High-performance quantum cascade laser sources for spectroscopic applications

DISS. ETH Nr. 18363

H IGH - PERFORMANCE QUANTUM CASCADE LASER SOURCES FOR SPECTROSCOPIC APPLICATIONS

A dissertation submitted to

ETH Z URICH for the degree of

D OCTOR OF S CIENCES presented by

A NDREAS W ITTMANN M.Sc., Technische Universität München born January 2nd, 1974 citizen of Zurich/ZH, Switzerland

accepted on the recommendation of Prof. Dr. J. Faist, supervisor Prof. Dr. M. W. Sigrist, co-examiner Prof. Dr. J. Wagner, co-examiner

2009

To my wife Nadia

Abstract Quantum cascade (QC) lasers are semiconductor lasers based on intersubband transitions in multi quantum well heterostructures, which rely on epitaxial growth techniques. They are very versatile mid-infrared sources for the realization of ultrasensitive and selective sensors for spectroscopic applications in the fields of environmental monitoring, industrial processes, security and military. However, for many applications, like the determination of isotopic ratios (e.g. of CO2), a high spectral resolution (in the MHz range) is an absolute necessity, which requires the laser source to operate in continuous wave (CW) mode. Cheap measurement systems for large volume applications also benefit from CW operating lasers since they can be combined with inexpensive dc current drivers, instead of pulse shaping electronics needed for pulse operated lasers. In addition, applications like breath analysis would profit from portable, low-power consuming devices allowing the realization of hand-held, battery-operated systems. Furthermore, broadly tunable sources with narrow linewidth are desirable for the detection of multiple absorption lines or mixtures with very broad resonances, as found in clinical medicine for non-invasive detection of glucose levels. Their broad frequency coverage combined with their higher spectral resolution (compared with Fourier transform infrared spectrometers) makes them very interesting for the detection of a variety of chemicals. In this work, low power consuming distributed feedback (DFB) based single mode QC lasers were developed, operating at !~9 µm in CW up to a temperature of 150 °C, which is the highest value reported in literature. Such devices are tunable by 1.3 % of its center wavelength. Low electrical power consumption of 1.6 W and 3.8 W for an optical output power of 16 mW and 100 mW has been demonstrated. The relatively small tuning range of a single DFB device, smaller than or equal to approximately 1 % of the wavelength, usually limits its efficiency for the detection of complex mixtures with multiple absorption lines. By using a broad-gain active region design and monolithic integration of different DFB gratings, high-performance devices

Abstract were realized with single-mode emission between 7.7 and 8.3 µm at a temperature of +30 °C. This corresponds to 8 % of the center wavelength. Some of these lasers have been selected for the NASA Mars Science Laboratory Mission to evaluate whether Mars was ever inhabitable. The combining of two of these broad-gain active region designs in the same device resulted in heterogeneous high performance QC lasers for broad-gain applications. They were tested in an external cavity setup, with single-mode tuning of the center wavelength at room temperature of 25 % in pulsed mode and 18 % in CW operation, which is the widest reported tuning range in literature. These devices are commercially available at Daylight Solutions, Poway, CA. Furthermore, a model to a priori calculate the temperature and field dependent intersubband linewidth in QC laser designs is presented; the same was experimentally verified with devices having different linewidths. This model constitutes a useful tool for the development of novel narrow gain and high wallplug efficiency active region designs or designs for broad gain applications.

ii

Kurzfassung Quantenkaskaden-Laser sind Halbleiterlaser, die auf Intersubband-Übergängen in Multi-Quantentopf-Schichtstrukturen basieren und mit Hilfe von epitaktischen Wachstumsverfahren hergestellt werden. Mit ihnen lassen sich sehr empfindliche und selektive Sensoren für spektroskopische Anwendungen in den Bereichen Industrie, Umwelt, Sicherheit und Militär realisieren. In vielen Fällen, wie beispielsweise für die Bestimmung von Isotop-Verhältnissen (etwa von CO2), ist eine hohe spektrale Auflösung (im MHz-Bereich) nötig, was Laserquellen im Dauerstrich-Betrieb erfordert. Aber auch die preiswerten Messsysteme für die Massenproduktion würden von dauerstrichbetriebenen Lasern profitieren, da diese mit Gleichstromquellen betrieben werden können, die im Vergleich zu Pulsgeneratoren relativ günstig sind. Zudem braucht es stromsparende batteriebetriebene Laserquellen, um tragbare Systeme zu realisieren, welche beispielsweise für die Atemanalyse mit portablen Geräten von Vorteil wären. Des Weiteren sind Breitband-Laserquellen mit schmaler Linienbreite sehr interessant für die Messung von Substanzen mit mehreren Absorptionslinien oder Mischungen mit breiten Absorptionsresonanzen, wie etwa zur nichtinvasiven Messung von Glukose. Der grosse Abstimmbereich zusammen mit einer, verglichen

mit

Fourier-Transformierten-Infrarot Spektrometern,

viel

höheren

spektralen Auflösung macht diese Laserquellen sehr interessant für die Messung einer Vielzahl von chemischen Substanzen. In dieser Arbeit wurden Laser mit verteilter Rückkopplung (DFB-Laser) für eine Emissionswellenlänge von 9 µm entwickelt, welche bis zu einer Temperatur von 150 °C im Dauerstrichbetrieb arbeiten, was die höchste publizierte Temperatur darstellt. Solche Laser sind um 1.3 % der Zentralwellenlänge durchstimmbar. Der elektrische Leistungsverbrauch eines solchen Lasers für optische Ausgangsleistungen von 16 mW bzw. 100 mW liegt bei 1.6 W bzw. 3.8 W. Der relativ kleine Abstimmbereich eines einzelnen DFB-Lasers von etwa 1 % oder weniger schränkt den Anwendungsbereich für Messungen von komplexen Mischungen

Kurzfassung mit

mehreren

Absorptionslinien

Verstärkermediums

und

der

ein.

Durch

Integration

den

Einsatz

mehrerer

eines

Breitband-

DFB-Gitter

konnten

Hochleistungslaser realisiert werden, die einen Wellenlängenbereich von 7.7 bis 8.3 µm bei einer Temperatur von 30 °C abdecken. Dies entspricht einem Durchstimmbereich von 8 % der Zentralwellenlänge. Einige von diesen Lasern wurden für die NASA Mars Science Laboratory Mission ausgewählt, deren Ziel es ist, herauszufinden, ob der Planet Mars jemals bewohnbar war. Die Kombination zweier solcher Breitband-Verstärkermedien im selben Bauteil erlaubte die Realisierung eines heterogenen Hochleistungs-Quantenkaskaden-Lasers, welcher mit Hilfe einer externen Kavität durchgestimmt wurde. Der Abstimmbereich eines solchen Lasers über 25 % der Zentralwellenlänge im Pulsbetrieb und 18 % im Dauerstrichbetrieb stellt den höchsten publizierten Wert für Quantenkaskaden-Laser dar. Diese Laser sind kommerziell bei Daylight Solutions (Poway, Kalifornien) erhältlich. Darüber hinaus wurde ein Modell für die Berechnung der temperatur- und feldabhängigen

Intersubband-Linienbreite

in

Quantenkaskaden-Lasern

erstellt

und

experimentell mit Lasern unterschiedlicher Linienbreite verifiziert. Dieses Modell stellt ein nützliches Werkzeug für die Entwicklung neuer aktiver Zonen mit schmalen Linienbreiten und hohem Gesamtwirkungsgrad oder neuartiger Designs für BreitbandAnwendungen dar.

iv

Table of content Abstract........................................................................................................................... i! Kurzfassung .................................................................................................................iii! 1.! Introduction .............................................................................................................. 1! 1.1.!Motivation ..................................................................................................................... 1! 1.2.!Scope and organization of this thesis......................................................................... 2! 1.3.!Continuous wave mid-infrared sources...................................................................... 4! 1.3.1.!Lead salt-based diode lasers............................................................................... 5! 1.3.2.!Antimonide-based diode lasers.......................................................................... 6! 1.3.3.!Interband cascade lasers..................................................................................... 7! 1.3.4.!Sources based on optical parametric frequency conversion............................ 8! 1.4.!The quantum cascade laser ...................................................................................... 13! 1.4.1.!Historical review of first intersubband laser ................................................... 13! 1.4.2.!Intersubband laser versus interband laser ...................................................... 17! 1.4.3.!Different architectures of active region designs............................................. 19! 1.4.4.!Material aspects and growth techniques ......................................................... 21! 1.4.5.!Continuous wave operation above room temperature .................................. 25! 1.4.6.!Broad-gain quantum cascade laser sources .................................................... 27! 1.4.7.!Tunable single-mode devices ........................................................................... 29! 1.4.7.1.! Distributed feedback quantum cascade lasers ................................. 29! 1.4.7.2.! External cavity tuned quantum cascade lasers ................................. 31!

2.! Theory...................................................................................................................... 35! 2.1.!Fundamentals ............................................................................................................. 35! 2.1.1.!Electronic states in multi-quantum well heterostructures............................. 35! 2.1.2.!Intersubband absorption and gain ................................................................... 40! 2.1.3.!Inter- and intrasubband scattering processes ................................................. 45! 2.1.4.!Intersubband linewidths ................................................................................... 49!

Table of content 2.1.5.!Rate equation approach ................................................................................... 53! 2.2.!Design Parameters ..................................................................................................... 56! 2.2.1.!Electrical point of view ..................................................................................... 56! 2.2.2.!Optical point of view ......................................................................................... 60! 2.2.3.!Thermal point of view ....................................................................................... 68! 2.3.!Mode control in QC lasers ........................................................................................ 73! 2.3.1.!Distributed feedback cavity .............................................................................. 74! 2.3.2.!External cavity feedback ................................................................................... 80!

3.! Technology .............................................................................................................. 84! 3.1.!Introduction ................................................................................................................ 84! 3.1.1.!Epitaxial growth................................................................................................. 84! 3.1.2.!Processing and assembly................................................................................... 86! 3.2.!Buried distributed feedback gratings ....................................................................... 88! 3.3.!Advanced waveguide etching I................................................................................... 89! 3.4.!Buried heterostructures............................................................................................. 91! 3.4.1.!Investigation of epitaxial blocking layers ........................................................ 92! 3.4.2.!Selective growth on non-planar structures...................................................... 96! 3.5.!Epi-side down mounting ............................................................................................ 98! 3.6.!Advanced waveguide etching II ................................................................................. 99!

4.! Two-phonon resonance versus bound-to-continuum design............................ 105! 4.1.!Introduction .............................................................................................................. 105! 4.2.!Design and experiment ............................................................................................ 105! 4.3.!Intersubband linewidth............................................................................................ 107! 4.4.!Laser performance ................................................................................................... 110! 4.4.1.!Pulsed and CW laser characteristics.............................................................. 110! 4.4.2.!Transport.......................................................................................................... 111! 4.4.3.!Waveguide losses............................................................................................. 112! 4.4.4.!Differential gain .............................................................................................. 114! 4.4.5.!Threshold current density and slope efficiency ............................................ 114! 4.5.!Conclusion................................................................................................................. 115!

vi

Table of content

5.! Low power consumption laser sources............................................................... 117! 5.1.!Introduction .............................................................................................................. 117! 5.2.!Design and experiment ............................................................................................ 117! 5.3.!Laser performance of moderately coupled devices ............................................... 118! 5.3.1.!CW laser characteristic ................................................................................... 118! 5.3.2.!Thermal resistance and temperature tuning................................................. 120! 5.3.3.!Cavity losses ..................................................................................................... 121! 5.3.4.!Longitudinal and lateral mode discrimination ............................................. 122! 5.4.!Laser performance of strongly coupled devices..................................................... 124! 5.5.!Conclusion................................................................................................................. 125!

6.! Quantum cascade lasers with widely spaced operation frequencies............... 126! 6.1.!Introduction .............................................................................................................. 126! 6.2.!Design and experiment ............................................................................................ 126! 6.3.!Laser performance ................................................................................................... 128! 6.3.1.!CW laser characteristic ................................................................................... 128! 6.3.2.!Thermal resistance and tuning properties .................................................... 130! 6.3.3.!Coupling strength and mode discrimination ................................................ 132! 6.3.4.!Extrapolated gain spectrum and differential gain........................................ 133! 6.4.!Evaluation of reliability for NASA Mars mission project .................................... 135! 6.5.!Conclusion................................................................................................................. 136!

7.! Broadly tunable heterogeneous quantum cascade laser sources .................... 138! 7.1.!Introduction .............................................................................................................. 138! 7.2.!Design and experiment ............................................................................................ 139! 7.2.1.!Active region design........................................................................................ 139! 7.2.2.!Waveguide and thermal design...................................................................... 141! 7.2.3.!Single mode control in external cavity setup ................................................ 142! 7.3.!Device characterization............................................................................................ 143! 7.3.1.!Gain chip performance ................................................................................... 143! 7.3.2.!Extrapolated gain spectrum ........................................................................... 147! 7.3.3.!Broadband tuning in external cavity setup.................................................... 147! 7.4.!Conclusion................................................................................................................. 150! vii

Table of content

8.! Conclusion and Outlook ...................................................................................... 151! List of abbreviations................................................................................................. 154! References.................................................................................................................. 156! Acknowledgement ..................................................................................................... 172! Curriculum vitae....................................................................................................... 175! Publications............................................................................................................... 176!

viii

Chapter 1 1. Introduction 1.1. Motivation The monitoring and control of our environment, as well as maintaining a high quality of life of an aging population has become one of the major challenges of today’s society and is of profound importance with regard to the technological development of the industrialized world. The diversity of applications include fields such as the environmental monitoring of important carbon gases in global warming (e.g. CH4, CO, CO2 and H2CO), urban (e.g. automobile traffic, power generation) and rural emissions (e.g. rice agro-ecosystems, horticultural greenhouses and fruit storage), industrial emissions, chemical analysis and process control for manufacturing processes (e.g. food, semiconductor and pharmaceutical), as well as toxic gases and explosives relevant to law enforcement and public safety. An important field in clinical medicine is the analysis of breath metabolites (e.g. NO, CO, CO2, C2H6 and NH3) for the early detection of ulcers, cancer and diabetes. Breath analysis is very attractive because it is a non-invasive way to

monitor a patient’s physiological status. All these applications require the precise determination of concentration levels, for which several methods exist. Those based on chemical reactions are generally classified as electrochemical, measuring a change in output voltage due to a chemical interaction of the analyte with the sensing element. Other methods are based on changes of physical properties (thermal, mechanical or optical). Optical absorption techniques allow the realization of non-invasive and highly sensitive and selective measurement systems for both gases and analytes dissolved in liquids. Furthermore, they are fast, consume no material (as in the case of electrochemical methods), and can be employed in harsh environments. Optical

Introduction absorption techniques also enable the probing of the overtone and fundamental rotational-vibrational frequencies of target molecules, most of which are located in the near-infrared (0.7–3 µm) and mid-infrared (3–24 µm) range, and also allow the obtaining of an unambiguous signature of the investigated gas or liquid. Optical techniques are well established in chemistry, but instruments such as the Fourier transform infrared (FTIR) spectrometer are bulky, expensive, power-consuming and limited in spectral resolution. Recent progress in the telecommunication industry allows the fabrication of semiconductor optical sources with very high performance levels, low electrical power consumption and low manufacturing costs. The invention of the quantum cascade (QC) laser and recent improvements of its room temperature performance allow the generation of single-mode emission at room temperature across the mid-infrared (MIR) wavelength range, where most of the relevant target molecules have absorption lines several orders of magnitudes stronger than in the near-infrared (NIR). Concentrations in the parts-per-billion (ppb) and parts-per-trillion (ppt) ranges are detectable. Furthermore, the two atmospheric transmission windows in the MIR at 3–5 µm and 8–12 µm allow remote sensing. However, one needs portable, low powerconsuming, selective and sensitive measurement systems, which are capable of analyzing the chemical composition of small quantities in reasonable time. Furthermore, broadly tunable room temperature operated sources with narrow linewidth, compared with the well-established FTIR techniques, would open new prospects in chemistry.

1.2. Scope and organization of this thesis The objective of this work is the development of high performance quantum cascade lasers for spectroscopic applications. For one part, the focus was on the development of low-power consumption laser sources suited for portable applications. They should possess sufficient tunability, preferably without cooling, to identify a specific gas by its fingerprint spectra. For the other part, the goal was to develop broadly tunable single mode laser sources for the detection of complex mixtures with multiple absorption lines, or mixtures with very broad lines - typically those with a liquid phase matrix. The challenge is to build sources with a narrow linewidth (10-4–10-5 cm-1), which makes continuous wave (CW) operation necessary, without the need of cryogenic cooling. 2

Scope and organization of this thesis Furthermore, for broadband tunability, a broad gain spectrum is required, which results in a lower differential gain. These demand on three totally different physical aspects that have to be considered, namely the electrical, the optical and finally the thermal design. Unfortunately, these three aspects cannot be regarded as independent and must all be solved. First of all, a short introduction on alternative mid-IR coherent sources will be given. After a brief review of the history of the first intersubband laser, an overview of today’s state-of-the-art quantum cascade lasers will be given. Chapter II describes the theoretical framework and design parameters of quantum cascade lasers. Chapter III describes the technological aspect. In Chapter IV, the two most promising active region designs for high performance operation are compared. Low power- consumption singlemode devices are the topic of Chapter V. The results for realizing broadly tunable quantum cascade lasers are presented in Chapters VI and VII. Finally, Chapter VIII concludes this work and gives an outlook. The material published by the author in the following papers and conference proceedings has been used in the different chapters of this work: Chapter 2: •

Appl. Phys. Lett. 93, 141103 (2008)

Chapter 3: •

IEEE J. Quantum Electron. 44, 36 (2008)

Chapter 4: •

Appl. Phys. Lett. 93, 141103 (2008)

Chapter 5: •

Photon. Techn. Lett., accepted for publication

Chapter 6: •

Appl. Phys. Lett. 89, 201115 (2006)

•

Proc. SPIE 6485, 64850P (2007)

Chapter 7: •

IEEE J. Quantum Electron. 44, 1083 (2008) 3

Introduction

1.3. Continuous wave mid-infrared sources Numerous trace gas species are detectable in the NIR from 1.3 to 3 µm using reliable, room

temperature,

single

mode

lasers,

that

were

primarily

developed

for

telecommunication, with output powers of tens of mW. However, these lasers access molecular overtone or combination band transitions that are typically a factor of 30-300 weaker than the fundamental transitions in the mid-IR [1]. The spectral region of fundamental vibrational molecular absorption bands from 3 to 24 µm is the most suitable for high sensitivity trace gas measurement. Fig. 1.1 shows the fingerprint spectra of spectroscopically interesting molecules within the two atmospheric transmission windows in the MIR.

Fig. 1.1 Fingerprint spectra of several gas molecules in the two atmospheric transparent windows [HITRAN 2000 database].

However, the usefulness of laser spectroscopy in this spectral range is limited by the availability of convenient tunable sources. Real world applications require the laser sources to be compact, efficient, reliable and operating close to room temperature. The 4

Continuous wave mid-infrared sources quantum cascade laser is not the only coherent source in the mid-infrared spectral region (see Fig. 1.2). In this section, the advantages and disadvantages of relevant alternative continuously tunable mid-IR sources are briefly discussed. Since this work focuses on lasers emitting with a narrow linewidth, I restricted the overview on continuous wave operating sources. Although CO and CO2 gas lasers are very popular for photoacoustic spectroscopy, which is due to its large output power (several hundreds of watts in CW operation), they will not be discussed here, since they are only linetunable on the rotational-vibrational transitions of the molecule (with gaps of 1-3 cm-1). A good overview on different solid-state mid-infrared laser sources is given in the book edited by Sorokina and Vodopyanov [2] and a follow-up edited by Ebrahim-Zadeh and Sorokina [3].

Fig. 1.2: Mid-infrared CW laser sources. The blue shaded areas represent the two atmospheric transmission windows at 3–5 and 8–12 µm [1].

1.3.1. Lead salt-based diode lasers Such sources have been developed since mid-1960s for the operation between 3 and 30 µm. Lead salt diode lasers are based on semiconductor IV-VI materials like PbTe, PbSe, and PbS. The active region is either realized as homojunction, grown by liquid phase epitaxy (LPE), or heterostructure, grown by molecular beam epitaxy (MBE), using the mentioned materials as barrier and the same materials combined with Cd, Eu, Sn or Yb for the active region. In contrast to most optoelectronic materials, the direct 5

Introduction bandgap is not located at the ! point but at the L point of the Brillouin zone. Laser action is based on the injection of electrons and holes across a forward biased pnjunction. Although the effective electron and hole masses are very similar which results in a reduced Auger recombination rate, the very small bandgap of these Pb-based materials and the low T0 value of such devices require cryogenic cooling for reaching population inversion in CW operation. This in turn demands on the entire laser packaging that makes such lasers rather large in size. The highest reported CW operation temperature of such devices is 223 K [4]. Since the emission energy depends on the temperature-dependent energy bandgap, the frequency of such devices can be shifted up to 100 cm-1 by direct temperature tuning or tens of cm-1 by current tuning. However, since those devices are normally Fabry-Pérot devices, both tuning mechanisms produce only continuous wavelength coverage of 1-2 cm-1 before the wavelength jumps to another longitudinal mode. A relatively large tuning coefficient of 2-5 cm-1/K is achieved but since the complete laser package must be heated, this mechanism is rather slow (in the order of seconds). On the other hand, since typical linewidths of many applications are in the 0.001 cm-1 range, stable operations requires temperature control to better than 1 mK over long times. In contrast to direct temperature tuning, current tuning is very fast and allows to employ high frequency modulation techniques in the kHz and MHz regime. Typical linewidths of 0.6-25 MHz (full-width at half maximum, FWHM) have been achieved [5]. Temperature cycling reduces the reliability of such devices in terms of wavelength stability and spatial mode quality and leads to a reduction of output power. Output power levels in the range of 0.1-0.5 mW are relatively small compared to quantum cascade lasers.

1.3.2. Antimonide-based diode lasers Type-I quantum well (QW) lasers based on compressively-strained InGaAsSb QWs incorporated in AlGaAsSb barriers on GaSb substrates provide hundreds of mW output power at room temperature in CW within the spectral range of "=2.3 to 2.8 µm [6-8]. The wavelength in such devices is mainly adjusted by the amount of Indium in the QW. For longer wavelengths, this has to be accompanied by increasing the Arsen content in the QW in order to avoid strain-relaxation. However, this significantly reduces the hole 6

Continuous wave mid-infrared sources confinement and results in degrading the laser efficiency. Using quinternary AlInGaAsSb allows the increase of the barriers. This resulted in type-I devices at !=3.0 µm with an output power of 130 mW [9] and !=3.36 µm with 15 mW [10] at room temperature. Another successful approach is to use GaSb barriers instead of Alcontaining barriers. The lower barrier height results in lower quantization energies and consequently a red-shift of the emission wavelength at constant In content in the QW. Although this results in a reduced hole confinement, it should allow for a more homogeneous pumping of the multi-QWs. DFB devices incorporating GaSb barriers lased up to room temperature with 3 mW output power at !=3.0 µm [11].

1.3.3. Interband cascade lasers Interband cascade (IC) lasers with a Sb-type-II “W” active region design [12] are very promising for sources in the first atmospheric window between 3 and 5 µm [13, 14]. They take advantage of the broken bandgap alignment in Sb-based type-II quantum wells to re-use injected electrons in cascade stages for photon generation, first proposed by Yang et al. [15]. Fig. 1.3 shows the band diagram of such a device. Electrons injected into the InAs QW emit a photon while undergoing a diagonal transition (E1"H1) to the valence band of the InGaSb hole QW. The second InAs QW (“W”-shaped active region) increases the matrix element of the optical transition due to a strong overlap of wavefunctions (shown in upper part of Fig. 1.3). Electrons tunnel then via hole states from the InGaSb QW into the GaSb well, following resonant interband tunneling into the InAs well of the n-doped chirped InAs-(In)AlSb superlattice. The function of the GaSb well and second AlSb barrier is to prevent electron escape from the active region by tunneling. The electrons are finally injected into the active region of the next cascade. In contrast to QC lasers, IC lasers use interband optical transitions without involving fast phonon scattering and the reduced Auger recombination by eliminating inter-valence resonances (between the bandgap energy and split-off band energy #0) [16], making it possible to achieve very low threshold current densities (<10 A/cm2 at 80 K). However, such devices show rather small values of T0=40-60 K associated primarily with Auger recombination, increasing internal losses and decreasing internal efficiencies with 7

Introduction temperature. Nevertheless, CW operation on a Peltier cooler was demonstrated for !=3.3, 4.05, and 4.1 µm [17-19]. The highest CW operation temperature to date for an IC laser is 319 K, using a 5-stage active region, which emits at !=3.75 µm. At 300 K, this device emits 10 mW of optical power [20].

Fig. 1.3: Band diagram of type-II “W” interband cascade (IC) laser, reprinted from [14]. Shown are the moduli squared of the relevant wavefunctions in the conduction band (E1) and valcence band (H1).

1.3.4. Sources based on optical parametric frequency conversion Another well established way to generate mid-IR coherent light sources is the use of frequency conversion in a nonlinear optical material. There are in principle two arrangements for this process: In difference frequency generation (DFG), two optical beams customarily called pump (highest frequency) and signal (intermediate frequency), are focused into a nonlinear optical crystal to generate (in a single pass) idler (lowest frequency) radiation which equals the energy difference of signal and pump (Fig. 1.4a). In an optical parametric oscillator (OPO), the incoming (pump) beam is converted into two (signal and idler) beams and the phase matching condition defines which frequencies are generated (Fig. 1.4b). Before discussing the specifics of DFGs and OPOs, common properties are discussed.

8

Continuous wave mid-infrared sources In both cases, pump, signal and idler frequencies are related by the energy conservation:

!! pump = !! signal + !! idler . In this process, momentum conservation is needed, i.e. !k = kpump " ksignal " kidler = 0 , where !k is the so-called phase mismatch. If the phase matching condition is not met, after each coherence length lc=!/!k, the newly generated light will destructively interfere with the light generated in the previous coherence length. Thus after twice the coherence length all generated light will be destroyed. The phase matching condition can be satisfied in birefringent materials, like "-BaB2O4 (BBO) and LiB3O5 (LBO), where the ordinary and extraordinary polarization axis exhibit different dispersions. However, the limited transparency in the mentioned materials confine them to idler wavelengths below 2 µm.

Fig. 1.4: a) Schematics for difference frequency generation (DFG) and b) optical parametric oscillator (OPO).

Newer materials (like KTP, KTA and RTA) offer improved effective nonlinearities and deeper transparencies up to 5 µm. Unfortunately, these materials show non-optimal phase-matching conditions. The breakthrough came with advent of quasi-phase-matched (QPM) nonlinear crystals, particularly periodically-poled LiNbO3 (PPLN), which is 9

Introduction today’s most used material for sources based on optical parametric frequency conversion. In these materials, the phase mismatch is compensated by a periodical change of the polarization by 180° after each coherence length (poling period !QPM=2lc) by means of a relatively high dc external electric field. Thus, the light will constructively interfere with the light from the previous coherence length and a build-up of the generated light is observed. For a quasi-phase-matching process, the phase mismatch

!k = 2" / # QPM = kpump $ ksignal $ kidler . PPLN is transparent up to "4-5 µm and is therefore the material of choice for wavelengths between 2 and 5 µm. Above 5 µm, the crystal is strongly absorbing. For higher wavelength ranges, there exist orientation-patterned GaAs (OP-GaAs) and birefringent materials like AgGaS2, AgGaSe2 and ZnGeP2. However, the short wavelength absorption cutoff well above 1 µm precludes the direct use of widespread solid-state Nd pump lasers (#"1.06 µm) in many of these crystals, so that successful implementation often requires cascaded two-step pumping arrangements to extend the pumping wavelength into the material transparency. GaAs has excellent characteristics for parametric frequency conversion since it is widely transparent (0.917 µm), has a high thermal conductivity, low optical dispersion that leads to a large coherence length and a huge effective nonlinear optical coefficient (94 pm/V at #=4 µm, which is 5 times larger compared with PPLN) [21, 22]. QPM in OP-GaAs cannot be achieved by periodically poling since this material is not ferroelectric, but by regrowth of laterally

orientation-patterned

GaAs

films,

fabricated

using

GaAs/Ge/GaAs

heteroepitaxy [23, 24]. Another approach to obtain QPM in GaAs and other semiconductors, like InP or ZnSe, is to use the Fresnel phase shift at total internal reflections (TIR-QPM) in a plane-parallel crystal where each leg of the zigzag path is approximately an odd number of lc. Parallel and perpendicular polarized waves display different reflection coefficients. A large differentiating mechanism between the two waves can be achieved which allows large tuning and alleviates the phase matching condition [25, 26]. In the following, the particular features of the DFG and OPO are discussed.

10

Continuous wave mid-infrared sources Difference frequency generation (DFG) The combination of a PPLN nonlinear crystal, telecommunication diode lasers and/or advanced optical fiber lasers allow the realization of very compact and robust sensors [27, 28]. The narrow linewidths of pump and signal laser convolve during the frequency conversion process, resulting in a similarly narrow linewidth for the idler. Moreover, the frequency tuning range of pump and signal wave is transferred to the idler wave resulting in a large total tuning range. This is mainly limited by the phase-matching bandwidth but can be extended by integrating several poling periods in the nonlinear crystal or by using a fan-out geometry. Another approach involves changing the temperature of the crystal and tuning both the pump and signal wavelength. Richter et al. report a multi-component gas senor based on a fiber coupled tunable near-IR external cavity (EC) diode laser (814-870 nm) and an Yb-fiber-amplified distributed Bragg reflector (DBR) diode laser (1083 nm) [29]. Using a fan-out-type PPLN, a large tuning range from 3.3 to 4.4 µm (28 % of center frequency) was achieved. However, the relatively low output power of 2.9 µW forbids the use of advanced detection techniques such as dual-beam detection. The low output powers (typically below 100 µW) and low optical conversion efficiencies (0.2 %W-1) can be markedly increased by fabricating PPLN ridge waveguides. Denzer et al. reported conversion efficiencies of 45 %W-1, resulting in an output power of 0.26 mW at !=3.3 µm [30]. Recently, an output power of 65 mW was reported. This resulted from the high damage resistance of Zn-doped PPLN waveguide which allowed input powers of 444 mW (from a YDFA amplified 1.064 µm diode laser) and 558 mW (from a EDFA amplified 1.55 µm EC diode laser) resulting in a conversion efficiency of 35 %W-1 [31]. Vasilyev et al. demonstrated a DFG sensor based on OP-GaAs, which could be widely tuned from 7.6 to 8.2 µm (7.6 % of center frequency) with an output power of 0.5 mW using 1.5 and 2 µm fiber laser sources [32]. Optical parametric oscillator (OPO) As in a conventional laser oscillator, the OPO is characterized by a threshold condition, defined by the pumping intensity at which the growth of the parametric wave in one round trip in the optical cavity just compensates the total losses. Unfortunately, the low 11

Introduction differential gain (in CW mode operation) necessitates the use of high-power CW pump lasers with Watt to tens of Watt level. Doubly resonant oscillators (for both, idler and signal wave), triply resonant oscillators (for all three waves) or pump-enhanced (PE-) singly resonant oscillators (SRO) substantially reduce the threshold compared with SRO. Typical CW pump power threshold of 100 mW are reported for PE-SROs [33]. However, this is achieved at the expenses of increased spectral and power instabilities in the idler output arising from the difficulty in maintaining resonance for more than one optical wave in a single cavity. Therefore, PE-SROs require active stabilization techniques to control output power and frequency stability. As a consequence, most of the OPO-based systems use PPLN, which shows lower thresholds compared with other materials, in combination with singly resonant cavities. An etalon within the cavity serves as a frequency-selective element enhancing stable single mode operation. Coarse tuning is achieved by selection of poling period and fine-tuning is performed by varying temperature, pump frequency, cavity length or etalon. With the use of a 3 W CW single mode diode-pumped Nd:YAG laser at 1.064 µm, van Herpen et al. demonstrated a tuning range from 3.0 to 3.8 µm by using a fan-out PPLN crystal in a singly resonant cavity. The oscillator threshold was found to be 3 W and an idler power of 1.5 W (at !=3.3 µm) was achieved for a pump power of 9 W [34]. Using a multi-grating PPLN crystal, together with the same pump laser, provided an extended tuning range from 3.74.7 µm. Unfortunately, in this spectral range the absorption of the idler wave in PPLN is significant, causing the oscillator threshold to increase from 5 to 7.5 W and the output power to decrease from 1.2 W at !=3.9 µm to 120 mW at !=4.7 µm [35]. Although these tuning ranges are fairly broad, the spectrum is not always continuous. Ngai et al. reported a continuous tuning over 450 cm-1 per poling period [36]. With a fiberamplified DFB diode laser, the same group demonstrated a continuous spectral coverage of 16.5 cm-1 by pure pump source tuning [37].

12

The quantum cascade laser

1.4. The quantum cascade laser 1.4.1. Historical review of first intersubband laser More than 35 year ago, very important developments set the basis for today’s success of the quantum cascade laser: In 1971, Kazarinov and Suris proposed light amplification in intersubband transitions by photon-assisted tunneling when electrons are transported vertically through a superlattice in a multi-QW heterostructure [38, 39]. In their proposal, electrons tunnel from the ground state of a QW to the excited state of the neighboring QW, with the simultaneous emission of a photon (see Fig. 1.5). After a nonradiative relaxation to the ground state, electrons are injected into the next state by sequential tunneling. Population inversion is realized by the relative long scattering time associated with the diagonal transition between wells (inter-well) compared with very short intra-well relaxation.

Fig. 1.5: Principle of the first proposal of light amplification in intersubband transitions by Kzarinov and Suris in 1971.

In the same year, A. Y. Cho and J. R. Arthur invented the molecular beam epitaxy enabling the growth of such superlattices, where layers as thin as several monolayers can be grown with atomic precision [40, 41]. A superlattice, first described by Esaki and Tsu [42] in 1970, is a periodic repetition of two materials of different composition, for example a repeated quantum well and barrier. Dingle et al. demonstrated that electrons confined in such structures show quantization effects [43]. However, intersubband absorption was already discovered in 1966 [44] from a two-dimensional electron gas in a Si MOS transistor [45]. In 1976, Gornik et al. showed intersubband emission using such a 13

Introduction structure [46]. It took a decade after the invention of the MBE until intersubband absorption was demonstrated in a GaAs/AlGaAs multi-quantum well structure [47], and the first observation of sequential resonant tunneling in a superlattice by Capasso et al. in 1986 [48]. Helm et al. were the first to observe intersubband emission in the terahertz frequency (2.2 THz), initially pumped by thermal excitation [49] and then by resonant tunneling [50]. At that time it was assumed that intersubband lasers with a radiative energy smaller than the optical phonon energy would be easier to realize, since ultra-fast non-radiative relaxations via LO phonon emission would be energetically forbidden, resulting in lifetimes two orders of magnitude larger, limited by acoustic phonons. However, as we know today, it is much easier to operate an intersubband laser in the mid-infrared, where the large subband energy separation makes the establishment of population inversion less difficult and where free-carrier absorption in the waveguide is much lower. The original proposal of Kazarino and Suris turned out to be inapplicable for laser action due to the difficulty of obtaining population inversion and the tendency to break up into high-field domains. The breakthrough came in 1994 at Bell Labs in the group of Federico Capasso, where Jérôme Faist and co-workers developed the first intersubband laser. This was the birth of the quantum cascade (QC) laser [51]. Since then there has been an incredible fast development of QC lasers. The most significant achievements to date are summarized in the following sections. Operation principle of first quantum cascade laser The first device was grown by MBE in the Ga0.47In0.53As-Al0.48In0.52As heterojunction material system lattice matched to InP and operated at a wavelength of 4.2 µm. Lasing took only place in pulsed mode at cryogenic temperatures with a threshold current density of 14 kA/cm2. The bandstructure and the moduli squared of the relevant wave functions are depicted in Fig. 1.6 for two out of 25 cascades. Each cascade consists of an active part and a relaxation/injector region. The active part, composed of three coupled quantum wells, is a three-level system in which population inversion between level 2 and 3 is achieved by engineering of lifetimes and optical matrix element.

14

The quantum cascade laser

Fig. 1.6: Bandstructure and moduli squared of the relevant wavefunctions of the first quantum cascade laser at an electric field of 95 kV/cm, reprinted from Ref. [51]. Each cascade of the structure consists of an active part and a relaxation/injection region. In this three-level system, the lifetime of the optical transition (3!2) has to be longer than the lifetime of level 2 in order to realize population inversion.

The wavy arrow indicates the optical transition in the active part between level 3 and 2, which is diagonal in real space. The reduced spatial separation of the overlap of the wavefunctions increases the non-radiative relaxation time between these levels. Depopulation of the lower laser level 2 is realized by designing the subband spacing between level 1 and 2 equal to the optical phonon resonance energy (see Fig. 1.7), which very efficiently empties the lower laser level 2 via electron-phonon inelastic scattering (with nearly zero momentum transfer). This scattering is much more efficient than the non-radiative relaxation between level 3 and 2 due to the necessary large in-plane momentum exchange (which was also the reason for choosing the wavelength of 4.2 µm ( =300 meV) since the momentum exchange decreases at higher transition energies). In !!

addition, the diagonal laser transition decreases also the escape rate of electrons into the continuum.

15

Introduction

Fig. 1.7: Schematic dispersion of the subband levels 1, 2 and 3 parallel to the layers, reprinted from [51]. The quasi-Fermi energy EFn corresponds to the population inversion at threshold. The radiative transitions, indicated by the wavy arrows, have essentially the same wavelength. Straight lines indicate the non-radiative LO phonon scattering process. Ultra-fast relaxation is possible between subband levels 2 and 1 due to negligible momentum transfer.

The active part is left undoped since doping broadens the laser transition by introducing a tail of impurity states [52]. The injector/relaxation region consists of a digitally graded alloy superlattice (with constant period shorter than the electron de Broglie wavelength, and varying duty cycle) to obtain a graded gap pseudoquaternary alloy. On one hand, its purpose is to collect the carriers from level 2 and to cool down the electron distribution by non-radiative phonon processes. On the other hand, its function is to inject carriers into the excited state 3 of the downstream cascade by resonant tunneling through the injection barrier. Furthermore, the injector introduces an additional energy drop between the lower laser level and the ground state of the cascade which is important to reduce thermal backfilling of carriers into the lower laser level. Finally, the injector is also used as electron reservoir, ensuring that the total negative charge is compensated by positive donors, thus avoiding the formation of space-charge domains. Therefore, the injector region is partly n-doped with Si. The structure is embedded in a waveguide (for details see [51]) that ensures an overlap of the active region with the optical TM mode (which is due to the intersubband selection rules normal to the layers polarized).

16

The quantum cascade laser

1.4.2. Intersubband laser versus interband laser Intersubband lasers differ in many ways from conventional diode lasers: •

Interband semiconductor lasers (semiconductor diode lasers) rely on transitions between energy bands in which conduction band electrons and valence band holes, injected into the active region through a forward biased pn-junction, radiatively recombine across the band gap (see Fig. 1.8). In contrast, the quantum cascade laser is an unipolar device, operating with only one kind of carriers (in our case electrons), and the optical transitions between subband states arise from size quantization within the same band (in our case the conduction band) of semiconductor heterostructures (see Fig. 1.6). So far, no QC lasers relying on confined states in the valence band could be realized and only electroluminescence has been demonstrated in p-type QC structures [53]. The unipolar property results also in a higher device reliability (no damage due to electron-hole recombination at the facets).

Fig. 1.8: Schematic bandstructure of an interband diode laser relying on transitions between conduction and valence band.

•

Due to the opposite curvature of conduction band and valence band in interband semiconductor lasers and Pauli’s exclusion principle, which ensures a broadly distributed population inversion, the resulting gain spectrum is relatively broad and asymmetric (see Fig. 1.9a). In contrast, intersubband transitions have an atomic-like joint density of states (delta-like function when broadening is neglected) because the subbands have same curvature resulting in narrow and essential symmetric linewidths (see Fig. 1.9b). As will be shown later, the linewidth of a single transition of a MIRQC laser is mainly a result of lifetime-broadening and interface roughness scattering.

17

Introduction

Fig. 1.9: Band diagram, in-plane energy dispersion and gain spectrum of a) an interband and b) an intersubband transition.

•

In quantum cascade lasers, the emitting wavelength is not related to the band-gap of the quantum well material. Therefore, mature materials like GaAs and InP-based heterostructures, which are technologically mastered, can be used and one has not to rely on temperature-sensitive small-gap semiconductors. The lower limit for the wavelength is the conduction band offset (!50 % of its value). In principle, there is no limit on the long-wavelength side (except within the Reststrahlen region).

•

Threshold currents are intrinsically very high in quantum cascade lasers compared to diode lasers, which is due to the ultra-short non-radiative lifetime (in the picosecond range) of the upper state level. However, quantum cascade lasers are less sensitive to temperature (large characteristic T0 of 130-200 K) because the upper laser state relaxation time based on the emission of an optical phonon is less temperature dependent compared to Auger recombination in diode lasers and the gain is only indirectly broadened by temperature due to collisions.

•

The cascade concept recycles electrons by re-injecting them into the upper laser state of a subsequent cascade (see Fig. 1.6). Therefore, an electron can trigger more than one photon while passing the gain material. The external quantum efficiency scales therefore with the number of cascades and an efficiency greater than one is possible. Furthermore, the threshold current density is inversely proportional to the number of cascades. This is contrast to interband multi-QW lasers where adding more QWs

18

The quantum cascade laser will result in an increased threshold current since a larger active region volume must reach transparency. •

In order to avoid the formation of space-charge domains, the QC laser has to be doped. The amount of doping defines the maximum injectable current density. This is in contrast to interband lasers where the maximum injectable current is limited by thermal issues or the catastrophic optical mirror damage (COMD) at the front facet.

•

A very small linewidth enhancement factor is the consequence of the symmetric gain spectrum (see Fig. 1.9b) because the Kramers-Kronig relation predicts no variation of the real part of the refractive index for a symmetric gain shape [54-56]. This results in a narrow laser linewidth (of a single optical transition), which should be as narrow as predicted by the Shawlow-Townes formula modified by Henry [57, 58].

•

For transition energies larger than the optical phonon resonance, the emission of optical phonon is the dominant scattering mechanism, with (upper state) lifetimes in the picosecond-range. The ultra-short lifetime of the upper state allows in principle high frequency modulation in the order of 100 GHz without relaxation oscillations.

1.4.3. Different architectures of active region designs After the birth of the quantum cascade lasers, several new active region proposals were realized, which resulted in a dramatic improvement in performance: •

Faist et al. demonstrated a new active region design relying on a vertical transition combined with a Bragg confinement of the upper state. In this two-well active region design the aim of the vertical transition, i.e., with the upper and final laser state centered in the same well, was to be less sensitive to interface roughness and impurity fluctuations. They also introduced a new injector design that acts as Bragg reflector at higher energies, which suppresses electrons from tunneling out of the excited state 3 into the continuum. This device resulted in a threshold current density of 3 kA/cm2 at 100 K [59].

•

In 1996, Faist et al. presented an active region design relying still on a vertical transition but using three coupled wells. The very thin additional well selectively pushes the upper laser state’s wavefunction into the injector region which maximizes the injection efficiency by increasing the overlap between the upper laser states and 19

Introduction the ground state wavefunction of the preceding cascade. At the same time, this narrow well reduces the overlap of the ground state with the lower laser states reducing unintentional injection (leakage) into these states. Lasers using such a design worked up to a temperature of 320 K [60]. •

In 1997, Scamarcio et al., also at Bell Labs, used a completely different concept for achieving gain by using a superlattice (SL) active region rather than establishing gain between discrete energy levels. In this concept, electrons emit photons corresponding to the energy gap (minigap) between two superlattice conduction bands (minibands). A distinctive design feature of this concept is the high oscillator strength of the optical transition at the mini-Brillouin zone boundary of the superlattice. Population inversion is automatically ensured due to the very short lifetime at the top of the first miniband (!0.1 ps) compared to the relative long scattering time (!10 ps) from the second miniband to the first miniband, resulting from the much larger momentum transfer for interminiband optical phonon emission. The large oscillator strength and the high current capacity of this designs (no level misalignment when the applied voltage is increased) favors high optical powers (750 mW at 80 K). However, the need to dope the active SL region for maintaining a flat SL band profile under external bias resulted in higher optical losses, broadening of the linewidth and reduced population inversion at higher temperatures which limited the maximum operation temperature to 240 K [61]. A year later, Tredicucci et al. presented a chirped SL active region design which overcomes the need to dope the active region and the doping is restricted to the injector region. Thus room temperature operation in pulsed mode was achieved [62, 63]. This SL active region design is especially interesting at long wavelength. Colombelli et al. showed laser operation up to 24 µm [64].

However, none of the above mentioned designs could be operated in CW at room temperature which was the result of different reasons: Although the three-quantum-well design demonstrates high injection efficiency into the upper laser level, it suffers from insufficient extraction from the lower laser level. The SL active region design 20

The quantum cascade laser demonstrates excellent extraction due to the very fast intraminiband scattering time but lacks efficient current injection in the upper laser miniband. In 2001, new active region designs were demonstrated in the Faist group addressing these deficiencies: •

The bound-to-continuum design [65] utilizes resonant tunneling injection into the upper laser state (like in the three quantum well design) and a SL type lower laser miniband (like in the SL active region design).

•

The two-phonon resonance design [66] utilizes also resonant tunneling injection into the upper laser level but the active part consists of four-quantum wells realizing three lower levels that are spaced by the energy of the LO phonon resonance energy which efficiently reduces backfilling into the lower laser state.

Today, these two designs are the most promising for high performance operation, we will focus on them in the following.

1.4.4. Material aspects and growth techniques As already mentioned, the realization of an intersubband lasers is not fundamentally bound to a specific material system. Besides the original InGaAs/AlInAs/InP material system, devices were demonstrated very soon in other heterostructure material systems (see Fig. 1.10). Here is a brief discussion of material systems that have been explored for QC lasers: •

In the lattice matched InGaAs/InAlAs/InP material system, used throughout the present work, the large conduction band discontinuity of 0.52 eV allows wavelengths as low as 4.3 µm. Furthermore, the electron masses are relatively small (InGaAs:

m* = 0.043m0 )

compared

with

the

GaAs/AlGaAs

material

system

(GaAs:

m* = 0.067m0 ). This permits to use larger quantum well widths Lw making thickness fluctuations less critical and leads to a larger matrix element zij2 ! L2w ! 1 / m* , longer non-radiative relaxation lifetimes ! " 1 / m* and consequently a higher differential gain gd ! " # zij2 ! 1 / 3 m* , which is about a factor of two larger than in the GaAs/AlGaAs material system. This explains the better performance achieved with the InGaAs/InAlAs/InP-based system for the mid-IR spectral range. The lower 21

Introduction refractive index of InP compared with both InGaAs and InAlAs makes this material an ideal candidate for a waveguide cladding layer. Furthermore, the binary nature of InP provides a good thermal transport compared to ternary materials. Lasers emitting at 3.4 µm were realized using strain compensated layers [68], where the band offset can be extended to about 0.72 eV. Wavelengths as long as 85 µm are presently achieved with this material system [69].

Fig. 1.10: Conduction band offset !Ec," at the " point and effective band offset !Ec,eff of different material systems. Inset: "-valley conduction band edges of the (Ga,In)As, and Al(As,Sb) material systems (reprinted from [67]).

•

QC lasers based on GaAs/AlxGa1-xAs have been demonstrated [70]. While the shortest possible wavelength in this system is around 8 µm, this material system is very popular for long-wavelength QC lasers in the THz region. The main advantage of this system is the property that regardless of the Al fraction, this material is lattice matched to GaAs, enabling more flexible designs and somewhat relaxed growth requirements (an Al content x=0.33-0.45 results in a !Ec," #0.3-0.4 eV). While the higher effective mass is a penalty in terms of gain (compared with the InP-based

22

The quantum cascade laser system), this results in lower free-carrier losses ! fc " # 2 / me* , particularly important for longer wavelengths. It was this material system in which the first THz laser at 67 µm was realized by Köhler et al., using a chirped superlattice design [71]. The longest wavelength, achieved to date (without magnetic field enhancement but using shallow barriers with x=0.1), was demonstrated by Walther et al. at 250 µm (1.2 THz) [72]. •

An alternative for short wavelengths is the lattice matched InGaAs/AlAsSb/InP material system, which exhibits a large conduction band discontinuity !Ec,"#1.6 eV. However, intervalley scattering ("$X) at higher transition energies results in an effective band discontinuity !Ec,eff#0.53 eV (see Fig. 1.10). The main advantage is the lattice matching to InP, which provides a low refractive index cladding, high thermal conductivity and compatibility with well established quantum cascade laser fabrication technologies. Lasers operating up to 310 K in the 3.7–3.9 µm wavelength range have been demonstrated [73]. Laser action at 3.05 µm was observed at 20 K [74]. Using strain balanced active region (containing more Indium in the InGaAs layers) should result in a !Ec,eff#0.6 eV [75].

•

The quasi-lattice-matched (slightly mismatched) InAs/AlSb material system grown on InAs or GaSb substrates with !Ec,"#2.1 eV and !Ec,eff#0.73 eV ("$L) is very promising for short wavelength QC lasers to cover the 3-5 µm atmospheric window. Neglecting non-parabolicity, the very low effective mass me* = 0.023m0 (InAs) should result in gain 2.5 times higher than in the InGaAs/AlInAs/InP material system [7678]. In the early stages, the realization of short wavelength InAs-based QCLs was hampered by the lack of suitable waveguides [79], but finally, InAs plasmon enhanced cladding layers and InAs/AlSb superlattice spacers enabled the fabrication of InAs/AlSb QC lasers emitting below 3.5 µm [80]. Recently, QC lasers based on this material system (on a InAs substrate) pushed the short wavelength frontier down to 2.7 µm [81]. Devices operating at 3.3 µm operate in pulsed mode up to 400 K with about 1 W of peak power at room temperature [82].

23

Introduction •

Another approach uses the strain-compensated InxGa1-xAs/AlxIn1-xAs/AlAs material system on InP, which is closer to the original material system, and results in a !Ec"1.3 eV at the #-point for x=0.70. The thickness of the AlAs needs to be about 1/3 that of Ga0.27In0.73As. The InAs-AlAs system grown pseudomorphically strained on InP would result in !Ec"1.5 eV, however InAs is very challenging to grow on InP and has the tendency to form self-organized nanostructures. Lasers based on this material system work up to 330 K in pulsed mode (using two-component Al0.45In0.55As-AlAs barriers in addition to pure AlAs barriers which allows to tune the barrier thicknesses and the net strain almost independently) [83]. Recently, lasers emitting at 3.05 µm (at 80 K) were realized using a very spatial diagonal transition and different well materials for the upper and lower laser level [84]. This design is beneficially because it results in a increased transition energy due to the electrical field induced stark-shift (diagonal transition), enables the use of different well materials for the upper (In0.55Al0.45As) and lower (In0.73Ga0.27As) laser level which further increase the transition energy, and suppresses leakage from the upper laser state into L or X [85].

•

Optical communication would potentially benefit from the high frequency modulation properties of QC lasers. Intersubband transitions in group-III nitrides are of great interest for optical devices operating at telecommunication wavelengths at $=1.3 and 1.55 µm, thanks to the large conduction band offset of ~2 eV [86, 87]. Wavelengths

as

short

as

$=1.08 µm

have

been

observed

in

AlN/GaN

heterostructures grown on sapphire [88]. •

While silicon diode lasers are impossible to realize due to the indirect bandgap, Si/SiGe quantum cascade lasers are in principle possible and would pave the road for integrated active optical components into silicon-based technology. Furthermore, this material system should allow operation in the 20-50 µm range, not easy to access with InP or GaAs based devices (reststrahlen band). In contrast to the other material systems, the optical transition is designed in the valence band, which is a result of the much lighter effective hole mass. Intersubband electroluminescence from siliconbased quantum cascade structures was reported in 2000 [53]. However, no Si-based

24

The quantum cascade laser QC laser has been realized so far. The main obstacles are accommodation of the large built-in strain (4 % mismatch between Si and Ge lattices), the physically more complex valence band (coupled heavy and light hole, larger effective masses), smaller band offsets and interface roughness. So far, the heterostructure of the active region has been grown by either solid source [51] or gas source [89] MBE. An alternative is the metal organic vapor phase epitaxy (MOVPE) growth technique. This technology is a widely established platform for highvolume production of reliable semiconductor lasers since it offers several advantages: reactors can be scaled for multi-wafer deposition; it does not require elaborate baking cycles to recover from atmospheric contamination, resulting in long down times of the system; growth of phosphide materials is simplified; wide range of growth rates (~15 µm/h) significantly reduces growth times. In 2003, Roberts et al. demonstrated the first atmospheric pressure MOVPE grown QC laser based on the AlGaAs/GaAs material system [90]. In a follow-up work they demonstrated room temperature operation of a QC laser, emitting at !=8.5 µm, based on the three-quantum-well design in the InGaAs/AlInAs/InP material system, using low-pressure MOVPE. In order to obtain the necessary interface abruptness and layer thicknesses, the growth rate was kept at ~0.8 µm/h (which is comparable to that of an MBE system) while the growth rate was increased to 3 µm/h for the waveguide layers [91]. The laser performance is comparable to that of similar MBE grown structures.

1.4.5. Continuous wave operation above room temperature For many applications, high spectral resolution (in the MHz range) is an absolute necessity. Therefore, the devices must be operated in CW operation in order to avoid thermal chirp (shifting of the emission wavelength by thermal heating of the device during the pulse). However, for almost one decade CW operation was just feasible at cryogenic temperatures. The main limitation was bad thermal management of the device, leading to an overheating of the active region that resulted in a reduction of differential gain and high waveguide losses. After 2001, device performance

25

Introduction improvements (in terms of CW operation) were mainly achieved by improving the thermal management and optimization of the injector doping levels. •

In 2002, Beck et al. demonstrated the first QC laser operating in CW at room temperature (up to a temperature of 312 K) with an output power of 17 mW at 292 K using the two-phonon resonance active design, emitting at 9 µm [92]. This was facilitated by burying the waveguide in undoped InP and epi-down mounting on diamond, resulting in a dramatic reduction of the thermal resistance of the device.

•

One year later, Yu et al. reported CW operation up to 308 K of a laser emitting at 6 µm. The device was grown in a single step using gas source MBE. The active region is based on a two-phonon extraction design similar to [66]. Instead of a buried waveguide, they processed double-channel ridge waveguide and electroplated a 5 µm-thick Au layer on top of the ridge for heat-removal. Finally, the device was mounted epi-up on copper submounts [93].

•

In 2006, Prof. Capasso’s group at Harvard University in collaboration with AdTech Optics Inc., Palo Alto, CA, demonstrated CW operation up to 380 and 400 K and output powers at 300 K of 312 and 204 mW at !=5.3 and 8.4 µm, respectively [94, 95]. These outstanding results were achieved by using a combination of dry and wet etching for producing very narrow ridges and by using Iron-doped InP for burying the ridges. The two-phonon resonance active region design [66] was grown by MOVPE.

•

The previous mentioned results are based on the two-phonon resonance design, which exhibits a relative small gain width of <165 cm-1 (FWHM) [96]. Spectroscopic applications need tunable devices, preferably over a large frequency range. This necessitates an active region design with a broad gain spectrum. In this respect, the relative small gain width, which favors high performance operation, is a drawback. In contrast to this, the bound-to-continuum design exhibits a FWHM of 200–300 cm-1. Wittmann et al. presented high-performance bound-to-continuum quantum cascade lasers, tailored for emission at !=8.6 µm, that operated CW up to 383 K [97]. This was achieved by selective and non-selective multi-etching of the waveguide and

26

The quantum cascade laser subsequent burying with Fe-doped InP. Finally, the devices were mounted epi-down on diamond submounts. Details are shown in subsequent chapter. •

Recently, watt-level output power has been demonstrated at !=4.6 µm, independently by two research groups: Bai et al. demonstrated 1.3 W output power at room temperature by epi-down mounting a buried strain-balanced QC laser on diamond. This accomplishment was achieved by optimizing the core doping and the width of the waveguide. [98]. Lyakh et al. reached similar results by introducing a five-quantum well active region design aiming to improve efficient injection and extraction into/from the active region. In addition, they mounted the devices with buried waveguides epi-down on AlN [99].

•

Free carrier absorption and thermal population of the lower laser state force a strong downward trend of the wallplug efficiency in QC lasers with increasing wavelength [100]. However, progress has been made in increasing wallplug efficiencies in QC lasers. Recently, Bai et al. demonstrated a record wallplug efficiency at room temperature of 12.5 % for a MOVPE grown QC laser, emitting at !=4.6 µm, which was processed into a 4.8 mm-long double-channel ridge waveguide device and subsequent epi-down mounted on a diamond submount. The emitted power of this device was 2.5 W at room temperature [101].

1.4.6. Broad-gain quantum cascade laser sources As was already mentioned, gain in quantum cascade lasers is essentially narrow. For many applications, a broader gain width would be desirable. However, since differential gain is inversely proportional to the gain width, realizing a broad gain spectrum results in higher threshold current densities. As will be shown later, the linewidth mainly results from interface roughness scattering, which is primarily related on the type of the transition (diagonal/vertical): •

The first QC laser, emitting at 4.2 µm and based on a diagonal transition, shows an electroluminescence linewidth of 21 meV (FWHM) at 10 K [52].

•

As expected, the electroluminescence linewidth is much narrower in a design with a vertical transition (two-quantum-well design), resulting in only 12.4 meV (FWHM) at 10 K [59]. 27

Introduction •

The three-quantum well design, which is more a vertical than a diagonal transition, shows a similar linewidth of 16 meV at 10 K. The linewidth increases to 28 meV (FWHM) at 300 K.

•

The two-phonon resonance design shows linewidths that are mainly bias independent and approximately 20 meV (FWHM) at room temperature [96, 102].

•

The bound-to-continuum design [65, 103] exhibits a broader gain spectrum of 18– 38 meV (FWHM), which is strongly bias depending [102]. The temperature and bias dependent linewidths of the two-phonon resonance and bound-to-continuum design will be discussed in detail in this thesis.

Four characteristics of intersubband transition can be combined to engineer a broadgain spectrum: a peak energy that can be freely selected (only limited by the choice of material), an optical dipole matrix element that can be similarly tailored, transparency for frequencies on either side of the laser transition, and the possibility of cascading: •

Gmachl et al. demonstrated a so-called super-continuum QC laser, which shows laser action between 6 and 8 µm at cryogenic temperatures. The active region consists of 36 cascades with dissimilar optical transitions of the three-quantum well design [60]. The peak gain was kept constant by bandstructure engineering and the waveguide-dependent losses were compensated with the confinement factor and the number of stacks. A broad electroluminescence spectrum of 93 meV (FWHM) centered at 6.5 µm was attained at cryogenic temperature [104].

•

Maulini et al. used a different approach: They combined two bound-tocontinuum

designs

resulting

in

a

heterogeneous

QC

laser

with

an

electroluminescence width of 43 meV (FWHM). The center wavelength of the individual stacks (20 cascades of each design) was designed for emission at 8.4 µm and 9.6 µm ensuring a spectral overlap [105]. This is in contrast to the supercontinuum laser [104] where the individual gain regions are not overlapping resulting in an inhomogeneous gain spectrum. In principle, an even broader gain 28

The quantum cascade laser width can be engineered by combining several bound-to-continuum designs. However, in order to end up with a homogeneous gain spectrum, both a spectral and spatial overlap of the individual gain media is required.

1.4.7. Tunable single-mode devices Spectroscopic applications require tunable single-mode sources. For this reason, a frequency selective element is necessary that favors one longitudinal mode against the others.

1.4.7.1. Distributed feedback quantum cascade lasers Most applications use a distributed feedback (DFB) grating along the waveguide forcing the laser to emit on the so-called Bragg frequency. A side-mode suppression ratio (SMSR) of 47 dB (which approaches that of NIR telecom lasers) was measured from residual transmission measurements of a CW operated DFB QC laser, emitting at !=5.3 µm [106]. The frequency can be tuned continuously by a heat-induced change of the refractive index. Heating can be direct by changing the device temperature ("#/"T=0.05 to -0.15 cm-1/K) or indirect by current heating ("#/"I=$-0.02 cm-1/mA). •

Distributed feedback quantum cascade lasers were first demonstrated by Faist et al. in 1997 [107]. Feedback was achieved mainly by loss-coupling using the top metal after etching the first order grating in the top waveguide cladding layer.

•

One year later, Gmachl et al. presented an index coupled DFB QC laser where the grating was etched in the upper InGaAs cladding layer of the active region which was subsequently overgrown with InP [108]. Most of todays DFB QC lasers rely on this concept.

•

Two years after the first demonstration of CW at room temperature by Beck et al. [92], Aellen et al. demonstrated the first CW DFB-QC laser operating on a Peltier cooler (up to a temperature of 260 K) using the same active region design, emitting at 9 µm [109].

•

Northwestern University demonstrated CW DFB QC lasers operating up to 60 °C at 4.8 µm [110], 40 °C at 7.8 µm [111] and 50 °C at 9.6 µm [112]. This was achieved by 29

Introduction processing double-channel ridge waveguides and electroplating them with thick Au. The long-wavelength device was further mounted epi-down on AlN submounts. •

The relatively small temperature tuning range on a Peltier cooler of a single device usually limits the possibilities of gas analysis. This is particularly true for complex mixtures with multiple absorption lines or with very broad lines (typically those with a liquid phase matrix). By using a bound-to-continuum broad-gain active region and integrating several different DFB gratings on the same piece of gain material, Wittmann et al. demonstrated stable single mode emission over 100 cm-1 in CW above RT, that is from !=7.7 to 8.3 µm [113]. In the gain center, a temperature of 63 °C was attained [114]. These high-performance devices are discussed in detail later on. Some of these lasers have been selected for the NASA Mars Science Laboratory Mission with the goal to evaluate whether Mars was ever inhabitable.

•

Based on the same concept, Lee et al. demonstrated a QC laser spectrometer which works in pulsed mode from !=8.7 to 9.4 µm using an array of 32 buried DFB gratings monolithically integrated into the same epi-layer [115]. They performed absorption spectroscopy on isopropanol, acetone and methanol. The results compare favorably with spectra obtained by a conventional FTIR spectrometer.

•

Recently, single-mode QC lasers for low-power consumption applications operating at !!9 µm in continuous wave up to 423 K (150 °C) were demonstrated. This was achieved by the combination of strong distributed feedback coupling, a narrow gain active region design, low intersubband and free-carrier losses as well as a good thermal management. Tuning of 10 cm-1 was achieved by heating the device. The threshold current density varies from 1.1 kA/cm2 at 303 K to 2.4 kA/cm2 at 423 K. Other devices with low electrical power consumption of 1.6 W and 3.8 W for an optical output power of 16 mW and 100 mW have been demonstrated [116]. Details are shown in subsequent chapter.

30

The quantum cascade laser

1.4.7.2. External cavity tuned quantum cascade lasers As we have seen, the tuning range of a thermo-opto-tuned DFB QC laser on a Peltier cooler is limited and the frequency coverage can be extended by arrays of DFB lasers. However, some applications, such as the detection of complex organic molecules or the analysis of multi-component gases, will benefit from more broadly tunable sources. Therefore, it is more convenient to use a broad gain Fabry-Pérot QC laser source in an external cavity configuration, although setups are getting more complicate and bulky. In such a setup, an external grating acts as a spectral filter and the selected wavelength is fed-back into the laser, forcing the device to emit there. Furthermore, a good antireflection (AR) coating is needed for suppressing the chip modes for extended off-gain peak operation. In an ideal setup, the tuning range is then only limited by the bandwidth of the gain medium. •

The first realization of an EC tuned QC laser was shown by Luo et al. The QC laser gain chip [117] is based on the three-quantum-well design with a vertical transition [60]. The EC setup used the Littrow configuration [118] and the uncoated chip (no AR coating) was mounted in a cryostat with an AR coated window. Tuning ranges in pulsed operation of 32 cm-1 and 33 cm-1 have been achieved at 80 K for two lasers emitting at !~4.5 µm and 5.1 µm, respectively. Increasing the heat sink temperature to 203 K reduced the tuning range to only 10 cm-1 [119]. One year later, Luo et al. demonstrated the results of an AR coated 5.1 µm laser, with a residual reflectivity of 3-5 %. The mode discrimination was good enough to allow tuning between the FP modes and the tuning range at 243 K could be extended to 49 cm-1 [120].

•

The first Peltier cooled EC tuned QC laser was reported by Totschnig et al. [121] using a 10.4 µm QC laser from Alpes Lasers SA. At -30 °C, they achieved a tuning range of 7 cm-1 without using an antireflection coating.

•

Maulini et al. demonstrated tuning over 150 cm-1, which is 15 % of center wavelength (10 µm) in pulsed mode at room temperature [122]. The front facet was coated with a quarter wave of ZnS, which resulted in a residual reflectivity of 4 %. The broad tunability was mainly achieved by the broader gain spectrum (297 cm-1) of the boundto-continuum design compared with the three-quantum well and two-phonon 31

Introduction resonance design. Due to the fact that all transitions share the same upper state, laser action at a particular wavelength results in a homogeneous gain clamping. However, the SMSR is very poor (<25 dB) since at the beginning of each pulse, the chip FP modes are present. •

A year later, Maulini et al. presented a gain chip that can be operated in CW at -30 °C in an EC setup [122]. The gain chip is based on the bound-to-continuum design with a center wavelength of 5.15 µm. The chip could be tuned over 140 cm-1 in single-mode operation with a SMSR>30 dB (limited by the instrument). The output power was in excess of 10 mW over 100 cm-1. The linewidth of this laser was examined by heterodyning it with a reference laser. The superimposed beams were detected using high-speed room temperature mercury cadmium telluride (MCT) detector. The beat note on the spectrum analyzer showed a width of 5 MHz (FWHM). Although this is sufficient for most of the applications, this relatively large value is a consequence of temperature and current fluctuations of the reference laser. Wysocki et al. demonstrated direct absorption spectroscopy of nitric oxide (NO) and water (H2O) with this gain chip [123]. Their setup allows mode-hop-free tuning by simultaneous tuning of cavity length, current and angle. The narrow laser linewidth allowed resolving two spectral peaks in NO which are separated by 0.006 cm-1.

•

Using the heterogeneous QC laser structure as mentioned in 1.4.6 and applying a broadband AR coating, consisting of YF3 and ZnSe, with very low residual reflectivity, Maulini et al. demonstrated tuning from 8.2 to 10.4 µm (265 cm-1 or 24 %), in pulsed mode near room temperature [105]. The strong spectral and spatial overlap of the individual gain spectra resulted in a clamping of the total gain spectrum. However, the broad gain spectrum combined with a relatively high doping level resulting in a large threshold current and an insufficient thermal management disallowed CW operation.

•

So far, CW operation of a gain chip in an EC configuration was limited to cryogenic or very low temperatures on a Peltier element which makes is necessary to operate the setup in a closed environment resulting in complicate and bulky setups.

32

The quantum cascade laser Wittmann et al. developed a gain chip for high-performance broad-gain applications, emitting at 8.4 µm [97]. Arun et al. used such a gain chip, mounted epiup on copper, and achieved room temperature CW operation of an EC tuned QC laser. Single-mode tuning from 7.96 to 8.84 µm (over 126 cm-1 or 10 %), was archived [124]. However, the extracted power was only 1.2 mW in the gain center. The output power could be increased by a modified Littrow setup with back extraction of the light that resulted in a power of 20 mW at the gain center. It was later found that the submount temperature must have been much higher than room temperature due to the large thermal resistance between submount and Peltier. Mounting the gain chip epi-down on diamond, as described in [97], resulted in a large output power of 137 mW in gain maximum and more than 40 mW over 85 cm-1 (temperature was now measured on the submount). However, the higher residual reflectivity of the AR coating resulted in a reduced tuning range. •

Wysocki et al. used the gain chip developed by the group of Capasso in collaboration with AdTech Optics (described above) [95], in their mode-hop-free EC setup. At -30 °C, they demonstrated tuning from 7.77 to 9.05 µm (182 cm-1 or 15 %) in CW and a maximum output power of 50 mW. Nitrous oxide (N2O), methane (CH4), sulfur dioxide (SO2), and ammonia (NH3) are within this tuning range. This result is attributed to the combination of a high performance QC laser gain chip, a very high quality AR coating (residual reflectivity of 0.046 %) and a strong EC feedback [125].

•

In 2008, Wittmann and Hugi et al. presented a heterogeneous high performance gain chip for ultra-broad tuning in an EC configuration. A coarse tuning of 292 and 201 cm-1 (25 and 18 % of center frequency) was achieved in pulsed and CW operation at room temperature, respectively. At gain maximum, 135 mW could be extracted in CW. This gain chip represents a very promising solution for laser photoacoustic spectroscopy (L-PAS) since it can be tuned over 172 cm-1 with output powers in excess of 20 mW along with a room temperature operated EC setup [126]. This gain chip is discussed in details later on. Fig. 1.11 shows tuning ranges of EC systems in pulsed operation available from Daylight Solutions, Poway, CA. The heterogeneous QC laser gain chips presented in this work (red curve in Fig. 1.11, marked with an 33

Introduction arrow) have been sold by Alpes Lasers SA to Daylight Solutions, which confirmed our measurement (see press release of Daylight Solutions [127]).

Fig. 1.11: Tuning ranges of different EC tuned QC laser gain chips. The heterogeneous high-performance QC laser gain chip shows a tuning of 25 % in pulsed mode with a peak power of 480 mW (red curve) [Courtesy of Daylight Solutions].

34

Chapter 2 2. Theory 2.1. Fundamentals The success of quantum cascade lasers is based on the knowledge of band structure engineering. In the first section of this chapter, the relevant quantum mechanical models are sketched, especially the simplifications, which are sufficient to accurately model our devices. This includes a model to a priori calculate the temperature and field dependent intersubband linewidth in quantum cascade laser designs. In the last section, the rate equation approach will be presented which leads to the macroscopic accessible quantities such as threshold current density and slope efficiency.

2.1.1. Electronic states in multi-quantum well heterostructures The quantum cascade laser is composed of several hundred of layers of alternating materials (indicated by A and B) that have different band-edge profiles, forming an alternating potential Vc (z) of wells and barriers. Moreover, the layer thicknesses are in the order of the de Broglie wavelength resulting in quantization of energy states along the growth direction. The problem that has to be solved is the computation of these electronic states in (planar) heterostructures. In a very efficient and elegant manner this can be done by using the envelope function approximation [128] which allows to separate the three-dimensional wave function ! into a slowly varying “envelope” and a fast varying unit cell (Bloch function):

!(r) = " Fl ,kA, B (r) # ulA,,kB=0 (r) l

!

(2.1)

Theory where Fl ,kA, B (r) is the envelope function, ulA,,kB=0 (r) is the Bloch function and l is the index !

of the considered bands. Furthermore, we assume that the Bloch functions are identical in both materials, i.e. ulA,k =0 (r) = ulB,k =0 (r) . Because of the in-plane translational invariance, the envelope function can be written as:

Fl ,k (r) = !

1 Sact

e

ik! r!

! l (z)

(2.2)

where Sact is the sample area, k! = (k x , k y ) is the in-plane wavevector and ! l (z) is the l-component envelope function. In the general case, this involves the conduction band, the heavy-hole, light-hole, split-off valence bands and results in an eight bands model (taking into account the spin). While it is essential to solve the full model for the valence band, fortunately, simplification can be made if one is only interested in the conduction band. We start with a simple pure one-band model (Ben-Daniel Duke model) [129]. The Schrödinger equation reads:

# & (2.3) ! 2 "2 ! + V (z) ( ) c (z) = E ) c (z) % * 2 %$ 2m (z) "z (' Here, the bands are assumed to have parabolic curvatures, given by the effective mass m* = m0 Eg / (Eg + EP ) . Since the Kane’s energy EP is very similar for different materials (around 22 eV) and EP ! Eg , the effective mass depends mainly on the band-gap Eg resulting in a very low effective mass m* for low band-gap materials. Of course, the effective mass has to be dependent on the position z, since the heterostructure is composed by different materials. Equation (2.3) can be solved by introducing the boundary conditions at the interface between materials A and B:

36

! cA (z) = ! cB (z)

(2.4)

A B 1 !" c (z) 1 !" c (z) = * mB (z) !z m*A (z) !z

(2.5)

Fundamentals Including the effective mass in (2.5) ensures probability current conservation. However, the conduction band wavefunction has a discontinuity of the slope at each interface when the effective mass is discontinuous. This pure one-band model works surprisingly well for thick QWs in the conduction band, when the confinement energies E are much smaller than Eg (or for isolated bands like the heavy hole valence band). However, it fails to predict the levels in our laser devices since at least the upper laser state lies close to the top of the barrier. We now want to refine our model by taking into account an effective valence band (substituting the light hole, heavy hole and split-off bands). Neglecting the in-plane momentum k! = 0 , the wavefunction for this two-band model reads:

!(r) = " c (z) # uc,k =0 (r) + " v (z) # uv,k =0 (r)

(2.6)

Instead of treating this model now as a full two-band model, only the conduction band wavefunction ! c (z) has to satisfy the modified Schrödinger equation:

# !2 " & (2.7) 1 " + V (z) ( ) c (z) = E ) c (z) %! * %$ 2 "z m (E, z) "z (' whereas the contribution of the valence band is taken into account by an energy dependent effective mass [130]:

" E ! V (z) % m* (E, z) = m* (z) $ 1 + ' Eg,eff & #

(2.8)

where the effective band gap Eg,eff = ! 2 / (2! m* (z)) is related to the nonparabolicity coefficent ! . This model is called effective one-band model, since we finally end up again with a one-band model but considering the valence band by the energy dependent mass. Note that this energy dependent mass causes non-parabolicity since the energy dispersion Ec (k) = Ec (k = 0) + ! 2 k 2 / (2m* (E, z)) (which is the solution of (2.7)) is not anymore parabolic. The edge of the well material is taken as zero point for the electron energy E. V (z) will be replaced by zero in case of a well and by the conduction band 37

Theory discontinuity in case of a barrier. Of course, the boundary conditions are the same as for the one band model but now taking into account an energy dependent mass. However, the conduction band wavefunction ! c (z) is not the complete envelope function. Therefore, the conduction band wavefunction must be normalized, taking into account the valence band [131]:

!c 1 +

E " Ec (z) E " Ev (z)

(2.9)

!c = 1

The effective one-band model, which is used in our calculations, is accurate enough to predict the resonance energies Ei (i is the subband index) with a typical error of a few meV, which is less than the uncertainty introduced by growth fluctuations. A comparison with the pure one-band model is shown in Fig. 2.1.

Fig. 2.1: Computation of the energy levels Ei and conduction band wavefunctions

! c,i in a 90 nm-wide QW applying the pure one-band model (dashed lines) and the *

*

effective one-band model (solid lines) using mInGaAs =0.0427 m0 , mAlInAs =0.076 m0 and a non-parabolicity coefficient ! =1.13 x 10-18 m2.

38

Fundamentals The influence of the valence band also has to be considered when calculating the matrix element zij = ! i z ! j

of the optical transition between an initial | i! and a final state

| j! [131]:

zij =

!i! 1 1 " c,i pz * + * p " 2(Ei ! E j ) m (Ei , z) m (E j , z) z c, j

(2.10)

where the momentum operator is defined as pz = !i! "z" . In order to drive current through the laser structure, an external bias !V (z) has to be added to the pure heterostructure band-edge profile Vc (z) . Furthermore, the Hartree potential VH (z) must be considered for accurate predictions:

V (z) = Vc (z) + !V (z) + VH (z)

(2.11)

The Hartree potential results from ionized donors (that are needed to avoid the formation of space-charge domains) and conduction electrons that result in a local charge density: 2( % !(z) = q0 ' N D (z) " $ ni # i (z) * & ) i

(2.12)

where N D (z) is the doping profile of ionized dopants and ni is the sheet carrier density in the ith subband. The Hartree potential is computed from !(z) using Poisson’s equation:

! 2VH (z) !z

2

="

#(z) $$ 0

(2.13)

The electonic densities ni on the subbands depend on the transport through the device and are therefore not known. However a good approximation is to assume that the electron distribution is thermal, based on a Fermi-Dirac distribution and a common chemical potential ! (measured from the ground state of each period), and that charge neutrality is achieved in each period: 39

Theory

! n =! " D (E) f i

i

i

dist

(2.14)

(E) dE (electrons)

i

= ! N D (z) dz = ns (dopants) where the density of states Di (E) = m* (E) / (! ! 2 ) " # (E $ Ei ) is the density of states in the ith subband and ! (E " Ei ) is the Heavyside function, f dist (E) = (1 + exp([E ! !] / kT )!1 is the Fermi distribution function, and ns is the total carrier sheet density. Since the Hartree potential is a function of the conduction band wavefunction and therefore of the solution of the Schrödinger equation, both Schrödinger’s and Poisson’s equation must be solved iteratively until convergence is achieved.

2.1.2. Intersubband absorption and gain In this section we consider possible transitions within quantized states and derive an expression for the intersubband absorption, which will be further used for the calculation of gain in QC structures. The interaction between the electronic system and a polarized electromagnetic (EM) field gives rise to scattering events of electrons from one state to another and results in absorption (or emission) of photons. We start from Fermi’s golden rule for the transition rate from a state | i, k! ! to a state | j, k!' ! .

Wij,k k ' = ! !

2! " i,k H ' " j,k ' ! ! "

2

(

# E j (k!' ) $ Ei (k! ) ± "%

)

(2.15)

where the upper sign is for emission and the lower sign for absorption of a photon and

H ' is the perturbation Hamiltonian. This is schematically illustrated in Fig. 2.2a. To calculate the absorption rate from state | i! to all possible final states | j! , one has to sum over all electronic states:

Wabs,i

2! = & & " i,k" H ' " j,k"' ! j k k'

2

(

)

(

# E j (k"' ) $ Ei (k" ) $ !% ' fdist,i 1 $ fdist, j

)

(2.16)

" "

where the Fermi-Dirac function fdist,i = f dist (Ei (k! )) represents the probability that the

(

)

initial state is occupied and 1 ! fdist, j the probability that the final state is empty. The

40

Fundamentals corresponding emission rate Wem can be simply derived by inverting the probability functions.

Fig. 2.2: Schematics of a scattering event a) from an initial state | i, k! ! to a final ' state | j, k! ! and b) from an initial | i! to a final state | j! having same momentum.

The absorption coefficient is defined through the ratio of the absorbed energy per unit volume and time !! "Wnet / V (with the net total rate Wnet = Wabs ! Wem ) and the average intensity I, where the volume V = Sact ! Lp ( Lp is the length of one period of the QC laser active region). The absorption coefficient ! ISB = !" #Wnet / (Sact # Lp # I ) summed over all occupied initial and empty final states results in:

! ISB

!" 2# !" = ' ' $ i,k" H ' $ j,k"' Lp Sact I ! ij k k '

( )

2

(

)(

% E j (k"' ) & Ei (k" ) & !" ( fdist,i & fdist, j

)

(2.17)

" "

The perturbation Hamiltonian can be written as:

H'= !

q0 m0

A" p

(2.18)

The vector potential A is related to the polarized EM wave E = E0! cos(kr " # t) ( E0 is the electrical field amplitude, ! is the polarization vector and k is the wavevector) by

E = !"A / "t and reads:

A=

iE0! i(kr # " t) e + c.c. 2"

(2.19)

41

Theory Since the ! ! Lp ( Lp is the characteristic dimension over which the wavefunction spreads, which is in the case of the QC laser at maximum the length of one cascade), the dipole approximation can be applied and the matrix element in (2.17) can be written:

q02 E02

2

! i,k H ' ! j,k ' !

=

!

2

4m02" 2

(2.20)

! i,k # $ p ! j,k ' !

!

Using (2.1), the matrix element in (2.20) can be separated in the following way:

! i,k " # p ! f ,k ' = " # uv p uc !

!

Fi,k (z) Fj,k ' (z) + " # uv uc !

!

F(z)i,k p Fj,k ' (z) !

(2.21)

!

where c and v are the band indices. Since our transitions are within the same band, the Bloch functions have same parity and therefore, the first term in (2.21) vanishes (in contrast to interband transitions where there is a change in parity because uv (r) ! uc (r) ). In the second term, the overlap integral of Bloch functions becomes unity and it remains the dipole matrix element of envelope functions, which reads with (2.2):

F(z)i,k ! " p Fj,k ' (z) = !

!

1 Sact

e

ik! r!

# i (z) ! x px + ! y p y + ! z pz

1 Sact

e

ik!' r!

# j (z)

(2.22)

Only the z-component remains since the contributions in x and y direction vanish. As a result, the polarization of the electromagnetic field has to be in z direction (growth direction, TM polarization) in order to couple to the electronic system. Exactly this is the polarization selection rule for intersubband transitions. Liu et al. validated this result in a photocurrent experiment where they found that the absorption of TE polarized light was only 0.2 % of the TM one [132]. Furthermore, initial and final states must share the same momentum k! = k!' , which is nothing else than the momentum conservation, depicted schematically in Fig. 2.2b. Inserting the remaining matrix element into (2.20) and substituting the momentum matrix element with the position matrix element results in: 2

! i,k H ' ! j,k ' !

42

!

=

q02 E02 Eij2 4" " 2

2

2

zij # k k '

! !

(2.23)

Fundamentals Now we can insert our result into (2.17) together with the average intensity

I = 12 E02 neff ! 0 c ( neff is the refractive index, c is the speed of light) and the absorption coefficient reads:

( )

! ISB !" =

2# 2 q02

( z (& ( E (k ) ' E (k ) ' !" )( f 2

$ 0 neff %0 Lp Sact

ij

' "

j

ij

k"

i

"

' fdist, j dist,i

)

(2.24)

Taking into account the in-plane symmetry, one can replace the sum with an integral "

1 1 = k dk . Including the double spin occupation by a over all k! -states: $ Sact k! (2! )2 #0 ! ! factor of two, the absorption coefficient can be written:

( )

! ISB !" =

q02

# 0 neff $0 Lp

)

zij

2

ij

'

(% (E

j

& Ei & !"

0

)( f

dist,i

)

& fdist, j k" dk

(2.25)

Solving this equation for the case of parabolic bands would result in an infinite value. In reality, scattering processes result in broadening which can be usually described by replacing the delta-function with the Lorentzian function with a half-width at half maximum (HWHM) of ! ij :

( )

L !! =

" ij / #

(2.26)

(!! $ E ) + " 2

ij

2 ij

Integrating over the Fermi-Dirac distributions, an analytical solution can be derived [133]:

( )

! ISB !" =

q02 kT 2# 0 cneff !Lp

+ ij

(

% 1 + exp [! $ E ] / kT i f ij ln ' ' 1 + exp [! $ E j ] / kT &

(

) (* , L

) *)

( !" )

(2.27)

where µ is the chemical potential and the oscillator strength has been introduced which reads:

f ij = 2

m0 Eij !2

2

zij =

2 ! i pz ! j m0 Eij

2

(2.28)

43

Theory As can be shown for transitions between the first two states in a QW, the oscillator strength is proportional to the inverse effective mass f 21 ! 1 / (m* / m0 ) and is therefore very helpful in comparing different materials. For example in an infinite QW with an energy spacing of !E21 = (22 " 12 )! 2# 2 / (2m* L2w ) for the first two states and the corresponding matrix element of z21 = 16Lw / (9! 2 ) , the resulting oscillator strength

f 21 = 0.96 / (m* / m0 ) . An interesting property of the oscillator strength is that it obeys the sum rule

!

j

f ij = m0 / m* where downward transitions have negative sign. As a

consequence, upwards transitions have an oscillator strength that increases with the initial state index i and therefore, transitions between excited states naturally yield larger intersubband absorptions. Gain between subbands is defined simply as negative absorption g(!! ) = "# (!! ) . Assuming parabolic subbands and a Lorentzian lineshape for the optical emission (which includes the Fermi-distributions in the states i and j), the material gain [in cm-1] between states | i! and | j! can be written as:

( )

G !! =

2" 2 q02 zij

2

# 0 neff $0 Lp

(

(2.29)

)

% n j & ni % L (E & Eij , ' ij )

(

)

where the difference in carrier sheet density n j ! ni in subbands i and j replaces the term ( fdist,i ! fdist, j ) / Sact in (2.24). The peak material gain reads:

4! q02 zij

2

(

1 Gp = % n j & ni " 0 neff #0 Lp 2$ ij

)

(2.30)

Note, that the peak material gain is inversely proportional to the linewidth. This equation shows that the gain theoretically can be arbitrarily large depending on the ability to efficiently inject current in the upper laser state. Replacing the carrier density by the pumping current J = q0 n / ! (and assuming that the lower laser level is depleted) leads to the value of differential gain [in cm/kA]: 44

Fundamentals

Gp

4" q0 zij

2

(2.31)

1 gd = = ! up J # 0 neff $0 Lp 2% ij where ! up is the effective upper state lifetime.

As we have seen, one needs an overlap of the (TM polarized) optical mode and the gain region. As a consequence, only the part of the optical mode overlapping with the gain

( )

( )

medium contributes to the modal gain. The modal gain reads GM !! = GP !! " , where ! is the overlap factor. Another important quantity is the gain cross section

gc = GM / !n [in cm], which will later be used in the rate equation approach.

2.1.3. Inter- and intrasubband scattering processes A proper understanding of inter- and intrasubband scattering between energy states in QC lasers is essential for the engineering of population inversion and gain. Electrons in excited subbands can scatter to lower subbands by various ways: Radiatively by spontaneous emission of a photon, or non-radiatively by longitudinal optical (LO) and acoustic (LA) phonons, electron-electron interactions, impurities and interface defects.

Fig. 2.3: Schematics of a) intersubband scattering between states | i! and | j! spaced by more than the LO phonon energy: shown are the stimulated emission of a photon with E21 and the dominant non-radiative scattering induced by LO phonons, and b) intrasubband scattering of a LO phonon.

45

Theory For subband spacings larger than the optical phonon energy !! LO , the most efficient scattering process is the emission of LO phonons [134, 135] (see Fig.

2.3a).

Intrasubband scattering of LO phonon can also happen when the thermal energy exceeds the phonon energy (Fig. 2.3b). Although elastic scattering (allow disorder and interface roughness) adds to the scattering rate [136], this contribution to the intersubband scattering is small compared to inelastic LO phonon scattering and is neglected in our model. However, as will be shown later, interface roughness will be considered in the linewidth broadening. Spontaneous emission Spontaneous emission between an initial | i! and a final | j! state is possible when the matrix element is non-zero. The spontaneous emission rate can also be derived from Fermi’s golden rule and reads for a single polarization mode [137]: 2

Rijsp =

1

! sp,ij

=

q02 neff zij Eij3 3" c3# 0 ! 4

Fig. 2.4: Radiative spontaneous lifetime versus transition energy E21 in an infinite QW with an oscillator strength f 21 = 22 .

46

(2.32)

Fundamentals Equation (2.32) gives the impression that the spontaneous carrier lifetime is inversely proportional to the cubic of the energy; however, this is not the case: using the oscillator strength (2.28), formula (2.32) can be rewritten:

R = sp ij

1

! sp,ij

=

q02 neff f ij Eij2 6" m0 c # 0 ! 3

(2.33)

2

which shows that ! sp is inversely depending on the square of Eij (see Fig. 2.4). For a typical mid-IR wavelength of 8 µm, ! sp is in the order of 40 ns which is very long compared to the non-radiative lifetime ! non , which is in the ps range. This results in a fairly poor radiative efficiency !rad = (1 + " sp / " non )#1 $ 10#5 and therefore, an intersubband light emitting diode (LED) is not very efficient. LO phonon scattering Since the dominant non-radiative scattering mechanism in our devices is the emission of LO phonons, we are only considering this scattering mechanism in our calculations. Since the density of electrons in the subband of the upper laser state is very low (!1011 cm-1), we assume the electrons to be at k! =0 in this subband. Following the approach of Ferreira and Bastard for dispersion-less bulk phonons, which neglects any heterostructure effects on the phonon dispersion [134], the scattering rate for the spontaneous emission of LO phonons at a temperature of 0 K reads:

RijLO =

1

! LO,ij

=

" m*q02# LO ! $ pQij 2

' dz ' dz ' % (z) % i

f

(z)e

&Qij z & z '

% i (z ') % f (z ')

(2.34)

= ! #"1 " ! s"1 and Qij is the in-plane momentum defined as where ! "1 p Qij = 2m* (Ei ! E j ! !" LO ) !

(2.35)

As one quickly sees from (2.34), the smaller the in-plane momentum Q, the shorter the LO scattering time; or the closer the transition energy to the energy of the optical phonon !! LO (InGaAs: 34 meV), the faster the non-radiative depopulation. The resulting scattering times are in the ps range. Setting Q=0 results in lifetimes in the order of ! LO,ij =0.25 ps. Note however, that (2.34) is based on Fermi’s golden rule and is 47

Theory not able to compute an exact value at resonance. Interesting to note is the inverse dependence of the effective mass on the scattering time: ! LO " 1 / m* , resulting in larger lifetimes for small-gap materials. In the end, we are interested in the non-radiative lifetime ! non,ij (T ) at temperature T. Therefore, we need to include absorption and stimulated emission of LO phonons in our calculations. For intersubband transitions, the LO phonon scattering rate reads then:

1

! non,ij (T )

=

1

! LO,ij

nLO (T ) +

1

! LO,ij

(1 + n

LO

(T )

)

(2.36)

where the first term on the right hand side stands for the absorption and the second part accounts for the emission (including spontaneous events) of LO phonons. The phonon population nLO is given by the Bose-Einstein factor: nLO (T ) =

1

(2.37)

exp(!! LO / kT ) " 1

The Bose-Einstein factor is the origin for the weak temperature dependence in QC lasers (see Fig. 2.5). Nevertheless, this quantity is one of the dominating factors that reduce differential gain with increasing temperature.

Fig. 2.5: Ratio of lifetimes ! non,ij (T ) / ! non,ij (0K) for a phonon energy of

!! LO =34 meV. 48

Fundamentals Finally, we can calculate the lifetime of a state | i! by simply summing over all possible final states j:

1 1 =" !i j ! ij

(2.38)

LO phonon scattering can also happen within the same subband. Intrasubband scattering happens on a much faster scale since the in-plane momentum Q is much smaller. The spontaneous emission lifetime ! LO,ii is computed by taking the same initial and final state in (2.34). However, the number of photons which have sufficient energy above the optical phonon is reduced. Consequently, the probability to emit an optical phonon decreases exponentially with the optical phonon energy (Bolzmann distribution). Considering this in (2.36) results in the intrasubband lifetime of state | i! :

1

! non,ii (T )

=

1

! LO,ii

nLO (T ) +

1

! LO,ii

(1 + n

LO

$ "!# LO ' (T ) exp & ) % kT (

)

(2.39)

The intrasubband lifetime is a quantity that will be utilized in the computation of the linewidth of intersubband transitions.

2.1.4. Intersubband linewidths The finite upper state lifetime and inhomogeneities transform the linewidth from a delta function to a linewidth with a finite energy width, normally assumed to be Lorentzian. The standard procedure for calculating gain (see (2.29)) relies on the empirical fit of experimental data of electroluminescence linewidth 2! ij , which are not known for new active region designs. In this thesis, a model will be presented to a priori calculate the temperature and field dependent intersubband linewidth of the optical transition in QC laser design. In our model, we consider lifetime broadening due to LO phonon and interface roughness scattering. Since the electron densities in our QC lasers are fairly low ( ns ! 10!11 cm-2) and the relatively wide band-gap Eg of InGaAs compared with the intersubband 49

Theory transition energy Eij , the broadening of the linewidth due to non-parabolicity

! non-parab " E F # Eij / Eg , where EF is the fermi level, is small [138]. Furthermore, impurity scattering is also insignificant since the doped region is separated from the optical transition. Lifetime broadening is due to ultrafast intra- and intersubband relaxations. Only interand intrasubband scattering of LO phonons are taken into account since this is the dominant scattering mechanism in mid-IR QC lasers (seen in previous sections). The total lifetime broadening reads [133]:*

(

#1 #1 2! opt = ! " inter + 2" intra

)

(2.40)

where ! inter equals the lifetime of the upper laser state and ! intra is the intrasubband scattering of the same. Essential is that lifetime broadening contributes half as much to the broadening as does pure dephasing. Furthermore, note that intrasubband scattering contributes much stronger to the total broadening since ! inter > ! intra . Campman et al. observed in an intersubband absorption experiment that by narrowing the QW width, the linewidth increases, which in case of lifetime broadening should decrease (from (2.34) follows that a larger energy spacing results in a larger lifetime). They attributed this to interface roughness scattering, arising from monolayer fluctuations of QW interfaces [139]. Unuma et al. showed theoretically and experimentally that interface roughness is the dominant scattering mechanism in QWs [140, 141]. Their model is based on a statistical description of the interface roughness assuming that the roughness height !(r) at the in-plane position r = (x, y) along the interface has a correlation function:

$ " r " r' 2 ' ) !(r)!(r') = ! 2 exp & &% # 2 )(

*

(2.41)

Following the literature, although this is only correct for an infinite lower laser state lifetime. In our structures, the finite lower laser lifetime would add to the linewidth broadening but this does not change the general interpretation of the data.

50

Fundamentals where ! is the mean height of the roughness and ! is the correlation length. We first consider a single quantum well with energy states | 0! and |1! . The difference of the intrasubband scattering matrix elements results in roughness broadening [140]:

! IFR =

m* " 2 # 2 F00 $ F11 !2

(

&

) ' d% e 2

$ q2 #2 / 4

(2.42)

0

where Fmn = (!Em / !Lw ) " (!En / !Lw ) expresses the influence of the interfaces on the energy levels and Lw is the quantum well width. The interface parameter product !" is fixed for a given set of epitaxial growth parameters. The two-dimensional scattering vector q = k ! k ' is defined as q 2 = 4m* E / ! 2 ! (1 " cos# ) and ! is the scattering angle. It is interesting to note that, apart from the additional angular dependence, transport

( )

broadening ! tr = ! / "# tr $ = !q0 / µ m* differs from (2.42), mainly by the term F00 which

(

)

replaces F00 ! F11 for the optical transition, where F11 > F00 (in the infinite barrier approximation,

is four times larger than

F11

scattering element F01 (which replaces

(F

00

F00 ). Although the intersubband

! F11

)

in (2.42)) formally adds to the

interface roughness broadening, its contribution is much smaller (due to a much larger q 2 , that differs from the above one) and is neglected. Note that the interface roughness

is proportional to the effective mass and scales quadratically with the band offset. When the wavefunctions extend over several interfaces k, one has to take into account all those interfaces. Substituting Fnnk = !U " c (zk )

2

(where !U is the conduction band

offset and ! c is the wavefunction), considering that the integral approaches ! for typical values of ! and assuming further that the interfaces are uncorrelated to each other, the roughness broadening can be written [142]:

!

IFR ij

2 " m* 2 2 2 = 2 # $ %U , () & i2 (zk ) ' & 2j (zk ) *+ ! k

(2.43)

51

Theory In this model, interface roughness broadening is treated as lifetime broadening due to elastic scattering of conduction electrons (homogeneous broadening) following the theory of Ando for transport properties [143]. Khurgin presented an inhomogneous model for interface roughness broadening in which the momentum selection rule is relaxed by the interface roughness allowing for non-vertical intersubband transitions [144]. His formula deviates by a factor of 1.6 from (2.43), which is attributed to the Gaussian rather Lorentzian lineshape. The linewidth of the optical transition between states | i! and | j! reads then:

(

2! ij = 2 ! opt + ! ijIFR

)

(2.44)

In our structures, not only the wavefunctions extend over several interfaces but also several optical transition needs to be considered. In order to calculate the lineshape of the multi-optical transition power spectrum Lspon (E) , each optical transition with its specific Lorenzian lineshape, has to be weighted by the oscillator strength and the cubic energy:

Lspon (E) ! % Rijsp " Eij " L (E # Eij , $ ij ) !% f ij " Eij3 " L (E # Eij , $ ij ) j

(2.45)

j

As will be shown later, the correct linewidth for different active region designs could be calculated [102]. However, one has to be aware that gain (2.29) has a different lineshape for multi-optical transitons:

(

)

Lgain (E) ! % f ij " ni # n j " L (E # Eij , $ ij ) j

(2.46)

For the active region designs considered here, one can neglect the lower state population (strong inversion) and the gain spectrum can be extrapolated from the spontaneous emission power spectrum:

Lgain (E) !

52

Lspon (E) E3

(2.47)

Fundamentals

2.1.5. Rate equation approach The macroscopically accessible quantities such as threshold current density and slope efficiency of the QC laser can be derived in a very simple way using a rate equation approach, which considers the time evolution of populations (carrier sheet density per cascade [in cm-2]) in the upper and lower laser state coupled to the photon flux S (defined per cascade and active region width [in cm-1s-1]). Fig. 2.6 depicts a schematic illustration of the rate equation approach, where the upper and lower state lifetimes read | ! 3 " and | ! 2 " and the lifetime between those states is | ! 32 " .

Fig. 2.6: Schematic illustration of energy states and lifetimes in the rate equation approach.

The rate equations for one cascade read as follows [145]:

dn3 J n3 = ! ! Sg c (n3 ! n2 ) dt q0 " 3

(2.48)

n " n2therm dn2 n3 = + Sg c (n3 " n2 ) " 2 dt ! 32 !2

(2.49)

n ( c % dS non-res = S+# 3 * ' g c n3 ! n2 ! " tot $ sp *) dt neff '&

(2.50)

( (

)

)

where ! is the fraction of spontaneous emission coupled into the lasing mode, ! sp is the non-res spontaneous emission lifetime, ! tot

are the non-resonant total losses and

n2therm = ng exp(!" inj / kTel ) represents an approximation for the thermal population 53

Theory (backfilling) of the lower laser level. In the last equation, ng is the sheet doping density of the injector, Tel is the electronic temperature and ! inj the energy difference between the lower laser state and the Fermi level of the injector’s ground state | g! . Note that the lifetime due to stimulated emission is ! stim = (Sg c )"1 . Below threshold, S is zero (the contribution of the spontaneous emission can be neglected since ! sp ! ! 3 ), and from (2.48) an expression which relates the upper state population and the pumping current is derived:

n3 = J ! 3 / q0

(2.51)

The population inversion as function of pumping current is obtained from (2.49) using (2.51) and n2 = n3 ! "n :

!n =

J" J" 3 $ "2 ' 1 # # n2therm = eff # n2therm & ) q0 % " 32 ( q0

(2.52)

where the effective upper state lifetime ! eff = ! 3 (1 " ! 2 / ! 32 ) relates the population inversion to the pumping current. ! eff converges to the upper state lifetime ! 3 when

! 32 ! ! 2 , and then !n converges to n3 when backfilling is negligible. The threshold condition is derived from (2.50) by setting the derivative to zero and neglecting the contribution of the spontaneous emission. The population inversion at threshold reads:

(

)

non-res !nth = n3 " n2 = # tot / gc

(2.53)

with the non-resonant losses defined as: non-res non-res empty ! tot = "! ISB + ! wg + ! m,f + ! m,b

(2.54)

empty where ! wg are the free carrier losses in the waveguide (excluding any doping in the

active region) and ! m,i are the mirror losses of front and back facet. The finite linewidth of the (off resonance) intersubband absorptions in the active regions results in non-res absorption at the lasing wavelength that is taken into account by !" ISB . In a similar

54

Fundamentals way, one can replace the thermal population of the lower laser level with an equivalent res res / gc , where ! ISB (resonant) loss term: n2therm = !" ISB are the intersubband losses at c

resonance. Since the carrier populations of all the energy levels are known, calculating the intersubband absorption using (2.27) is much more precise than assuming a two level system and all the carriers in the ground state. The threshold current density can be attained by replacing the population inversion in (2.52) with the threshold condition (2.53):

J th =

(" g

q0

! eff

non-res tot

)

res + #" ISB =

c

q0" tot

! eff gc

=

" tot #gd

(2.55)

where the gain cross section is replaced with the differential gain using (2.31) and (2.52). non-res res ! tot = ! tot + "! ISB indicates that the threshold current density also has to compensate

the resonant losses. Now, we consider the situation above threshold. The photon flux is obtained from (2.49) by setting the derivative to zero. Since the gain is clamped above threshold one can substitute the population inversion by the threshold condition (2.53). One is tempted to use (2.51) to replace n3 , however this equation is only valid below threshold. Instead of

(

)

non-res that one has to derive n3 from (2.48) which results in n3 = ! 3 J / q0 " S# tot . The

photon flux can then be written as:

S=

(J ! "

)

q / (gc# eff ) # eff

tot 0

non-res q0" tot (# eff + # 2 )

=

( J ! J )# th

eff

(2.56)

non-res q0" tot (# eff + # 2 )

Note, that the photon flux is independent of the resonant losses. So far, all the quantities are related to a single cascade. The total power within the laser cavity, which takes into account N p cascades, is Pin = N p ! !" ! S ! wact ( wact is the active region width). The emitting power from the front facet reads: Pout = Pin (1 ! Rm, f ) (assuming that the back facet is high-reflection coated). A very important quantity is the slope efficiency

dP , dI

55

Theory which is proportional to the number of cascades and also to the internal ( !int ) and external ( !ext ) quantum efficiencies:

$ eff dP dS !! # m,f !! = N p !! " # m,f = Np = Np % % non-res q0 # tot $ eff + $ 2 q0 ext int dI dI

(2.57)

2.2. Design Parameters In this section, the relevant electrical, optical and thermal design parameters in QC lasers will be presented, giving the background for understanding the difficulties that need to be overcome for achieving the goals of this work.

2.2.1. Electrical point of view From equations (2.55) and (2.57) it is clear that an active region design for a lowthreshold and high-efficient QC laser should have the following properties: • Large oscillator strength f32 • Large upper state lifetime ! 3 • Large ratio between ! 32 / ! 2 • Low intersubband losses ! ISB • Narrow transition linewidth ! 32 Furthermore, the following issues need attention: • Thermionic emission of carriers from the upper state into the continuum • Efficient injection in the upper laser states and quenching of scattering into the lower laser state • The escape time ! esc from the lower states into the injector

To date, the most promising active region designs for high performance are the twophonon resonance and bound-to-continuum design, invented in 2001 [65, 66]. Based on the band diagram of the two-phonon resonance design, depicted in Fig. 2.7, the relevant parameters will be discussed.

56

Design Parameters

Fig. 2.7: Band diagram of the two-phonon resonance design. The radiative transition takes place between the states | 3! and | 2! . The states | 2! , |1! and |1'! are spaced by the optical phonon energy !! LO . ! inj is the energy seperation between the ground state | g! and the lower laser state | 2! . The crosses indicate scattering events that are strongly suppressed in this design.

Injection efficiency Injection in the upper laser state is achieved by resonant tunneling through an injection barrier from the ground state | g! into the upper laser state | 3! . Special care has to be taken to ensure a good injection efficiency while quenching injection into the lower laser state | 2! . If !3 significantly deviates from unity, the population inversion in (2.52) needs

(

)

to be modified: !n = J / q0 " &'# 3$3 1 % # 2 / # 32 % # 2$2 () . This problem has been successfully solved in the two-phonon resonance and bound-to-continuum designs by introducing a thin well close to the injection barrier. This approach not only results in a deeper penetration of the wavefunction of | 3! into the injector barrier, and therefore ensures a good injection efficiency, it also ensures a strong spatial separation of the injector ground state and the lower laser level, avoiding leakage into the latter.

57

Theory Oscillator strength and upper state lifetime The upper state lifetime ! 3 cannot be engineered independently from the oscillator strength since both are coupled: a vertical transition results in a good overlap of wavefunctions, compared to a diagonal transition, and therefore in a large oscillator strength f32 , while the lifetime will be approximately half the value of the diagonal transition. In general a more diagonal transition results in a higher product f32! 3 . However, a diagonal transition broadens the linewidth due to more interface roughness scattering. Since the product f32! 3 " (m* )#3 2 , a large product can be attained by choosing a material system with a low effective mass. Therefore, the InGaAs/InAlAs/InP material system is a good choice. The matrix element can be further increased by use of excited states for the laser transition. ! 3 can be extended by suppressing leakage into the continuum. The simplest way would be to increase the thickness of the downstream barrier. However, this would also reduce the escape time ! esc from the lower states of the gain region into the injector and therefore this approach is not advised. In a very efficient way leakage can be suppressed by designing the injector as a Bragg mirror for the upper state, which has a large minigap around the upper laser state and a miniband where the lower states of the gain region are situated, ensuring a high escape rate into the injector (see Fig. 2.7). When the energy of the upper laser state is close to the band edge, electrons can be thermally activated to continuum states. In order to avoid this, one can increase the barrier by using strained structures (necessary for QC lasers emitting in the 5-6 µm range in the InGaAs/InAlAs/InP material system) or move to material systems with larger band discontinuity. Lower laser state lifetime and depopulation An ultra-short lifetime ! 2 results by designing the spacing between the states | 2! and |1! resonant to the optical phonon energy. However, one should not forget that the extraction barrier of the gain section (see Fig. 2.7) poses an obstacle for fast extraction of carriers out of the gain region since the escape time ! esc > ! 2 . Thus, thermal population can result in backfilling of scattered electrons into the lower laser level. A 58

Design Parameters very efficient solution has been found, which gave the two-phonon resonance design its name, where a ladder of three states (instead of just two) spaced by the energy of the optical phonon are used which significantly reduced the population of the lower laser state. The bound-to-continuum design uses another approach: Instead of three discrete levels, it uses a miniband that spans the full length of the cascade. The lifetime ! 2 of the upper state in the lower miniband is very short since the large phase space allows for scattering to any point in the miniband. The upper state is created within the first minigap by inserting a narrow QW at the beginning of the cascade. Resonant and non-resonant intersubband losses The active region has to be doped to ensure global charge neutrality in each cascade in order to avoid the formation of space charge domains. The doping in QC lasers defines the maximum injectable current density J max = q0 ns / (! trans + ! tunnel ) , where ns is the doping sheet density and ! trans is the transit time for traversing one cascade. 2

2

! tunnel = (1 + " 2! !2 + 4 # ! 3! ! ) / (2 # ! ! ) is the resonant tunneling time between the injector ground state | g! and the upper lasing level | 3! [38, 39, 146], where 2! ! is the energy splitting at resonance between | g! and | 3! (which should be designed to be less than the broadening, 2! ! " ! / " # ), !! is the energy detuning from resonance, and ! ! is the dephasing time. Since scattering by ionized impurities result in a dramatic broadening of the electroluminescence spectrum, the doping is placed in the injector region. However, not only J max increases linearly with the doping [96] but also the nonnon-res = g ISB " ns , where ns is the sheet doping density and resonant intersubband losses ! ISB

g ISB is the gain cross section for intersubband losses. Therefore, the doping has to be kept to a minimum in order to realize a low threshold current density J th but sufficiently high that the laser has some dynamic range (J max ! J th ) / J th . An optimum in the doping concentration has to be found which depends strongly on the wavelength, the particular active region structure and the intended application (e.g. low power consumption or high output power). 59

Theory

Thermal backfilling of carriers in the lower laser level increases linearly with doping and res results in resonant losses ! ISB . This can be sufficiently suppressed by designing a large

energy difference ! inj between the lower laser level and the chemical potential of the injector. However, since the operation bias U ! N p (!" / q0 + # inj ) increases with ! inj , a good compromise is a value of 120-150 meV [147]. Intersubband linewidth The ultra-short lower state lifetime (!0.2 ps) in the two-phonon resonance and boundto-continuum design allows to keep the ratio ! 32 / ! 2 sufficiently high, although both designs use a vertical transition. The vertical transition will result in a narrower linewidth for an optical transition. However, the use of a lower laser miniband in the bound-to-continuum results in several strong optical transitions and therefore a broader gain spectrum. While this is a nice feature for broadband tuning, this should result in an overall weaker laser performance since the threshold current density is inversely proportional to the gain width. Nevertheless, a pulse operation temperature up to 150 °C has been shown with this design [103]. The two-phonon resonance and the bound-to-continuum designs show a T0 of 180-200 K and seem to be promising for realizing high performance devices for either lowthreshold current CW lasers or broadly tunable CW sources. Both designs will be compared in the experimental part of this thesis.

2.2.2. Optical point of view Lasers are composed of two components: a gain element (active region) and a resonator (waveguide and mirrors). A resonator with low losses and a large overlap factor ! is crucial for achieving laser action at very low threshold current density. Both overlap factor and (empty) waveguide losses depend on the waveguide design. Vertical confinement in QC lasers is achieved by sandwiching the active region within cladding

60

Design Parameters layers, which normally have a refractive index lower than in the active region. The lateral waveguide is conventionally realized by fabricating ridge waveguides. Overlap factor One of the main problems in realizing a laser in the MIR is to confine a large optical mode into the small active region, where the length of one cascade is only ~50-75 nm resulting in a small overlap factor ! p . The total overlap factor between the mode and

N p cascades is: Np

! = "!p

(2.58)

p =1

When the individual overlap factors ! p are similar (e.g. in the center of the mode), this expression can be simplified to ! = N p ! p . In this case, the threshold current density (2.55) can be written as J th = ! tot / (gd N p " p ) # N p$1 , showing that the threshold current is inversely proportional to the number of states. However, adding more cascades increases the necessary bias voltage U ! N p (!" / q0 + # inj ) and the injected electrical power at threshold Pth = U th ! J th " N p ! (!# / q0 + $ inj ) ! N p-1 " (!# / q0 + $ inj ) is constant. Nevertheless, the reduction of the threshold current density is beneficial because it also reduces the population inversion in each cascade, and consequently one can reduce the active region doping level which further causes less intersubband absorption. A decrease in threshold current density reduces also joule heating ! (R " I )2 . In addition, the slope efficiency is directly proportional to N p . However, adding more and more cascades will decrease ! p . In the wavelength range of 7-9 µm, a good compromise is a number of

N p =35 [148], which we use in most of the designs presented in this thesis.

61

Theory Losses in QC lasers There are three reasons for losses that have to be considered: • Mirror losses at the end facets of the laser • Intersubband losses in the active region (already treated in the previous section) • Free carrier losses in doped semiconductor layers and metals

Mirror losses The mirror losses of one facet are ! m,i = " ln(Ri ) / (2L) , where L is the resonator length,

Ri is the facet reflectivity and the index i stands for the front (f) or back (b) facet. Rm,i =0.27 is used for a cleaved facet and Rm,b =0.97 for the high reflecting (HR) coated (Al2O3/Au) back facet. For anti-reflection (AR) coatings, we use a bi-stack of quarterwave layers of YF3/ZnSe resulting in Rm,i < 10!3 . Using a dispersive feedback element (either a distributed feedback grating or an external cavity grating) will selectively influence the cavity losses, which will be discussed in the next section.

Free carrier losses in doped semiconductor layers The semiconductor layers of the waveguide have to be doped in order to enable current flow and avoid joule heating. However, doping will change the refractive index and results in losses due to free carrier effects. The Drude theory for conductivity is used to obtain the contribution to the complex refractive index [149]: , & $ P2 i )/ 1 + n! = ! " .1 # 2 +1 2 ( .- $ (1 + 1 / ($% tr ) ) ' $% tr * 10 2

(2.59)

where the plasma frequency reads:

! P2 =

ne q02

(2.60)

m " #" 0 *

where ! " is the high frequency dielectric constant, and ne the carrier concentration, which is equal to the doping concentration at 300 K. The scattering time

62

Design Parameters

! tr (ne ) = µ (ne ) " m# / q0 is calculated from mobility µ (ne ) measurements. From (2.59), the loss part can be written as [150]:

! = ! = "2k0 #( n)

q03$02 4% c neff & 0 (m ) µ 2 3

* 2

'

$02 ne

(2.61)

*

m

where it becomes clear that the losses in a semiconductor layer scale linearly with the doping level (neglecting the rise of the effective mass with increasing carrier concentration) and quadratically with the wavelength. Furthermore, for better waveguiding, the refractive index can be markedly decreased by increasing the doping level until the plasma frequency is close to the laser frequency while the losses are still relatively low (Fig. 2.8). Such a layer is then used in plasmon-enhanced waveguides [151].

Fig. 2.8: Calculated refractive index and absorption vs doping for InGaAs at 300 K for 6, 8 and 10 µm wavelength using experimental mobility data. The circles indicate the doping level at which ! p equals frequency of the emitted light.

Calculation of (empty) waveguide losses and overlap factor Each layer i has a thickness di and a complex refractive index n!i . The layers are assumed to be homogeneous, isotropic, non-magnetic and non-conducting. One has to solve the wave equation which reads for layer i [152]:

63

Theory

" !2 !2 % 2 2 2 + $ !x 2 !y 2 ' E(x, y) ( ) ( k0 n!i E(x, y) = 0 # &

(

)

(2.62)

where x is along the growth direction, y is the in-plane coordinate perpendicular to the ridge, ! is the propagation constant along z direction, k0 is the free-space propagation constant and E(x, y) is the electrical field amplitude. Note that the used coordinate system is standard for EM waves, and differs from that used in previous sections where z is the growth direction. Since in the majority of cases, the layers are absorbing and/or the waveguide is leaky, for each mode, a solver needs to find the complex root in order to compute the propagation constant ! . As long as wact ! ! one can treat the vertical structure as a one-dimensional multi-layer slab waveguide, where the layers range from minus to plus infinity in the y- and zdirection and therefore, the propagation in z-direction can be assumed to be independent of y and ! / !y = 0 . Based on the polarization selection rule for intersubband transitions (2.22), the transversal modes are TM polarized and only the component in x direction has to be considered (see Fig. 2.9). Consequently, the solution of (2.62) reads:

(

) ( )

Ex,i (x) = E R,i ! exp(iks,i ! x) + E L,i ! exp("iks,i ! x) ! # / k0 n!i

(2.63)

where E R,i and E L,i are the complex field amplitudes of layer i for the right and left propagating wave and ks,i = k02 n!i2 ! " 2 . The boundary conditions at each interface read:

(E

R,i

(x) + E L,i (x) ! n!i = E R,i+1 (x) + E L,i+1 (x) ! n!i+1

) ( (x) ) " # = ( ! E

(! E

R,i

(x) + E L,i

i

)

R,i+1

)

(x) + E L,i+1 (x) " # i+1

(2.64) (2.65)

where ! i = 1 " # 2 / (k0 n!i )2 . In contrast to the TE modes, the TM modes show a discontinuity at each interface when there is a change in the refractive index. Once the field solutions are known, one can obtain the overlap factor from:

" !=

act $

"

#$

64

2

Ex dx 2

E dx

(2.66)

Design Parameters

Fig. 2.9: Slab waveguide, showing the electrical and magnetic field vector, the propagation constant ! and the free-space propagation constant k0 .

Fig. 2.10: TM mode intensity and refractive index of the vertical waveguide for a wavelength of 8.4 µm.

Although the surface plasmon mode at the semiconductor-metal would result in a tight confinement, this is not advised in the MIR (up to !"12 µm) since this would also introduce large waveguide losses. To separate the metal contact from the TM field would require a thick dielectric waveguide, which is impractical. However, since the plasma frequency of semiconductor layers is close to the emitting wavelength, one can 65

Theory make use of plasmon-enhanced layers to decouple the mode from the lossy metal. Fig. 2.10 shows the field distribution of the TM mode in a typical waveguide structure, where the overlap of the TM mode with the active region is 70 %. All waveguides presented below will use a plasmon-enhanced layer. So far, we have only considered the TM mode in planar waveguides. However, the mode is also confined laterally, conventionally by forming a ridge waveguide. The ridge sidewalls are normally passivated (e.g. Si3N4 or SiO2) following the contact layers. Such layers however interfere optical mode resulting in additional absorptions. In order to calculate the field distribution and the propagation constant, the two-dimensional wave equation (2.62) needs to be solved for which the finite-elements software package "COMSOL Multiphysics" was used which can compute the field distribution and the complex propagation constant. Fig. 2.11a shows the electrical field distribution of a ridge waveguide for an emission wavelength of 8.4 µm. The waveguide is surrounded by a thin Si3N4 passivation and gold contact layer.

Fig. 2.11: Simulation of the electrical field distribution of a) a 14 µm-wide conventional ridge waveguide design and b) a 10 µm-wide buried heterostucture waveguide design (using re-grown InP) for an emission wavelength of 8.4 µm.

From the field distribution, one can calculate the overlap factor, integrating now over x any y:

" !=

act $

"

#$

66

2

Ex dxdy 2

E dx dy

(2.67)

Design Parameters The complex propagation constant and the free-space propagation constant are linked by the complex effective index: ! = n!eff k0 , from which one can derive the (real) effective empty = "2k0 #( n!eff ) . In Fig. 2.12, the index neff = !( n!eff ) and the waveguide losses ! WG

computed waveguide losses and the overlap factor as function of the ridge width are shown for an emission wavelength of 8.4 µm. For ridge widths below 15 µm, the waveguide losses strongly increase while the overlap factor decreases. For low power consumption devices, a narrow ridge width is crucial in order to keep the total injected power to a minimum. One possibility to still keep low the waveguide losses is to bury the waveguide in a low absorbing (semiconductor) material with a lower refractive index compared with the active region (see Fig. 2.11b). Fig. 2.12 shows that the waveguide losses increase only marginally which is beneficially, although the overlap factor decreases faster than in the conventional design. However, this waveguide design is technological very demanding since it requires the re-growth of epitaxial material.

Fig. 2.12: Calculation of waveguide losses and overlap factor for an emission wavelength of 8.4 µm for two different waveguide designs.

67

Theory

2.2.3. Thermal point of view Since CW operation is required to reach the goals of this thesis, the thermal point of view is the most critical and demanding. This is because a huge amount of electrical power in the order of 20-50 kW/cm2 within the device must be dissipated, which results in self-heating. Impact of self-heating The self-heating of the QC laser dramatically degrades the laser operation as shown schematically in Fig. 2.13. The temperature affects inter- and intrasubband lifetimes by the Bose-Einstein factor (see Fig. 2.5). Although this is fortunately a weak coupling, the effective upper state lifetime decreases with increasing temperature affecting inversely the threshold current density. The atomic-like joint density of states (neglecting nonparabolicity) is beneficially since this will avoid direct temperature broadening of the linewidth. However, the linewitdh is collision broadened by the ultra-short inter- and intrasubband lifetimes. As already discussed, linewidth broadening has a detrimental effect on the gain cross section and increases the non-resonant intersubband losses, both reduce the threshold current density. Furthermore, the temperature increases the backfilling and consequently the larger non-resonant losses will increase the threshold current density.

Fig. 2.13: Schematic illustration of the positive feedback loop in QC lasers due to self-heating.

This self-heating results in an active region temperature Tact which is in a simple model related to the submount temperature Tsub by a single thermal resistance Rth [in K/W]: 68

Design Parameters

Tact = Tsub + Rth J op Sact !U op

(2.68)

where U op is the operation bias, J op is the operation current density and Sact is the active region area which is the product of laser length L and width wact . As in interband lasers, QC lasers follow the empirical formula for the temperature dependence of the threshold current density: J th = J 0 exp(Tact / T0 ) . The maximum active region temperature can be derived expressing the current density by the empirical threshold current density formula and by setting dTsub / dTact = 0 :

( ! ( !G T $ + $ + T0 Tsub,max = T0 * ln # ' 1- = T0 * ln # th 0 & ' 1& *) " RthU th J 0 Sact % -, *) " U th J 0 % -,

(2.69)

where Gth is the specific thermal conductance [in W/( m2K)]. There are obvious four possibilities to keep Tact close to Tsub : • An active region with a low (pulsed) threshold current density J th • Using an active region design with a large T0 • Reducing the width of the active region wact • Reducing of the thermal resistance Rth The first two items have already been discussed in the previous section: The two-phonon resonance and the bound-to-continuum design are well suited as an active region since both work up to high pulsed operation temperature. For CW operation, the doping has to be kept minimal in order to avoid intersubband losses and self-heating. The bias is defined by the number of cascades, which should be as high as possible (as long as the overlap factor increases linearly with the number of cascades), enabling to reduce the doping. The last two items concern the thermal waveguide design. The total injected power (and the dissipated heat) can be minimized by reducing the waveguide width. This in turn has a positive effect on the thermal conductance (as will be shown later). Finally, the thermal resistance can be reduced by optimization of the waveguide for better heat removal.

69

Theory Thermal waveguide optimization In 1999, Gmachl et al. used a finite-element software package to model the twodimentional isotropic lattice temperature distribution in the waveguide [153]. For the same purpose, we use the finite-elemente software package "COMSOL Multiphysics" to solve Fourier’s law of heat conduction:

(

)

!" # kth"T = Q

(2.70)

where kth is the thermal conductivity [in W/(m ! K)] and Q is the heat source density [in W/m3], which is assumed to be none-zero in the active region only. For the computation, we use the thermal conductivities given in Table 2.1. Table 2.1: Material thermal conductivities used in the heat dissipation model. The weighted average of the thermal conductivities of InGaAs and InAlAs was used for the thermal conductivity of the active region. Material

kth [W/(m ! K)]

InP

74

InGaAs

4.84

Si3N4

15

Au

317

Cu

384

AlN

257

Diamond

1200

In solder

81

SnAu solder

57

Active region

4.72

Fig. 2.14 shows the calculated temperature mappings of the front facet of QC laser devices having the same core structure (see Fig. 2.10), using Si3N4 as passivation layer, but different geometries: either conventional ridge waveguide with a gold top contact (either 0.2 or 4.0 µm thick) or buried heterostructures (BHs) (including a 4 µm thick gold top contact) which are mounted either epi-up or epi-down. The epi-down mounted device was soldered on diamond while the others were soldered to copper mounts. In both cases indium was used as solder. In all four cases, the cavity length is 3 mm, the 70

Design Parameters heat sink temperature is 300 K and the dissipated electrical power is 8.8 W. Due to the poor thermal conductivity of InGaAs compared to InP, InGaAs is restricted to the thin cladding layers surrounding the active region, the plasmon-enhanced layer and the contact layer. Si3N4, which has one order of magnitude higher thermal conductance than SiO2, was used as passivation material. In the conventional ridge waveguide, the heat is primarily removed along the growth direction toward the substrate (see Fig. 2.14a). The lateral heat removal can be improved by surrounding the ridge waveguide with a thick electroplated gold layer (Fig. 2.14b). Another option is the use of buried heterostructures, where the waveguide is buried in e.g. re-grown InP (Fig. 2.14c). This approach has the advantage that devices are planarize allowing for epi-down mounting (Fig. 2.14d), which further reduces the thermal resistance of the device. Fig. 2.15 shows the theoretical thermal resistance calculated using (2.68) as function of ridge width together with experimental data.

Fig. 2.14: Temperature mappings of the front facet of identical QC laser structures (with 12 µm-wide and 3 mm-long waveguides) and an input electrical power of 8.8 W (24.4 kW/cm2). Conventional ridge waveguide with 0.3 µm Si3N4 passivation and 0.2 µm (a) and 4.0 µm (b) top gold. Buried waveguide heterostructure (BH) waveguide design for epi-up (c) and epi-down (d) mounting.

71

Theory The shown experimental thermal resistances were derived from either spectral characteristics, using Rth = !T / !Pel = (!" / !Pel ) # (!" / !T )$1 , or from comparing of threshold current data in CW and pulsed operation. However, those two methods probe different thermal resistances. The threshold method will provide the thermal resistance of the active region while the spectral characteristic method extracts the thermal resistance of the active region and the waveguide. Good agreement has been found with experimental data although only bulk values (no anisotropy) for the thermal conductivity of the active region have been considered in the model. From Fig. 2.15 is becomes clear that a narrow ridge and a buried heterostructure design mounted epi-down is the most efficient way to reduce the thermal resistance of the device. However, the buried heterostructure designs necessitates additional sophisticated regrowth steps and special care has to be taken for avoiding parasitic current leakage in the current blocking layers.

Fig. 2.15: Experimental (markers) and theoretical (lines) data of the thermal resistance for different thermal waveguide designs: (blue) conventional waveguide with thick electroplated gold, (green) buried waveguide design and (red) buried waveguide mounted epi-down on diamond. Thermal resistances have been normalized in order to compare different active regions with area Sact and thickness dact (Rth = Rsp ! dact / Sact ) . The experimental data have been deduced either from the threshold currents (open marker) or spectral characteristics (filled marker).

72

Mode control in QC lasers

2.3. Mode control in QC lasers This section is devoted to mode control in QC lasers, since spectroscopic applications require single-mode sources. First, we consider modes in a Fabry-Pérot cavity. Those modes are determined by the stationary condition:

rf rb exp(2i! L) = 1

(2.71)

where ri = Ri are the reflectivity coefficients and the complex propagation constant comprising gain reads:

! = k0 n!eff = k0 neff " i

GM " # wg

(2.72)

2 The condition on the amplitude of (2.71) gives the threshold modal gain:

GM,th = ! wg +

1 " 1 % ln $ ' L # rf rb &

(2.73)

The phase condition reads:

2k0 neff L = N ! 2"

(2.74)

which gives the possible modes:

!=

2neff L

(2.75)

N where N is the mode index. The spacing between two Fabry-Pérot modes N and N-1, expressed in wavenumbers !" = !( # $1 ) , is:

!" = (2ng L)#1

(2.76)

where the group index ng = neff + ! " #neff / #(! ) takes into account the dispersion on the effective refractive index. For a typical cavity length the mode spacing is in the order of 0.5-2.0 cm-1 and therefore much smaller than the gain spectrum (FWHM of 100300 cm-1). As a consequence, the laser will emit at an unpredictable wavelength or even multi-mode. However, spectroscopy applications require a single mode source which is predictably tunable.

73

Theory

2.3.1. Distributed feedback cavity This section will briefly introduce the coupled-mode theory helpful in understanding the relevance of the coupling coefficient, which has to be properly designed in order to avoid under- and overcoupling. Then, the formalism for computing gratings is presented (including reflections and phase shifts introduced by the end facets), which allows to correlate the grating profile parameters to the coupling strength and finally to compute the cavity losses. Coupled-mode theory Kogelnik and Shank have derived the coupled-wave analysis of distributed feedback lasers [154], which will be presented here with slightly different notations. The modulation of the effective index and the losses in z-direction (propagation direction) induced by a sinusoidal grating reads: ' neff (z) = neff +

!n cos(2"0 z) 2

(2.77)

"! (2.78) cos(2#0 z) 2 where !n and !" are small deviations from the average refractive index and average

! ' (z) = ! +

losses and !0 is the Bragg propagation constant defined as:

!0 =

N " 2" neff = = k0 ( $B )neff # $B

(2.79)

where N characterizes the grating order and !B is the Bragg wavelength. From the last equation, one gets the grating period ! = N "B / (2neff ) . One sees immediately, that the grating period for a first order grating equals half the wavelength in the medium. The scalar wave equation for the electric field neglecting all transverse and lateral variations reads:

d2E + $% !! 2 + i2"!! + 4#!! cos(2!0 z) &' ( E = 0 2 dz

(2.80)

where !! = 2" neff / #0 = k( #0 )neff and the coupling coefficient for the sinusoidal grating reads: 74

Mode control in QC lasers

!=

"#n #% +i 4 2$0

(2.81)

which is a measure of the amount of reflection by unit length. Considering only wavelengths ! close to the Bragg wavelength !B ( !! = !0 + "! where !" ! "0 ), the electric field can be composed of two counterrunning electric fields with the complex amplitudes R(z) and S(z) :

E(z) = R(z)exp(!i"0 z) + S(z)exp(i"0 z)

(2.82)

Inserting (2.82) into (2.80), neglecting second derivatives of R(z) and S(z) and collecting terms with identical phase factors ( exp(!i"0 z) and exp(i!0 z) ) results in the coupledmode equations:

!

dR + (" ! i#$ )R = i% S dz

(2.83)

dS (2.84) + (! " i#$ )S = i% R dz Note that for a vanishing coupling coefficient (! = 0) , those equations are not any more coupled

and

result

in

the

trivial

solution

R(z) = R(0)exp([! " i#$ ]z)

and

S(z) = S(0)exp(![" ! i#$ ]z) and the field is nothing else than a pair of independent plane

waves

propagating

in

+z

and

–z

direction:

E(z) = R(0)exp([! " i#! ]z) + S(0)exp("[! " i#! ]z) . In the original paper, Kogelnik and Shank derived the solution of the coupled-wave equations for the case of anti-reflection coated facets, where the corresponding boundary condition is R(! 12 L) = S( 12 L) = 0 , for a devices spanning between ! 12 L and 1 2

L , which results in the transcendental equation ! = ±i" / sinh(" L) , where the complex

propagation constant ! follows the dispersion relation ! 2 = " 2 + (# $ i%& )2 . Finally, the field amplitudes can be written: R(z) = sinh(![z + 12 L]) and S(z) = ± sinh(![z " 12 L]) .

In general, the coupling coefficient will be complex. However, the gratings used in this work have a negligible loss coupling and the coupling coefficient is assumed to be real. 75

Theory Fig. 2.16 shows the calculation of the amplitudes R(z) and S(z) together with the intensity distribution for a 1.5 mm long cavity and different coupling products ! L . Knowing the complex propagation constant ! , one can use the dispersion relation to calculate the cavity losses ! DFB and the detuning !" for the modes at the stopband edge (see Fig. 2.17).

Fig. 2.16: a) Intensity distribution and b) amplitudes R(z) (solid) and S(z) (dashed) in a 1.5 mm-long DFB-QC laser for different ! L .

Although the device is symmetric and should emit on both modes at the edge of the stopband, in reality a small phase shift at the facets and/or process fluctuations will favor one mode over the other and the device should emit single mode. However, the modes are undercoupled for ! L ! 1 and this will most likely result in multimode operation. On the contrary, overcoupling ( ! L ! 1 ) will lead to gain saturation in the center of the device allowing the mode on the other stopband side to build up in the cavity and the laser will most likely emit bi-mode. In this work, the gratings were designed to result in

76

Mode control in QC lasers

! L " 3 which should not overcouple the device too much but lead to reasonably low cavity losses ! DFB .

Fig. 2.17: Detuning !" and cavity losses ! DFB of the modes at the stopband edge for different coupling products.

Coupling coefficient Loss coupling (e.g. by metal gratings) should be avoided in order to attain a high performance device. As a consequence, the gratings presented in this work are etched in the InGaAs cladding layers, surrounding the active region (see Fig. 2.10), followed by an InP regrowth. The gratings used in this work are rather square gratings (compared with the sinusoidal ones in Kogelnik and Shanks work) and the grating coefficient can be derived in a simple manner (schematically depicted in Fig. 2.18). At the first interface (from high to low index) the reflectance coefficient follows from the Fresnel equation and reads r = !n / 2neff . At the next interface (from low to high index) the Fresnel equation results in !r and so on. When the wavelength is equal to the Bragg wavelength, the phase shift !0 " = # after one roundtrip and the resulting reflections add up in phase. There are two reflections per grating period and the coupling coefficient reads:

!=

2r 1 #n = PF " " neff

(2.85)

77

Theory where the profile factor PF is the ratio of the first-order Fourier AC components of the ideal square grating, with 50 % duty cycle, and the real profile: "/2

PF =

! Profile(z)cos(2! z / ") dx h" # "$/ 2

(2.86)

where h is the grating etching depth. Note, assuming Profile = h / 2 ! cos(2" z / #) results in a profile factor PF = ! / 4 and a coupling product equivalent to the one in equation (2.81).

Fig. 2.18: Periodic modulation of the effective index in a square grating with 50 % duty cycle.

Computing DFB gratings So far only anti-reflection coated devices have been considered. In order to introduce a facet reflectivity and phase-shift, the simplest way is to treat the square grating as stack of alternating layers with different (effective) refractive indices, derived for the etched and unetched waveguide, and using the matrix method with the boundary conditions (2.64) and (2.65) at each interface to plot the transmission (with normal incidence). Facet coatings and phase shifts can be introduced by putting extra layers at the beginning and/or end of the stack. As an example, the transmission spectrum for a 1.5 mm-long device is plotted in Fig. 2.19, which was coated with a high reflectivity coating on one facet and left uncoated on the other side. The spectrum reveals the stopband and the cavity mode spectra around the Bragg resonance. In the next step, one derives the threshold gain for each mode. This can be done by adding gain to the imaginary part of the refractive index of each layer. The threshold gain (which equals 78

Mode control in QC lasers the cavity losses) can be found by successively increasing the gain until the transmission goes to infinity. Fig. 2.19 also shows the cavity losses for each of the cavity modes. While the cavity losses equal the mirror losses (4.46 cm-1) for modes far detuned from the Bragg condition, the losses decrease to 0.6 cm-1 on the right side of the stopband edge, leading to a strong mode discrimination !" between the Bragg mode and the FabryPérot modes.

Fig. 2.19: Transmission spectrum of a 1.5 mm-thick stack of alternating layers with

! =1.3, neff =3.19 and !n =0.01 and a phase shift introduced by reducing the thickness of the high index layer, before the HR coating (gold layer), by 30 %.

Tuning of DFB lasers A good device lases single-mode at the Bragg wavelength !B (T ) = 2neff (T )"(T ) and the wavelength can be shifted by temperature. The direct temperature tuning coefficient reads:

!=

1 d "B 1 dneff 1 d# = + "B dT neff dT # dT

(2.87)

However, the thermal expansion of InP (4.60 x 10-6 K-1) is one order of magnitude smaller than the tuning of the refractive index (~8 x 10-5 K-1), and the second part in (2.87) can be neglected. Indirect temperature tuning can be attained by the injected electrical power which results, due to the large thermal resistance of the device, in heating of the active region: 79

Theory

1 d !B dT 1 d !B = = " Rth !B dPel !B dT dPel

(2.88)

One drawback of a good thermal management is that the indirect temperature tuning coefficient decreases. However, a low thermal resistance allows higher CW operation temperatures and therefore a larger direct temperature range. The mode discrimination !" = " FP # " DFB allows in principle a large tuning range, as long as !" > !g . However, detuning from the gain peak will result in an increase of the threshold current density J th ( ! ) = J th ( !P ) " gd ( !P ) / gd ( ! ) , which requires some dynamic range (J max ! J th ) / J th for tuning. Therefore, the gain spectrum should be designed to peak closely to the Bragg resonance.

Fig. 2.20: Schematic illustration of gain g( ! ) and cavity losses ! ( " ) in a DFB laser.

2.3.2. External cavity feedback The Littrow and the Littman-Metcalf configurations are the most common external cavity configurations [118]. In order to achieve the broadest possible coarse tuning range, the Littrow configuration is selected, where the light is reflected only once by the grating providing a stronger feedback. The schematic configuration is shown in Fig. 2.21 where the zeroth order is extracted and the first-order diffracted beam is fed back into the QC laser cavity. Similar to (2.71), the stationary condition for the EC modes reads: 80

Mode control in QC lasers

rEC (! g , " ) # rb exp(2i$ L) = 1

(2.89)

where the reflectance coefficient of the external cavity (assuming zero reflectivity of the front facet) [155] reads:

rEC (! g , " ) = TL

% f 2 ( " # "g )2 ( RG exp ' # * 2 2 2 '& 2Wx $ cos ! g *)

(2.90)

where ! g is the grating selected wavelength, TL is the transmission of the lens, RG is the reflectivity of the grating, f is the distance between the laser and the grating, Wx is the width of the nearfield (calculated from the farfield angle tan ! 1 " 0.187 # $ / Wx ). Note, 2

that the last equation is derived for an ideal (diffraction limited) lens (otherwise, the spot size of the reflected beam is larger and the reflectance coefficient is reduced).

Fig. 2.21: Schematic illustration of an external cavity in Littrow configuration.

The condition on the amplitude results in the threshold modal gain:

GM,th = ! wg +

( 1 % 1 ln ' * L & rEC (" g , # ) $ rb )

(2.91)

The phase condition takes into account the phase of the reflectance coefficient:

2k0 neff L + arg #$ rEC (! g , " ) %& = N ' 2(

(2.92)

81

Theory For wavelengths far from !g , the reflectance coefficient of the external cavity rEC vanishes compared to the one of the (residual) front facet r f and results in the threshold modal gain (2.73) and mode spacing (2.74) of the Fabry-Pérot case. However, for wavelengths close to !g , rEC does not vanish and results in the threshold modal gain:

GM = ! wg +

1 " 1 % ln $ AR ' 2L # REC Rb &

(2.93)

The phase arg #$ rEC (! g , " ) %& ' 2ik0 LEC results in the mode spacing of the external cavity: !" =

1 2(Lneff + LEC )

(2.94)

Tuning of an EC laser Tuning in an external cavity setup is achieved by rotating the grating. The reflectance angles in respect to the incidence angle for various grating orders N are related as follows:

N" (2.95) # where ! is the grating period. The feedback in the Littrow configuration is maximal sin ! i + sin ! r , N =

when incident and reflected beam are collinear resulting in the grating selected wavelength:

!g = 2" sin # g

(2.96)

The tuning range is limited by the mode discrimination between Fabry-Pérot modes and the EC modes. Therefore, single mode tuning will be possible as long as the ratio of AR AR / " FP differential gain gd ( ! ) / gd ( !p ) " # , where ! = " EC (see Fig. 2.20) represents the

ratio of the total losses AR tot ! EC = ! wg "

with, and 82

(

1 AR HR ln REC Rb 2L

)

(2.97)

Mode control in QC lasers

(

)

1 (2.98) AR HR ln RFP Rb 2L without the feedback of the EC of the anti-reflection (AR) coated laser. A high ! AR tot ! FP = ! wg "

requires both, a good anti-reflection broadband coating on the front facet and a large AR REC . Even more important is to use an active region design with a relatively wide gain

media which is at the same time flat on the top of the spectrum.

83

Chapter 3 3. Technology 3.1. Introduction The achievements of this work are largely based on mastering the technology. In this chapter, the technology for device fabrication will be presented, carried out in ETH’s FIRST Center for Micro- and Nanoscience laboratory. MBE growth initially was done at the University of Neuchâtel and later at ETH. In this section, a brief overview will be given on epitaxial growth, standard processing and assembly of QC lasers. In the following section, the fabrication of buried (multi-wavelength) distributed feedback gratings is discussed. In advanced waveguide etching I, a procedure for etching of narrow waveguides is presented. In the following section, different blocking materials for lateral current confinement in buried heterostructures are investigated. The technology for burying waveguides in semi-insulating InP:Fe is shown, followed by a description on how such buried heterostructures can be mounted epi-down. Finally, in advanced waveguide etching II the waveguide etching procedure was further developed to end up with groove-free and mostly defect-free buried heterostructures.

3.1.1. Epitaxial growth The active region, composed of several hundred of layers of alternating InGaAs/InAlAs layers (each a few Angstroms thick), and the surrounding InGaAs cladding layers were grown by a VG V80H (Oxford Instruments) MBE system on low doped 2-inch InP substrates. The tool is equipped with As, Ga, Al, In and Si sources. Si was used as dopant of the active region. For homogeneous heat distribution, the wafer (or a quarter of a wafer) was mounted with In on the sample holder. The growth temperature of

Introduction ~530 °C ensured a sticking coefficient of nearly unity of the group-III component. The growth rate in the ultra-high vacuum (base pressure of 10-10-10-11 mbar), determined by the group-III flux, was normally ~1 µm/h. The MBE growth was carried out by Dr. Mattias Beck, Dr. Marcella Giovannini, Nicolas Hoyler and Milan Fischer. The much thicker planar waveguiding and contact layers (InP, InGaAs and InGaAsP) were grown by low pressure MOVPE (AIXTRON AIX 200/4). The metal organics Trimethylgallium Ga(CH 3 )3 and Trimethylindium In(CH 3 )3 are used as group-III element sources, which are transported into the horizontal reactor at 160 mbar using H 2 as carrier gas. The hydrides AsH 3 and PH 3 are used as group-V element sources and

SiH 4 is utilized as source for the n-type Si doping. The growth rate at a temperature of 630 °C was ~1.5-2.0 µm/h. Two 15 nm thick InGaAsP layers whose band-gaps correspond to photoluminescence maxima of 1.1 and 1.28 µm, respectively, were used for smoothing the conduction band offset between InP and InGaAs. The MOVPE growth was carried out by Martin Ebnöther and Dr. Emilio Gini. It is worth mentioning that any p-doping is highly unwanted in the unipolar QC laser since based on experience [156], it strongly reduces the efficiency of the laser, which might be due to impurity scattering. An analysis of MOVPE-grown undoped InP, using low temperature photoluminescence, revealed peaks that have been assigned to the incorporation of Zn (green curve in Fig. 3.1), which acts as p-doping. This was confirmed by a SuperSIMS measurement, carried out by Dr. Döbeli at the Institute of Particle Physics, ETH Zurich, which revealed an average Zn concentration of 4 x 1014 cm-3. As the quartz liner is by default cleaned before each run, using aqua regia, the origin for Zn was suspected in the susceptor and disk, which are also used by other groups in the FIRST laboratory. The red curve in Fig. 3.1 was measured from an undoped InP sample that was grown using a new disk and susceptor. Not only the peaks corresponding to Zn have disappeared but also a much stronger intensity of the exciton is observed. Since Zn has a very long memory effect, a new disk and susceptor unit, which were dedicated to the growth of n-doped material, were used for the samples shown in this thesis. 85

Technology

Fig. 3.1: Low temperature photoluminescence of intentionally non-doped InP grown by MOVPE on a common (P723) or dedicated (P771) susceptor and disk. Peaks have been assigned to reference values from [157].

3.1.2. Processing and assembly The conventional QC laser processing is sketched in Fig. 3.2. When no gratings are required, the processing starts after the MOVPE growth of the waveguide and contact layers. The ridge mask is defined using positive resist and a contact printing mask aligner (Karl

Süss

MA6).

Afterward,

the

ridges

are

etched

using

HBr(38 %):HNO3(65 %):H2O(100 %) (1:1:10). The waveguides are passivated with Si3N4 in a PECVD (plasma enhanced chemical vapor deposition) tool (Oxford Instruments 80+). Opening of the contact window was done using positive resist and etching with CHF3/O2 in a RIE (reactive ion etching) tool (Oxford Instruments RIE 80+). In the next step, the contact was evaporated in two runs using negative resist and an e-gun evaporator (Leybold Univex 500). First, the top contact (see Fig. 3.2e) consisting of Ti/Pt/Au (30/40/100 nm) was evaporated and in a second run, the extended contact (interconnected with each other) using Ti/Au (40/150 nm). The last gold evaporation serves as seed layer for a 4 µm-thick electroplated Au layer. After etching of the interconnections between different lasers the substrate was lapped down to 150 µm (Logitec PM5). Finally, either a Ti/Pt/Au (30/40/100 nm) contact or a Ge/Au/Ni/Au 86

Introduction (18/48/15/150 nm) alloyed contact was evaporated on the backside. Cleaved lasers were soldered with a precision die bonder (Cammax EDB80-P) to copper mounts using In and then wire bonded (Westbond 747677E). HR coatings (Al2O3/Au) were evaporated in an e-gun evaporator (Leybold Univex 450). Fig. 3.3 shows the front facet of a finished QC laser.

Fig. 3.2: Schematic illustration of the conventional QC laser fabrication process.

Fig. 3.3: Scanning electron microscope (SEM) picture of the waveguide profile of a conventional processed QC laser showing a large tail of the active region.

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3.2. Buried distributed feedback gratings The DFB gratings were etched into the InGaAs cladding layers surrounding the active region, which were then overgrown with InP. In contrast to previously holographically fabricated gratings, standard photolithography was used. This allows for placing several fields with different gratings on the same piece of epi-material. However, special care has to be taken for the cleanliness of sample, resist and mask. Gratings were fabricated using a thin positive resist (AZ 1505) and a contact printing mask aligner (Karl Süss MA6) applying low vacuum between mask and sample. The gratings

were

transferred

into

the

semiconductor

by

etching

with

H3PO4(85 %)H2O:H2O2(30 %) (1:5:1) at a temperature of 0 °C. The photolithography was slightly underdeveloped in order to compensate the underetching of the mask and to end up with a duty cycle as close to 50 % as possible. Fig. 3.4 shows an AFM picture of a grating (with period ! =1.270 µm) that was etched 168 nm into the InGaAs layer. After removal of the resist and proper cleaning, the samples were immediately loaded into the MOVPE system and the top waveguide was grown. Fig. 3.5 is an optical microscopy picture that shows an excellent regrowth topography and low defect density.

Fig. 3.4: Atomic force microscope (AFM) picture of a distributed feedback grating.

88

Advanced waveguide etching I

Fig. 3.5: Optical microscope picture of a distributed feedback grating that was overgrown with 2.6 µm InP and 300 nm InGaAs.

3.3. Advanced waveguide etching I As seen in Fig. 3.3, the active region (marked with a dashed line) shows a large difference between the top and bottom width. This results in inhomogeneities in the inversion density of different cascades, which might degrade the laser performance. Furthermore, the large tail defines the minimal ridge width. However, narrow ridge waveguides would strongly reduce the injected power and result in less self-heating of the device. In order to improve the ridge profile, a new procedure for waveguide etching has been developed during this work, schematically shown in Fig. 3.6.

Fig. 3.6: Schematic illustration of advanced waveguide etching I.

89

Technology In this procedure, the waveguide layers InGaAs(P) and InP are etched selectively. For this purpose, a SiO2 mask is preferred over photoresist, since underetching is strongly reduced, resulting in much smoother ridge profiles. After deposition of 300 nm SiO2 in the PECVD tool, the waveguide structure, oriented in the [011]-direction, is defined onto the oxide using positive resist, and transferred to the oxide using CHF3/Ar in the RIE system. In the first step, the InGaAs(P) layers are etched selectively using H3PO4(85 %):H2O:H2O2(30 %) (1:1:1) at a temperature of 0 °C, with InP acting as etch stop layer (see Fig. 3.6d). In the next step, InP is etched selectively using CH3COOH:HCl(32 %) (3:1) at room temperature, with InGaAs acting as mask. The SEM picture in Fig. 3.7 shows that the etching procedure results in steep ridge sidewalls with a slightly negative angle and stops onto the InGaAs cladding layers surrounding the active region.

Fig. 3.7: SEM picture of the waveguide after selective wet etching of InGaAs/InGaAsP and InP.

The etching of the active region is performed using the non-selective etching CH3COOH:HCl(32 %):H2O2 (30 %) (5:5:1) at a temperature of 0 °C. Further device processing and assembly is identical to the one descripted in section 3.1.2. Fig. 3.8 shows the SEM picture of such a device. The tail of the active region could be significantly reduced compared to conventional waveguide etching (shown in Fig. 3.3). Using this waveguide etching procedure in combination with a 4 µm-thick electroplated gold on top

90

Buried heterostructures of the ridge resulted in very low thermal resistances (see Fig. 2.15). Devices processed this way are presented in a subsequent chapter.

Fig. 3.8: SEM picture of a device that was fabricated using the advanced waveguide etching I procedure, with thick electroplated Au on top.

3.4. Buried heterostructures The buried heterostructure design requires the selective growth of epitaxial material without creating leakage channels. Fig. 3.9 shows a schematic illustration of the device where the arrows indicate the unwanted current paths.

Fig. 3.9: Schematic illustration of the buried heterostructure design. The arrows indicate possible leakage through the blocking layers that must be suppressed.

91

Technology However, if one is able to master the buried heterostructure technology, the advantages are: • a low thermal resistance of the device • low waveguide losses • possibility of epi-down mounting which further reduces the thermal resistance • better uniformity for optical coatings on the facets

3.4.1. Investigation of epitaxial blocking layers In the first buried QC laser, the waveguide was buried in undoped InP (i-InP) [158]. The parasitic current path, indicated by the arrows in Fig. 3.9, presents an n-i-n structure in which space-charge-limited current is the main conduction mechanism. The essential difference between a metal-semiconductor contact and an n-i-n structure is that in the former case, the barrier is fixed in space, whereas in the latter the barrier (mainly formed by a mobile charge injected into the i-region) moves toward the emitter contact with increasing current. Grinberg and Luryi presented a parametric model for calculating the IV characteristic of symmetric n-i-n structures [159]. The main assumption in their model is a constant value of the quasi-Fermi level in the n-regions and that the entire charge in the i-region is due to mobile carriers, injected from the doped n-regions. That means that they are neglecting both the fixed charge due to background doping and the mobile charge thermally generated across the forbidden gap. For high current densities and a large width w of the i-region (high current limit), their model goes over into the Mott-Gurney law (which simply ignores the field distribution in the i-region and the diffusion of injected carriers) and the current density reads:

J high = 9 µ!! 0U 2 / (32" w3 ) where µ is the mobility in the i-region. For the low current limit,

they

derived

an

equation

which

describes

the

linear

IV

regime:

2

J low = 2! 2 µ"" 0 kTU / (qw3[1 + #]) where ! = 2 3 w"1 (# 0# kT ) / (4$ q 2 N D ) exp(0.5) , where N D is the doping of the n-regions. Fig. 3.10 shows the computation of an n-i-n structure as function of applied bias for different i-region widths, where the n-regions are doped 1 x 1017 cm-3. For a 2 µm-wide i-region at a bias of 9 V (the typical operation bias of a QC

92

Buried heterostructures laser), this results in a current density of ~4 kA/cm2, which is 3-4 times higher than the typical pulsed threshold current density of a QC laser.

Fig. 3.10: Experimental data of the n-i-n structure with a 2 µm-wide i-region and theoretical approximations of the parametric IV for different widths of the intrinsic region.

In order to prove their theory, a test structure, consisting of a simple n-i-n structure, has been processed into mesas. The nominal layer thicknesses and doping levels are given in the figure caption of Fig. 3.11. The IV of the structure is shown in Fig. 3.10 (solid line). Within the uncertainty of the exact layer thickness of the i-region and considering the assumptions made in the model, reasonable agreement is found between model and experiment.

Fig. 3.11: Schematic illustration of the n-i-n teststructure. The growth started on a ~350 µm-thick InP substrate (~1-2 x 1017 cm-3), followed by the 2 µm-thick i-InP. The top contact consists of 100 nm InP (2 x 1018 cm-3) and 50 nm InGaAs (2 x 1019 cm-3). Ti/Pt/Au contacts were evaporated on the top and bottom.

93

Technology As demonstrated, i-InP is inappropriate for proper current confinement in buried heterostructures. In the framework of this thesis, two approaches have been investigated to reduce this parasitic current path. Since the space-charge-limited current is proportional to the mobility, which is actually relatively high in undoped materials (iInP: 3000 cm2V-1s-1 at room temperature), one strategy targets on reducing the mobility by inserting InAlAs barriers within the i-InP. Another possibility that we investigated is to use Iron-doped InP where the Iron acts as deep level defect (which pins the Fermi level near the middle of the band-gap) that cancels the net charge. The use of p-n-p-n blocking layers would have been another option but as already discussed, p-doping is not welcome in QC lasers and furthermore, a lower capacitance is expected in InP:Fe buried heterostructures that would enable higher modulation bandwidths. In order to evaluate the Fe-doping level in InP, a Si-doped compensation structure was grown, consisting of three sections, where two sections (each 300 nm thick) were doped with different Fe concentrations. Fig. 3.12 shows the effective doping profile of the structure, measured with a CV-profiler (Dage CVP 21). The derived Fe-doping levels are indicated.

Fig. 3.12: Effective doping level in a compensation structure that was grown on a doped InP wafer. All sections are doped with the same amount of Si. In addition, sections A and B are doped with two different amounts of Fe-doping.

94

Buried heterostructures Fig. 3.13 shows schematically the test structures that have been fabricated for evaluating the blocking characteristics. The detailed layer sequences are given in the figure caption.

Fig. 3.13: Schematic illustration of the blocking layer test structures. The growth started on a ~350 µm-thick InP substrate (doped ~1-2 x 1017 cm-3), followed by the blocking layer. The top contact consists of 100 nm-thick InP (Si, 2 x 1018 cm-3) and 50 nm-thick InGaAs (Si, 2 x 1019 cm-3). Ti/Pt/Au contacts were evaporated on the top and bottom. The blocking layer consists of a) 2 µm-thick InP (Fe, 3 x 1016 cm-3) and b) 8 stacks of 200 nm i-InP and 20 nm i-InAlAs followed by a layer of 200 nm iInP.

As seen in Fig. 3.14, introducing of InAlAs blocking layers has significantly reduced the leakage current density, compared with i-InP without blocking layers. The space-chargelimited current could be further reduced by using semi-insulating InP:Fe. The temperature dependence of the space-charge-limited current is shown in the Arrhenius plot depicted in Fig. 3.15. The examined temperature range is typical for the core temperature of a CW operated QC laser. Although the space-charge-limited current increases in InP:Fe over approximately two orders of magnitude more compared to iInP with InAlAs barriers, its absolute values at high temperature are still two orders of magnitude lower. Although one could have inserted more InAlAs blocking layers in i-InP, we decided to use semi-insulating InP:Fe since it would show a lower capacitance, and less problems in the regrowth on non-planar structures are expected (current channels along the ridge). Furthermore, the trapping of carriers should also result in less free-carrier absorption. 95

Technology

Fig. 3.14: IV of the test structures using i-InP, InP:Fe and i-InP with 8 InAlAs barriers as blocking layers.

Fig. 3.15: Arrhenius plot of i-InP with 8 InAlAs barriers and InP:Fe. An activation energy of 588 meV and 289 meV was extracted for Fe and AlInAs, respectively.

3.4.2. Selective growth on non-planar structures Selective growth means the restriction of the growth to semiconductor surfaces that are confined with a mask on which no growth is possible. Fortunately, the MOVPE growth characteristics for selective epitaxy are very similar to those on planar surfaces. However, the shape and orientation of mask and waveguide profile will strongly 96

Buried heterostructures influence the shape of the regrowth, which depends not only on the growth conditions (III/V-ratio, partial pressures and temperature) but also on the exposed crystallographic orientation that exhibit different growth rates and the possibility of surface migration. The requirement on the mask material is that no growth should happen at typical epitaxial growth temperatures. Furthermore, a good temperature stability and good adhesion on the semiconductor is required. Commonly, amorphous materials like Si3N4 and SiO2 are used as mask material. The growth conditions need to be chosen in such a way that desorption of precursors happens before the formation of nucleuses. In order to avoid the latter, a proper cleaning of the mask prior to the selective regrowth is very important. The masked area will influence the vertical growth rate which will increase, because the masking reduces the effective semiconductor surface. Since the growth proceeds not only vertically but also laterally, an important parameter is the overhang of the mask. Too small an overhang will favor lateral overgrowth of the mask but too much overhang will lead to an orifice between mask and regrown material, because the diffusion of precursors is limited resulting in a reduced growth rate, and as a consequence, in the formation of void. This would be undesirable for epi-down mounting.

Fig. 3.16: Schematics for the preparation of the sample for selective regrowth.

The fabrication of the SiO2 mask and the waveguide etching procedure is similar to the procedure described in the section 3.3, however, the thickness of the mask was increased to 400 nm which allows deeper underetching of the mask. The waveguide etching is 97

Technology tuned to end up with an overhang of 5-6 µm on each side of the ridge by increasing the selective underetching of InGaAs. The structure prior to the regrowth with InP:Fe is schematically shown in Fig. 3.16. Regrowth of InP:Fe was performed at a total pressure of 160 mbar, a V/III ratio of 66 and a temperature of 630 °C. Ferrocence (CP2Fe) was used as precursor for Fe doping (6 x 1016 cm-3). After regrowth, the device was passivated with Si3N4 in order to avoid possible leakage paths through defects, and a small window was opened on top of the ridge. An SEM picture of the finalized device is shown in Fig. 3.17. The thermal resistances of such buried structures are shown in the Fig. 2.15.

Fig. 3.17: SEM picture of a QC laser facet in buried heterostructure fashion. The dashed lines indicate the active region and the regrown blocking regions.

3.5. Epi-side down mounting As already pointed out, one of the advantages of the buried heterostructure design is its possibility to end up with planarized waveguides that are suited for epi-down mounting. Special care has to be taken to avoid shortening the device with the solder. For this reason, a 3-4 µm thick Au layer is electroplated on top of the device; its function is not only to spread the heat but also to act as spacer. In the first step, devices were soldered to submounts which were in a subsequent step mounted to copper mounts. Furthermore, the solder was deposited on the submount prior to mounting. Evaporated In is used as solder for mounting devices on diamond since it relaxes the requirement of having similar thermal expansion coefficients. SnAu eutectic solder is used for mounting on 98

Advanced waveguide etching II AlN. Fig. 3.18 depicts the thermal resistance versus temperature of a 9.5 µm-wide and 3 mm-long epi-down on diamond mounted QC laser. At 303 K, the device shows a thermal resistance (extracted from CW and pulsed threshold current values) of 4.28 K/W that equals a thermal conductivity of 820 W/(Kcm2). Surprisingly good agreement with theoretical values are achieved (see Fig. 2.15).

Fig. 3.18: Experimental data of the thermal resistance versus temperature of a 9.5 µm-wide and 3 mm-long epi-down on diamond mounted QC laser. Shown are the values for the uncoated and HR-coated device.

3.6. Advanced waveguide etching II The discussed waveguide etching procedure is well suited for conventional (non-buried) device fabrication. However, combining this etching procedure with the buried heterostructure design will result in non-planarized devices, showing a groove on both sides of the waveguide (see Fig. 3.17). Such a regrowth behavior was never observed in conventionally etched waveguides. These grooves may not only accumulate residuals of resist or other processing chemicals, possibly degrading the lifetime of the device, but can also reduce the heat flow out of the active region. The origins of the grooves were studied in a separate experiment in which a step (in [110] direction) was etched into InP pior to the regrowth (dashed line in Fig. 3.19). The 99

Technology regrowth consisted of InP:Fe (6 x 1016 cm-3) with 2 nm thick InAsP markers to study the growth behavior, which were spaced by 600 nm. In fact, the grooves, seen after the overgrowth of the QC laser structure, are also present after the regrowth of this simple geometry in InP. We believe that the slightly negative angle of the sidewalls in InP (caused by the selective etching) is responsible for the growth behavior since different crystallographic orientations exhibit different growth rates. Unfortunately, the exact growth behavior is not clear since the markers are not seen in the [111] direction, which might be due to a reduced sticking coefficient of the marker material along this growth direction.

Fig. 3.19: SEM picture showing the regrowth behavior on a step in InP (dashed line), oriented in [110] direction. The second groove on the very left side is the result of another etching step which is not shown.

Obviously, the etching of the active region with the non-selective etching CH3COOH:HCl:H2O2 (used to etch the active region after selective InP etching) is not sufficient enough to remove the negative angle in InP. A more isotropic etching is the HBr:HNO3:H2O etchant solution which removes all negative angles at the waveguide sidewalls when used for etching the active region. Regrowing InP:Fe on top of this resulted in a groove-free buried heterostructure (see Fig. 3.20).

100

Advanced waveguide etching II

Fig. 3.20: SEM picture of the buried QC laser structure shows no grooves.

However, lots of defects appeared after the regrowth (see Fig. 3.20 and Fig. 3.21). Since these defects are mainly located on and along the mask (which purpose is to prevent the growth), it is assumed that residual Bromine complexes contaminate the mask, preventing desorption and resulting in the formation of clusters (defects). As a consequence, further processing is almost impossible and devices will most likely suffer from high waveguide losses. In order to drastically reduce the defect density, an experiment with different cleaning procedures has been conducted. A full wafer, on which an active region and a waveguide have been grown, was cleaved in four quarters. After masking with SiO2, InGaAs(P) and InP was etched selectively followed by a mask cleaning according to Table 2.1. Subsequent, all samples were regrown in the same MOVPE run using InP:Fe.

Fig. 3.21: Microscope images revealing a large number of defects on and along the alignment figures and ridges.

101

Technology Table 3.1: List of active region etching and mask clean solutions (RT=room temperature). In all experiments InGaAs(P) and InP were etched selectively. Experiment:

Active region etching:

Cleaning solution:

A

CH3COOH:HCl:H2O2 (5:5:1), RT

-

B

HBr:HNO3:H2O (1:1:10), RT

H2SO4 (95 %), RT, 1 min

C

HBr:HNO3:H2O (1:1:10), RT

HCl:H2O (1:2), RT, 5 min

D

HBr:HNO3:H2O (1:1:10), RT

CH3COOH:HCl:H2O2 (5:5:1), 0 °C, 1 min

In experiment A, CH3COOH:HCl:H2O2 was used for etching the active region but now at room temperature, which should result in a more isotropic etching resulting in a positve angle in InP. In the experiments B, C and D, different acids were tried for cleaning the mask after etching the active region with the Bromine etchant. While H2SO4 and HCl:H2O (1:2) should not cause any additional etching of the waveguide, CH3COOH:HCl:H2O2 at 0 °C will etch ~0.5 µm, however, the positive angle of the sidewalls should be retained. Fig. 3.22 illustrates the defect density on the ridges after regrowth. Using CH3COOH:HCl:H2O2 at room temperature for etching the active region resulted in inhomogeneous underetching of the mask leading to rough sidewalls and a large number of defects (mainly beside the mask). This might be the result of the extremely high activity of the etchant at room temperature. Experiment B shows an even higher defect density on the ridges than without cleaning, disqualifying this cleaning procedure. In contrast, experiments C and D reveal defect-free masks demonstrating the efficiency of the cleaning. Fig. 3.23 reveals that using CH3COOH:HCl:H2O2 at room temperature still results in grooves after the regrowth (experiment A). The SEM picture for experiment B shows that most of the regrowth material was deposited on top of the mask resulting in a very low growth rate around the ridge. Astonishingly, experiment C resulted again in grooves which leads to the assumption that diluted HCl still etches InP (reshaping the negative angle in InP). Fortunately, experiment D resulted in the desired regrowth behavior.

102

Advanced waveguide etching II

Fig. 3.22: Microscope pictures show the defect density on the regrown waveguides.

Fig. 3.23: SEM pictures of the front facet of buried QC laser structure after different cleaning attempts. The arrows indicate grooves.

103

Technology In summary, selective etching of InGaAs(P) and InP combined with the Bromine containing acid for etching the active region and CH3COOH:HCl:H2O2 for the mask cleaning results in groove-free and almost defect-free buried heterostructure QC lasers. Fig. 3.24 shows the front facet of a QC laser where the ridge width is as narrow as 3.5 µm.

Fig. 3.24: SEM picture of a QC laser front facet showing a width of the active region of 3.5 µm.

104

Chapter 4 4. Two-phonon resonance versus bound-tocontinuum design 4.1. Introduction As already discussed, the two-phonon resonance and the bound-to-continuum design are the most promising active region designs for high performance. In this chapter, their performances will be compared utilizing otherwise identical devices. One goal of this work was to investigate the gain spectrum of those two designs. Therefore, the intersubband linewidth was measured at different bias voltages and temperatures. Differential gain, waveguide losses, threshold current densities and slope efficiencies of lasing devices are compared. Furthermore, since both designs show completely different linewidths, these experimental data are used to validate the model for the intersubband linewidth, presented in section 2.1.4.

4.2. Design and experiment The active region band structures are depicted in Fig. 4.1, both tailored for emission at 8.4 µm. The active regions (consisting of 35 cascades) were grown on low doped substrates (1-2 x 1017 cm-3) in subsequent runs in the MBE system, sandwiched between a lower 220 nm and an upper 310 nm thick InGaAs layer (6 x 1016 cm-3). The exact layer sequences and the doping profiles are given in the figure caption of Fig. 4.1. X-ray measurement revealed 5.9 % thicker layers than designed for the bound-to-continuum type, which was considered in following calculations. Subsequently, the samples were overgrown in the MOVPE system. The waveguide consists of a 4 µm thick InP layer (Si,

Two-phonon resonance versus bound-to-continuum design 1 x 1017 cm-3), two 15 nm thick quaternary InGaAsP layers (Si, 1 x 1018 cm-3), with band gaps corresponding to photoluminescence maxima of 1.1 and 1.28 µm, respectively, and a 300 nm thick plasmon-enhanced layer (Si, 9 x 1018 cm-3). The growth was terminated by a 50 nm thick contact layer (Si, 2 x 1019 cm-3). Ridges 8.5 to 11.5 µm wide were then wet-etched and subsequently buried with InP:Fe. After passivation with Si3N4, a window was etched on top of the ridge. After contact evaporation, a 3 µm thick layer of gold was electroplated on the top. Finally, devices were cleaved, soldered with In to copper mounts, and wire bonded.

Fig. 4.1: Bandstructure and the moduli squared of the relevant wave functions for one out of Np=35 cascades under an applied electric field of 33 kV/cm. The layer sequence of one active cell, given in nanometers and starting from the injector barrier of a) the two-phonon resonance design is 4.3/ 1.7/ 0.9/ 5.4/ 1.1/ 5.3/ 1.2/ 4.7/ 2.2*/ 4.3/ 1.5/ 3.8/ 1.6/ 3.4/ 1.8/ 3.0/ 2.1/2.8/ 2.5/ 2.7/ 3.2/ 2.7/ 3.6/ 2.5 and b) the bound-to-continuum design is 4.4/ 1.7/ 0.9/ 5.3/ 1.1/ 5.2/ 1.2/ 4.7/ 1.3*/ 4.2/ 1.5/ 3.9/ 1.6/ 3.4/ 1.8/ 3.1/ 2.1/2.8/ 2.5/ 2.7/ 3.2/ 2.7/ 3.6/ 2.5, where InAlAs barriers are in bold face, InGaAs wells are shown in normal face, numbers underlined correspond to the n-doped layers (Si, 1.5 x 1017 cm!3), and the asterisk denotes the extraction barrier.

106

Intersubband linewidth

4.3. Intersubband linewidth Electroluminescence was measured using a fourier-transform infrared spectrometer (Nicolet 860) together with a LN2 cooled MCT detector (EG&G J15D16-M208-S250U06) in step-scan mode and a lock-in amplifier (EG & G Instruments 7265). In order to avoid superluminescence, very short lasers (~170-230 nm) were cleaved, and the spontaneous emission was measured perpendicular to the waveguide. The FWHM of the linewidths for both designs are shown in Fig. 4.2. The linewidths broaden with increasing temperature. The bound-to-continuum design shows wider gain spectra; however, there is a marked narrowing of the linewidth with increasing bias, leading to widths comparable to the two-phonon resonance design at high bias.

Fig. 4.2: Theoretical and experimental linewidths vs bias voltage at different temperatures of a) the two-phonon resonance and b) the bound-to-continuum design.

Fig. 4.3a shows the measured spectra of the two-phonon resonance design at 303 K. The broad peak centered around 220 meV indicates injection from the ground state |g! into the second upper state |13!. This peak is also present in the bound-to-continuum design since both structures have an almost identical injector design. Applying equations (2.43)107

Two-phonon resonance versus bound-to-continuum design (2.47) to the experimental data at 8 V of the two-phonon resonance design, an interface roughness parameter product !" =0.973 nm2 for the growth of InGaAs/InAlAs layers in our MBE system is found, which is close to the one extracted in an earlier experiment (1.01 nm2) [142]. Using this parameter, the theoretical luminescence spectra were computed, which are shown in Fig. 4.3b. Comparison of theoretical and experimental curves indicates reduced injection efficiency at biases below 7 V.

Fig. 4.3: a) Experimental and b) theoretical lineshape at different bias voltages of the two-phonon resonance design.

The model was also applied to the bound-to-continuum data (using the interface roughness parameter product derived for the two-phonon resonance design). The calculated linewidths for both designs are shown in Fig. 4.2. In Fig. 4.4, the different contributions to the bias dependent linewidth are shown for a temperature of 303 K. Intra- and intersubband linewidth broadening is shown in Fig. 4.4a, which contributes ~5.3-5.8 meV to the linewidth and is dominated by intrasubband broadening. Interface roughness broadening of the different transitions (see Fig. 4.4b) shows a strong bias dependence. The different contributions to the linewidth are weighted by the oscillator strength depicted in Fig. 4.4c. The marked narrowing of the linewidth with increasing bias voltage in the bound-to-continuum design is explained by the number of states (with 108

Intersubband linewidth different transition energies Eij) over which the oscillator strength spreads (|11!, |10!, |9! and |8!), which decreases with increasing bias and finally is concentrated on the |11! state. In the two-phonon resonance design, the oscillator strength is mainly distributed over two transitions and we observe a narrowing with increasing bias because the active region is still coupled to the injector region. Since the temperature dependence of the interface roughness scattering is very weak, the dominating temperature broadening mechanism in MIR QC lasers is intrasubband lifetime broadening (Fig. 4.2).

Fig. 4.4: Theoretical calculation of a) lifetime broadening, b) interface roughness broadening and c) oscillator strength vs bias voltage for different transitions of the two-phonon resonance (left side) and bound-to-continuum design (right side) at 303 K.

109

Two-phonon resonance versus bound-to-continuum design

4.4. Laser performance For a fair comparison, two 3 mm-long lasers with identical ridge width (10.1 µm) were selected. In order to derive the resonant and non-resonant waveguide losses, the devices were measured before and after HR coating of the back facet.

4.4.1. Pulsed and CW laser characteristics Using a pulse generator (Agilent 8114A), the devices were first measured with 200 ns wide pulses and a repetition frequency of 99 kHz. Fig. 4.5 shows Light-Current-Voltage (LIV)-curves of both (HR coated) devices at different temperature, measured with a calibrated thermopile detector (Ophir Optronics 3A-SH).

Fig. 4.5: LIV-curves of the two-phonon resonance (solid line) and the bound-tocontinuum (dashed) QC laser measured in pulsed operation (200 ns, 99 kHz) for different temperatures. The setups’ collection efficiency of 74 % is not corrected in this plot.

Astonishingly, the laser characteristics of the two designs are very comparable. Although, based on the linewidth measurement, one would expect much higher threshold current densities, the bound-to-continuum designs shows only marginally larger values compared to the two-phonon resonance design. Fig. 4.6 shows the LIVcurves in CW operation measured with a dc laser driver (ILX Lightwave LDX-3232). 110

Laser performance These devices are lasing CW up to a temperature of 70 °C (bound-to-continuum) and 80 °C (two-phonon resonance), respectively. From CW and pulsed threshold current data, a thermal resistance of 8.8 and 9.0 K/W, which equals a thermal conductivity of 375 and 376 W/(Kcm2), was extracted for the bound-to-continuum and two-phonon resonance device, respectively.

Fig. 4.6: LIV-curves of the two-phonon resonance (solid line) and the bound-tocontinuum (dashed) QC laser measured in CW for different temperatures.

4.4.2. Transport The two active region designs differ mainly by a slightly thicker extraction barrier in the two-phonon design (marked with an asterisk in the figure caption of Fig. 4.1), which partly decouples the active region from the injector. An interesting question is whether the thicker extraction barrier significantly limits the transport. For an accurate estimation of the transport time ! trans , we consider the reduction of the upper state lifetime by the optical field (which affects the tunneling time ! tunnel ). For this reason,

J max = q0 ns / (! trans + ! tunnel ) is taken from the luminescence measurement at the bias equal to the laser’s roll over voltage. This is shown in Fig. 4.7 for the bound-to-continuum sample.

111

Two-phonon resonance versus bound-to-continuum design

Fig. 4.7: LIV-curve of the lasing and luminescence device (bound-to-continuum design) measured in pulsed mode (200 ns, 99 kHz). The arrow indicates the maximum injectable current (without the influence of the phonon field).

The lower J max in the bound-to-continuum design in respect to the two-phonon resonance design is explained by the longer tunneling time ( ! tunnel,BTC =2.06 ps and

! tunnel,2Ph =1.23 ps at 303 K) through the 5.9 % thicker injection barrier (resulting from the higher growth rate). Since the measured doping level equals in both designs, we find that the slightly thicker extraction barrier in the two-phonon design is not significantly limiting the transport time ( ! transit,BTC =2.0 ps and ! transit,2Ph =2.1 ps at 303 K).

4.4.3. Waveguide losses Fig. 4.8 shows the experimental total waveguide losses extracted from the ratio of threshold

currents

of

uncoated

(CL)

and

coated

device

(HR):

! wg = (! m,HR " ! m,CL # J th,HR / J th,CL ) / ([J th,HR / J th,CL ] " 1) . In addition, the ratio of slope efficiencies are used for the extraction of the non-resonant losses (excluding resonant losses, see section 2.1.5). As we assume a sub-linear dependence of gain on the injection current, we extract the non-resonant losses from the slope efficiencies at 243 K and extrapolate the temperature dependence from the derivative of the slope efficiency itself.

112

Laser performance

Fig. 4.8: Theoretical and experimental total and non-resonant waveguide losses for the bound-to-continuum (BTC) and two-phonon resonance (2Ph) design.

As seen from Fig. 4.8, the total waveguide losses of the two designs are very similar. This is actually not too surprising, since both designs have an almost identical injector design. The fact that the total waveguide losses increase faster with temperature than the nonresonant losses is a clear indication of increased backfilling (resonant losses). Fig. 4.8 also shows the theoretical waveguide losses comprising the empty waveguide losses (assumed temperature independent) and the intersubband losses. The intersubband losses are split in resonant losses, arising from thermal backfilling, and the non-resonant losses, due to the tail of the absorption in the injector. In this calculation, we assume a fixed line-broadening for the intersubband losses, taken from the theoretical linewidth calculations at high bias (only one optical transition involved). Although it is a very crude approach to use a single linewidth value for all the different transitions, reasonable agreement between experiment and theory was achieved. It could be improved by calculating the individual linewidth for each transition.

113

Two-phonon resonance versus bound-to-continuum design

4.4.4. Differential gain Differential gain was derived from the experimental threshold current densities and total waveguide losses shown in Fig. 4.9. Within errors, differential gain is very similar in both designs. The theoretical differential gain, as discussed in section 2.1.2, is also shown. Excellent agreement between theory and experiment was attained for the twophonon resonance design. The model results in a lower differential gain for the boundto-continuum design because the calculated linewidths are wider than in reality (see Fig. 3.1).

Fig. 4.9: Theoretical and experimental differential gain versus temperature for the two-phonon resonance (2Ph) and bound-to-continuum (BTC) design.

4.4.5. Threshold current density and slope efficiency Experimental threshold current densities do not show a significant difference between the two designs (Fig. 4.10a). This is explained by the larger matrix element in the boundto-continuum design ( z BTC =2.72 nm and z2Ph =2.5 nm at 300 K), which largely compensates for the broader gain spectrum. Theoretical threshold current calculations show a difference between the two designs, which is due to the difference between theoretical and experimental linewidths for the bound-to-continuum type. The theoretical slope efficiency (calculated using the non-resonant waveguide losses) deviates at low temperature from the measured values, indicating that the losses are not 114

Conclusion correctly predicted (Fig. 4.10b). In fact, applying the experimental non-resonant losses for the slope efficiency calculation improves correlation with the measurement (black curves).

Fig. 4.10: Theoretical and experimental values of a) threshold current density and b) slope efficiency of the bound-to-continuum (BTC) and two-phonon resonance (2Ph) design. The setups’ collection efficiency was taken into account.

4.5. Conclusion Key parameters of the bound-to-continuum and two-phonon resonance active region design were experimentally and theoretically compared. The two-phonon resonance design shows very narrow linewidths and seems most promising for performance in terms of low threshold current densities and therefore low power consumption. However, the bound-to-continuum design shows wider gain spectra and is therefore interesting for broad gain applications. Fortunately, the stronger matrix

115

Two-phonon resonance versus bound-to-continuum design element in the bound-to-continuum compensates to a large extent for the larger linewidths. Furthermore, the model for the calculation of the temperature and field dependent intersubband linewidth in mid-IR quantum cascade laser designs was verified. Excellent agreement with the experiment was found for the two-phonon resonance design. Linewidths are slightly overestimated in the bound-to-continuum design. Differential gain and threshold current density are in excellent agreement for the two-phonon resonance design. Although the slope efficiency is somewhat underestimated at low temperatures, there is still reasonable agreement with the experiment. In conclusion, this simple model constitutes a useful evaluation tool for quantum cascade laser designs to a priori predict their linewidths.

116

Chapter 5 5. Low power consumption laser sources 5.1. Introduction The focus in this chapter is the realization of single mode devices with very low threshold current densities but enough dynamic range for large thermal tuning in CW operation. This will permit fabrication of hand-held or remotely deployed, batteryoperated systems using infrared sources with very low electrical power consumption but high tunability and output power.

5.2. Design and experiment As seen in the previous section, the two-phonon resonance design shows the best performance in terms of low threshold current densities. Therefore, this design was selected for the realization of a low power consumption device. In this experiment, the active region design is tailored for an emission at !!9 µm; it was already used for the first demonstration of CW operation at room temperature in 2002 [92]. However, the doping levels of injector and top and bottom waveguide were strongly reduced in order to reduce intersubband and empty waveguide losses. Furthermore, the devices were designed in a narrow–ridge buried heterostructure fashion and mounted epi-down. This allows to significantly reduce the CW threshold current. In addition, a strongly coupled grating was used to further reduce the DFB cavity losses. The fabrication of these lasers started with a 200 nm InGaAs lower confinement layer (Si, 4x1016 cm!3) by molecular beam epitaxy, followed by the active region, and a 300 nm InGaAs upper confinement layer (Si, 4x1016 cm!3). The layer sequence of one active cell,

Low power consumption laser sources out of NP=35 cascades, given in nanometers and starting from the injector barrier is 4.0/ 1.9/ 0.7/ 5.8/ 0.9/ 5.7/ 0.9/ 5.0/ 2.2/ 3.4/ 1.4/ 3.3/ 1.3/ 3.2/ 1.5/ 3.1/ 1.9/3.0/ 2.3/ 2.9/ 2.5/ 2.9, where InAlAs barriers are in bold face, InGaAs wells are shown in normal face, and numbers underlined correspond to the n-doped layers (Si, 7x1016 cm!3). All these layers were lattice matched to the low doped InP substrate (Si, 1–2 x 1016 cm!3). The DFB gratings were etched 0.17 µm deep into the top confinement layer and overgrown by the MOVPE with a 4.4 µm InP cladding layer (Si, 5 x 1016 cm!3) and two 15 nm quaternary InGaAsP layers (Si, 2 x 1016 cm!3), for smoothing the conduction band offset. The growth was terminated by a 330 nm plasmon layer (Si, 7 x 1018 cm!3) and a 50 nm, highly doped contact layer (Si, 2 x 1019 cm!3). The advanced waveguide etching procedure II was used to etch ridges 11 to 14 µm wide and the waveguides were re-introduced into the MOVPE system and buried in InP:Fe. Further processing was identical to that described in chapter 4. Finally, the lasers were mounted either epi-up on copper mounts using indium solder, or epi-down on AlN submounts which were then soldered to copper mounts using tin-gold solder for both steps.

5.3. Laser performance of moderately coupled devices Mounted lasers were placed on a high-temperature Peltier element and the temperature was monitored on the submount with a thermistor. Optical power was measured using a calibrated thermopile detector. The collection efficiency of our setup of 62 % was taken into account. Spectra were recorded using a FTIR spectrometer Nicolet 860 together with a deuterated triglycine sulphate (DTGS) detector.

5.3.1. CW laser characteristic First, two HR coated devices, mounted epi-up and epi-down, were compared, having identical length (1.5 mm) and only slightly differing ridge width of 12.0 µm (epi-up) and 12.7 µm (epi-down) and grating period ! =1.419 µm (epi-up) and ! =1.426 µm (epidown). The epi-up mounted device lased in CW up to a temperature of 353 K (80 °C), while the one mounted epi-down showed a maximum CW temperature of 406 K (133 °C), proving the importance of good thermal management. Fig. 5.1 shows the LIVcurves of the epi-down mounted device. 118

Laser performance of moderately coupled devices

Fig. 5.1: LIV-curves of a 12.7 µm-wide and 1.5 mm-long epi-down mounted HR coated device in CW operation.

Fig. 5.2: High resolution spectra of the 1.5 mm-long epi-down on AlN mounted device at various temperatures and currents, showing a SMSR >25 dB (limited by the spectrometer resolution).

At 303 K, the epi-down mounted device shows a threshold current density of 1.14 kA/cm2 which increases to 2.2 kA/cm2 at 406 K. The consumed electrical power of 1.6 W for an optical output power of 16 mW is comparable to results recently obtained for QC lasers emitting at !!5.2 µm [160]. For an optical output power of 100 mW, an 119

Low power consumption laser sources electrical power of 3.8 W is consumed. This corresponds to wallplug efficiencies of 1.0 and 2.6 %. At room temperature, an electrical power of 1.7 W is consumed for an optical output power of 1 mW, which is comparable with very short QC lasers emitting at !!5.3 µm, where 1 mW was the maximum optical power achieved at room temperature [161]. Fig. 5.2 shows the spectra of the epi-down mounted device. A total tuning range of 12.1 cm-1 (13.6 cm-1) for the epi-up (epi-down) mounted device on a Peltier element was achieved.

5.3.2. Thermal resistance and temperature tuning In order to determine the thermal resistance, the two devices were measured also in pulsed operation (200 ns, 99 kHz). The threshold current density values are plotted together with the CW data in Fig. 5.3. The two devices are comparable in terms of active region performance and waveguide losses, as shown by the extracted pulsed operation values T0 and J0 (see Table 5.1) from the empirical equation Jth=J0exp(T/T0). For fitting the CW data, the increase in temperature of the active region was taken into account by using

the

implicit

equation

for

the

threshold

current

density,

Jth=J0exp([T+RthJthUthSact]/T0), where Sact is the area of active region and Uth the bias at threshold. As one sees from Table 5.1, T0 and J0 are in good agreement with those from our pulsed measurements and the published pulsed value for Fabry-Pérot devices [92]. A direct temperature tuning (1/")(#"/#T) of -7.9 x 10-5 K-1 (-6.6 x 10-5 K-1) and electrical power tuning (1/")(#"/#P) of -1.0 x 10-3 W-1 (-5.2 x 10-4 W-1) was extracted for the epi-up (epi-down) mounted device. As expected, the difference of direct temperature tuning coefficients is small due to the only weak temperature dependence of the tuning coefficient, but the !50 % lower electrical power tuning in the epi-down mounted device is a clear result of the better thermal management. The thermal resistance derived from the spectral characteristics is also shown in Table 5.1. The epi-up mounted device shows a larger Rth for the active region compared with the one deduced from the spectral characteristics, indicating that its active region is hotter than the area seen by the optical mode. 120

Laser performance of moderately coupled devices

Fig. 5.3: Threshold current density versus temperature for pulsed and CW operation. The pulsed data were fitted using the empirical formula Jth=J0exp(T/T0). The dotted lines serve as guide to the eye for the CW data. For calculation of T0 and Rth, see text.

Table 5.1: Values T0 and J0 of the epi-up and epi-down mounted devices, derived from pulsed and CW data. Thermal resistance Rth for the active region (act) and active region plus waveguide.

T0 J0 Rth

Pulsed CW Pulsed CW Active region act+waveguide

Epi-up 171±1 174±9 183±3 187±9 17.5±3.5 12.7±0.7

Epi-down 187±3 182±9 217±5 204±11 5.6±2.0 7.9±0.6

[K] [K] [A/cm2] [A/cm2] [K/W] [K/W]

5.3.3. Cavity losses The very low doping of injector, waveguide and substrate leads to computed empty empty waveguide losses ! wg of 1.8 cm-1 and intersubband losses ! ISB of 8 cm-1. Using the empty + "! ISB of 6.7 cm-1 calculated overlap factor !=0.62, total waveguide losses ! wg = ! wg

are computed. This value is in very good agreement with the experimental value of

! wg =6.6 cm-1, which was extracted from a 3 mm-long Fabry-Pérot device, using the threshold current values at 303 K of the uncoated and HR coated device. Using the 121

Low power consumption laser sources threshold current density of the same device, we calculated a differential gain

gd =10.25 cm/kA. From these data, we can derive the DFB cavity losses

! DFB = J th "gd # ! wg !0.7 cm-1 from the threshold current density at 303 K of the epi-down mounted DFB device.

5.3.4. Longitudinal and lateral mode discrimination Fig. 5.4 shows the subthreshold emission spectra of the epi-up mounted device, measured with the Nicolet 860 and a LN2 cooled MCT detector (EG&G J15D16-M208S250U-06), with the stopbands of the fundamental and first-order mode.

Fig. 5.4: Sub-threshold dc current spectrum of the epi-up mounted device, measured at 220 mA and 303 K. Also shown is the laser spectrum just above threshold.

However, the laser spectrum just above threshold (also shown in Fig. 5.4) indicates that the device operates on the fundamental mode. From the stopband width !" =2.049 cm-1 and

the

effective

index

neff = 1 / (2!") =3.167,

a

coupling

coefficient

! = "#$ neff =20.4 cm-1 was calculated, resulting for our 1.5 mm-long devices in a coupling product ! L of 3.1, which is three times larger than the critical coupling product

! L !1 [154]. Stable single mode CW operation with a side-mode suppression ratio >25

122

Laser performance of moderately coupled devices dB (limited by the spectrometer resolution) was observed within the entire examined frequency, power and temperature range for both devices. Spectroscopic applications require not only longitudinal single mode operation, but also lasing on the fundamental lateral mode is highly desired. This is more difficult to achieve in QC lasers in buried heterostructure fashion since the higher lateral modes are not as efficiently damped as in the case of conventional waveguides, where the overlap with the passivation and Au layer induces high optical losses. Fig. 5.5 shows the calculated modal gain difference (using the software package "COMSOL Multiphysics" to solve the twodimentional wave equation) between the fundamental and two higher order modes for DFB cavity losses between 0.2 and 1.3 cm-1. A modal gain difference !g m =0.2–0.4 cm-1 between the fundamental and first-order lateral mode was calculated. In fact, stable single mode operation on the fundamental lateral mode was observed in the evaluated devices. Moreover, we found that even 14 µm-wide devices with a !g m of only 0.1–0.2 cm-1 lase on the fundamental lateral mode.

Fig. 5.5: Calculated modal gain difference versus ridge width between the fundamental and first and second order mode for different DFB cavity losses.

123

Low power consumption laser sources

5.4. Laser performance of strongly coupled devices Increasing the coupling product should allow to further reduce the DFB cavity losses. Therefore, a 2.25 mm long and 11 µm wide device was epi-down mounted on AlN ( ! =1.419 µm). The threshold current density reduced to 1.07 kA/cm2 at 303 K, indicating DFB cavity losses of only 0.3 cm-1. Fig. 5.6 depicts LIV-curves of this chip, which lased in CW up to a temperature of 423 K (150 °C) with the threshold current density increasing to only 2.4 kA/cm2. To our knowledge, this is the highest reported CW operation temperature for an intersubband laser. Fitting of the implicit equation for the threshold current density results in a T0 of 189±11 K, a J0 of 195±16 A/cm2 and a Rth of 7.6±2.8 K/W. Fig. 5.7 shows the single-mode spectra of this device. The total tuning range achieved on a Peltier element is 14.2 cm-1 or 1.3 % of center frequency, which is the largest value reported for CW DFB QC lasers. However, for temperatures below 373 K, the device emits bi-mode for currents higher than 1.25 ! I th , which is due to the strong distributed feedback coupling ( ! L !4.6).

Fig. 5.6: LI-curves of a 2.25 mm-long device mounted epi-down on AlN submounts. Inset: Threshold current density vs temperature for CW operation. The dotted line serves as guide to the eye. For calculation of T0 and Rth, see text.

124

Conclusion

Fig. 5.7: High resolution spectra (taken at about 1.1 x Ith) of the 2.25 mm-long epidown on AlN mounted device, showing a SMSR>25 dB (limited by the spectrometer resolution).

5.5. Conclusion In conclusion, reducing the waveguide losses using a low doping level and strong DFB coupling in combination with a narrow-gain active region and a good thermal management allowed to fabricate low-threshold current density and low power consumption single-mode devices with high CW operation temperature. The doping of the active region was sufficient to have some dynamic range that allows large thermal tuning in CW. Tuning of 10 cm-1 or 0.9 % of center frequency was achieved by heating the device. The threshold current density varies from 1.07 kA/cm2 at 303 K to 2.4 kA/cm2 at 423 K. Low electrical power consumption of 1.6 W and 3.8 W for an optical output power of 16 mW and 100 mW have been demonstrated. The width of the waveguides is sufficiently narrow to favor the fundamental lateral mode. Stable single mode operation was observed in the entire frequency, power and temperature range with a SMSR >25 dB.

125

Chapter 6 6. Quantum cascade lasers with widely spaced operation frequencies 6.1. Introduction In the previous chapter, low power consumption DFB QC lasers showing a tuning range of approximately 1 % of the wavelength have been demonstrated. However, this tuning range may be too small to scan complex mixtures with multiple absorption lines or mixtures with very broad lines. In order to scan over a wider frequency range, it would be more appropriate to build a device integrating several DFB lasers on one chip. The spacing of the different DFB lasers has to be selected in such a way as to cause the single tuning ranges to overlap in order to access a continuum of frequencies. Such a device would hereby constitute a multi-channel laser spectrometer. In this chapter, the results of monolithically integrated DFB lasers with widely spaced operation frequencies are presented.

6.2. Design and experiment In order to integrate several DFB lasers with widely spaced operation frequencies and reasonable high operation temperatures and powers on one chip, a gain medium with a broad spectral width is required. Therefore, the bound-to-continuum design was selected for this type of application. Furthermore, to reach single-mode operation, the coupling strength of the DFB gratings must be large enough to ensure that the mode discrimination is larger than the threshold gain difference, even in off-gain peak

Design and experiment operation. At the same time, the coupling strength should not be too high, in order to avoid overcoupling. The growth of the laser structure starts with the waveguide core (lower confinement layer, active region and upper confinement layer), which is grown by MBE. After this, the gratings are defined into the upper confinement. Then the following layers are grown by MOVPE. All layers are lattice-matched to the InP substrate. The InGaAs/InAlAs based active region, which is designed for a center emission at 7.9 µm (1270 cm-1), consists of 35 periods. The layer sequence of one active cell of the bound-tocontinuum design, given in nanometers and starting from the injector barrier, is 4.2/ 1.7/ 0.9/ 5.3/ 1.1/ 5.2/ 1.2/ 4.7/ 1.3/ 3.9/ 1.5/ 3.5/ 1.6/ 3.3/ 1.8/ 3.1/ 2.1/ 2.8/ 2.5/ 2.7/ 2.9/ 2.6/ 3.3/ 2.4, where InAlAs barriers are in bold, InGaAs wells in roman, and the numbers underlined correspond to the n-doped layers (Si, 8 x 1016 cm-3). The lower 220 nm and the upper 310 nm-thick confinement layers consist of low n-doped InGaAs

(Si,

4 x 1016 cm-3) and are grown on an n-doped InP wafer (Si, 1–2 x 1017 cm-3). The DFB gratings were defined in a single optical lithography step using a mask integrating 25 different grating fields. The first-order DFB grating periods range from 1.185 to 1.305 µm with a constant duty cycle of 50 %. Having defined the grating masks, 0.17 µmdeep gratings were etched into the upper confinement layer (see photograph in Fig. 6.1).

Fig. 6.1: Photograph of a quarter of a two inch wafer after etching of the gratings.

The growth proceeded with a 4 µm-thick InP cladding layer (Si, 1 x 1017 cm-3) and two 15 nm thick quaternary InGaAsP layers (Si, 1 x 1018 cm-3) with band gap energies of 1.127 and 0.969 eV, respectively. Finally, the structure was terminated with a 300 nm-thick Plasmon-enhanced layer (Si, 9 x 1018 cm-3) and a 50 nm-thick, highly doped contact layer 127

Quantum cascade lasers with widely spaced operation frequencies (Si, 2 x 1019 cm-3), both layers consisting of InGaAs. In the next step, ridge waveguides were formed by using the advanced waveguide etching procedure I and passivated by deposition of a Si3N4 layer (the buried heterostructure technology was not developed at that time). After opening the nitride on top of the waveguides, contacts were evaporated and finally a 3 µm-thick layer of gold was electroplated on top in order to improve the heat removal capacity of the device. A high-reflection coating was applied to the back of 1.5 mm-long laser bars. Finally, the lasers were epi-side up mounted onto copper heatsinks with indium.

6.3. Laser performance For the discussion of the optical and spectral characterization, three samples with three different grating periods (A: 1.3 µm, B: 1.25 µm, and C: 1.2 µm, out of the 25 fabricated) were chosen. The Bragg resonance of sample B lies close to center of the gain curve whereas samples A and C are located towards the lower/upper limits of the available wavelength range. Mounted lasers were placed on a high-temperature Peltier element. The laser power was measured using a calibrated thermopile detector. The collection efficiency of our setup of 74 % was not taken into account. Spectra were recorded using a Bruker Vertex 70 FTIR spectrometer equipped with a DTGS detector.

6.3.1. CW laser characteristic Fig. 6.2 shows a series of LIV-curves for all three lasers. At a temperature of +30 °C, maximum output powers and slope efficiencies of 35 mW and 245 mW/A were observed for laser B, whereas A and C show lower powers and slope efficiencies. In addition, sample B reaches a maximum operation temperature of 60 °C while samples A and C stop lasing CW at 35 and 45 °C, respectively. Fig. 6.3 is a scatter graph of the threshold current density values of all investigated lasers at +30 °C. Although the plot contains data for different ridge widths as well as intermediate grating periods (not belonging to class A, B, or C), one can clearly see the overall trends. The threshold current densities increase from the 1.87 kA/cm2 (sample B) to 2.62 kA/cm2 (sample A) and 2.45 kA/cm2 (sample C).

128

Laser performance

Fig. 6.2: Optical power and voltage versus current of samples A, B, and C at different heatsink temperatures. Sample B is close to the center of the gain curve, sample A and C are located towards the lower/upper limits of available frequency range (corresponding spectra in Fig. 6.4).

An increasing specific thermal conductivity with decreasing ridge width was observed. This effect should also decrease the threshold current density of continuous wave lasers, as was reported for very wide and heavily doped lasers [162]. Nevertheless, narrower ridges also tend to suffer from larger waveguide losses due to the stronger interaction 129

Quantum cascade lasers with widely spaced operation frequencies between the optical mode and the gold metallization. By comparing low doped and relatively narrow devices, it is not expected to see a clear trend of threshold current density with ridge width, as already discussed in section 2.2.2. Furthermore, the threshold current of our DFB devices also depends on the relative phase of the grating reflectivity and that of the facet. This explains the scattering of the data in Fig. 6.3 for different ridge widths.

Fig. 6.3: Threshold current density in CW operation at +30 °C versus wavenumbers for devices with different ridge widths. The threshold current densities increase from 1.87 kA/cm2 (sample B) to 2.62 kA/cm2 (sample A) and 2.45 kA/cm2 (sample C).

6.3.2. Thermal resistance and tuning properties Fig. 6.4 shows CW emission spectra of the three devices at different heatsink temperatures. Emission energies (wavelengths) of 1206 cm-1 (8.3 µm), 1256 cm-1 (8.0 µm) and 1302 cm-1 (7.7 µm), respectively, were observed at +30 °C. Taking into account the temperature tuning range of samples A and C leads to a total wavelength coverage of more than 100 cm-1 (i.e. 8 % of the center frequency). Stable single-mode CW operation with a side-mode suppression ratio > 25 dB was observed within the entire examined frequency and temperature range.

130

Laser performance

Fig. 6.4: High resolution single mode CW spectra of samples A, B, and C showing operation with a side-mode suppression ratio >25 dB. Depicted are the spectra at 1.1 x threshold and 30 °C and at the extremes of single laser tuning range achieved by the variation of temperature. The corresponding single tuning ranges for samples A, B, and C are 10, 15 and 12 cm-1, respectively.

Thermal resistances Rth and thermal tuning coefficients ! = (1/!)("!/"T) for samples A, B, and C were extracted from the spectral characteristics. An average thermal tuning coefficient ! =-8.88 x 10-5 K-1 and an average thermal resistance Rth of 12.4 K/W were computed, which corresponds to an average specific conductance of 455 W/(Kcm2). Excellent agreement with theoretical values are found (see Fig. 2.15). The electrical power tuning (1 / ! )("! / "P) = Rth # $ of -1.1 x 10-3 W-1 is two times larger than the one of the epi-down mounted device in the previous chapter. The thermal resistance of sample B was also calculated from the comparison of threshold currents in CW and pulsed operation. A thermal resistance of 18.1 K/W was found. The higher value obtained with this method compared to the spectral analysis is due to the non-unity ‘thermal overlap’ factor of the active region, already discussed in section 2.2.3.

131

Quantum cascade lasers with widely spaced operation frequencies

6.3.3. Coupling strength and mode discrimination The theoretical coupling coefficient ! of the DFB laser is derived by optical mode calculations. From the SEM picture in Fig. 6.5, one finds that the grating was indeed etched 170 nm deep into the 310 nm-thick InGaAs confinement layer. Using these figures, a modulation of the effective index of !neff =0.01 was calculated. Assuming a perfectly

rectangular

grating

with

a

duty

cycle

of

50 %

yields

! = 1 / " # $neff / neff =25.5 cm-1. In this case, a coupling product of ! L =3.8 is computed.

Fig. 6.5: SEM picture of the 170 nm-deep DFB grating, etched into the top 310 nm-thick InGaAs cladding layer (period "=1.245 µm).

Experimentally, !

can be estimated from the stopband measurement of the

subthreshold emission spectrum. Fig. 6.6 shows the subthreshold emission spectra of sample C, measured at 350 mA and +30 °C in CW operation with a Bruker FTIR IFS 66/S and an LN2 cooled MCT detector. The FP mode spacing, measured sufficiently far away from the stopband, is 0.979 cm-1 and the stopband width is 2.17 cm-1. This yields a coupling coefficient ! = "# $ % $ neff =21.8 cm-1 and a coupling product ! L =3.25. The discrepancy between the theoretical and the experimental calculations can easily be explained by examining the profile of the real grating profile (see Fig. 6.5), which reveals that the profile is not rectangular and the duty cycle is not exactly 50 %. The real shape of the profile can be taken into account by weighting the theoretically calculated value by the ratio of the first-order Fourier components of the exact profile and the real 132

Laser performance profile. This yields !=21.6 cm-1, which corresponds perfectly to the result obtained in the experiment. Although our coupling product is three times larger than the critical coupling product (!"L!1), our DFB lasers yield stable single mode operation over the total investigated spectral range.

Fig. 6.6: Subthreshold high-resolution emission spectra of sample C, measured at 350 mA and 30 °C in CW operation. The FP mode spacing is 0.979 cm-1 and the stopband is 2.17 cm-1 wide.

6.3.4. Extrapolated gain spectrum and differential gain In Fig. 6.7, the extrapolated gain spectrum, derived from the electroluminescence measurement using (2.47), is shown together with the normalized inverse threshold current densities of the three samples A, B, and C. The electroluminescence was measured under an applied bias voltage of 9.6 V, a duty cycle of 4 % and a temperature of 300 K. It exhibits a large FWHM value of 33.9 meV (274 cm-1), which corresponds to a relative width of #$/$0= 21 %. In order to get a fair comparison between the threshold values and the electroluminescence, samples A, B, and C were measured in pulsed mode as well. Their inverse threshold current densities at 2% duty cycle are normalized to sample B. Good agreement is found with the extrapolated gain spectrum. The overall behavior leads to the conclusion that the gain must have its maximum close to the Bragg resonance of sample B. 133

Quantum cascade lasers with widely spaced operation frequencies

Fig. 6.7: Dashed line: Normalized electroluminescence spectrum at 300 K measured under an applied bias voltage of 9.6 V. Solid line: Extrapolated gain spectrum. Crosses: Normalized inverse threshold current density of the three samples A, B, and C measured in pulse mode.

An interesting question is obviously, how far away from the gain center such a DFB laser could still yield single mode operation. In order to estimate the gain margin between the mode discrimination !" and the threshold gain difference !g , the difference between samples A and B, which are separated by approximately 50 cm-1, was calculated. Since the gain margin is dependent upon the thermal heat sinking of the device, this study is only valid for pulsed operation. For two DFB lasers fabricated from the same piece of material, the threshold gain g th (! , J th ) = J th gd (! ) is the same. However, sample B, which has its Bragg reflectance close to the gain maximum, exhibits a lower threshold current density compared with sample A, due to a higher differential gain. The ratio of the differential

gain

can

be

expressed

in

terms

of

threshold

current

density

gd (! A ) / gd (! B ) = J th,B / J th,A . From the values measured for samples A and B, this ratio is

gd (! A ) / gd (! B ) = 0.82. In other words, as one moves away from the gain maximum (sample B), the 20 % higher threshold current density of sample A goes along with an approximate 20 % reduction on the gain curve. Consequently, the threshold gain difference between samples A and B can be written as !g = g th,B (1 " J th,B / J th,A ) . For 134

Evaluation of reliability for NASA Mars mission project modes that have been sufficiently separated, !" is the difference between the threshold gain

of

the

Fabry-Pérot

empty g th,FP = ! wg + "! ISB + ! m,FP

and

the

DFB

cavity

empty empty g th,DFB = ! wg + "! ISB + ! m,DFB . Empty waveguide losses ! wg of 3.4 cm-1, intersubband

losses ! ISB of 9.8 cm-1, cavity losses ! m,DFB of 0.7 cm-1, mirror losses "FP of 4.47 cm-1 and an overlap factor ! of 74 % were computed. Since !" is as large as 3.8 cm-1, whereas !g accounts for only about 2.0 cm-1, single mode operation is guaranteed, and could potentially be extended over an even wider frequency range.

6.4. Evaluation of reliability for NASA Mars mission project Some of these lasers have been selected for the NASA Mars Science Laboratory Mission project. Based on an isotopic measurement at 7.79 µm (1283.6 cm-1) for CO2 and H2O2, the goal is to evaluate whether Mars was ever inhabitable. To prove the robustness of the lasers, an aging test at constant DC current of 360 mA was performed at Alpes Lasers SA, using an 11 µm-wide and 1.5 mm-long DFB device (grating period 1.22 µm), which was HR coated on the back facet. This laser was mounted epi-layer up on an AlN submount with Indium solder and finally packaged in a module (see Fig. 6.8), which was then sealed with 90 % N2 and 10 % He. With a thermoelectric cooler, the heatsink temperature was maintained at 10 °C, corresponding to an active region aging temperature of approximately 70 °C (estimated by using the calculated thermal resistance).

Fig. 6.8: Photograph of a hermetical sealed module dedicated for the NASA Mars Science Laboratory Mission [Courtesy of Alpes Lasers].

135

Quantum cascade lasers with widely spaced operation frequencies Optical power was measured using a calibrated thermopile detector placed directly in front of the laser. Output powers and voltages of the device were recorded for more than 11000 h at constant DC current. No significant long-term degradation of the measured bias was observed within the recorded period. The power fluctuations are mainly attributed to the alignment of the power meter with respect to the laser facet since the power meter was also used for other measurement purposes. Fluctuations in the temperature of the environment (laboratory was not tempered) also added to the scattering of power and voltage data.

Fig. 6.9: Output power and voltage versus operation time of a hermetically sealed QC laser at !=7.79 µm [Courtesy of Alpes Lasers].

6.5. Conclusion Single-mode devices emitting CW at room temperature based on the bound-tocontinuum active region have been developed. The broad gain spectrum of this design allows the fabrication of high-performance devices over a large wavelength range. By using DFB gratings with 25 different periods, single-mode CW operation between 7.7 and 8.3 µm at a temperature of +30 °C was demonstrated from devices fabricated in a single processing run, i.e. from one piece of material. This frequency span corresponds to 8 % of the center frequency. This experiment demonstrated the usability of the bound-to-continuum design for monolithic integration of high-performance DFB lasers 136

Conclusion emitting at different wavelengths. Furthermore, an aging test was performed to prove the reliability of such devices for real-life applications, such as in multi-channel laser spectrometers.

137

Chapter 7 7. Broadly tunable heterogeneous quantum cascade laser sources 7.1. Introduction Some applications would strongly benefit from an even broader tuning range than attained in the previous chapter. Broadening of the tuning range by simply increasing the number of integrated DFB QC lasers is not very feasible because this will reduce the fabrication yield of fully functional chip arrays and further complicate the optical alignment of the different beams. An external cavity (EC) configuration is very promising for this type of application [163], where the tuning range is mainly limited by the shape of the gain spectrum of the QC laser architecture. EC systems designed for QC laser have been undergoing constant improvement: the development of mode-hop free tuning, CW operation at room-temperature, and recently the emergence of handheld, battery-operated modules, also suitable for field-deployment [124], [123], [164]. While significant progress has been made in the development of EC setups over the past few years, the accessible range of frequencies is presently limited by the lack of suitable gain chips, which are not only optimized for high-power and high-temperature operation, but also for ultra-broad gain operation in CW, in order to achieve narrow linewidths. Furthermore, operation at room temperature is most advantageous as it eliminates the need for complicated and bulky setups. In this chapter, a broadly tunable high performance QC laser source for broadband applications is presented. Furthermore, the usability for broadband tuning at room temperature in an EC setup is demonstrated.

Design and experiment

7.2. Design and experiment Since differential gain is inversely proportional to the gain width, realizing both a broad gain spectrum and at the same time a low threshold current value are two mutually exclusive optimization parameters for CW operation at room temperature. Therefore, in order to realize a high-performance broad gain chip, a careful selection of design parameters is crucial.

7.2.1. Active region design The tuning range is limited by the mode discrimination between Fabry-Pérot (FP) modes and the EC mode. Therefore, single mode tuning will be possible as long as the AR AR / " FP represents the ratio of the ratio of differential gain gd (! ) / g max " # , where ! = " EC

total losses with and without the feedback of the EC of the anti-reflection (AR) coated laser. In this experiment, two bound-to-continuum active regions with different center wavelengths are combined within the same waveguide (see Fig. 7.1) and should allow a broad gain spectrum. However, this can only be achieved as long as the spectral overlap is strong enough to ensure gain clamping since it presents an inhomogeneous gain medium. Such a heterogeneous QC laser based on two bound-to-continuum active region designs was first demonstrated by Maulini et al. [105]. The same layer sequence was chosen for our experiment: one region is centered at 8.2 µm (1220 cm-1, design A) and the other at 9.3 µm (1075 cm-1, design B).

Fig. 7.1: Schematic illustration of the heterogeneous QC laser in buried heterostructure fashion.

139

Broadly tunable heterogeneous quantum cascade laser sources In order to avoid resonant losses at the lasing wavelength and therefore an increase of the threshold current density, significant backfilling from the ground state into the lower laser level must be avoided. Therefore, the energy difference ! inj between the lower laser state and the chemical potential of the injector should be as large as possible. As already discussed in section 2.2.1, since the operation bias of the device

U ! N p (!" / q0 + # inj ) increases with ! inj , a good compromise is a ! inj of 120-150 meV [147]. Our injector design should result in a ! inj of 142 and 127 meV, applying a field of 48 and 40 kV/cm and defining the optical transition with the largest matrix element (E12!E10) as the center transition, 151 meV (8.2 µm) and 133.5 meV (9.28 µm), for designs A and B respectively. This energy separation should be sufficient to avoid backfilling and should result in an operation voltage of 11 V. The layer sequence of the active region, given in nanometer and starting from the injection barrier, is for design A (8.2 µm): 4.3/ 1.8/ 0.7/ 5.5/ 0.9/ 5.3/ 1.1/ 4.8/1.4/ 3.7/ 1.5/ 3.5/ 1.6/ 3.3/ 1.8/ 3.1/ 2.0/ 2.9/ 2.4/ 2.9/2.6/2.7/3.0/2.7, and for design B (9.3 µm): 3.9/2.2/0.8/6/0.9/5.9/1.0/5.2/1.3/4.3/1.4/3.8/ 1.5/3.6/1.6/3.4/1.9/3.3/2.3/3.2/2.5/3.2/2.9/3.1, where InAlAs barriers are in bold print, InGaAs wells are shown in roman numerals, and underlined values correspond to the ndoped layers. Another key design parameter is the doping of the injector. Doping leads to nonresonant losses arising from the injector, as well as resonant losses resulting from thermal backfilling. In order to realize low threshold currents, the doping should be as low as possible but sufficient to ensure that tuning is limited by the mode discrimination

!" between Fabry-Pérot modes and external cavity modes and not by the gain. Therefore, enough current needs to be supplied so that at least the threshold condition AR AR can be reached: g(! ) / g max = J th,EC (g max ) / J th,EC (! ) . In order to have some dynamic range

AR AR (J max ! J th,EC ) / J th,EC to attain an output power level enabling high performance, the

(

)

lower bound of the Si doping can be estimated by: ns = J max ! tunnel + ! trans / q0 . A sheetdensity of 1.0 x 1011 cm-2 was chosen, resulting in a calculated maximum injectable 140

Design and experiment current J max of 5.35 kA/cm2, which should be sufficient to allow some dynamic range. In this calculation, we assumed a transit time ! trans of the electron across a period of the active region at resonance of 1.4 ps (derived by multiplying the number of LO phonon energy steps after the first intersubband scattering event N = (!! + " inj ) / !! LO # 1 with the LO phonon time of 0.2 ps [96]) and a injection barrier tunneling time 2

2

! tunnel = (1 + 4 " ! 3! ! ) / (2 " ! ! ) of 1.59 ps (using a dephasing time ! ! of 40 fs, an upper state lifetime ! 3 of 0.56 ps and an energy splitting at resonance 2! ! of 6.78 meV).

7.2.2. Waveguide and thermal design Doping of the waveguide layers was kept to a minimum since it affects the total waveguide losses by free-carrier absorption. The growth started with MBE. The active region was sandwiched between a lower 220 nm and an upper 300 nm-thick InGaAs (Si, 4 x 1016 cm-3) layer. Subsequently, the sample was introduced into the MOVPE. The layer sequence and doping levels of the MOVPE grown layers was identical to that described in chapter 5.

Fig. 7.2: SEM picture of an epi-side down on diamond mounted QC laser chip. Inset: Close-up view of buried active region and Au heat spreader soldered to the diamond.

141

Broadly tunable heterogeneous quantum cascade laser sources Choosing 20 stages for each active region design resulted in an overlap factor of 74 %. empty Empty waveguide losses ! wg of 2.1 and 2.5 cm-1 for designs A and B were calculated.

Since the difference between the waveguide losses is minimal, no compensation of the losses by the number of stages has been considered. After wet-etching 10 to 13 µm-wide ridges, the waveguides were re-introduced into the MOPVE and buried with InP:Fe. Further processing was identical to that described in chapter 4. After cleaving in 3 mmlong devices, the lasers were Indium-mounted epi-side down on diamond submounts, which had previously been soldered on copper heatsinks. Fig. 6.1 shows an SEM picture of such a mounted device.

7.2.3. Single mode control in external cavity setup A strong mode discrimination !" between FP and EC modes is realized by a broadband multi-layer anti-reflection coating for the chip and a strong EC feedback. The EC setup (shown in Fig. 7.3) is realized in Littrow configuration, where the firstorder diffracted beam from a 4 by 4 cm Au-coated grating (150 grooves/mm, blazed for 9.3 µm) is directly fed back into the laser cavity through an AR coated (3-24 µm) Germanium aspheric lens (f/0.8).

Fig. 7.3: Photograph of the external cavity setup for continuous wave operation. The ZnSe window of the laser housing (Alpes Lasers LLH-100) was removed. Condensation is suppressed by operating the laser close to room temperature and purging of the laser housing with N2.

142

Device characterization The buried heterostructure design is very effective, since the planar facet allows the deposition of uniform coatings and a more symmetric farfield pattern compared to ridge waveguides. Since the light was extraced from the zeroth order of the grating (front extraction), a HR coating could be evaporated on the back facet.

7.3. Device characterization 7.3.1. Gain chip performance For characterization in terms of light output in CW and pulsed operation, the laser power was measured using a calibrated thermopile detector. Spectra were recorded using a Nicolet 860 FTIR spectrometer, together with a DTGS detector. Mounted lasers were placed on a high-temperature thermoelectric cooler/heater and the temperature was monitored on the submount with a thermistor. Fig. 7.4 depicts a series of LIV-curves of an 11.8 µm-wide device at different temperatures.

Fig. 7.4: Optical power and voltage versus DC current of an 11.8 µm-wide and 3 mm-long HR coated device. Measurement was terminated at 4.9 kA/cm2 in order to avoid damage of the device.

In order to avoid damage of the device, the maximum current density was limited to 4.9 kA/cm2. At 30 °C, a threshold current density of 3.97 kA/cm2 and a slope efficiency of 143

Broadly tunable heterogeneous quantum cascade laser sources 363 mW/A were observed. An output power of 100 mW was attained at a current density of 4.9 kA/cm2. Despite the broad gain design, a maximum CW operation temperature of 50 °C with still 10 mW output power was achieved. Fig. 7.5 shows the spectrum of this device measured in pulse operation indicating laser action over 180 cm-1, which takes place mainly between the center wavelengths of designs A and B.

Fig. 7.5: High-resolution spectra taken at 1665 mA at 303 K in pulsed operation (50 ns, 380 kHz) spanning over approximately 181 cm-1. The arrows indicate the center frequency of the two active region designs. Inset: LI-curve, measured in pulsed mode (100 ns, 99 kHz), exhibits a peak power of 1 W at 298 K at the electrical roll-over at 3 A.

In order to investigate the thermal behavior, the device was also measured in pulsed operation at different temperatures. At 30 °C, a current density of 2.97 kA/cm2 and a slope efficiency of 698 mW/A were measured. The threshold current densities for different temperatures are plotted in Fig. 7.6, together with the CW data. A characteristic temperature T0 of 117 and 206 K for CW and pulsed operation is extracted, respectively. The extracted thermal resistance of 4.8 K/W accounts for the buried heterostructure design and epi-down mounting on diamond. Although this is a very low value, at a current density of 4.9 kA/cm2, the active region reaches a

144

Device characterization temperature of 110 °C in CW (heatsink temperature of 30 °C), thus demonstrating the paramount importance of a good active region design and heatsinking.

Fig. 7.6: Threshold current density versus submount temperature in CW and pulse operation (200 ns, 99 kHz). The experimental data were fitted with the empirical formula J th = J 0 exp(T / T0 ) , resulting in a T0 of 117 and 206 K for CW and pulsed operation, respectively.

Fig. 7.7: Solid line: CV-profile of the MBE-grown layers normalized by the measured thickness using selective etching. Dashed line: The measured doping profile reveals a 54±5 % higher active region doping level compared to the nominal values.

145

Broadly tunable heterogeneous quantum cascade laser sources The inset of Fig. 7.5 shows the LI-curve taken in pulsed operation at room temperature with a peak power of 1 W. The device has a large dynamic range with the roll-over at a current density of 8.47 kA/cm2. This value is higher than the one estimated in section 7.2.1. In order to clarify this point, the doping levels of the active regions were measured. It turned out that the average doping level over one period is 54±5 % higher than the nominal one (see Fig. 7.7), resulting in a carrier sheet density of 1.54 x 1011 cm-2 and a J max of 8.24 kA/cm2. This is in good agreement with the measurement.

The total waveguide losses (resonant and non-resonant losses) were extracted from the ratio of the threshold current densities of the coated and uncoated device, resulting in tot ! wg =10 cm-1. The non-resonant waveguide losses comprising losses from the empty non-res empty non-res = ! wg + "! ISB waveguide and non-resonant intersubband (ISB) losses ! wg are

derived from the slope efficiencies of the coated and uncoated device, resulting in res res 4.8 cm-1. This leads to resonant losses from backfilling ! wg = "! ISB of 5.2 cm-1. However,

since there might be a sub-linear dependence of the gain on the injection current, this value has to be considered as an upper bound for the resonant losses. One possible explanation for those rather high resonant losses is found from the low threshold voltage of 8.2 V which indicates that the threshold fields are only 33 and 28 kV/cm for designs A and B. In fact, only a ! inj of 85 and 78 meV for designs A and B corresponds to the threshold fields (defining the center transition energies (E12!E9) at 145.8 meV for design A and 129.74 meV for design B). These values are approximately 40 % less than those calculated in section 7.2.1 and may explain the rather strong backfilling at the threshold voltage. Higher ! inj should result for CW operation since the device operates between 9 and 10 V. Using the pulsed threshold current densities at 30 °C, a gaingamma product g! of 4.1 cm/kA was calculated.

146

Device characterization

7.3.2. Extrapolated gain spectrum The spontaneous emission of our device was measured at 303 K and 9 V in pulsed operation with an FTIR in step-scan mode and an LN2-cooled MCT detector. In order to avoid super-luminescence, a short laser (212 µm-long) was prepared and the light was extracted perpendicular to the waveguide. Fig. 7.8 depicts the extrapolated gain spectrum, which was corrected by the approximate 1/energy dependence of the detector sensitivity, showing a width of 350 cm-1 (FWHM). The shoulder at 156 meV reveals transitions from a higher state above the upper laser level. The data can be well fitted by a sum of two Gaussian functions centered at 8.1 µm (1226 cm-1) and 9.4 µm (1065 cm-1), which is in good agreement with our simulation.

Fig. 7.8: Solid line: Extrapolated gain spectrum shows a width of 350 cm-1 (FWHM). Dashed line: Fitting by a sum of two Gaussians centered at 8.1 and 9.4 µm. Crosses: Normalized inverse threshold current density measured in pulsed mode with EC feedback at 303 K. The dotted line indicates the limit of the tuning range ! =0.61, given by the mode discrimination.

7.3.3. Broadband tuning in external cavity setup From the threshold current densities of the uncoated and AR coated front facet of the laser, a residual reflectivity of 0.245 % was calculated. The laser was mounted in a standard laboratory housing (Alpes Lasers LLH-100), where the ZnSe window was 147

Broadly tunable heterogeneous quantum cascade laser sources removed, and purged with nitrogen during operation to avoid condensation on the laser and Peltier element. Spectra were measured with a Nicolet 800 FTIR spectrometer. First, the device was tested in pulsed operation (400 ns, 99 kHz) at 30 °C and 1.6 A. The device could be tuned from 1013 cm-1 (9.87 µm) to 1305 cm-1 (7.66 µm). The operation spanning over 292 cm-1 (2.2 µm) equals 25 % of center frequency (see Fig. 7.9). From earlier experiments, it is known that the Fabry-Pérot modes, centered at 1080 cm-1, are just present within the first 12-15 ns of the pulse [105] until mode competition has built up.

Fig. 7.9: High-resolution spectra at the extremes of the tuning range, accessible with our EC configuration at 30 °C in pulsed operation (400 ns, 99 kHz) and spanning over 292 cm-1.

At the gain maximum (!1200 cm-1), a peak power of 800 mW and a threshold current density of 2.97 kA/cm2 were observed, which is very close to the threshold current value of

the

(

)

uncoated

(

front

facet

without

EC

feedback.

Since

)

CL AR CL AR J th,FP g max / J th,EC g max = ! FP / ! EC , one can conclude that the effective feedback of the

external cavity results in a reflectivity of REC =27 %. With the calculated waveguide losses and mirror losses of 2.23 cm-1 for the uncoated laser chip, this result in a mode AR AR discrimination !" of 7.8 cm-1 and a ! = " EC / " FP of 0.61.

148

Device characterization In Fig. 7.8, the inverse threshold current densities normalized to the threshold current at the gain maximum are plotted. There is good agreement with the extrapolated gain spectrum. Taking the ratio of the differential gain to the gain maximum from the

()

()

threshold current densities results in g ! / g max = J th,max / J th ! =0.67, which is very close to the calculated value of ! and demonstrates that the tuning is not gain limited.

In the next step, our device was tested in CW. In this operation mode, it could be tuned from 1045 cm-1 (9.6 µm) to 1246 cm-1 (8.0 µm) while operating the device between 13 and 18 °C (see Fig. 7.10). This covers a tuning range of 201 cm-1, which equals 18 % of the center frequency. The side-mode suppression ratio was more than 35 dB over the full tuning range.

Fig. 7.10: High-resolution CW spectra at the extremes of the tuning range.

Fig. 7.11 shows the CW output power of the external cavity as function of frequency. The output power was in excess of 20 mW over 162 cm-1 at 23 °C and over 172 cm-1 at 18 °C. At gain maximum at 15 °C, a CW output power of 135 mW was measured.

149

Broadly tunable heterogeneous quantum cascade laser sources

Fig. 7.11: CW output power of external cavity as function of frequency for three different sets of operation conditions.

7.4. Conclusion A heterogeneous high performance quantum cascade laser gain chip comprising two bound-to-continuum active region designs emitting at 8.2 and 9.3 µm was realized, with an extrapolated gain spectrum FWHM of 350 cm-1. Though a broad gain bandwidth invariably results in a reduced gain cross section, devices with a high-reflection coated back facet still lased CW up to a temperature of 50 °C and showed output powers in excess of 100 mW at 30 °C. To prove the usability for broadband tuning, this chip was used in our EC setup operated at room temperature. In pulsed mode, the gain chip could be tuned over 292 cm-1, which is 25 % of center frequency. In CW, a coarse tuning range of 201 cm-1 (18 %) and an output power in excess of 135 mW at the gain maximum at 15 °C was reached. This gain chip represents a very promising solution for laser photoacoustic spectroscopy (L-PAS) needs since it can be tuned over 172 cm-1 with output powers in excess of 20 mW in a room-temperature operated EC setup.

150

Chapter 8 8. Conclusion and Outlook This work on high performance quantum cascade lasers for spectroscopic applications demonstrates the maturity of this type of mid-IR laser source for the realization of compact, reliable and lightweight, ultra-sensitive and selective sensors for real-world applications requiring high spectral resolution. The success of this work was largely based on mastering the technology. In the first buried QC laser in 2001, the waveguide was embedded in non-intentional doped InP (iInP), where the parasitic structure presented an n-i-n structure. We demonstrated experimentally that space charge limited current in such blocking structures gives rise to a large leakage current, as predicted in the paper of Grinberg and Luryi for n-i-n structures. Since these leakage current densities are 3-4 times higher than typical pulsed threshold current densities of QC lasers, undoped InP is inappropriate for proper current confinement in buried heterostructures. In the framework of this thesis, two approaches that could significantly reduce this parasitic current path have been investigated. One strategy targets on reducing the mobility by inserting InAlAs barriers within the i-InP. Another possibility is to use Iron-doped InP, where the Iron acts as a deep level defect that cancels the net charge. We decided to use semi-insulating InP:Fe as blocking material, since less problems in the regrowth on non-planar structures are expected, and trapping of carriers should result in less free-carrier absorption. Furthermore, a new procedure for the etching of narrow waveguides was presented, which allows the fabrication of ridge widths as narrow as 3.5 µm.

Conclusion and Outlook We experimentally and theoretically compared the key parameters of the most promising active region designs for high performance using quantum cascade lasers otherwise identical. The two-phonon resonance design shows the lowest threshold current densities, which is due to narrow linewidths in this design. Therefore, this design is most promising for the realization of low power-consumption single-mode devices. However, the wider gain spectra in the bound-to-continuum design makes this design very interesting for broad gain applications. Fortunately, the stronger matrix element in the bound-to-continuum compensates to a large extent for the wider linewidths. Furthermore, since the two active region designs show different linewidths, the experimental data were used to verify a model to calculate a priori the temperature and field dependent intersubband linewidth in quantum cascade laser designs. We conclude that this model constitutes a useful tool for the development of novel narrow-gain and high wallplug efficiency active region designs or designs for broad gain applications. Our results on low power consumption DFB-based single-mode devices in the 9 µm wavelength range demonstrate the feasibility of realizing portable applications. Low electrical power consumption of 1.6 W and 3.8 W for an optical output power of 16 mW and 100 mW has been demonstrated. While attaining room temperature was a challenge a few years ago, devices operating up to 150 °C in continuous wave were presented. Such devices are tunable by 1.3 % of its center wavelength. We demonstrated that the tuning range of an individual DFB laser of about 1 % could be increased to 8 % of center wavelength by using a broad gain active region design and monolithic integration of different DFB gratings. We achieved high-performance devices with single-mode emission between 7.7 and 8.3 µm at a temperature of +30 °C. Furthermore, an aging test over 11,000 hours revealed no significant long-term degradation and proved the reliability of such devices for real-life applications, such as in multi-channel laser spectrometers for the detection of complex mixtures with multiple absorption lines.

152

Conclusion and Outlook Even broader tuning was attained by using a heterogeneous high-performance quantum cascade laser gain chip comprising two bound-to-continuum active region designs emitting at 8.2 and 9.3 µm. Though a broad gain bandwidth invariably results in a reduced gain cross section, devices with a high-reflection coated back facet still lased CW up to a temperature of 50 °C and showed output powers in excess of 100 mW at 30 °C. This chip was used in our external cavity (EC) setup, operated at room temperature. We demonstrated single-mode tuning of the center wavelength at room temperature of 25 % in pulsed mode and 18 % in CW operation, which is the widest reported tuning range in literature. This gain chip represents a very promising tool for laser photoacoustic spectroscopy (L-PAS) since it can be tuned over 172 cm-1 with output powers in excess of 20 mW in a room-temperature operated EC setup. An output power in excess of 135 mW was reached at the gain maximum in CW mode. Extrapolating from our results at 7-10 µm, devices emitting at 5 µm which consume less than 1 W of electrical power should be feasible, since the waveguide width scales down with the wavelength. This should allow for uncooled applications. A larger frequency coverage can be attained by using heterogeneous quantum cascade lasers with several active regions. However, CW operation will become more and more challenging, requiring more efficient active region designs. An alternative way to engineer a broadband source might be self-assembled quantum dots embedded in quantum cascade structures. This should allow for reducing the non-radiative relaxation rate of the upper laser level by the suppression of LO phonon scattering since the electron motion is quantized in three dimensions [165]. Since these quantum dots result naturally in a nonuniform growth, a broad-gain spectrum is to be expected. Recently, room temperature mid-IR electroluminescence was observed from InAs quantum dots [166].

153

List of abbreviations 2Ph

Two-phonon resonance

AFM

Atomic force microscope

AO

Acoustic optical

AR

Anti reflection

BH

Buried heterostructure

BTC

Bound-to-continuum

CL

As cleaved, uncoated

COMD

Catastrophic optical mirror damage

CW

Continuous wave

DBR

Distributed Bragg reflector

DFB

Distributed feedback

DFG

Difference frequency generation

DTGS

Deuterated triglycine sulphate

EC

External cavity

EDFA

Erbium-doped fiber amplifier

EM

electromagnetic

FP

Fabry-Pérôt

FTIR

Fourier transform infrared

FWHM

Full-width at half maximum

HR

High reflection

HWHM

Half-width half maximum

IC

Interband cascade

ISB

Intersubband

L-PAS

Laser photoacoustic spectroscopy

LED

Light emitting diode

LIV

Light-current-voltage

LO

Longitudinal optical

LPE

Liquid phase epitaxy

List of abbreviations MBE

Molecular beam epitaxy

MCT

Mercury cadmium telluride

MIR

Mid-infrared

MOVPE

Metal organic vapor phase epitaxy

NIR

Near-infrared

OP-GaAs

Orientation-patterned GaAs

OPO

Optical parametric oscillator

PE-SRO

Plasma-enhanced singly resonant oscillator

ppb

Parts-per-billion

PPLN

Periodically-poled LiNbO3

ppt

Parts-per-trillion

QC

Quantum cascade

QPM

Quasi-phase-matched

QW

Quantum well

RT

Room temperature

SEM

Scanning electron microscope

SEM

Scanning electron microscope

SIMS

Secondary ion mass spectroscopy

SL

Superlattice

SMSR

Side-mode suppression ratio

SRO

Singly resonant oscillator

TIR

Total internal reflection

TM

Transversal magnetic

155

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[2]

"Solid-state mid-infrared laser sources," edited by I. T. Sorokina, K. L. Vodopyanov, Topics Appl. Phys. 89 (2003).

[3]

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References unattended monitoring of nitric oxide in the atmosphere,” Opt. Lett. 31, 2012 (2006). [107] J. Faist, C. Gmachl, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. Y. Cho, “Distributed feedback quantum cascade lasers,” Appl. Phys. Lett. 70, 2670 (1997). [108] C. Gmachl, F. Capasso, J. Faist, A. L. Hutchinson, A. Tredicucci, D. L. Sivco, J. N. Baillargeon, S. N. G. Chu, A. Y. Cho, “Continuous-wave and high-power pulsed operation of index-coupled distributed feedback quantum cascade laser at lambda approximate to 8.5 mu m,” Appl. Phys. Lett. 72, 1430 (1998). [109] T. Aellen, S. Blaser, M. Beck, D. Hofstetter, J. Faist, E. Gini, “Continuous-wave distributed-feedback quantum-cascade lasers on a Peltier cooler,” Appl. Phys. Lett. 83, 1929 (2003). [110] J. S. Yu, S. Slivken, S. R. Darvish, A. Evans, B. Gokden, M. Razeghi, “Highpower, room-temperature, and continuous-wave operation of distributedfeedback quantum-cascade lasers at lambda ~ 4.8 µm,” Appl. Phys. Lett. 87, 041104 (2005). [111] S. R. Darvish, W. Zhang, A. Evans, J. S. Yu, S. Slivken, M. Razeghi, “Highpower, continuous-wave operation of distributed-feedback quantum-cascade lasers at lambda ~ 7.8 µm,” Appl. Phys. Lett. 89, 251119 (2006). [112] S. R. Darvish, S. Slivken, A. Evans, J. S. Yu, M. Razeghi, “Room-temperature, high-power, and continuous-wave operation of distributed-feedback quantumcascade lasers at lambda ~ 9.6 µm,” Appl. Phys. Lett. 88, 201114 (2006). [113] A. Wittmann, M. Giovannini, J. Faist, L. Hvozdara, S. Blaser, D. Hofstetter, E. Gini, “Room temperature, continuous wave operation of distributed feedback quantum cascade lasers with widely spaced operation frequencies,” Appl. Phys. Lett. 89, 201115 (2006). [114] A. Wittmann, L. Hvozdara, S. Blaser, M. Giovannini, J. Faist, D. Hofstetter, M. Beck, E. Gini, “High-performamce continuous wave quantum cascade lasers with widely spaced operation frequencies,” Proc. SPIE 6485, 64850P (2007). [115] B. G. Lee, M. A. Belkin, R. Audet, J. MacArthur, L. Diehl, C. Pflugl, F. Capasso, D. C. Oakley, D. Chapman, A. Napoleone, D. Bour, S. Corzine, G. Hofler, J. 166

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References [138] J. Faist, private communication. [139] K. L. Campman, H. Schmidt, A. Imamoglu, A. C. Gossard, “Interface roughness and alloy-disorder scattering contributions to intersubband transition linewidths,” Appl. Phys. Lett. 69, 2554 (1996). [140] T. Unuma, T. Takahashi, T. Noda, M. Yoshita, H. Sakaki, M. Baba, H. Akiyama, “Effects of interface roughness and phonon scattering on intersubband absorption linewidth in a GaAs quantum well,” Appl. Phys. Lett. 78, 3448 (2001). [141] T. Unuma, M. Yoshita, T. Noda, H. Sakaki, H. Akiyama, “Intersubband absorption linewidth in GaAs quantum wells due to scattering by interface roughness, phonons, alloy disorder, and impurities,” J. Appl. Phys. 93, 1586 (2003). [142] S. Tsujino, A. Borak, E. Muller, M. Scheinert, C. V. Falub, H. Sigg, D. Grutzmacher, M. Giovannini, J. Faist, “Interface-roughness-induced broadening of intersubband electroluminescence in p-SiGe and n-GaInAs/AlInAs quantumcascade structures,” Appl. Phys. Lett. 86, 062113 (2005). [143] T. Ando, A. B. Fowler, F. Stern, “Electronic properties of two-dimensional systems,” Rev. Mod. Phys. 54, 437 (1982). [144] J. B. Khurgin, “Inhomogeneous origin of the interface roughness broadening of intersubband transitions,” Appl. Phys. Lett. 93, 091104 (2008). [145] J. Faist, F. Capasso, C. Sirtori, D. Sivco, A. Y. Cho, “Quantum cascade lasers,” in Intersubband transitions in quantum wells: Physics and device applications II, edited by H. C. Liu, F. Capasso, Academic Press, San Diego, 1 (2000). [146] C. Sirtori, F. Capasso, J. Faist, A. L. Hutchinson, D. L. Sivco, A. Y. Cho, “Resonant tunneling in quantum cascade lasers,” IEEE J. of Quantum Electron. 34, 1722 (1998). [147] S. S. Howard, Z. J. Liu, D. Wasserman, A. J. Hoffman, T. S. Ko, C. E. Gmachl, “High-performance quantum cascade lasers: Optimized design through waveguide and thermal Modeling,” IEEE J. Sel. Topics in Quantum Electron. 13, 1054 (2007). [148] C. Gmachl, F. Capasso, A. Tredicucci, D. L. Sivco, R. Köhler, A. L. Hutchinson, A. Y. Cho, “Dependence of the device performance on the number of stages in 169

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References [160] S. Blaser, A. Baechle, S. Jochum, L. Hvozdara, G. Vandeputte, S. Brunner, S. Hansmann, A. Muller, J. Faist, “Low-consumption (below 2W) continuous-wave singlemode quantum-cascade lasers grown by metal-organic vapour-phase epitaxy,” Electron. Lett. 43, 1201 (2007). [161] Z. Liu, C. F. Gmachl, C. G. Caneau, C. Zah, “Very small (<1.2-1.7 W) heat dissipation, room temperature, continuous-wave quantum cascade lasers at lambda~5.3 µm,” CLEO/QELS 2008 CTuF2, 1 (2008). [162] S. Slivken, J. S. Yu, A. Evans, J. David, L. Doris, M. Razeghi, “Ridge-width dependence on high-temperature continuous-wave quantum-cascade laser operation,” IEEE Photon. Techn. Lett. 16, 744 (2004). [163] R. Maulini, M. Beck, J. Faist, E. Gini, “Broadband tuning of external cavity bound-to-continuum quantum-cascade lasers,” Appl. Phys. Lett. 84, 1659 (2004). [164] M. Pushkarsky, M. Weida, T. Day, D. Arnone, R. Pritchett, D. Caffey, S. Crivello, “High-power tunable external cavity quantum cascade laser in the 5-11 micron regime,” Proc. SPIE 6871, 68711X (2008). [165] N. S. Wingreen, C. A. Stafford, “Quantum-Dot Cascade Laser: Proposal for an Ultralow-Threshold Semiconductor Laser,” IEEE J. of Quantum Electron. 33, 1170 (1997). [166] D. Wasserman, T. Ribaudo, S. A. Lyon, S. K. Lyo, E. A. Shaner, “Room temperature midinfrared electroluminescence from InAs quantum dots,” Appl. Phys. Lett. 94, 061101 (2009).

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Acknowledgement I would like to express my gratitude to many people for this fruitful time as a PhD student. First and foremost, I wish to thank Prof. Dr. Jérôme Faist for giving me the opportunity to work in his group. He gave me the chance to do research on quantum cascade lasers and semiconductor processing technology. He supported me during the sometimes very challenging 4 12 years of my PhD, and was always available to discuss the physics of our devices and offer me advice and direction concerning the progression of my work. I would also like to express my gratitude to several others: Prof. Dr. M. W. Sigrist and Prof. Dr. J. Wagner for their willingness to be my coexaminers. Dr. Yargo Bonetti for proofreading this work. It was a pleasure sharing the office and most of my lunch breaks with you. The MBE/MOVPE team: Dr. Mattias Beck, Martin Ebnöther, Milan Fischer, Dr. Emilio Gini, Dr. Marcella Giovannini and Nicolas Hoyler for the epitaxial growth and regrowth of my samples. Res Neiger for the high-precision lapping of my samples. There was just one accident in four years when the sample was thinned down to 90 µm instead of 150 µm, which saved me a lot of measurement time. Andreas Hugi for his staying power until late at night when we explored our devices in the external cavity setup while enjoying pizza. When we left the Institute at around 3.00 AM, we had beaten all world records in broadband tuning. Dr. Max Döbeli for the Super-SIMS measurement. Hansruedi Scherrer and his trainees for the evaporation of Indium on our diamond mounts.

Acknowledgement Hansjakob Rusterholz for keeping a cool head while replacing the hard drive of my iBook. Furthermore, I would like to thank all the people I met while working in ETH’s FIRST laboratory for sharing their technological tricks and support, especially Andreas Alt, Dr. Peter Cristea, Yuriy Fedoryshyn, Dr. Matthias Golling, Peter Kaspar, Dr. Hans-Jörg Lohe, Dr. Frank Robin, Dr. Andreas Rutz, Dr. Patric Strasser, Dr. Heiko Unold, Dr. Werner Vogt and Dr. Yohan Barbarin. Likewise, I am very grateful to the FIRST team: Dominique Aeschbacher, Sandro Bellini, Petra Burkard, Martin Ebnöther, Christian Fausch, Dr. Emilio Gini, Dr. Otte Homan, Maria Leibinger, Hansjakob Rusterholz, Dr. Silke Schön for keeping the cleanroom running and for giving me their constant support. I would like to thank Walter Bachmann, Marcel Baer, Harald Hediger, Andreas Stuker and the workshop team for their excellent work. Special thanks to all the current and former QOE members not previously mentioned: Dr. Thiery Aellen, Dr. Lassad Ajili, Maria Amanti-Bismuto, Alfredo Bismuto, Kemal Celebi, Dr. Laurent Diehl, Milan Fischer, Dr. Marcella Giovannini, Tobias Gresch, Nicolas Hoyler, Erna Hug, Dr. James Lloyd-Hughes, Dr. Valeria Liverini, Dr. Richard Maulini, Dr. Laurent Nevou, Dr. Giacomo Scalari, Dr. Maxi Scheinert, Dr. Lorenzo Sirigu, Romain Terazzi, Christoph Walther, Samuel Wiesendanger, Dr. Dmitri Yarekha. It was a great pleasure working with you. I am also grateful to the staff members of our Industrial Partners, Alpes Lasers SA (Neuchâtel, Switzerland) and AL Technology GmbH (Darmstadt, Germany), to which we sucessfully transferred the developed high-yield fabrication process: Dr. Andreas Bächle,

Dr.

Stéphane

Blaser,

Sophie

Brunner,

Steffen

Bunzel,

Emmanuel

Gentilhomme, Stéphane Goeckeler, Dr. Stefan Hansmann, Sandra Hofmann, Dr. Martin Honsberg, Sandrine Huin, Dr. Lubos Hvozdara, Dr. Stephan Jochum, Dr. Antoine Müller, Lim-Vitou Nam, Vanessa Piot and Guillaume Vandeputte.

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Acknowledgement Many thanks to all our friends, especially Dr. Ernst-Eberhard Latta, René, Esther and Cornelia Lips, Penelope and Werner Pfleger, Daniel und Maja Suter for their support, encouragement, counsel, advice and the enjoyable times we spent together. Finally, I would like to express my gratitude to the members of my family: my parents, Günther and Hildegund Wittmann, my parents-in-law, Boris and Gudrun Soucek, my sister, Christine and my brother, Wolfgang and his wife Suzan, as well as my brother and sister-in-law, Sinja and Alex Matter. Last but not least, I would like to thank my wife, Nadia, for her love and great support during my Master and PhD studies. I would not have been able to do this without you! This project was financially supported by the Swiss Commission for Technology and Innovation (CTI) and the Swiss National Science Foundation (NCCR-Quantum Photonics). Zurich, April 27, 2009

Andreas Wittmann

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Curriculum vitae Personal data Name

Andreas Wittmann

Date of birth

2nd January 1974 (Neuburg an der Donau, Germany)

Nationality

German, Swiss (dual nationality)

Marital status

Married, 1 daughter

Education 2009

PhD degree in Physics from the Swiss Federal Institute of Technology Zurich (ETH Zurich), Switzerland

2007 – 2009

PhD studies in Physics at Swiss Federal Institute of Technology Zurich (ETH Zurich), Switzerland

2004 – 2007

PhD studies in Physics at the University of Neuchâtel, Switzerland

2004

Master’s degree in Electrical Engineering from Technical University of Munich (TUM), Germany

2002 – 2004

Master studies in Electrical Engineering at Technical University of Munich (TUM), Germany

1997

Diploma degree in Precision and Micro Engineering, University of Applied Sciences Nuremberg, Germany

1992 – 1997

Bachelor studies in Precision and Micro Engineering, University of Applied Sciences Nuremberg, Germany

Professional experience Nortel Networks Optical Components AG, Zurich Switzerland (former JDS Uniphase, Laser Enterprise, spin-off of IBM Research Laboratory Zurich) 2001 – 2002

Group leader of the mirror-coating & electro-optical testing division

2000 – 2001

Project leader for the realization of a new production line

1998 – 2002

Process engineer for semiconductor laser mirror coatings

Publications Journal papers 1.

A. Wittmann, Y. Bonetti, M. Fischer, J. Faist, S. Blaser, E. Gini, Distributed Feedback Quantum Cascade Lasers at 9 µm Operating in Continuous Wave up to 423 K, Photon. Techn. Lett., accepted for publication.

2.

B. G. Lee, H. A. Zhang, C. Pflügl, L. Diehl, M. A. Belkin, M. Fischer, A. Wittmann, J. Faist, F. Capasso, Broadband distributed feedback quantum cascade laser array operating from 8.0 to 9.8 microns, Photon. Techn. Lett., accepted for publication.

3.

A. Wittmann, A. Hugi, E. Gini, N. Hoyler, J. Faist, Heterogeneous highperformance quantum cascade laser sources for broadband tuning, IEEE J. Quantum Electron. 44, 1083 (2008).

4.

R. Terazzi, T. Gresch, A. Wittmann, J. Faist, Sequential resonant tunneling in quantum cascade lasers, Phys. Rev. B 78, 155328 (2008).

5.

C. Pflügl, M. A. Belkin, Q. J. Wang, M. Geiser, A. Belyanin, M. Fischer, A. Wittmann, J. Faist and F. Capasso, Surface-emitting THz quantum cascade laser source based on intracavity difference-frequency generation, Appl. Phys. Lett. 93, 161110 (2008).

6.

A. Wittmann, Y. Bonetti, J. Faist, E. Gini, M. Giovannini, Intersubband linewidths in quantum cascade laser designs, Appl. Phys. Lett. 93, 141103 (2008).

7.

M. A. Belkin, F. Capasso, F. Xie, A. Belyanin, M. Fischer, A. Wittmann, J. Faist, Room temperature terahertz quantum cascade laser source based on intracavity difference-frequency generation, Appl. Phys. Lett. 92, 201101 (2008).

8.

A. Wittmann, T. Gresch, E. Gini, L. Hvozdara, N. Hoyler, M. Giovannini, J. Faist, High-Performance Bound-to-Continuum Quantum-Cascade Lasers for Broad-Gain Applications, IEEE J. Quantum Electron. 44, 36 (2008).

Publications 9.

A. Mohan, A. Wittmann, A. Hugi, S. Blaser, M. Giovannini, J. Faist, Room temperature continuous-wave operation of an external-cavity quantum cascade laser, Opt. Lett. 32, 2792 (2007).

10. A. Wittmann, M. Giovannini, J. Faist, L. Hvozdara, S. Blaser, D. Hofstetter, E. Gini, Room temperature, continuous-wave operation of distributed feedback quantum cascade lasers with widely spaced operation frequencies, Appl. Phys. Lett. 89, 201115 (2006). Patent 11. A. Wittmann, M. Gotza, M. Solar, E.-E. Latta, T. Kellner, M. Krejci, Antireflection coatings for semi-conductor lasers, US 2004/0151226 (2004). Invited Talk 12. A. Wittmann, A. Hugi, Y. Bonetti, M. Fischer, M. Beck, J. Faist, L. Hvozdara, S. Blaser, E. Gini, Single-mode quantum cascade lasers for spectroscopy, Laser seminar ETH Zurich, Zurich (Switzerland), October 20 (2008). Talks and conference proceedings 13. S. Blaser, L. Hvozdara, P. Horodysky, S. Brunner, G. Vandeputte, A. Muller, A. Bächle, S. Jochum, M. Honsberg, A. Wittmann, Y. Bonetti, M. Beck, E. Gini and J. Faist, MOVPE grown single-mode quantum-cascade lasers, International Quantum Cascade Lasers School & Workshop, Monte Verita (Switzerland), September 14-19 (2008). 14. A. Hugi, A. Wittmann, R. Terazzi, E. Gini, S. Blaser, M. Beck, J. Faist, Broadband external-cavity quantum cascade laser, International Quantum Cascade Lasers School & Workshop, Monte Verita (Switzerland), September 14-19 (2008). 15. A. Wittmann, A. Hugi, Y. Bonetti, M. Fischer, M. Beck, J. Faist, M. Giovannini, N. Hoyler, D. Hofstetter, L. Hvozdara, and S. Blaser, High-performance singlemode and broadly tunable quantum cascade laser sources, Mid-Infrared

177

Publications Optoelectronics: Materials and Devices (MIOMD-IX), Freiburg (Germany), September 7-11 (2008). 16. L. Hvozdara, S. Blaser, S. Brunner, G. Vandeputte, A. Muller, A. Bächle, S. Jochum, M. Honsberg, A. Wittmann, M. Beck, J. Faist and E. Gini, Prospects of the quantum cascade lasers in spectroscopic applications, 3rd International Workshop on Infrared Plasma Spectroscopy (IPS2008), Greifswald (Germany), July 23-25 (2008). 17. A. Hugi, A. Wittmann, A. Mohan, S. Blaser, M. Giovannini, J. Faist, Broadband external-cavity quantum cascade laser, Annual Meeting of Swiss Physical Society, Geneva (Switzerland), March 26-27 (2008). 18. A. Muller, S. Blaser, L. Hvozdara, S. Brunner, G. Vandeputte, A. Bächle, S. Jochum, M. Honsberg, S. Hansmann, A. Wittmann and J. Faist, Continuous-wave quantum cascade lasers, Field Laser Applications in Industry and Research (FLAIR 2007), Florence (Italy), September 2-7 (2007). 19. A. Wittmann, L. Hvozdara, S. Blaser, M. Giovannini, J. Faist, D. Hofstetter, M. Beck, E. Gini, High-performamce continuous wave quantum cascade lasers with widely spaced operation frequencies, Proc. SPIE 6485, 64850P (2007). 20. A. Wittmann, L. Hvozdara, S. Blaser, M. Giovannini, J. Faist, D. Hofstetter, M. Beck, E. Gini, High-performamce continuous wave quantum cascade lasers with widely spaced operation frequencies, Novel In-Plane Semiconductor Lasers VI, Photonics West 2007, San Jose (USA), January 20-25 (2007). 21. A. Muller, S. Blaser, L. Hvozdara, A. Wittmann, N. Hoyler, M. Giovannini, J. Faist, W. Vogt and E. Gini, Room-temperature continuous-wave single-mode quantum cascade lasers, The 2nd International Workshop on Quantum Cascade Lasers, Marina di Ostuni, Brindisi (Italy), September 6-9 (2006). 22. B. Schmidt, S. Pawlik, N. Matuschek, J. Muller, T. Pliska, J. Troger, N. Lichtenstein, A. Wittmann, S. Mohrdiek, B. Sverdlov, C. Harder, 980 nm single mode modules yielding 700 mW fiber coupled pump power, OFC 2002, 702 (2002).

178