (Gauss)
-1.0x10-5 h AIN:Co 3% 500 Oe
-1.1x10-5 i? E (U
-1.2x101-5 ^T J^^^-^^.^-^^ -1.3x10-5 50
100
150
200
250^ 300
Temperature (K) Figure 14.25. Magnetization (300 K) as a function of field (top) and FC and ZFC magnetization as a function of temperature (bottom) for AIN implanted with 3 X 10^^ cm"^ Co^ and annealed at 950°C, 2 min.
Ferromagnetism in GaN and Related Materials
419
temperature of 745 K. Thus, secondary ferromagnetic phases are not responsible for the observed magnetic properties. The origin of the observed ferromagnetism is not likely to be carrier-mediated due to the insulating nature of the AIN. Wu et al. [53] suggested that substitutional Al^^Cri-^cN random alloys would have Curie temperatures over 600 K, as estimated from a multicomponent mean-field theory in which the ferromagnetism occurs in a midgap defect band. Another possible mechanism for the observed magnetic properties is that the Mn is not randomly distributed on Al sites but is present as atomic scale clusters. Some mean field theories suggest that Mn clustering can significantly influence TQ as a result of the localization of spin polarized holes near regions of higher Mn concentration. There is also some support for this assertion from local spin density approximation calculations, which predict that it is energetically favorable for the formation of magnetic ion dimers 6x10-6 4x10-6
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if
111.::-
-6x10-6 -1000
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500
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H (Gauss)
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500 Oe
E S
-1.7x10-^
-1.8x10-^ .
-1.9x10-5
•
'
50
100
•
'
•
150
200
I
I
250
L I
i_
300
Tennperature (K)
Figure 14.26. Magnetization (100 K) as a function of field (top) and FC and ZFC magnetization as a function of temperature (bottom) for AIN implanted with 3 X 10^^ cm"^ Mn+ and annealed at 950°C, 2 min.
420
Optoelectronic Devices: Ill-Nitride
and trimers at second nearest-neighbor sites which are ferromagnetic. The percolation network-Hke model for ferromagnetism in low carrier concentration systems suggested by several groups is another potential mechanism. High doses (3 X 10^^ cm~^) of ion-implanted Co"^, Cr"^ or Mn"^ ions into AIN epilayers on AI2O3 substrates severely degrades the band-edge luminescence, which is not recovered by annealing up to 950°C. In each case the implanted AIN shows ferromagnetic ordering as evidenced by the presence of hysteresis in M versus H loops. The hysteresis persists up to > 3 0 0 K in the case of Cr^ or Co"^ implantation and 100 K for Mn"^ implantation. Less than ~ 20% of the implanted ions contribute to the magnetization, but this might be increased by the use of much higher annealing temperatures. Simple twoterminal resistivity measurements show that the implanted AIN remains insulating (> 10^ n cm) and thus conventional carrier-mediated ferromagnetism is not a likely mechanism for the observed magnetic properties. Implantation provides a versatile method of introducing different transition metal dopants into AIN for examination of their effect on the structural and magnetic properties.
14.6. AlGaN There is also an interest in the use of transition metal-doped AlGaN for possible applications in spintronic devices such as polarized light emitter or spin transistors. The latter exploits quantum interference effects provided electrons with a particular spin can be injected into the channel of the device and a gate bias can be applied to cause splitting of spin-up and spin-down states. A key requirement for spin-based semiconductor devices is the achievement of ferromagnetism, preferably above room temperature. The properties of implanted transition metals in AlGaN is of particular relevance for realization of polarized light emitters or spin transistors since it could serve as the cladding layer in the former and the wide bandgap part of the heterostructure in the latter. 0-26 XRD scans from the n-AlGaN before and after Mn"^, Co"^ or Cr"^ implantation and annealing at 1000°C did not show any observable differences. The highest intensity peaks in all spectra correspond to the expected AlGaN (0 0 0 2) and (0 0 0 4) lines and AI2O3 (0 0 0 2), (0 0 0 6) and (0 0 0 12) substrate peaks. We did not observe any peaks due to second phases that could exhibit ferromagnetism. For example, in the Mn-implanted material, Mn^^N is ferromagnetic with a Curie temperature of 745 K and GaMn is also ferromagnetic with a Curie temperature near 300 K (metallic Mn is antiferromagnetic). In the Co"^-implanted AlGaN, metallic Co has a Curie temperature of 1382 K and Co^^N phases are all Pauli ferromagnetic. Finally, in the Cr'^-implanted AlGaN, CrO is a halfmetallic, while Cr, CrN, Cr2N, Al;,Cr_y and Ga^^Cr^ are not ferromagnetic [36]. However, in such thin layers, it could be possible for small quantities of second phases to be present and remain undetectable by XRD.
Ferromagnetism in GaN and Related Materials
All
Well-defined hysteresis at 300 K was observed for the Co-implanted Alo.38Grao.62N, as shown at the top of Figure 14.27. The coercive field was ~ 85 Oe at 300 K and ~ 75 Oe at 10 K. The saturation magnetization was ~ 0.4 emu/cm^ or ~ 0.76^lB calculated saturation moment. This is slightly higher than the value reported for Co~^ implantation into pure AIN under similar conditions (0.52/XB). which is consistent with the higher vacancy concentrations expected to be created in AlGaN due to its lower bond strength. 0.6
1
0.4 I1
£ 0)
'
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T
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n-AIGaN:Co
T = 300K
0.2 I-
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1
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-: • • -0.2 CD
-0.4
-0.6
I
.
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.
-500
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-0.34 -0.35 -0.36 -0.37 -0.38-1 -0.39 H -0.40 -0.41 -0.42 -0.43 H -0.44 -0.45 -0.46 -0.47
1
.
0 H(Oe)
1
•
500
1 1
1000
- Zero field cooled - Field cooled H = 250Oe n-AIGaN:Co
^
50
•|i^-o'5. ^ ^ ^
100 150 200 Temperature (K)
250
300
Figure 14.27. Magnetization (300 K) as a function of field (top) and field-cooled (FC) and zero field-cooled (ZFC) magnetization versus temperature for AlGaN implanted with 3 X 10^^ Co^ annealed at 1000°C for 2 min.
422
Optoelectronic Devices: Ill-Nitride
The bottom part of Figure 14.27 shows the temperature dependence of FC and ZFC magnetization for the Co'^-implanted AlGaN. The fact that these have different values out to ~ 230 K is a further indication of the presence of ferromagnetism in the material. In both epitaxial and ion-implanted transition metal-doped semiconductors, we have found the general result that the hysteresis can be detected to higher temperatures than the difference in FC and ZFC magnetization. As mentioned earlier, the samples exhibited low carrier densities ( < 3 X lO^^cm"^ from Hall measurements) after implantation and annealing, and therefore, carrier-mediated ferromagnetism by free electrons is not expected to be operative. In addition, the Co ionization level is expected to be deep in the AlGaN bandgap, so that there will be no significant contribution to the carrier density from the substitutional fraction of these atoms. More recent percolation network models for ferromagnetism in DMSs suggest that localized carriers may mediate the interaction between magnetic ions in low carrier density systems. The Mn-implanted p-type AlGaN also showed a well-defined hysteresis loop at 300 K, with a coercivity of ~ 6 0 O e (Figure 14.28, top). The saturation moment, MQ = SIHBS where g is the degeneracy factor, /xg the Bohr magneton and S the total number of spins was calculated to be ~ 0.57/XB- The theoretical value would be four if all of the implanted Mn was participating towards the ferromagnetism, so the lower experimental value indicates that only a fraction of the Mn is substitutional and magnetically active. The saturation moment for AlGaN is significantly larger than the value of 0.17/^3 reported for Mn implantation into pure AIN. The temperature dependence of FC and ZFC magnetization is shown at the bottom of Figure 14.28. The ferromagnetism is very weak above ~ 125 K, but is detectable through the hysteresis. By sharp contrast to the case of Mn implanted into p-AlGaN, when we performed the same implants into n-AlGaN, the resulting differences in FC and ZFC magnetization were very weak and hysteresis loops even at 10 K did not show clear evidence of ferromagnetism. The differences from the p-type material may result from the higher AIN mole fraction in the n-type AlGaN, which makes it harder for the implanted ions to become substitutional upon annealing. An alternative explanation is that holes are more efficient at ferromagnetic coupling between the Mn spins than are electrons. This has been reported previously for both n- and p-type GaAs and GaP doped with Mn. We also did not observe any clear evidence for ferromagnetism in the Cr-implanted n-AlGaN. This is a clear difference from the case of Cr-implanted AIN, where hysteresis was reported at 300 K. In conventional DMSs such as (Ga,Mn)As, the magnetization is given by [11] M = ^,^,SNoX,,Bs[
k^^T + T^,)
J
in the mean-field approach, where S is the localized spin, NQ is the concentration of cation sites, Xgff is the effective spin concentration, B^ is the Brillouin function and FQ(M) is the hole contribution to the free-energy functional F (which depends on the magnetization of
Ferromagnetism in GaN and Related Materials
423
0.4 0.3 p-AIGaN:Mn 0.2
T = 300 K
0.1
^hii
0.0
• • -0.1 -0.2
iiii*'
-0.3 -0.4
-1000
-500
0
500
1000
H(Oe)
E o 0 c
-0.085 4 -0.090 4 -0.095 4 -0.100 4 -0.105 4 -0.110 4 -0.1154 -0.120 4 -0.125 4 -0.130 4 -0.135 4 -0.140 4 -0.145 4 -0.150 4 -0.155 4 -0.160 4
Zero field cooled Field cooled H = 250 Oe
50
100 150 200 Temperature (K)
250
300
Figure 14.28. Magnetization (300 K) as a function of field (top) and field-cooled (FC) and zero field-cooled (ZFC) magnetization versus temperature for AlGaN implanted with 3 X 10^^ Mn^ annealed at 1000°C for 2 min.
the localized spin). The validity of this model depends on having a high carrier concentration in the magnetic semiconductor and experimentally we do not observe this in the AlGaN and correspondingly we do not observe a Brillouin-like dependence of magnetization on temperature. In pure AIN, Mn produces an absorption line at ~ 1.5 eV from the valence band, suggesting the Mn^^^^"^ acceptor level is deep in the gap and makes
424
Optoelectronic Devices: Ill-Nitride
the realization of carrier-mediated ferromagnetism unlikely. The mean field models have also shown that Mn clustering can enhance the Curie temperature through localization of localized carriers at these clustered regions. Some calculations suggest it is energetically favorable to form ferromagnetic transition metal ion dimers and trimers at second nearestneighbor sites. Distant pairs would be weakly ferromagnetic or antiferromagnetic. These predictions suggest that the ferromagnetism will be a very strong function of the synthesis conditions used for the magnetic semiconductor. They also suggest that non-equilibrium methods such as ion implantation possess inherent advantages in trying to maximize the Curie temperature because of their ability to achieve solid solubilities for dopants well above those possible with equilibrium synthesis methods.
14.7. POTENTIAL DEVICE APPLICATIONS
Previous articles have discussed some spintronic device concepts such as spin junction diodes and solar cells, optical isolators and electrically controlled ferromagnets [76-80]. The realization of LEDs with a degree of polarized output has been used to measure spin injection efficiency in heterostructures. While the expected advantages of spin-based devices include non-volatility, higher integration densities, lower power operation and higher switching speeds, there are many factors still to consider in whether any of these can be realized. These factors include whether the signal sizes due to spin effects are large enough at room temperature to justify the extra development work needed to make spintronic devices and whether the expected added functionality possible will materialize. Among such devices the simplest seems to be the concept of an LED with one of the contact layers made ferromagnetic by incorporation of transition metal impurities, a socalled spin-LED [77-79]. Such a device should allow to modulate the polarization of the light emitted by the spin-LED by application of an external magnetic field. The most straightforward approach to achieve this goal would be to implant Mn into the top contact p-GaN layer of the standard GaN/InGaN LED. The electrical and luminescent properties of such devices show that they do produce electroluminescence, but due to the difficulty in annealing out all radiation defects the series resistance and the turn-on voltage of such spin-LEDs are very much higher than for ordinary LEDs and the electroluminescence intensity EL is lower. GaMnN layers produced by MBE have a lower density of defects and may be better suited for spin-LEDs. One of the problems with the latter approach is that the MBE-grown GaMnN films with high Curie temperature have n-type conductivity. Therefore, to incorporate such layers into the GaN-based LEDs one has to reverse the usual order of layers and grow an LED structure with the contact n-layer up. It was shown that problems such as higher series resistance due to lower lateral conductivity of p-GaN compared to n-GaN are inherent to these inverted diodes. Also it was shown that it is more
Ferromagnetism in GaN and Related Materials
425
difficult to attain a high quahty of the GaN/InGaN multi-quantum-well (MQW) active region when growing it on top of a very heavily Mg-doped p-GaN layer. Incorporation of Mn into the top contact layer also produced a relatively high resistivity of the GaMnN and poorer quality of the ohmic contact. In addition, the ferromagnetism in GaMnN is found to be unstable against the type of high temperature (900°C) anneals used to minimize contact resistance. The reference n-LED structure studied consisted of 2-|ULm-thick undoped semiinsulating GaN, 2-|xm-thick p-GaN(Mg), five undoped QWs of InGaN (—40% In, 3 nm), separated by Si-doped n-GaN barriers (10 nm each) and about 170-nm-thick top n-GaN contact layer. All the layers but the top n-GaN layer were grown by MOCVD in the regime similar to the one used to fabricate standard p-LED structures. The n-type layer was grown by MBE at 700°C. The spin-LED structure differed from the n-LED structure by the structure of the top n-layer which consisted of 20 nm of n-GaN(Si) and 150 nm of GaMnN with the Mn concentration close to 3%. The GaMnN layer was grown at 700°C. All structures were subjected to rapid thermal anneal in nitrogen to activate the Mg acceptors. However, the spin-LED structure was given only a 750°C anneal since the degree of magnetic ordering in the GaMnN MBE-grown layer was greatly reduced upon annealing at temperatures exceeding 800°C. A schematic of the LED structure is shown in Figure 14.29, along with an electroluminescence spectrum taken at 300 K. Room temperature I-V characteristics of the reference structure and the spin-LED structure are compared in Figure 14.30. The spin-LED structure shows a reduced current in both forward and reverse directions. For comparison we also present the I-V characteristic measured on the similarly grown spin-LED structure for which the contacts annealing temperature was 900°C. Obviously, the reduced contact annealing temperature leads to further decrease of the current, because the contact resistance to the p-type layer was higher. This is confirmed by I-V measurements in the dark and with illumination at 85 K. In the test structure the open-circuit voltage deduced from these measurements was about - 0.5 V and had the right sign. For the spin-LED structure studied in this paper the sign of the open circuit voltage upon illumination was positive and the open-circuit voltage was about 1 V, i.e. opposite to normal, most likely due to the parasitic Schottky contact with the lower p-type contact layer. With increasing temperature the situation improved and the sign of the open-circuit voltage became negative, i.e. normal, at temperatures close to 160 K, but the impact of the parasitic Schottky diode was felt at all temperatures in the decreased current and decreased capacitance. For the reference diode, the temperature dependence was slight in both directions showing an activation energy of about 0.17 eV and ideality factor at temperatures higher than room temperature close to 2.5. This was explained by thermally assisted tunneling via the active MQW region. The onset of measurable electroluminescence signal in the test structure was close to 4 V. For the spin-LED structure corresponding activation energies
426
Optoelectronic Devices: Ill-Nitride ffW^^^^MM^W
GaN : Si 100 GaMnN
100 nm
GaN : Si 20 nm GaN : Si 10 nm InGaNM 3 nm GaN i
B I ^^^^^^^ GaN
V c y / ^ ^
lOnm
Mg 2|Lim
GaN i
2|im
Sapphire
420
430
440
450 460 470 Wavelength (nm)
480
490
Figure 14.29. Schematic of led structure (top) and measured 300 K EL spectrum (bottom).
as deduced from Arrhenius plots were close to 0.5-0.6 eV. The ideality factor in the forward direction, if deduced formally from I-V curves, was very high, close to 10. For higher forward voltages between approximately 5 and 10 V the temperature dependence of the forward current was small. Measurable EL signal could be detected at forward voltages close to 15 V and at these forward voltages the temperature dependence of the current again became relatively strong and showed an activation energy of 0.27 eV. At low forward biases the / - V dependences were of the form / - V " with a= 1.4. At higher biases the slope increases to 2.5. At voltages near 2 V the current jumps to another a = 2.5 region that prevails up to about 10 V when the current starts to increase sharply and shows an exponent value of about 8.4, but actually increases exponentially. The magnitude of the jump becomes lower with increasing temperature and the temperature dependence of the current at the second a = 2.5 region is very slight. Illumination of the diode in the rested state with UV light of the deuterium lamp led to a very strong increase of the current and the current remained considerably higher than the dark value after the light was switched off. Illumination of the diode with extrinsic light of either GaAs LED arrays (peak photon energy of 1.4 eV) or AlGaAs LED arrays (peak photon energy of
Ferromagnetism in GaN and Related Materials
- 1 6 - 1 4 - 1 2 -10 - 8
-6
-4
All
-2
Voltage (V) Figure 14.30. Room temperature / - V characteristics of control LED (curve 1), of the old spin-LED amiealed at 900°C to form contacts (curve 2) and of the new spin-LED annealed at 750°C to form contacts (curve 3).
1.9 eV) led to much lower than intrinsic UV light increase of photocurrent in the reverse direction and for low forward voltages. Both spin-LEDs showed lower capacitance on the low-frequency plateau indicating that some high-resistivity Schottky diode is switched in series with the normal Schottky diode. This is also confirmed by C-V measurements that, for control sample, show a normal voltage intercept of 1.9 V and a concentration of IXlO^^cm"^ while both spin-LEDs show an un-physically high intercept values exceeding the bandgap of GaN and very high apparent concentrations on the order of 10^^ cm~^. The PICTS spectrum measured on our spin-LED structure at 0.5 V with the deuterium UV lamp light source showed three major features. The first feature was a negative-sign peak (relative to the ordinary sign of the peaks in PICTS) near 120 K with apparent activation energy of 0.16 eV. At these temperatures the sign of photocurrent is "wrong" due to the parasitic Schottky diode with the lower p-GaN contact layer which explains the wrong sign of the peak and allows us to unambiguously relate it to the lower p-type layer. The second feature was a normal-sign shoulder near 320 K with apparent activation energy of 0.8 eV. Finally, at higher temperatures one could see a steady increase in signal due to some very deep trap whose peak position (>1.4eV) could not be measured even with the longest time windows used (current relaxation curves measured for 100 s at each temperature point up to 400 K). Room temperature MCL and EL spectra of the new spin-LED both showed an intense line peaked near 2.7 eV is dominant, which comes from the GaN/InGaN MQW active region. At 90 K the MCL spectra showed, in addition to the intense 2.7 eV band, two bands peaked near 2.5 and 2.95 eV. The position of the 2.7 and 2.95 eV bands shifted to lower
428
Optoelectronic Devices: Ill-Nitride
energies with increased excitation intensity. The 2.95 eV band is due to some Mn-related centers with a level near 0.5 eV below the bottom of conduction band as discussed in some detail in Refs. [20,21,25]. The 2.5 eV band is thought to be due to luminescence from InGaN QWs with higher In contents formed due to partial separation of the solid solution. The parasitic diode formed with the lower p-GaN layer is detrimental to the device performance. Two approaches could be tried to alleviate the problem. The first is to check if donor co-doping of the GaMnN layer could be achieved without compromising the high Curie temperature of the material. If successful, this procedure should improve the led turn-on voltage. The second approach would be to try to incorporate one more n-GaN layer on top of the GaMnN film. This should improve the ohmic contact to the n-type portion of the structure and improve electron injection into the GaMnN film and thus into the active GaN/InGaN MQW region of the structure. We have shown that measurable electroluminescence signals could be obtained from spin-LED structures with the n-GaMnN layer on top even when the contact annealing temperature is maintained below 800°C in order not to destroy the magnetic ordering in the GaMnN film. With this low process temperature, however, a parasitic Schottky diode with the lower p-GaN contact layer is formed and manifests itself in reduced forward current at high voltages, reduced capacitance of the structure, higher threshold voltage for obtaining a measurable EL signal. In addition, the current at low forward voltages and at reverse voltage is limited by another parasitic junction which we believe to be the i-GaMnN/n-GaN junction in the top contact layer. The forward current at low voltages shows signs of the trap-filling regime and from the activation energy of the current in this region the main traps believed to be located in the GaMnN film have the levels near 0.5-0.6 eV from the bottom of conduction band and could be the same Mn-related centers observed previously in Mn-implanted films and in GaMnN films grown by MBE. Deep level spectra measurements in these spin-LEDs reveal the presence of 0.16 eV Mg acceptors and 0.4 eV hole traps in the p-GaN region and of 0.55 and 0.8 eV traps that are located most likely in the GaMnN layer.
14.8. ISSUES TO BE RESOLVED
The mean-field models consider the ferromagnetism to be mediated by delocalized or weakly localized holes in the p-type materials. The magnetic Mn ion provides a localized spin and acts as an acceptor in most III-V semiconductors so that it can also provide holes. In these models, the TQ is proportional to the density of Mn ions and the hole density. Many aspects of the experimental data can be explained by the basic mean-field model. However, ferromagnetism has been observed in samples that have very low hole concentrations, in insulating material and more recently in n-type material.
Ferromagnetism in GaN and Related Materials
429
More work is also needed to establish the energy levels of the Mn, whether there are more effective magnetic dopant atoms and how the magnetic properties are influenced by carrier density and type. Even basic measurements such as how the bandgap changes with Mn concentration in GaN have not been performed. The control of spin injection and manipulation of spin transport by external means such as voltage from a gate contact or magnetic fields from adjacent current lines or ferromagnetic contacts is at the heart of whether spintronics can be exploited in device structures and these areas are still in their infancy.
ACKNOWLEDGEMENTS The work at UF was partially supported by NSF-DMR 0101438 and by the US Army Research Office under grants nos. ARO DAAD 19-01-1-0710 and DAAD 19-02-1-0420, while the work at SNU was partially supported by KOSEF and Samsung Electronics Endowment through CSCMR and by the Seoul National University Research Foundation. The authors are very grateful to their collaborators A.F. Hebard, D.P. Norton, S.N.G. Chu, J.S. Lee, and Z.G. Khim.
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[17] Bhatt, R.N., Berciu, M., Kennett, M.D. & Wan, X. (2002) J. Superconduct.: Incorporating Novel Magnet., 15, 71. [18 Litvinov, V.I. & Dugaev, V.A. (2001) Phys. Rev. Lett., 86, 5593. [19 Konig, J., Lin, H.H. & MacDonald, A.H. (2001) Phys. Rev. Lett., 84, 5628. [20 Schliemann, J., Konig, J. & MacDonald, A.H. (2001) Phys. Rev. B, 64, 165201. [21 Reed, M.L., Ritums, M.K., Stadelmaier, H.H., Reed, M.J., Parker, C.A., Bedair, S.M. & El-Masry, N.A. (2001) Mater Lett., 51, 500. [22: Reed, M.L., El-Masry, N.A., Stadelmaier, H., Ritums, M.E., Reed, N.J., Parker, C.A., Roberts, J.C. & Bedair, S.M. (2001) A/?/?/. Phys. Lett., 79, 3473. [23 Theodoropoulou, N., Hebard, A.F., Overberg, M.E., Abemathy, C.R., Pearton, S.J., Chu, S.N.G. & Wilson, R.G. (2001) Appl. Phys. Lett., 78, 3475. [24: Overberg, M.E., Abemathy, C.R., Pearton, S.J., Theodoropoulou, N.A., McCarthy, K.T. & Hebard, A.F. (2001) Appl. Phys. Lett., 79, 1312. [25 Sonoda, S., Shimizu, S., Sasaki, T., Yamamoto, Y. & Hori, H. (2002) /. Cryst. Growth, 237-239, 1358. [26: Kim, K.H., Lee, K.J., Kim, D.J., Kim, H.J., Ihm, Y.E., Djayaprawira, D., Takahashi, M., Kim, C.S., Kim, C.G. & You, S.H. (2003) Appl. Phys. Lett., 82, 1775. [27: So, Y.L., Kioseoglou, G., Kim, S., Huang, S., Koo, Y.H., Kuwarbara, S., Owa, S., Kondo, T. & Munekata, H. (2001) Appl. Phys. Lett., 79, 3926. [28: Kuwabara, S., Kondo, T., Chikyou, T., Ahmet, P. & Munekata, H. (2001) Jpn. J. Appl. Phys., 40, L724. [29 Thaler, G.T., Overberg, M.E., Gila, B., Frazier, R., Abemathy, C.R., Pearton, S.J., Lee, J.S., Lee, S.Y., Park, Y.D., Khim, Z.G., Kim, J. & Ren, F. (2002) Appl. Phys. Lett., 80, 3964. [3o: Hori, H., Sonoda, S., Sasaki, T., Yamamoto, Y., Shimizu, S., Suga, K. & Kindo, K. (2002) Physica B, 324, 142. [31 Pearton, S.J., Abemathy, C.R., Norton, D.P., Hebard, A.F., Park, Y.D., Boatner, L.A. & Budai, J.D. (2003) Mat. Sci. Eng., R40, 137. [32: Pearton, S.J., Abemathy, C.R., Overberg, M.E., Theodoropoulou, N., Hebard, A.F., Park, Y.D., Ren, F., Kim, J. & Boatner, L.A. (2003) /. Appl. Phys., 93, 1. [33 Dhar, S., Brandt, O., Trampert, A., Daweritz, L., Friedland, K.J., Ploog, K.H., Keller, J., Beschoten, B. & Guntherhold, G. (2003) Appl. Phys. Lett., 82, 2077. [34 Park, M.C., Huh, K.S., Hyong, J.M., Lee, J.M., Chung, J.Y., Lee, K.I., Han, S.H. & Lee, W.Y. (2002) Solid State Commun., 124, 11. [35 Lee, J.S., Lim, J.D., Kim, G., Park, Y.D., Pearton, S.J. & Chu, S.N.G. (2003) J. Appl. Phys., 93, 4512. [36: Ando, K. (2003) Appl. Phys. Lett., 82, 100. [37 Baik, J.M., Kim, J.K., Yang, H.W., Shon, Y., Kang, T.W. & Lee, J.L. (2002) Phys. Stat. Sol. (b), 234, 943. [38 Sarder, K., Raju, A.R., Basal, B., Venkataraman, V. & Rao, C.N.R. (2003) Solid State Commun., 125, 55. [39: Baik, J.M., Yang, H.W., Kim, J.K. & Lee, J.-L. (2003) Appl. Phys. Lett., 82, 583. [40: Shon, Y., Kwon, Y.H., Yuldashev, Sh.U., Park, Y.S., Fu, D.J., Kim, D.Y., Kim, H.S. & Kang, T.W. (2003) J. Appl. Phys., 93, 1546. [41 Dietl, T., Ohno, H. & Matsukura, F. (2001) Phys. Rev. B, 63, 195205. [42 Dugaev, V.K., Litvinov, V.I., Bames, J. & Viera, M. (2003) Phys. Rev. B, 67, 033201. [43 Schliemann, J. (2003) Phys. Rev. B, 67, 045202. [44: Rao, B.K. & Jena, P. (2002) Phys. Rev. Lett., 89, 185504.
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[45] Korotkov, R.Y., Gregie, J.M. & Wessels, B.W. (2002) Appl Phys. Lett, 80, 1731. [46] Graf, T., Gjukic, M., Brandt, M.S., Stutzmann, M. & Ambacher, O. (2002) Appl. Phys. Lett., 81, 5159. [47] Polyakov, A.Y., Govorkov, A.V., Smimov, N.B., Pashkova, N.Y., Thaler, G.T., Overberg, M.E., Frazier, R., Abemathy, C.R., Pearton, S.J., Kim, J. & Ren, F. (2002) /. Appl. Phys., 92, 4989. [48] Theodoropoulou, N.A., Hebard, A.F., Chu, S.N.G., Overberg, M.E., Abemathy, C.R., Pearton, S.J., Wilson, R.G. & Zavada, J.M. (2001) Appl. Phys. Lett., 79, 3452. [49] Pearton, S.J., Overberg, M.E., Thaler, G., Abemathy, C.R., Theodoropoulou, N., Hebard, A.F., Chu, S.N.G., Wilson, R.G., Zavada, J.M., Polyakov, A.Y., Osinsky, A. & Park, Y.D. (2002) /. Vac. Sci. TechnoL, A20, 583. [50] Akinaga, H., Nemeth, S., De Boeck, J., Nistor, L., Bender, H., Borghs, G., Ofuchi, H. & Oshima, M. (2000) Appl. Phys. Lett., 77, 4377. [51] Hashimoto, M., Zhou, Y.Z., Kanamura, M. & Asahi, H. (2002) Solid State Commun., 122, 37. [52] Yang, S.G., Pakhomov, A.B., Hung, S.T. & Wong, C.Y. (2002) Appl. Phys. Lett., 81, 2418. [53] Wu, S.Y., Liu, H.X., Gu, L., Singh, R.K., Budd, L., Schilfgaaarde, M., McCartney, M.R., Smith, D.J., & Newman, N., to be published. [54] Liu, C , Alves, E., Ramos, A.R., da Silva, M.F., Soares, J.C, Matsutani, T. & Kiuchi, M. (2002) Nucl. Inst. Meth. Phys. B, 191, 544. [55] Ohno, H., Shen, S., Matsukura, F., Oiwa, A., Endo, A., Katsumoto, S. & lye, Y. (1996) Appl. Phys. Lett., 69, 363. [56] Janotti, L., Wei, S. & Bellaiche, L. (2003) Appl. Phys. Lett., 82, 766. [57] Martin, A.L., Spalding, CM., Dimitrova, E.I., Van Patten, P.G., Caldwell, M.C., Kordesch, M.E. & Richardson, H.H. (2001) /. Vac. Sci. TechnoL, A19, 1894. [58] Lu, F., Carius, R., Alam, A., Heuken, M. & Buchal, Ch. (2002) /. Appl. Phys., 92, 2457. [59] Cho, D.-H., Shimizu, M., Ide, T., Ookita, H. & Koumwa, H. (2002) Jpn. J. Appl. Phys., 41, 4481. [60] Hu, X., Deng, J., Pala, N., Gaska, R., Shur, M.S., Chen, C.Q., Yang, J., Simin, G., Khan, M.A., Rojo, J.C. & Schwalker, Z.J. (2003) Appl Phys. Lett., 82, 1299. [61] Serina, F., Ng, K.Y.S., Huang, C , Amer, G.W., Romni, L. & Naik, R. {20Q2) Appl. Phys. Lett., 79, 3350. [62] Lee, S.-H., Lee, J.-K. & Yoon, K.H. (2003) /. Vac. Sci. TechnoL, A21, 1. [63] Takagaki, Y., Santos, P., Wiebicke, E., Brandt, O., Schmerr, J.D. & Ploog, K. (2002) AppL Phys. Lett., 81, 2538. [64] Kipshidze, G., Kuryatkov, V., Zhu, K., Vorizov, B., Holtz, M., Nikishin, S. & Temldn, H. (2003) /. AppL Phys., 93, 1363. [65] Nishida, T., Kobayashi, N. & Ban, T. (2003) AppL Phys. Lett., 82, 1. [66] Gaska, R., Chen, C , Yang, J., Kookstis, E., Kahn, M.A., Tamulaitis, G., Yilmog, I., Shur, M.S., Rojo, J.C. & Schowalter, L.J. (2002) AppL Phys. Lett., 81, 4658. [67] Yang, S.G., Pakhomov, A.B., Hung, S.T. & Wong, C.Y. (2002) AppL Phys. Lett., 81, 2418. [68] Theodoropoulou, N., Hebard, A.F., Overberg, M.E., Abemathy, C.R., Pearton, S.J., Chu, S.N.G. & Wilson, R.G. (2003) Phys. Rev. Lett., 89, 107203. [69] Kucheyev, S.O., WiUiams, J.S., Zou, J., Jaegadish, C , Pophristic, M., Guo, S., Ferguson, LT. & Manasreh, M.O. (2002) /. AppL Phys., 92, 3554. [70] Li, J., Nam, K.B., Nakarmi, M.C., Lin, J.Y. & Jiang, H.X. (2002) AppL Phys. Lett., 81, 3365. [71] Hashimoto, M., Zhou, Y.-K., Kanamura, M. & Asahi, H. (2002) Solid State Commun., 122, 37. [72] Nam, K.B., Li, J., Kim, K.H., Lin, J.Y. & Jiang, H.X. (2001) AppL Phys. Lett., 78, 3690.
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Optoelectronic Devices: Ill-Nitride M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 15
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk and Dimensionally Confined Semiconductors and Their Device Implications Michael Stroscio^'^'"^ and Mitra Dutta*'*' ^Department of Bioengineering, University of Illinois at Chicago,Chicago, IL 60607, USA Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA ^Department of Physics, University of Illinois at Chicago, Chicago, IL 60607, USA
Fundamental properties of phonons in III-V nitrides are examined with a view toward understanding processes important in the operation of III-V nitride devices. Firstly, confined, interface and propagating modes in wurtzite quantum wells are described in terms of Loudon's model for uniaxial semiconductors and the dielectric continuum model. Basic properties of the phonon modes and carrier-phonon interactions are considered on the basis of this treatment of dimensionally confined phonons in both bulk and lowdimensional wurtzite structures. A key feature of these phonon modes is their enhanced dispersion and its origin from the non-isotropic nature of the wurtzites. As will be discussed, this dispersion has important consequences for phonon propagation and phonon energy spectra. The experimental results of the phonons in the wurtzites are summarized. An analysis of Raman linewidths measured for AIN and GaN wurtzites is made to estimate phonon lifetimes. The second-order phonon decay process of combined point-defect scattering and anharmonic decay is examined as a means of estimating line broadening associated with the decay of phonons in III-V nitrides of wurtzite structure containing point defects. Finally, the importance of understanding the role of interface-phonon interactions and surface-phonon interactions in the case of quantum dot lasers is discussed with the recent use of phonon-assisted transitions to improve the performance of semiconductor lasers by enhancing the population inversion. There has been much interest recently on compound semiconductors formed of group III elements and nitrogen. They have significant potential for optoelectronic and electronic devices due to the interesting properties of this system, including the relatively large bandgap, the large piezoelectric field, the relatively strong electron-phonon
E-mail address: [email protected] (M. Dutta).
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coupling and the relatively high polar-optical phonon energy [1-10]. This chapter concentrates on the phonons in this system of bulk materials as well as the lower dimensional structures; moreover, this chapter focuses on the understanding of how these phonons behave in these structures and their impact in device applications. This group of compounds called nitrides may be either in cubic or hexagonal structure. There has been much investigation of the cubic crystal systems, the archetypical case being the well-studied gallium arsenide-based compounds, and their vibrational modes in the bulk as well as in the lower dimensional systems are better understood both with respect to their basic properties as well as in the manner in which they impact device properties. The behavior of the phonons in the cubic nitrides is similar to those in these systems except for the values of their frequencies. The binary nitride compounds, GaN, AIN and InN can be grown both as wurtzites as well as in zinc blende structures [11-15]. The same is true of the ternary alloys of these materials. However, they are more common and are highly stable in the wurtzite structure [11] and most of the discussion in this chapter will dwell in the materials in this structure. However in some thin films, polymorphs are possible and Raman scattering to identify the phonons has been used as a method to determine the structure as well as the purity of the materials.
15.1.
PHONON MODES IN WURTZITE NITRIDE STRUCTURES
Wurtzite crystals have a more complicated unit-cell structure compared to zinc blende ones, as shown in Figure 15.1. They have four atoms per unit cell and are of lower
Figure 15.1. Unit cell of wurtzite structure.
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
435
Table 15.1. Phonon frequencies in cm~ ^ of wurtzite GaN modes from Raman scattering experiments Reference
E\
El
Ai(TO)
[21] [22] [23] [24] [25] [26] [27]
145
568 568 569 568 570 569 567
533 533 532 533
144 143 144 142
533 530
Ai(LO)
738 735
^i(TO)
^i(LO)
559 559 560 559
726
561 558
743
symmetry than the zinc blende crystals. As a result, they have nine optical and three acoustic phonon modes. The space group that the wurtzite crystals belong to is C^^ and the zone centered optical modes are Aj + IBi + £"1 + 2E2 from group theoretical considerations. The Ai.Ei and the two E2 modes are Raman active while the Ex modes are not observed in Raman scattering or are silent [16]. The Aj and the Ex modes are polar as there is a long-range electrostatic field in the crystal. This polar field splits the A^ and the El mode into the longitudinal and transverse components, creating Ai(LO,TO) and £'i(LO,TO) modes. Due to the optical anisotropy of uniaxial crystals, the long-wavelength lattice vibrations can be classified according to mutual orientation between the c-axis, the phonon wave vector q, the electric field E, and the polarization P [17,18]. This divides the lattice vibrations into two groups of phonons: the ordinary and extraordinary. For the ordinary phonon, E and P are both perpendicular to q and the c-axis, dispersionless, while the extraordinary phonon frequencies are dependent upon the angle between the phonon wave vector and the c-axis, 6^. Two of the optical extraordinary branches correspond to the A^ and Ex modes at the F point. For an arbitrary ^^, extraordinary phonons exhibit mixed polarization. The zinc blende structure is much simpler [19,20], with two atoms per unit cell, and belongs to the T2d space group. There is only one Raman active mode of F2 representation which due to the polar nature splits into the TO and LO modes. The Raman frequencies of the phonon modes of GaN are listed below (Table 15.1). The frequencies of the phonons are close in the two structures and can be attributed to the fact that the dispersion curve of the phonons in the wurtzite structure in the [0001] can be obtained by folding the zinc blende phonon dispersion along the [111] direction as one would expect from the increased number of atoms in the unit cell. The growth of the nitride materials has been an ongoing research effort for a while and crystalline forms of the materials have been obtained as needles, platelets as well as more recently in epitaxial layers. The first identification of the phonons in GaN that were Raman active in the wurtzite form were done by IVIanchon et al. [21], Lemos et al. [22], Bums et al. [23], IVlurugkar et al. [24], Cingolani et al. [25] and Azuhata et al. [26].
436
Optoelectronic Devices: Ill-Nitride Table 15.2. Phonon frequencies in cm~^ of zinc blende GaN modes from Raman scattering experiments Reference
TO
LO
[12] [14] [15] [28]
555
737 730 740 740
554 555
The measurements have been much more extensive in the wurtzite material compared to the zinc blende materials as good quality materials in this latter form are not easily obtained. However, measurements of phonons by Raman scattering have been reported by Miyoshi et al. [14] on zinc blende GaN grown in GaAs by metallorganic vapor phase epitaxy. Phonons of zinc blende, wurtzite and mixed phase GaN films grown by molecular beam epitaxy on GaAs substrates were studied by Giehler et al. [15]. Here the differences in the growth conditions were studied and the structural properties were analyzed by X-ray scattering and electron diffraction as well. It was shown here that samples grown under Ga-rich conditions grew predominantly in the wurtzite structure and those grown under the N-rich condition were in the zinc blende condition. Table 15.2 lists the frequencies for the phonons observed under different configurations in Raman scattering. Phonons in the two different structural conditions were also reported by Tabata et al. [12]. Here the GaN samples were grown on GaAs substrates via molecular beam epitaxy. Again the Ga to N flux ratio was used to obtain the different growth conditions. Aluminum nitride AIN and indium nitride InN also are like GaN in that in the stable state they have a wurtzite structure as well as a zinc blende structure. The Raman selection modes and the selection rules for the phonon modes are thus similar (Table 15.3).
Table 15.3. Phonon frequencies in cm ^ of wurtzite AIN and InN modes from Raman scattering experiments Reference
E\
El
Ai(TO)
Ai(LO)
^i(TO)
Wurtzite AIN [29] [30] [27] [31]
241 252 246 249
660 660 655 657
607 614 608 610
893 890
673 668
Wurtzite InN [32] [33]
495 491
^i(LO)
924 916 913
596 590
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
437
Some information exists on the stresses in the nitride layers obtained from growing on different nitrides by looking at the shifts in the frequency of the phonon modes [34-36].
15.2. DIELECTRIC CONTINUUM AND LOUDON'S MODEL
In uniaxial materials, Loudon [17,18] showed that the polar phonon characteristics may be affected via two interaction mechanisms: that due to the long-range electrostatic field and the other due to short-range field which has the anisotropy of the force constants. The phonon dynamics that results is due to the dominance of the two mechanisms. If the long-range electrostatic field is the dominant mechanism, the interaction of the polar phonons with the long-range electrostatic field may result in a significant frequency separation between the group of the transverse optical (TO) phonons and the longitudinal optical (LO) phonons and the TO phonons and the LO phonons are separately grouped in a fairly narrow frequency range. As shown by Loudon, the dielectric continuum model [37] may be used to discuss the phonons in a wurtzite structure. This can be done by treating the dielectric constant as having one value parallel to the c-axis and another value, perpendicular to the c-axis. It was shown by Loudon that the phonons in the wurtzite structure can be accurately described by the dielectric continuum model. Nusimovici and Birman [38] provided detailed results later on the lattice dynamics of CdS which has a wurtizite structure. The application of Loudon's model to describe the carrier-polar-optical-phonon interaction as well as the corresponding electron-optical-phonon scattering rates in wurtzite crystals will be discussed further, both for the bulk material and the lower dimensional structure. At ambient temperatures, scattering by polar optical phonons is the main mechanism influencing electron transport [39]. Phonon interactions play very important roles in intersubband laser devices, especially in optical-phonon-assisted intersubband transitions [37,40,41]; thus, a complete and thorough understanding of electron-phonon interaction mechanisms and rates is essential. The dielectric continuum model and the uniaxial model of Loudon were used by Lee et al. [42] to formulate a theory of confined optical phonons in wurtzite heterostructure systems. The Frohlich interaction Hamiltonian was derived for bulk wurtzite, and the subsequent scattering rates were calculated. Loudon's model [17,18] describing the macroscopic equations of uniaxial polar crystals by introducing one dielectric constant associated with the direction parallel to the c-axis, e^, and another dielectric constant associated with the direction perpendicular to the c-axis, s^ h useful in allowing extension to the uniaxial case. For phonon mode displacements, it is convenient to separate the displacements parallel
438
Optoelectronic Devices: Ill-Nitride "T
800
LO-Like 600 TO-Like 400
200 0
30
60
90
Angle 6,^ (deg) Figure 15.2. Angular variation of phonon frequencies in bulk GaN.
to the c-axis, denoted u^, and those perpendicular to it, denoted Uj_ [42]. The phonon frequency for ordinary phonons has a trivial solution (o= cj^ and E(r) = 0, while the phonon frequencies for extraordinary phonons can be obtained by 8j_(a>)sin^(^) + 8,(cu)cos^(^) = 0.
(15.1)
where s^((o)
«2-
- «iz. -0,2
0,20,2-
-^r
(15.2) (15.3)
For the wurtzite materials, the solutions become ^ o = ^zL cos^(^) + WIL sin^(^).
(15.4)
ft^o = ^z sin^(^) + (ol cos^(^).
(15.5)
These are predominantly longitudinal and transverse modes, respectively. Figure 15.2 shows the angular variation of the optical-phonon frequencies for GaN. The LO-like mode is almost flat thus indicating that the mode is weakly dependent upon the direction and the TO-like mode exhibits anisotropy. Recently, the angular variation for ZnO, CdS and CdSe have also been calculated [43]. The work of Shapiro and Axe [44] provided a detailed classification of the phonons in the wurtzite structures. In particular, Shapiro and Axe showed that the frequencies of
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
439
the phonons change with the change of the angle between the propagation direction and the c-axis. In directions that are not the principal axis of the crystal the phonons are of mixed symmetry and are termed quasi-LO or quasi-TO modes. These modes have been studied in Raman scattering by Filippidis et al. [45] and by Bergman et al. [46].
15.3. TERNARY ALLOYS Mixed crystals of the form ABi_^Q are classified into two main groups according to the behavior for the ^ ~ 0 optical phonons. There are two possible situations for zinc blende materials which have been well-studied and referred to as one mode and two-mode behavior [47]. In general, if the frequencies of the modes of the binary materials, AB and AC differ by a large amount then the mixed crystal follows the two mode behavior. If the mixed crystal follows the one-mode behavior then the frequencies of the two binaries that make up the ternary alloy have a much closer values. In addition, there is a third class where the ternary alloy has a one-mode behavior in one frequency range and a twomode behavior in another frequency range. There is a lack of consensus in the early experimental results where the work of Hayashi et al. [48] showed that in the composition range of 0 < jc < 0.15 the AlGaN alloy system exhibits a one-mode behavior. In another study, by Behr et al.[49] found that while the Ai(LO) phonon behaved in a one-mode fashion the E2 phonon showed no change due to alloying. The work of Cros et al. [50] indicated that the E2 mode was a two-mode type while the Al was one-mode. Demangeot et al. [51] found similar results in that Ai(LO), Ai(TO) and the Ei (TO) were all one-mode although infrared measurements of Wisniewski [52] et al. indicated conflicting results for the £'i(TO) modes. This underlines the lack of understanding of the vibrational properties of the alloys which are possibly tied to the difficulties in obtaining consistent material quality under differing growers and growth conditions. The polar phonons in three III-N ternary alloys have been studied theoretically [53] by using the modified random-element isodisplacement (MREI) model. The anisotropy wurtzite structure and the additional modes were added to previous models for the zinc blende structures. It was demonstrated that the polar modes of the ternary alloys GaAlN and GaInN follow a one-mode behavior. These results agree well with the experiments of Ref. [53] except for the £^i(TO) case. The one-mode behavior can be understood qualitatively in view of the fact that the nitrogen mass is significantly less than the mass of the other ions. Indeed, the nitrogen ions oscillate with one frequency with respect to planes of mixed group III elements. Demangeot et al. [51] have analyzed Raman data on Gai_^Al_^N based on a generalized dielectric model for coupled LO modes and have obtained support for the apparent one-mode behavior of the polar LO phonons. The MREI model [53] also demonstrates that the Aj and Ex optical
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Optoelectronic Devices: Ill-Nitride
phonons in Ga;cAli-;cN and In^^-Gai-^^N exhibit one-mode behavior unUke Ga;<:Ali_;»-As and In^Gsii-j^As, which exhibit two-mode behavior. Since the isotope mass affects the phonon frequency, Raman analysis of isotopic films may convey information on the elements controlling the mode-vibrations. Studies on the wurtzite structure of the GaN made from natural Ga and N have been compared with those with the isotope ^^N have been reported by Zhang et al. [54]. First-order Raman scattering measurements [54] in GaN made from isotopically pure ^^N and natural N (99.63% ^"^N), demonstrate that the Raman frequencies of the Ai(TO,LO) and £'i(TO,LO) modes shift as expected with the inverse square root of the reduced masses. However, the E2 modes do not follow this scaling and it appears that these modes involve mixed Ga and N vibrations. In the sample with the isotopic element, all the phonon modes were observed at a lower frequency than the natural modes except for the £"2 mode. The frequencies were shifted according to the inverse square root of the reduced masses of the elements, as one would expect from first principle lattice dynamics. The non-polar modes E2 and E^ were different with the major deviation for the E^ mode which appears not to be modified at all. Zhang et al. [54] concluded that the phonon modes are thus due to the vibration of the nitrogen molecules except for the E\ mode which involves the vibration of the heavier gallium modes and are thus unaffected by the isotope substitution. The explanation for this is due to the large mass difference between the nitrogen and the other alloy constituents. Since the atomic mass of nitrogen is much smaller than that of gallium, indium and aluminum, the reduced masses of GaN, InN and AIN are almost the same as that for nitrogen. As a result no distinct GaN-like modes and AlN-like modes exist in the alloy systems. Ordering in the AlGaN is as seen by Korakakis et al. [55], with X-ray diffraction and by Bergman et al. by Raman and X-ray measurements [56]. Long-range order was seen in the X-ray analysis of Korakakis [55] in the MBE grown films while the AlGaN films, which were grown by MOCVD were more disordered as indicated by the linewidths of the phonon modes. The difference in quality was attributed to the difference in growth temperature.
15.4. ELECTRON-LONGITUDINAL-OPTICAL-PHONON SCATTERING Lee et al. [42] and Kominrenko et al. [57] have also treated the electron-optical-phonon scattering in bulk wurtzite based on the dielectric model. The angle dependence of the infrared frequency phonons leads to an angular dependence in the matrix elements for the optical phonon absorption as well as to an angular dependence of the scattering rate. As discussed before, the anisotropy of the crystal leads to the mixed longitudinal and transverse modes in the optical phonons.
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
441
Each phonon mode needs to be normahzed and the normaUzed electron-opticalphonon Hamiltonian for the bulk uniaxial material is given as T1/2
47Te^hV~^
"=1
-e^\a^ q
+ a%)
L 9w
(wi - wO(w^ - o)^)
= XV2^e2^/yc.-^ 1
—( X-e^\aq
+ a\).
(15.6)
where al^ and a^ are the creation and annihilation operators, respectively, and the transition probability from electron state k to k' per unit time, is calculated from the Fermi golden rule. Mq the transition matrix element based on the electron-phonon interaction Hamiltonian can be written as . ^ ,2
2'2i:&h 7Te^ft 1 /
X
1
1\
{w\ - off{(ol - a/f (s'i - e'Dcoliojl - (o^)hm\e)-\-(s^, - s^W.iwl
- o?fcos\e)
(15.7)
where ^p^ is the phonon occupation number. Figure 15.3 depicts the matrix element for GaN. While both of the LO- and TO-like modes exhibit anisoptropy, the anisotropy for the TO-like mode is very strong. The scattering rates due to the longitudinal-like modes are similar to those obtained with the cubic case, however, the scattering rates due to the transverse-like modes can be strongly enhanced over a range of angles with respect to the c-axis. Then, the scattering rate W(k) can be written as W(k) = ^ W ( k , k ' )
(15.8)
and calculated with the total scattering rates for LO-like and TO-like phonons for GaN being shown in Figure 15.4 as a function of the incident angle of the electron with respect to the c-axis, 6^, with an initial electron energy of 0.3 eV for the wurtzite GaN, and Figure 15.5 shows the scattering rates as the function of electron energies for Ok = 0.
442
Optoelectronic Devices: Ill-Nitride
1.5
zi <
LO-Like
1 0.5
\TO-Like 30
60
90
Angle 0^ (deg) Figure 15.3. Angular variation of the matrix element IM^ I for phonon absorption in bulk GaN,
For emission of phonons, o- is a step function defined as
(
0,
for cos(kq)
2,
otherwise
(15.9)
and for absorption of phonons, a = 1. There is little angular dependence associated with the scattering of the longitudinaloptical-Uke modes; however, due to the mixing of the longitudinal-optical (LO) 10^5 10^4
Emission, LO-like
10^3
Absorption, LO-like
^-v
^ 0)
2
10^2
a5
10^1
Emission, TO-like Absorption, LO-like
CD
o
CO
10^0 10^
10^ 4
—I—
60 30 Angle 6,^ (deg)
90
Figure 15.4. Scattering rate W(k) versus electron incident angle 6^ with an initial electron energy of 0.3 eV for bulk GaN.
Phonons and Electron-Phonon Interactions in III-nitride Bulk
443
1015
r
Emission, LO-iike
CO
Absorption, LO-like
Emission, TO-like
I 1012
Absorption, LO-like (^ 10''°
ioM 10
0.2
0.4 0.6 Energy (eV)
0.8
1.0
Figure 15.5. Scattering rate W(k) versus initial electron energy with incident angle 6^ = 0 for bulk GaN.
and transverse-optical (TO) modes in the wurtzite structure, there is a significant angular dependence associated with the absorption of TO-like optical modes. The large contribution of the LO-like modes in these scattering processes has been supported by experimental studies based on subpicosecond time-resolved Raman spectroscopy [58,59]. It is seen for a number of wurtzite materials [60], the emission LO-like phonon has the highest scattering rate in the order of 10^^-10^"^ events per second, while the absorption TO-like phonon has the lowest scattering rate in the order of 10^^-10^^ events per second. Figure 15.5 illustrates that the scattering rates are weakly dependent upon the initial electron energy when said electron energy is sufficiently large. This dependence is most pronounced for the emission of phonons and is best seen with electrons of energies in the range of 0.1-0.2 eV, corresponding to the threshold values of phonon emission.
15.5. EXTENSION OF MODEL TO LOW-DIMENSIONAL WURTZITE STRUCTURES The dielectric continuum model provides a convenient formalism for extending the application of Loudon's model from the case of the bulk phonons to that of the dimensionally confined wurtzite systems [60]. Through this application we find that there is a complex spectrum of confined phonon modes for the III-V nitrides of wurtzite crystal system. For the case where dimension confinement plays a role, it is found that there is a complex spectrum of confined phonon modes for the III-V nitrides (III-N) of wurtzite crystal structure. This complex spectrum is shown in the Figure 15.6 for heterostructures
Optoelectronic Devices: Ill-Nitride
444
532-559
611-671
890-912
AIN
m
GaN
N—H
InN
4
4
4
446-475
574 734-741 Figure 15.6. Frequency intervals where oscillating and damped phonon modes occur in A1N-, GaN- and Inn-based wurtizite heterostructures. The cross-hatched regions support oscillating modes and the regions denoted by giruzibak arrows support decaying modes.
of AIN, GaN and InN. The confined modes are found to be more complicated than the corresponding modes in crystals of cubic symmetry and it is found that propagating modes occur as a result of the significant angular dependence of the phonon dispersion. Specifically, when the product of the parallel and perpendicular dielectric constants in a heterolayer is negative, oscillating phonon modes are allowed. On the other hand, when this product is positive, the phonon modes are damped strongly. The parallel direction is taken to be along the z-axis that coincides with the c-axis of the wurtzite material. The regions of oscillating and decaying modes are identified easily upon inspection of the parallel and perpendicular components of the dielectric constants for GaN-AlN-based structures. Based on this analysis, one may determine readily the regions of oscillating and damped phonon modes for a variety of III-N wurtzite structures. Figure 15.6 depicts such results for A1N-, GaN-, and InN-based heterostructures. In Figure 15.6 the cross-hatched regions denote oscillating modes and the regions with horizontal arrows are those with decaying modes such as the well-known interface (IF) phonon modes. Interface modes have been observed in Raman scattering experiments in GaN-AIN superlattice structures that agree in their frequencies and lineshapes with the calculations [61].
15.6. PHONON LINE BROADENING ASSOCIATED WITH THE DECAY OF PHONONS DUE TO SCATTERING BY POINT DEFECTS
We now focus on an analysis relating experimental measurements of Raman linewidth as they relate to line broadening associated with phonon decay processes. Specifically, the second-order phonon decay process of combined point-defect scattering and anharmonic decay is examined as a means of estimating line broadening associated with the decay of phonons in III-V nitrides of wurtzite structure containing point defects.
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
445
It is well-known that phonon decay processes are important in determining many of the important properties of electronic and optoelectronic devices. Accordingly, Raman analyses, anharmonic decay processes and phonon decay in the presence of point defects, are considered herein [62-70]. Since the longitudinal-optical (LO) phonon mode at the zone center is at an extreme frequency which precludes elastic scattering out of this mode, Klemens has suggested [71] that the decay of zone-center optical phonons in wurtzite structures containing point defects is due to combined phonon-point-defect scattering and anharmonic decay via an intermediate state. The second order process takes a phonon from qo ~ 0 by point-defect scattering to a mode q; this intermediate state differs in energy from the initial state by approximately h^o)^2ll = h(Ooq^/2i;k^
(15.10)
The second step is an anharmonic three-phonon process taking the phonon from mode q into two phonons qi and q2, of frequencies coi and 0)2, such that a)Q = (Oi -^ (02
but q = qi + q2-
(15.11)
Thus energy is conserved in the overall process, while total phonon wave vector is conserved in the second step, the anharmonic three-phonon process, but not overall. Moreover, the system may attain the same final state through a different process: a preexisting phonon in mode q decays anharmonically into a phonon each in modes qi and q2, with an energy difference of -hAco/ln, followed by point-defect scattering from mode qo into mode q. The effective Hamiltonian linking the initial to the final state via these two intermediate states is thus ifeff = (2iT/hAo))iPH,, - H,^P).
(15.12)
Here P is the perturbation Hamiltonian linking modes qo to q by point defects, and //an the perturbation Hamiltonian linking mode qo or q to modes qi and q2. The rate of decay of the original state, specified by A^o^ is proportional to l^eff I' - l^e*ff I' = {A^o(A^i + 1)(A^2 + 1) - (A^o + l)A^iA^2}
(15.13)
where the A^s are now the average values. The next step is to sum over all these modes subject to overall conservation of frequency and wave vector. To obtain the interaction rate, one must sum over all q. With this, and the value of the concentration of the defects, one can then obtain the value for the broadening of the lifetimes of the phonons due to this effect. Raman experimental measurements yield similar values to those obtained from these calculations [72]. Bergman et al. [72] have conducted a Raman analysis of phonon lifetimes in AIN and GaN of wurtzite structure. The above theory based on combined phonon-point-defect scattering and anharmonic delay of zone-center optical phonons in wurtzite structures containing point defects well explains the fine widths of the Ai(LO) phonons. A sihcon
446
Optoelectronic Devices: Ill-Nitride
impurity concentration of —0.1% caused the Ai(LO) Raman line width to broaden by ~ 50% as is also predicted by the theory. Additionally, the lifetime of the non-polar mode Ej is seen to be twice as long as the Ai(LO) mode, indicating the strong anharmonic delay of the LO mode. In addition, the £"2 mode was seen to be nearly an order of magnitude longer. This long lifetime is not unexpected due to the factors determining the anharmonic lifetimes such as the energy conservation constraints, the density of the decay states and the anharmonic coefficient. This mode lies at the low energy part of the phonon dispersion curve and only acoustic phonons are available as channels for decay and the density of states of these is small.
15.7. TRANSMITTANCE IN THE WURTZITE NITRIDES
The values of the LO and the TO phonons may be used to determine the dielectric constants of a material via the Lyddane-Sachs-Teller relations of the crystal. The relative dielectric function gj. is defined as Sj. = S/EQ, and may be written as s, = (n-\-ikf,
(15.14)
where n is the optical index of refraction and k is the extinction coefficient. The reflectivity may be expressed as ^-(„+l)2+^2-
(15.15)
From Eq. (15.1), it is clear that for s^ < 0, n = 0 and k 9^ 0. As a result, Eq. (15.2) predicts a reflectivity equal to 1. That is, any incident wave with a frequency falling into the range o)^ < co < (Oi will experience total reflection and is not able to propagate inside the crystal. For any crystal, the frequencies of the transverse-optical (TO) and longitudinal-optical (LO) modes correspond to poles and zeros of dielectric function E((ji)( of the material and the transmission in that frequency region falls to zero. Wurtzite semiconductors exhibit strong restrahlen-related absorption of radiation due to the interaction with optical phonons. For the nitride-based wurtzites, the optical phonon frequencies fall into the infrared region. This may be used to understand the experimental results [73] of why the absorption region for the first harmonic is much wider than the restrahlen band and to extract the damping factor for the material. The transmission is proportional to the exponential factor (—ad) where a is an attenuation constant determined by 4iTk/\Q. This attenuation constant is associated with phonon-phonon scattering events and causes broadening. The 3D graph of Figure 15.7 demonstrates the relationship between the transmittance T and energy E and sample thickness d for the first harmonic. For wurtzite materials such as AIN, GaN and ZnO, the region of reduced transmission corresponding to the second harmonic of the restrahlen band is confined
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
447
Figure 15.7. Transmission T of GaN versus energy E and layer thickness d in centimeters of the first harmonic.
approximately to the region, 2O^Q < W < 2a^o ^^^ the phonon effects are strong enough to manifest a drastically reduced transmission even in the second harmonic band. We have recently extracted these damping factors by comparing these calculations to the experimental results [73]. Filters with specific stop bands can be designed with specific spectral characteristics. 15.8. APPLICATIONS IN SEMICONDUCTOR LASERS
The importance of understanding the role of interface-phonon interactions is highlighted further by the recent use of phonon-assisted transitions to enhance the performance of semiconductor lasers. Indeed the longitudinal-optical (LO) phonon assisted transitions are known to enhance the population inversion in a laser device [74-76]. Consider the technique of enhancing population inversion, and therefore, gain, in asymmetric double quantum-well zinc blende laser structures [75]. This technique is illustrated in Figure 15.8. In this scheme, the quantum well of the active laser transitions—well A—is adjacent to a second quantum well—well D—that has two quasi-bound states D2 and Dl with the special properties that levels D2 and Al are nearly degenerate and Al and Dl differ by the energy of an optical phonon. As shown in Stroscio et al. [75], the population inversion in such a structure may be enhanced by an order of magnitude or more in such a heterostructure through engineering the phonons and electronic states in this heterostructure so that (a) phononassisted transitions from level Al to Dl have a large transition probability and (b) the near degeneracy of A2 and D2 results in electronic wavefunctions that enhance the phonon-assisted transitions from Al to Dl. These effects were shown [75] to lead to an order of magnitude enhancement in the population inversion between levels
448
Optoelectronic Devices: Ill-Nitride
A1 A2
— photon emission
A1
_
>f
D2l
\^^^
n
Dl\\
^
phonon assisted depopulation A
D2 D1
D
Figure 15.8. Double quantum-well heterostructure for enhanced population inversions in semiconductor lasers.
A2 and Al. Due to the anisotropy these effects will be much stronger in nitride-based heterostructures.
15.9.
QUANTUM DOT STRUCTURES
Quantum-dot-like structures play a key role in determining the operational properties of heterostructure lasers. The transition rates for phonon-assisted transitions between quasibound states in quantum dots and processes have significant roles in energy relaxation processes in III-V lasers. The interaction Hamiltonians needed to model these processes have been formulated and applied by a number of groups including the authors for the cases where optical-phonon effects play a dominant role [37,75-84]. In complementary studies, acoustic phonon interaction Hamiltonians have been formulated and investigated as contributing to the Unewidths of optical transitions [85-88]. Moreover, longitudinaloptical phonon-assisted tunneling transitions in quantum-dot-based lasers have been used recently as a filter to select the dots [89] that participate in the lasing process and thereby, add to the effective homogeneity of the dot size. In quantum dots, these interface phonons are frequently referred to as surface-optical (SO) phonons. The Frohlich interaction between electrons and surface-optical phonons is studied by using the dielectric continuum model [90]. First, the eigenfrequencies of the surface phonons are calculated. There are two possible solutions, one corresponding to the confined mode, and the other, which corresponds to the surface mode. Several studies have reported the calculation of the Hamiltonian of polar quantum dots in a non-polar matrix [79,81-84,91]. Using an improved form of the phonon normalization constant and starting
Phonons and Electron-Phonon Interactions in Ill-nitride Bulk
449
from the basic equations, the Frohlich interaction Hamiltonian and the phonon modes for a quantum dot are derived. Then scattering rates in such a system are calculated. The electron scattering rate provides a way to measure the rate of electron energy loss to a lower energy level in these device structures The electric potential may be written as
^(^) = S Y.^khikr)YT{e.
(15.16)
k
Thus, in the case of e = 0, (/> vanishes outside the sphere and at its surface. The LO phonon dispersion relation is not continuous for confined structures, but is represented by a set of discrete modes. In the second case, A) (/)(r) = Bi^^r~^~^YT{d, (/>)
for r < R, for r > R.
(15.17a) (15.17b)
A/^ and 5 / ^ are the normalization constants. If the outside matrix in which the quantum dot is placed is also a polar material, the frequency of the LO phonon may be obtained, and it is seen that for any given (/, m), there are only two SO modes, one, whose frequency is between the LO mode frequencies and the TO mode frequencies of the dots and the other is between the LO mode frequencies and the TO mode frequencies of the surrounding matrix material. In the case where the surrounding matrix material is a non-polar material, there is only one SO mode. To gain a more complete understanding of phonon-assisted transitions in quantum dots, a corrected form of the SO-phonon-carrier interaction Hamiltonian provides examples illustrating its use in SO-phonon-assisted intersubband transitions. By using the boundary condition of polar quantum dots in a matrix, the surface phonon energy and the radii of the different dots in different matrix materials may be calculated for different quantum numbers. These calculated mode frequencies are Hsted in Table 15.4. Chen et al. [89] have calculated the SO mode frequencies of different quantum dots in the vacuum as well as the SO-phonon-assisted transition rates. Table 15.5 depicts the relaxation rate, w, with different additional linewidths r(from 0 to 10 eV) for GaN quantum dots in vacuum. In addition. Table 15.5 summarizes Table 15.4. Calculated surface modes of different / hoi^Qi (meV)
/= 1
1= 2
/= 3
GaN AIN BN
85.28 92.53 195.95
86.47 93.8 196.64
87.83 95.9 197.45
450
Optoelectronic
Devices:
Ill-Nitride
Table 15.5. The scattering rates with different Hnewidths for GaN, AIN and BN at the resonant radius r(eV) GaN(s~^) AlN(s"^) BN(s"^)
10
1
0.1
0.05
0
1.82X10^' 3.03X10^^ 1.97 X 10'^
1.82X10^^ 3.02 X 10^^ 1.97X10^^
1.72 X 10^^ 2.77 X 10^^ 1.86X10'^
3.03 X 10^^ 4.64 X 10^^ 3.25 X 10^^
7.45 X 10^^ 9.60 X 10^^ 7.75 X 10^^
the relaxation rates for GaN, AIN and BN quantum dots for different Hnewidths at resonance radius which are 11.3, 4.56, 2.96 and 2.39 nm, respectively [90]. The rates considered in this chapter are very roughly within an order-of-magnitude of tens of femtoseconds for GaN quantum dots. These times are generally shorter than the fastest recombination times, which are typically picoseconds. Thus this may provide the dominant depopulation mechanism for the intersubband quantum dots lasers. ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of DARPA, ARO and AFOSR and the support and discussions with Dr. John Carrano, Dr. Michael Gerhold, Dr. Todd Steiner and collaboration with Dr. Gail J. Brown. REFERENCES [1] Walker, D., Kung, P., Saxler, A., Zhang, X. & Razeghi, M. (1996) Inst. Phys. Conf. Ser 145, lOP Publishing Ltd, London, Chapter 9; p. 1133; Paper Presented at 22nd International Symposium on Compound Semiconductors, Cheju Island, Korea, 28 August-2 September 1995. [2] Razeghi, M., Kung, P., Walker, D., Hamilton, M. & Diaz, J. (1999) SPIE Proc, 3725, 14. [3] Oberhuber, R., Zandler, G. & Vogl, P. (1998) Appl. Phys. Lett., 73, 818. [4] Litvinov, V.I. & Razeghi, M. (1999) Phys. Rev. B, 59, 9783. [5] Bemardini, F. & Fiorentini, V. (1998) Phys. Rev. B, 57, R9427. [6] Morkoc, H. (1999) Nitride Semiconductors and Devices, Springer, Berlin. [7] Bhuiyan, A.G., Hashimoto, A. & Yamamoto, A. (2003) /. Appl. Phys., 94, 2779. [8] Levinshtein, M.E., Ivanov, P.A., Khan, M.A., Simin, G, Zhang, J., Hu, X. & Yang, J. (2003) Semicond. Sci. TechnoL, 18, 666. [9] Davis, R.F., Roskowski, A.M., Preble, E.A., Speck, J.S., Heying, B., Freitas, J.A., Jr., Glacer, E.R. & Carlos, W.E. (2002) Proc. IEEE, 90, 993. [10] Paidi, v., Shouxuan, X., Coffie, R., Moran, B., Heikman, S., Keller, S., Chini, A., DenBaars, S.P., Mishra, U.K., Long, S. & Rodwell, M.J.W. (2003) IEEE Trans. Microwave J. Theory Tech., 51, 643. [11] Lawaetz, P. (1972) Phys. Rev. B, 5, 4039. [12] Tabata, A., Enderlein, R., Leite, J.R., da Silva, S.W., Galzerani, J.C., Schikora, D., Kloidt, M. & Lischka, K. (1996) I. Appl. Phys., 79, 4137.
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Optoelectronic Devices: Ill-Nitride M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 16
Phase Separation and Ordering in Cubic Ternary and Quaternary Nitride Alloys L.M.R. Scolfaro^, L.K. Teles% M. Marques^, L.G. Ferreira^ and J.R. Leitea,t ^Instituto de Fisica da Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, SP, Brazil Instituto de Fisica Gleb Wataghin da Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas, SP, Brazil
The recent developments achieved in the study of group-III nitride alloys are reviewed, focusing on the thermodynamic properties of the ternaries AlGaN, InGaN, InAlN, BGaN, BAIN, as well as the quaternary AlGaInN alloys in their cubic (zinc blende) phase. The properties of the alloys have been studied by means of ab initio total energy and electronic structure calculations, combined with cluster expansion (CE) methods, for the treatment of disorder and composition effects, either within a generalized quasi-chemical approach (GQCA) or using Monte Carlo (MC) simulations. In particular for InGaN the results of the calculations presented here are discussed with focus on the origin of the light emission process in the InGaN-based optoelectronic devices through a comparison with recent high resolution X-ray and Raman spectroscopy measurements.
16.1. INTRODUCTION The group-III nitride-based semiconductors have been intensively studied in virtue of their important applications in electronic and optoelectronic device technologies. The recent progress in this field, leading to the fabrication of efficient green-blue and ultraviolet (UV) light emitting diodes (LEDs), blue-violet laser diodes (LDs), UV detectors. X-ray detectors, and high-voltage, high-temperature, and high-frequency electronic devices has been reviewed by several authors [1-7]. Besides the binaries InN, GaN, AIN, and their ternary compounds InGaN, InAlN, AlGaN, also the quaternary AlGaInN alloys may be involved in some way in the design of the devices. Although most of the work reported so far refers to the stable hexagonal (h-) phase of the materials, the metastable cubic (c-) modification could be an advantageous alternative for device applications [8,9]. In contrast
In Memoriam. E-mail address: [email protected] (L.M.R. Scolfaro).
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Optoelectronic Devices: Ill-Nitride
to their hexagonal counterparts, the cubic structures are free from modulation due to spontaneous polarization and strain-induced piezoelectric effects [10]. Cubic-GaN grown by metal organic chemical vapor deposition (MOCVD) and by plasma-assisted molecular beam epitaxy (MBE) on GaAs (001) substrates was used to make p - n junction LEDs [11,12]. The fabrication of LEDs from c-GaN grown on SiC/Si substrates by MBE and the first c-InGaN/GaN double-heterostructure LED grown on GaAs (001) substrates by MOCVD have also been reported [13,14]. One way of increasing the flexibility of nitride compounds is to alloy with boron. The boron-related ternary alloys, B;^-Gai_;»:N and B;,Ali_^N have been less investigated. Boron nitride films are very useful for many applications due to their unique properties such as high thermal conductivity, hardness, excellent chemical stability and optical transparency over a wide spectral range. Moreover, the boron-related alloys can be lattice matched to SiC. Nevertheless, as the other nitride alloys, BGaN and BAIN are prone to phase separation due to the very large differences in the bond lengths. Experimental works have reported a successful growth of BGaN and BAIN alloys only for very small B content [15-17]. The structure of the nitride-based devices comprises, for example, GaN/InGaN or AlGaN/GaN (multiple) quantum wells, in which GaN and AlGaN act as barrier materials. However, the increase of the Al and/or In compositions in these structures is hindered by the degradation of the interfaces due to the large lattice mismatches. The need to simultaneously control both, the band gap and the lattice constant, prompted interest in not only ternary but also in quaternary alloys. In this sense, the Al;,Ga^Ini_;c _ ^N quaternary alloys have emerged as promising materials, especially for the device applications in the UV region [3]. The use of AlInGaN allows one, through variation of the Al and In contents in the alloy, to obtain lattice-matched heterointerfaces. Examples are the recent production of nearly lattice matched AlInGaN/InGaN UV LDs [18], AlInGaN/AlInGaN deep-UV LEDs [19,20], and GaN/AlInGaN UV LDs [21]. Besides the lattice and bandgap engineering, the use of the quaternary AlInGaN alloys has shown to be an effective approach to improve optical quality of the alloy layer [22]. In contrast to ternary alloys, the growth of cubic AlGaInN structures has not been reported yet. Contrary to the alloys formed with other III-V compounds, and as it was mentioned above, nitride alloys derived from large mismatched binaries undergo phase separation giving rise to large miscibility gaps [23-29]. Phenomena such as phase separation and composition fluctuations in the nitride alloys, or more generally speaking tendency of the alloy atoms to cluster into ordered or disordered phases of particular stoichiometrics have been observed. Such properties of In;tGai_;cN, for example, play an important role on the radioactive emission process taking place in the nitride-based commercial optoelectronic devices. There are strong evidences that an important emission mechanism for the bluegreen emission originates from phase-separated quantum dots (QDs) formed by spinodal decomposition taking place in the InGaN alloys, the active media in these devices [30-33]. It was also shown that the biaxial strain due to the pseudomorphic growth
Phase Separation and Ordering
457
process in InGaN may suppress the phase separation effects, and even giving rise to the formation of ordered phases [34-36]. From the theoretical point of view, the thermodynamics of group-III ternary and quaternary alloys has been investigated through the simplified regular solution model, either using the valence force field approach or the delta lattice parameter model [37-44], and more recently by adopting more sophisticated methods through CEs [23-28,35,36,45]. These later have been used in connection with the GQCA or together with MC simulations, in order to explore the thermodynamic consequences of not only the "freestanding" bulk soHd, but also the coherent epitaxial layers. It is the purpose of this chapter to review the thermodynamic properties of the ternary and quaternary nitride alloys in their cubic phase, by obtaining and analyzing their phase diagrams, as well as the influence of the biaxial strain induced by the pseudomorphic growth on them. The chapter is organized as follows. In Section 16.2 we give a short description of the theoretical models adopted in the calculations. In Section 16.3 we present the results for the ternary alloys. Section 16.4 is devoted to the study of ordered phases in AlGaN and InGaN alloys. In Section 16.5 we analyze the phase separation process in the quaternary InAlGaN alloy. A summary is presented in Section 16.6.
16.2.
THEORETICAL MODELS
In order to describe the thermodynamic properties of the alloys, we combine ab initio total energy calculations with the CE method, within a GQCA [46] to disorder and fluctuations in the alloy or through MC simulations. In the following, the steps performed for these calculations are described in some detail. 16.2,1 Generalized Quasi-chemical Approach for Ternary Alloys In order to study the stability of a ternary (or pseudobinary) alloy, one needs to calculate the Helmholtz free energy F{x, T) as a function of the alloy compositions and of the temperature T. We may express the free energy F of an A_^Ci_j^.N (A,C = In, Ga, Al, B) alloy as Fix, T) = Fo(x, T) + AF(x, T)
(16.1)
where Fo(x, T) = {1- x)F^(T)
+ xFc^iT)
(16.2)
describes the free energy of a macroscopic mixture of the binary AN and CN components with free energies FAN and FQN^ respectively, and AF(x, T) = AU(x, T) - TAS(x, T).
(16.3)
This later expression gives the mixing free energy AF, as a sum of the mixing enthalpy of the alloy At/ and the mixing free entropy AS, and can be described using the CE method within
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Optoelectronic Devices: Ill-Nitride
the framework of the GQC A [46,47]. From AF we can construct the phase diagrams as it will be described in more detail in Section 16.3. In this approach, the A^^Ci-^^N alloy is divided into an ensemble of clusters, each of which is taken to be statistically and energetically independent of the surrounding atomic configuration. According to the Connolly-Williams method [48], each clustery with a certain number ofA and C atoms is realized in the alloy with a probability x,; the configurationally averaged quantity describing a property, P, of the alloy is given by a sum of the kind J
P(x,T) = Y.^jPj,
(16.4)
j=0
where Pj is the corresponding property for the specific cluster/ In order to obtain the internal energy of the alloy, within the GQC A, one has to consider clusters of adequate size and to calculate the energies Ej of each one. In this approach the total mixing internal energy is then given by AU(x, T) = M\ Y^XjEj - [(1 - x)E^ + xEj] I,
(16.5)
with M being the number of clusters in the alloy. The mixing entropy can be calculated from the Boltzmann definition A5'(x, T) = kQlnW, where W is the number of ways to configure the alloy with the set MQ,MI,...,MJ of clusters [46]. In the Stirling hmit, it holds AS(x,T)=
-kAN[x\wc-\-(l
-A:)ln(l - x ) ] + M ^ j c ^ Inf ^ ] L
(16.6)
where x^ is given by the fraction of clusters of kind 7 for a given composition x in a regular solid solution, and A^ is the number of sites in the cation sublattice on which the In, Al, B, or Ga atoms assume some configuration. The cluster fractions Xj are unknown. However, they can be interpreted as variational parameters, being obtained by minimizing the mixing free energy of the alloy under the constraints concerning the compositions [23]. We adopt eight-atom cubic supercells (see Figure 16.1) as basic clusters to describe the fully relaxed ternary alloys. They represent the smallest clusters (16-bonds) that consider local correlation, and are given by a central N atom and four alloying atoms bound to the environment by 12 second-neighbor A^ atoms [23,26]. 16,2.2 Ising-like Hamiltonian for Ternary Alloys Another way to obtain the temperature-composition phase diagram in a "first-principles manner" is by using a CE, in which the energies of different configurations are described by a generalized Ising Hamiltonian. For each configuration, one assigns a set of spins for
Phase Separation and Ordering
459
o o
Figure 16.1. Schematic representation of the eight-atom supercell adopted to study the fully relaxed ternary alloys.
the A^ sites of the lattice. Then, for an alloy as A^^Bi-^^C, if the site is occupied by an A atom, S = —\ and, if it is occupied by a B atom, 5 = + 1 . Therefore, for each configuration a we have a set of spin variables Si, with / = 1,2, ...,N. The total energy of each configuration, Ej^picf), is calculated by first-principles (FP) methods, and the idea of the CE consists of mapping the set of Ejjp((f) onto an Ising-like series. The energy of any configuration a can be written as E(a) = /o + X •^^^^<^) + S V K ^ ) ^ / ^ ) + X JijkSi(cT)Sj(a)Sk(a) + • • -, i
j
(16.7)
k<j
where the Js are the interaction energies, and the first summation is over all sites in the lattice, the second over all pairs of sites, the third over all triplets, and so on. Points (sites), the many pairs, triangles, etc., constitute the basic figures of the lattice. The interaction energies are the same for all configurations a. Thus, if the Js are known the energy E((T) for any crcan be obtained by simply calculating the spin products and summing; therefore, one can readily find the ground state structures [49], as well as, use statistical mechanics techniques as MC simulations to access the thermodynamic properties of the alloy. This approach was extensively used in the study of the traditional semiconductor alloys by Ferreira et al. [50] and Wei et al. [51], and fairly good results were obtained for phase diagrams and alloy equilibrium properties. The CE is specially useful when it converges fast. In the case of non-metals the Coulomb interaction (1/r) and the elastic interaction between different sized atoms (1/r^) are long range and require far extended CE (or a different method, as Ewald's in the case of the Coulomb interaction). These long-ranged expansions—because the many parameters are obtained by fitting the configuration energies of a large set—^present new dangers because wrong (or incomplete) long-range interactions may enhance the importance
460
Optoelectronic Devices: Ill-Nitride
(nearness to the ground state) of wholly unphysical configurations. Recently, we proposed a new approach, a relatively short-ranged novel CE but with a number of parameters larger than the usual short range expansions, but sufficient to fit the energies of a large set of configurations with tolerable errors [52]. The novel CE begins by rewriting Eq. (16.7) as
^(^) = I I TT X -^/^"^W- • •Sf,,,v,,
(16.8)
where/means a figure-type (empty figure, point, pairs, triangles, etc.) with Vf vertices, one of which is the site n being summed. Df is the number of figures of type/per site. In other words, we sum over all figures with a vertex at site n and then sum over all sites. Since there are Df figures of type/per site, and those figures have Vf vertices, the sum over the figures/with a vertex at n has VfDf terms. The product S^Sf^^x ' '^fXVf nfi^^ns the product of spins at the Vf vertices of the k\h figure/having one vertex at n. In this product, the spin of the second vertex of the figure is 5^^ 2 ^^^ the spin of the V^th vertex is Sf^^^Vf Written as in Eq. (16.8) the CE can be readily generalized by making the interaction to be site-dependent through its "local concentration" Jfix^). The procedure comes as necessary whenever the number of interactions Jf is small and the elastic interaction, due to the different atomic sizes, is important. For a general configuration its global concentration could be used to define the interactions 7. But such a definition is inadequate for those configurations, like the longperiod superlattices, having large domains of off-average concentration. Considering this fact, the /s are considered to be dependent on the local concentration. In the approach of Ref. [52], the local concentration jc„ is defined as an average over the sites until the second shell of neighbors. Since the local concentration was defined, the /s are expanded in a power series J fix,) = Y^JfMn - 0.5)^ = Y.^~'jf,iSl /=0
(16.9)
/=0
and the Hamiltonian becomes /.ax
f N
-.
yjDf
^
E(cT) = £ 2-^ X S 17 Z JfXSnSf,k,2Sf,kX • -^Mv, [. 1=0
\^n=l f
^f k=l
(16.10)
J
For a given set of first-principles calculated configurations, the Hamiltonian of Eq. (16.10) is fitted with the parameters Jfj. Once the JfjS are known the energy E{a) for any o-can be calculated for any configuration, and one can readily find the ground state structures, as well as, use statistical mechanics techniques to calculate the thermodynamic properties of the alloy.
Phase Separation and Ordering
461
16,2.3 Monte Carlo Method References to the MC Method are countless, very good and complete. In the web and in book catalogs, the reader will find complete reviews. In this section we discuss what is peculiar to our use of MC, in connection with the unusual Hamiltonians such as that of Eq. (16.10). Our MC follows the recipe of MetropoHs et al. [53]. It consists of sequences of attempts at switching atoms between two lattice sites. At each attempt we compute the excitation energy 8x^2- If that is negative the system is made to switch atoms, if positive the switching has probability exp(-6i_^2/^B^) of being made. At each temperature T one needs a sequence of switch attempts to equilibrate the MC cell, and a sequence to measure averages of thermodynamic variables. The size of these sequences depends on the number of sites in the periodic MC cell and the temperature itself. Of course, due to the k^T denominator in the probability, higher temperatures favor switching even to states of higher energies and lower temperatures make switching unlikely, or difficulty to equilibrate the system. 16.2.3.1 Ternary Alloys, In the case of the ternaries we used MC cells of 12^ = 1728 sites and about 1000 switch attempts/site to equilibrate and an equal number in the measuring cycle. The calculation of the excitation energy 81^2 ^^ the case of Eq. (16.10) is slightly more complicated than usual. Because the spin 5„ is averaged on the neighbors of site n, flipping a spin changes not only the figures containing the flipped spin but also all the figures containing the spins that are neighbor to the flipped spin. Thus, effectively the local concentration extends the range of interaction between sites. 16.2.3.2 Quaternary Alloys, In a quaternary (or pseudotemary) A^ByCi-x - yD alloy, the sites of the crystal lattice are occupied in different configurations by atoms A, B, and C. In order to perform MC studies in such a system it is necessary, in principle, a sampling of the 3^ possible configurations for placing A, B, and C atoms on A^ sites, with N ^ 10"^. This is a tremendous task for first-principles electronic structure methods, as it involves a huge number of calculations. To circumvent this problem it is necessary for a method to describe any arrangement of N atoms in terms of few arrangements of a much smaller number of atoms. The classical way to accomplish this description is by means of a CE. In the case of binary (A^^Bi-^,) or pseudobinary (A^Bi_;,C) alloys, CEs have reached a high degree of sophistication [49,54,55]. In the case of ternary or pseudotemary alloys, though the theory is well developed [56], CEs are not as useful because they are not as simple. Here then, instead of CEs we adopt a different approach. We consider all the arrangements of atoms A, B, and C in a periodic fee lattice with repeating unit vectors (Oaa), (aOa), and (aaO). These are twice the primitive vectors (Of f), (f Of), and (f f 0) of the fee lattice so that the unit cell contains eight fee sites. Therefore, the number of
462
Optoelectronic Devices: Ill-Nitride
possible arrangements of atoms is 3^ = 6561. Most arrangements are related by the rotation-inversions of the T^ point group (group of the regular tetrahedron) and by the translations of the fee lattice. Grouping the symmetry related arrangements we obtain 141 classes. This will be the number of first-principles total energy calculations that must be carried out to describe any arrangement of the pseudotemary system. The 8-site unit cell is a hexahedron (stretched cube along a body diagonal) which can be chosen as any of the four listed in Table 16.1. The energy of each site is considered as the average of the energies for the four hexahedra listed in Table 16.1. The MC cell used to study the quaternaries had 23^ = 12,167 sites and 10"^ switch attempts per site were made. 16.2.4 Total Energy Calculations The ab initio total energy calculations carried out here for each alloy configuration were performed by using a first-principles pseudopotential plane-wave method and the density functional theory within the local density approximation (DFT-LDA) [57,58], specifically the "Vienna Ab Initio Simulation Package" (VASP code) [59,60]. Besides the valence electrons also the semicore Ga3d and In4d states are explicitly considered. Their interaction with the atomic cores is treated by non-normconserving ab initio Vanderbilt pseudopotentials [61]. The many-body electron-electron interaction is described within the Ceperley-Alder scheme as parametrized by Perdew and Zunger [62]. The k-space integrals are approximated by sums over a 5 X 5 X 5 special-point of the Monkhorst-Pack type [63] within the irreducible part of the Brillouin zone. Our calculations employ the conjugate-gradient method to minimize the total energy. The structure of each configuration is optimized by minimizing its total energy with respect to the lattice constant and to the atomic positions within the unit cell. Further details of the parameters used in the calculations for the different alloy systems may be found elsewhere [23-26,35,45,52]. 16.2.5 Method to Identify Order in the MC Sample The method to identify order in a MC sample is similar to what one does with real physical samples: scattering experiments (X-rays, neutrons or electrons). Thus, consider a MC periodic sample with A^MC sites. We assume that thermal equilibrium has been reached. Define the Fourier transform of the spin distribution S(k) = Y^sClW^^\
(16.11)
where 8(1) is the spin (±1) at the lattice site /. We use very large MC samples, or ergodically calculate the MC average {S(k)S(ky) = X e^^'^^"^'\5(/)5(?)).
(16.12)
Phase Separation and Ordering Cs| (N CN
(N (N of I
" " of
I
I
^-^
i
^
V ^ o -^ 1 •^
1
w
1
I '. o o ^. ^
I ^^ I
O
q 1^ 1^ ^^
^ I I of o^ of o~ I
^
I r^
r^
^
^ I
o" I of of ^ o I I
o o o o o" o' o"
PQ
^
oi en
^
463
464
Optoelectronic Devices: Ill-Nitride
Suppose there is a long-range order so that the spins at a certain basis vector site b is the same as the spin at ^ + L. L is a lattice vector of the ordered configuration which has A^ceii sites (orders of magnitude smaller than A^MC)- The spins at b and at ^ + L need not be exactly equal but we may assume that there is a probability/? of the sample being ordered and \ — p of being disordered. Let aib) be the spin (± 1) at M n the perfectly ordered sample and let S be the average spin. When order is not perfect we write {S(b + L)) = paib) + (1 - p)~S.
(16.13)
Then we assume the sites are statistically independent, or {s(l)sCt)) = {S(b)){S(b')} = Ipaib) + (1 - p)S][p(jih + (1 - pyS].
(16.14)
The assumption of statistical independence excludes the possibility of short-range order [64], but here we want to only call attention to the terms indicating the long-range order. Corresponding to the lattice vectors L of the ordered configuration, we define the reciprocal lattice vectors G. Then we obtain
(S(k)S(kr) = NMC- ^X1^^^)
+ (1 ~ ^ > ^ '
b diffuse scattering
+«(^'^te)V
,e'^*
(16.15)
Bragg peaks
The terms marked as diffuse scattering are not ^-dependent (though they would be if we had not assumed the statistical independence of Eq. (16.14)) but is A^MC times smaller than the Bragg peaks term. The latter term clearly identifies the order by peaking at the reciprocal lattice vectors G. Figure 16.7, that was actually calculated for the MC sample of InGaN, exemplifies the identification of order. If there is an ordered phase, at lower temperatures {S(k)S(ky) peaks at the reciprocal lattice vector of the ordered configuration, as it will be seen in Section 16.4. As the temperature is raised, the peak decreases and disappears above the transition temperature.
16.3. PHASE SEPARATION IN THE TERNARY ALLOYS In this section we discuss the phase diagrams obtained for the BGaN, BAIN, AlGaN, InGaN, and InAlN alloys, as calculated by combining the first-principles total energy calculations with the GQCA to disorder and compositional fluctuations.
Phase Separation and Ordering
465
16.3.1 BGaN and BAIN In order to exemplify the procedure carried out for obtaining the alloy temperaturecomposition phase diagrams, we show in Figure 16.2 the calculated mixing free energies AF from which we derive the T X x curve for the B;,Ali_;,N alloy. Note that the shape of the curves of both, AF X x and 7 X x is asymmetric. This is due to the fact that the cluster energies, Ej do not vary linearly with the cluster kind, 7, leading to asymmetric dependence of the mixing free energy. As the temperature increases, the typical two-minima behavior of the mixing free energy changes to a single-minimum behavior, as can be seen in Figure 16.2(a). The solid (dashed) line in Figure 16.2(b) corresponds to the binodal (spinodal) curve. Below the critical temperature at T^ ~ 9500 K, the two-minima behavior of AF reflects in the occurrence of a miscibility gap for x in the interval Xi < x < X2. The points x = Xi and x = X2 correspond to those at which the common tangent line touches
(a) 0.05
-
^^-"^000
^
^ ^s._^
0.00
8oog__
CD Q.
5
-0.05
LL
<
-0.10
- \
-0.15
-
\
10500^ _A
(b)
1 Xi
^1
10000
2^ ^>—'
(D 6000
^
•
\ ^
i^rT
8000
1
if.
^ -^ ' ^ ^—
1 i
•
X2 i
X2
"^""^^ \ ^! ^ -H \ \ \
X / / ^ _/ / / / / ^
\
2 8. 4000 J / E / / (D 1 ^ 12000 1 /
\ \
\
[/
n
1 \\
/
:
0.0
1
\
1
0.2
0.4
•
0.6
•
.
0.8
•
\
1.0
Boron content x Figure 16.2. Mixing free energy AF for three different temperatures (a) T X x phase diagram (b), as functions of the B composition, for the B^^-Ali-^N alloy. Solid line: binodal curve; dashed line: spinodal curve.
466
Optoelectronic Devices: Ill-Nitride
the AF curve (which defines the binodal curve). The two composition values, JC = jcj and X = X2» correspond to the inflection points in the AF curve (which defines the spinodal curve). ¥oYXx < x < xliOxx!2< x < X2 the alloy is metastable against local decomposition because the value of AF for any x in these regions is lower than the average value of AF with any two compositions in the neighborhood of x. This increase in AF acts as a temporary energy barrier against alloy decomposition into its final equilibrium concentrations Xi and X2. For an alloy with concentration between Xj and JC2 there is no such decomposition barrier and the alloy is inherently unstable [46]. Figure 16.3 depicts the temperature versus composition phase diagrams for the B;cCrai _;^N and B^^Ali -^. The behavior observed for both alloys is very similar, with very high critical temperatures, T^ ~ 9500 K, which result in a very large miscibility gap. Recent calculations carried out within the framework of the strictly regular solution model combined with a valence force field approach lead to the critical temperatures 11,400 and 8330 K for wurtzite phase BGaN and BAIN, respectively [43]. These results lead to the conclusion that it is very difficult to grow a nitride alloy based on boron, at least in the unstrained case. For typical growth temperatures for BGaN (—lOOOK) and BAIN (~ 1300 K), we observe phase separation for a wide range of composition. For these temperatures the phase diagrams shown in Figure 16.3(a) and (b) indicate that there is a spinodal decomposition in the interval 0.028 < jc < 0.995 for B;,Gai_;cN, and in the interval 11000
-
•
9000 -
/ / /
8000
g 0)
3
7000 6000 -
1 1
/ f
1
/
/
/
\
-
\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
L
1
1
1
1
1
1
0.4 0.6 0.8 Composition x
/
/
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ' \ \ \ \
/
I
1 1
1 /
1 1 1 1 1 1 1
/
/
- , 1
0.2
/ / /
/
1 1 /
:
1
X
1 1
1
0" 0.0
/
1 / j /
-
1 1 1
K
1000
/
/
1 1
1 1 1 1
1 1 1 1 1
2000
j
\
1
/ /
/ / / / / / / / / / / / / / 1 / 1 /
"
1 1 1
f
-
/ /
]
\ \ \ \
/ \
4000 3000
\
/
/ / / / / / / / / / / /
g. 5000 E H
BxGai_,N
BxAli_xN
10000
1 1 1
1
1
1.0
0.0
1
0.2
1
1
0.4
1
1
1
0.6
1
0.8
1
1.0
Composition x
Figure 16.3. Phase diagrams T X jc for the B^Ali _;,N and BJ3ai -J>i alloys. The horizontal dashed lines around T ^ 1000-1300 K delimit the range of growth temperatures.
Phase Separation and Ordering
467
0.037 < X < 0.949 for Bj^Ali-^^N. Such a picture is consistent with the experimental findings, explaining why successful growth of these boron-related alloys is achieved only for very small B content, x ^ 0.03 (0.08) for BGaN (BAIN) at growth temperatures [16,65,66]. 16.3.2 AlGaN, InGaN, and InAlN Figure 16.4 depicts the temperature-composition phase diagrams for the AlGaN, InGaN, and InAlN alloys. More in detail they show the spinodal and binodal curves calculated within the GQCA and the ab initio total energy method. We observe that a very low critical temperature, Tc — 70 K, is obtained for the Al^^Gai-^^N alloy, thus for growth temperatures no miscibility gap exists for AlGaN. In contrast to AlGaN, for the In^^-Gai-^^N alloy there is a large miscibility gap at typical growth temperatures, ~ 1000 K, therefore, indicating that unstrained InGaN presents phase separation effects, or spinodal decomposition, with an In-rich phase of x ~ 0.8 (and an In-poor phase of JC ~ 0.2). The phase separation, which should occur at growth temperatures in In^^Gai -j^, is driven by the internal strain due to the mixing of the two lattice-mismatched components InN and GaN. Similar features are obtained when MC simulations are used. The predicted phase separation for the InGaN alloys is in very good agreement with experimental data [67]. Figure 16.5 depicts the calculated phase diagram for In^^Gai-^cN together with the data (filled circles in the figure) for the In-rich phase compositions,
1600
T = 70 K
ln^Gai_^N V1295K
1400 1200 £ (D
0 Q.
E 0
1000 800 h 600 400 200 NTNJ 0 j^S 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Composition x Composition x Composition x
Figure 16.4. Phase diagrams, T X jc, for the Al;cGai -^^N, In;cGai -^^N, and In^^Ali - ^ alloys. The values obtained from the calculations for the critical temperature, T^, are also shown.
468
Optoelectronic Devices: Ill-Nitride 1500 ln^Gai_^N 1250 -
1000
2
1
750
/ / / / / / 1 1 1 1 1 11 /
1
\
\ \
1
/ • / . / / /
\
\\
• \
f
\ \ \
Q.
E
\ \ \ \ \
0
500 -
250
1
0.0
1
0.2
1
I
0.4
I
I
.
0.6
J
0.8
1
1.0
Indium content x Figure 16.5. Calculated TXx phase diagram for unstrained c-In^^-Gai-^N. The horizontal dotted lines give the range of the growth temperatures. The filled circles (experimental results as extracted from Ref. [67]) denote the Indium contents of three different samples, x = 0.07, 0.19, and 0.33. The dashed rectangle denotes the observed In-rich phase, jc = 0.8 ± 0.08 [33,34].
as obtained from X-ray diffraction and resonant Raman spectroscopy measurements performed on c-InGaN thick layers grown on GaAs (001) substrates by IVIBE withx = 0.07, 0.19, and 0.33 [67]. An In-rich phase with x ~ 0.8 is observed in the three samples as obtained from the calculated phase diagram. We should point out that a range of X = 0.72 - 0.88 (shown by the dashed rectangle in Figure 16.5) has been obtained from micro-Raman spectroscopy measurements. We observe for the In;,Ali_;,N alloy the same behavior as for In;,Gai_;,N with a Httle higher critical temperature, T^ = 1485 K. The result depicted in Figure 16.4 indicates that for T ~ 1000 K there is a phase separation for a wide range of composition, for In content between 15 and 79%. This result is in good agreement with experimental findings that show a tendency of phase separation for jc > 0.17 [68]. There are few theoretical works in
Phase Separation and Ordering
469
the literature which analyze the thermodynamic stability in the InAlN alloy, and all of them use the strictly regular solution model, with only one alloy configuration [39,43,44,69] or some but not all configurations [70]. They found a range for the critical temperature which varies from 1474 to 3400 K. The phase diagram shown in Figure 16.4 is much more asymmetric than those obtained through the regular solution model, and we obtain a larger range of miscibility for higher In molar fractions x. The phase boundaries are also found to be steeper for x —• 0 and jv: —^ 1 than for ideal alloys.
16.4.
ORDERED PHASES IN InGaN AND AlGaN ALLOYS
In this section, we discuss the tendency of the InGaN and AlGaN alloys to order, and the influence of the coherently epitaxial growth on them. We would like to know whether, during the growth, the individual components would tend on a microscopic scale to attract or repeal each other, so that there is a short-range order. We would also like to know whether the individual components will tend on a macroscopic scale to cluster into ordered phases of particular stoichiometrics. We have already seen in the section before, that the InGaN alloy has a tendency to "unmix" and the AlGaN alloy to form a solid solution. Besides these behaviors it was already reported the existence of ordered phases in both alloys. Therefore, in this section we analyze the possibility of ordering formation in both alloys for (i) the bulk phase, in other words, when they are unstrained; (ii) the case when the alloys are coherently grown on substrate with different lattice constant, then, in this case, they will be "externally" strained. If the alloy is incoherent with the substrate, then it is free to adopt the in-plane lattice constant that minimizes its free energy. If the alloy is coherent with the substrate, then it must adopt the in-plane lattice constant of the substrate; the resulting elastic strain energy can increase its overall free energy significantly. We will find that the thermodynamic properties of InGaN depend greatly on whether the alloy is coherent or incoherent with the substrate. In fact, such coherence constraints greatly suppress the tendency for alloys to separate into their pure-component "endpoint" phases, and at the same time greatly enhance their tendency to form ordered compounds at certain stoichiometric compositions. These tendencies can be understood from a CE method together with ab initio calculations and MC simulations, as described in Section 16.2.2. As reported, the basic structure of the method involves the calculation of the total energies by a first-principles method, E^p(a), of some configurations, these are then used via Eq. (16.10) to obtain the interaction energies Jfj, which can be used to perform a ground state search and phase diagram calculations. Schematically, first-principles calculations => {EYp(a)} => [Jfi] => ground state search => thermodynamics. In the sequence, we describe each step more in detail and the respective results obtained for InGaN and AlGaN alloys.
470
Optoelectronic Devices: Ill-Nitride
16.4.1 First Principles Calculations We start by performing first-principles calculations according to Section 16.2.4 in order to obtain the total energies of the set of configurations to be used in the CE (Eq. (16.10)). The set of configurations includes all with 2 and 4 cations per unit cell, and 7I and yl (MoPt2), and the superlattice [3,3] along the (001) direction. The configurations are named as in Ref. [71] to which, for an alloy as A^Bi-xC, we add a fraction n/m, like 1/2 or 3/4, saying that among the m sites of the unit cell n are occupied by an A atom and m — nby 3. B atom. In particular, the name of the configuration "40" (chalcopyrite) was changed to DO222/4 because it has the same unit vectors as D022In the case where the alloys are "externally" strained, we consider that they were grown on a buffer of GaN, as it is usual experimentally. Then, in order to determine the total energy of each configuration under the macroscopic strain produced by the pseudomorphic growth, the lattice parameter in the plane (001), a\\, was held fixed and equal to that of GaN. In this case, most of the configurations may be oriented in two ways, one mostly oriented in the (001) direction, the other mostly oriented perpendicularly. In particular, the configurations Lli, V, and LI2 do not split due to the lattice uniaxial deformation. The configuration total energies were calculated as functions of the lattice parameter c along the (001) direction and minimized with respect to the atomic positions within the unit cell. 16.4.2 The {Jfi} and the Ground State The obtained total energies are then used to determine the interaction energies JfjS. The quality of the CE is determined by comparing the energies for the configurations determined by the CE with the energies determined by a direct calculation (first-principles calculations). If necessary, one can repeat this procedure by adding extra Jfjs until the difference between the predicted energies for {a} and the direct calculated energies are smaller than some prescribed tolerance. In the particular case of InGaN and AlGaN, respectively, we found that the interaction energies parameters {/o,0' -^0,1' -^0,2» J 1,1^ J2,0^ J2,2' -^3,0' -^3,1' A O ' A 2 ' -^2,2» ^ , 0 ' ^ , 2 ' ^2,0^ ^ 2 , 2 } ^^^
{-^0,0' JQ,\^ J0,2^ J\,\^ J\,2^ ^2,1^ J2,2^
-^3,1' JA,2^ ^2,2. ^ , 0 ' ^ , 1 ' ^,2^ ^2,0' ^2,2} ^^c scts able to predict the energies of all the important configurations with tolerable errors. The set of the obtained interaction energies /y^/S is then used in the novel CE (Eq. (16.10)) to predict the energies of new configurations a. This was made for a large set of configurations, a total of 5868. Then, by using the same procedure as in Ref. [49] to identify those structures which minimize the energy expression at each x, we obtained the ground state line (GSL). The GSL is made of straight line pieces in the plane AE" versus x such that any configuration has energy greater or equal to the two phase mixtures corresponding to the straight Hne pieces. A^" is the standard definition of the alloy excess energy taken as the difference between the alloy energy and the mixture energy of the binaries, AE" = E{&) - [xEp^ + (1 - Jc)£'GaN]. where A = In or Al.
Phase Separation and Ordering
All
We first address the results for the unstrained or fully relaxed alloys. It was found for both AlGaN and InGaN alloys that for all alloy compositions there are no stable ordered structures. Then we investigated the relative stability of ordered and disordered phases, considering the coherent growth case, for which a\\ = aoaN- The resulting GSL for AlGaN and InGaN are shown in Figure 16.6(a) and (b), respectively. The results shown in Figure 16.6 comprise interesting features: (i) there are ordered structures with AE < 0, which means that at T = OK these structures are more stable than phase separation; (ii) the biaxial strain induced by the GaN buffer suppresses the phase separation process and acts as a driving force for the ordering formation; (iii) the GSLs are very different in (a)
J^ - 1 4 (b) 0 LJJ
<1
0.2
0.4 0.6 Composition x
0.8
1.0
Figure 16.6. Excess energy AE for ground state ordered structures for the (a) Al^j^Gai-^^N and (b) In^^Gai-^^N alloys pseudomorphically grown on rigid GaN (001) buffer layers. The solid curves, made of straight-line pieces, give the alloy ground state line; the dashed lines represent the random alloys; and the dotted lines connect the two binary (Al,In)N and GaN constituents taken as the reference to calculate AE. Note that the energies for the Al alloy are much smaller than in the case of the In alloys.
472
Optoelectronic Devices: Ill-Nitride
each case, for the AlGaN, it is almost continuous and its difference to the random case (represented by the dashed Hne in the figure) is not significant, on the contrary, for InGaN, the GSL is composed by three Hne pieces, connecting the binaries to the two predicted ordered phases, and its difference from the random case is high enough to give a certain stabiHty to these phases. In the case of InGaN the GSL had two inflection points: the one at x = 0.5 is the DO222/4 structure, the chalcopyrite, which is a superlattice along the (210) axis with alternation of planes [InlnGaGa]; the second at JC = 0.625 is also a (210)-oriented superlattice with alternation [InlnlnGalnlnGaGa]. It is worth to point out that there were some other structures, in the range 0.5 < ;c < 0.67 with energy very close to the GSL and most were (210)-oriented superlattices. These structures compete to become the second inflection point of the GSL, the uncertainty resulting from the incomplete CE. On the other hand, the first inflection point always is the DO222/4 structure, even for small variations in the parameters of the CE. Therefore, the GSL is composed by the DO222/4 structure and another (210)-oriented superlattice in the range of composition 0.5 < jc < 0.67. Recently we published a study on the ordering of InGaN alloys, based on an entirely different method requiring a small number of ab initio calculations. That method is expected to be less precise and yet it lead to the same qualitative result, i.e. the formation of stable ordered structures around x = 0.5 [35].
16.4.3 The Thermodynamics via Monte Carlo Simulations Ordering is sensitive to the growth conditions, occurring only in a determined temperature range because a minimum temperature is needed for the surface atoms to diffuse to their ordered positions while a higher temperature would tend to drive the system into the disordered phase. Therefore, having identified the ground state structures, it remains to be seen whether the stability-limit temperature, T^, is sufficiently high to allow the growth of these ordered phases. For this purpose, we proceeded with the MC thermodynamics, as described in Section 16.2.3.1. Knowing the Hamiltonian Eq. (16.10), defining the MC periodic cell, and choosing the temperature, one attempts switching spins between two sites, accepting the motion or refusing it according to the Metropolis recipe [53]. It is also important to point out that we explored the thermodynamic consequences of the coherent epitaxy rather than its kinetic aspects. The only imposed kinetic limitation was to restrict diffusion to the exchange of nearest-neighbor atoms. We observed ordering via the intensity of the Bragg reflection peaks, as explained in Section 16.2.5. In Figure 16.7 the intensity of the Bragg reflection peaks for three different temperatures in (a) for the Alo.5Gao.5N and (b) for the Ino.5Gao.5N alloy is depicted. In the case of (a) the AlGaN alloy, we can observe that even for very low temperatures as T = 400 K, there is already diffuse scattering, and it is not possible to identify a Bragg peak position corresponding to
Phase Separation and Ordering
413
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Figure 16.7. Intensity of the "Bragg" lines for all k in the first Brillouin zone for three temperatures, (a) for Alo.5Gao.5N and (b) for Ino.5Gao.5N.
an ordered phase, which means that the AlGaN is a solid solution. In the case of (b) the InGaN alloy, from the Bragg peak positions in the first Brillouin zone one unequivocally identifies the ordered phase as DO222/4. In other words, the MC calculation confirms the ground state search in that it also sets the configuration DO222/4 as the most stable at x = 0.5. Observe that, unlike predicted by the first term in Eq. (16.15), above the transition, when there is no long-range order, we still obtain a ^-dependent scattering. That comes from the short-range correlations neglected in Eq. (16.14) [64]. In order to establish the value of the transition temperature of the InGaN alloy to the disordered phase, the behavior of the intensity of the peak corresponding to the DO222/4 structure was studied by varying the temperature. This behavior is depicted in Figure 16.8. We can observe that the intensity of the Bragg lines has a continuous behavior as the temperature increases, and that there is a smooth transition from 0 K to about 1000 K with an inflection at about 700 K, possibly indicating afirst-ordertransition. Therefore, the strained cIno.5Gao.5N has a stable DO222/4 phase with a broad enough temperature window of stability. It is interesting to point out that there exists a large class of tetrahedrally bonded semiconductors with the DO222/4 (chalcopyrite) structure for which the critical temperature is known to be very high [72]. In particular, for another system also with
474
Optoelectronic Devices: Ill-Nitride
400
600 800 1000 Temperature (K)
1200
1400
Figure 16.8. Intensity of the "Bragg" line (210) as a function of temperature, obtained when heating the MC sample from perfect chalcopyrite order.
large size mismatch, the GaAS;».Sbi_;^, it was predicted that the coherent epitaxy leads to the formation of the D0222/4-type ordered alloys [73]. For the GaAsi-^^N^c alloys it was also found that the (111) or (100) direction are energetically less stable than the chalcopyrite structure, where the strain is maximally relieved by intermixing [74]. Recently, PL and high-resolution X-ray diffraction (HRXRD) experiments were combined to observe light emission from In-rich QDs in c-GaN/InGaN/GaN double heterostructures (DHs), grown on GaAs(OOl) substrates at 600°C, with In content varying from x = 0.09 to 0.33 [33]. The structures consisted of a 300 nm thick GaN buffer layer previously grown on a GaAs(OOl) substrate, a 30 nm thick In;,Gai_;tN layer with X in the range 0.09-0.33, and a 30 nm thick GaN cap layer. The striking feature of the HRXRD reflexes is the fact that all the samples comprise In-rich QDs with In content of about x = 0.55, which is very different from what was formerly predicted and observed for a fully relaxed InGaN layer (see Section 16.3.2). Thus, there is a strong indication that these In-rich phases observed in these samples are mainly ordered Ino.5Gao.5N domains of (210)-oriented superlattice structures with In concentration ranging from 0.5 to approximately 0.625. This is in agreement with the In contents, measured by HRXRD in these DHs, of about 0.55 instead of exact 0.5. Although, ordering remains to be detected in the cubic modification of the alloy.
16.5. THERMODYNAMICS OF THE QUATERNARY AlGaInN ALLOYS We applied the method described in Section 16.2.3.2 for the Al;^:Ga3;Ini_;, _ yN quaternary alloy. The use of an energy expansion in the energies of the 141 clusters allows us to perform
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Figure 16.9. Distribution of atoms in the MC cell for T < Tc showing the In-rich phase, as obtained from Monte Carlo calculations for the Alo.5Gao.83Ino.02N quaternary alloy. Only the Al, Ga and In atoms are shown. The value T^. = 1100 K for the critical temperature was determined from the annealing simulation process.
a ground state search, comparing different structures of the same composition [49]. The ground state search leads to an equilateral triangle whose vertices connect the binaries (AIN, GaN and InN) that form the quaternary alloy [75], which means that there is no stable ordered phase and the quaternary alloy tends to phase separate. Since we have identified the ground state structures, we perform MC simulations to calculate the temperature and composition ranges of the solid solutions centered at the binaries. The way we made the MC dynamics (spin switching between two sites) guaranteed that the concentrations x and y remained fixed (canonical Monte Carlo). The two sites were chosen among the 12 cation nearest neighbors of the first site, as we did in the case of the ternary alloys. It is known that, at a given composition, the phase separation occurs below a critical temperature T^ while a higher temperature would tend to drive the system into the disordered solid solution phase. In Figure 16.9 we show the cations distribution in the equilibrium MC cell for an Al^Ga^Ini-^, _-^N quaternary alloy with typical growth compositions x = 0.15 and y = 0.83. We can clearly see a phase separation for T < T^ governed by the In nucleation. If the temperature is raised above T^, an homogeneous distribution is found to take place as expected. Further theoretical studies on these quaternary alloys are in progress, aiming also a deeper understanding of the emission processes occurring in these systems. 16.6. SUMMARY Summarizing, we reviewed here the recent progresses which were achieved in the understanding of the thermodynamic properties of the group-Ill ternary and quaternary alloys in their cubic (zinc blende) phases. The occurrence of phase separation and ordered phases in the alloys were addressed by means of state-of-the-art first-principles total energy calculations in combination with CE methods for the treatment of alloy disorder
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and compositional fluctuations. Phase separation is found to take place in the unstrained InGaN, InAlN, BGaN, BAIN, and AlGaInN alloys. For InGaN and AlGaN, the effect of a biaxial strain induced by the GaN buffer layer was considered in the calculations. It is found that the strain suppresses the phase separation in InGaN, and in both, InGaN and AlGaN it gives rise to ordered phases formation. The theoretical predictions for InGaN were used to interpret the results obtained from recent high resolution X-ray and Raman spectroscopy measurements.
ACKNOWLEDGEMENTS We acknowledge the very fruitful collaboration on the study of properties of group-Ill nitrides with D.J. As, F. Bechstedt, T. Frey, J. Furthmiiller, A. Kharchenko, V. Lemos, K. Lischka, D. Schikora, E. Silveira, and A. Tabata. LKT and MM were sponsored by the Brazilian funding agency FAPESP. LMRS would like to acknowledge the partial financial support received from the Brazilian National Research Council (CNPq) under contract NanoSemiMat/CNPq # 550.015/01-9.
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optoelectronic Devices: Ill-Nitrides M. Razeghi and M. Henini (Eds.) © 2004 Elsevier Ltd. All rights reserved.
Chapter 17
Electronic Properties of Intrinsic and Heavily Doped 3C-, nH-SiC (n = 2, 4, 6) and III-N (III = B, Al, Ga, In) Clas Persson^ and Antonio Ferreira da Silva** ^Applied Materials Physics, Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm SE-100 44, Sweden ^Instituto de Fisica, Universidade Federal da Bahia, Campus Universitdrio de Ondina, Salvador 40210 340, Bahia, Brazil
17.1. INTRODUCTION Cubic and hexagonal SiC, BN, AIN and GaN are all wide bandgap semiconductors, whereas the fundamental bandgap energy of InN is believed to be below 1.0 eV. The main difference between SiC and the group-III-nitrides is that most stable SiC polytypes have indirect fundamental bandgaps whereas the most common Ill-nitrides have direct bandgaps. The physical properties of SiC make it an outstanding candidate in power switching device applications where Si and GaAs based devices present a very low performance [1]. SiC has a wide indirect fundamental gap of 2.4-3.4 eV, depending on polytype, and a large electrical breakdown field strength (~3 X 10^ V/cm which is about 10 times larger than in Si) [2]. This makes SiC one of the most interesting semiconductor for high-power devices, despite the fact that SiC has a low electronic mobility; the electron and hole mobilities are about 300-900 and 50 cm^A^ s, respectively, whereas the corresponding mobilities are 1400 and 400 cm^A^ s in Si [2]. Moreover, SiC has a high thermal conductivity (~ 4 W/cm K, which is about three times larger than in Si) and a high thermal stability, and SiC-based devices can, therefore, operate at high temperatures and require less cooling. In addition, the large saturation drift velocity of SiC (~2 X 10^ cm/s, about two times larger than in Si) is used in high-frequency device technology. The crystal has, because of its high thermal conductivity, large bandgap, strong bonds, high-radiation resistance, and chemical inertness, become a prominent material for high-power, high-temperature, and high-frequency devices. Devices like field effect transistors, bipolar storage capacitors, and ultraviolet detectors have been fabricated [3,4]. Despite its E-mail addresses: [email protected] (C. Persson) and [email protected] (A. Ferreira da Silva)
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technological importance, there have been so far only a few reports on the electronic and optical properties of n- or p-type doped SiC polytype [5-11]. First-principles calculations of the electronic band structure of SiC were performed as early as in the 1960s by Bassani in 1963 [12] and by Herman et al. in 1969[13], using the pseudopotential-based orthogonalized plane wave (OPW) method. The Ill-nitrides are wide-bandgap semiconductor materials with low compressibility, good thermal stability, and with chemical and radiation inertness. GaN-based wide bandgap semiconductors have drawn much current intensive research, mostly because of their potential applications for optical devices such as emitting diodes and, hightemperature electronics [14-27]. Since the appearance of the first blue laser diode based on GaN operating at room temperature, the investigation of group-III nitrides has increased rapidly [28-30]. The recent technological developments of the group-III nitrides semiconductor compounds cover a wide photon-energy range which span from — 0.7 eV for InN to ~ 7 eV for BN [2,31-36], i.e. encompass the near-infrared region extending well into the ultraviolet spectral range, thereby bridging the entire visible spectrum. Therefore, the Ill-nitrides are of great importance in the design of optical waveguides in laser diodes. A theoretical comparison between zinc-blende (zb) and wurtzite (wz) SiC, AIN, and GaN based on a linear-muffin-tin-orbital method within the atomic sphere approximation (ASA) have been made by Lambrecht and Segall [37]. They found rather similar equilibrium cohesive energies, bulk modulus, and pressure derivatives for the different materials. The group Ill-nitride semiconductors GaN, AIN, InN and their ternary and quaternary alloys have been extensively applied in optoelectronic and electronic device technology [38-41]. Most of the work reported so far refers to the stable hexagonal wz phase of the materials. However, the metastable cubic zb modification arises as an advantageous alternative for device applications. The fact that the zb-GaN based structures are free from modulation due to spontaneous polarization and strain-induced piezoelectric effects makes the studies of their basic properties very important for the understanding of the device characteristic and improvement of their performance [42,43]. As far as the zb nitrides are concerned relatively little work has been done up to now [41]. Most of the effort has been concentrated on as-grown and doped zb-GaN, while the experimental studies of the electrical properties of zb-AlN do not exist and of zb-InN is at the beginning stage [44,45]. Early peudopotential calculations by Bloom [46], Jones and Lettington [47], Bourne and Jacobs [48] and Foley and Tansley [49] as well as orthogonal plane-wave calculation by Hejda [50] show accurate band structures of AIN, GaN, and InN. Furthermore, as a result of the recent progress in crystal growth, one can also produce thin films of cubic InN [51-53], which opens up for further technological applications involving Ill-nitride alloys. The electronic structures of hexagonal and cubic BN have been investigated for decades, both theoretically and experimentally [2,54-59]. Early peudopotential calculations [60-62] of zb-BN yield indirect bandgap energies in
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the range of 7.6-10 eV. BN is analogous to diamond in chemical inertness, wide bandgap, high thermal stabiHty, high hardness and high thermal conductivity. However, BN has an advantage compared to diamond concerning to mechanical ferrous applications. At high temperature, for instance, diamond, in contrast to BN, reacts to form soot, which is not much desired [63]. Recently Zhang et al. [64], using the chemical vapour deposition techniques based on fluorine chemistries, achieved high quality cubic BN films with a thickness of up to 20 iJim. The present theoretical study of the electronic structure and the effective masses of 3C-, nH-SiC (n = 2, 4, 6) and III-N (III = B, Al, Ga, In) are based on the local density approximation (LDA) within the density functional theory (DFT), employing the firstprinciples, full-potential linearized augmented plane wave (FPLAPW) method [65]. We use the exchange-correlation potential of Perdew and Wang (PW) [66]. The spin-orbit interaction is treated variationally outside the self-consistency loop. See Refs. [67-70] for details about the computational method. The LDA is known to underestimate the bandgap energy E^ for semiconductors. We have, therefore, made an estimate of the correction A^ to the bandgap by using a quasi-particle method proposed by Bechstedt and Del Sole [71,72]. Geometric optimization of the crystals results in lattice constants confirming the experimental values. It is demonstrated that even small variations in the internal atomic positions have a strong impact on the crystal-field splitting of the uppermost valence bands in the hexagonal SiC. The uppermost valence bands in all materials considered here have been found to be non-parabolic in the vicinity of the /"point and, furthermore, the lowest conduction band in 6H-SiC has a very flat and non-parabolic double-well structure. We provide a symmetry classification of the electron states, both for the single and the double space groups. Photothermal spectroscopy has achieved great developments in the last two decades, and it has been successfully applied to semiconductors samples in case of powders, nonpolished samples, crystalline, polycrystalline or amorphous thin films, multilayered structure, etc. One of the principal advantages of photoacoustic spectroscopy over other optical measurements, e.g. optical absorption, is that it produces similar spectra, and may provide direct information of the non-radiative recombination process and, consequently, compliments the absorption and the photoluminescence spectroscopy. In the present work, we investigate the bandgap energies of SiC experimentally by photoacoustic spectroscopy. Many fundamental physical properties of semiconductors are governed by the detailed structure of the energy bands near the band edges. The effective electron and hole masses are fundamental quantities of semiconductors, used in numerous analysis of experiments and theoretical modellings. Motions of the electrons in the conduction band and the holes in the valence band can be represented by the effective electron and hole mass, respectively, which is usually anisotropic depending on the shape of the corresponding bands. The masses are defined from the curvature of the energy bands, and can be
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experimentally determined through their correlation with other parameters in processes involving the transport of motion of electrons and/or holes. The effective electron- (or hole-) mass tensor describes thus the response of an electron (a hole) in the conduction band (in the valence band) to an applied electric field. To date, there is a lack of experimental information about the effective masses, especially the effective hole masses. The full-potential LDA calculations can predict with a rather good accuracy the effective masses in most semiconductors. Our calculated effective electron and hole masses in both SiC and III-N confirm the few available measured values in these materials. We show that inclusion of the spin-orbit interaction is crucial for accurately calculating the effective hole masses, even in light materials. In order to properly design semiconductor devices, it is necessary to understand the effects on the electronic band structure due to doping. In heavily doped semiconductors the impurity-impurity interaction causes a shift in the electronic structure which strongly affects the electronic and optical properties of the materials. We study these dopinginduced effects on the electronic structure by calculating the self-energy for the lowest conduction-band states and for the uppermost valence-band states in n- and p-type SiC, GaN, and AIN, utilizing a zero-temperature Green's function formalism. The correlation interaction was described within the random phase approximation (RPA) [73,74] with a local-field correction of Hubbard [75], and the electron-impurity ion interaction was obtained from second-order perturbation theory [76]. The resulting energy shifts of the fundamental bandgap and of the optical bandgap have been calculated. It is found [5,6,70,77] that the non-parabolicities of the energy bands strongly influence the calculated bandgap narrowing (BGN) for high doping concentration. By comparing the calculated total energies of the localized donor electrons in the non-metallic phase and of the electron gas in the metallic phase the critical concentrations for the doping-induced metal-non-metal (MNM) transition Mott transition have been estimated for n- and p-type SiC, AIN, and GaN [5,70,78-80]. The purpose of this chapter is to review the latest calculations and measurements of the electronic properties of intrinsic and heavily n- and p-type doped 3C-, n H-SiC {n = 2,4,6) and cubic and hexagonal III-N (III = B, Al, Ga, In). We present the calculations of the energy bands near the fundamental energy bandgap, which is important for the understanding of the electronic transport properties in these materials. Special attention has been paid on the non-parabolicities of the energy bands near the band edges. In Section 17.2 we describe the cubic and hexagonal crystalline structures of SiC and III-N. We define the utilized notation of symmetry points of the Brillouin zone (BZ) as well as the point-group notation of the irreducible representations of the eigenstates. Section 17.3 gives a description of the electronic band structure and the effective electron and hole masses in SiC obtained from the relativistic full-potential calculations. The bandgap energy of SiC has been investigated experimentally by photoacoustic and transmission measurements. We also present the calculated dielectric constants of
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intrinsic nH-SiC in the long wavelength limit. In Section 17.4, we describe the effects on the electronic properties of the semiconductors due to heavily n- and p-type doping. The critical concentration for the doping-induced MNM transition in both n- and p-type SiC is calculated as well as the impacts on the bandgap energies due to doping. Section 17.5 gives a description of the electronic band structures as well as the effective electron and hole masses in cubic and hexagonal BN, AIN, GaN, and InN. We also present the calculated dielectric constants of intrinsic zb- and wz-III-N. In Section 17.6, we present the doping-induced effects on the reduced and optical band in heavily n- and p-type doping of cubic and hexagonal GaN and AIN. In Section 17.7, we give a brief summary.
17.2. CRYSTALLINE STRUCTURES Most group IV-IV and III-V semiconductors crystallize in cubic zinc-blende (zb) structure with Tj space-group symmetry or hexagonal wurtzite (wz) structure having Cg^ space-group symmetry, see Figure 17.1. These structures create the natural tetrahedron
Figure 17.1. (a) Cubic SiC and III-N possess zinc-blende structure, whereas (b) the hexagonal structures are formed by stacking hexagonal bi-layers along the (0001) direction. We show in (b) the wurtzite structure with the stacking sequence BC BC (see text). The Brillouin zones of (c) zinc-blende and (d) hexagonal SiC and III-N structures.
Optoelectronic Devices: Ill-Nitrides
484
cation-anion bonds. The exception is BN, which has metastable zb and wz structures, and the most stable structure is an open hexagonal structure. Moreover, SiC is known to easily form different polytypes, up to more than 200 different structures. The most common SiC structures are the zb structure (denoted 3C-SiC), the wz structure (denote 2H-SiC), and two more hexagonal close-packed structure, namely, 4 H - and 6H-SiC, also possessing the Cl^ space-group symmetry. The polytypes of the zinc-blende and the hexagonal close-packed structures can be constructed by stacking hexagonal bilayers in different sequences (see Figure 17.2). In the zb structures, the hexagonal planes are perpendicular to the (111) direction. For SiC, defining u^^ij) and UQ(J) as the location along the c-axis (i.e. the (0001) direction) of thejth hexagonal silicon andjth hexagonal carbon planes, respectively, then a bilayer consists of two close-lying hexagonal planes (the 7th Si plane plus the 7th C plane) having same atomic xy-positions within the hexagonal plane. The bond length in the z-direction is lwsi(/) ~ wc(/)l, and the bond length is approximately 0.3750(2c/n) [where n is the number of bi-layers in the unit cell; « = 2, 4, and 6 for 2H-, 4H-, and 6H-SiC, respectively]. Normally, one defines plane A as the hexagonal bilayer containing a silicon atom at (0,0, Msi(/)) ^iid ^ carbon atom at (0,0, UQ{J)). Moreover, the 5-plane here is defined as the hexagonal bilayer with a silicon atom at (2/3,1/3, Wsi(/)) ^^^ ^ carbon atom at (2/3,1/3, UQ(J)) and the C-plane is defined as the hexagonal bilayer with a silicon atom at (1/3,2/3, Msi(/)) and a carbon atom at (1/3,2/3, Uc(j))> The different polytypes of SiC can be generated by stacking the three planes in different sequences and for the present
O A-siie A a-site • C-site
\ i-o
:
:
I
hk-o :
i>o
:
I
:
i i-o:
I
:
:
4>0-t \
• C-atom ® Si-atom
I
!
:
:
o
04 i L 6 4 -i wsi(6) I I o4Wsi(5)
o
\ i^O-i Wsi(3) ^>6 I : t/si(2)
1 i>6wsi(4) o--^ . _l_ _!__,__
ABC 3C-SiC zb-lll-N
-f-i-i--BC 2H-SiC wz-lll-N
t-f
C A 4H-SiC
A B CA 6H-SiC
Figure 17.2. Stacking sequences of the hexagonal bi-layers in the cubic and hexagonal SiC and III-N structures.
Sic and III-N Heavily Doped
485
calculations we have chosen the periodic stacking sequences (ABC ABC.) for zb-III-N and 3C-SiC, {BCBC.) for wz-III-N and 2H-SiC, {ACAB ACAB...) for 4H-SiC, and {ABCACB ABCACB...) for 6H-SiC. For each bilayer there is one inequivalent Si and one inequivalent C atom, and thus 2H-, 4 H - , and 6H-SiC have 4, 8, and 12 atoms per unit cell, respectively. Hence, the unit cell of 2H-SiC has the smallest extension in the z-direction and the unit cell of 6H-SiC has the largest extension of the polytypes considered here. The Brillouin zones (BZs) of cubic and hexagonal SiC and III-N are shown in Figure 17.1(c) and (d). The symmetry points and the symmetry lines of the BZ are marked. The height of the hexagonal BZ is lirlc, and since 6H-SiC has a large unit cell, its corresponding BZ is rather small. This has been shown [81] to influence the electronic properties of 6H-SiC, because a smaller BZ implies less k^-states in the first BZ. The crystalline anisotropy of the hexagonal structures are reflected by the anisotropic electronic and optical properties of these materials. To describe the anisotropic properties of these materials, the longitudinal (||) direction of the hexagonal structures here is defined as the directions along the c-axis, i.e. the hexagonal (0001) direction. The in-plane transverse ( ± ) direction is the hexagonal plane perpendicular to the longitudinal direction. For the considered zinc-blende structures, the longitudinal direction is defined as the (100) direction. The transverse direction is the plane perpendicular to the longitudinal direction. The single-particle electron states can be classified within the theory of groups [82]. Here, the subscripts of rj(^) denote the irreducible representation of the double (J) and the single {s) point groups. In this work, we have classified the irreducible representation according to the notation of Koster et al. [83]. Although no physical properties depend on the choice of origin of the coordinate system, it is important to note that the point-group notation of the irreducible representations depends for certain k-points lying on the BZ surface on the choice of atomic positions [82,84]. In this work, a Si or cation III atom is positioned at (0,0,0) in the zinc-blende structures (i.e. 3C-SiC, and zb-III-N), at (2/3,1/3,0) in the wurtzite structure (i.e. 2H-SiC, and wz-III-N), and at (0,0,0) in the 4 H - and 6H-SiC structures.
17.3.
ELECTRONIC PROPERTIES OF SiC
The first calculations of the electronic band structure of SiC were performed in the 1960s by Bassani [12] in 1963 and by Herman et al. [13] in 1969, using the first-principles OPW method. The calculations were performed for 3C-SiC and, in the latter calculation, also for 2H-SiC structures, and even though these early calculations give somewhat quantitatively different band structures compared to corresponding calculations in the late 1990s [37,67-70,85-102], the band structures are qualitatively very similar. The calculated electronic structures have, in many cases, been found to accurately describe electronic properties of SiC, and calculations have also predicted properties that later have
486
Optoelectronic Devices: Ill-Nitrides
been verified experimentally. The effective electron masses in different SiC polytypes were calculated by Wenzien et al. [85], Willatzen et al. [86], Lambrecht et al. [91], and Persson et al. [67-70]. Moreover, taking into account the polaronic effects (i.e. interaction with longitudinal optical phonons) the calculations of hole masses of 4 H - and 6H-SiC by Persson et al. [68,103] have been confirmed by cyclotron resonance measurements by Son et al. [103-105]. Due to the lack of high-quality single-crystalline SiC crystals, there are still electronic properties of SiC that are established only by theoretical studies [103]. Heavy doping of semiconductors changes the electronic and optical properties of the materials. Above a certain concentration N^ the semiconductors reveal metallic behavior also in the low temperature region. The earlier published theoretical investigation of heavily doped SiC was performed by Lindefelt [106] who calculated the bandgap renormalization in heavily n- and p-type doped 3C-, 2H-, and 6H-SiC using a modified semi-empirical method to obtained the electron-electron correlation interaction. In this work, we present a many-particle calculation [5,6,73-78] expounded within the RPA with a Hubbard local-field correction. The calculations of the critical concentration N^ were performed with three different methods described in Section 17.4. Moreover, the calculation of the doping-induced effects on the band structure show strong BON at high doping concentrations, especially for p-type doping. In the calculations, we take into account the lowest conduction band (cl) and the three uppermost valence bands (vl, v2, and v3, where vl is the uppermost band). In cubic materials vl, v2, and v3 correspond to heavy-hole (hh), light-hole (Ih), and spin-orbit (so) split-off bands, respectively. 17,3,1 Electronic Band Structure The lattice constant a of the zinc-blende structure was obtained by minimizing the total energy with respect to the unit cell volume. The hexagonal lattice constants a and c, and the internal lattice parameter u (i.e. the position of the hexagonal planes within the Cg^ symmetry) were obtained by minimizing the total energy with respect to changes in the atom positions. The minimization was carried out by first varying the parameters a and c at the experimental values of the volume and of M, whereupon the volume was varied, by keeping the ratio c/a fixed. Thereafter, the internal lattice parameter was varied. The theoretically determined lattice constants and internal lattice parameters are in good agreement with experiments [2]. Having established the geometric structure of the crystals, the electronic band structures are calculated for 3C-, 2H-, 4H-, and 6H-SiC (Figure 17.3) using the fully relativistic FPLAPW within the LDA. The band structures of the hexagonal polytypes show clear similarities, especially for the valence-band structure although 4 H - and 6H-SiC has more bands than 2H-SiC due to larger crystalline unit cells in the c-direction. These additional bands in the larger SiC structures compared to 2H-SiC can to some extent be regarded as band folding of the bands in the c-direction, especially for the additional valence bands.
487
Sic and III-N Heavily Doped (b)
(a)
X
10
K^
10
^ ^ :
^ 5 > ^ 0 P -5
5 1
0
^^
-5
-in
iS -10
-.
-15
u X
r
L
J:
i
-15 M
w
K
r A 2H-SiC
3C-SiC
L
M
(c) ^f^^
^
10 ^
5
:
> ^ B
0 -5
3
Q)
LU - 1 0
-15 M
K
:
r A
K
L M
4H-SiC
FA 6H-SiC
Figure 17.3. Electronic band structures of (a) 3C-, (b) 2H-, (c) 4H-, and (d) 6H-SiC, obtained from the fully relativistic FPLAPW LDA + QP calculation.
The LDA is well known to underestimate the bandgap energy E^ for most semiconductors. Because of the incorrect bandgap, one cannot guarantee that the calculations yield accurate properties related to the excitation effects. However, it has been shown by Del Sole and Girlanda [71] that the LDA combined with the constant bandgap correction A^ describes the optical absorption spectrum rather well. We have, therefore, made an estimate of the correction A^ to the bandgap by using a quasi-particle (QP) method proposed by Bechstedt and Del Sole [72]. Their model for the correction is based on the difference in self-energies obtained from the LDA and the GW approximation, and the correction is given by 2178(0)
f(x) =
Jo IT? [(1 -
ap)/(^TF^AO + (1 +
«P)/(^TF^BO]'
3 - lOx^ + 3x^ 3(1+Jc2)^
'
rA =
477X1.6
^B =
a 417X1.8
(17.1a) (17.1b)
In the equation above e is the elementary charge, ^XF is the Thomas-Fermi wave number, 8(0) is the static dielectric constant, and a^ is the polarity of the interatomic
488
Optoelectronic Devices: Ill-Nitrides
interaction [72,107]. With the QP model we correct the LDA bandgap energies with the constant energy shift A^. The QP correction is almost equal for all four SiC polytypes considered here (^g = 1.13-1.17 eV) which means that for these polytypes LDA without any corrections gives the correct energy variation of the bandgap with respect to the polytypes. The LDA + QP fundamental bandgaps are J^g + Zlg = 2.46, 3.26, 3.34, and 3.10 eV, for 3C-, 2H-, 4 H - , and 6H-SiC, respectively, which are very close to measured values (Table 17.1). Whereas both Si and diamond have their conduction-band minima along the Zl-line, the lowest conduction-band minimum of 3C-SiC is located at the X-point (with D2d pointgroup symmetry). The irreducible representation of the minimum is Xc7(4), using the notation of Koster et al. [83]. Also the second conduction-band minimum of 3C-SiC is at the X-point, and the energy difference between the two minima is [68] A£'(Xc6(i)-Xc7(4)) = 2.92eV. The measured value of this energy difference by Patrick and Choyke [113] is 3.1 eV obtained from optical absorption of n-type 3C-SiC. In 2H-SiC, the lowest conduction-band minimum is at the A'-point (C^v point-group synmietry) having the irreducible representation ^^4(2)- The conduction-band minimum of
Table 17.1. Lattice parameters a, and c of 3C-, 2H-, 4H-, 6H-SiC
a (A) c(A) "Sid)
"c(l) usi(2)
uci2) us.O) "c(3) CBM ^^(eV)
£g + 4 ^g
VBO (eV) 4 f (eV) ^so (meV)
LDA Expt. LDA Expt.[2] LDA LDA LDA LDA LDA LDA LDA/Expt.[2,108-110] LDA LDA + QP Expt. PA Expt.[2] LDA LDA LDA Expt. [111,112]
3C-SiC
2H-SiC
4H-SiC
6H-SiC
4.343 4.360
3.061 3.076 5.034 5.048 BO.O B 0.3757
3.067 3.073 10.032 10.052 A 0.0 A 0.3750 C 0.5000 C 0.8760
X 1.30 2.46 2.44 2.40 0.00
K 2.11 3.26
M 2.17 3.34 3.30 3.29 0.06 0.050 8.4
3.080 3.081 15.114 15.117 A 0.0 A 0.3750 B 0.5001 5 0.8751 C 0.9996 C 1.3746 U 1.97 3.10 3.03 3.10 0.05 0.038 8.1 7
14.5 10
3.33 0.12 0.131 8.8
The internal lattice parameters u^yc (/) of the A, B, and C-planes (see Figure 17.2) are in units of 2c/n, where n is the number of bilayers (i.e. 2,4, and 6 for 2H-, 4H-, and 6H-SiC, respectively) The notation of the symmetry k-point position of the conduction-band minimum (CBM) is according to Figure 17.1. Fundamental bandgap energy Eg with and without quasi-particle correction Ag. The valence-band offset (VBO) is relative to VBO of 3 C SiC. The crystal-field zl^f ^nd spin-orbit A^ split-off energies are at valence-band maximum with a fully relaxed LDA calculation. Eg is also obtained experimentally by photoacoustic (PA) measurements.
489
Sic and III-N Heavily Doped
4H-SiC is at the M-point (C2v point-group symmetry) with the irreducible representation ^c5(4). whereas the minimum of 6H-SiC is along the ML-line (also C2v point-group symmetry) with the irreducible representation t/c5(4)- Thus, 2H-SiC has two, 4H-SiC has three and 6H-SiC has six equivalent minima in the first BZ. The second lowest conduction-band minimum is located at the M-point for 2H-, 4 H - , and 6H-SiC, and consequently in 4H-SiC, like in 3C-SiC, there can be direct transitions between the two conduction-band minima. The energy difference between the two lowest minima is small in 4H-SiC [AEiMc^^i^-M^^^^^) = 0.12 eV], which is close to the experimental value of — 0.14 eV, obtained by Im et al. [114] from ballistic electron emission microscopy. This energy difference of the two minima is close to the optical phonon energies of 0.10-0.12 eV [115]. The second band will, therefore, influence the electronic transport properties at high temperatures and/or when high electric fields are applied. In 2 H - and 6H-SiC the second minimum is A£:(Mc5(i) - A^c4(2)) = 0.60 eV and AE(Mc5(4) - Uc5(4))= 1.16QY, respectively, above the lowest conduction-band minimum. Backes et al. [116] interpreted the different SiC polytypes as superlattices consisting of mutually twisted cubic layers. Using the empirical pseudopotential model of SiC, they obtained very reasonable bandgap energies for the hexagonal polytypes, with the largest error (0.70 eV) for 2H-SiC. The lowest conduction band of 6H-SiC is very flat along the ML-line (Figure 17.4). The difference in energy between the minimum and the M- (L-) point is only 5.3 (45.6) meV. Since the minimum is not at a symmetry point, the band has a double-well-like nature (a "camel's back") along the LML-line with M as a saddle point. Therefore, intervalley scattering can easily occur between the two close-lying minima, which will have a direct consequence on the electronic transport. The non-parabolic curvature along the ML-line
(a) • 6H-SiC . CBM
\
'-5(104)
•
H
40 £ 0)
c LU
20 •
^5(4)
U 5 ( 4 ) / ^-Q-Q^
0 M
3.10 Wave vector (arb. units)
3.15 Energy (eV)
Figure 17.4. (a) The shape of the lowest conduction band in 6H-SiC along the ML line. Open circles show the fitted polynomial of Eq. (17.2). (b) Density-of-states of the conduction band [121]. Dotted line represents a parabolic approximation of the conduction-band minimum.
490
Optoelectronic Devices: Ill-Nitrides
can be described by the polynomial: £,!(/:„) = E,,(kM) - (a,ki\f + (a2^t
- (a,^)\
(17.2)
with the fitted parameters ai = 1.102 A(eV)^''^, ^2 = 2.980 A(eV)^^\ and ^3 = 2.961 A(eV)^^^. A strong efifect on the electronic mobility due this non-parabolicity in 6H-SiC has been seen in recent Monte Carlo studies of SiC based MESFETs by Bertilsson et al. [81]. The camel's back structure has been confirmed by optical detection of cyclotron resonance (ODCR) experiments [117]. The ODCR results [118] could also explain the sizable anisotropy of the electron Hall mobility in 6H-SiC as measured by Hall effect [119,120]. In order to investigate the sensibility of the ML curvature, we have performed an LDA calculation with the lattice constants a = 3.089 A and c/p = 2.528 A, which represent the crystal at the temperature ~ 700 K. The conduction-band minimum was almost unaffected by this change in volume. However, a many-particle calculation of doping-induced effect in SiC [5] shows that a band filling (n^ ~ 10^^ cm~^) of the conduction band strongly modifies the band curvature, whereas the inclusion of the electron-optical phonon coupling has only a relatively small effect on the double-well structure. We investigate experimentally the electronic bandgap by photoacoustic (PA) spectroscopies. PA spectroscopy is directly related the periodic heat generated in a sample due to the absorption of modulated light. Generally the PA experimental set up consists of a sample enclosed in a sealed cell at atmospheric pressure coupled to a sensitive microphone. Therefore, the temperature of the encapsulated gas is modulated at the excitation frequency and the microphone detects the resulting dynamic pressure. The signal generated by this process depends on the amount of heat generated in the sample due to its optical absorption coefficient, the non-radioactive processes efficiency, and the thermal diffusivity. The study of the dependence of the sample absorption coefficient on the light source wavelength allows one to determine optical and electronic properties of opaque and transparent materials [122]. In order to minimize the background noise a new designed PA cell with double walls was built. This new device consists of two concentric cylindrical wall cells with UV-quartz windows. The space between the walls was filled with air at atmospheric pressure. The internal cell cavity was gold plated in order to minimize unwanted radiation absorption. Air was used as coupling media between the sample and the microphone. A 1/2-in. condenser microphone (Bruel and Kjaer, model 3547) was used to monitor the change in the pressure inside the cell. A 150 W Xe lamp, with an ellipsoidal reflector, coupled to a 0.22 m double monocromator (Spex model 1680) was used as variable wavelength light source. The light was chopped at a frequency of 5 Hz, to improve the signal/noise ratio. The measured PA bandgap energies (Table 17.1) confirm the theoretical values. For optical properties, the direct bandgap transition energy is important. The lowest energy for direct transitions from the valence band to the conduction band
Sic and III-N Heavily Doped
491
is A£(Z,6(i) - X,6(5)) = 5.65 eV, Ai^(M,5(i) - M.^^)) = 5.08 eV, AE(M,5(4) " M,5(2)) = 4.48 eV, AE(M,5(4) - M^s(3)) = 4.22 eV, for 3C-, 2H-, 4 H - , and 6H-SiC, respectively, calculated with the LDA + QP model. The direct T-point transition energy in 3C-, 2H-, 4 H - , and 6H-SiC is AE(r,6(i) - r,8(5)) = 7.53 eV, A£(r,8(3) " ^9(5)) = 6.04 eV, A^(r,7(i) - r,9(5)) = 6.31 eV, and AE(r,8(3) - r,g^5)) = 6.25 eV, respectively. The differences between the different SiC polytypes in the fundamental bandgap energy as well as in the bandgap energy for direct transitions are important quantities for alloying different SiC polytypes. For instance, it has been shown by Lindefelt et al. [123] that cubic 3C-SiC inclusion in terms of hexagonal stacking faults in 4 H - and 6H-SiC (i.e. reordering of the hexagonal bi-layers A, B, and C, see Figure 17.2) creates localized conduction band states in at the dislocation. Since the heat of formation of the four polytypes is very similar (in the order of meV per atom), the stacking faults can easily be formed at improper growth conditions. We find from our first-principles LDA calculations that the valence-band offset (VBO) between the four SiC polytypes is at most —0.1 eV (Table 17.1). Our calculated VBO values agree well with earlier first-principles LDA pseudopotential plane-wave calculations by Bechstedt et al. [101]. We find that the energy difference of the Si (and C) Is core levels at alloying is almost zero between the different polytypes which can be explained by the fact that all polytypes have similar bonds and bond lengths. Thus, by, for instance, randomly alloying 3C-SiC and 4H-SiC, the energetic position of the valence-band maximum is not much affected, but the lowest overall conduction-band minimum will have contribution mainly from the 3C-SiC polytype. Despite similar values of the calculated lattice constants and bandgap energies among different authors [67-69,85-89,91] there is an evident deviation in the valence-band crystal-field split-off energy of the hexagonal polytypes [67-69,85-89,91]. The present values from a fully relaxed LDA calculation are A^f = 131,50, and 38 meV for 2H-, 4H-, and 6H-SiC, respectively [69]. Other published calculated values are 132, 66, and 46 meV by Lambrecht et al. [87], and 97, 56, and 36 meV by Kackel et al. [89] The reason for this deviation is the different internal positions of the hexagonal layers. We have found [69] (see also Ref. [124]) that changing the internal lattice parameter in 2H-SiC by 0.2% changes A^.f by as much as ~ 22%, whereas the effects on the fundamental bandgap and the effective hole masses are almost negligible. Thus, a careful structural relaxation is necessary in order to accurately calculate the crystal-field split-off energy. One would also expect that alloying, surface relaxation, and large structural defects will affect relatively strongly the crystal-field split-off energy. Experimentally, a lower limit of the crystal-field spHt-off energy A^f > 30 meV has been reported for 6H-SiC by Choyke and Patrick from photoluminescence measurements [125]. Qteish et al. [126] obtained A^f = 0.12 eV for 2H-SiC using a supercell pseudopotential approach to calculate the spontaneous polarization. Their VBO between unrelaxed 3 C - and 2H-SiC is similar to the fullpotential results. In Figure 17.5 we summarize the most important band-structure quantities of 3C-, 2H-, 4 H - , and 6H-SiC by showing the bandgap energies, the VBO
Optoelectronic Devices: Ill-Nitrides
492
1
1.2 (0
• • ^
0.9
ID c (75
•^
0.6
3 O CD O O
£
0.3
1
/
/
o
'
r /
3
^
1
3C-SiC 4H-SiC 6H-SiC
y /
•• •
1
/
1
• /
1
1
3.0 Energy (eV)
2.5
1
3.5
Figure 17.5. Measured photoacoustic (PA) signals as a function of energy for 3C - , and 4H-, and 6 H - SiC. The spectra of the samples were normaUzed to the spectra of a highly absorbing film [122].
(with respect to the VBO of 3C-SiC), the energy differences between the two lowest conduction-band minima, and the valence-band split-off bands. The dielectric function s((o) = Si((o)-\-is2(co) of the semiconductors describe the response of the material due to a change in the charge distribution. The dielectric function is thus an important property for describing the screening of the semiconductor near dopants, defects, and other structural perturbations of the crystal. For instance, the static dielectric constant is used to determine the correction to the LDA bandgap energy [Eq. (17.1)] and in the calculation of the polaron masses (Eq. (17.6), see the next section). Within the linear response theory the dielectric function in the long wavelength limit (q = 0) is calculated directly from the electronic structure via the joint density-of-states and the optical matrix elements according to (Figure 17.6) sf\o)) = ^ 2 2
X
X/k/l -Af)8(Ef(k)
- Ejik) - hoi)
(17.3)
Here, /k, is the Fermi distribution function. The real part of the dielectric function is obtained from the Kramers-Kronig transformation relation 8,(^) = 1 + -
\doJs2{oI){-j^
+ -1^]
(17.4)
Sic and III-N Heavily Doped 3C-SiC
2H-SiC
493 6H-SiC
4H-SiC
M5(4)
X6(1)
f 2.92 eV
1.16
K4(2)
f
3.26
CBM
A
OeV
3.34 (3.30) (3.30)
I
0 06^3^3^ I 0
^^15(51, VBM
i
8.8r7(5)^
Aso=145meV/l
JT;;,
3.10
(3.03)
io.12r9(5) ^ \
r8(5)
I
M5(4)
X7(4)
2.46 eV (2.44 eV) f
2nd min.
y^
0.60 I
^
M5(1)
^T
8.4r7(5r4"' 8.ir7(5)" "f
--_—:
I f Acf=131
r7(i) t
j
50 t p7^^^ ^
LL^
soband
38 r7(i) f
cf-band
/
Figure 17.6. Calculated SiC fundamental bandgap energies, the energy difference between the two lowest conduction-band minima, and the valence-band offset (VBO) with respect to VBO of 3C-SiC (in units of eV). The crystal-field split-off, and the spin-orbit split-off energies are in units of meV. The bandgap energies in brackets are the PA measured results.
The summation over the Brillouin zone in Eq. (17.3) is calculated using linear interpolation on a k-mesh containing about uniformly distributed 400 k-points, i.e. the tetrahedron method. Matrix elements, eigenvalues, and eigenvectors are calculated in the irreducible part of the Brillouin-zone using the FPLAPW electronic structure. The delta Dirac function in Eq. (17.3) shows that a correct description of the fundamental bandgap energy is important to obtain dielectric function. It has been shown by Del Sole and Girlanda [71] that the LDA combined with the constant bandgap correction describes the optical absorption spectrum rather well. We, therefore, apply the LDA + QP to calculate the static si(0) and the high-frequency Si(oo) dielectric constants. The electronic structure calculations do not include electron-phonon interactions. However, in polar semiconductors the optical phonons play an important role for the low-frequency dielectric function. The static 8i(0) dielectric constant can in polar materials be determined only by taking into account the electron-phonon interactions. The screening from the electron-optical phonon (ep) interaction can approximately be taken into account through a delta function in S2((o) at the transverse
494
Optoelectronic Devices: Ill-Nitrides
Table 17.2. The dielectric constants of intrinsic SiC obtained from the LDA + QP calculation Polytype
Expt.,, Refs. [2]
This Work 8(0)
8(00)
3C-SiC
8
9.52 (10.69)
6.33 (7.15)
2H-SiC
ei
9.53 (10.69) 9.96(11.23)
6.33 (7.15) 6.62(7.51)
9.63 (10.85) 9.94(11.29)
6.40 (7.24) 6.62 (7.54)
9.70 (10.93) 10.00(11.29)
6.45 (7.29) 6.64 (7.54)
«ll 4H-SiC
ei
^11 6H-SiC
ei fill
e(0)
8(00)
9.72
6.52
9.66 10.03
6.52 6.68
The values in brackets represent the LDA results without the bandgap correction. The static dielectric constant e(0) was determined by taking into account the electron-phonon interaction.
phonon frequency a>ro [127,128] assuming constant optical phonon frequency distribution. sf( , o ) ^ 8 K o o ) % ^ ^
(17.5)
To calculate the contribution to the dielectric function due to this electron-phonon interaction, experimental values [2] of the two phonon frequencies a>ro and a>ro are employed. The measured frequencies by Raman's spectroscopy are supported by the calculated phonon frequencies of the optical (and acoustic) modes using an adiabatic bond-charge model by Bechstedt et al. [101]. Our calculated results of the dielectric constants are presented in Table 17.2 both with (i.e. LDA + QP) and without (i.e. LDA) the bandgap correction. With the bandgap correction and including the electronphonon interaction, the calculated dielectric constants agree very well with experimental [2] values. Earlier calculations by Cheng et al. [129], Wellenhofer et al. [130], Karch et al. [131], and Adolph et al. [132] of the high-frequency dielectric constants have been published. The optical properties of SiC polytypes calculated by Lambrecht et al. [87], using mainly the full-potential (but partly also the ASA) linear muffin-tin orbital method plus an additional 1 eV constant energy correction of the LDA bandgap, show quantitatively similar dielectric constants as here. 17,3.2 Effective Electron and Hole Masses The effective mass tensor m(k) is defined as l/m(k)^^ = ±d^Ej(k)/h^ dk^^dk^ where + (—) stands for electrons (holes). We determine the effective masses in the three principal directions directly from the first-principles FPLAPW electronic energies. Although the Si-C bonds in SiC are covalent, carbon atoms are more electronegative than silicon atoms and hence the material is partly ionic. Therefore, when vibrating.
Sic and III-N Heavily Doped
495
the longitudinal optical (LO) phonons will build up an electric field along the direction of vibration. This field will interact with electrons and holes (known as the polaron effect), resulting in a change in the effective masses. The polaron mass m^ can be estimated from the energy of the LO phonon, /ia>Lo. and the dielectric constants 8(0) and 8(00), assuming non-degenerate bands, harmonic oscillation of the ions, interactions only with long wavelength phonons (with constant frequency a>Lo)' ^^^ ^^^ effective mass approximation: [2,5,133] 1 -O.OOOSa^ ,, ,^,_i " ^ ^ " l - a / 6 + 0.0034a^^"^^""^'^ '
STTS(0)ho)i^O V 8(00)
,,^^ , ^''''^^
8(0) /
where a is the Frohlich constant. For the static and the "high"-frequency dielectric constants we use the calculated LDA + QP values as given in the previous section. The phonon frequency is taken to be the experimental values [2,134]: ho)i^o = 121 and 120 meV for 3C-, and 6H-SiC, respectively. For 2 H - and 4H-SiC we use the parameters of 6H-SiC since optical properties are similar for the hexagonal poly types [2,101] The k-point location of the minimum in the first BZ determines if the masses can be anisotropic or not. The A'-point minimum of 2H-SiC is required to have isotropic transverse masses, whereas the effective electron masses of the other investigated minima show strong transverse anisotropy. We present in Table 17.3 our LDA effective electron masses for the two lowest conduction-band minima. Since the QP correction yield a constant shift with respect to momentum k, the LDA + QP model results in the same effective mass values as the LDA. The most direct method for measuring the effective masses is based on the cyclotron resonance. The first successful far-infrared electron cyclotron resonance experiment of SiC was performed by Kaplan et al. [135] for the 3C-SiC (m^ = 0.247mo; m\\ = 0.677mo). The results were confirmed by Kono et al. [136]. Our calculated values for the bare effective electron masses in 3C-SiC are m^ = 0.23mo, and m\\ = 0.68mo and the corresponding polaron masses is m^ = 0.24mo, and my = O.lSniQ. Calculations of the bare masses by Wenzien et al. [85] yield m^ = 0.24mo, and m\\ = 0.67mo and calculation of Willatzen et al. [86] yield m^ = 0.29mo, and m\\ = 0.60mo. The lack of reliable experimental data due to low crystalline quality of hexagonal SiC in the early measurements together with the use of an over-simplified effective mass model have resulted in largely scattered values of the effective masses for the hexagonal polytypes. Recent ODCR experiments by Son, Meyer, Volm et al. [90,107,117,137] have been used to determine the effective electron masses in 4H-SiC. The obtained values (tfiMr — 0.58mo; ^MK = 0.3Imo; m^L = 0.33mo) are in excellent agreement with our theoretical polaron values (m^/-= 0.61mo; m^^ = 0.29mo; m^^ = 0.33mo). Most full-potential LDA
496
Optoelectronic Devices: Ill-Nitrides
Table 17.3. The effective electron masses and corresponding polaron masses nip of the two lowest conductionband minima in SiC Polytype
m^
2H-SiC
0.23 0.68
0.24 0.73
m^ mil
0.43 0.26
0.46 0.27
niMr
0.57 0.28 0.31
0.61 0.29 0.33
0.75 0.24 1.83
0.81 0.25 2.07
m„
This work m mp
Expt
This work m Wp 3C - SiC
Second minimum
First minimum
Electron mass (mo)
0.25 1.00
0.26 1.10
0.96 0.14 1.07
1.05 0.14 1.18
0.58 (c) 0.31 (c) 0.33 (c)
0.78 0.16 0.71
0.85 0.17 0.77
y/rriMrniML = 0.48 (e), 0.485 (t) 2.0 (d), 3-6 (e)
1.08 0.17 0.56
0.18 0.60
0.247 (a), 0.25 (b) 0.667 (a), 0.68 (b) rriMr rnMK rriML
4H-SiC
fnMK ^ML
6H-SiC fnMK f^ML
1.19
The measured cyclotron resonance results are from (a) Ref. [135], (b) Ref. [136], (c) Ref. [90], (d) Ref. [118], (e) Ref. [105], and (f) Ref. [117]
calculations [5,67-69,85-88,91] yield similar values of the bare effective electron masses. For instance, the results of Wenzien et al. [85] (m^/- = 0.60mo; rrif^x — 0.28mo; m^/^ = 0.19mo) and of Lambrecht et al. [91] (m^/-= 0.58mo; m^/j^ = 0.28mo; ^ML ~ 0.3Imo) are showing the same anisotropy of the 4H-SiC effective electron mass tensor. One exception to the good agreement between different calculations is the longitudinal effective electron mass in 6H-SiC. For instance, early k-dependent quasi-particle calculations by Wenzien et al. [85] located the 6H-SiC minimum at the M-point, which resulted in a very small mass value: m^^ = 0.5 Imo- However, the calculated quasi-particle curvature did not have sufficient accuracy to be confirmative [85]. Their corresponding LDA result was a minimum along the ML-line with nif^i = 1.95mo. A full-potential linearmuffin-tin-orbital LDA calculations by Lambrecht et al. [91] resulted in a camel's back minimum with m^i = IAIMQ for 6H-SiC. In Ref. [91], it was suggested that renormalization due to the polaron effects could be the reason for the small deviation between their calculated results and early optical detected cyclotron resonance measurement {mj^i = 2.0mo) by Son et al. [118]. Although, the polaron coupling is strong in 6H-SiC, this effect alone is too small to explain the deviation according to our calculations. Recent measurements by Son et al. [105] reveals puzzling results: the measured low-magnetic field cyclotron resonance corresponds to a mass value of m^^ = 3 — SMQ. The origin to this very large mass value is not yet clear, and thus, the electronic band structure of 6H-SiC is not fully understood. Moreover, the anisotropy of the two transverse
Sic and III-N Heavily Doped
497
effective masses has not yet been extracted due to the poor cyclotron resonance resolution, but the average effective electron mass {mMr^MK)^'^ = 0.48mo [105,118] agrees with our calculated polaron mass value of 0.45mo. We conclude that the very flat and non-parabolic conduction-band in combination with its sensitivity for band filling require a careful theoretical analysis in order to compare calculated and experimental results. The effective hole masses are determined directly from the FPLAPW curvature of valence-band maximum which is shown in Figure 17.7. The three uppermost valencebands of 3C-SiC can be parametrized according to the relativistic k-p approximation [68]: (A ± ^B^ + C^m
-hh,lh (k):
f{0,
(17.7b)
sin 6 cos (^ sin (p-\- sin 0 cos 0 £so(k) = - 4 o +
(a)
(17.7a)
IMQ
1
2m,
(17.7c)
-A,
H
r8(5)
0 A 5(204)
>
• A 5(204)
(D
-0.1 ;
n o
/^y
/y r ? (5)V\
VE3(1)
/ 7^5(1)
hhi • f^/so
_54(2) Z3(2r^
-
i:4(iA ^3(1)\
A(C2v) r(Td) 3C-SiC
A nCev) 4H-SiC
5:(Cs)
nos)
A(C6v)
nCev) 2H-SiC
A r(C6v)
n^s)
^(Cs) 6H-SiC
Figure 17.7. The valence-band maximum of (a) 3C-, (b) 2H-, (c) 4H-, and (d) 6H-SiC. We show 15% of the total length to the BZ boundary. The solid (dotted) lines represent LDA calculations with (without) spin-orbit coupling.
498
Optoelectronic Devices: Ill-Nitrides
The spin-orbit (so) interaction splits the heavy- and Hght-hole (hh,lh) bands at the T-point. The spin-orbit split-off energy in 3C-SiC is calculated to be ^so = 14.5 meV, which is ~ 5 meV larger than the experimental value of about lOmeV [111,112]. The energy difference between the spin-up and spin-down like states (i.e. the spin-split) is small (see Figure 17.7), and the above k p parametrization assumes equal spin-up- and spin-down-like states i.e. [%(k) = %(k)]. The k-p parameters for 3C-SiC are A = -1.96, \B\ = 0.30, and \C\ = 2.27, obtained from fitting Eq. (17.7) to the calculated LDA band structure of the valence-band maximum. From the k-p expression of Eq. (17.7) one can analytically derive the effective hole mass tensor from the second derivative of the energy dispersion with respect to the momentum k. The effective hole masses of the hh- and the Ih-bands in 3C-SiC depend strongly on k-direction, which was demonstrated in Ref. [70]. A spherical average mass value can be obtained by integrating over angles in k-space [68].
Ia=—\
+ C^aY
I ,/l+^^^^^p^^2^ ^""ilo \of
,
(17.8a)
(17.8b)
Eq. (17.8) has been used with /« = 1 and a = 1/6, derived by Lax and Mavroides [138]. However, we show in Refs. [68,70] that a Taylor expansion of /^ reveals that better accuracy is obtained with /^^ = 1 and a = 1/5 for various semiconductors. In order to calculate the effective hole masses, it is crucial to include the spin-orbit interaction. The three uppermost valence band in 3C-SiC in Figure 17.7 have been calculated both excluding (dotted lines) and including (soHd lines) the spin-orbit interaction. The very noticeable flat curvature in the 2 direction for the hh-band implies an extremely large effective hole mass if spin-orbit interaction is excluded. This flat curvature in this direction is strongly affected by the spin-orbit interaction, whereas the band curvatures in the A and A directions remain essentially unchanged. Even though the spin-orbit splitting is small (A^^ ~ 14 meV in 3C-SiC) the impact on the effective masses at the T-point is very strong. In the directions FK = X and /X = A in 3C-SiC, the effective hole masses of the uppermost (second uppermost) valence band is mpf- = 15.0mo (0.59mo) and m/x = 1.64mo (1.64mo), respectively, if spin-orbit interaction is excluded. Corresponding values including the spin-orbit interaction (Table 17.4) are m/^ = 1.32mo (0.32mo) and mpi = 1.65mo (0.30mo). Thus, the effective hole mass of the uppermost valence band is reduced by 91% in the /X-direction due to the spin-orbit coupling, and the effective hole mass of the second uppermost valence band is reduced by 82% in the /X-direction. According to the k p approximation (Eq. (17.7)) the effective hole masses in cubic materials are independent of the size of A^^. Indeed, we find [70] that with the fictive 10 times smaller spin-orbit interaction, the values of the effective masses are essentially
Sic and III-N Heavily Doped >o i n »o i n in in in in
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500
Optoelectronic Devices: Ill-Nitrides
unaffected: mpk = 1.35mo (0.32mo) and mn = 1.65mo (0.30mo), although the spin-orbit spHt-off energy is now only 4^0 ~ 1.4 meV. This demonstrates that the spin-orbit interaction is important also for light materials, like SiC and III-N. The reason for the very strong effect on the masses even in relatively Hght materials is that the spin-orbit interaction splits the valence-band degeneracy (e.g. r^®Di/2 =» - T T ^ A ^^ T^ symmetry). This split changes the symmetry of the eigenfunctions in the vicinity of the maximium, and consequently it also changes the curvatures of the bands. Also in the hexagonal SiC poly types the spin-orbit interaction affects the valence-band maximum strongly. Parameterization of the three uppermost valence bands has been performed with k p expressions, valid for wurtzite structures and if the crystal-field split-off energy is sufficiently large [68].
£w,v2(k) = - % + ^
( 4 + dkl ± ^ ^ + ( ^ " ^ 1 ) ^ 1 ,
(17.9a)
The longitudinal and transverse hole masses for the two uppermost bands are obtained as m\\ = -MQIC and m^ = mo/d. The parameter d" is found to be 1.33, 1.39, and 1.41 for 2H-, 4 H - , and 6H-SiC, respectively. The transverse mass for the first (second) valence band is decreased (increased) by a factor of about 5 (2) when the spin-orbit interaction is included. The third valence band is not affected by the spin-orbit interaction in the vicinity of the T-point, but in the X direction the spin-split is strong when the split-off band and the crystal-field splitted band interact (see Figure 17.7). The LDA spin-orbit split-off energies of 2H-, 4H-, and 6H-SiC are very similar: A^^ = 8.8, 8.4, and 8.1 meV, respectively. A measured value of ~ 7 meV for 6H-SiC has been reported by Humphreys et al. [112] and Choyke and Patrick report [125] a spin-orbit energy of 4.8-8 meV from photoluminescence measurements. Relativistic full-potential LDA calculations of the hole masses in SiC have been performed also by Willatzen et al. [86] and Lambrecht et al. [87]. The analysis of the effective hole masses in these calculations are based on k-p expressions, and the results agree well with our findings. Recently, ODCR experiment by Son et al. [104,105] have revealed the effective hole masses of the uppermost valence band in 4H-SiC (rrij^ = 0.66mo and m\\ = 1.75mo) and in 6H-SiC (mj^ = 0.66mo and m|| = 1.85mo). Their measured values involve the polaron interaction. This effect is relatively strong for the holes in the hexagonal SiC polytypes since the FrohHch constant (Eq. (17.3)) has an m^^^ dependence and the bare effective hole masses are relatively large. By including the polaron effect in the calculation, both 4H-SiC (m^ = 0.61 MQ and m\\ = 1.76mo)
Sic and III-N Heavily Doped
501
and 6H-SiC (m^ = 0.65mo and m\\ = l.SOmo) effective hole masses are in excellent agreement with the ODCR results.
17.4. DOPING INDUCED BANDGAP NARROWING IN SiC Heavy doping of a semiconductor reveals in particular two interesting physical behavior of the material. First, above a certain critical concentration N^ the semiconductor possesses metallic properties also in the low temperature regime. Thus, above a certain doping concentration the system energetically prefers to be in an ionized impurity phases. The critical concentration at this phase transition is the doping-induced MNM Mott transition concentration [139]. Second, for donor concentration A^^ (n-type materials) or acceptor concentrations N/^ (p-type materials) above this critical concentration, the fundamental bandgap energy is smaller than in the intrinsic material. Thus, the metallic phase narrows the semiconductor bandgap. This is the so-called doping-induced BGN. In this section we describe theoretically the mechanisms behind the MNM transition and the BGN. The expression below is derived for n-type materials with ionized donors, but there are analogues expressions for p-type materials with ionized acceptors. We calculate the critical concentration of SiC polytypes (Section 17.4.1) using three different methods [78], namely the original Mott model (model No. 1), the extended Mott-Hubbard method (model No. 2), and a model based on the total energy (model No. 3), and we calculate (Section 17.4.2) the doping-induced BGN in heavily n- and p-type doped SiC polytypes. In Sections 17.6.1 and 17.6.2 we present the corresponding calculations for zb and wz GaN and AIN. In an undoped semiconductor the Hamiltonian HQ describes the interactions between electrons and ions in the intrinsic crystal. The eigenvalue problem of HQ in the present work is solved by the FPLAPW band-structure calculation, resulting in the Kohn-Sham single-particle energies £^(k) and the fundamental bandgap energy £'g. In an n-type semiconductor, the crystal also contains donor atoms, which can be ionized either thermally or through a phase transition (the Mott transition) at a certain critical concentration A^^- The ionized donors and the associated electron gas form an interacting impurity system. Now, the total Hamiltonian H also contains the additional interactions between the crystal electrons and this impurity system. If the crystal is polar, also the electron-phonon interactions are important. The additional interaction terms are treated as a perturbation; H = HQ -\- H^ where Hi is the perturbation Hamiltonian describing the additional interactions. The total energy of the interacting system is calculated as E^^ = (t^lHi I ^ ) . The eigenvalue problem of H results in the single-electron energies Ej(k) and the bandgap energy E^ which differ from the corresponding energies of the unperturbed eigenvalue problem. The energy shift £ / k ) - £^(k) = Re[/iX;(k,^(k)/;i)] is the real part self-energy of the electron state [73-76]. The imaginary part of the self-energy is associated with the lifetime of the electron state and will not be considered in this work.
Optoelectronic Devices: Ill-Nitrides
502
This energy shift is normally positive for the valence-band maximum and negative for the conduction-band minimum, causing a narrowing of the fundamental bandgap: Eg = £^ + A^c ~ AEy = i ^ 4- A£g, where AEg is normally a negative quantity (Figure 17.8). Both the critical concentration A^^ of the MNM transition and the single-particle selfenergy Rt[hY.j(^,E^(^)lh'\, leading to the BGN, can be determined from the total energy E^^^ of the interacting system using a perturbation method. In the many-particle theory, the total energy is expressed in the time-ordered, single-particle, unperturbed Green's function (^(kj2 ~ h)= ~i(^l?^kj(^2)^kj(^i)'^'^h^^^ ^ ^^ ^^ ^™^ ordering operator, and the dielectric function e(q, a>) of the electron gas associated with the impurity electrons. The unperturbed Green's function describes the propagation of a noninteracting electron in the crystal and 8(q, o)) describes the response of the electron gas due to a perturbation in the electron distribution. The Fourier transformed unperturbed.
(a) Intrinsic
(b) Low-doped
(c) Heavily doped
Figure 17.8. Schematic picture of the electronic band structure in n-type materials, (a) The energy bands £^(k) of the intrinsic material with completely occupied valence bands and completely unoccupied conduction bands. The upper panel shows schematically the crystalhne structure (i.e. the atomic positions) and the lower panel shows the electronic band structure with the fundamental bandgap energy £^. The Fermi level Ep is the mid-gap energy for intrinsic semiconductors at zero temperature, (b) At low donor concentration the donor electrons act like localized hydrogen-like wavefunction. The impurity electrons are almost non-interacting, and the semiconductor is still in its non-metallic phase with an (almost) intrinsic bandgap energy £^. (c) For heavy doping the donor electrons strongly overlaps and the system gain energy by ionizing the donors and forming a corresponding electron gas. This is the metallic phase. Due to interactions with the electron gas and the ionized donors the resulting band structure energies £^/k) are modified. The states at the conduction-band minimum and at the valence-band maximum are now affected by the screening electron gas, and as a result, the fundamental bandgap energy £g = £^ + Af'c - A£v = t^g-\- A£^g is narrowed compared to the intrinsic bandgap energy.
Sic and III-N Heavily Doped
503
time-ordered, single-electron Green's function is G^(K CO) =
"^^
+ - ^ ^ ^ ^ ^
(17.10a)
^(k) = Ef(k)/h
(17.10b)
where 8 is an infinitesimal, positive number and rjjik) is 1 if the state lk,7) is populated and 0 otherwise. Within the RPA [73,74] with a local-field correction /(q) of Hubbard [75] the (testparticle-particle) dielectric function 8(q, o)) of the electron gas is related to the polarizability a^Cq, w) by [5,6,73-77] 8(q, CO) = 1 + [1 - / ( q ) ] a ' ( q , co)
0^
^
Kq) f dk r
(17.11a)
^^'
hs{(jS)
where the summation runs over all bands which are populated by the electron gas (or the hole gap in p-type materials). In the present materials7=/ = cl for n-type materials (and 7 , / = vl, v2, and v3 for p-type materials). The electron-phonon interaction is included in the frequency dependent dielectric function [73,74]: 1
1
e{<jt)) 8(00)
(8(0)-s(oo))o>Lof 28(0)8(oo)
1
io)-\-o)i^Q — i8
1 o)—O)]^Q-\-
I.}
(17.12)
We employ the experimental values [2] for the lattice dielectric constants. For 3 C - (6H-) SiC 8(0) = 9.72 (9.78), 8(00) = 6.52 (6.58), and /ICOLO^ 0.121 (0.120) eV. The dielectric constants for 6H-SiC are the geometric average values of the transverse and the longitudinal components: 8j^(0) = 9.66, 8||(0)= 10.03, 8^(oo) = 6.52, and 8||(oo) = 6.70. Furthermore, 2 H - and 4H-SiC are presumed to have the same lattice dielectric function as 6H-SiC. For n-type materials, the averaged Hubbard local-field correction is [5,6,75]
^'^'
2A^;i£?i(Ak, + q) + £F
where £'F is the Fermi energy of free electron gas, and Ak^ = k^ ^ - k^ j is the momentum vector between the A different equivalent conduction-band minima and one specific conduction-band minimum at k^ j . Analogously, for p-type materials the averaged localfield correction is [5,6,75]
^ ^^-^M^^MzM
(17.14)
504
Optoelectronic Devices: Ill-Nitrides
where Vp is the number of hole populated valence bands (which depends on the ionized acceptor concentration), and the Fermi energy of the hole gas is obtained from Refs. [5,6,121]. 1 ^ = ^
^^ /2m \^^^ Z ( ^ [ ^ ( ^ > - ^Fl^^y'CO) - £p)j
(17.15)
The total energy E{^^ of the interacting system in the heavily doped metallic phase arises from the kinetic energy f of the electron gas, the exchange-correlation energy of the electron-electron interaction Vge, and the electron-ion interaction %^ between the electron gas and the ionized impurity ions at their equilibrium positions. For ionic materials, the electron-phonon interactions has to be considered [73,74]. The phonons of importance in the electron-phonon interaction Vgp are the longitudinal optical phonons with long wavelengths, since these phonons create a strong macroscopic electric field. This electron-phonon interaction can be treated as an additional frequency-dependent screening of the electron-electron interaction [73,74]. Thus, the perturbation Hamiltonian of the impurity system (i.e. the electron gas, the impurity ions, and the optical phonons) is H^ = f-\- V^^ + V^^ + Vgp- We calculate the total energy from E^^ = ( ^ I ^ J ^ by using the zero-temperature RPA with a local field approximation of Hubbard (see Refs. [70,73,74] for details). The resulting total energy is divided into the kinetic energy E^jn, the exchange-correlation energy £'xc, and the energy from the electron-ion interaction E^^^ caused by electron relaxation near the donor ions. Since lattice vibrations are not taken into account in the intrinsic band structure, one also has to include the polaron energy E^ describing the interaction between the electrons and the optical phonons. The kinetic energy is calculated as
f^
J
J
(2'TT)'^
which equals 3£'F/5 if only a single conduction band is populated by electrons up to the Fermi energy Ep of the electron gas with concentration n. If scattering due to the electron-electron interaction is approximated by (k,7;k^/lyeelk^/;M « ^A,-^.,(k,k^)
A,y (k, k') = ^
^
IJ dr u%{\i. v)u%{\^, r)|
(17.17a)
(17.17b)
(T,o'=\i
where q = k^ - k, the Coulomb potential v(q) = 4'Tr^^/q^, and A^j/(k,kO is the spinindependent overlap integral for the periodic part u^a-^, r) of the Bloch functions, then
Sic and III-N Heavily Doped
505
the Hartree-Fock exchange-energy is expressed as [5,70,73,74]
(17.18b)
co-[^(ko-^(k)]+i6;
The second term in Eq. (17.18a) is the electrostatic self-interaction energy of the electrons. In the Hartree-Fock exchange energy, the direct Coulomb term of the electron repulsion is cancelled by treating the ionized donors as a uniform distribution of positive ions. The summation runs over all bands, but since only the lowest conduction band is populated by the electron gas, only j = c\ contribute to )^{i{, (o). The exchange energy is a well-defined quantity, whereas the correlation energy contains the remaining many-particle interaction. Within the RPA with an ^-independent localfield correction, the correlation energy of the electron gas is [5,70,73,74] h C dq
C-
doj(ln(8(q,
CO))
.
\
The present correlation contribution from the electron-ion interaction has been derived by Semelius and Berggren [74] from second-order perturbation theory, presuming a random distribution of the ions with infinitely large mass:
'''°"
_ -A^D r dq v(q) a°(q,0) 2« J (2^)3 £(0) £(q,0) •
^'^-^"^
The electron-ion interaction describes the relaxation of the electrons around the donors, and the inhomogeneity of the electron gas is comprised 79 in Eq. (17.20). Since part of electron-ion interaction already has been taken into account in the Hartree-Fock exchange energy [i.e. in Eq. (17.18)], £"1011 describes the energy of the difference in the electron density between a system with uniform distribution of ion charges and a system of randomly distributed point-like charges. The distribution of the impurity ions has been shown [74,140] to be of major importance for the results, and the present calculations are assuming a random distribution of impurities. Interactions with the non-ionized impurity atoms are neglected. Since we are treating only the ionized impurities, the calculation does not depend on the choice of type of dopant atom.
506
Optoelectronic Devices: Ill-Nitrides
Finally, in ionic materials, there is the additional contribution from the electron-optical phonon interaction: ^ f ^
dq
p
dcc;/v(q)
2n J (ZTTy J -00 IZTT \ S((0)
e^ I 2m (
v(q) \ o,
x
,
^
^
ni ^^ ^
8(oo) /
1
1 \
..^..ix
This polaron energy is independent of doping concentration and can been seen as a modification of the electrostatic self-interaction energy in the intrinsic semiconductor. One can, therefore, treat it as an exchange energy contribution. The total energy of the interacting impurity system in the heavily doped region is E^^ = E^^ -\-E^-\-E^-\- E-^^^ + E^. The kinetic, exchange, correlation, electron-ion, and polaron energies of the electron gas have been calculated using the full energy dispersion from the first-principles FPLAPW calculations, and by calculating the Bloch function overlap integral Ayj/(k,kO using the FPLAPW eigenfunctions. To study the effects due to the non-parabolocity of the energy bands, we have also calculated the total energy (and corresponding single-particle self-energies) using a parabolic approximation. In this parabolic approximation, we treat the energy bands as perfect paraboUc bands and the overlap integral is parametrized according to Refs. [5,6], where the details of the computational method is described. This parabolic approximation is normally fairly accurate for conduction-band minimum, but we show below that it is not a proper approximation for the valence-band maximum. Moreover, the non-parabolicity of the 6H-SiC double-well minimum needs a complete treatment of the energy dispersion. In Figure 17.9 the resulting energies per electron for n-type 3 C - and 6H-SiC are shown as functions of ionized donor concentration. The solid lines represent the different contributions and the dashed lines show the total energy. At low ionized donor concentration the electron-ion interaction dominates, whereas at high donor concentrations the kinetic energy dominates. For 3C-SiC we have also calculated the exchange and correlation energies using a constant dielectric function, S{(JS) = 8(0) (dotted lines in Figure 17.9(a)), which should be a reasonable approximation for small ho), and one can see that for small impurity concentrations the constant 8(0)-approximation describes the energies rather accurately. At and above a concentration of A^D = 11^ 0-8, 1.3, 4.4 X 10^^ cm~^ in 3C-, 2H-, 4 H - , and 6H-SiC, respectively, the band filling of the lowest (unperturbed) conduction band implies a Fermi energy of fp = /ic<>Lo- At higher concentrations the frequency-dependent lattice constant is needed to accurately describe the electron-optical phonon interaction. For large donor concentrations the double-well structure in 6H-SiC has a strong influence on the total energies, especially on the kinetic part of the total energy. In Figure 17.9(b) the dotted fines represent the parabolic approximation of the energy
507
Sic and III-N Heavily Doped (b)
(a) •
•
• ' " " 1
1
••V
1
3C-SiC
/
I
^kinJ '
50
50
L
M
;
0
50
h
^^>.
^s>>.
N;~
100 c LJJ
\^x,pY ^ion\
•
150
-
•\7"
• ^ ^ •
.
"
"
- <\ -
••'
10'
-
M \\ ^ ^tot \ . \
100 \ 10'
]
^^^~~~~~~~~~~~~^^^^^:::^^ ^•v
""-\.
\
0
1
^ ^ ^ 7 ^ ^ = = ^ ' ^ 50
1
^—.^ ^
• •
^kin/
E
t=^^^£c
/
/
/ E
_ 6H-SiC
- ^
.21
10"
Ionized donor concentration (cnn ^)
10^^
10^'
10^^
Ionized donor concentration (cnn~^)
Figure 17.9. Energy contributions to the total energy per electron (meV): kinetic E^in energy, the exchange plus polaron E^p = E^+E^ energy, the correlation E^ energy, and the ion E^^^^ energy (solid lines) of the impurity system of n-type (a) 3C-SiC and (b) 6H-SiC metallic phase. Dashed line show the total energy ^^^tThe dotted lines for the correlation and exchange energies in (a) represent the e(0)-approximation [i.e., e(a>) = 8(0)]. The dotted lines in (b) represent the parabolic approximation (see text) with m\\ = 1.83mo for the conduction band in 6H-SiC.
dispersion with m\\ = 1.83mo. At concentrations larger than about —10 cm~ the electron gas concentration is so high that the band filling exceed the parabolic region of the double-well minimum in 6H-SiC. 17,4,1 Metal-Non-metal Transition Above a certain critical doping concentration A^^^ the donors (in n-type materials) or acceptors (in p-type materials) spontaneously become ionized due to strong impurityimpurity interaction. This metallic phase is of great technological importance for designing for instance p-i-n-diodes. We calculated this critical concentration from three different models [78]. The first two models (model No. 1 and No. 2) are based on the Mott picture [139] of overlapping impurity electrons, assuming hydrogen-like wave functions. The third model (model No. 3) is comparing the total energy of the nonmetallic weakly interacting impurity electrons, and the total energy of the metallic strongly interacting impurity system. 17,4,1.1 The Original Mott Model (Model No, 1), In the Mott model of impurity systems [139], the doping-induced MNM transition occurs at the critical impurity
508
Optoelectronic Devices: Ill-Nitrides
concentration A^c given by
-(f)' al = "
e^
(17.22a)
(17.22b)
28(0)ED,A
where the effective Bohr radius a^ is calculated from the ionization energy E^ ^ of a single donor electron (or acceptor hole) since the impurity electron wave function is assumed to be associated with only one conduction or valence band, that is, the many valley effects are neglected. 17.4,1.2 The Mott-Hubbard Model (Model No. 2). Through the use of a MottHubbard tight-binding Hamiltonian, the impurity density-of-states associated with it present two sub-bands that overlap with increasing concentration. This would occur at an impurity concentration for which [141-143] AW = 1.15, (17.23) U where AW is the unperturbed impurity band width in units of £'D,A' ^^^ ^ is the intra-impurity Coulomb interaction energy, also known as the Hubbard-(7, given by U = 0.96ED [144,145]. Such a scenario is well known as the Mott-Hubbard picture for the MNM transition. AW is related to the hopping integral energy T, between adjacent sites / and 7, as [143,144] AW = 21(7)1,
(17.24)
where (T) is defined as the average hopping energy [143,144] {T)= {T(R)P(R)dR
(17.25)
P(R) describes the distribution of the donors. Moreover, T(R) and U are given by [146] T(R) = j ilJi(r)H, (A/(r - R,)dr,
(17.26a)
U = { |^i(ri)PliA2(r2)l'^7Tn^ fdridr^. (17.26b) J e(0)lri - r2l Hi is the one-particle Hamiltonian in the effective-theory, including the kinetic energy operator and the Coulomb interaction of the positively charged donor ion electron. 0)(r - Rj) is the simple hydrogenic wave function for the donor ground state at the randomly located site R,. Moreover, we have used a random like Poisson distribution P(R) of the donors with
Sic and III-N Heavily Doped
509
the probability that the nearest donor neighbor lies at a distance (in units of an). P ( / ? ) =3- ^^ / 1 + -R^ ^
Rl\
Y,
(17.27a)
RU) '
where
«„, = ( M - ) - " .
(„.27b,
Eqs. (17.23)-(17.27) show that the values of U and the donor (or acceptor) impurity concentration A^^ ^are both related to the ionization energy ^'DA- Using these equations, we have calculated the values of the critical concentration A/^. 17.4,1.3 The Total Energy Approach (Model No. 3). The third model follows a method expounded by Semelius and Berggren [74], where the total energy E^^ of the localized donor electrons in the non-metallic phase is determined and compared with the total energy E^^ of the electron gas in the metallic phase. For low donor concentrations, the total energy of the localized electrons is lower than the corresponding energy of the electron gas, and thus the non-metallic phase is favored. For high donor concentrations the situation is reversed, unless the ionization energy very large. The critical concentration for the transition is obtained as the concentration at which the total energies of the two phases are equal, i.e. Ef^ = E^^. The total energy of the metallic phase is calculated from Eqs. (17.13)-(17.18). The total energy for the non-metallic phase is directly related to the dielectric function of the localized electrons associated with the donors. Leroux Hugon and Ghazali [147], have derived the dielectric function of the donor electrons as a function of impurity concentration, where a hydrogenic wave function was presumed. When the concentration is increased, the donor electrons screen the Coulomb potential of the impurities more strongly, whereby the dielectric function is increased. The change in the dielectric function will modify the ionization energy of the electrons, and thereby, also the total energy. The total energy (expressed in energy per electrons) of the donor electrons in the non-metallic phase is obtained as [5,74]. ,3/2-
z^NM ^tot
In Figure 17.10 we show the total energy per electron in n-type Si (doped with P) and n-type SiC polytypes (doped with N) as functions of donor concentrations for the metallic phase and for the non-metallic phase. It is clear that at low donor concentrations the weakly interacting non-metallic phase is energetically favored, but at concentration above cm the ionized metallic phase is energetically favored. In SiC, the main contribution to this spontaneous ionization is coming from the electron-ion interaction.
Optoelectronic Devices: Ill-Nitrides
510
(b)
(a)
1
u
' '
1
^tot
\^tot
> 0
1 "
25
^D(P)=\: 50 _ 4 6 m e V ^ ^ \ NM
'
ED(N)
75
-
\
2H -SiCy
> ^
50
C
o "o
Si / /
(D
^tot HD(N)=
52meV
HD(N)=
81 m e v \
4H- SiC -
100
\
= 54 meV 3C-SiC
0
-
10^^ 10^^ 10^^ Ionized donor concentration (cm~3)
-
6H- -SiC^
10^ 10' 10^ Ionized donor concentration (cm~3)
Figure 17.10. The total energies per particle of the metallic ^^^t (solid lines) and the non-metallic E^^ (dashed line) phases in n-type (a) 3C-SiC and Si, and in (b) 2H-, 4H-, and 6C-SiC as functions of donor concentration A^^. The dashed lines represents the estimate of the total energy of the electron in the non-metalUc phase of Si:P, 3C-, 2H-, 4H-, and 6C-SiC:N, where the donor binding energies are the low concentrations values.
The critical concentration A^^ is obtained from the intersection point E{ E^f The main ^tot difference between the total energy of the metallic phases of 2H-, 4H-, and 6H-SiC is the number of conduction-band minima which affect the band-filling and the Fermi energy of the electron gas [5,6]. For very high doping concentrations, the kinetic energy of the electron gas dominates. At an impurity concentration of 10^^ cm~^ the total energy per electron in 4H-SiC is about 30% lower than in 2H-SiC and most of this difference arises from the kinetic energy. The calculated critical concentrations for the different n- and p-type SiC materials are presented in Table 17.5. Note that the extended Mott-Hubbard model gives normally slightly smaller A^c than Mott's original model, but all the three computational methods give the same order of A^^ • Moreover, the present results for p-type Si agree with earlier published calculations of Nubile and Ferreira da Silva [143]. The resulting critical concentrations for p-type SiC poly types are high; for Ga and B (with large ionization energies) N^ is near the upper limit to the dopant concentrations of interest in devices. In Mott's model, the critical concentration is proportional to £'D,A' The same relation holds also, with fairly good accuracy, in the Mott-Hubbard model. For the total-energy calculation, however, this is no longer true [5,6], especially for large ionization energies. For sufficiently large ionization energy E^^ does not become equal to f^^ at any concentration, but for these large ionization energies (about 0.35 eV in p-type SiC) one can question the accuracy of using hydrogenic wave functions together with the effective mass approximation.
Sic and III-N Heavily Doped
511
Table 17.5. Critical concentrations for the MNM transition of n- and p-type SiC, calculated using three different methods (see the text) Polytype
Dopant
Si
P B
n-type p-type
3C-SiC
N Al Ga
n-type p-type p-type
4H-SiC
N Al B
n-type p-type p-type
Ga
p-type
N
n-type
Al
p-type
Sc B Ga
p-type p-type p-type
6H-SiC
Critical concentration Nc (cm
^D,A (meV) [2]
45.6 46 54 257 344 52 and 92 191 234-326 267 81, 137.6, and 142,4 239 249 240 320 333
')
Mott
Mott-Hubbard
Total energy
Expt.
7.0X10^^ 7.2X10^^
5.7 X 10^^ 5.9 X 10^^
3.8 X 10^^ 4.3 X 10^^
3.5 X 10^^^^^ 5.0 X 10^^^^^ 4.06 X 10^^^"^
6.0 X 10^^ 6.5 X 10^^ 1.6X10^^
4.9 X 10^^ 4.7 X 10^° 1.2X10^^
3.5 X 10^^ 2.3 X 10^^ 7.9 X 10^^
5.5 X 10^^ 2.7 X 10^° (0.50-1.4) X10^° 7.5 X 10^^
5.6X10^^ 2.1 X 10^° (0.39-1.0) XIO^^ 5.8 X 10^°
5.6X10^^ 8.8 X 10^^ (0.22-1.0) XlO^^ 4.3 X 10^^
2.1 X 10^^
2.8 X 10^^
2.6 X 10^^
5.3 6.0 5.4 1.3 1.4
4.2 X 10^° 4.7 X 10^° 4.3 X 10^° 1.0 X 10^^ 1.2X10^^
2.6 X 10^^ 3.2 X 10^^ 2.7 X 10^^ 8.9 X 10^^ 1.0X10^^
X X X X X
10^° 10^° 10^° 10^^ 10^^
For comparison we also present the calculated and measured values of n-type Si:P and p-type Si:B. Measured critical concentrations are from (a) Refs. [148,149], (b) Ref. [150], and (c) Ref. [151].
Experimental investigations of the critical concentration for n- and p-type SiC polytypes are lacking. We, therefore, compare our corresponding calculations of n-type Si:P and p-type Si:B with measurements. Our calculations of the critical concentration of Si:P (Nc = 3.8 X 10^^ cm~^) is in good agreement with capacitance measurements performed by Castner et al. [149] (A^^ = 3.5 X 10^^ cm~^). Corresponding calculation of Si:B [Nc = (4.3-7.2) X 10^^ cm~^] is in good agreement with Hall measurements by Kubiak et al. [150] (Nc = 5.0 X 10^^ cm"^), and with resistivity measurements by Dai et al. [151] (Nc = 4.06 X 10^^ cm~^). Mott's original model seems to give shghtly too large Nc for both n- and p-type materials, except for n-type 4 H - and 6H-SiC polytypes, when two and three different ionization energies, respectively, are involved [152]. 17,4.2 Reduced and Optical Bandgap Energies For doping concentrations above the MNM critical concentration, the free electron (or hole) gas associated with the ionized donors (acceptors) will screen the crystal host electrons. This screening results in an energy shift in the single-particle energies.
512
Optoelectronic Devices: Ill-Nitrides
described by the real part of the self-energy Rc[hY,j (k, E^(k)/h)]. The energy shifts of the valence-band maximum A^^i and of the conduction-band minimum AE^i will cause a narrowing of the fundamental bandgap energy. This is the doping-induced BGN. We calculate the single-particle self-energy from the total energy E^^ of the interacting (or perturbed) system consisting of the electron gas and the ionized impurities: E^^ = {'^\Hi I ^ . The self-energy represents the interaction in the total system and the resulting excitation energies include, therefore, not only the single electron excitations but also the collective excitations. However, in the present work only the single-electron excitation energies are relevant. We use the Rayleigh-Schrodinger approximation which relates the total energy to the single-particle energies via [76]:
17/k)
^
^-^
^
The Rayleigh-Schrodinger model states that for a many-particle system with n electrons, the energy of the single-electron state can approximately be taken to be the whole change in the total energy of the many-particle system when an electron in the corresponding state is added or removed. The exchange part of the self-energy is obtained from Eqs. (17.7)(17.18) and (17.27) as [5,6,73,74]
VM>f + "' 2
^
Va.-[^(k')-
-
\
\l
a>-[^(k')-^(k)]+i8Jj (17.30)
Similarly, the correlation contribution to the self-energy is [5,6,73,74]
xXA/(k,k^)G^(k^c.+ ^(k)) /
(1731)
Finally, the self-energy from the electron-impurity ion interaction, presuming a random distribution of the ions with infinitely large masses, is obtained by [5,6,73,74]
Sic and III-N Heavily Doped
513
The self-energy expressions above is valid for an eigenstate either at the minimum of the lowest conduction band or at the maximum of the uppermost valence band. If a general eigenstate is considered, an additional polaron term is necessary [5]. The energy shifts of the conduction-band minimum AE^i and of the valence-band maximum AE^i are calculated as functions of ionized impurity concentration for both n-type and p-type 3 C - , 2H-, 4 H - , 6H-SiC, using the RPA-h Hubbard approach described above. A simple approach to incorporate the electronic structure of the unperturbed crystal (that is, £^(k)) into the equations above is to use the parabolic approximation (i.e. using parabolic energy dispersions, represented by the effective masses, and a modelled parametrization of the overlap integrals A;j/(k, k')). However, in this work, we use the "true" energy dispersions and overlap integrals, i.e. the energy dispersions and the overlap integrals from FPLAPW band structure calculations of Persson and Lindefelt [67,68]. We show below that the non-parabolicity of the valence-band curvatures affects the calculated self-energies of the valence-band maximum. Also the double-well structure of the lowest conduction band in 6H-SiC has a strong influence on the self-energies, especially for high concentrations of ionized impurity. See Refs. [5,6,70] for detailed information of the computational method. The doping-induced energy shifts of the lowest conduction-band minimum AE'^i and of the uppermost valence-band maximum AE^i in n-type material are obtained as A£,i = Re[/iXci*m, & ( k . ) ) ] + Re[ftXci*m, ^i(k^))]
+ R 4 ^ S i T * - ' ^i(km))l; *- ^
(n-type)
J
A£:,i = Re[;iXvi(0' ^vim] + R 4 ^ S T ( « ' ^i(^))]'
(17.33a)
(^-type)
(i^-^^^)
where k^ = kx, k^, kM, and ku in 3 C - , 2H-, 4H-, and 6H-SiC, respectively. The shift of the valence band does not contain exchange contribution since the valence-bands states of the undoped materials are (almost) completely occupied by electrons and the exchange interaction in the valence bands is, therefore, already contained in the valence-band electronic structure of the intrinsic material. The corresponding expressions for p-type materials can easily be obtained by treating the holes as particles and the electrons as antiparticles. This implies that the self-energies Re[;i5;,(k,^(k))] should be replaced by -Re[n j ; ^ ( k , - ^ ( k ) ) ] . Thus, the dopinginduced energy shifts of the lowest conduction-band minimum AE'^i and of the uppermost valence-band maximum LE^x in p-type material are obtained as A^,i = R e [ - ; i X c i ( k m , - ^ i ( k ^ ) ) ] + R e [ - / ^ X c T * - ' - ^ i ( ^ - ) ) ] '
^P'^^P^) (^^'^^^^
514
Optoelectronic Devices: Ill-Nitrides
+ R e [ - ; i X r r ( « ' -^i(O))],
(p-type)
(17.34b)
The energy shifts of the conduction-band minimum A^'^i and the valence-band maximum AE^i in n- and p-type 3 C - , 2H-, 4 H - , and 6H-SiC have been analyzed and parametrized in Refs. [5,6]. In this work, we present the resulting shift of the fundamental energy gap AEg = A^'^i - A^^i and the optical bandgap energy. For both n- and p-type materials the fundamental (reduced) E^ and the optical {opt) E^g^ bandgap energies are obtained as (see also Figure 17.8): £g = 4 + A^g = 4 + ^ ^ c i - A £ v i
(17.35a)
£|P' = £g + A£^P^ = £g+£F = 4 + ^F + A E , i - A ^ , i
(17.35b)
The optical bandgap in the present n-type materials is defined as the energy needed to promote one electron from the top of the valence band to the Fermi energy of the electron gas. Thus, the optical bandgap includes band filling. To calculate this band-filling, it is presumed that the curvature of the conduction band (in the case of n-type material) or the valence bands (in the case of p-type materials) is not affected by the doping. This approximation has been found to be reasonable [5]. Moreover, Eq. (17.34) is valid for materials with indirect bandgaps. For material with a direct bandgap, one normally includes the Bumstein-Moss shift (see Section 17.6.2). In Figure 17.11, we show the resulting energy shifts of the fundamental (or reduced) bandgap A^^g (solid lines) and of the optical bandgap LE^g^ (dashed lines) as functions of ionized donor concentrations for the n-type SiC polytypes. For comparison, we also show the calculations of n-type Si. The marks in Figure 11(a) indicate measured energy shifts of the fundamental bandgap [153-155] (open circles, triangles, squares, and plus signs) and of the optical bandgap [153] (filled circles) in Si. There is a very good agreement between calculated and available measured values of both AEg and LE^g^. It is obvious that the reduced bandgap is strongly narrowed by the interaction with the ionized donor system. For instance, the fundamental bandgap is narrowed by —0.2 eV in 4H-SiC at a donor concentration of 4 X 10^^ cm~^. However, the energy shift of the optical bandgap is almost zero for Si. This is a consequence of the fact that the band filling (i.e. the Fermi level £'F of the electron gas in the conduction band) is almost equal to the energy shift AEg of the fundamental bandgap. For SiC the energy shift of the optical bandgap is larger than in Si, mainly because the narrowing of the reduced bandgap energy is larger. The non-parabolic double-well structure of the lowest conduction band in 6H-SiC has an important effect on A£'g and i^E^^ for high ionized donor concentrations (>5Xl0^^cm~^).
Sic and III-N Heavily Doped (b)
515 «-type
Oh
-200 D) 0 C LJJ
-300
-400 1017
10^2
10^9
1020
Ionized impurity concentration [cm~^]
1017
10^^
10^9
1020
Ionized impurity concentration [cm~^]
Figure 17.11. The energy shifts of the fundamental AEg (solid lines) and optical AE^^^ (dashed lines) bandgaps in n-type (a) 3C-SiC and (b) 2H-, 4 H - , and 6H-SiC. For comparison, we also show the results of n-type Si. Open circles [153], triangles [153], squares [154], and plus signs [155] are measured values of A£g for Si and filled circles [153] are corresponding values for AE^^^.
In Figure 17.12, we show the resulting energy shifts of the fundamental bandgap AE^ (soHd lines) and of the optical bandgap A^^g^^ (dashed lines) as functions of ionized acceptor concentrations A^^ fo^ the p-type SiC polytypes. For comparison, we also show the calculations of p-type Si. The rather small differences in the energy shifts of both the fundamental bandgap and the optical bandgap between the poly types 2H-, 4 H - , and 6H-SiC are a consequence of the similar valence-band structures for the hexagonal polytypes. The dotted lines in Figure 17.12 represent the calculation within the parabolic approximation. The details in the curvature of A£'g for the hexagonal polytypes can be explained directly from the energy dispersions of the three valence bands (see Figure 17.7). For hole concentrations p = Ix 10^^-1 X 10^^ cm~^ only the very top of the uppermost valence band is populated by holes and in this energy region (E^ > - 4 meV) the band is essentially parabolic and, therefore, the parabolic approximation is good for these concentrations. At a hole concentration of 1 X 10^^ cm~^ the Fermi energy is about - 4 meV in all three hexagonal polytypes and at this energy the uppermost valence bands becomes non-parabolic and thus the parabolic approximation becomes inaccurate. At the hole concentrationsp = 6,9, and 9 X 10^^ cm~^ in 2H-, 4 H - , and 6H-SiC, respectively, the second uppermost valence bands start to be populated. Here, the effect on AE^i is most prominent in 2H-SiC, because 2H-SiC has the lowest concentration for the onset of
516
Optoelectronic Devices: Ill-Nitrides (a)
p-type 1 •' 1
0
-50 E 0 c LU
(b)
p-type
-50
"3C-- S i C ^
-100
£.-100
2H-SicJ^yV^ 0)
-150
\
V
liJ -150 h
4H-SiC/>N^ 6H-Sic)\ANJ
-200
• 1 • ••••1
10^^
•_
10^^
i
10^9
'
• "
•
1
10^0
Ionized acceptor concentration [cnrr-^]
-200 h
- , , J
10^^ lO^s 10^9 1020 Ionized acceptor concentration [cm~^]
Figure 17.12. The energy shifts of the reduced A£g (solid lines) and optical AE^^^ (dashed lines) bandgaps in p-type (a) 3C-SiC and Si and (b) 2H-, 4 H - , and 6H-SiC. The dotted line in (a) represents calculated shift AEg for Si assuming parabolic energy bands. Open circles and triangles are measured values [153] of AEg for Si, and filled circles are corresponding vales AE!^^\
populating the second uppermost valence band and, moreover, the band curvature [5] of the valence bands in 2H-SiC are less flat than the corresponding curvatures in the other two hexagonal polytypes. This results in a larger energy shift AE^ for 2H-SiC than for 4 H - and 6H-SiC. For low ionized acceptor concentrations the parabolic approximation gives a good description of the energy shifts. This is what could be expected, since the employed crystal parameters for the parabolic approximation were chosen to describe the energies at the very top of the valence bands. For high hole concentrations, however, the parabolic approximation of the valence bands fails to represent the true Fermi energy and the resulting energy shifts AE^ and A£^^^ differ from the results obtained by using the numerical energy dispersions. The marks in Figure 17.12 indicate measured [153] energy shifts of the fundamental bandgap (filled circles and triangles) and of the optical bandgap (open circles) in p-type Si. As in the case of n-type Si the calculated and measured values of A£'g agree well, whereas calculated A£^^^ are somewhat overestimated, although a part of the deviation can be measured inaccurately. The dotted line in Figure 17.12(a) represents the calculated shift AEg in Si using the parabolic approximation. It is obvious that the nonparabolic treatment of the valence bands, within the present FPLAPW calculation, results in much better agreement between calculated and measured values at high acceptor concentrations. The parabolic approximation strongly overestimates the narrowing of the fundamental bandgap. We have found [156] the same qualitative
Sic and III-N Heavily Doped
517
shortcomings of the parabolic approximation for heavily doped p-type GaAs. The parametrization of the valence bands and the corresponding overlap integrals (like in the parabolic approximation) can be strongly improved by employing the k-p parametrization of the bands [157]. In this k-p approximation, the main non-parabolicity of the valence bands is taken into account. Since the non-parabolicity of the valence-band maximum is arising from the spin-orbit interaction, we conclude that a fully relativistic treatment of the energy bands is crucial for calculating the BGN of especially p-type semiconductors. This is true for most semiconductors, even the light materials. The reason is that even in light materials, the curvatures of the bands (compare with the effective hole masses in Section 17.3.2) are strongly affected by the spin-orbit interaction. Moreover, the spin-orbit split-off energies are normally in the range 5-100 meV, which corresponds to a moderate to high band filling of holes in the valence bands (e.g. k^T ~ 25 meV at room temperature). Thus, the spin-orbit interaction affects both the curvature of the valance bands and the degeneracy of the valence-band maximum. Both these effects will affect the band-filling and thus the Fermi energy of the hole gas. The computational method was based on a zero-temperature formalism [5,6,73-76] and the results are in a strict sense valid only for impurity concentrations above the critical concentration for the MNM transition, which is about 4 X 10^^ cm~^ in n-type Si and 3C-SiC and about 0.3-7 X 10^^ cm~^ in n-type 4 H - and 6H-SiC according to previous section. For n-type Si a finite-temperature RPA calculation has been performed by Semelius [158] and by Thuselt and Rosier [159], showing that the zero-temperature calculation is a good approximation for calculations of A^'^i even at finite temperatures, mainly due to compensating effects between the correlation and the exchange interactions. However, in n-type materials AE^i does not depend on the exchange energy and this shift might, therefore, be more affected by the temperature. Nevertheless, it is believed that the zero-temperature calculations presented here can, with reasonable accuracy, be applied for finite temperatures for concentrations below the Mott transition where the impurities are partly or fully thermally ionized. In this case, the ionized impurity concentration depends on the impurity concentration and the absolute temperature. The temperature-dependent ionized impurity concentration has been worked out for Al doped 4H-SiC and N doped 6H-SiC by Persson and Lindefelt [121]. In Ref. [160], we present the calculation of plasma-induced BGN, i.e. a narrowing of the fundamental bandgap due to heavily excitation of electrons from the valence band to the conduction band in 3C-, 2H-, 4 H - , 6H-SiC, and Si. The results show that the nonparabolicity of the valence bands and the 6H-SiC double-well structure have only a moderate effect on the resulting BGN for the plasma concentration of 10^^-10^^ cm~^. Hence, the parabolic approximation of the band edges are valid for this moderate excitation concentration.
518
Optoelectronic Devices: Ill-Nitrides
17.5. ELECTRONIC PROPERTIES OF III-N The electronic structures of the III-Ns have been studied theoretically in the early 1960s. Early pseudopotential calculations [60-62] of zb-BN yield indirect bandgap energy in the range of 7.6-10 eV. Orthogonal plane-wave calculation of wz-AlN by Hejda [50] resulted in bandgap energies of £g = 3.91 eV, which is lower than the measured value of 6.28 eV [161]. Pseudopotential calculations of wz-AIN by Bloom [46] and Jones et al. [47] resulted in bandgap energies of 5.25 and 5.31 eV, respectively. Early calculations of wz-GaN were performed by Bloom [46] and Bourne et al. [48] using the pseudopotential method. Later first-principles pseudopotential calculations [162-166] and full-potential band structure calculations [56,167-171] on the Ill-nitrides have been reported, primarily on wz-GaN and wz-AIN [167-169]. Quasi-particle calculations of III-N by Palummo et al. [172], Rubio et al. [173], and Blase et al. [174] show similar band structures as the LDA-based calculation apart from an almost constant energy difference between the occupied and unoccupied states. Most band-structure calculations give similar results for the conduction bands, but there are noticeable and important differences in the energy dispersion of the valence-band maximum; the calculated valence bands in semiconductors are in general more dependent on the choice of lattice parameters and computational method compared to the corresponding calculated conduction bands. To date, the bandgap energy of InN is not established. Early interband absorption measurements [175-177] gave a wide-gap material (£"2 ~ 1.7-2.0 eV) which was consistent with the bandgap trends with respect to the variations in ionic bonds (i.e. by comparing with InAs, InP, AIN, and GaN). However, no photoluminescence measurements were presented. The large bandgap energy of 1.7 eV has, at least partly, be attributed to oxygen incorporation in the materials [178]. Recent photoluminescence measurements [33,179-181] of high-quahty single crystal InN (e.g. radio-frequency plasma-excited molecular beam epitaxy) with relatively low carrier concentration reveal a bandgap energy of about 0.7-1.0 eV. However, the relatively low measured [33] pressure coefficient and temperature dependence of the low energy level is still a puzzling property. The low bandgap energy level may be attributed to be a broad impurity level. The LDA calculations gives zero (or almost zero) bandgap energies for both zb- and wz-InN [182,183]. Our LDA + QP yields Eg = 0.59 and 0.67 eV for zb-, and wz-InN, respectively. Similar quasi-particle correction to the LDA by Bechstedt and Furthmiiller [184] gives bandgap energies of 0.6-0.7 and 0.8-0.9 eV for zb-, and wz-InN, respectively. A modelled potential correction to the LDA by Wei et al. [185] fitted to the band structure energies of AlP, GaP, and InP yielded a bandgap of 0.70 and 0.85 eV for zb- and wz-InN. However, neither the experiments nor the calculations have so far been able to establish the bandgap energy of InN. Empirical pseudopotential calculations by Foley et al. [49] of wz-InN yields an electron masses of m^ = 0.12mo and the hole
Sic and III-N Heavily Doped
519
masses m^i = 0.5mo and m^2 = OJIMQ. Pseudopotential LDA calculations of zb-InN by Tsai et al. [186] yield a bandgap energy of £'g = 1.3 eV and m^ = (0.34 - 0.37)mo. 17.5,1 Electronic Band Structure The calculated electronic structure of zb-BN, zb-AlN, zb-GaN, and zb-InN are show in Figure 17.13, where the conduction bands have been shifted by 4g according to the LDA + QP approach (Eq. (17.1)). The bandgap of zb-BN and zb-AIN are indirect with conduction-band minimum at the X-point (with the D2d point-group irreducible representation ^7(4) having a cation located at the origin). The bandgap of zb-GaN and zb-InN are direct. Thus, zb-BN and zb-AIN have three equivalent conduction-band minima, whereas zb-GaN and zb-InN have only one minimum. The QP correction is 4g = 2.15, 1.87, 1.59, and 0.59 eV for zb BN, AIN, GaN, and InN, respectively. One can observe smaller correction with the decrease of cation atom number (which is partly related to the electronegativity). With the QP correction the calculated bandgap becomes very close to the experimental values (Table 17.6). The calculated bandgap values for zb-BN and zb-GaN are E^-}- Ag = 6.49 and 3.24 eV, respectively. The experimental (a)
"^—:
10 r^^^^^\ '>
5
0
\
>.
0
^
-5 •
\N.
LJJ
-10 -15
\
_^^
^ u X
r
W
U X
u X Zb-GaN
r
r zb-AIN
zb-BN
u X
r Zb-InN
Figure 17.13. Electronic band structures of zinc-blende BN, AIN GaN, and InN, obtained from the LDA + QP calculations.
520
Optoelectronic Devices: Ill-Nitrides
Table 17.6. Lattice constant a and fundamental bandgap energy E^ in zinc-blende III-N (with and without the QP correction A^
a{k) CBM £g (eV)
^8+4 ^so (meV)
LDA Expt. [2,188-190] LDA,Expt. [2,187] LDA LDA + QP Expt. [187,191,192] LDA Expt. [192]
zb-BN
zb-AlN
zb-GaN
3.584 3.616 X 4.34 6.49 6.45 21.3
4.353 4.38 X 3.24 5.11 5.34 19.4
4.468 4.49, 4.54
r
1.83 3.42 3.2, 3.3 11.9 17
zb-InN 4.937
r
0.002 0.59 326
The notation of the symmetry k-point position of the conduction-band minimum (CBM) is according to Figure 17.1. The valence-band spin-orbit A^ spUt-oflF energy is obtained from a fully relaxed LDA calculation.
values are 6.45 and 3.2-3.3 eV, respectively. The bandgap of zb-AIN is theoretically predicted to be indirect with £'g + 4g = 5.11 eV. The extinction coefficient data of Thompson et al. [187] indicates that zb-AIN is an indirect semiconductor with a bandgap energy of ~5.34eV. The bandgap of InN is not established neither experimentally nor theoretically. Our calculated LDA -h QP value for zb-InN is 0.59 eV which is similar to the calculated bandgap energy of Bechstedt and Furthmiiller [183]. Since the FPLAPW calculation with the LDA potential gives metallic ground state for zb-InN, the correction was obtained with an estimate of the low-frequency limit of the dielectric function (see Eq. (17.1)). One can notice from the figure that the energy difference between the conduction-band states at the symmetry point X and at the /"becomes larger for the heavier cations. Thus, InN has a much deeper F-point conduction-band state than BN. The direct bandgap transition energy is important for optical transitions. The calculated LDA -h QP direct T-point transition energy for zb-BN, zb-AIN, zb-GaN, and zb-InN is A£(r,7(5) - ^8(5)) = 10.81 eV, A£(r,6(i) - ^8(5)) = 6.17 eV, ^E{^,^^,^ - r,8(5)) = 3.42 eV, and A£'(rc7(5) - F^^iS)) = 0.59 eV, respectively. The direct transitions from the valence band to the conduction band at the X-point is A£(X^7(4) — ^^7(5)) = 11.41 eV, AE(X,7(4) - X,6(5)) = 6.89 eV, A£(X,7(4) " ^v6(5)) = 7.63 eV, and A£(X,7(4) - X,6(5)) = 5.81 eV, for zb-BN, zb-AIN, zb-GaN, and zb-InN, respectively. The LDA -h QP electronic structures of wz-BN, wz-AlN, wz-GaN, and wz-InN are show in Figure 17.14. wz-BN has indirect bandgap with the conduction-band minimum at the A^-point (with irreducible representation K^Q>^ of the C^^y point-group symmetry), whereas the other wz-III-Ns have direct bandgaps. The QP correction is almost equal for the zb and the wz structures: A^ = 2.15,1.85,1.63, and 0.67 eV for wz BN, AIN, GaN, and InN, respectively, with a decrease of the bandgap correction with increase of cation atom number. With the QP correction the calculated bandgap becomes very close to the experimental values (Table 17.7). The LDA H- QP fundamental bandgap of wz-AIN, and wz-GaN is £"2 + ^^ = 6.05 and 3.55 eV, respectively, which is close to
Sic and III-N Heavily Doped (a) 10
•^-.^CT^
\!^^-~^^^
i
-5
-. ^^^
10
"^^-^
0 C
^
5
Q)
521
UJ
15 •
M
^
K wz-BN
M
wz-AIN
K F A wz-GaN
Figure 17.14. Electronic band structures of wurtzite BN, AIN GaN, and InN, obtained from the LDA + QP calculation. Table 17.7. Lattice constants a and c, and the internal atom parameter u determined from the LDA calculations wz-AlN
wz-GaN
wz-InN
3.096 3.110,3.112 4.959 4.980, 4.982 0.3818 0.3821
3.159 3.190, 3.189 5.147 5.189, 5.185 0.3765 0.377
3.487 3.545 5.705 5.703 0.3795
r
r1.92
wz-BN a (A) c(A) u CBM E, (eV)
^g + 4 4 f (eV) ^so (meV)
LDA Expt. [2,197-199] LDA Expt.[197-199] LDA Expt. [197-199] LDA LDA LDA + QP Expt. [33,161,179-181,193] LDA Expt. [200,201] LDA Expt. [200,201]
2.525 4.177 0.3748 K 5.02 7.17 0.207
4.20 6.05 6.28 0.212
14.1
13.2
3.55 3.50 0.034 0.039, 0.029 5.5 8
r
0.00 0.67 0.7-1.0 0.044 3.8
The fundamental bandgap energy £g in wurtzite III-N is obtained with and without the QP correction A^. The notation of the symmetry k-point position of the conduction-band minimum (CBM) is according to Figure 17.1. The crystal-field A^f and spin-orbit A^^, split-oflf energies are at the valence-band maximum.
522
Optoelectronic Devices: Ill-Nitrides
the measured values of 6.28 eV [161] and 3.50 eV [193], respectively. The LDA + QP bandgap energy is Eg-\- A^ = 0.59 eV in zb-InN and Eg-\- Ag = 0.67 eV in wz-InN. This is consistent with recent measured photoluminescence results [33,179-181]. In the measurements and calculations by Yu et al. [31], they found a strong difference between the photoluminescence and absorption bandgap energies. This difference in the measured bandgap energies arises due to band filling of electrons in the conduction band. Photoluminescence measures the fundamental bandgap, whereas the absorption measurement detects the optical bandgap. Spectroscopy ellipsometry determined temperature dependence of the bandgap energies of zb- and wz-GaN by Petalas et al. [194] show significantly larger temperature coefficient for the wz structure (—dEg/dT = 0.30 and 0.56meV/K in temperature regions 100-300 and 300-500 K, respectively) compared to the zb structure (0.21 and 0.34 meV/K, respectively). Modulated photoreflectance measurements on zb-GaN by Noriega et al. [195] show similar temperature dependence. Similar to the zb structures, the energy difference between the conduction-band energy at the /"-point in wz-III-N becomes deeper than the conduction-band energy at the Z-point for increasing cation atom number. The calculated LDA + QP direct T-point transition energy for wz-BN, wz-AlN, wz-GaN, and wz-InN is ^EiF^-j^s) — r^9(5)) = 10.51 eV, A£(r,v(i) - ^7(1)) = 6.05 eV, ^E{^,,^,^ - ^9(5)) = 3.55 eV, and AE(r,,^s) " ^9(5)) = 0.67 eV, respectively. These T-point direct transition energies are very similar to the corresponding transition energies in the zb-structures. The direct transitions from the valence band to the conduction band at the M-point is AEiM^s^i) — M^^^^)) — 1104 eV, A£(M,5(i) - M,5(3)) = 8.18 eV, AE(M,sii) - M,s(3)) = 7.66 eV, and AEiM.sQ) ' ^v5(3)) = 5.51 eV, for wz-BN, wz-AIN, wz-GaN, and wz-InN, respectively. The crystal-field split-off energy ^^f of the uppermost valence bands in the wurtzite structures was determined in the absence of spin-orbit interaction. The value of A^f differs between different authors [167-169]. For instance, Suzuki et al. [167] report the value A,f = 58 (73) meV using u = 0.375 (0.375) for AIN (GaN). Kim et al. [168] report the value 4 f = 215 (36) meV using u = 0.377 (0.382). Our value 4 f = 207, 212, 34, and 44 meV for BN, AIN, GaN, and InN, respectively, using u = 0.3748, 0.3821, 0.3765, and 0.3795 are very similar to the result of Kim et al. The origin of the discrepancy of the calculated crystal-field splitting between different authors arises most likely due to the different internal lattice parameters. It has been shown that the crystal-field splitting in hexagonal structures strongly depends on u [69,196] (see also Section 17.3.1). The VBO and the conduction-band offset (CBO) of the nitrides has been calculated within the LDA [196,202]. Normally these VBO/CBO calculations assume strain free bulklike interfaces, and the calculations should consider surface orientation dependence. X-ray photoemission spectroscopy by Martin et al. [203] reveals a valence-band discontinuity of 1.05, 0.70, and 1.81 eV in wz InN/GaN, GaN/AlN, and InN/AlN heterojunctions, respectively. Cociorva et al. [204] computed the VBO of zb and wz AlN/GaN interfaces using the many-particle GW method and considering AIN, GaN, and 6H-SiC as substrates.
Sic and III-N Heavily Doped
523
They found that the VBO and CBM depend on the in-plane lattice constant, which could explain the measurement VBOs [205,206] ranging from 0.5 to 1.4 eV. Moreover, the VBO and CBO were found [204] to have rather weak dependence on the interface orientation. The valence-band offset between zb-III-N and corresponding wz structure is small. In contrast to SiC, the bandgap energy of zb- and wz-GaN (and may be also InN) are very comparable. Also the direct bandgap energies of zb- and wz-AlN are similar. This means that structural phase related defects (like cluster formations and dislocations in the (111) direction) or alloying of zb- and wz-GaN will not automatically create localized states as in SiC (see Section 17.3.1), due to differences in the conduction or valence-band edges. Since the crystal-field split-off energy is small in wz-GaN, there will be very small effect on this valence-band due to alloying, since the so-band in the zb structure and the cf- and so-bands in the wz structure are all (at the T-point) energetically close to valence-band maximum. Thus, growth of good quality GaN is not very sensitive to polytype inclusion. The relatively large VBO between GaN and GaAs can be partly explained [207] by the short and strong Ga-N bond which lowers the N-2p-like valence-band maximum in GaN by ~ 2 e V compared to the As-3p-like valence-band maximum in GaAs. Similarly, by alloying the nitrides as isostructure and isovalent ternary A^Bi__^N the chemical and structural effects create a non-linear variation of the bandgap with respect to the composition. It has been shown by Ferthat et al. [208] by using LDA pseudopotential that the strong bandgap bowing in In^^Gai-j^N is mainly induced by structural relaxation. The cation-(i states play an important roll in GaN. Lambrecht and Segall [37] have shown that the Ga-3d states in GaN hybridize with the energetically close-lying N 2s states for k-point away from the T-point. This is obvious from Figures 17.13(c) and 17.14(c), where the cation-d and anion-s are hybridized at about - 13 eV (according to the LDA results). Omission of this hybridzation influence the calculations of the equilibrium volume and the bandgap energy. The Ga-3d states were further investigated by Fiorentini et al. [209] as well as Wright and Nelson [210]. LDA underestimates the self-interaction of the localized d-states, and in GaN the LDA binding energy of the d-states are ~ 3-4 eV to small [211,212] compared to photoemission results [203]. This LDA error will affect the calculated hybridization between Ga-3d and N-2s in GaN [212]. However, Persson and Zunger [207,213] show that including a self-interaction correction to both the Ga-3d and N-2s, the hybridization is still noticeable. Moreover, the cation-d anion-s hybridization creates an additional N-2p-like state within the Ga-d band. This N-p state has been observed by Smith et al. [214] in soft X-ray nitrogen ^-emission measurements. Since InN has rather similar cation-d anion-s hybridization (see Figures 17.13(d) and 17.14(d)), the discussion above for GaN should also be true for InN. In Table 17.8, we present the calculated dielectric constants of intrinsic zb- and wz-III-N using the LDA + QP method. For comparison we also present the results for the LDA calculation (in brackets) without the bandgap correction. To calculate the static dielectric constant 8(0), one needs to include the electron-optical phonon interaction as in
524
Optoelectronic Devices: Ill-Nitrides
Table 17.8. The dielectric constants of zinc-blende and wurtzite III-N obtained from the LD A + QP calculation.
m-N
zb-BN zb-AlN zb-GaN zb-InN wz-BN
s e e e fii
^11 wz-AlN
ei fill
wz-GaN
ei
^11 wz-InN
Expt.
This work
ei
^11
e(0)
e(oo)
6.45 (7.23) 8.35 (9.26) 9.56 (10.73) 10.24(15.10) 6.40(7.17) 6.54 (7.41) 8.19 (9.02) 8.49 (9.44) 9.50 (10.59) 9.69 (10.88) 9.51 (14.00) 9.41 (13.87)
4.14(4.67) 4.46 (5.24) 5.32 (6.12) 8.88 (12.91) 4.11 (4.63) 4.22 (4.80) 4.37(5.10) 4.54 (5.32) 5.26 (6.09) 5.38 (6.24) 8.21 (11.63) 8.11 (11.51)
e(oo)
e(0) 7.1 (a)
4.5 (a) 5.29 (g) 5.3 (h) 5.7 (i)
8.5 (b) 8.9 (b), 9.5 (b) 8.1 (k), 15.3 (1)
4.95 (j) 4.1 (j) 4.68 (b), 4.84 (b) 4.14 (c), 4.13 (d) 4.32 (c), 4.27 (d) 5.35 (b) 5.18 (d), 5.14 (e) 5.14 (f) 5.31 (d), 5.31 (e)5.31 (f) 9.3(2), 5.8 (k), 8.4 (1)
The values in brackets represent the LDA results without the bandgap correction. The static dielectric constant e(0) was determined by taking into account the electron-phonon interaction. Measured results are from (a) Ref. [2] (b) Ref. [215], (c) Ref. [218], (d) Ref. [219], (e) Ref. [220], (f) Ref. [221], (g) Ref. [222], (h) Ref. [223], (i) Ref. [224], (j) Ref. [217], (k) Ref. [225], and (1) Ref. [226].
Section 17.3.1. For in the optical phonon energies (see Eq. (17.5)), we used the experimental values [215]: /ift>ro = 130.8, 82.7, 66.0, and 59.3 meV and HCOI^Q = 161.8, 112.8, 88.0, and 86.0 meV in wz BN, AIN, GaN, and InN, respectively. We presume the same values for zb structures. By adding sf(a)) to 82(^) (see Eqs. (17.3)-(17.5)), and thereafter calculating ei(o>) through the Kramers-Kronig dispersion relation, we obtain a more reaUstic static dielectric constant. Early LDA calculations of the high-frequency dielectric constants of zb- and wz-IH-N was performed by Cristensen and Corzyca [171] The resulting high-frequency dielectric constant are £(oo) = 4.14,3.90,4.78,6.15 in zb BN, AIN, and GaN, InN, respectively, obtained from a linear mufihn-tin orbital ASA calculation with the underestimate LDA bandgap energies. LDA pseudopotential calculations (including a local field corrections) of the high-frequency s{oo) dielectric function of zband wz-in-N by Karch et al. [216] yield very similar results as our LDA + QP values. For instance, they obtained 8(oo) = 4.54,4.46, and 5.41 in zb BN, AIN, and GaN, respectively, and our corresponding FPLAPW LDA + QP result is s(oo) = 4.14, 4.46, and 5.32, respectively. 17.5.2 Effective Electron and Hole Masses First-principles empirical pseudopotential [49,169,186,227] as well as first-principles fullpotential band structure calculations [77,107,167,168,170,228,229] show fairly similar effective electron masses, but there are noticeable differences in the calculated effective hole masses. For instance, Suzuki et al. [167] have presented one of the first full-potential calculation of the effective electron and hole messes of wz GaN and AIN, using a linearized
Sic and III-N Heavily Doped
525
augmented plane wave method within the LDA (using ideal values for the internal atomic positions) and including the spin-orbit coupling. Kim et al. [168] have presented a fullpotential linearized muffin-tin orbital calculation within the LDA. The spin-orbit interaction was taken into account within the ASA. The band structures of Kim et al. [168] agree overall fairly well with earlier published results, but surprisingly, they found that zb-AlN has its valence-band maximum along the JX-direction, and not at the Apoint. This implies negative effective hole mass values at the F-point. Persson et al. [77,107] also found that the valence-band maximum is along the /X-direction in a scalar-relativistic calculation (i.e. excluding the spin-orbit interaction), but in the fully relativistic calculation (i.e. including the spin-orbit interaction) the valence-band maximum is at the T-point since the uppermost valence bands are energetically lifted by about A^J?^. This small correction to the uppermost valence band in zb-AIN is enough to make the valenceband maximum to be located at the F-point. The energy dispersions of the bands near the fundamental bandgap in zb-BN, zb-AIN, zb-GaN and zb-InN are shown in Figure 17.13, obtained from the first-principles fuUyrelativistic FPLAPW LDA + QP calculations [77,107]. As one can see from the figure, the zb-GaN and zb-InN has a direct bandgap, whereas the conduction-band minimum in zb-BN and zb-AIN is at the Z-point (thus, three equivalent conduction-band minima). This implies that the electron mass-tensor in zb-GaN and zb-InN is represented by a single mass component m^, whereas in zb-BN and zb-AIN the electron mass-tensor is represented by a transverse m^j^ and a longitudinal mc\\\ effective mass. The anisotropy of one conduction-band minimum in zb-BN and zb-AIN is mc\Jmc\\\ = 3.03 and 1.62, respectively. The calculated electron masses for the zb III-Ns are presented in Table 17.9. Since the zb-BN and zb-AIN have their second lowest conduction-band minimum at Table 17.9. The effective electron masses and corresponding polaron masses trip (see Eq. (17.3)) of the two lowest conduction-band minima in zinc-blende m-N
zb-m-N
Electron mass (mo)
Second minimum
First minimum
This work
This work m
mp
0.30 0.91
0.32 0.99
m,j
0.32 0.52
0.36 0.58
mp
0,17
0.18
zb-BN mil zb-AIN zb-GaN
m^
m
Mp
Mf
0.87
0.98
nif
0.31
0-35
m^
0.32 0.77
0.35 0.86
m„ zb-InN
Mf
0,06
0.33 1.46
526
Optoelectronic Devices: Ill-Nitrides
the r-point, and zb-GaN and zb-InN have their second lowest conduction-band minimum at the X-point, and these second minima are important for alloying the III-Ns, we also present the effective electron masses of the second minimum. One can see from Table 17.9 that the Apoint effective electron masses are relatively small (except for zb-BN). This is true for many direct bandgap semiconductors [2,230,231]. LDA underestimate often these Apoint effective electron masses by ~ 10-50%, and Persson and Mirbt [230] show that this underestimate is due to a too strong couphng between the conduction and the valence bands. In GaAs, the LDA effective electron mass value (m^ = O.Olmo) is only ~ 15% of the experimental value of m^ = 0.067mo [156,232]. One can, therefore, expect that the calculated LDA T-point effective electron masses in Table 17.9 are slightly underestimated, and that the T-point mass value for InN could be substantially inaccurate since the LDA incorrectly assigns InN to be a zero bandgap semiconductor. However, the effective electron masses away from the T-point (e.g. at the X-point) are expected to be accurate [230]. In the table, we also present the calculated effective polaron masses (except for zb-InN because of the inaccurate bandgap value) according to Eq. (17.3). The polaron masses are only shghtly larger than the corresponding bare masses since the effective electron masses in the III-Ns are relatively small and the Frohlich constant is proportionan to m^^^. To our knowledge, there are no experimental values of the effective electron masses for the zb structures of the III-Ns. The energy dispersions of the bands near the fundamental bandgap in wz-BN, wz-AlN, wz-GaN and wz-InN are shown in Figure 17.14. Since the conduction-band minimum of wz-AIN, wz-GaN, and wz-InN is located at the T-point (with C^^ symmetry), the effective electron mass-tensor can be represented by a transverse m^n and a longitudinal m^iii mass. Also the effective electron mass-tensor of the conductionband minimum of wz-BN, located at the A'-point with C^y symmetry, can be represented by a transverse and a longitudinal mass. The calculated effective electron masses are presented in Table 17.10. Measurements of the effective electron masses in the III-N have mainly been performed on wz-GaN, primarily by using indirect techniques like plasma reflection, Faraday rotation, and donor transition energies for determining the masses [233-246]. The latest experimental results are in the range of (0.20-0.24)mo and the anisotropy mjm\\ is small [237]. Cyclotron measurements by Drechsler et al. [234] yield m^ = 0.20mo. Our calculated values for wz-GaN are md^ = 0.1 Smg and mc\\\ = 0.16mo, and the corresponding calculated polaron masses are m d i = 0.19mo and mc\\\ = OAIMQ, which are close to, but somewhat smaller than, the experimental results. As described above, one may expect [230] underestimated LDA effective electron masses for these direct bandgap materials. By combining infrared ellipsometry data analysis with Hall-effect measurements, the isotropic average effective electron masses in wz-InN was determined to be 0.14mo by Kasic et al. [247]. Measurements of the plasma edge frequency in reflection
Sic and III-N Heavily Doped
527
Table 17.10. The effective electron masses and corresponding polaron masses nip (see Eq. (17.3)) of the lowest conduction-band minimum in wurtzite III-N
wz-ni-N
First minimum
Electron mass (wio)
Expt. m
rhis worls m
Wp
0.49 0.30
0.53 0.32
0.32 0.30
0.36 0.33
m,|
0.18 0.16
0.19 0.17
mil
0.03 0.80
wz-BN m,, wz-AlN wz-GaN
wz-InN
0.22 (d), 0.237 (g) 0.228 (g) 0.22 (a), 0.222 (b), 0.23 (c)
0.14(e), 0.07(f) Measurements are from (a) Ref [234], (b) Ref [235], (c) Ref [236], (d) Ref [233], (e) Ref [247], (f) Ref [248], (g) Ref [237].
measurements by Wu et al. [248] yield a small density-of-states effective electron mass in wz-InN of O.OTmQ. These measurements were done with samples containing high free carrier concentrations which affects both the electronic structure [77] as well as the analysis due to band-filling effects. Both the calculated effective electron masses of wz-GaN and of wz-AIN show almost spherical energy dispersions of the lowest conduction band [107]. Since the bandgap energy is small, this spherical behavior of the conduction band is valid up to an energy of about 0.4 eV above the minimum. One can compare this parabolic behavior with Ge and GaAs which both have small direct bandgaps, and their lowest conduction bands are rather non-parabolic [70,249]. The anisotropy of effective electron mass tensor in wz-AIN and wz-GaN is small, which is in consistent with the measurements [237]. However, the calculated anisotropy is very large in wz-InN, but this anisotropy is probably caused by overestimated conduction- to valence-band coupling [230] in this zero LDA bandgap energy. We also present the calculated effective polaron masses (except for wz-InN due to the LDA bandgap problem). Just like for the zb structures, the polaron masses are only slightly larger than the corresponding bare masses since the effective electron masses in the III-Ns are relatively small. Earlier calculations [49,77,107,167-170,227-229] of the bare effective electron masses in zb and wz III-Ns give similar results as presented here. For instance, Ramos et al. [228] have calculated the effective electron (and hole) masses of zb BN, AIN, and GaN using a full-potential linearized augmented plane-wave method. They found m^ = 0.23mo; m\\ = 0.94mo in zb-BN, m^ = 1.95mo; m\\ = 0.53mo in zb-AlN, and m = 0.14mo
528
Optoelectronic Devices: Ill-Nitrides
in zb-GaN which is similar to our bare effective electron masses m^ = 0.30mo; m\\ = 0.91mo in zb-BN, m^ = 0.32mo; my = 0.52mo in zb-AlN, and m = OAITUQ in zb-GaN, apart from the transverse effective electron mass in zb-AIN which differs considerably. Our results of this bare effective electron mass component in zb-AIN (mj_ = 0.32mo) are closer to the calculated results of Suzuki et al. [167] (m^ = 0.25mo) and Fan et al. [227] (m^= 0.31mo). Today, most theoretical studies of the electronic structure are based on the LDA/DFT, either by using pseudopotential or full-potential methods. Even if band-structure calculations based on quasi-particle models (like GW) are frequently presenting the single-particle energies of the high-symmetry k-points, there are only a few published GW studies of the effective masses of semiconductors. The reason is partly due to the accuracy and the dense k-mesh (which means time-consuming GW calculations) needed in an accurate calculation of the effective masses. However, Oshoikiri et al. [250] calculated the effective electron masses for wz-AlN and wz-GaN using the GW technique. They obtained the values nij^ = 0.37mo and m|| = 0.38mo for wz-AIN and m^ = 0.21 mo and m\\ = 0A9mQ for wz-GaN. Their corresponding LDA values (m^ = 0.32mo and 0.17mo for AIN and GaN, respectively) are somewhat lower than the GW results. This is consistent with the finding by Persson and Mirbt [230] that the LDA overestimates the coupling between the conduction and valence-band maximum at the jT-point, which results in too small values of the Apoint effective electron mass and the effective light-hole (Ih) mass. The band structures of the three (six if spin is considered) uppermost valence bands in zb BN, AIN GaN, and InN are shown in Figure 17.15. We show 15% of the total length to the BZ boundary, from the T-point and along two synmietry directions (i.e. the (100) rx = A direction and the (110) FK = S direction). The spin-orbit interaction causes the splitting r^®Di,2 => TySrs for the T^ symmetry with 4 o = 21, 19, 12, and 326 meV in zb BN, AIN, GaN, and InN, respectively. The four-fold degenerate Fg state is lifted by ~ A^J?> whereas the double degenerate split-off band F-f is lowered by ~ 1A^J?>. This splitting affects the valence-band curvatures strongly in the vicinity of the T-point. The dotted lines in Figure 17.15 represent the energy dispersions when spin-orbit interaction is excluded. Noticeable is the strong effect on the two uppermost valence band in the /X-direction (the (llO)-direction), especially in zb-AIN. Without spin-orbit coupling the valence-band maximum is about 10% away from the /"-point in this direction. Furthermore, the band is very flat, which also has been reported by Kim et al. [168]. This implies a negative hole-mass component at the /"-point in the /X-direction. However, by including the spin-orbit interaction, and thereby forcing the bands to split, the resulting valence-band maximum is at the /"-point with a positive hole mass value at the /"-point. This results in a large and negative hole-mass component for the uppermost valence band at the T-point: m^i(FK) = -253.07mo and m^2(^^) = IMniQ. However, by including the spin-orbit interaction, and thereby, forcing the bands to split.
Sic and III-N Heavily Doped (a)
529
1
b)
^^ J
r8(5)
0
y;^^/^^^ \//?
-0.1
c LU
//
/
\ \so
\ 1 N
-0?
(c)
h
¥
[ A5(2®4)
0 C LU
- I
\
r(T^)
SCCg)
A(C2v)
r(Trf)
2:(C,)
]
T8{5) / ^'^ (5)\
/ ^
-
X.
\ r
A(C2v) zb-A[N
zb-BN
/^
/
-0.1
\ ^ \
J*^ E3(2n N$a:3(i) j
\ E4(1)\ : ^5(204)
-0.2 2b-GaN
^5(1)
A(C2,)
\2:4(i) 2:3(1) \
m^)
\ ^ ]
2(Cs)
zb-InN
Figure 17.15. The valence-band maximum of zinc-blende (a) BN, (b) AIN, (c) GaN, and (d) InN along two symmetry directions. We show 15% of the total length to the BZ boundary. The solid (dotted) lines represent LDA calculations with (without) spin-orbit coupling.
the valence-band maximum is at the F-point with a positive mass value: m^iiFK) = 3.06mo and m^2(^^) = 0.38mo. Thus, it is crucial to include the spin-orbit coupling for determining the effective hole masses even in light insulators and semiconductors. The spherical average values (m^i, m^2» ^^^ ^v^) have been determined according to Eqs. (17.7) and (17.8). Our calculated effective hole masses agree well with the calculated results of zb BN, AIN, and GaN of Ramos et al. [228]. The relativistic FPLAPW calculation of the valence-band maximum yields the k p Luttinger parameters (see Eq. (17.7)) A = - 1 . 9 1 , \B\ = 0.00, and ICl = 1.93 for zb-BN, A = -1.46, \B\ = 0.77, and \C\ = 1.68 for zb-AlN, and A = -2.80, \B\ = 1.75, and \C\ = 2.29 for zb-GaN. The LDA cannot produce accurate curvature of the valence-band maximum in InN due to the problem with the zero LDA bandgap energy, and we do, therefore, not present the Luttinger parameters of InN. Thus, the present LDA effective hole masses of both zb- and wz-InN are maybe not reliable due to this incorrect LDA description of the valence bands. The optical transition from the hh-lh-band and the so-band to the conduction band as functions of temperature were measured by Ramires-Flores et al. [192] using modulated
Optoelectronic Devices: Ill-Nitrides
530
photoreflectance. They obtain A^^ = 11 meV for zb-GaN. This value is sHghtly larger than the calculated spin-orbit split-off energy of 12 meV. A detailed fully relativistic band structure of the three uppermost valence bands in wz BN, AIN GaN, and InN is presented in Figure 17.16 by the solid lines. Dotted lines are the corresponding energy dispersion when neglecting the spin-orbit interaction. We show 15% of the total length to the BZ boundary, from the T-point and along two symmetry directions (i.e. the (001) TA = Zi direction and the (100) TM = i; direction). The crystal-field split-off energy A^f = 207, 212, 34, and 44 meV in wz BN, AIN, GaN and InN, respectively, was obtained as the single-particle energy difference between the valence 7^5 and Fi bands, excluding the spin-orbit interaction. The spin-orbit interaction causes the splitting r^®Dy2 =^ rje>rg and ri®Dy2 => r^ for the C^^ symmetry with A,^ = 14, 13, 5, and 4 meV in wz BN, AIN, GaN and InN, respectively. In GaN, the two uppermost bands have r^ and Fg symmetry, and the third crystal-field split-off band has Fj symmetry is about 34 meV below the second band. In AIN it is different. The uppermost band is the crystalfield split-off band with Fj symmetry and the two bands with Fj and Fg symmetry are about 212 meV below the uppermost band. The very large crystal-field splitting and the fact that
1
(a)
r9(5) V1___ V2
r? (5)
X C LU
-0.2 7
r? (1) V3^
-0.3 -0.4 1
i:4{2r^
V:4(i) I3(1)\ --.13(1) \
A(C6v) nCev) wz-BN
= : :
i4(ir^-v.A^ 2:(Cs)
(c)
> -0.1 P
r(C2v)
^Cs)
wz-InN Figure 17.16. The valence-band maximum of wurtzite (a) BN (b) AIN, (c) GaN, and (d) InN along two synmietry directions. We show 15% of the total length to the BZ boundary. The solid (dotted) lines represent LDA calculations with (without) spin-orbit coupling.
Sic and III-N Heavily Doped
531
the uppermost valence band in AIN is the crystal-field split-off band, result in a parabolic valence-band maximum in a large energy range. Thus, the effective hole masses m^j^ and m^ill in wz-AlN represent the band not only in the vicinity of the T-point but also down to about - 200 meV. However, in the other three wz structures, the non-parabolicity of the two uppermost bands due to the spin-orbit coupling becomes apparent at about - 5 meV, and below this energy the effective hole masses fail to describe the bands accurately. The dotted lines in Figure 17.15 represent the energy dispersions when spin-orbit interaction is excluded. Even though the spin-orbit interaction splits up the bands by only 5-8 meV, the interaction has a strong effect on the effective hole masses. For instance, the transverse hole mass of the uppermost (second uppermost) valence band in zb-GaN (zb-AlN) is 2.22mo (17.20mo) if spin-orbit interaction is excluded, and 0.32mo (4.46mo) if spin-orbit interaction is included. However, the longitudinal mass of this band is less affected by the spin-orbit interaction. Just like for the zb III-Ns, there is a lack of reliable experimental data for the valence bands in wz III-Ns. The measured effective hole mass in wz-GaN ranges between m^i = 0.3mo and lArriQ [200,237,251-260] which is somewhat larger than our density-of-states mass (m^i||-m^i^-m^i^)^^^ = 0.60mo. An estimate of the corresponding polaron mass Table 17.11. Efifective hole masses and corresponding polaron masses ntp (see Eq. (17.3)) of zb III-N calculated by including the spin-orbit interaction zb-III-N
Hole mass (mo)
so -band
Ih-band
hh-band
This work
This work
This work m
mp
m
mp
m
mp
zb-BN
mrx mrK mri m^^"
0.52 1.06 1.24 1.06
0.59 1.21 1.42 1.21
0.52 0.35 0.34 0.35
0.59 0.40 0.38 0.40
0.52 0.52 0.52 0.52
0.57 0.57 0.57 0.57
zb-AIN
mrx mrK mpL m"^^
1.42 3.04 4.32 2.60
2.02 4.39 6.24 3.75
0.44 0.38 0.37 0.39
0.63 0.55 0.54 0.55
0.67 0.67 0.66 0.67
0.78 0.78 0.78 0.78
zb-GaN
mrx mrK fnri m^^"
0.89 1.55 1.95 1.29
1.11 1.91 2.40 1.60
0.23 0.21 0.21 0.21
0.28 0.25 0.25 0.25
0.36 0.35 0.35 0.36
0.39 0.39 0.39 0.39
zb-InN
mrx mpK mn
0.26 0.41 0.58
0.47 0.61 1.00
The polaron masses of InN are not presented due to the zero LDA bandgap energy of InN.
0.05 0.05 0.05
532
Optoelectronic Devices: Ill-Nitrides o
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d
-a
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PQ
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oo
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d
^
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11
Sic and III-N Heavily Doped
533
according to Eq. (17.3) gives 0.69mo which is within the experimental values. Infrared spectroscopy ellipsometry of p-type wz-GaN by Kasic et al. [237] reveals a hole mass of 1.40mo. However, no anisotropy was found within 25%, and that is not in agreement with our calculated effective hole masses. This could be due to high hole concentration in the measurements (assumed to be ~ 8 X 10^^ cm~^) which will affect the results since the spin-orbit split-off energy is small (—5-10 meV) in wz-GaN. Small spin-orbit split-off energy means that even moderate band filling of the valence bands will exceeds the parabolic region in the vicinity of the T-point, and thus, the measurements will measure an average effective hole mass, or the hole mass at the hole Fermi energy, instead of the mass value at the Apoint. The measurements of Torii et al. [256] and Santic [260] show, however, strong anisotropy: m^ix = 0.27mo, m^i\\ = 0.87mo, m^2L = 0.37mo, ^^211 = 0.87mo, m^3x =0.51 m^, and m^sji = 0.17mo, which is somewhat comparable to our calculated values including the polaron interaction m^ix — 0.37mo, m^iw = 2.36mo, ^viL — 0.36mo, m^2|| — l-43mo, m^si = 1.30mo, and m^2>\\ — OAIMQ. Suzuki et al. [167] and Kim et al. [168] have calculated the hole masses in wz-GaN and wz-AlN from fitted Luttinger parameters. Our results, obtained directly from the FPLAPW energy dispersion in the vicinity of the F-point show rather similar results. However, we find a stronger anisotropy of the uppermost valence bands these earlier calculations, especially for wz-GaN. Moreover, in contrast to both Suzuki et al., we obtain a difference between m^m and my2\\ in wz-GaN. Also in hexagonal polytypes of SiC, one finds that these two masses differ if the crystal-field splitting is sufficient small [68,69] like in wzGaN. In wz-BN, which has a large crystal-field splitting, we get m^m ~ m^2\\ and ntyij^ « ^v2i- This is also the case for the second and third uppermost valence bands, i.e. m^2\\ ~ m^2\\ and my2± ^ ^v3i' in wz-AlN. Our LDA calculation seems to overestimate A^o slightly compared to experiments (see Table 17.12). However, most of the available measurements are based on excitonic band transitions, which might differ from true band transitions. Moreover, we shown in Section 17.3.2 that the strength of the spin-orbit coupling does not directly affect the values of the effective hole masses in the zb structure. In the wz structure, the spin-orbit coupling as described within the k p method has a small effect on the effective hole masses [68].
17.6. DOPING INDUCED BANDGAP NARROWING IN III-N
Heavy n-type or p-type doping above a certain critical concentration N^ of a semiconductor gives metallic character of the material also in the low temperature regime, as described in Section 17.4. The free carriers in this metallic phase screen the crystal electrons, which thereby results in energy shifts of the single-particle energies. The fundamental bandgap energy is normally narrowed due to the energy shifts of
534
Optoelectronic Devices: Ill-Nitrides
the conduction-band minimum and the valence-band maximum. The role of impurities is very important in fabricating devices. The efficiency of these devices is strongly affected by the incorporation of impurities. Despite the technological importance of GaN [3,15-26], there is to date a lack of reported detailed investigation of the doping-induced effects on the electronic and optical properties of the III-Ns. However, available experimental results [26,27,261] on doped semiconductors, above the impurity critical concentration for the doping-induced MNM transition, reveal a bandgap shift even beyond 10-20% of the reduced bandgap energy of the intrinsic material. In this section, we report about the calculated MNM critical concentration [80] for n- and p-type zb-AlN, zb-GaN wz-AlN, wz-GaN, and zb-InN. We also present the results of the doping-induced BGN calculations [77,262,263] of n- and p-type AIN and GaN, using the RPA + Hubbard approach including the FPLAPW band structure results, described in Section 17.4. 17,6.1 Metal-Non-metal Transition We calculated the critical concentration Nc using three different models (see Section 17.4.1). The first two models (model No. 1 and No. 2) are based on the Mott picture [139] of overlapping impurity electrons, assuming hydrogen-like wave functions. In these models, the impurity electrons become strongly overlapping at a critical concentration and thus behave like conducting electrons. In the third model [5,74] (model No. 3), the total energy E^^ of the non-metallic weakly interacting impurity electrons (assuming hydrogen-like wave functions), and the total energy E^^ of the metallic strongly interacting impurity system (assuming free electrons in an electron gas) are compared. The critical concentration is obtained as the concentration when E^^ = E^^. In Figure 17.17, we show the total energies as functions of ionized donor concentration (in the case of n-type materials) or acceptor concentration (in the case of p-type materials). At very low doping concentrations the total energy of the non-metallic phase is lower than the corresponding total energy of the metallic phase. Thus, for low concentrations the system will be in the non-metalUc phase. For high doping concentrations, the strong impurity-impurity interaction energetically favors ionized donors (or acceptors) with an associated free electron (or hole) gas. Now, the semiconductor will have the metallic properties, due to the spontaneous impurity ionization. As one can see in Figure 17.17, the critical concentration (at which E^^ = E^^) is larger in p-type materials (~ 10^^10^^ cm~^) than in n-type materials (~ 10^^ cm~^) which is mainly due to the larger ionization energies for p-type dopants. Within the effective mass approximation the ionization energy is proportional to the effective mass. From Tables 17.9-17.12 it is obvious that the effective hole masses are normally larger than the effective electron mass. This is true especially for semiconductors with direct bandgap (i.e. having the conductionband minimum at the T-point like most of the III-N) which normally implies small effective electron masses. One can thus partly explain the larger critical concentration in
5/c afZ(i ///-A^ Heavily Doped (a)
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(c)
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M ^tot
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^tot
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100 150 200
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NM ^tot
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0
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^Q2:
Acceptor concentration [cm"-^]
Donor concentration [cm~'^]
E
-,019
-,019
Donor concentration [cnn~^]
-,020
-,017
-,019
i_
-,021
Acceptor concentration [cm~^]
Figure 17.17. The total energies per particle of the metallic E^^ (solid line) and in the non-metallic Ef^ (dashed line) phases in n- and p-type cubic and hexagonal GaN as functions of dopant concentration.
p-type materials by the fact that the effective hole masses are normally much larger than the effective electron mass. The calculated critical concentrations for MNM transition in various n-type and ptype zb- and wz-III-Ns as are presented in Table 17.13. There are two model calculations for the ionization energies of n-type wz- and zb-GaN [267,268] and many discussions about their values obtained experimentally [215,264-276]. The values obtained for Si, O, and C levels lead to E^^ < EQ < EQ. Moreover, Moore et al. [268] have recently claimed to find an unidentified (ui) donor level, E^:^ in wz-GaN which
536
Optoelectronic Devices: Ill-Nitrides
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Sic and III-N Heavily Doped
537
leads to ^si < ^ui < ^ o or 30.2 < 31.2 < 33.2 meV. We use in the calculation the values obtained experimentally, which are in the range of 25-34 meV [264-266,268]. Gotz et al. [270] have obtained from Hall measurements a metallic regime for n-type wz-GaN in a range of 7.0 X 10^^ < N^ < 2.0 X 10^^ cm~^. The nature of the involved shallow donor and acceptor in zb-GaN has not yet been identified clearly, but As et al. [264,273] have identified C and Mg as acceptors. The main reason for the high values of Nc (>10^^cm~^) in p-type GaN originates from the large acceptor ionization energies. From the table, one can notice that the extended Mott-Hubbard model gives slightly smaller A^^ that the Mott's original model for the materials considered here. Furthermore, the method based on the total energy results in even lower critical concentrations, except for n-type zb-GaN with ED(ui) = 32 meV. However, the three computational methods give similar values of Nc, even though two of the models are derived by using rather different approaches. The Mott-Hubbard model describes the actual MNM phase transition in terms of the intra-impurity Coulomb interaction and the hopping integral, whereas the total energy calculation describes the low-concentration and highconcentration phases. Although the Mott-Hubbard (and the original Mott) model and the total energy model have different approaches to describe the phase transition, the three computational methods give the same order of the critical concentration. The first two methods (i.e. Mott and Mott-Hubbard) do not depend on the structure of the material. The third method, based on total energies of the metallic and non-metallic phases, depends on the crystalline structure of the considered material (i.e. wz or zb) as was described in the text. In Table 17.13, we can see this difference for zb-GaN:Mg and wz-GaN:Si. In the Mott's model, the critical concentration is proportional to £'D,A- The same relation holds, with fairly good accuracy, also in the Mott-Hubbard model. For the total energy calculation, however, this is no longer true, especially not for large ionization energies. For sufficiently large ionization energy (estimated to be > 50-100 meV in n-type GaN), the total energies per particle in the metalHc E^^ and in the non-metallic Ef^ phases may not become equal at any concentration since the average kinetic energy of the free electron gas (in the single conduction band) is too high, which implies too large energy for a phase transition. That can be seen in Figure 17.17, where we show E^^ and Ef^ of n-type GaN. For high donor concentrations, E^^ is increasing drastically due to large kinetic energy of the electrons in the electron gas. The large kinetic energy is directly related to the small effective electron mass of the single conduction-band minimum. For p-type zb-, and wzGaN, as presented in Figure 17.17, the flat band structure the valence-band maximum (consisting of three valence bands) results in relatively low kinetic energies of the hole gas also at high hole concentrations. Hence, the phase transition in p-type GaN can occur at relatively high acceptor concentrations. However, the resulting critical concentrations for p-type GaN are high for Mg as acceptor in wz-GaN (with large ionization energies) and A^^
538
Optoelectronic Devices: Ill-Nitrides
is near the upper limit of solubility or the upper limit to the doping concentrations of interest in devices. The critical concentration for the MNM transition can also be obtained from measurements and calculations of the resistivity (Figure 17.18). For the zb-GaN the resistivity has been obtained by means of Hall-effect measurements as a function of temperature [21,79]. Due to the high residual acceptor concentration, the n-type character of the samples with concentrations lower than 10^^ cm~^ was not obtained. Thus, the region of concentrations where one would expect to find the MNM transition could not be measured. For n-type Si- and O-doped wz-GaN Leroux et al. [277] have done photoluminescence and Hall measurements and found Nc = l.QxXQi^^ cvcT^. The calculations of the resistivity have been performed using generalized Drude approximation (GDA) which has been applied for different n- and p-type materials, i.e. Si, GaN and GaAs [79,263,278,279]. The GDA is based on the dynamical conductivity and derived for the general case of a polar semiconductor by Semelius [280]. Both measured and calculated resistivity curves present similar behaviors, converging to a specific value of the impurty concentration for vanishing of the temperature dependent resistivity, which is determined to be the critical concentration for the MNM transition. The resistivity calculations [79] yielded Nc = l.^XlQ^^ and 1.90 X lO^^cm"^ for n-type Si-doped zb-GaN and zb-InN, respectively. Moreover, a total energy calculation (similar to model No. 3 in the present work) in Ref. [79], yields N^ = 3.7 X 10^\ 1.0 X 10^^ and 1.92 X 10^^ cm"^ for n-type Si-doped zb-AlN, zb-GaN and zb-InN, respectively, using the donor ionization energies i^oCSi) = 63.2, 34.8, and 94.5 meV, respectively (see Table 17.13).
10^ GDA theory wz - GaN : Si
10°
Bs 10^ >^ •
> 10-^ • > - *
%
^-> t/l 0)
i
10^
\ k
«
^ J^\
10-^ 1010'
T(K) 4 12 50 100 200 300
10^ Donor concentration [cm ^]
Figure 17.18. Calculated resistivity in wurtzite GaNiSi according to Ferreira da Silva et al. [263].
Sic and III-N Heavily Doped
539
17.6.2 Reduced and Optical Bandgap Energies In a lightly n-type doped semiconductor, low-temperature spectroscopic measurements exhibit a series of atomic like lines which correspond to the optical transitions of isolated impurity atoms. As the impurity concentration increases (but is still below the MNM concentration), donor cluster formations rapidly become important. As the clusters get more dense the absorption edge drops since one would expect that the donor clusters will absorb at low energies, below the ionization and transition levels of the isolated impurities [281-283]. This produces a low-energy Is —^ 2p± transition corresponding to the energy £•*. There are many discussions about the Is —»> 2p± transitions of shallow donor GaNiSi, GaN:0 and GaN:C [267-271], as described in the previous section. The first attempts to explain such low-energy peak in n-type GaAs as arising from donor-cluster transitions were carried out by Nagasaka and Narita [284], who adopted the Heitler-London approximation, and by Golka and Piela [285], who used a Hartree-Fock method [283]. Canuto and Ferreira da Silva [282] calculated the dielectric function of the triad molecule using the self-consistent field (SCF) model. However, these authors failed to explain the low-energy absorption peak. We have here pursued the investigation of ntype wz-GaN [286] along the lines of a donor-triad-cluster model, employing an ab initio multiconfigurational self-consistent field (MCSCF) approach to electronic structure determination. For computational details, see Ref. [286], where we also present consisting results for n-type GaAs. The ionization energy from the H3 transition corresponds to the energy required to promote one electron from the three-donor molecule to the bottom of the conduction band. Since a multi-determinant description of the wave function is imperative in order to break chemical bonds, the present MCSCF ionization potential [286] is significantly improved compared to the SCF for configurations with large interatomic distances. In Figure 17.19(a) we show the difference in ionization energy between calculated SCF and MCSCF for the triangular donor-cluster configuration. It is clear that MCSCF gives lower ionization in the relatively large interatomic distance compared to SCF, and thus the full MCSCF treatment of the electron correlation is needed for accurately describing the H3 -^ H3" transitions in the three-donor molecules with interatomic distance of about four times the effective Bohr radius. In the limit of very large interatomic distance the ionization energies for both SCF and MCSCF converge to the single hydrogen ionization energy, as expected. For lightly doped semiconductors, the effective Bohr radius a^ = ao/E'ls(0) is obtained from the experimental values of the ionization energy E* and the low-frequency dielectric constant: 8(0) = 10.0. The dielectric function is directly related to the absorption a(o)) = -Im((G(ct;,/?)))/7r, where ((G((w,/?))), means average disorder of the Green's function propagator [282]. For the ground state energies a((o)= {dRP(R)8(ho)-E^(R))
(17.36)
540
Optoelectronic Devices: Ill-Nitrides
where £f = ^^(Hg^) - £^(H3) is the ionization energy of the lowest state of the three-donor molecules and P{R) is the triad distribution function at separation R\ see Refs. [282,284]. The imaginary part 82(<^) of the dielectric function describes the optical response of the tri-donor cluster, and is obtained from n{(o) = n-\-
1
f ,
,a{(J)
—dco—^2 217 J (x)'"^ — 0)
S2i(o) ~ 2 Re[n((o)]lm[n((o)]
(17.37a) (17.37b)
The results for S2(h(o) in tri-donor cluster wz-GaN, which properly describes the positions of the absorption bands, are shown in Figure 17.19(b). In the inset of Figure 17.19(b), £(N1) = E;^(ls-2p±),E(N2) = £o(ls-2p±),and£(N3)= £*i(ls-2p±). From the GaN:Si, GaNrO, and GaN:C systems as well as in n-type GaAs, InP, and CdTe in Refs. [267-271], weobserve that the transitions are roughly related to £'(ls-2p+) ~ 0.16E* and E(X) « 0.79£'(ls-2p±), which yield E{X) « 0.6£*. For recent experimental data
(a)
"I—'—I—'—I—'—I—'—I—'—I—'—I—'—I—'—r
1.05k
0.90 k P(R)—, 0.75
S
0.60
LU
< 0.45 k
0.30
0.15h
Figure 17.19. (a) Difference AE = E^Q^ ~ ^MCSCF ^^ ionization energies as a function of interatomic distance R. P(R) is the distribution function of the three-donor molecule, (b) Imaginary part of the dielectric function for three-donor clusters in n-type wz-GaN. The inset shows the relative absorption given by Moore et al. [268],
Sic and III-N Heavily Doped
541
T
(b)
wz-GaN 1.0
0.8 18 20 22 24 26 28 30 Energy (meV)
0.6 13
MCSCF GaN:Si^
MCSCF unidentified MCSCF GaN:0 experimental
0.4
0.2
0.0 17.0
17.5
18.0
18.5
19.0
19.5
20.0
Figure 17.19 Continued.
[286], we show in Figure 17.19(b), the full curve of the expected lineX, and compare it to the corresponding calculated line for different ionization energies that correspond to GaN:Si, GaN:N3, and GaNiO. The calculated MCSCF peak energy EiX) = 19.3 meV for the transition derived from the ionization energy of oxygen in GaN [268] is in excellent agreement with the experimental finding of ~19.2meV. Moreover, the transition at 16.7 meV recently found by Moore et al. [287] is identified here as E(X) for GaN:Si with E ^ i ^ 30.18 meV. We thus find that it is crucial to take into account the all-electron correlation (as in the MCSCF) in the optical absorption calculation of donor clusters in moderately doped semiconductors. Including the full correlation we identify the observed low energy peaks in GaNiO and GaN: Si as electronic transitions of triad clusters, and we predict a transition energy of 18.3 meV of the unidentified donor in n-type wz-GaN. The investigation above of the donor-triad-cluster was performed for donor concentrations below the critical concentration for the MNM transition. Now, we will discuss the effect of heavily doping above the critical concentration. Above this critical
542
Optoelectronic Devices: Ill-Nitrides
MNM concentration the impurities are fully ionized even at zero absolute temperature. Thus, for high impurity concentration it is not expected to see transitions arising from localized donor-cluster states, instead one expects to see physical properties arising from delocalized screening electrons. The concentration for the doping-induced Mott MNM transition has been estimated to be in the order of ~ 10^^ cm~^ in n-type III-Ns and in the order of ~ 10^^-10^^ cm~^ in p-type III-Ns. The ionized donors (in the case of ntype materials) or acceptors (in the case of p-type materials) and the associated electron gas (for n-type materials) or hole gas (for p-type materials) introduce additional screening and interactions into the crystal. This affects the electronic band structure and the optical properties of the materials [73-77,262,263]. Thus, in order to design semiconductor devices properly, the effects on the semiconductor properties due to doping have to be understood. In this section, we present the calculated [77,262,263] doping-induced BGN of n- and p-type AIN and GaN. We consider both zb and wz structures. The theoretical method to calculate the single-particle self-energy Re[/iX7( k, ^(k))], and the resulting energy shifts of the fundamental (reduced) and optical (opt) bandgaps, is described in Section 17.4.2. The doping-induced energy shift ^E^ of the conduction-band minimum and the energy shift AE^i of the valence-band maximum have been calculated with in the RPA + Hubbard approach according to Section 17.4.2, using the fully relativistic FPLAPW electronic structure of the unperturbed intrinsic materials. For both n- and p-type materials the doping-induced reduced E^ and optical E^^^ bandgap energies in materials with direct bandgaps are obtained as £g = 4 + ^^g = 4 + ^^ci - A^vi
(17.38a)
£|P^ = £g + A£BM = £^ + A£,i - A£,i + A£BM
(17.38b)
where the Burstein-Moss (BM) shift for direct bandgap materials is A£BM = [^ciCkp) - ^ci(O)] + [£vi(0) - £:/kF)]
(17.39)
where 7 = Vj, V2, V3, and ^^^(kp) = Ep. This Burstein-Moss term takes into account the curvature of both the conduction and the valence bands for direct (q = 0) transition (see Figure 17.8 and the inset in Figure 17.20(a)). The Burstein-Moss term can for indirect bandgap materials (like the SiC polytypes) be considered to be the Fermi energy A^BM ~ ^F ~ ^c\^m) for n-type materials and A^BM ~ £'F ~ ^vi(O) foi* P-type materials since the transition between the valence-band maximum to the conduction-band minimum are assumed to be mainly phonon assisted indirect transitions in these materials. The probability for vertical transitions in indirect materials is, therefore, small. However, for direct semiconductors, the optical bandgap is defined as the energy of zero-phononinduced transitions, and the curvatures of both the valence band and the conduction band
Sic and III-N Heavily Doped (b) 6.4
(a) 5.2
^0i7
10^^
10^9
10^0
10^^
(c) O.H 3.4
o.o
zb-GaN
D°
n
3.2
\^
0 v2A v2Z v1A
2.8 -,017
v3A"
\
vv • \v1z\
Eg\ ^Q^8
>^Q^9
\
^o20
Ionized donor concentration [cm~^]
10^«
1020
10
wz-
s;i&5j>
•
:^^^j/3Z'
^ 3
543
3.4
>
^ ^ s n
''^""
0 0)
3.2
c LU
v2|\ v1|| \
3
Eg\
A^ \ •
10^^ 10^^ 10^9 10^0 Ionized donor concentration [cm"-^]
Figure 17.20. The energy of the reduced E^ and the k-dependent optical £^^^ bandgap energies (to the three valence bands Vi, V2 and V3) in n-type (a) zb-AlN, (b) zb-GaN, (c) wz-AlN, and (d) wz-GaN. "nv" stands for the non-vertical transition. The inset in (a) shows schematically the different transitions across the bandgap. The squares in (c) represent the photoluminescence measurements of n-type zb-GaN:Si by Fernandez et al. [791 and the circles and squares in (d) represent the photoluminescence measurements of n-type wz-GaN:Si by Yoshikawa et al. ([27].
has to be considered. One needs thus the full k-dependent energy dispersion of the energy bands in order to calculate the Burstein-Moss shift properly. In Figure 17.20 we show the doping-induced reduced and the optical bandgap energies in n-type zb-AIN, wz-AIN, zb-GaN, and wz-GaN as functions of ionized donor concentrations. The inset in Figure 17.20(a) shows the different transitions for the optical bandgap energy, where "nv" stands for the phonon-assisted non-vertical transition. The energy shift of the reduced bandgap is large, about 0.2-0.3 eV for a doping concentration of 10^^ cm~^. The energy of the optical transitions in n-type wz-GaN depends strongly on the k-vector of the recombining electron-hole pair. This is a result of the valence bands having different energy dispersions along the transverse and the longitudinal directions, which is reflected in the Burstein-Moss shift and thereby also in the optical bandgap energy. Figure 17.20 shows only transitions in the two principal symmetry directions
544
Optoelectronic Devices: Ill-Nitrides
(II and ± ), and thus a recombination in an arbitrary direction can have a recombination energy between the energy for the transverse and the longitudinal directions. The differences in both the reduced and the optical bandgap between zb-GaN and zb-AlN arise mainly from the conduction-band structure. zb-GaN has only one minimum, whereas zb-AIN has three equivalent minima and this affects the band filling. Furthermore, the effective electron masses are larger in zb-AIN than in zb-GaN (see Table 17.9). This makes the bandgap shift and the Burstein-Moss shift much smaller in zb-AIN. The differences in the optical bandgap energies between wz-GaN and wz-AlN arise from the different valence-band maxima of the two crystals. In contrast to wz-GaN, the uppermost valence band in wz-AIN is the crystal-field split-off band, with a band maximum more than 0.2 eV above the second and the third uppermost valence bands. Therefore, only the uppermost band is important for low electric field transport properties in wz-AlN. However, the shift of the reduced bandgap is quite comparable in the two wz crystals since this bandgap energy does not depend on the band filling. The circles and squares in Figure 17.20 are the low-energy and the high-energy cut-off photoluminescence results of Yoshikawa et al. [27], obtained from a 1-2.5 fxm Si-doped GaN layer on an undoped buffer GaN layer, using metal-organic chemical vapor deposition. It has been shown [262] that by using constant hole masses for describing the energy dispersion, the photoluminescence results cannot be fully explained. Yoshikawa et al. [27] interpreted their results as originating from the reduced bandgap and non-vertical transitions to the valence-band maximum, thus without conservation of momentum. There are two arguments against this interpretation. First, our calculated reduced bandgap is much smaller than the energy of the low-energy photoluminescence edge. For A^D = 1 X 10^^ cm~^, the calculated energy shift is about twice as large as the corresponding measured low-energy edge. Second, the phonon-induced non-vertical transitions are normally much less probable than the corresponding vertical transitions in direct bandgap semiconductors. However, with the full band structure calculation of the BGN, we can identify the photoluminescence results of Yoshikawa et al. as different vertical transitions to the three uppermost valence bands in different directions of the k-space. Our calculations in Ref. [262] suggest that the photoluminescence spectra of Yoshikawa et al. [27] describe zero-phonon-induced recombinations between electrons at the Fermi level and non-thermahzed holes in the different valence bands. The calculated optical bandgap energy of n-type zb-GaN (Figure 17.20(b)) is not in agreement with the low temperature photoluminescence measurements of Fernandez et al. [79]. At T = 2K the spectrum of the sample grown with the lowest Si-flux (8.5 X 10^ cm~^ s~^; T^i = 750°C) is dominated [79] by an excitonic transition and by a donor-acceptor pair transition. The measured optical bandgap energies are E^^^ = 3.290, 3.3208, and 3.343 eV for N^=lJxlO^\ 3.9 X 10^^ and 6.2 X 10^^ cm~^ respectively, which is close to the bandgap energy of intrinsic zb-GaN
Sic and III-N Heavily Doped
545
(£^ = 3.2 - 3.3 eV (Refs. [191,192]), whereas the calculations show E^^^ < £^. It is worth to mention that, whereas the photoluminescence measurements were made at 2 K, the carrier concentrations are measured at room temperature. This may cause a shift in the real concentration and even lead to a bandgap widening as recently observed for Si:P and Si:Bi [261]. Another possible explanation to this discrepancy could be that the Si-doped zb-GaN sample has p-type character instead of n-type character since p-type zb-GaN shows an increasing optical bandgap energy (see below) in contrast to n-type zb-GaN. Further theoretical and experimental investigations are necessary to establish the optical bandgap energy of zb-GaN. In Figure 17.21, we present the doping-induced reduced E^ and optical Ef^^^ bandgap energies in p-type zb-AlN, wz-AlN, zb-GaN, and wz-GaN as functions of ionized acceptor concentration Np,. The inset in Figure 17.21(a) shows schematically the different transitions. The optical bandgap is obtained as the zero-phonon-induced recombinations, except in the case of zb-AIN where the indirect recombinations are assumed to
(a) 5.2
zb-AIN
5.1
>
5
V
i 4.8 ^
A
LU
> ^
4.7
^^i v3'
4.5^ o.o
Z
7/r y
4.6
yj)
/Eg
1018
10^
Zb-GaN
3.5
/
3.4 ^
1020
3.3
na
•
>* P 3.2
v2X
y.2.y
P^^VlAD_^^
ET^^"^^^^
c
LU 3.1
V3A/
v3i:
3 1017
^Q^8
10^9
1020
Ionized acceptor concentration [cm"-^]
10^^
10^^
10^9
1020
Ionized acceptor concentration [cm~^]
Figure 17.21. The energy of the reduced E^ and optical bandgap E^^^ energies in p-type type (a) zb-AIN, (b) zb-GaN, (c) wz-AIN, and (d) wz-GaN. The inset in (a) shows the different transition across the bandgap. The squares in (c) represent the photoluminescence measurements of p-type zb-GaN:C by Fernandez et al. [288].
546
Optoelectronic Devices: Ill-Nitrides
occur between the states at kp in the valence bands to the conduction-band minimum at the X-point (cf. Figure 17.13). The valence-band maximum is strongly k-dependent in both the zb and wz structures (cf. Figure 17.15). The effects on the optical bandgap energy due to this k-dependence can be seen in Figures 17.21(b) for p-type zb-GaN. The spherical approximation would result in the same transition energies in the .S-direction as in the 4-direction (i.e. vlX = v\A and vlX = v2A) since in this approximation the effective hole mass tensor is considered to be constant (i.e. spherical mass). The full band-structure calculations yield, however, completely different results for the two principal directions. Moreover, in the calculations of Ref. [263], spherical energy dispersion is used also for the hexagonal structures. That resulted in v^^ = vm and V21 = V2\\ whereas our full bandstructure calculation shows strong anisotropy. The details in E^ and E^^^ as functions of the ionized acceptor concentration can primarily be explained directly from the energy dispersion of the three uppermost valence bands (cf. Figures 17.15, 17.16 and 17.21), especially for the hexagonal crystals. For different hole concentrations, the number of populated valence bands differs. This will have a direct consequence on the polarizability of the hole gas, and thus also affects the self-energies. In wz-AlN the valence-band maximum consists of the single crystal-field split-off band (see Figure 17.16), and hence, neither the second nor the third uppermost valence band contribute to the hole-gas polarizability. Since there are no empty states in the second and third uppermost valence bands, we do not expect optical transitions from these bands. In wz-GaN, the optical recombinations between states in the conduction band and states in the uppermost valence band (in both the transverse and longitudinal directions) as well as states in the second uppermost valence band (in the longitudinal direction) result in large photon energies. Thus, the band-filling, which is directly related to the valence-band curvatures, has a strong effect on the reduced bandgap energy in ptype materials, and on the optical bandgap energy in both n- and p-type materials, except in the case of wz-AIN which has a parabolic single-band valence-band maximum. The very flat curvature (i.e. the large density-of-states) of the uppermost valence band in zbAIN results in a very low Fermi energy, and thus the optical bandgap (here, the nonvertical transitions) is close to the reduced bandgap. In zb-GaN, it is the uppermost valence band in the X— direction that yields the largest shift of the optical bandgap. The square marks in Figure 17.21(b) show the measured photoluminescence excitation bandgap energies of C-doped zb-GaN by Fernandez et al. [288]. There is a good agreement between the measured and the calculated optical bandgap energy. Gorczyca et al. [289] have calculated formation energies and binding energies of several native and extrinsic dopants in zb GaN and AIN using a Green's function method based on LDA linear-muffin-tin-orbitals. They found that CN and Mgca in zb-GaN are very shallow acceptors. X-ray A'-edge absorption measurements by Lawniczak-Jablonska [184] of Mg and Zn dopants in GaN reveal that Mgca and Zuca defects are formed in the bandgap region but not as a sharp defect level.
Sic and III-N Heavily Doped
547
By comparing Figures 17.20 and 17.21, one notices that the shift of the reduced bandgap is much smaller in p-type doped GaN and AIN (for both zb and wz structures) than in corresponding n-type doped materials. Materials with large number of populated valence bands and/or large effective hole masses results in small bandgap shifts. Moreover, the non-parabolicity of the valence bands normally reduces the energy shift [262]. We have seen this effect also in p-type Si, p-type SiC, and p-type GaAs [6,156,157], where better agreement between calculations and measurements was obtained with a full description of the valence bands as in the FPLAPW approach. Like in the case of n-type doping, the differences in the optical bandgap energy between GaN and AIN (for both zb and wz structures) arise mainly from the different valence-band curvature of the crystals. Both zbAIN and wz-AlN have very large effective hole masses, and that give small dopinginduced BGN. Now, since we also have band filling of the valence bands (which yields a screening caused by the hole gas), the differences between AIN and GaN are more pronounced for p-type doping than for corresponding n-type doping. The spin-orbit interaction affects the energy dispersion of the uppermost valence bands, and we have shown [5,6,262] that the non-parabolicity of the bands has a strong impact on the resulting self-energies, especially for p-type doping (see Section 17.4.2). We thus conclude that a fully relativistic treatment of the energy bands is crucial for calculating the BGN of p-type semiconductors. This is true for most semiconductors, even the light materials. One exception is wz-AIN in which the uppermost valence band is the crystal-field split-off band. Here, the curvature of this uppermost valence band is not affected by the spin-orbit interaction (see Figure 17.16), and moreover, the band filling will only be in the single uppermost band since A^f ~ 0.2 eV. Strain has an important role in the growth of the nitrides. Strain is also technologically interesting since it can suppress Auger recombinations. In the present work, we have investigated the BGN of unstrained materials only. In the photoluminescence measurements on wz-GaN of Yoshikawa et al. [27] the effect on the bandgap due to strain is estimated to be smaller than 7 meV. In the calculations of the optical bandgap energy, we assumed that the band curvatures, for describing the band filling, are not modified by the doping. This approximation is consistent with the performed perturbation approach. However, it has been shown [77] that for very high impurity concentration there will be a band tailing in GaN and AIN, mainly due to the polaron coupling. This band distortion affects the band filling and will, therefore, increase the optical bandgap energy slightly. From Ref. [77], we can estimate this effect in n-type GaN to be less than 8 and 25 meV for A^D = 1.0 X 10^^ cm"^ and 1.0 X 10^^ cm~^, respectively. However, the band tailing effect will change the curvature of the bands, and thus the effective masses will be affected. For polar materials, the energy band will become very non-parabolic. We have studied these effects in SiC, AIN, and GaN materials in Refs. [5,77]. We show that although the effective electron masses
548
Optoelectronic Devices: Ill-Nitrides
at the conduction-band minimum are reduced in those materials, the effective electron masses at the Fermi energy is almost unaffected. The method of calculating the bandgap shifts was based on a zero-temperature formalism and the results are in a strict sense valid only for impurity concentration above the concentration for the MNM transition, which is about N^ — (3.3-7.1) X 10^^, (1.01.2) X 10^^ and (1.9-2.4) X 10^^ cm~^ for n-type zb-AlN:Si, zb-GaN:Si and zb-InN:Si, respectively. However, it is believed that the zero-temperature calculations presented here can, with reasonable accuracy, be applied also for finite temperatures for doping concentrations below the Mott transition where the impurities are partly or fully ionized thermally.
17.7. SUMMARY To summarize, we have reviewed the latest calculations of the electronic properties of intrinsic and heavily doped 3C-, n H-SiC (n = 2,4,6) and zb-, wz-III-N (III = B, Al, Ga, In). We present the first-principles, fully relativistic FPLAPW calculation of the electronic band structure, the effective electron and hole masses, and the dielectric constants for intrinsic materials masses [67-69,77,90,102,107,121,122,127,128,134,230], which is important for the understanding of the electronic transport properties in these semiconductors. Special attention has been paid on the non-parabolicities of the energy bands near the band edges. The LDA bandgap error was corrected by a quasi-particle energy shift which has an effect on the high-frequency dielectric constant s(oo). The static dielectric constant 8(0) was calculated assuming a constant optical phonon frequency dispersion. The anisotropy of the dielectric function is small in wz SiC and III-N. The effective electron and hole masses were presented both as the bare effective masses and by including the polaron interaction. We show that it is crucial to taking into account the spin-orbit interaction for determining the effective hole masses even in light semiconductor materials [67-69,107,230]. The effective hole masses can change by more than 10 times due to the split of degeneration caused by the spin-orbit interaction. Moreover, the valence-band maximum in zb-AlN is located along the (110) direction away from the T-point in a scalar relativistic calculation (i.e. neglecting the spin-orbit interaction), whereas in the fully relativistic calculation [107] (i.e. including the spinorbit interaction) the maximum is located at the T-point. Furthermore, we have calculated the impact on the electronic properties due to heavily n- and p-type doping. The critical concentration for the doping-induced MNM transition in both 3C-, nH-SiC, and zb-, wz-III-N, as well as the doping-induced BGN are calculated by means of a many-particle Green's function perturbation method, using the FPLAPW electronic structure of the intrinsic semiconductors. The MNM critical concentration depends on the ionization energy (N^ «= E\jy in the Mott original model), and it is in
Sic and III-N Heavily Doped
549
the order of ~(0.3-2)X 10^^ cm"^ in n-type SiC, ~ 1 X 10^^ cm~^ in n-type III-N ( ~ 2 X 10^^cm~^inInN:Si), > 1 X lO^^cm"^ inp-typeSiC, and ~(0.3-2) X lO^^cm"^ in p-type III-N [5,78-80]. The reduced bandgap energy in n-type material is narrowed in the order of ~0.2eV in SiC [5,6], AIN, and GaN [262,263] for an ionized donor concentration of 10^^ cm~^. For corresponding p-type material the narrowing is in the order of ~ 0.1 eV for the same ionized acceptor concentration. We show that it is crucial to include a full description of the valence-band structure (i.e. to go beyond the parabolic approximation) and to include the spin-orbit interaction for accurately determining the BGN of heavily p-type materials. The optical bandgap energy in n-type GaN is roughly equal to the fundamental bandgap energy in the intrisic limit, since the BGN is cancelled out by the band filling. In moderately to heavily doped GaN and GaAs (i.e. below the MNM critical concentration) the absorption measurements reveal peaks below the transition energy of the single isolated dopant. We have shown [286] that only with a full treatment of electron correlation within the MCSCF model, these peaks can theoretically be attributed to the formations of three-donor cluster. We found that the ionization energy of the three-donor cluster is ~ 0.6E*, where E^ is the ionization energy of the shallow donor in the dilute limit.
ACKNOWLEDGEMENTS
This work was supported by the Swedish Research Council (VR) and the Brazilian National Research Council (CNPq). We acknowledge the discussion/collaboration with Ulf Lindefelt, Nguyen Tien Son, Bo E. Semelius, Hans Arwin, Kenneth Jarrendahl, O.P. Alexander Lindquist (Linkoping University), Rajeev Ahuja and Borje Johansson (Uppsala University). We also appreciate the valuable input from Niels E. Christensen (Arhus University), Walter R.L. Lambrecht (Case Western Reserve University, Cleveland), Friedhelm Bechstedt (Friedrich-Schiller University, Jena), Donat As (Paderbom Universiy), and Joachim Wagner (Fraunhofer Institute for Applied SolidState Physics, Freiburg).
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Index ab initio energy calculations 457, 462 absorbance 270-1 absorption coefficients 145-6 doping induced bandgap narrowing 539-40 ferromagnetism 399-400 GaN substrates 198-9 phonon transmittance 446-7 acceptor ionization energy 168-9 acoustic properties 172-3 activation energy 162-5, 220-1, 236-7 active layers 372-3 adduct formation 60 AIXTRON group 39 AlGaInN alloys 23-4, 222-3, 474-5 AlGaN 69-93 alternating gas flow growth 306-10 conductivity control 160-9 deep UV emitters 285-320 doping 219-22 ferromagnetism 389, 420-4 growth 218-19, 289-96, 306-10 impurity parameters 160-9 optical properties 289-96 ordering 469-74 p-i-n photodiodes 257-62, 267-8 phase separation 467-9 polarization 146-50 quantum dot growth 116-17, 121 quantum wells 28-30, 291-6 Schottky MSM detectors 255-6 threading dislocation 31-2 UV light-emitting diodes 5-6, 218-19, 222-4, 227, 289-96 UV photodetectors 252, 255-62, 267-8 AlInGaN alloys 23-4, 222-3, 474-5 see also quaternary InAlGaN all-electron correlation 541
AlMnN alloys 389, 413-20 AIN bandgap narrowing 533-48 buffers 216-17 electronic properties doped semiconductors 479-81, 518-49 homoepitaxial films 204-5 substrates 195, 199-203 epitaxial layers aluminum vacancy complexes 156-60 conductivity control 160-9 exciton recombination 150-6 field emission devices 173-5 impurity parameters 160-9 optical properties 140-60 polarization 146-50 surface acoustic waves 172-3 templates 169-72 ultraviolet photonics 133-77 vacancy complexes 156-60 ferromagnetism 387, 389, 413-20 homoepitaxial films 204-5 optical properties 140-60, 195, 199-203 phonon frequencies 436 quantum dots 100-3, 107-10, 114-15 quantum wells 292-6 self-assembled quantum dots 108-10 substrates electronic properties 195, 199-203 growth 190-1 optical properties 195, 199-203 structural properties 192-4 UV hght-emitting diodes 216-17 UV photodetectors 252 alternating gas flow growth 306-10 aluminium incorporation in MOCVD growth 69, 78-9 aluminum vacancy complexes 156-60 angular variation, frequency 438-43 561
562 anti-surfactants 96, 98-9, 115-21 areal density 4, 213 as-grown AIN epitaxial layers 157-60 ASA see atomic sphere approximation astronomy 14-15 atomic distances 217 atomic sphere approximation (ASA) 480 Auger recombination 329 avalanche breakdown 324, 329 avalanche photodiodes 262-3 averaged Hubbard local-field correction 503-4 back-emission AlGaN 227 back-illuminated p-i-n photodiodes AlGaN 260-2 characterization 269-73 growth 268-73 measurements 268, 274-6 processing 268, 273-4 BAIN phase separation 465-7 band filling III-N 547 band structure doped semiconductors 482, 485-501, 519-24 wurtzite AIN 140-6 bandgap energy 482-3 bandgap narrowing 511-17, 539-48 GaN NDRs 352-3, 365 InN semiconductors 518-19 introduction 2 - 3 , 9-11, 16-18 quantum dot growth 98 rise of Ill-nitrides 9-11, 16-18 SiC doped semiconductors 490-2 UV LEDs 216 bandgap narrowing (BGN) 501-17, 539-48 bandgap renormalization 155 bandgap temperature dependence 324-5 bare effective electron masses 527-8 barriers 291-2, 294, 407-8, 410-12 BGaN phase separation 465-7 BGN see bandgap narrowing biasing voltage 371
Index binding energy 162-3 biochemical hazards 6-7 biological agent detection 5-6, 15, 214 blue light-emitting devices 24-36 BM see Burstein-Moss BMP see bound magnetic polarons BN doped semiconductors 479-80, 518-49 bound magnetic polarons (BMP) 390-2 bowing parameters 146-7 Brag spot intensity 100-2 Bragg reflection 373-4 Braggs peaks 464, 472-4 breakdown voltages 337-8 Brillouin zones 492-3 buffer thickness 291-2 bulk AIN 190-1, 199-203 bulk diode arrays 346-9 bulk GaAlN 69-93 bulk GaN 69-93, 187-90, 195-9 Burstein-Moss (BM) shift 542-4 C-V see capacitance-voltage cameras 278-9 capacitance-voltage characteristics 89-90, 402-3,407-13,425-7 capacitive transimpedance input amplifiers (CTIA) 276-7 carrier concentration 9-10, 72-3, 79-82, 96-7, 326 carrier density 79-82, 86-7, 96-7 carrier gas composition 57 cathodoluminescence (CL) 200-3, 298, 300 cation-J states 523 CCS see close-coupled showerhead CD/DVD systems 3-4, 14 CDF see computational fluid dynamics CE see cluster expansion chalcopyrites 388-9 characterization p-i-n photodiodes 269-73 quaternary InAlGaN UV LEDs 296-306 UV LEDs 227-35 UV photonic AIN epitaxial layers 135-40
Index charge inhomogeneity 353-5 chemical bonding 9-11 chemical kinetics 59-60 chemical potential 118-19 chemical stability 10 CL see cathodoluminescence close-coupled showerhead (CCS) reactors 47-57 cluster expansion (CE) 455, 457, 459-60, 475-6 clustering in ferromagnetism 390-2 Co implantation AlGaN ferromagnetism 420-2 AIN epitaxial layers 157-60 AIN ferromagnetism 416-20 (GaMn)N ferromagnetism 401-2, 404-6 coalescence 52-3, 101, 103 conmiunications 6-7, 14-15, 214-15, 251 composition phase diagrams 466-9 composition uniformity 57 computational fluid dynamics (CFD) 62 computational modelling 57-62 concentration dependent mobility model 327 conduction bands 488-90, 495-6, 513-17, 522-3 conductivity control 160-9 continuum mechanical models 61-2 correlation energy 505 covert conmiunications 6-7, 14-15, 214-15, 251 Cr implantation 157-60, 416-20, 422 crack-free surfaces 24, 26-7, 188, 218-19 critical concentration bandgap narrowing 502-3, 510-11, 534-7, 542 GaNNDRs 353, 361-2 critical electric fields 331 critical temperatures 472-4 critical voltages 365-7 crystal growth 24-7, 30-5 crystal-field splitting 142-3, 148, 522 crystalline structures 483-5 crystallographic structures 9-10
563 CTIA see capacitive transimpedance input amplifiers Curie temperatures 8, 388-94 current crowding 234-46 current density 239, 341-4, 407-8, 410-11 current gain 74-5 current spreading lengths 239-41 current-light (I-L) curves 317-18 current-voltage characteristics (I-V) GaN MESFETs 74-5 GaN NDRs 365-7, 371, 374-5, 383 high power rectifiers 342-4, 347-9 p-i-n photodiodes 274-5 quaternary InAlGaN UV LEDs 317-18 UV Hght-emitting diodes 229-32, 242-3, 317-18 dark current 266 DC power 369-70 decay processes 151-6, 444-6 deep UV emitters 171, 242-6, 285-320 deep UV laser spectroscopy 137-8 defect-free quantum dot growth 96-7 defects 346-7 degree of polarization 147-8 density control 122-4 density functional theory (DFT) 462, 481, 528 density of states 95-6, 325-6 depleted region thickness 403 design, high power rectifiers 336-41 detectivity 263-4, 267-8 development overviews 11-15, 253-63, 277-9 device simulations 362-73 DFT see density functional theory diamond heterojunctions 171-2 dielectric constants 3, 492-4, 523-4 dielectric continuum 437-9, 443-4 dielectric function 492-4, 503, 539-40 dielectric material 336-9 differential dielectric relaxation times 360 differential mobility 352, 355 diffuse scattering 464
564
Index
digital cameras 278-9 dilute magnetic semiconductors (DMS) 8, 389-429 dipole domains 354-5, 368-9 dipole transitions \A1-A direct bandgap energy 2 - 3 , 23-4, 285-6, 490-1 dislocations 237, 408-9 see also threading... DLTS spectra 403-5 DMS see dilute magnetic semiconductors donor activation energy 162-5 donor-triad clusters 540-2 doping AlGaN layers 219-22 bandgap narrowing 501-17, 533-48 concentration 354, 358-62 exciton recombination 154-6 heteroepitaxial films 185-6, 188-9, 196-7 induced bandgap narrowing 501-17,533-48 p-i-n photodiodes 272-3 double heterostructures 215-16 drain currents 70, 90 drift velocity 360 edge termination design 336-46 edge-emitting laser diodes 149 effective Bohr radius III-N 539 effective density of states 325-6 effective lattice constants 16-18 effective mass 3, 10, 481-2,494-501, 524-35 efficiency power 74, 76, 84-5, 369-73 UV light-emitting diodes 32-3 wall-plug 242 see also external quantum... EL see electroluminescence electric field dynamics 323, 367-71 electric field vectors 435 electric vehicles 323, 335-6 electrical characteristics HEMT devices 78-82 homoepitaxial films 203-5
electroabsorption 375-6 electroluminescence (EL) 242-3, 313-14, 317-18,427-8 electronic device structure growth 45-7, 56-7 electronic properties 479-549 AIN 195, 199-203, 479-81, 518-49 BN 479, 518-49 GaN 194-9,479,518-49 homoepitaxial films 204-5 InN 479, 518-49 SiC 485-518 substrates 194-203 electrons concentration 196, 368-71 drift 360, 409 effective mass 3, 10, 481-2, 494-501, 524-33 electron-hole pairs 329 electron-phonon interactions 433-50, 493-4, 503-7, 523-4 gas structures 56-7 mobility 86-7, 352, 356-8, 363-6, 407-13 saturation 23-4 transit time 356-7 traps 403-6 velocity 376 emissivity 63-6 energy activation 162-5, 220-1, 236-7 bandgap narrowing 501-4, 508-17, 525-7, 533-5, 539-48 dispersion 525-7 ionization 168-9 magnesium acceptors 167-8 phase separation/ordering 457, 462, 464 relaxation time 364-5 shifts513-17, 533-4, 542-8 ternary alloy ordering 469-74 see also bandgap energy epilayer structure 74, 139, 145-6 epitaxial growth 11-13, 17-18, 135-40 epitaxial layers 133-77 EQE see external quantum efficiency
565
Index equivalent noise voltage spectral density 76-7 evolution of nitride semiconductors 23-36 crystal growth 24-7, 30-5 research 25-6, 28-30 threading dislocation density 24-5, 30-5 UV light-emitting diodes 25, 32-5 evolution timelines 213-14 exchange energy 505 excitation energy 461 exciton recombination dynamics 150-6 excitonic emission lines 196-7 extended Mott model 501, 508-9, 537 external quantum efficiency (EQE) AIN epitaxial layers 170-1 blue light-emitting devices 27-8 deep UV LEDs 245-6 evolution of nitride semiconductors 27-8, 32-3, 35 quaternary InAlGaN UV LEDs 287, 314, 318-19 UV light-emitting diodes 234-5 fabrication AIN ferromagnetism 414, 416 GaN MESFETs 74 GaN NDRs 378-82 Fermi distribution function 492-3 ferromagnetism 387-429 AIN 387, 389, 413-20 device applications 424-8 GaN 387, 389, 392-413 mechanisms 390-2 MnN 387, 389, 392-413 FIB see focused ion-beams field dependent mobility model 327 field effect transistors (FETs) 24 field emission devices 173-5 field loops 395-8 field plate termination 336-9 figures of merit 15-16 flame detection 15 flicker noise 264-5, 267-8 flip-chip bonded devices 232-3
floating field rings 342-3 fluid flow dynamics 58-9, 61 focal plane arrays (FPA) 276-9 focused ion-beams (FIB) 123-4 forced convection 58 forward bias 342-4 forward current 34-5 Fourier transforms 462, 464 FPA see focal plane arrays FPLAPW481, 497-8, 529 frequency efficiency 369-73 phonons 435-6, 438-43 surface acoustic waves 172-3 Frohlich interactions 448-9 full width at half maxima (FSVHM) 73-7, 148 full-potential linearized augmented plane waves (FPLAPW) 481, 497-8, 529 Fulop's form 330 furnace monitoring 15 FWHM 73-7, 148 FX transition lines 141-2 Ga vacancies 157 GaAlN alloys 69-93 HEMT devices 71, 78-93 see also AlGaN GaAs alloys 361, 365 GaN absorption coefficients 145-6 anti-surfactant growth 115-20 bandgap narrowing 533-48 doped semiconductors 479-81, 518-49 electronic properties 203-4, 479-81, 518-49 epilayers 139, 145-6 ferromagnetism 387, 389, 392-413 growth optimization 69-93 HEMT structures 71-93 high power rectifiers 323-49 bulk diode arrays 346-9 design 336-41
566 edge termination design 336-41 high breakdown lateral diodes 342-6 homoepitaxial films 203-4 LP-MOCVD growth optimization 69-93 MESFETs 71-93 negative differential resistance (NDR) components device approaches 373-8 device simulation 362-73 fabrication 378-82 operating principles 352-5 superlattices 373-8 terahertz operation 351-85 testing 382-4 transport properties 355-62 nucleation layers 87-8 p-i-n photodiodes 259-62, 265-7 power Schottky diodes 323-49 quantum dots 115-20 quantum wells 28-30, 53-6, 294-5 Schottky MSM detectors 255-7 self-assembled quantum dots 100-15 substrates electronic properties 194-9 growth 187-90 optical properties 194-9 quaternary InAlGaN UV LEDs 314-19 structural properties 192-4 UV LEDs 225-6 template growth 51-3 threading dislocation density 30-1 UV Ught-emitting diodes 222-3 gas flow 57, 306-10 Gas Foil Rotation (GFR) 41, 44 gas phase transport phenomena 58-60 gate widths 92 generalized quasi-chemical approach (GQCA) 455, 457-8, 464 generation rates 328-9 GF^ see Gas Foil Rotation GQCA see generalized quasi-chemical approach Grashof numbers 58
Index Green's function 503 ground state energy 469-72, 539-40 growth AlGaN 289-96, 306-10 AIN epitaxial layers 135-40 AIN ferromagnetism 414, 416 close-coupled showerhead reactors 51-7 GaN ferromagnetism 392-4 GaN NDRs 353 MOVPE 39-67, 296-7, 305-6 p-i-n photodiodes 268-73 planetary reactors 44-7 quantum dots 95-129 quaternary InAlGaN UV LEDs 296-306 temperatures 57 ternary alloy ordering 469 UV LEDs 216-22, 227-35, 289-306 guard rings 339-46 Gunn effect 352 GW approximation 487-8, 522, 528 Hall carrier concentration 72-3, 79-82 Hall effect measurements 161-2, 164-5, 228-9, 307-9 Hall mobility 79-82, 86-7 Hamiltonians 441, 445, 458-60, 501 Hartree-Fock exchange energy 505 heat capacity 10 heat transfer 58-9, 61 heavily doped semiconductors bandgap narrowing 501-17, 539-48 electronic properties 479-549 Helmholtz free energy 457-8 HEMTs see high electron mobility transistors heteroepitaxial films 185-6, 188-9, 196-7 heterostructures 57, 69-93 high breakdown lateral diodes 342-6 high electron mobility transistors (HEMTs) 70-1 high frequency testing 383-4 high power rectifiers 323-49 high-aluminum content p-type AlGaN 306-10
Index high-density memory 286-7 high-performance UV Hght-emitting diodes 25, 287-320 high-power electronic devices 15 high-power, high-frequency power transistors 4-5 GaAlN HEMT devices 78-93 GaNMESFETs 71-93 MOCVD growth 69-93 high-pressure solution (HPS) technique 187-90, 193, 195-6, 203 historical overviews 11-15 hole concentration 307-8 hole conductivity 307-8 hole effective mass 3, 10, 481-2, 494-501, 524-33 homoepitaxial films 203-5 Hooge's parameters 77 hopping energy 508 horizontal tube reactors 40-2 Hubbard local-field correction 503-4 HVPE see hydride vapor phase epitaxy hybrid electric vehicles 323, 335-6 hydrazine derivatives 60 hydride vapor phase epitaxy (HVPE) 188-90 hysteresis loops 395-8, 414-16 I-L see current-light I-V see current-voltage ideaUty factor 230-2, 275 impact ionization coefficients 329-30 impurity atoms 327 impurity parameters 160-9 in situ MOVPE technologies 62-7 in-plane lattice parameters 23-4, 100-2 InAlGaN ultraviolet light-emitting diodes see quaternary... InAlN phase separation 467-9 incomplete ionization 327 indium 270, 467-9 inflection points 364 infrared (IR) absorption spectra 198-9
567
InGaN multiple-quantum wells 169-71 ordering 469-74 phase separation 467 - 9 quantum dots 104-6, 110-13, 119-23 quantum wells 53-6 self-assembled quantum dots 104-6, 115 UV hght-emitting diodes 222-3 injection currents 232-3, 244-5, 311-12 InN bandgap narrowing 533-48 electronic properties 479-80, 518-49 phonon frequencies 436 quantum dots 113 integrating in situ MOVPE technologies 65-6 interaction energy 469-74 interfacial atomic structure 216-17 intrinsic carrier concentration 9-10, 326 intrinsically doped semiconductors 479-549 ion implantation 401-2, 404-6, 416-20 ionization energy 162-5, 168-9 ionized donor concentration 509-11 IR see infrared Ising-like Hamiltonians 458-60 IBS see junction barrier controlled Schottky jetting 48-9 Johnson figure of merit (JEM) 15-16 Johnson noise 265 junction barrier controlled Schottky (JBS) rectifiers 343 junction terminations 339-41 k-space integrals 462 Keyes figure of merit (KFM) 15-16 kinetic energy 504 kinetics 59-60 Kramers-Kronif transformation 492-3 L-T see low-temperature-deposited laser diodes (LD) AIN epitaxial layers 149 development overviews 13-14
568
Index
evolution of nitride semiconductors 24 GaN quantum dots 119 introduction 3 lasers 111-12,447-8 lateral electron mobility 408-9 lattice constants 2 - 3 AIN ferromagnetism 414 evolution of nitride semiconductors 23-4 quantum dot growth 98 quaternary InAlGaN UV LEDs 285-6 rise of m-nitrides 9-10, 16-18 lattice mismatch 16-18, 70-1 lattice parameters Ill-nitride doped semiconductors 519-21, 523 rise of m-nitrides 9-10, 16-18 SiC doped semiconductors 486-8, 491-2 substrate structural properties 191-3 layer property measurements 62-3 layer thickness control 57 LD see laser diodes LDA see local density approximation leakage current density 412 LEDs see light-emitting diodes lifetimes 445-6 light-emitting diodes (LEDs) 3-8 AIN epitaxial layers 149-50 close-coupled showerhead reactors 53-6 development overviews 13-14 evolution of nitride semiconductors 24-5, 32-5 ferromagnetism 424-8 see also quaternary InAlGaN...; ultraviolet... line broadening, phonons 444-6 linear-muffin-tin-orbital method 480 LO see longitudinal optical load-pull measurements 70, 83-5, 93 local density approximation (LDA) AIN band structure 142 doped semiconductors 481, 487-8, 495, 500-1,520-4,528,533 phase separation/ordering 462 long-range order 464
longitudinal hole masses 500 longitudinal optical (LO) phonons 437, 438-44 Loudon's model 437-9, 443-4 low-dimensional wurtzite structures 443-4 low-dislocation-density devices 24-5, 30-5 low-temperature AIN buffers 216-17 low-temperature nucleation layers 13 low-temperature-deposited (L-T) buffer layers 26-7, 36 LP-MOCVD growth optimization 69-93 Luttinger parameters 529, 533 magnesium 165-9, 220-2, 306-8 magnetization ordering temperature 388-9 remanence 414-16 versus field loops 395-8 see also ferromagnetism mass transfer 58-9, 61-2 material parameters 360-1 material properties 78-82, 87-93 materials, spintronics 388-9 mathematical models 61-2 MBE see molecular beam epitaxy MC see Monte Carlo (MC) MCL spectra 402, 427-8 MCSCF see multiconfigurational self-consistent fields mean-field theory 390-2, 428 measurements Hall effect 161-2, 164-5, 228-9, 307-9 MOVPE 62-6 p-i-n photodiodes 268, 274-6 mechanical integration 65-6 mechanical strength 10 medical systems 7, 286-7 melting conditions 187 melting points 10, 17-18 memory 286-7 mesa geometries 241-2 MESFETs 69, 71-93 metal overlap effect 336-9
Index metal-non-metal (MNM) transitions 482, 501-2, 507-8, 510-11, 534-9 metal-organic chemical vapor deposition (MOCVD) high-power, high-frequency applications 69-93 quantum dot growth 108-15, 122-3, 125-6 quaternary InAlGaN UV LEDs 296 self-assembled quantum dots 108-15, 122-3 metal-organic vapor phase epitaxy (MOVPE) 39-67 computational modeUing 57-62 quaternary InAlGaN UV LEDs 296-7, 305-6 reactor types 40-57 in situ technologies 62-7 metal-semiconductor-metal (MSM) detectors 255-7 metallic droplet nitridation 126 microwave performance 83-4 microwave testing 383-4 miniband electrons 373-4 mixing free energy 465-6 Mn implantation AIN epitaxial layers 157-60 ferromagnetism 416-20, 422-4, 428-9 MNM see metal-non-metal MnN alloys 387, 389, 392-413 mobility models 327-8 MOCVD see metal-organic chemical vapor deposition modeUing MOVPE production 57-62 molecular beam epitaxy (MBE) ferromagnetism 392-4, 416 quantum dots 100-8, 126 momentum 495, 517 Monte Carlo (MC) method 376-8,455,461 - 4 , 472-4 Mott-Hubbard model 501, 508-9, 537 Mott's model 482, 501, 507-8, 537-8 MSM see metal-semiconductor-metal
569
multiconfigurational self-consistent fields (MCSCF) 539 multiple-quantum wells 169-71 n-type AlGaN 160-5 n-type doping 27, 219-20 negative differential resistance (NDR) 351-85 see also GaN NEP see noise equivalent power nitrogen vacancy complexes 156-60 NLOS see non-line-of-sight noise analysis 263-8 noise equivalent power (NEP) 263-4 noise power 264-7 noise voltage spectral density 76-7 nominally unintentional doped heteroepitaxial fihns 185-6, 188-9, 196-7 non-line-of-sight (NLOS) communication 214-15,251 non-punchthrough junction diodes 331-3 non-radiative centers 235-7 novel techniques in quantum dot growth 125-8 nucleation layers 87-90 ODCR see optical detection of cyclotron resonance on-state resistance 323-4, 333-6 on-wafer technology 379-82 operating pressures 57 operating voltages 34-5 optical bandgap energy 511-17, 539-48 optical detection of cyclotron resonance (ODCR) 490 optical emission uniformity 55-6 optical properties AlGaN 289-96 AIN 140-60 GaN 103-4, 119-21 homoepitaxial films 203-5 InGaN quantum dots 110-13 quantum dots 103-4, 119-21 SiC 485-501 substrates 194-203
570
Index
optical quality 53-6 optical transition selection rules 143-5 optical transmission 270-1, 400-2 ordering 455-76 Monte Carlo method 462, 464 ternary alloys 469-74 output power AIN epitaxial layers 170-1 HEMT devices 84-5, 91-3 UV light-emitting diodes 34-5, 233-4, 243-4 wavelength variation 34-5 p guard rings 342-3 p-i-n photodiodes 257-62, 265-7 p-n junctions AIN epitaxial layers 171-2 diodes2, 4, 27, 341-4 light emitting diodes 2, 4, 27 p-type AlGaN 220-2, 306-10 /7-type doping 220-2, 271-3 /7-type GaN 13, 24, 27 PA see photoacoustic PAE see power added efficiency paramagnetism 394 PAW see photoassisted wet phase separation ordering 455-76 quaternary alloys 455,456-7,461-3,474-5 ternary alloys 457-61, 464-9 phenylalanine 5-6 phonons 433-50 decay 444-6 dielectric continuum 437-9, 443-4 electric field vectors 435 laser applications 447-8 line broadening 444-6 Loudon's model 437-9, 443-4 polarization vectors 435 quantum dots 448-50 scattering 440-6 ternary alloys 439-40 transmittance 446-7
wave vectors 435, 445 wurtzite structures 434-7 photoacoustic (PA) spectroscopy 490, 492 photoassisted wet (PAW) etching 123-4 photoconductors 254-5 photodetectors 3-4, 14-15, 24, 263-8 photoluminescence AlGaN quantum wells 292-6 AIN epitaxial layers 137-42 bandgap narrowing 543-7 GaN 72-3, 196-7 InGaN 120-1 quantum dots 105-6, 109, 111-12, 120-1 UV Ught-emitting diodes 235-7,298, 300-6 photoresponse 272, 275-6 photothermal spectroscopy 481 photovoltaic effects 259 physical properties 3, 10-11, 17-18 HEMT structures 71-93 piezoelectric polarization 221-2 pinch-off voltages 70, 83, 89-90 planar junction terminations 339-41 plane with nearest match 16-18 planetary reactors 42-7 plasma induced bandgap narrowing in SiC 517 plastic relaxation 78 platinum Schottky diodes 410-13 point defect scattering 444-6 polar phonons 437, 439-40 polarization AlGaN alloys 146-50 AIN 143-4, 146-50 doped AlGaN layers 221-2 phonons 435 polarons 495-7, 499-501, 525-7, 531-3 pollutants 286-7 position control 122 potential energy 118 potential gradients 118-19 power added efficiency (PAE) 74, 76, 84-5 conditioning 323 density 84-5, 91-3
571
Index dissipation 381-2 efficiency 74, 76, 84-5, 369-73 gain 74-5 Schottky diodes 323-49 processing/7-/-n photodiodes 268, 273-4 processing UV light-emitting diodes 227-35 pyrometric wafer temperatures 64-6 quality 53-6, 136-7 quantum dots growth 95-129 anti-surfactants 96, 98-9, 115-21 MBE 105-6, 126 MOCVD 108-15, 122-3, 125-6 novel techniques 125-8 selective epitaxy 96, 99, 122-5 strain-induced quantum dots 99-115 Stranski-Krastanow growth mode 95-7 phonon interactions 448-50 quantum structures, evolution 28-30 quantum wells AlGaN 28-30, 291-6 AIN 292-6 close-coupled showerhead reactors 53-6 GaN 28-30, 53-6, 294-5 InGaN 53-6, 169-71 phonon interactions 447-50 quantum dot growth 95-6 quaternary InAlGaN UV LEDs 291-306 reciprocal space maps 53, 55 size effects 28-30 quantum wires 95-6 quasi-chemical theory 457-8 quasi-particle (QP) model 487-8, 491, 493-5, 519-25 quaternary alloys AlGaInN 474-5 phase separation/ordering 455-7, 461-3, 474-5 thermodynamics 474-5 quaternary InAlGaN ultraviolet Hght-emitting diodes 285-320 characterization 296-306
GaN substrates 314-19 growth 296-306 quantum wells 291-306 sapphire 312-14 silicon carbide 310-12 radiative decay lifetimes 153-6 Raman active phonons 435-6 Raman line widths 444-6 Raman scattering (RS) 193-4 random phase approximation (RPA) 482 Rayleigh numbers 58 Rayleigh-Schrodinger approximation 512 reaction rate constants 59-60 reactive ion etching (RIE) 111-12, 379 reactor types 40-57 readout integrated circuits (ROIC) 276-7 reciprocal space maps 53, 55 recombination dynamics 150-6, 328-9 reduced bandgap energy 511-17, 539-48 reference diodes 425-6 reflectivity 72-3, 446 refractive indices 10-11 relative dielectric function 446 relaxation bandgap narrowing 505 differential dielectric times 360 frequency 364-5 phonon interactions 449-50 plastic 78 time 360, 364-5 reproducibility 45, 46 research 25-6, 28-30, 39 residual electron concentration 27 resistance 229-30 resistivity AIN epitaxial layers 164 bandgap narrowing in III-N 538 ferromagnetism 398-9, 400, 403 UV Hght-emitting diodes 240-1 resonant tunneling diodes (RTD) 375 responsivity 259, 263, 267-8 reverse bias 341-2
572 reverse breakdown voltages 324, 329-33, 344-6 RF power efficiency 369-73 RF transmission 4 - 5 RF-microwave-millimeter wave devices 15 RIE see reactive ion etching ROIC see readout integrated circuits room temperature ferromagnetism 388-429 RPA see random phase approximation RS see Raman scattering sapphire AIN buffers 217 p-i-n photodiodes 261-2 physical parameters 3 quaternary InAlGaN UV LEDs 312-14 substrates 71-85, 217, 225-6 templates 169-71 UV LEDs 225-6 SAQDs see self-assembled quantum dots saturation current 407-8, 410-11 saturation magnetization 414-16 SAW see surface acoustic wave scattering bandgap narrowing in SiC 504-5 diffuse 464 dislocations 408-9 phonons 440-6 Raman 193-4 SiC doped semiconductors 489-90 SCF see self-consistent fields Schockley-Read-Hall (SRH) lifetimes 328-9 Schottky barrier photodiodes 257-8 Schottky diodes 323-49, 410-13 Schottky metal - semiconductor - metal detectors 255-7 screening 511-12 secure communications 6-7, 14-15, 214-15,251 selection rules 143-5 selective epitaxy 96, 99, 122-5 self-assembled quantum dots (SAQDs)
Index growth 97, 99 MBE growth 100-8 MOCVD 108-15 stacking 113-15 self-consistent fields (SCF) 539 self-energy 512-13 self-heating effects 234-46, 381-2 series resistance 229-31, 274-5 SET see density functional theory sheet carrier density 79-82, 86-7 sheet charge density 79-82 sheet resistance 79-83, 89-90 sheet resistivity 398-400, 403 short range order 464 short-wavelength devices 223-46 shot noise 265-6 Si-N bonds 117-19 SiC bandgap narrowing 501-18 electronic properties 479-81, 485-518 HEMT devices 86-93 high power rectifiers 323-6 power Schottky diodes 323 quaternary InAlGaN UV LEDs 301-2, 310-12 substrates 71, 86-93 signal-to-noise performance 263-4 silicon doping 154-6, 160-5, 174-5, 219-20 silicon oxide 337-8 single-electron Green's function 503 SK see Stranski-Krastanow software 62, 66-7 solar UV spectrum 251 solar-blind detectors 14-15, 257, 260-2, 268-76 solar-blind photodetectors 14-15 space charge inhomogeneity 353 specific on-state resistance 333-5 specular surfaces 24, 26-7 spherical average mass 498 spin distribution 462, 464 spin field effect transistors (Spin FET) 410 spin polarizers 8
Index spin transfer electronics 387-429 spin transistors 8 spin-orbit interactions 498, 500, 531-3 spintronics 387-429 spontaneous polarization 221-2 spot area 3-4 SQUID see superconducting quantum interference devices SRH see Schockley-Read-Hall stacking 110-15 stand-alone fabrication 379-80 strain 79, 547 strain-induced quantum dots 99-115 Stranski-Krastanow (SK) growth mode 95-7, 99-115 structural parameters 33-4 structural properties 191-4 structure, UV LEDs 215-22 substrates AIN 190-5, 199-203 electronic properties 194-203 GaN 187-90, 192-9, 225-6, 314-19 growth 187-91 optical properties 194-203 sapphire 71-85, 217, 225-6 SiC 71, 86-93 structural properties 191-4 surface preparation 88-9 thick-films 187-91, 195-203 superconducting quantum interference devices (SQUID) 392, 395 superlattices 373-8 surface acoustic wave (SAW) devices 172-3 surface morphology 139-40 surface passivation 128 surface pre-treatments 126-8 surface reaction mechanisms 59-60 surface temperature measurements 63-6 surface-optical phonons 448-9 temperature dependence exciton recombination 153-4 hall mobility 79-80, 86-7
573
high power rectifiers 324-5, 327, 345-6 hole concentration 308, 310 MOVPE 63-6 quaternary InAlGaN UV LEDs 304-6 reverse voltages 345-6 sheet resistance 80, 86-7 transport properties 358-60 temperature-composition phase diagrams 457-60, 466-9 templates 169-72 tensile strain 218-19 terahertz operation 351-85 termination techniques 342-6 ternary alloys Ising-like Hamiltonians 458-60 ordering 469-74 phase separation 457-61, 464-74 phonons 439-40 quasi-chemical theory 457-8 thermodynamics 472-4 testing 382-4 tetraethylsilane 98, 117-21 thermal buoyancy 48-9 thermal chemistry 39 thermal conductivity 3,17-18, 70-1 thermal cracking 60 thermal decomposition 60 thermal effects GaN NDRs 381-2 high-power, high-frequency devices 70 thermal expansion 70-1 coefficients 3, 10, 17-18 thermal properties 17-18, 172-3 thermal stability 70-1 thermochemical properties 60 thermodynamics 472-5 thick-films 187-91, 195-203 Thomas Swan showerhead 50 threading dislocations 24-5, 30-5 ferromagnetism 408-9 GaN NDRs 356, 358 quaternary InAlGaN UV LEDs 288, 296-7, 314-15
574
Index
threshold power 27-9 TO see transverse optical top-emission AlGaN 223-4 total energy bandgap narrowing 501-4, 509-11, 534-5 phase separation/ordering 457, 462, 464 Toyota Prius electric vehicles 335-6 transition temperatures 473 transition-metal-doped GaN 387-429 transmittance 446-7 transparency 270-1 transport GaAlN/GaN HEMT devices 79-82, 86-7 (GaMn)N ferromagnetism 395-413 GaN 355-62 gas phase phenomena 58-60 NDRs 355-62 transverse hole masses 500 transverse optical (TO) phonons 437-40 tri-donor clusters 540-2 trimethylindium 112-13, 126-8 turn-on delays 323 turn-on voltages 274-5, 323, 348 two-dimensional electron gas structures 56-7 ultra-dense non-volatile semiconductor memory 8 ultraviolet (UV) cameras 278-9 ultraviolet (UV) digital cameras 278-9 ultraviolet (UV) laser diodes 3 ultraviolet (UV) light emitters 213-46 growth 216-22 need for 213-15 ultraviolet (UV) light-emitting diodes AlGaN 222-3 AlGaN alloys 149-50 AlInGaN 222-3 AIN epitaxial layers 149-50 basic structure 215-22 evolution of nitride semiconductors 25, 32-5 GaN 222-3 GaN substrates 225-6
growth 216-22 InGaN 222-3 introduction 5-8 short-wavelength devices 223-46 see also quaternary InAlGaN... ultraviolet (UV) photoconductors 251-80 ultraviolet (UV) photodetectors 251-80 development overviews 14-15, 253-63 evolution of nitride semiconductors 24 noise analysis 263-8 photodetector parameters 263-8 ultraviolet (UV) photonic AIN epitaxial layers 133-77 characterization 135-40 conductivity control 160-9 device applications 169-75 epitaxial growth 135-40 impurity parameters 160-9 optical properties 140-60 templates 169-72 ultraviolet (UV) solar-blind photodetectors 4-7 ultraviolet (UV) transparency 270-1 unintentionally doped heteroepitaxial films 185-6, 188-9, 196-7 unit cells 434-5 up-scaling close-coupled showerhead reactors 51 up-scaling planetary reactors 43-4 UV see ultraviolet vacancy complexes 156-60 valence-bands AIN epitaxial layers 146 effective masses 497-8, 528-31 offset 491-3, 522-3 VASP see Vienna Ab Initio Simulation Package velocity-field characteristics 352, 356, 364-6 vertical electron mobility 407-9 Vienna Ab Initio Simulation Package (VASP) 462 visible-blind UV photodetectors 14-15
575
Index Volmer-Weber growth mode 97 voltage biasing 371 breakdown 337-8 capacitance characteristics 89-90, 402-3, 407-13,425-7 critical 365-7 equivalent noise spectral density 76-7 operating 34-5 pinch-off70, 83, 89-90 reverse breakdown 324, 329-33, 344-6 turn-on 274-5, 323, 348 see also current-voltage... wafer temperatures 64-6 wall-plug efficiency 242 wave vectors 435, 445 wavelength variation 33-5
wetting layers 109-10 white Hght generation 7, 214, 286-7 wide bandgap oxides 388-9 wurtzite AIN 140-6, 192-3 wurtziteGaN 351-85 wurtzite structures 9-10, 434-7, 440-4, 446-7 X-ray diffraction (XRD) powder scans 395 rocking curves 136-7, 298-9 X-ray rocking curves 81-2, 87, 136-7, 298-9 XRD see X-ray diffraction Zener magnetism 394 zero-temperature formalism 517, 548 zinc blende GaN 351-85
