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Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series / Editor in Chief: W. Martienssen
Group III: Condensed Matter Volume 33
Diffusion in Semiconductors and Non-Metallic Solids Subvolume A Diffusion in Semiconductors Editor D.L. Beke Authors C.E. Allen, D.L. Beke, H. Bracht, C.M. Bruff, M.B. Dutt, G. Erdélyi, P. Gas, F.M. d'Heurle, G.E. Murch, E.G. Seebauer, B.L. Sharma, N.A. Stolwijk
13
ISSN 0942-7988 (Condensed Matter) ISBN 3-540-60964-4 Springer-Verlag Berlin Heidelberg New York Library of Congress Cataloging in Publication Data Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie Editor in Chief: W. Martienssen Vol. III/33A: Editor: D. Beke At head of title: Landolt-Börnstein. Added t.p.: : Numerical data and functional relationships in science and technology. Tables chiefly in English. Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Börnstein of which the 6th ed. began publication in 1950 under title: Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik. Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag Includes bibliographies. 1. Physics--Tables. 2. Chemistry--Tables. 3. Engineering--Tables. I. Börnstein, R. (Richard), 1852-1913. II. Landolt, H. (Hans), 1831-1910. III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology. QC61.23 502'.12 62-53136
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from SpringerVerlag. Violations are liable for prosecution act under German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Product Liability: The data and other information in this handbook have been carefully extracted and evaluated by experts from the original literature. Furthermore, they have been checked for correctness by authors and the editorial staff before printing. Nevertheless, the publisher can give no guarantee for the correctness of the data and information provided. In any individual case of application, the respective user must check the correctness by consulting other relevant sources of information. Cover layout: Erich Kirchner, Heidelberg Typesetting: Files from redaction Landolt-Börnstein, Darmstadt Printing: Computer to plate, Mercedes-Druck, Berlin Binding: Lüderitz & Bauer, Berlin SPIN: 10426818
63/3020 - 5 4 3 2 1 0 - Printed of acid-free paper
Editor D.L. Beke Department of Solid State Physics, L. Kossuth University, 4010 Debrecen, Hungary
Authors C.E. Allen Department of Chemical Engineering, University of Illinois, Urbana, IL 61801-3792, USA Surface diffusion on semiconductors (subvolume A, Chap. 7) Surface diffusion on non-metallic solids (subvolume B, Chap. 12)
D.L. Beke Department of Solid State Physics, L. Kossuth University, 4010 Debrecen, Hungary General introduction (subvolume A and B, Chap. 1) Grain-boundary and dislocation diffusion in semiconductors and silicides (subvolume A, Chap. 6) Grain-boundary and dislocation diffusion in non-metallic solids (subvolume B, Chap. 11)
F. Bénière Groupe Matière Condensée et Matériaux, Université de Rennes, F-35042 Rennes Cedex, France Diffusion in alkali and alkaline earth halides (subvolume B, Chap. 2)
H. Bracht Institut für Metallforschung, Universität Münster, D-48149 Münster, Germany Diffusion in silicon, germanium and their alloys (subvolume A, Chap. 2)
C.M. Bruff Department of Mechanical Engineering, The University of Newcastle, Newcastle, NSW 2308, Australia Chemical diffusion in bulk inhomogeneous semiconductors (subvolume A, Chap. 5) Chemical diffusion in bulk inhomogeneous non-metallic compounds (subvolume B, Chap. 10)
A.W. Chadwick Chemical Laboratory, University of Kent, Canterbury, Kent CT2 6NH, UK Diffusion in fast-ion conducting solids (subvolume B, Chap. 3) Diffusion in molecular solids (subvolume B, Chap. 8)
F.M. d'Heurle IBM Research Center, Yorktown Heights, NY 10598, USA Royal Institute of Technology, (F.T.E. - KTH) 16440 Kista-Stockholm, Sweden Diffusion in silicides (subvolume A, Chap. 4)
M.B. Dutt Solid State Physics Laboratory, Delhi-110054, India Diffusion in compound semiconductors (subvolume A, Chap. 3)
G. Erdélyi Department of Solid State Physics, L. Kossuth University, 4010 Debrecen, Hungary Grain-boundary and dislocation diffusion in semiconductors and silicides (subvolume A, Chap. 6) Diffusion in miscellaneous ionic substances (subvolume B, Chap. 4) Grain-boundary and dislocation diffusion in non-metallic compounds (subvolume B, Chap. 11)
F. Faupel Lehrstuhl für Materialverbunde, Christian-Albrechts-Universität, D-24143 Kiel, Germany Diffusion in glassy and semicrystalline polymeres (subvolume B, Chap. 9)
P. Gas Laboratoire de Metallurgie, CNRS - Université Aix-Marseille III, F-13397 Marseille Cedex 20, France Diffusion in silicides (subvolume A, Chap. 4)
C.H. Hsieh Department of Material Science and Engineering, Whitaker Laboratory, Leigh University, Bethlehem, PA 18015-3195, USA Diffusion in oxide glasses (subvolume B, Chap. 7)
H. Jain Department of Material Science and Engineering, Whitaker Laboratory, Leigh University, Bethlehem, PA 18015-3195, USA Diffusion in oxide glasses (subvolume B, Chap. 7)
G. Kroll Lehrstuhl für Materialverbunde, Christian-Albrechts-Universität, D-24143 Kiel, Germany Diffusion in glassy and semicrystalline polymeres (subvolume B, Chap. 9)
Hj. Matzke Institut für Transuran Elemente (ITU), Angewandte Physik, D-76125 Karlsruhe, Germany Diffusion in carbides, hydrides, nitrides, and borides (subvolume B, Chap. 5)
C.J.A. Monty CNRS Institut de Science et de Génie des Materiaux et Procédés, Odeillo, F-66125 Font-Romeu, Cedex, France Diffusion in oxides (subvolume B, Chap. 6)
G.E. Murch Department of Mechanical Engineering, The University of Newcastle, Newcastle, NSW 2308, Australia Chemical diffusion in semiconductors (subvolume A, Chap. 5) Chemical diffusion in non-metallic solids (subvolume B, Chap. 10)
V. Rondinella Institut für Transuran Elemente (ITU), Angewandte Physik, D-76125 Karlsruhe, Germany Diffusion in carbides, hydrides, nitrides, and borides (subvolume B, Chap. 5)
E.G. Seebauer Department of Chemical Engineering, University of Illinois, Urbana, IL 61801-3792, USA Surface diffusion on semiconductors (subvolume A, Chap. 7) Surface diffusion on non-metallic solids (subvolume B, Chap. 12)
B.L. Sharma Solid State Physics Laboratory, Delhi-110054, India Diffusion in compound semiconductors (subvolume A, Chap. 3)
N.A. Stolwijk Institut für Metallforschung Universität Münster D-48149 Münster, Germany Diffusion in silicon, germanium and their alloys (subvolume A, Chap. 2)
Preface
This new volume of Landolt-Börnstein consists of two subvolumes. Originally we intended to collect all data on diffusion in non-metalllic solids in one volume, but during the collation and selection of experimental data it turned out that both the field and the number of data are too large to be compressed into a single volume only. Thus, finally, it was decided to publish two subvolumes: A on "Diffusion in Semiconductors" and B on "Diffusion in Non-Metallic Solids". This separation - we hope - also reflects the expected difference in the interest of potential users. Since a volume on Diffusion in Solid Metals and Alloys (Landolt-Börnstein, New Series, Volume III/26), edited by H. Mehrer, had already been published in 1990, we wanted to follow its excellent and clear presentation. We, therefore, hope that these new two subvolumes and the previous one on diffusion can be considered as a truly complete collection of selected data on diffusion in solids. However, there are some minor differences between these and the previous volume. First of all, the atomic mechanism of diffusion in non-metallic solids proved to comprise more complex phenomena than the transport in metallic systems. Usually, in order to interpret the results, various defects, site preferences and mechanisms should be taken into account even for bulk diffusion. For example, the importance of self interstitials, the kick-out and the dissociative mechanism, the role of sources and sinks (surfaces, dislocations) in the case of volume heterodiffusion in silicon was recognised only at the beginning of the eighties. Furthermore, the problem of the deviation from stoichiometry (and the effect of the partial overpressure of components) or the presence of some dopants, (small amounts of which can result in an extrinsic diffusion regime where the concentration of the diffusion vehicles is determined not by thermal activation, but, for example by the number of charge compensating vacancies), makes the interpretation of experimental results more difficult. Secondly, especially in materials important in different technological applications (semiconductors, different oxides) - because of the practical demand for any data on diffusion - a huge number of investigations already have been carried out starting in the fifties. In these measurements some of the possible complications (arising, for example, from sources listed above) were neglected (e.g. the control of one or more additional parameters was not made) and also in their interpretation - because of the insufficiency of the relevant theories available at that time - crude approximations were applied. This situation made the work of the contributing authors very complicated and time-consuming. This fact, perhaps, can make some delay forgivable in the appearance of these volumes as compared to our original intent and partly explains that sometimes the extent of the introductions at certain chapters is longer than would generally be expected. The critical compilation of data was carried out by 21 experts in diffusion. Subvolume A consists of 6 chapters for the following materials and properties: diffusion in silicon, germanium and their alloys, diffusion in compound semiconductors, diffusion in silicides, chemical diffusion in bulk inhomogeneous semiconductors, grain-boundary and dislocation diffusion in semiconductors and silicides and surface diffusion on semiconductors. Although most of the silicides are not semiconducting, because a number of them have become integrated in the Si technology and because they were not covered in the previous volume on diffusion in metallic substances this chapter is included here. Furthermore, there is an increasing number of measurements on chemical diffusion in thin multilayer systems, and since the vast majority of them are made on amorphous or crystalline semiconductors (mostly on SixGe1−x multilayers) these data were collected in the chapter on diffusion in silicon, germanium and their alloys. Subvolume B contains 11 chapters on diffusion in alkali and alkaline earth halides, diffusion in fast-ion conducting solids, diffusion in borates, chlorates, molibdenates, niobates, phosphates, silicates and sulfates, diffusion in carbides, hydrides, nitrides and borides, diffusion in oxides, diffusion in oxide glasses, diffusion in molecular solids, diffusion in glassy and semicrsytalline polymers, chemical diffusion in bulk inhomogeneous non-metallic compounds, grain-boundary and dislocation diffusion in non-metallic
compounds and surface diffusion on non-metallic solids. Both subvolumes contain the same general introductory chapter acquainting the user with the basic concepts and experimental methods of the field. I am very grateful to the authors of the chapters for their co-operation in many details. The excellent collaboration with the editors-in-chief, O. Madelung and W. Martienssen, and with the editorial staff of Landolt-Börnstein, in particular with Dr. R. Poerschke and Dr. H. Seemüller was always encouraging. I would also like to express my gratitude to all members of the diffusion group of our Department here in Debrecen and to my secretary for helping me very efficiently during the preparation of these subvolumes.
Debrecen, December 1997
Dezsô Beke
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-1
5 Chemical diffusion in bulk inhomogeneous semiconductors C.M. BRUFF AND G.E. MURCH
5.1 Introduction In this chapter data are listed on chemical diffusion coefficients in bulk inhomogeneous semiconductors. ~ 2 µm are presented, thus ‘thin film’ data are not listed. Only Only data for essentially ‘bulk’ samples ( > ) technologically important semiconductors are listed in this chapter. Chemical diffusion data in other nonmetallic compounds are listed elsewhere in this volume. ~ The diffusion coefficient D which is measured in a chemical composition gradient, is usually called the chemical diffusion coefficient or occasionally the mutual or collective diffusion coefficient. Infrequently it may even be called a ‘self’ diffusion coefficient but this is definitely inconsistent with general usage which reserves the name self diffusion coefficient for the diffusion coefficient measured in a tracer gradient or the latter diffusion coefficient divided by the tracer correlation factor. Where there is diffusion in diffusion couples such as CdS - CdSe (where the chalcogen components move) or CdTe - ZnTe (where both metal components move) the chemical diffusion coefficient is often termed the interdiffusion coefficient. For diffusion studies in solids in the present context there are three experimental situations that commonly occur: 1
A nonstoichiometric compound changes composition. An example would be CdS changing composition after the cadmium partial pressure in equilibrium with it has altered to some new value. It is usually expected that the new partial pressure would still retain the compound within the same phase field. In general, diffusion of both atomic species could in principle contribute to the change in composition but in practice at the temperatures of measurement one atomic component is usually much slower than the other.
2
Interdiffusion of two compounds from a diffusion couple to form a single phase(s). An example here would be CdS - CdTe. Although it is a ternary system the analysis can be treated in a way very similarly to that for a binary metal couple and the well-known Boltzmann-Matano analysis can be usefully applied.
3
Impurity diffusion in a semiconductor. Ideally, in a formal impurity diffusion experiment, the impurity is present at very low concentrations, so low that it does not affect the diffusion coefficient of the host or the defect concentration, i.e. defect production does not accompany the impurity. When these conditions are obviously not met, the experiment is strictly a chemical diffusion experiment. Clearly it will be subjective in some cases as to specify what was actually measured. We have taken the view that if the author(s) considered the experiment to be a chemical diffusion one then the data are presented here. Otherwise, the data are listed in the impurity chapter in this volume.
Lando lt -Bö rnst ein New Series III/33A
5-2
5 Chemical diffusion in bulk inhomogeneous semiconductors
[Ref. p. 5-25
5.2 Use of the tables In many solids the chemical coefficient is conveniently expressed by an Arrhenius-like equation
~ D = D 0 exp( − Q RT ) ;
(1)
where D0 is the pre-exponential factor, sometimes called the frequency factor, Q is the activation enthalpy, ~ R is the ideal gas constant (R = 8.3145 J mol−1 K−1) and T is the absolute temperature. Since D is usually considered a composite quantity arising from the diffusion coefficients of the individual components as well as including a thermodynamic factor, the activation enthalpy Q does not usually have any useful fundamental meaning. The Arrhenius form of Eq. 1 should be considered at best a convenient empirical form appropriate only over the stated temperature range. Extrapolation outside that range should only be done with considerable caution. It should also be recognised that low temperature chemical diffusion is probably frequently dominated by grain boundary diffusion, the quantitative role of which, unlike its tracer diffusion counterpart, is unfortunately rarely established. In the tables the metal atoms are listed alphabetically irrespective of the nonmetallic component.
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-3
5.3 Data (1 kJ/mol = 0.0104 eV) Composition
~ D0 Q D −4 2 [10 m /s] [kJ/mol] [m2/s]
T - range [K]
Method, Remarks
Fig. no.
Ref.
433
Electrochemical method
1
93S1
433 - 573
Electrochemical method
2
85Y1
CdS
933 - 1033
Electrochemical method
3
71K1
CdS - ZnS
1373
Diffusion couple (growth of CdS on ZnS)
4
71B1
1064 - 1281
S-Se source for indiffusion. ~ D independent of x in the range 0<x<0.5
1023 - 1223
Diffusion couple
Ag2+δTe
CdS - CdSe (CdS1-xSex)
2.2.10−1
253
CdSe - CdTe (Metal rich)
82N1
5
74L1
wCdTe 209
0.1
1.0.10−2 9.0.10−3
0.3
1.0.10−3
175.6
0.5
5.0.10−4
167.2
0.7
7.0.10−4
167.2
0.9
3.0.10−3 9.0.10−3
175.6
0.0
1.0
200.6
183.9
(Chalcogen rich)
6
wCdTe 200.6
0.7
2.0.10−1 4.0.10−2
0.9
2.0.10−3
142.1
CdSe - ZnSe (Metal rich)
6.39.10−4 180.3
0.5
CdTe
Lando lt -Börnst ein New Series III/33A
179.7
973 - 1223
Cd (or CdSe) indiffusion
873 - 1073
Electrical conductivity
73M1
7
70Z1
5-4
Composition
5 Chemical diffusion in bulk inhomogeneous semiconductors ~ D0 Q D −4 2 [10 m /s] [kJ/mol] [m2/s]
[Ref. p. 5-25
T - range [K]
Method, Remarks
573 - 873
8 Diffusion couple. Activation energies at different compositions and Hg overpressures given in reference
87T1 87T2
823 - 873
Growth kinetics method
9, 10
75S1
623 - 853
Diffusion couple
11, 12 63B1
675 - 855
Diffusion couple. Data for 13 In and Cu doped material given in reference.
66B1
553 - 613
Hg indiffusion. No difference between nand p-type crystals
84T1
(CdxHg1−xTe)
723 - 973
Vapour phase growth method
14
87F1
x = 0.03, 0.2, 0.39
663
Cd - Hg source
15
91Y1
x = 0.2
623 - 773
CdTe - HgTe
5.103
192.8
748 - 898
Fig. no.
Ref.
17 Diffusion couple
81L1
Doped with 1 mol.% In
17
Doped with 1 mol.% Ag
18
Metal rich Te rich Stoichiometric CdTe - ZnTe
973 - 1283
Diffusion couple. Some additional data given in reference for polycrystalline material
73B1
298
Electrochemical method. Compositions not stated.
88K1
wCdTe 0.0
1.3
221.1
0.1
1.5
218.2
0.3
1.1
211.9
0.5
1.8
211.9
0.7
2.5
211.9
0.9
2.1
204.0
1.0
0.4
181.8
CuInS2
~ D = 2.3.10−13 - 3.2.10−10
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
Composition
~ D0 Q D −4 2 [10 m /s] [kJ/mol] [m2/s]
T - range [K]
Method, Remarks
CuInSe2
~ D = 4.0.10−13 - 2.7.10−9
298
Electrochemical method. Compositions not stated.
1073 - 1373
P indiffusion
GaAs - GaP
5-5
Fig. no.
Ref. 88K1
19, 20 76J1
GaP - InP
7.102
303.6
923 - 998
X-ray diffraction method. Results averaged over 2 values of degree of interdiffusion.
89V1
GeTe - SnTe
1.3.10−5
58.1
723 - 893
Diffusion couple
70A1
623 - 773
Diffusion couple
77L1
HgSe - HgTe Undoped
21 - 23
Chalcogen rich
24 - 26
Metal rich
27 - 29
HgTe - ZnTe
673 - 873
Diffusion couple
30
86P1
863
Diffusion couple
31
74L3
PbS - PbSe Undoped
Diffusion couple 923 - 1223
79L1 32 - 34
Chalcogen rich
35 - 37
Lead rich
1073 - 1273
PbSe
573 - 900
Vapour phase
41
Pb0.93Sn0.07Se
573 - 773
transport method
42
PbSe - PbTe Undoped
38 - 40
Diffusion couple 773 - 1068
74L2 43 - 45
Chalcogen rich
673 - 923
46 - 48
Lead rich
923 - 1073
49 - 51
Lando lt -Bö rnst ein New Series III/33A
68C1
5-6
Composition
5 Chemical diffusion in bulk inhomogeneous semiconductors ~ D0 Q D −4 2 [10 m /s] [kJ/mol] [m2/s]
T - range [K]
Method, Remarks
[Ref. p. 5-25
Fig. no.
PbSe - SnSe
Ref. 75L1
(Minimum pressure)
52
wPbSe 0.0
0.31 5.3.101
200.6
0.1 0.2
1.2.102
246.2
0.3
1.2.102
246.6
0.38
1.2.102
246.6
0.56
5.6
223.2
0.6
2.7
217.4
0.7
0.43 6.5.10−2
202.3
1.0.10−2 1.6.10−3
172.2
0.8 0.9 1.0
239.9
187.3 157.2
(Selenium rich)
53
wPbSe 151.7
0.1
9.6.10−3 3.7.10−3
0.2
1.6.10−3
139.2
0.3
134.2
0.38
7.7.10−4 4.4.10−4
0.56
2.6.10−4
112.4
0.6
2.3.10−4
113.7
0.7
117.0
0.8
1.9.10−4 1.6.10−4
0.9
1.4.10−4
125.0
1.0
1.3.10−4
130.0
0.0
145.0
130.4
120.8
(Metal rich)
873 - 1023
54
wPbSe 0.0
0.94 7.5.10−2
200.6
0.1 0.2
1.0.10−2
160.9
0.3
2.8.10−3
150.5
0.38
1.5.10−3
145.5
0.56
138.8
0.6
2.6.10−3 2.0.10−3
0.7
9.8.10−4
138.8
178.5
138.8
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
Composition
5 Chemical diffusion in bulk inhomogeneous semiconductors ~ D0 Q D −4 2 [10 m /s] [kJ/mol] [m2/s]
T - range [K]
Method, Remarks
5-7
Fig. no.
Ref.
PbSe - SnSe (cont.) wPbSe 139.6
0.9
5.3.10−4 1.3.10−3
1.0
0.11
196.9
0.8
153.4
PbTe - SnTe (Pb1−xSnxTe) (initial) x: 6.2.10−2
Vapour phase transport method
3.9.10−2
4.3.10−16 5.4.10−16
6.5.10−2 11.3.10−2
1.8.10−16 3.9.10−16
5.7.10−2 5.3.10−2 (Bi doped)
3.9.10−16 5.0.10−16
PbTe - SnTe
88A1
873
Diffusion couple
(Minimum pressure)
75L1 55
wPbTe 9.8.10−4 1.1.10−3
127.1 131.3
0.3
1.3.10−3 1.6.10−3
0.4
1.8.10−3
137.1
0.5
2.1.10−3
140.4
0.6
143.8
0.7
2.4.10−3 2.5.10−3
0.8
2.8.10−3
150.9
0.9
3.0.10−3
155.1
1.0
3.3.10−3
159.3
127.1
0.1
3.2.10−3 1.9.10−2
0.2
7.2.10−2
155.5
0.3
0.16
164.3
0.4
0.23
170.1
0.5
0.29
174.3
0.0 0.1 0.2
129.2 134.2
147.1
(Tellurium rich) wPbTe 0.0
Lando lt -Bö rnst ein New Series III/33A
56 143.0
5-8
Composition
5 Chemical diffusion in bulk inhomogeneous semiconductors ~ D0 Q D −4 2 [10 m /s] [kJ/mol] [m2/s]
T - range [K]
Method, Remarks
[Ref. p. 5-25
Fig. no.
Ref.
PbTe - SnTe (cont.) wPbTe 0.6
0.33
178.1
0.7
0.31
180.6
0.8
180.2
0.9
0.22 8.3.10−2
1.0
3.5.10−3
153.8
175.6
(Metal rich) wPbTe
873 - 1023
0.0
0.34
184.3
0.1
0.13 5.3.10−2
176.8
0.2 0.3
2.2.10−2
163.0
0.4
1.0.10−2
157.2
0.5
4.8.10−3
151.3
0.6
145.9
0.7
2.4.10−3 1.6.10−3
0.8
2.1.10−3
144.6
0.9
1.5.10−2
159.7
1.0
0.2
178.9
57
169.7
142.5
ZnSe - ZnTe
1123 - 1223
Diffusion couple
74L1
(Stoichiometric)
58
(Chalcogen rich)
59
wZnTe 0.5
4.10−1
213.2
(Metal rich)
60
wZnTe 405.5
0.1
5.0.105 7.104
0.3
4.104
376.2
0.5
1.106
405.5
0.7
438.9
0.9
6.107 7.106
1.0
2.106
392.9
0.0
388.7
409.6
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-9
Figures for 5 0.35 0.30
Chem.diff.coeff. D [10 m s ]
– 6 2 –1
0.25 0.20 0.15 0.10
0
2 –1
6 4
9 8 7 6
0.50
0.75 3
1.00
1.25
1.50
–14
2⋅10
CdS - ZnS
CdS
T = 1373 K
–14
10
4 2 –1
Chem.diff.coeff. D [m s ]
8
3
2
–10
0.90
0.25
2
10 δ ~ Fig. 2. Ag2+δTe. Chemical diffusion coefficient D as a function of δ in Ag2+δTe at different temperatures T = 433 K, 523 K and 573 K [85Y1].
5
10
3
0
-2.5
–9
Chem.diff.coeff. D [m s ]
8
1
-7.5 -5.0 -10.0 -12.5 4 10 δ ~ Fig. 1. Ag2+δTe. Chemical diffusion coefficient D as a function of δ in Ag2+δTe at T = 433 K [93S1].
10
1 T = 433 K 523 K 2 573 K 3
2
0.05 2.5
Ag2+δ Te
10
T = 433 K
– 4 2 –1
Chem.diff.coeff. D [10 m s ]
12
Ag2+δ Te
0.94
0.98 1.02 –3 –1 Inv. temp. 1/T [10 K ]
1.06
1.10
~ Fig. 3. CdS. Chemical diffusion coefficient D in CdS as a function of inverse temperature 1/T [71K1].
6
4
2
–15
10
–16
6⋅10
0
20
40 60 Concentration of Zn [at %]
80
100
~ Fig. 4. CdS-ZnS. Chemical diffusion coefficient D in CdS-ZnS as a function of at% Zn at T = 1373 K [71B4].
Lando lt -Bö rnst ein New Series III/33A
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-10
–14
–13
4⋅10
4⋅10
CdSe - CdTe
T = 1223 K
–13
Cd Se - CdTe
T = 1223 K
10 2 –1
2 –1
Chem.diff.coeff. D [m s ]
10
Chem.diff.coeff. D [m s ]
–14
1123 K –15
1123 K –14
10
10
1023 K –16
1023 K –15
10
10
–17
10
[Ref. p. 5-25
CdSe
0.2
0.4 0.6 Mass fraction CdTe wCdTe
0.8
CdTe
~ Fig. 5. CdSe-CdTe. Chemical diffusion coefficient D in cadmium rich CdSe-CdTe as a function of mass fraction CdTe wCdTe for T = 1023-1223 K [74L1).
–16
10
CdSe
0.2
0.4 0.6 Mass fraction CdTe wCdTe
0.8
CdTe
~ Fig. 6. CdSe-CdTe. Chemical diffusion coefficient D in chalcogen rich CdSe-CdTe as a function of mass fraction of CdTe wCdTe for T = 1023-1223 K [74L1].
–9
2⋅10
CdTe
–9 8
T = 1073 K
6
2 –1
Chem.diff.coeff. D [m s ]
10
4
minimum Cd pressure
973 K
2 –10
10
8
873 K
6
Cd-rich liquidus
4 –11
2⋅10
–4
10
–3
10
–2
10 Cd pressure pCd [atm]
–1
10
1
~ Fig. 7. CdTe. Chemical diffusion coefficient D in CdTe as a function of cadmium partial pressure pCd and various temperatures: T = 873 K, 973 K, and 1073 K. Solid and open symbols correspond to data taken before and after changing sample dimension to ensure ~ that D was not dependent on sample size [70Z1].
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
3
–13
4⋅10
10 8
CdTe - HgTe (CdxHg1-xTe)
–13
10
6
2
Te rich Hg rich (–)
–14
2
10
–15
10 2 –1
2 –1
Chem.diff.coeff. D [µm h ]
T=
87 3K
77 3K
–16
10
62 3K
–18
10
Growth (1 atm Hg in excess Annealing (8.3 atm Hg)
4 2 8 6 4 2
1
8 6
72 3K
–17
8 6
T = 823 K
10
82 3K
10
CdTe - HgTe (CdxHg1-xTe)
4
10
Chem.diff.coeff. D [m s ]
5-11
4
67 3K
2 –1
10
0
0.2
0.4 0.6 Composition x
0.8
1.0
~ Fig. 9. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of composition x (CdxHg1-xTe) at T = 823 K [75S1].
57 3K –19
10
2
4⋅10 –20
0
0.2
0.4 0.6 Composition x
0.8
1.0
2
10
10
Lando lt -Bö rnst ein New Series III/33A
T = 823 K x = 0.1 0.2 0.3
2
0.4
8 6
0.5
4
0.6
2
1
~ Fig. 10. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of added mercury pressure pHg at different values of composition x (CdxHg1-xTe) at T = 823 K [75S1].
8 6 4
2 –1
~ Fig. 8. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of composition x (CdxHg1-xTe) for T = 573-873 K [87T1, 87T2].
CdTe - HgTe (CdxHg1-xTe)
2
Chem.diff.coeff. D [µm h ]
10
0.7
8 6
0.8
4
0.9
2 –1
10
0
1
2 3 4 Hg pressure in excess pHg [atm]
5
6
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-12
2
10
2
8 6
CdTe - HgTe (CdxHg1-xTe)
4
1
10 2 –1
Chem.diff.coeff. D [µm h ]
8 6 4 2
1
8 6
4
2
–1
10
0.1 0 0.2 0
2
8 –2
6⋅10
0.4 0.6 0.8 1.0 Composition x Fig. 12. CdTe-HgTe. Activation energy Q for chemical diffusion in CdTe-HgTe as a function of composition x (CdxHg1-xTe) [63B1].
–1
10
6
x=
4
0 0.4
8 6 4
0 0.9
2
0.7 5
CdTe - HgTe (CdxHg1-xTe)
8
Activ.energy Q [eV]
2
[Ref. p. 5-25
0.6 0
0.1
0.2
–2
10
1.1
1.2
1.3 1.4 1.5 –3 –1 Inv. temp. 1/T [10 K ]
1.6
1.7
2
10
8 6
~ Fig. 11. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of inverse temperature 1/T at various values of composition x (CdxHg1-xTe) [63B1].
CdTe - HgTe (CdxHg1-xTe)
4 2
10 2 –1
Chem.diff.coeff. D [µm h ]
8 6 4 2
1
8 6
x=
0.1 0.2
4 2 –1
10
0.4
8 6 4 2
0.9
~ Fig. 13. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of inverse temperature 1/T for various starting concentrations x = x0 (CdxHg1-xTe) [66B1].
–2
10
1.1
1.2
0.6
0.8
1.3 1.4 1.5 –3 –1 Inv. temp. 1/T [10 K ]
1.6
1.7
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
–12 8 6
10
T=
4
923 K
2 –13 10 8 6
CdTe - HgTe (CdxHg1-xTe)
2
–15
10
823 K
–14 8 6
10
8 6 4
2 –1
4
773 K
2 –15 10 8 6
723 K
4
–16 8 6 4
10
–16 8 6
10
2
–18
10
2
0
0.1
0.2
0.3 0.4 Composition x
0.5
0.6
0.7
250
CdTe - HgTe (CdxHg1-xTe)
–15
2 –1
Chem.diff.coeff. D [m s ]
–1
8 6 4
T = 773 K 683 K 663 K 623 K
2 –16 8 6 4
10
0.2
0.4 0.6 Composition x
0.8
CdTe - HgTe
1.0
3
225
Activ. energy Q [kJ mol ]
2
2
200
1
150
5
125
4
100
2 –17 8 6 4
10
75 CdTe
2 –18
10
0
~ Fig. 15. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe at T = 663 K as a function of composition x (CdxHg1-xTe) at various starting values of x = 0.03, 0.20 and 0.39 [91Y1].
–15
4⋅10
10
x = 0.03 0.20 0.39
2
4
–17
T = 663 K
–17 10 8 6 4
2
10
CdTe - HgTe (CdxHg1-xTe)
2
Chem.diff.coeff. D [m s ]
2 –1
~ Fig. 14. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of composition x (CdxHg1-xTe) for T = 723-973 K. Different sets of symbols represent data from different growth runs [87F1].
873 K
4
Chem.diff.coeff. D [m s ]
973 K
5-13
0
0.2
0.4 0.6 Composition x
0.8
1.0
~ Fig. 16. CdTe-HgTe. Chemical diffusion coefficient D in CdTe-HgTe as a function of composition x (CdxHg1-xTe) for 623-773 K at a starting value of x = 0.2 [91Y1].
Lando lt -Bö rnst ein New Series III/33A
0.2
0.4 0.6 Mass fraction HgTe wHgTe
0.8
HgTe
Fig. 17. CdTe-HgTe. Activation energy Q for chemical diffusion in CdTe-HgTe as a function of mass fraction of HgTe wHgTe. 1: metal saturated, 2: Te saturated, 3: minimum pressure (stoichiometric), 4: 1 mol.% Ag, 5: 1 mol% In [81L1].
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-14
–14
4
10
2 1 2 –1
2 –1
–4
10
5
–6
10
–8
10
–10
4
10
–12
10
–15
10
8 6
T = 1373 K
4
1273 K
2 –16
10
–14
10
8 6
1073 K
4
–16
10
2
–18
10
–17
10
–20
0.2
0.4 0.6 Mass fraction HgTe wHgTe
0.8
HgTe
Fig. 18. CdTe-HgTe. Pre-exponential factor D0 for chemical diffusion in CdTe-HgTe as a function of mass fraction of HgTe wHgTe. 1: metal saturated, 2: Te saturated, 3: minimum pressure (stoichiometric), 4: 1 mol.% Ag, 5: 1 mol.% In [81L1]. 2.5
20
10
2
4
21 6 8 10
2
4
6 8 –3
22
10
2
22
4⋅10
Conc. of P CP [atoms cm ]
~ Fig. 19. GaAs-GaP. Chemical diffusion coefficient D in GaAs-GaP as a function of concentration of P, CP, for T = 1073-1373 K [76J1].
–12
10
GaAs - GaP (PxAs1-xGa)
2.0
HgSe - HgTe –13
10
–1
Activ.energy Q [eV atom ]
GaAs - GaP
2
Chem.diff.coeff. D [m s ]
–2
10
CdTe
8 6 4
1
Pre-exp.factor D0 [m s ]
10
3
CdTe - HgTe
2
10
10
[Ref. p. 5-25
2 –1
Chem.diff.coeff. D [m s ]
1.5 1.0
–14
10
T = 773 K
–15
10
0.5
723 K –16
0
0.2
0.4 0.6 0.8 1.0 Composition(1–x) Fig. 20. GaAs-GaP. Activation energy Q for chemical diffusion in GaAs-GaP as a function of composition (1-x) (PxAs1-xGa) [76J1].
10
–17
10
HgTe
673 K 623 K 0.2
0.4 0.6 Mass fraction HgSe wHgSe
0.8
HgSe
~ Fig. 21. HgSe-HgTe. Chemical diffusion coefficient D in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in undoped material for T = 623-773 K [77L1].
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
225
HgSe - HgTe
10 2 –1
Pre-exp.factor D0 [m s ]
150 125 100 0.2
0.4 0.6 Mass fraction HgSe wHgSe
0.8
–3
10
–5
10
10
HgSe
–9
Fig. 22. HgSe-HgTe. Activation energy Q for chemical diffusion in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in undoped material [77L1].
10
HgTe
250
–12
HgSe - HgTe
225
–13 –1
Activ.energy Q [kJ mol ]
10
–14
10
T = 723 K
–15
10
623 K 10
573 K
0.4 0.6 Mass fraction HgSe wHgSe
0.8
HgSe
~ Fig. 24. HgSe-HgTe. Chemical diffusion coefficient D in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in chalcogen rich material for T = 573-723 K [77L1].
Lando lt -Bö rnst ein New Series III/33A
HgSe
HgSe - HgTe
175 150 125
0.2
0.4 0.6 Mass fraction HgSe wHgSe
0.8
HgSe
Fig. 25. HgSe-HgTe. Activation energy Q for chemical diffusion in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in chalcogen rich material [77L1].
–17
0.2
0.8
200
75 HgTe
–16
10
HgTe
0.4 0.6 Mass fraction HgSe wHgSe
100
673 K
–18
0.2
Fig. 23. HgSe-HgTe. Pre-exponential factor D0 for chemical diffusion in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in undoped material [77L1].
10
2 –1
–1
10
–7
75 HgTe
Chem.diff.coeff. D [m s ]
HgSe - HgTe
1
175
10
5-15
3
10
–1
Activ.energy Q [kJ mol ]
200
5 Chemical diffusion in bulk inhomogeneous semiconductors
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-16
–13
4
10
[Ref. p. 5-25
10
HgSe - HgTe
HgSe - HgTe
2
T = 923 K
10
–14
2 –1
Chem.diff.coeff. D [m s ]
2 –1
Pre-exp.factor D0 [m s ]
10
1 –2
873 K –15
10
10
–4
10
823 K –16
10
–6
10
–8
10
HgTe
–17
0.2
0.4 0.6 Mass fraction HgSe wHgSe
0.8
Fig. 26. HgSe-HgTe. Pre-exponential factor D0 for chemical diffusion in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in chalcogen rich material [77L1].
0.4 0.6 Mass fraction HgSe wHgSe
0.8
HgSe
4
10
HgSe - HgTe
HgSe - HgTe 2
10
250 225 200 175 150 HgTe
0.2
2 –1
–1
Activ.energy Q [kJ mol ]
275
HgTe
~ Fig. 27. HgSe-HgTe. Chemical diffusion coefficient D in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in metal rich material for T = 823-923 K [77L1].
Pre-exp.factor D0 [m s ]
300
10
HgSe
1 –2
10
–4
10 0.2
0.4 0.6 0.8 HgSe Mass fraction HgSe wHgSe Fig. 28. HgSe-HgTe. Activation energy Q for chemical diffusion in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in metal rich material [77L1].
–6
10
HgTe
0.2
0.4 0.6 Mass fraction HgSe wHgSe
0.8
HgSe
Fig. 29. HgSe-HgTe. Pre-exponential factor D0 for chemical diffusion in HgSe-HgTe as a function of mass fraction of HgSe wHgSe in metal rich material [77L1].
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
2
–12
4⋅10
10
HgTe - ZnTe
T = 873 K 773 K 723 K 673 K
(ZnxHg1-xTe)
2
2
2 –1
Chem.diff.coeff. D [m s ]
4
10
T = 863 K
–13
2 –1
8 6
HgTe - ZnTe 10
Chem.diff.coeff. D [m s ]
2
10
5-17
–14
10
8 6
–15
10
4 2
1
–16
10
8 6 4 2
–1
10
0
0.2
0.4 0.6 Composition x
0.8
1.0
ZnTe
0.2
0.4 0.6 Mass fraction HgTe wHgTe
0.8
HgTe
~ Fig. 31. HgTe-ZnTe. Chemical diffusion coefficient D in HgTe-ZnTe as a function of mass fraction of HgTe wHgTe at T = 863 K [74L3].
~ Fig. 30. HgTe-ZnTe. Chemical diffusion coefficient D in HgTe-ZnTe as a function of composition x (ZnxHg1-xTe) for T = 673-873 K [86P1]. –13
10
8 6
230
PbS - PbSe
PbS - PbSe
4
2 –1
Chem.diff.coeff. D [m s ]
8 6
1123 K
4 2
1073 K
–15
10
–1
1173 K
–14
10
Activ.energy Q [kJ mol ]
T = 1223 K
2
8 6
973 K
–16
200
0.4 0.6 0.8 PbSe Mass fraction PbSe wPbSe Fig. 33. PbS-PbSe. Activation energy Q for chemical diffusion in PbS-PbSe as a function of mass fraction of PbSe wPbSe in undoped material [79L1].
2
10
210
190 PbS
1023 K
4
220
8 6
0.2
4
923 K
2 –17
10
PbS
Lando lt -Bö rnst ein New Series III/33A
0.2
0.4 0.6 Mass fraction PbSe wPbSe
0.8
PbSe
~ Fig. 32. PbS-PbSe. Chemical diffusion coefficient D in PbS-PbSe as a function of mass fraction of PbSe wPbSe for T = 923-1223 K in undoped material [79L1].
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-18
–12
10
–4 2
8
PbS - PbSe
6
8 6
2
4
8 6 –6
PbS
10
0.2
0.4 0.6 Mass fraction PbSe wPbSe
0.8
PbSe
Fig. 34. PbS-PbSe. Pre-exponential factor D0 for chemical diffusion in PbS-PbSe as a function of mass fraction of PbSe wPbSe in undoped material [79L1].
1223 K
8
2 –1
–5
4⋅10
T = 1273 K
–13
2
10
PbS - PbSe
4
–4
10
Chem.diff.coeff. D [m s ]
2 –1
Pre-exp.factor D0 [m s ]
4⋅10
[Ref. p. 5-25
6 4
1173 K
2
1123 K
–14
10
1073 K
8 6 4
2 –15
10
PbS
0.2
0.4 0.6 0.8 Mass fraction PbSe wPbSe
PbSe
~ Fig. 35. PbS-PbSe. Chemical diffusion coefficient D in PbS-PbSe as a function of mass fraction of PbSe wPbSe in chalcogen saturated material for T = 1073-1273 K [79L1].
–5
4⋅10
200 190
2 2 –1
Pre-exp.factor D0 [m s ]
–1
Activ.energy Q [kJ mol ]
PbS - PbSe 180 170 160 150 PbS
PbS - PbSe
–5
10
8 6 4 2
–6
10
8 6 –7
0.2
0.4 0.6 0.8 PbSe Mass fraction PbSe wPbSe Fig. 36. PbS-PbSe. Activation energy Q for chemical diffusion in PbS-PbSe as a function of mass fraction of PbSe wPbSe in chalcogen saturated material [79L1].
4⋅10
PbS
0.2
0.4 0.6 0.8 PbSe Mass fraction PbSe wPbSe Fig. 37. PbS-PbSe. Pre-exponential factor D0 for chemical diffusion in PbS-PbSe as a function of mass fraction of PbSe wPbSe in chalcogen saturated material [79L1].
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
–12 6
250
PbS - PbSe
PbS - PbSe –1
8
Activ.energy Q [kJ mol ]
10
4
2
T = 1273 K
2 –1
Chem.diff.coeff. D [m s ]
–13
10
1223 K
8 6
2
190
0.4 0.6 0.8 PbSe Mass fraction PbSe wPbSe Fig. 39. PbS-PbSe. Activation energy Q for chemical diffusion in PbS-PbSe as a function of mass fraction of PbSe wPbSe in lead saturated material [79L1].
8
1073 K
6
210
150 PbS
1123 K
–14
10
230
170
1173 K
4
5-19
0.2
4
2 –15
10
PbS
0.2
0.4 0.6 0.8 Mass fraction PbSe wPbSe
PbSe
~ Fig. 38. PbS-PbSe. Chemical diffusion coefficient D in PbS-PbSe as a function of of mass fraction of PbSe wPbSe in lead saturated material for T = 1073-1273 K [79L1].
–4 8 6
–11
10
PbS - PbSe
4
2 –1
–12
2
2 –1
–5
10
PbS
–13
–14
10
2
–6
Diffusion of excess Se into n-Type substrate
10
8 6 4
10
PbSe
10 Chem.diff.coeff. D [m s ]
Pre-exp.factor D0 [m s ]
10
0.2
0.4 0.6 0.8 PbSe Mass fraction PbSe wPbSe Fig. 40. PbS-PbSe. Pre-exponential factor D0 for chemical diffusion in PbS-PbSe as a function of of mass fraction of PbSe wPbSe in lead saturated material [79L1].
Diffusion of excess Pb into p-Type substrate
–15
10
–16
10
1.05
1.15
1.25 1.35 1.45 1.55 –3 –1 Inv.temp. 1/T [10 K ]
1.65
1.75
~ Fig. 41. PbSe. Chemical diffusion coefficients D of excess Pb and Se in PbSe as a function of inverse temperature 1/T [68C1]. Lando lt -Bö rnst ein New Series III/33A
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-20
–12
–15
10
4⋅10
Pb0.93Sn0.07Se
2
–13
2 –1
Chem.diff.coeff. D [m s ]
10
–15
10
8 6
–14 2 –1
Chem.diff.coeff. D [m s ]
10
Diffusion of excess Se into n-Type substrate
–15
10
–16
68 K T = 10
4
K 1023
2
973 K
8 6
923 K
4
873 K
2 –17
10
–17
1.05
PbSe - PbTe
–16
10
10 10
[Ref. p. 5-25
1.15
1.25 1.35 1.45 1.55 –3 –1 Inv.temp. 1/T [10 K ]
1.65
823 K
8 6
1.75
4
~ Fig. 42. PbSe-SnSe. Chemical diffusion coefficient D in Pb0.93Sn0.07Se as a function of inverse temperature 1/T [68C1].
K 773
2 –18
10
PbSe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
~ Fig. 43. PbSe-PbTe. Chemical diffusion coefficient D at minimum pressure in PbSe-PbTe as a function of mass fraction of PbTe wPbTe for T = 773-868 K [74L2].
10
34
–9 2 –1
33 32
31 30 PbSe
PbSe - PbTe Pre-exp.factor D0 [10 m s ]
–1
Activ.energy Q [kcal mol ]
PbSe - PbTe
0.2
0.4 0.6 0.8 PbTe Mass fraction PbTe wPbTe Fig. 44. PbSe-PbTe. Activation energy Q for chemical diffusion at minimum pressure in PbSe-PbTe as a function of mass fraction of PbTe wPbTe [74L2]. (1 kcal mol–1 = 4.2 kJ mol–1).
8 6 4 2 0 PbSe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
Fig. 45. PbSe-PbTe. Pre-exponential factor D0 for chemical diffusion at minimum pressure in PbSe-PbTe as a function of mass fraction of PbTe wPbTe [74L2].
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors 20
–13
PbSe - PbTe –1
8 6
Activ.energy Q [kcal mol ]
10
4 2
2 –1
–14
10
Chem.diff.coeff. D [m s ]
T = 923 K
8 6
873 K
4
8 6
16 14
0.4 0.6 0.8 PbTe Mass fraction PbTe wPbTe Fig. 47. PbSe-PbTe. Activation energy Q for chemical diffusion in PbSe-PbTe for chalcogen-rich material as a function of mass fraction of PbTe wPbTe [74L2]. (1 kcal mol–1 = 4.2 kJ mol–1).
723 K 673 K
4
18
10 PbSe
773 K
–15
10
PbSe - PbTe
12
823 K
2
5-21
2
0.2
–16
10
PbSe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
~ Fig. 46. PbSe-PbTe. Chemical diffusion coefficient D in PbSe-PbTe for chalcogen-rich material as a function of mass fraction of PbTe wPbTe for T = 673-923 K [74L2]. –14
4⋅10
PbSe - PbTe
2
160
PbSe - PbTe
–15
10
120
8 6
2 –1
80
0 PbSe
2 –16
10
40
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
Fig. 48. PbSe-PbTe. Pre-exponential factor D0for chemical diffusion in PbSe-PbTe for chalcogen-rich material as a function of mass fraction of PbTe wPbTe [74L2].
T = 1073 K 1043 K 1023 K 973 K
4
Chem.diff.coeff. D [m s ]
–12 2 –1
Pre-exp.factor D0 [10 m s ]
200
923 K
8 6 4 2
–17
10
8 6 4
823 K
2 –18
10
PbSe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
~ Fig. 49. PbSe-PbTe. Chemical diffusion coefficient D in PbSe-PbTe in lead-rich material for T = 823-1073 K as a function of mass fraction of PbTe wPbTe [74L2].
Lando lt -Bö rnst ein New Series III/33A
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-22
4
PbSe - PbTe Pre-exp.factor D0 [10 m s ]
41
40
39 38 PbSe
0.4 0.6 0.8 PbTe Mass fraction PbTe wPbTe Fig. 50. PbSe-PbTe. Activation energy Q for chemical diffusion in PbSe-PbTe for lead-rich material as a function of mass fraction of PbTe wPbTe [74L2]. (1 kcal mol–1 = 4.2 kJ mol–1).
8 6
2 1
0 PbSe
0.2
PbSe - SnSe T = 1023 K
Chem.diff.coeff. D [m s ]
2 –1
2 –1
Chem.diff.coeff. D [m s ]
2
–15 8 6
973 K
4 2
923 K
–16
–14
10
0.8
PbTe
973 K T = 1023 K
8 6
973 K
923 K 873 K
923 K
–15 8 6
873 K
4
873 K
2
T = 1023 K
2
10
8 6
2 –16
–17
SnSe
PbSe - SnSe
4
4
10
8 6 4
2
10
0.4 0.6 Mass fraction PbTe wPbTe
–13
10
4
10
0.2
Fig. 51. PbSe-PbTe. Pre-exponential factor D0 for chemical diffusion in PbSe-PbTe for lead-rich material as a function of mass fraction of PbTe wPbTe [74L2].
–14
10
PbSe - PbTe
3
–7 2 –1
–1
Activ.energy Q [kcal mol ]
42
[Ref. p. 5-25
0.2
0.4 0.6 Mass fraction PbSe wPbSe
0.8
PbSe
~ Fig. 52. PbSe-SnSe. Chemical diffusion coefficient D at minimum pressure in PbSe-SnSe for T = 873-973 K as a function of mass fraction of PbSe wPbSe (lines are calculated from D0 and Q (q.v.)) [75L1].
10
SnSe
0.2
0.4 0.6 Mass fraction PbSe wPbSe
0.8
PbSe
~ Fig. 53. PbSe-SnSe. Chemical diffusion coefficient D in PbSe-SnSe for T = 873-973 K for selenium-rich material as a function of mass fraction of PbSe wPbSe (lines are calculated from D0 and Q (q.v.)) [75L1].
Landolt -Börnst ein New Series III/33A
Ref. p. 5-25]
5 Chemical diffusion in bulk inhomogeneous semiconductors
–13
–13
10
8 6
10
PbSe - SnSe T = 1023 K T = 1023 K
973 K
973 K
923 K
4
2 2 –1
8 6
2 –1
Chem.diff.coeff. D [m s ]
2
923 K
–15
10
8 6
10
873 K
923 K
8 6
873 K
4 2 –16
10
8 6 4 2
–17
SnSe
973 K
–15
10
–16
10
8 6
2
2
10
T = 1023 K
4
873 K
4
PbTe - SnTe
–14
Chem.diff.coeff. D [m s ]
2 –14
8 6 4
4
10
5-23
0.2
0.4 0.6 Mass fraction PbSe wPbSe
0.8
PbSe
~ Fig. 54. PbSe-SnSe. Chemical diffusion coefficient D PbSe-SnSe for T = 873-973 K for metal-rich material as a function of mass fraction of PbSe wPbSe (lines are calculated from D0 and Q (q.v.)) [75L1].
SnTe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
~ Fig. 55. PbTe-SnTe. Chemical diffusion coefficient D at minimum pressure in PbTe-SnTe for T = 873-973 K as a function of mass fraction of PbTe wPbTe (lines are calculated from D0 and Q (q.v.)) [75L1].
–13
4⋅10
PbTe - SnTe –13
10
8 6 4
T = 1023 K
2
10
Chem.diff.coeff. D [m s ]
2 –1
–14
4
Lando lt -Bö rnst ein New Series III/33A
923 K
2 –15
10
~ Fig. 56. PbTe-SnTe. Chemical diffusion coefficient D in PbTe-SnTe for T = 873-973 K for tellurium-rich material as a function of mass fraction of PbTe wPbTe (lines are calculated from D0 and Q (q.v.)) [75L1].
973 K
8 6
873 K
8 6 4 2
–16
10
SnTe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-24
–14
4⋅10
–15
4⋅10
Chem.diff.coeff. D [m s ]
PbTe - SnTe –14 8
2 –1
Chem.diff.coeff. D [m s ]
6 4
4 2
10
2
10
6 4
ZnSe
0.2
0.4 0.6 Mass fraction ZnTe wZnTe
0.8
ZnTe
~ Fig. 58. ZnSe-ZnTe. Chemical diffusion coefficient D in ZnSe-ZnTe for stoichiometric material as as a function of mass fraction of ZnTe wZnTe at 1223 K [75L1].
923 K
8
8 6
–16
973 K
–15
T = 1223 K
–15
10
T = 1023 K
ZnSe - ZnTe
2
2 –1
2
10
[Ref. p. 5-25
873 K
2 –16
10
SnTe
0.2
0.4 0.6 Mass fraction PbTe wPbTe
0.8
PbTe
~ Fig. 57. PbTe-SnTe. Chemical diffusion coefficient D in PbTe-SnTe for metal-rich material for T = 873-973 K as a function of mass fraction of PbTe wPbTe (lines are calculated from D0 and Q (q.v.)) [75L1].
–15
4⋅10
–13
2⋅10
–13
10
ZnSe - ZnTe
8 6
2
8 6 4
2 –1
Chem.diff.coeff. D [m s ]
2 –1
Chem.diff.coeff. D [m s ]
4
1173 K
–14
10
1123 K
4
–16 8 6
2 –17
–15
10
8 6
8 6 4
4
–18
–16
2⋅10
ZnSe
1123 K
4
2
10
1173 K
2
10
8 6
T = 1223 K
–15
10
T = 1223 K
2
ZnSe - ZnTe
0.2
0.4 0.6 Mass fraction ZnTe wZnTe
0.8
ZnTe
~ Fig. 59. ZnSe-ZnTe. Chemical diffusion coefficient D in ZnSe-ZnTe for T = 1123-1223 K for chalcogen-rich material as a function of mass fraction of ZnTe wZnTe [75L1].
2⋅10
ZnSe
0.2
0.4 0.6 Mass fraction ZnTe wZnTe
0.8
ZnTe
~ Fig. 60. ZnSe-ZnTe. Chemical diffusion coefficient D in ZnSe-ZnTe for T = 1123-1223 K for metal-rich material as a function of mass fraction of ZnTe wZnTe [75L1].
Landolt -Börnst ein New Series III/33A
5 Chemical diffusion in bulk inhomogeneous semiconductors
5-25
5.4 References for 5
63B1 66B1 68C1 70A1 70Z1 71B1 71K1 73B1 73M1 74L1 74L2 74L3 75L1 75S1 76J1 76K1 76S1 77L1 79L1 81L1 82N1 84T1 85Y1 86P1 86Z1 87F1 87T1 87T2 88A1 88K1 89V1 91Y1 93S1
Bailly, F., Cohen-Solal, G., Marfaing, Y.: C. R. Acad. Sci. Paris 257 (1963) 103. Bailly, F.: C. R. Acad. Sci. Paris Ser. B 262 (1966) 635. Calawa, A.R., Harman, T.C., Finn, M., Youtz, P.: Trans. AIME 242 (1968) 374. Agafonova, A.V., Vasil’kova, O.G., Lebedeva, V.E., Myuller, N.M.: Zavod. Lab. 36 (1970) 1091. Zanio, K.: J. Appl. Phys. 41 (1970) 1935. Biter, W.J., Williams, F.: J. Lumin. 3 (1971) 395. Kumar, V., Kröger, F.A.: J. Solid State Chem. 3 (1971) 406. Butler, E.M., Meyer, R.O.: J. Nucl. Mater. 47 (1973) 229. Martin, W.E.: J. Appl. Phys. 44 (1973) 5639. Leute, V., Blomer, F.: Z. Phys. Chem. (Frankfurt) 89 (1974) 15. Leute, V., Hornischer, R.: Z. Phys. Chem. 93 (1974) 33. Leute, V., Stratmann, W.: Z. Phys. Chem. (Frankfurt) 90 (1974) 172. Leute, V., Schmidtke, H.: Ber. Bunsenges. Phys. Chem. 79 (1975) 1134. Svob, L., Marfaing, Y., Triboulet, R., Bailly, F., Cohen-Solal, G.: J. Appl. Phys. 46 (1975) 4251. Jain, G.C., Sadana, D.K., Das, B.K.: Solid State Electron 19 (1976) 731. Khludkov, S.S., Lavrishchev, T.T.: Izv. Akad. Nauk. SSSR, Neorg. Mater. 12 (1976) 1163. Sinha, A.K., Smith, T.E., Read, M.H., Poate, J.M.: Solid State Electron. 19 (1976) 489. Leute, V., Stratmann, W.: Ber. Bunsenges. Phys. Chem. 81 (1977) 761. Leute, V., Böttner, H., Schmidtke, H.: Z. Naturforsch. A 34 (1979) 89. Leute, V., Schmidtke, H.M., Stratmann, W., Winking, W.: Phys. Status Solidi (a) 67 (1981) 183. Nakano, M., Igaki, K.: Trans. Jpn. Inst. Met. 23 (1982) 103. Takita, K., Murakami, K., Otake, H., Masuda, K., Seki, S., Kudo, H.: Appl. Phys. Lett. 44 (1984) 996. Yakshibaev, R.A., Chebotin, V.N., Knyazeva, S.V.: Inorganic Materials 21 (1985) 795. Pobla, C., Granger, R., Rolland, S., Triboulet, R.: J. Cryst. Growth 79 (1986) 515. Zanio, K., Massopust, T.: J. Electron. Mater. 15 (1986) 103. Fleming, J.G., Stevenson, D.A.: Phys. Status Solidi (a) 105 (1987) 77. Tang, M.F.S., Stevenson, D.A.: Appl. Phys. Lett. 50 (1987) 1272. Tang, M.F.S., Stevenson, D.A.: J. Vac. Sci. Technol. A 5 (1987) 3124. Al-Salhi, M.S., Shaw, D., Bryant, F.J., Hogg, J.H.C.: Semicond. Sci. Technol. 3 (1988) 1063. Kleinfeld, M., Wiemhöfer, H.-D.: Solid State Ionics 28 - 30 (1988) 1111. Voland, U., Cerny, R., Deus, P., Bergner, D., Fenninger, G.: Cryst. Res. Technol. 24 (1989) 1177. Yang, J., Yu, Z., Liu, J., Tang, D.: J. Cryst. Growth 114 (1991) 351. Sitte, W.: Solid State Ionics 59 (1993) 117.
Lando lt -Bö rnst ein New Series III/33A
Ref. p. 1-21]
1 Introduction
1-1
1 General introduction D.L. BEKE
1.1 Atomic fluxes According to Onsager's theorem [91P1, 93A1] in a binary AB system the flux of atoms A, relative to the lattice planes, - if driving forces other than given by the gradients of the chemical potential, µA, are zero - can be given as JA = − LAAgrad µA ,
(1.1)
where LAA is the Onsager coefficient and JA is expressed in number of particles or moles per unit area and unit time. It is also well-known from elementary statistical physics that the chemical potential can be expressed as [72F1]
µ A = µ 0 + kT lnγ A X A ,
(1.2)
where k is the Boltzmann-constant and T is the temperature. XA and γA are the atomic or mole fraction and the activity coefficient, respectively. Combining Eqs. 1.1 and 1.2 and using that cA∂XA/∂cA = XA and cA + cB = const., where e.g. cA is the number of A atoms or moles per unit volume, one receives: JA =
−
kTLAA cA
∂lnγ A kTLAA Φ ⋅ gradcA = − DA ⋅ gradcA , 1 + ⋅ gradc A = − cA ∂lnX A
(1.3)
where Φ is denoted as thermodynamic factor (see Eq. 1.12) and DA is the intrinsic diffusion coefficient. It can be seen that Eq. 1.3 is just the well-known Fick's first law and DA has the dimension m2s−1. Simple considerations show [91P1, 68M1] that in this expression the first term corresponds to the current related to the Brownian-migration of atoms. In this case the jumps between two adjacent atomic planes are the same in both directions and a current, perpendicular to the planes, arises only because the number of atoms in the two planes are different. The (Brownian) diffusion coefficient corresponding to this term is given as D
A
=
kTLAA cA
= α ⋅ Γa , 2
(1.4)
where Γ and a are the atomic jump frequency and the jump distance, respectively. α is a geometrical factor, whose value for a simple cubic lattice is 1/6. Indeed, according to Fig. 1a, if the number of atoms or moles per unit area, n, varies slightly with the distance perpendicular to the atomic planes, we can write nA = n A ( x ) − 1
1
a
dn A
2
dx
1
dn A
, (1.5)
nA = nA ( x ) + 2
Lando lt -Bö rnst ein New Series III/33A
2
a
dx
1-2
1 Introduction
[Ref. p. 1-21
and the atomic current is given as JA ( x ) = nA 1 Γ 12 − n A 2 Γ 21 .
(1.6)
Here e.g. Γ12 is the number of jumps per unit time from plane 1 to 2. Combining these equations and using nA/a = cA we arrive at JA ( x ) = − a
2
Γ12 + Γ21 dcA dx
2
(
+ cA a Γ12 − Γ21
).
(1.7)
It can be seen that if Γ12 = Γ21 then αΓ = (Γ12 +Γ21)/2 = Γ0 and one gets Eq. 1.4. The second term in Eq. 1.3 is related to the chemistry of the system. If γA = 1 (dilute or ideal solid solution) this chemical term is zero. The effect of the chemical driving force, Fch, can be formally expressed in the form of a convective term:
JA = − D A gradcA + cA v ,
(1.8)
and v = a (Γ12 − Γ21 ). The convective velocity, v can be different from zero only if the probabilities of jumps into x and −x directions are different. In general this can be caused by an external potential field u(x), related to the driving force by F = −gradu(x). Fig. 1b illustrates the potential field inside the crystal in the presence of such an external potential. Then, supposing that ∆ = Fa is small as compared to the original height of the potential well, ε, we can write ∆ ∆ Γ 12 = Γ 0 exp − ≈ Γ 0 1 − 2 kT 2 kT
Γ 21
(1.9)
∆ ∆ = Γ 0 exp + ≈ Γ 0 1 + , 2 kT 2 kT
where Γ0 = exp(−ε / kT). From the second term in Eq. 1.7 v = aα Γ ⋅ ∆ kT = D A F kT ,
(1.10)
which is the well-known Nernst-Einstein equation. From the comparison of Eqs. 1.8 and 1.3 the chemical driving force is given by Fch = − kTgrad(lnγA). The effect of other driving forces (electric potential gradient, temperature gradient, pressure gradient, etc.) can be treated similarly [91P1, 73G1]. a ε
12
21
u(x )
n(x ) ∆ 12
1 a
Position x
21
2 b
Position x
ε Fig. 1a, b. Jump frequencies between neighbouring atomic planes (labelled 1 and 2) when only the concentration varies (a) and when an external potential field is present (b). The symbols are explained in the text.
Landolt -Börnst ein New Series III/33A
Ref. p. 1-21]
1 Introduction
1-3
Since the chemical potential in a binary system is the partial Gibbs free energy determined by the intersection of the tangent to the free-energy curve g(XA) with vertical axes XA = 0 and XA = 1: dg µA = g + (1 − XA) , dXA T
(1.11)
the factor Φ in Eq. 1.3 can be written in the form ∂ ln γ A X A ∂µ A X A (1 − X A ) d 2 g = Φ = 1 + . = dX 2 kT ∂ ln X A kT ∂X A A
(1.12)
T
The value and the sign of Φ is determined by the concentration dependence of g. For stable systems the second derivative of g (g") is positive, but for example in spinodal systems g'' < 0 and the sign of the intrinsic diffusion coefficient is also negative. This is the case of "up-hill diffusion", when the flux flows in the direction of increasing concentrations. Equation 1.3 also shows that in general DA is a tensor quantity. Although in many cases it is a scalar, in anisotropic crystals it can be described by three principal diffusion coefficients [90M1], or in uniaxial systems by D⊥ and D|| which are the diffusion coefficients perpendicular and parallel to the unique axis.
1.2 Equations for diffusion Any real crystal contains extended lattice defects such as dislocations, grain boundaries and free surfaces. Since diffusion along such defects are usually characterized by higher diffusivity as compared to the bulk, they are denoted as diffusion short-circuits or paths of high diffusivity (Fig. 2). First we will consider the diffusion in an ideal bulk material, where the number and effects of the above defects are negligible. Rel.temperature T/Tm 0.5 Tm
T –6 m 10
0.3 Tm
–8
10
–10
10
Diff. coeff. D [m s ]
2 –1
–12
10
surf ace gra in b oun dar y
–14
10
–16
10
–18
on ati loc dis
10
–20
k bul
10
–22
10
1.0
Lando lt -Bö rnst ein New Series III/33A
1.5
2.0 2.5 Rel. inv. temp Tm /T
3.0
3.5
Fig. 2. Schematic illustration of the order of magnitude of different diffusion coefficients D on the inverse temperature relative to the melting temperature Tm / T (Arrhenius diagram).
1-4
1 Introduction
[Ref. p. 1-21
1.2.1 Bulk diffusion While steady state methods for measuring diffusion are directly based on Fick's first law (for example by setting JA = 0 in Eq. 1.8) for non-steady state methods the concentration varies with time as well. For these cases the continuity equation should be also considered, which - for particles undergoing no reactions has the form;
∂c A ∂t
+ divJ A = 0.
(1.13)
Combining Eqs. 1.3 and 1.13 yields
∂c A = div ( DA gradcA ) , ∂t
(1.14)
which is Fick's second law for anisotropic crystals. In isotropic solids, when the concentration varies only along the x direction Eq. 1.14 becomes
∂c A ∂t
=
∂c A ∂ DA . ∂x ∂x
(1.15)
If furthermore DA is independent of concentration and hence of position this simplifies to
∂c A ∂ 2 cA = DA . ∂t ∂x 2
(1.16)
It is important to note that the above relations are valid only in the continuum limit, i.e. neglecting the discontinuous structure of crystalline materials on an atomic scale [77M1]. For short times or in the presence of large gradients approximations used in the derivation of Eqs. 1.4, 1.7 and 1.13 can lead to errors. For example if the characteristic distance along which the concentration changes is shorter than 10a, corrections according to the discrete equations instead of continuous ones can be significant. This can be the case e.g. for diffusion in synthetic multilayer structures [96G1] or in spinodal decomposition [85G1]. In the evaluation of diffusion experiments, solutions of the above differential equations with appropriate initial and boundary conditions are fitted to the experimentally measured cA(x, t) curves and DA is calculated. Since the solutions of Eqs. 1.15 or 1.16 for various initial and boundary conditions are collected in many text books [59C1, 64J1, 66A1, 75C1, 89S1, 90M1, 91P1], only solutions for the experimentally most widely used cases are listed here. For other special solutions, important in some particular systems, see also the text in the chapters with data collections. 1.2.1.1 Tracer diffusion in a homogeneous matrix The simplest solutions of Fick's second law can be obtained for constant diffusion coefficients (see Eq. 1.16). This can be realized when radioactive tracer elements diffuse in a chemically homogeneous system. Because of the high sensitivity of this technique extremely small amounts of tracer atoms are enough to determine the concentration distribution and the system remains essentially homogeneous during the diffusion. If the tracer diffuses into a pure matrix of the same element we speak about selfdiffusion. When the matrix is a homogeneous AB alloy then one can measure both the solvent and solute self-diffusion coefficient at different concentrations. In general the tracer diffusion coefficient measured is related to DA, defined in Eq. 1.4, by D
A∗
A
=D f,
(1.17)
Landolt -Börnst ein New Series III/33A
Ref. p. 1-21]
1 Introduction
1-5
where f is the correlation factor. Its presence is necessary because the migration of the marked (tracer) atom is not always completely random [70L1]. When the successive jumps of the migrating particle are not independent of each other, the jump frequencies in different directions deviate from the probabilities obtained from a complete random walk, the jumps are correlated. In the case of self-diffusion f (≤1) is usually a numerical factor depending on the crystal structure and diffusion mechanism. For impurity or heterodiffusion (the tracer is different from the atoms of the matrix) this factor can depend on the temperature as well [70L1]. In dilute alloys the concentration dependence of D for both constituents can be represented in terms of
[
( )
]
i∗ i∗ DAB X B = DAB 1 + B1 X B + B2 X B +... ,
i = A, B, ...
(1.18)
and the Bi factors are the solvent or solute enhancement factors [93L1]. For concentrated alloys there are usually no general analytical expressions for the concentration dependence [84B1], although some empirical rules can be found in the literature (for a review see e.g. [92B1]). Beside the primary/terminal solid solutions in many alloy systems intermediate phases can also exist and they usually have chemically ordered structures. Tracer diffusion in these crystals can also be carried out, but the atomistic interpretation should be more sophisticated [84B1] (see also Sect. 1.3). In the following part of this section, for the sake of simplicity, lower and upper indexes of D and c will be dropped, and some typical solutions of Eqs. 1.15 or 1.16 will be listed. The thin layer solution of Eq. 1.16 can be given in the form x2 , exp − 4 Dt πDt M
c( x , t ) =
(1.19)
where M is the total amount of diffusant per unit area at t = 0. Equation 1.19 is valid if the thickness of the layer deposited on the surface of a semi-infinite sample is much smaller than the diffusion length 2(Dt)1/2. This solution is most frequently used in the evaluation of tracer experiments. If the concentration at the surface of a semi-infinite sample is kept constant, i.e. c(0,t) = cs, the corresponding solution of Eq. 1.16 is: x c − cs = erf , c0 − cs 2 Dt
(1.20)
where z
erf z =
2
π
∫e
−u
2
du
(1.21)
0
is the error function and c0 is the initial homogeneous concentration in the sample. If c0 = 0 Eq. 1.20 simplifies to x c = erfc , cs 2 Dt
(1.22)
and the complementary error function is defined by erfc z = 1 − erf z .
Lando lt -Bö rnst ein New Series III/33A
(1.23)
1-6
1 Introduction
[Ref. p. 1-21
On the other hand if cs = 0, we have x c = erf , c0 2 Dt
(1.24)
which is the solution for evaporation from a semi-infinite sample. The diffusion flux per unit area, perpendicular to the initial surface, is Dcs ⁄(πDt)1/2 in case of Eq. 1.22 and −Dc0 ⁄(πDt)1/2 for Eq. 1.24. The total amount of the material penetrated/evaporated into/from the sample is M (t ) = 2cs Dtπ
(1.25)
M (t ) = 2c0 Dtπ ,
(1.26)
or
respectively. These equations can be used for the determination of D in experiments where the total amount of material taken up or lost is measured. The above solutions are applicable only if the sample can be considered semi-infinite, i.e. when 2(Dt)1/2 is much smaller than the length of the sample. Otherwise, corrections according to reflections from the ends are necessary [75C1]. Thus solutions in a finite slab, cylinder or sphere are usually more complicated and can be given e.g. as sums of different trigonometric, exponential or Bessel functions [59C1, 75C1, 90M1]. 1.2.1.2 Chemical diffusion If we have a contact between two initially homogeneous but different materials, the diffusional mixing can be described by Eq. 1.15 because in general D will be dependent on concentration. Before giving the possible solutions of this equation for most typical initial and boundary conditions we have to consider one important feature of this type of mixing. Usually the atomic currents between the partners A and B of the diffusion couple are not equal (see Fig. 3). Thus there will be a resultant volume transport (JAVA ≠ JBVB, where VA and VB are the partial molar volumes of A and B, respectively) as well. This is
A
JA
B
JB Position x
a markers
Matano plane
A Concentration c
B
porosity b
initial interface Position x
Fig. 3a, b. Atomic currents JA and JB (a) and the result of interdiffusion (b) schematically in an AB diffusion couple. For the definition of the Matano plane, please see Fig. 4.
Landolt -Börnst ein New Series III/33A
Ref. p. 1-21]
1 Introduction
1-7
equivalent to the creation of a non-uniform stress-free strain [88S1]: on one side of the diffusion zone contractions, while on the other side extensions will arise. The stress field related to this stress-free strain contributes to the atomic currents across the driving force Fp = − Ωgradp, and could cause a plastic deformation (by creep or by dislocation glide) as well. The plastic flow obviously relaxes the stress developed and results in a complex feed-back effect [96B1]. The description of the interdiffusion process then depends on the ratio of the relaxation time of the plastic flow, τ, and the time of diffusion t. An order of magnitude estimation of the relaxation time of this process can be obtained from τ ≅ η/E, where η is the dynamic viscosity and E is the Young modulus [88S1]. If t τ the relaxation of stresses can be considered to be fast and almost complete. In this case the additional term to Eq. 1.3, caused by the stress gradient as a driving force, can be neglected. However, the relaxation of stresses is equivalent to a convective transport in the diffusion zone: e.g. for vacancy mechanism expansions, as well as contractions on the different sides of the diffusion zone can be realized by annihilation and creation of vacancies at edge dislocations. This will lead to an additional convective term - in laboratory frame - to the right hand side of Eq. 1.3: cAvK, where vK is the Kirkendall-velocity. This limit was originally treated by Darken [48D1] and its results were widely used in the evaluation of inter or chemical diffusion experiments in the last decades. Indeed, if we suppose that the number of lattice sites is conserved [95B1], i.e. ∂(cA + cB)/∂t = 0, we will arrive at
∼ ∼ J A' = − DgradcA = − J B' = Dgradc B ,
(1.27)
where the prime indicates that the currents now are expressed in the laboratory frame. It can be seen that the diffusion mixing can be described by a unique diffusion coefficient for both components called chemical or interdiffusion coefficient: ∼ (1.28) D = X B DA + X A DB or
∼ D = c BV B DA + cAVA DB,
(1.29)
if the molar volumes change during the process [91P1]. Furthermore for the Kirkendall-velocity v k = ( DA − DB )gradX A
(1.30)
holds. The shift of lattice planes with respect to axes fixed at the end of the sample, can be determined by inserting inert markers (insoluble particles, wires) into the initial interface and by measuring their shift. On the other hand, if t τ (but t is long enough for the development of the stress gradient) than we can be in the second limit, when practically there is no stress relaxation at all (vk ≅ 0). But, now an additional term, proportional to the stress (pressure) gradient should be added to the right hand side of Eq. 1.3 and it can be shown [74B1, 95B1] that the mixing process is controlled by ~ DNP =
DA ⋅ DB X A DA + X B DB
(1.31)
Here the index NP indicates that this is the so called Nernst-Planck limit. After an initial transient period the pressure gradient developed makes the two currents equal, i.e. the volume transport will be determined by the slower intrinsic diffusion coefficient (series coupling of currents) in contrast to the Darken's limit (parallel coupling) where the chemical diffusion coefficient is determined by the faster one. In a more sophisticated treatment of the problem [88S1] it can be also shown that an intermediate creep controlled mixing regime is also possible. In macroscopic experiments it was supposed that the Darken's limit can be realized and Eqs. 1.27, 1.28 and 1.30 were used in the evaluation of experimental data. For long diffusion distances or annealing times this can be accepted as a reasonable (an order of magnitude) approximation even if we take into account the following two additional problems as well. First, in a more precise treatment we have to take
Lando lt -Bö rnst ein New Series III/33A
1-8
1 Introduction
[Ref. p. 1-21
into account that there is a resultant vacancy flow and the effect of this, "vacancy wind" can be included into the intrinsic diffusion coefficient by a vacancy wind factor rA [68M1, 91P1]: A
DA = D ⋅ Φ rA .
(1.32)
Secondly, the resultant vacancy flow can lead to a supersaturation and precipitation of vacancies in the diffusion zone. This is an illustration of violation of suppositions used in the derivation of above relations [96B1], and it results in a decrease of the diffusional cross section as well. Furthermore, it was observed that there is a competition between such porosity formation and the Kirkendall-shift: the application of small (∼100 bar) hydrostatic pressures can prohibit the porosity formation [58B1, 56G1]. In the case of short diffusion distances (where t can be very short), however - as it was shown recently [94Y1, 85G1] - a considerable slowing down of the intermixing process can be observed. In amorphous ~ multilayers, with a modulation length of a few nanometers, orders of magnitude smaller D were observed as compared to values obtained in macroscopic samples, indicating the violation of the Darken's limit [94Y1]. The first question is to know which intrinsic diffusion coefficient (or the creep process) controls the ~ mixing. Moreover, if D is independent of time, - for isotropic case - the solutions of Eq. 1.15 are necessary to evaluate the experiments. In order to simplify Eq. 1.15, let us introduce a new variable λ = x/t1/2 (Boltzman transformation [91P1]). Then Eq. 1.12 will be transformed into −
λ dc 2 dλ
=
d ~ dc D , dλ dλ
(1.33)
the solution of which is some function c(λ). This transformation can be applied only when the initial and boundary conditions are themselves functions only of the variable λ. As is illustrated in Fig. 3 this will be the case in a diffusion couple consisting of slabs thick enough as compared to 2(Dt)1/2. Then integration of Eq. 1.33 gives; −
1 2
c
~ dc
∫ λdc = D dλ
c1
c
~ dc −D dλ
~ dc , =D dλ c
c1
(1.34)
from which c
∫ λdc
c
∫ xd c 1 c1 1 c1 ~ =− D=− 2 (dc/dλ ) c 2t (dc/ d x ) c
.
(1.35)
~ This Boltzmann-Matano equation allows the evaluation of D (see Fig. 4). The origin of x, which is denoted as the Matano plane, is determined by the condition c2
c2
c1
c1
∫ λdc = 0 = ∫ xdc =0 .
(1.36)
This interface fixes two equal areas on the c(x) profile (Fig. 4); through this plane equal amounts of mate~ rial moved in the positive and negative directions. For concentration independent D the Matano plane ~ coincides with the initial position of the interface. Methods for the calculation of D without determining the Matano interface, and the case of variable molar volumes can be found e.g. in [91P1] and [90M1], respectively. Since the solution of Eq. 1.33 - if the Boltzmann-Matano transformation can be applied - is a function of λ = x/(t)1/2, a front of constant concentration should move as the square root of time; x ~ t1/2. This Landolt -Börnst ein New Series III/33A
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1-9
is also valid for the Kirkendall-shift, as measured from the movement of inert markers placed at the initial weld interface, because they move together with a plane of fixed concentration (marker plane). Similarly, in multiphase diffusion (i.e. when there is no complete solid state miscibility of the components: Fig. 5) the Boltzmann-Matano method is applicable, because the phase boundaries are points of constant concentration. Furthermore, it can be shown that the thickness ξ of a growing phase should also follow the parabolic law (if the role of reactions at the interfaces and the possible competition between simultaneously growing phases is neglected) [91P1];
ξ 2 = κt.
(1.37)
Here κ is the growth rate constant and can be related to the intrinsic diffusion coefficients and to the thermodynamic data (e.g. limiting concentrations in the phase diagram). Although, the atomic interpretation of κ in general can be rather complicated, it can be easily measured and its knowledge is very useful in many solid state reactions (see e.g. Chap. 4 in subvolume III/33a).
Concentration c
c2
M
(dc/dx)c
c
Fig. 4. Illustration of the calculation of the interdiffusion coefficient from the concentration profile according to the Boltzmann-Matano method. M indicates the Matano plane with
x dc
c
c1
c2
c1
∫ xd c = 0 .
x=0 Position x
c1
(See text and Fig. 3).
0 a
T1
1
η
Concentration c
Concentration c
1
Position x
0 b
η
Temperature T
Fig. 5a, b. Concentration distribution in the diffusion zone, when the constiuents have restricted solubility (a) and an intermediate phase η exists also in the phase diagram (b).
1.2.2 Grain boundary diffusion In mathematical models describing the grain boundary diffusion it is supposed that the boundary is a homogeneous slab of thickness δ (Fig. 6), with a high diffusivity, D', as compared to the bulk (D1, D2). In principle - depending on the time of the heat treatment and on the grain size d - three types of kinetic behaviour may be distinguished as proposed first by Harrison [61H1] (Fig. 7). 1) Type-C kinetics. This refers to the limit when the bulk diffusion length (Dt)1/2is negligible as compared to δ. In this case the diffusion is restricted to the grain boundaries only and for the determination of D' all the solutions listed in 1.2.1.1 can be used, except methods based on the measurement of the absolute concentration (e.g. permeation technique), where the knowledge of the grain boundary volume fraction, g ≈ δ /d, is also necessary. Lando lt -Bö rnst ein New Series III/33A
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Position x
Position x
Diff. direction y, η
δ
d
type A
c'
c1 , D1
ψ
1/2
d
(Dt)
c2 , D2 Diff. direction y, η
D' δ
1/2
(Dt)
type B
Fig. 6. Isoconcentration contour according to Fisher´s model for grain boundary diffusion. (See text).
1/2
100 δ < (Dt) < d/20
1/2
type C
(D't)
1/2
20(Dt) < δ
Fig. 7. Different types of diffusion regimes for grain boundary diffusion.
2) Type-A kinetics. Here the diffusion fields, developed around each boundary in the bulk, overlap because (Dt)1/2 d. Thus the diffusion process can be characterized by an effective diffusivity Deff = gD ' +(1−g)D.
(1.38)
This Hart's equation is obtained simply by averaging over the whole period of the migration of the diffusant; the time fractions spent in the boundary and inside the grains are proportional to g and 1-g, respectively [95K1]. For the determination of Deff the same methods can be used as for the bulk diffusion coefficient. 3) Type-B kinetics. This is the generally realized situation in most experiments. The basic equations can be written in the form:
∂c ' ∂t
∂ c' 2
= D'
∂y
2
+
1 ∂c D1 δ ∂x
x =δ / 2
+ D2
∂c ∂x
x =−δ / 2
(1.39)
∂ 2c ∂ 2c ∂c = D1 , + ∂t ∂x 2 ∂y 2 (1.40) ∂ 2c ∂ 2c ∂c = D2 2 + 2 . ∂t ∂y ∂x These are the equations of the so called Fisher-model [51F1, 95K1, 88K1], where it is supposed that δ is small enough (c' is constant along δ ), D' D1, D2 and the current is continuous at the interface of the slab. Landolt -Börnst ein New Series III/33A
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Eq. 1.39 states that ∂c'/∂t is caused by the divergence of the flux along the boundary and by the exchange of matter between the boundary and the grain ("leakage" of atoms into the bulk). If D1 = D2 = D we speak about grain boundary diffusion, while in the general case of interphase boundary diffusion D1 ≠ D2. Then the modified Eqs. 1.39 and 1.40 for grain boundary diffusion (the last two terms in Eq. 1.39 as well as the two Eqs. 1.40 are combined together) have to be solved with appropriate boundary and initial conditions. For example for constant surface concentration: c(x, 0, t) = c0 , c(x, y, 0) = 0 c(x, ∞, t) = 0
t=0 (1.41)
and a matching condition at the interface c( δ/2, y, t) = f(c')
(1.42)
should hold. 1.2.2.1 Self-diffusion For self-diffuison Eq. 1.42 simplifies to c' = c.
(1.43)
Exact solution of the modified Eqs. 1.39, 1.40 with 1.41 and 1.43 was given by Whipple [54W1], while for thin film boundary condition by Suzuoka [61S1, 64S1]. Now, if
α = δ/(Dt)1/2 < 0.01 and β = P/2D(Dt)1/2 > 10,
(1.44)
(where P = δD'), both solutions can be expressed as the function of a combination of two parameters η = y/(Dt)1/2 and β: c = F(ηβ −1/2 ),
(1.45)
and c is the laterally averaged (tracer) concentration in the plane perpendicular to y. Furthermore, Levin and McCallum [60L1] have shown that −
∂ ln c − 1/ 2 ∂ ηβ
6/5
= A,
(1.46)
where A is approximately constant in both cases if
ηβ −1/2 > 2.
(1.47)
Thus, using the definition of β and d −1/ 2 d ηβ
[
n
]
n y d = −1/ 2 , dy ηβ
(1.48)
the parameter P can be expressed as ∂ ln c P = − 6 / 5 ∂y
−5 / 3
4D t
1/ 2
A 5/ 3 ,
(1.49)
and A = 0.78 for Whipple and A = 0.72β0.008 for Suzuoka solution [63L1]. The value of A is the same within 6% for both solutions in most of the practically interesting cases. For some refinements at different values of β see e.g. [95K1]. Lando lt -Bö rnst ein New Series III/33A
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[Ref. p. 1-21
It is a big advantage that the form of the tracer penetration function, ln c vs. y6/5, is practically independent of the boundary conditions, and if the requirements of the validity of Eq. 1.49 (i.e. Eqs. 1.47 and 1.44) are fulfilled, the product P = δD' can be determined, if the bulk diffusion coefficient is known. Besides the tracer sectioning technique some other methods were sometimes also used for the determination of P or D'. For example by the technique of autoradiography (made on a cross section of the specimen after the diffusion of the tracer) the concentration contour illustrated in Fig. 6 can be measured. Here, of course, the ψ angle has also to be determined. There is also an approximate way of the determination of P from Coble-creep data [63C1] or from sintering kinetics. From the surface accumulation method - i.e. when the originally pure top surface of a thin film, with relatively high density of grain boundaries, is gradually covered by the material transported by grain boundary diffusion from the bottom surface of the film directly D' can be determined. For the details, see the Chapter ''Grain boundary and dislocation diffusion". 1.2.2.2 Impurity diffusion and segregation If we would like to measure the hetero- or impurity diffusion along grain boundaries the matching condition at the interface has to be modified [58B2, 66G1]. The simplest form of Eq. 1.42 can be achieved if we suppose a Henry-type segregation isotherm, i.e. c = c'/K,
(1.50)
where K is the segregation coefficient and has an Arrhenius-type temperature dependence: K = exp(Fs/kT).
(1.51)
Here Fs is the free-energy of segregation. In this case all the results obtained for self diffusion remain valid replacing δ by Kδ. Then the P parameter P = KδD' is called grain boundary triple product. In real systems, however, the segregation isotherm is more complicated and the form of Eq. 1.42 should be modified if we have e.g. a McLean or Fowler-Guggenheim segregation behaviour. In [92B2] and [95B2] the effect of these more complicated segregation conditions for the solution of the grain boundary problem was analyzed and it was shown that this can lead to an upward or downward curvature on the grain boundary penetration plot for segregating or desegregating diffusant, respectively. An experimental verification of these results has been published recently [96B2] in the Cu(Ag) system.
1.2.3 Dislocation diffusion The mathematical model of diffusion along dislocations can be created similarly as for grain boundary diffusion with the only difference that now the dislocation can be considered as a homogeneous cylinder of radius a [84L1]. Accordingly, one can again distinguish between three different types of kinetics and thus the tracer methods can be classified according to this. In type-C kinetics one can measure the coefficient of dislocation diffusion, D", directly, while in type-A kinetics the Hart model (analogous to Eq. 1.38) can be used. For type-B kinetics the exact solution of the problem is as complicated as for the case of grain boundary diffusion. It was shown in [84L1] that now the dislocation penetration plot, ln c vs. y will be linear and from the slope of this plot, the dislocation triple product D"a2 K" can be determined: D"a2 K" = DA'2 (dln c /dy)2,
(1.52)
where A' is a constant [84L1], depending weakly on the ratio a2/(Dt)1/2 but for most practical purposes lies between 0.5 and 0.8. K" is the dislocation segregation coefficient. This offers the most accurate method for determining the dislocation triple product. Other methods for the determination of the triple product or D" are treated in the Chapter "Grain boundary and dislocation diffusion".
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1.2.4 Surface diffusion Surface diffusion is the motion of adsorbates (adatoms, molecules) on the top of the surface. Usually two types of intrinsic surface diffusion coefficients can be measured for both self- and hetero-diffusion. The tracer surface diffusion coefficient (not equal to the diffusion coefficient obtained by the use of radioactive tracers! [90B1]) corresponds to DA defined by Eq. 1.4 and describes the random walk diffusion, i.e. it can be determined if there are no interactions between the adsorbates (very low coverage). On the other hand the chemical surface diffusion coefficient corresponds to DA (see Eq. 1.3), and can be measured when the interactions between the adsorbates are not neglected and the surface activity coefficient is different from unity. Furthermore we have also to make a distinction between the mass transfer and the intrinsic surface diffusion coefficients, DM and DI. respectively. The mass transfer coefficient can be obtained when the number of mobile particles varies if e.g. the temperature is varied. DM and DI are formally related by [90B1] DM = nDI/ns,
(1.53)
where n is defined after Eq. 1.4 and ns is the maximal value of n. Deeper interpretation of the meaning of these coefficients can be given only on the basis of the detailed description of the real surface with various defects. For this and also for the description of different methods of measuring DM and DI the reader is referred to the Chapter "Surface diffusion".
1.3 Atomic mechanisms of diffusion The diffusion coefficient of different atoms, at a given temperature and pressure, obviously strongly depends on the mechanism of diffusion. Indeed the product of the jump frequency and the square of the jump distance in Eq. 1.4 as well as the value of the correlation factor f in Eq. 1.17 may be different: thus D may differ by many orders of magnitude for different mechanisms. In this section a short description of the main atomic mechanisms of diffusion (Fig. 8) is given and for details, see e.g. [66A1, 91P1, 90M1].
d a
e b f c Fig. 8. Atomic mechanisms of diffusion: a: direct interstitial, b: indirect interstitial, c: ring, d: vacancy, e: dissociative, f: kick-out mechanisms.
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[Ref. p. 1-21
1.3.1 Direct interstitial mechanism Atoms in interstitial positions are point defects, the successive jumps of them on interstitial sites are not correlated (Fig. 8, a). This is the direct interstitial mechanism which is typical for atoms of considerably smaller size than the atoms of the host crystal (the atomic fraction of self-interstitials is usually negligible in comparision to other intrinsic point defects).
1.3.2 Indirect interstitial or interstitialcy mechanism This is a variant of the above mechanism: the tracer atom now has a correlated migration occurring on both substitutional and interstitial positions during subsequent jumps (Fig. 8, b). For example this is the mechanism of self- and some substitutional impurity diffusion in silicon.
1.3.3 Ring mechanism This is a direct exchange of atoms on substitutional lattice sites; in principle the ring can consist of two atoms as well (Fig. 8, c). There are no experimental evidences of this mechanism, because the substitutional diffusion by intrinsic point defects (diffusion vehicles) is usually more favourable.
1.3.4 Vacancy mechanism In this case the migration of a tagged atom occurs via vacant lattice sites by jumping into a neighbouring vacancy (Fig. 8, d). The process can be considered as the migration of either the tracer atom or a vacancy, but while the migration of the vacancy is random, the migration of the tracer is correlated. Indeed, in this case the factor Γ in Eq. 1.4 will be expressed as the product of the vacancy fraction nv, the exchange frequency ωv of the atom and the vacancy, and the correlation factor f: DA* = αa2nvωv f.
(1.54)
For substitutional impurity diffusion interactions between the vacancy and the solute may cause both higher or lower diffusivities as compared to self-diffusion.
1.3.5 Interstitial-substitutional mechanisms Some alloying elements can be dissolved into interstitial (Ai) or substitutional (As) sites of the host matrix. In this case the mechanism is a mixture of two of the above mechanisms and the diffusivity is usually high because of the high diffusivity along interstitial positions. If the Ai atoms make an interchange with vacancies according to the reaction Ai + V ↔ As
(1.55)
then we have the dissociative mechanism (Fig. 8, e). In the case of kick-out mechanism (Fig. 8, f) the interchange of Ai involves self-interstitials (I) according to the reaction Ai ↔ As + I.
(1.56)
This mechanism operates for some rapidly diffusing impurities in silicon (see Chap. 2 in subvolume III/33A).
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1.3.6 Other mechanisms Besides the interstitial-substitutional mechanism there are many cases when the mixture of two or more mechanisms or diffusion vehicles take part in the diffusion. Thus diffusion in ordered structures depends on the types and concentrations of defects on the sublattices and is also sensitive to deviations from stoichiometry. For example in ionic crystals the dominant defects can be different for different types [91P1]: − Schottky-defects (vacancies on the anion or cation sublattice) in alkali halides − Frenkel defects ( vacancies and interstitials) in silver halides on the cation sublattice − Frenkel defects on the anion sublattice in CaF2 type structures as well as in chalcogenides and oxides with fluorite structures. However, usually we have to expect complications even for self-diffusion because of the charge effects (e.g. contribution of neutral vacancy pairs in alkali halides [76B1]) or because the migration is not restricted to one sublattice only, but involves the creation and/or annihilation of antisite defects as well (e.g. ring mechanism in which the overall order is not destroyed after a cycle [84B1], or diffusion by a triple defect consisting of a vacancy-pair and an antisite atom). Furthermore, sometimes even a small amount of dopants can result in self-diffusion not in the intrinsic but in the extrinsic regime, where the concentration of the diffusion vehicles is determined not by the thermal activation in pure crystal (see also Sect. 1.5) but e.g. by the number of charge compensating vacancies (see e.g. Chap. 3 in subvolume III/33A and Chap. 2 in subvolume III/33B). Deviations from the stoichiometry can also lead to transition to the extrinsic behaviour: for example in MgO the concentration of intrinsic defects is very small and a few ppm of impurities can cause a shift to the extrinsic region where the vacancy concentration on the metallic sublattice is much higher than on the oxide sublattice. The deviation from stoichiometry depends on the temperature and on the partial pressure of the volatile component as well. The self-diffusion coefficient in the presence of more than one mechanism can be written as D* = ∑αi ai2niωi fi ,
(1.57)
where the sum is over all types of point defects present. Usually for the defect concentrations we have additional conditions from the law of mass action and charge balance [91P1]. For the details see references given in Sect. 1.8 and in the Chapters on the different materials.
1.4 Methods for measuring diffusion coefficients Experimental methods for the determination of diffusion coefficients are very comprehensively described in the Landolt-Börnstein, New Series, Vol. III/26 [90M1], here it is given only a summary, which gives the definitions of different methods in order to facilitate the reading and the use of tables. In some cases, when a particular method plays a key role in special material(s), the description is given in the corresponding chapter. Experimental techniques can be divided into two categories: − Macroscopic methods based on Fick's laws where the concentration profiles (the flux or the integral of the diffusion flux) are determined by direct (e.g. tracer) or indirect measurements. In these cases the diffusion distance is usually long as compared to the jump distance. − Microscopic methods based on the measurement of jump frequencies. In these cases relaxation times or frequencies, directly related to the jump frequencies of species of atoms, are determined. Thus they are sensitive to elementary jumps i.e. to small displacements of atoms (of the order of an interatomic spacing) [91P1].
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1.4.1 Macroscopic methods 1.4.1.1 Steady-state methods In these techniques the steady-state concentration distribution (∂c/∂t = 0) and the flux J is determined and D is calculated. The steady-state solution of Fick's second law, with constant D, e.g. for a membrane of thickness L, is given by: c − c1 c2 − c1
=
x L
,
(1.58)
i.e. the concentration changes linearly from c1 to c2 through the sheet. Then the flux, according to Eq. 1.3, J=D
c1 − c 2 , L
(1.59)
can be determined by performing a permeation measurement, and thus D can be determined. 1.4.1.2 Non steady-state methods In these cases the concentration profile, c(x,t) is established directly by destructive or non-destructive methods at fixed t, or the time dependence of c at a fixed distance (or the time dependence of an integral quantity related to the concentration distribution) is measured and from the comparison with the appropriate solution of the Fick's second law the constant or concentration dependent D can be determined. a) Direct profile measurement The most frequently used method for the determination of D is the sectioning of the sample parallel to the original end surface. After measuring the average concentration in each section the penetration function is compared with the appropriate solution of the Fick's second equation. Usually the thin film solution (see Sect. 1.2.1.1.) is used and a linear lnc vs. x2 plot is obtained. The concentration profile can be also determined on the cross-section parallel to the diffusion direction by analytical methods having good line resolution. For the experimental details of the different ways of sectioning and determination of the concentration of sections see [90M1, 84R1, 66A1]. The most frequently used techniques for the determination of the concentrations are: − radio-tracer technique (with the measurement of the activity of each section) − measurement of the residual activity of the tracer (after removing sections) − secondary ion mass spectroscopy (SIMS) or secondary neutral mass spectroscopy (SNMS) − Auger electron spectroscopy (AES) − Electron microprobe analysis (EMPA) − Rutherford back-scattering (RBS) (generally with He ions) − Nuclear reaction analysis (NRA) − Microscopic (metallographic chemical etching) method − Autoradiography b) Indirect methods Here the time dependence of c at a fixed distance (or the time dependence of an integral quantity related to the concentration distribution) is measured or the diffusion controlled process is followed by different methods.
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1 Introduction
1-17
Examples of these techniques: − Surface activity decrease (the time dependence of the activity at x = 0 is measured) − In and out diffusion methods (total amount of the change of the material is determined) − X-ray satellite method (measurement of the intensity of the first X-ray satellite originating from the interface reflections in alternate thin layers: the decrease of this peak is related to the interdiffusion mixing at the interface [85G1]) − Measurement of the electrical resistivity: Since the resistivity is a property sensitive to the changes in the structure of the sample, it can be used to monitor processes directly related to diffusion [66C1] or to migration of charged point defects or electrically active impurities. The description of the method and a guide to the interpretation of the results obtained see also in Chap. 2 of subvolume III/33A as well as in Chap. 2 of subvolume III/33B − Measurement of the growth rate of a new phase (see Eq. 1.37 in Sect. 1.2.1.2) − Measurement of the creep rate (see e.g. Chap. 12 in [90M1] ) − Measurement of sintering kinetics (see e.g. Chap. 12 in [90M1] )
1.4.2 Microscopic methods These methods can be divided into two categories: − Relaxation methods, where atomic motions are induced by external stimulus (e.g. mechanical stress, magnetic field) and their contribution to the relaxation of the exciting signal is measured [72N1]. − Nuclear methods, where the linewidth of different nuclear relaxations or scatterings are affected by the thermally activated motions of atoms. The most important microscopic methods used for the determination of the jump frequency or the residence time of the diffusing atoms are listed below. 1.4.2.1 Relaxation methods a) Internal friction Here special resonance peaks, caused by the mechanically excited jumps of different type of point defects are investigated as a function of the temperature or the frequency of excitation. If jumps of interstitial atoms (jumping between two interstitial positions) are induced we speak about the Snoek effect, while reorientation of substitutional solute pairs (or of any pairs of atoms causing a mechanical dipole) leads to the Zener effect. b) Gorski effect This is a relaxation of elastic stresses by the migration of centers of dilatation under a stress gradient produced e.g. by bending of the sample. The relaxation time is inversely proportional to the diffusion coeffcient [72V1, 84B2]. It has been mostly used for the study of hydrogen diffusion. c) Magnetic relaxation In ferromagnetic materials - because of the magnetic anisotropy - the magnetic field can be used for mechanical excitation. Measurement of the magnetization enables one to follow the relaxation process [91P1]. d) Dielectric relaxation Pairs of point defects forming electric dipoles, can result in relaxation effects similar to those described above for elastic or magnetic relaxations [91P1].
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1.4.2.2 Nuclear methods These techniques are usually very sophisticated and the atomic interpretation requires experience in the evaluation of nuclear spectra. a) Nuclear magnetic relaxation (NMR) The width of the resonance line and the spin-lattice relaxation time also reflect the thermally activated motion of atoms and their measurements allow the determination of the diffusion coefficient [91P1, 82K1, 84S1], if the diffusion species have a nuclear magnetic moment. b) Mössbauer spectroscopy (MBS) and quasielastic neutron scattering (QENS) The linewidth in both of these nuclear techniques has contributions from the atomic jumps. In single crystals the diffusion broadening depends on the orientation as well and the jump direction and the jump length can be also determined [84M1, 85V1].
1.5 Temperature, pressure and mass dependence of diffusion 1.5.1 Temperature and pressure dependence According to Eq. 1.54 the temperature and pressure dependence of D will be determined by the defect concentration n, the exchange frequency ω of the atom and the defect and by the correlation factor f (a2 and α are constants for a given mechanism). Since both the exchange frequency and the defect concentration usually can be treated as thermally activated processes [66A1, 72F1, 57V1, 89S1, 91P1], they can be given by q = exp(Sq /k)⋅exp(−{Eq+p∆Vq}/kT ),
q = n,ω.
(1.60)
Here S, E and ∆V denote the activation entropy, energy and volume necessary for the creation of a defect or for the elementary jump. Thus for those cases, when the correlation factor is temperature independent, the diffusion coeffcient has an Arrhenius-type temperature dependence: D = D0 exp(−Q/kT ),
(1.61)
where D0 and Q are the pre-exponential factor and the activation energy, respectively. For example the activation energy for vacancy mechanism is the sum of the formation and migration energy of vacancy, or for direct interstitial mechanism it contains only the migration energy. The correlation factor in general is temperature dependent, but sometimes it can be approximated with an Arrhenius type dependence [70L1] and then a new term C = k ∂lnf / ∂(1/T ),
(1.62)
appears in the activation energy. Arrhenius diagrams (lnD vs. 1/T ) determined experimentally are sometimes curved and the deviation from the linearity can be quite pronounced. This curvature can be attributed to different reasons: − Simultaneous operation of two or more diffusion mechanisms. They can be related to different thermally activated defects (diffusion vehicles) or to the transition from the intrinsic to extrinsic regime (see also Sect. 1.3.6). In these cases data may be fitted by a sum of two or more Arrhenius functions or a sum of one Arrhenius and one horizontal line.
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− The activation parameters depend on temperature. They are temperature independent only in harmonic approximation, thus anharmonicities result in curvatures of the Arrhenius function [89B1]. − The mechanisms of diffusion are the same but can contain more than one jump frequency. For example in the direct interstitial mechanism a mixture of jumps between different interstitial positions (tetrahedral and octahedrals sites) can occur, and their roles can depend on the temperature. The same comments as above hold for the pressure depedence of diffusion coeffcients. Usually simultaneous measurement of the temperature and pressure dependence can help to decide between different mechanisms and/or can help to separate different contributions to D.
1.5.2 Mass dependence Measurement of diffusion coeffcients can be performed with a mixture of two isotopes (denoted by α and β) of the same element. Then - because of the mass dependence - the diffusion coeffcients will be different for α and β, and the difference is sensitive to the atomic mechanism of diffusion. This isotope effect is characterized by the quantity Eα,β = (Dα/Dβ−1)/(mβ/mα−1),
(1.63)
where mα and mβ are the masses of atoms α and β. This parameter - under some conditions - can be written into the form [75P1, 85N1, 91P1, 70L1] Eα,β = fα ∆K,
(1.64)
where ∆K is the kinetic energy factor and is the fraction of the kinetic energy of the entire jump carried by the jumping atom. Thus the quantity Eα,β is directly related to the correlation factor fα.
1.6 Notations, use of the tables Since in the Landolt-Börnstein series the aim is to give a selected collection of experimental data and functional relationships, the most important parts of this book are the tables and figures. The notations in these follow the definitions given in this chapter, however in chapters on different materials the indices are usually dropped whenever it is clear which diffusion coefficient is considered. Furthermore, in each introduction of the chapters some additional information is given regarding the mechanisms, the special method of measurements or the special notations used as well. The experimental data are primarily reported in terms of the activation energy, Q, and the preexponential factor, D0 whenever it is possible. When several measurements exist for the same system an attempt has been made to select the most recommended ones and they are also shown in figures.
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1 Introduction
[Ref. p. 1-21
1.7 Further readings Since [90M1] contains a good list of textbooks, conference proceedings and sources of diffusion and defect data from the last decades, here only the publications, which appeared in the last ten years (except few sources important in these materials and not cited in [90M1]) are given.
1.7.1 Textbooks Boltaks, B.I.: Diffusion in Semiconductors, London: Insoferarch Ltd., 1963. Shaw, D.(ed.): Atomic Diffusion in Semiconductors, London: Plenum Press, 1973. Kirkaldy, J.S., Young, D.J.: Diffusion in the Condensed State. Brookfield, USA: The Institute of Metals, 1987. Borg, R.J., Dienes, G.J.: An Introduction to Solid State Diffusion, Boston: Academic Press, 1988. Ghez, R. : A Primer of Diffusion Problems, New York: John Wiley, 1988. Philibert, J.: Atom Movements. Diffusion and Mass Transport in Solids, Les Ulis, France, Les Editons des Physique, 1991. Murch, G. E.: Diffusion in Solids - Unsolved Problems, Zürich: Trans. Tech. Publ., 1992. Allnatt, A.R., Lidiard, A.B.: Atomic Transport in Solids, Cambridge: University Press, 1993. Paul, D.R., Yampolskii, Y.P., (eds.): Polymeric Gas Separation Membranes, Boca Raton: CRC, 1994. Kaur, I., Mishin, Y., Gust, W.: Fundamentals of Grain and Interphase Boundary Diffusion, Chichester, New York: John Wiley, 1995. Schmalzried, H.: Chemical Kinetics of Solids, Weinheim: VHC Verlag, 1995.
1.7.2 Proceedings Fundamentals of Diffusion Bonding, Proc. of First Seiken Int. Symp. Tokyo, 1985: Ishida, Y. (ed.): Studies in Physical and Theoretical Chemistry 48, Amsterdam: Elsevier, 1987. Lattice Defects in Ionic Crystals, Proc. of Fifth European Topical Conf., El Escorial, Spain, 1986: Agulló-López, F., Hodgson, E.R., López, F.J. (eds.): Crystal Lattice Defects and Amorphous Materials, Vols. 14 -17, 1987. Diffusion in High Technology Materials, Proc. of ASM Symposium, Cincinnati, USA, 1987: Gupta, D., Romig, A.D., Dayananda, M.A.(eds.): Aedermannsdorf, Switzerland: Trans. Tech. Publ. Ltd., 1988. The Physics and Chemistry of Carbides, Nitrides and Borides, Proc. of the Nato ARW, Manchester, 1989: Freer, R. (ed.): Dordrecht, The Netherlands: Kluwer Academic Press, 1990. DIMETA-88-Diffusion in Metals and Alloys, Proc. of Int. Conf., Balatonfüred, Hungary, 1988: Kedves, F.J., Beke, D.L. (eds.): Defect and Diffusion Forum Vol. 66 - 69, 1989. Diffusion in Materials. Proc. of the Nato ASI, Aussois, France, 1989: Laskar, A.L., Bocquet, J.L., Brebec, G., Monty, C.(eds.): Dordrecht, The Netherlands: Kluwer Academic Press, NATO ASI Series, Vol. 179, 1990. Lattice Defects in Ionic Crystals, Proc. of Sixth European Topical Conf., Groningen, The Netherlands, 1990: Den Hartog, H.W. (ed.): Radiation Effects and Defects in Solids, Vol. 119 - 121, 1991. Diffusion in Materials, Proc. of Int. Conf., Kyoto, Japan, 1992: Koiwa, K., Hirano, K. Nakajima, Okada, T. (eds.): Defect and Diffusion Forum, Vol. 95 - 96, 1993. Reactive Phase Formation at Interfaces and Diffusion Processes, Proc. of Int. Meeting, Aussois, France: Limoge, Y., Bocquet, J.L.: Materials Science Forum Vol. 155 -156, Trans. Tech. Publ. 1994. Defects in Insulating Materials Eurodim 94, Proc. of Seventh Europhysical Conf., Lyon, France, 1994: Blanchin, M.G., Davenas, J., Moine B., Pédrini, C., Treilleux, M., (eds.): Radiation Effects and Defects in Solids, Vol. 135 - 137, 1995. Diffusion and Stresses, Proc. of Int. Workshop, Balatonfüred, Hungary, 1985: Beke, D.L., Szabó, I.A. (eds.): Defect and Diffusion Forum, Vol. 129 - 130, 1996. Diffusion in Materials, Proc. of Int. Conf., Nordkirchen, Germany, 1996: Mehrer, H., Herczig, Chr., Stolwijk, N.A., Bracht, H. (eds.): Defect and Diffusion Forum, Vol. 143-147, 1997.
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1 Introduction
1-21
1.7.3 Collections of data Diffusion and Defect Data (DDD), series from 1967. Wölbier, F.H., Fisher, J.D. (eds.): Switzerland: Trans. Tech. Publ. Handbook of Grain and Interphase Boundary Diffusion Data, Vol.1 and 2: Kaur, I., Gust, W., Kozma, L., Stuttgart: Ziegler Press, 1989. Impurities and Defects in group IV elements and III-IV compounds, Schulz, M. (ed.), Landolt-Börnstein, New Series, Vol. III/22b, Berlin: Springer-Verlag, 1989. Diffusion in Solid Metals and Alloys, Mehrer, H. (ed.)., Landolt-Börnstein, New Series, Vol. 26, Berlin: Springer-Verlag, 1990.
1.7.4 Review articles Robertson, W.M.: Surface Diffusion of Oxides, J. Nucl. Mater. 30 (1969) 36. Matzke, Hj.: Science and Technology of Advanced LMFBR Fuels, Amsterdam: North Holland, 1986. Vrentas, J.S., Duda, J.L., in: Encycl. Polym. Sci. Eng. Vol. 5., New York, John Wiley & Sons, 1989. Matzke, Hj.: Diffusion in Ceramic Nitrides, Adv. Ceram. 23 (1987) 617. Sharma, B.L.: Diffusion in III-V compounds and their alloys. Defect and Diffusion Forum 64/64 (1989) 1. Sharma, B.L.: Diffusion in II-VI compounds and their alloys. Defect and Diffusion Forum 64/64 (1989) 77. Stern, S.A., Trohalaki, S., in: Barrier Polymers and Structures, Koros, W.J., (ed.), ACS Symposium Series Vol. 423, American Chemical Soc. Washington, D.C., 1990. Vieth, W.R.: Diffusion In and Through Polymers, Hanser, Munich, 1991. Gomer, R.: Diffusion of Adsorbates on Metal Surfaces, Rep. Prog. Phys. 53 (1991) 1. Seebauer, E.G., Allen, C.E.: Estimating Surface Diffusion Coefficients, Prog. Surf. Sci. 49 (1995) 265.
1.8 References for 1 48D1
Darken, L.S.: Trans. Am. Inst. Min. Metall. Eng. 175 (1948) 184.
54W1
Whipple, R.T.P.: Philos. Mag. 45 (1954) 1225.
51F1
Fisher, J.C.: J. Appl. Phys. 22 (1951) 74.
56G1
Geguzin, Yu.E.: Dokl. Akad. Nauk. SSSR (in Russian) 5 (1956) 839.
57V1
Vineyard, G.H.: J. Phys. Chem. Solids 3 (1957) 121.
58B1 58B2
Barnes, R.S., Mazey, D.J.: Acta Metall. 6 (1958) 1. Bokstein , B.S., Magidson, I.A., Svetlov, I.L.: Phys. Met. Metallogr. 6 (1968) 81.
59C1
Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Oxford: Clarendon Press, 1959.
60L1
Levin, H.S., MacCallum, C.J.: J. Appl. Phys. 31 (1960) 595.
61H1 61S1
Harrison, L.G.: Trans. Faraday Soc. 57 (1961) 1191. Suzuoka, T.: Trans. Jpn. Inst. Met. 2 (1961) 25.
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1-22
1 Introduction
63C1 63J1 63L1
Coble, R.L.: J. Appl. Phys. 34 (1963) 1679. Johnson, D.L. Cutler, I.B.: J. Am. Ceram. Soc. 46 (1963) 541, 545. LeClaire, A.D.: Br. J. Appl. Phys. 14 (1963) 351.
64J1
Jost, W.: Diffusion in Solids, Liquids and Gases (2nd Edition). New York: Academic Press, 1964. Suzuoka, T.: J. Phys. Soc. Jpn. 19 (1964) 839.
64S1 66A1 66C1 66G1
Adda, Y., Philibert, J.: La Diffusion dans les Solides. Paris: Presses Universitaires de France, 1966. Ceresara, S., Frederighi, T., Pieragostini, F.: Phys. Status Solidi 16 (1966) 439. Gibbs, G.B.: Phys. Status Solidi 16 (1966) K27.
68M1
Manning, J.R.: Diffusion Kinetics of Atoms in Crystals, Princeton: van Nostrand, 1968.
70L1
Le Claire, A.D.: Correlation Effects in Diffusion in Solids, in: Physical Chemistry an Advanced Treatise, Vol. X, Chapt. 5. New York: Academic Press, 1970.
72F1 72N1
Flynn, C.P.: Point Defects and Diffusion, Oxford, Clarendon Press, 1972. Nowick, A.S., Berry, B.S.: Anelastic Relaxation in Crystalline Solids . New York: Academic Press, 1972. Vökl, J.: Ber. Bunsen Ges. Phys. Chem. 76 (1972) 797.
72V1 73G1
Geguzin., Ya.E., Krivoglaz, M.A.: Migration of Macroscopic Inclusions in Solids, New York, Consultans Bureau (Plenum Publ.), 1973.
74B1
Bokstein, B.S., Zsukhovicki, Z. S.: Thermodynamics and kinetics of diffusion in solids (in Russian), Moscow: Metallurgya, 1974, p. 169
75C1 75P1
Crank, J.: The Mathematics of Diffusion (2nd Edition), Oxford: Clarendon Press, 1975. Peterson , N.L.: Isotope Effects in Diffusion, in : "Diffusion in Solids - Recent Developments", Nowick, A.S., Burton, J.J. (eds.), New York , London: Academic Press, 1975, p.115.
76B1
Beniere, M, Chemla, M., Beniere, F.: J. Phys. Chem. Solids 37 (1976) 525.
77M1
Martin, G., Benoist, P.: Scr. Metall. 11 (1977) 503.
82K1
Kanert, O: Phys. Rep. 91 (1982) 183.
84B1
Bakker, H., in: Diffusion in Crystalline Solids. Murch, G.E., Nowick, A.S. (eds.). New York: Academic Press, 1984, p.189. Berry, B.S., Pritchet, in: Nontraditional methods in diffusion, Proc. Symp. Philadelphia, USA 1983, W.C. Murch, G.E., Birnbaum, H.K., Cost, J.R. (eds.), The Metallurgical Society of AIME, 1984. Le Claire, A.D., Rabinovich, A.: in "Diffusion in Crystalline Solids", Chap. 5, Murch, G.E., Nowick, A.S. (eds.), New York: Academic Press, 1984. Murch, G.E., Birnbaum, H.K., Cost, J.R. (eds.) : Nontraditional methods in diffusion, Proc. Symp. Philadelphia, USA 1983, The Metallurgical Society of AIME, 1984. Rothman, S.J.: The Measurement of Tracer Diffusion Coefficients in Solids, in: Diffusion in Crystalline Solids, Murch, G.E., Nowick, A.S. (eds.), New York: Academic Press, 1984, p.1.
84B2
84L1 84M1 84R1
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1 Introduction
1-23
84S1
Stokes, H.T. in: Nontraditional methods in diffusion, Proc. Symp. Philadelphia, USA 1983, W.C. Murch, G.E., Birnbaum, H.K., Cost, J.R. (eds.), The Metallurgical Society of AIME, 1984.
85G1
Greer, A.L., Spaepen, F.: Synthetic Modulated Structures, Chang, L.L., Giessen, B.C. (eds.), New York: Academic Press, 1985, p. 419. Nakajima, H., Ishioka, S., Koiwa, M. : Philos. Mag. A 52 (1985) 743. Vogl, G., Petry, W.: Diffusion in Metals Studied by Mössbauer Spectroscopy and Quasielastic Neutron Scattering: Ferstkörperprobleme XXV (Advance in Solid State Physics), Grosse P. (ed.), Braunschweig: Friedrich Vieweg und Sohn, 1985, p. 655.
85N1 85V1
88K1 88S1
Kaur, I., Gust, W.: Fundamentals of Grain and Interphase Boundary Diffusion. Stuttgart. Zeigler Press, 1988. Stephenson, G.B.: Acta Metall. 36 (1988) 2663.
89B1 89S1
Beke, D.L. Neumann, G., Szabó, I.A.: Phys. Status Solidi (b) 155 (1989) 385. Shewmon, P.: Diffusion in Solids, (2nd Edition), Warrendale, Pennsylvania: The Minerals, Metals and Materials Society, 1989.
90B1
Bonzel, H.P., in: Diffusion in Solid Metals and Alloys, H. Mehrer (ed.), Landolt-Börnstein, New Series, Vol. III/26, Berlin: Springer-Verlag, 1990, p. 717. Mehrer, H., in: Diffusion in Solid Metals and Alloys, H. Mehrer (ed.), Landolt-Börnstein, New Series, Vol. III/26, Berlin: Springer-Verlag, 1990, p. 1. Philibert, J.: Atom movements. Diffusion and mass transport in solids, Les Ulis, France, Les Editons des Physique, 1991.
90M1 91P1
92B1 92B2
Beke, D.L., in: Diffusion in Solids - Unsolved Problems, Murch, G.E. (ed.), Zürich: Trans Tech. Publ., 1992, p. 31. Bokstein, B.S., Fradkov, V.E., Beke, D.L.: Philos. Mag. A 65 (1992) 277.
93A1 93L1
Allnatt, A.R., Lidiard, A.B.: Atomic Transport in Solids, Cambridge: University Press, 1993. Le Claire, A.D.: Defect Diffus. Forum 95-98 (1993) 19.
94Y1
Yang, F.L., Shin, W.C., Greer, A.L., in: Thin Films: "Stresses and Mechanical Properties", Baker, S.P., Bargensen, P., Townsend, P.H., Ross, C.A. (eds.), Proceedings of Fall Meeting of MRS, 1994.
95B1 95B2 95K1
Beke, D.L.: Key Eng. Mater. 103 (1995) 51. Bokstein, B.S., Ostrovsky, A.S., Rodin, A.O.: Philos. Mag. A 72 (1995) 829. Kaur, I., Mishin, Y., Gust, W.: Fundamentals of Grain and Interphase Boundary Diffusion. Chichester: John Wiley, 1995.
96B1 96B2 96G1
Beke, D.L.: Defect Diffus. Forum 129-130 (1996) 9. Benardini, J., Tökei, Zs., Beke, D.L.: Philos. Mag. A 73 (1996) 237. Greer, A.L.: Defect Diffus. Forum 129-130 (1996) 163.
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Ref. p. 4-35]
4 Diffusion in silicides
4-1
4 Diffusion in silicides P. GAS AND F.M. D'HEURLE
4.1 Introduction Why should a description of diffusion in silicides belong to a review of diffusion data in semiconductors? Some silicides [96L1] are semiconducting, but there are few of these, the vast majority being metallic; moreover, not much is known about diffusion in these semiconducting silicides, with the exceptions of CrSi2 [85H1], FeSi2 [91E1] and Ru2Si3 [82P1]. (The band gaps of the semiconducting silicides cover a range of values [96L1]: 0.1 - 0.4 eV for ReSi2, about 0.5 eV for CrSi2, 0.5 eV for MnSi1.7, 0.8 eV for FeSi2, often referred to as β-FeSi2, 0.9 eV for Ru2Si3, 1.6 eV for Ir3Si5. Moreover, three silicides of Os are reported to be semiconducting). The main justification lies elsewhere, namely, that a number of silicides have become integrated in Si technology, e.g. [93M1]. One notes also that while previous reviews, "Self Diffusion in Homogeneous Binary Alloys and Intermediate Phases" [90B1], and "Chemical Diffusion in Inhomogeneous Binary Alloys" [90M1] contain accounts of diffusion in solid solutions (Fe-Si, Ni-Si and V-Si), references to diffusion in silicide phases are missing. Readers interested about details concerning diffusion in silicides must up to now turn to the literature on materials for the electronic industry [95G1], where one may find more qualitative results than will be mentioned presently. Although there exist other reviews, the main sources of information about the behavior of silicides (with emphasis on electronic applications) are given in [83N1 and 95M1]. There are two dominant features of the work on silicides: a) most of the measurements of diffusion were made during reactive diffusion, namely during the formation of a silicide by reaction of a metal, or another silicide with Si, and b) most of this work concerns thin films. That latter aspect maximizes the effect of grain boundary transport. It also facilitates measurements because in films up to about 0.5 µm thick, at the temperatures and scales at which growth is observed to occur, phases generally form sequentially, which greatly simplifies the interpretation of growth kinetics. When plotted properly as λ2 vs. t (with λ being the thickness of the growing layer and t the time) the slope gives the growth constant κ, e.g. [96C1] (one must be aware that some authors give κ ' equal to κ/2). Measurements at different temperatures yield the activation energy. Interpretation of these results in terms of diffusion coefficients becomes something of a complex matter. Since growth occurs quite often at low temperatures with respect to the melting points of the different phases, grain boundary diffusion is likely to play a role. There are potentially two mobile elements and two sets of paths (lattice and grain boundaries), hence one may ultimately have to separate four different diffusion coefficients and four activation energies. Luckily some simplifications may be allowed. For an analysis of the growth conditions that obtain for thin film silicides, see [86H1]. Because many silicides exist only within very narrow limits of composition, and when this is not precisely true within poorly known limits of composition, growth results cannot be properly interpreted in terms of Fick's law (that is true also for many other intermetallic compounds). It is more useful to consider diffusion in terms of a modified Nernst-Einstein equation :
Lando lt -Bö rnst ein New Series III/33A
4-2
4 Diffusion in silicides jA = cA · (DA/kT) · (∆GA/λ) ,
[Ref. p. 4-35 (4.1)
where the flux of A atoms, jA, is properly expressed as the product of the concentration of A atoms, cA, their mobility (DA/kT) and the force on these atoms (∆GA/λ). Ideally, DA here is equal to DA*, the tracer diffusion coefficient in the formed compound. For the sake of simplicity, one takes ∆GA as the free energy change per moving A atom (from the free energy - or heat - of formation of the compound, at least in elemental A-B reactions), although literally the force should be expressed as dµA/dλ, the gradient of chemical potential. However, that would require complete knowledge of the free energies versus composition for the whole A−B system, and would become meaningful only if it were possible to determine the varying value of DA as a function of the chemical potential of A within the compound. If both the A and B atoms contribute to the formation of an AmBn compound, addition of two equations [95B1,96C1] such as the one above yields an overall diffusion coefficient equal to Darken's [53D1]: DA, B = (m /(m + n)) · DB + (n /(m + n)) · DA .
(4.2)
Use of this diffusion coefficient to evaluate phase growth requires that the appropriate value of ∆G be selected, see [96C1]. For a phase growing alone from the interaction of A and B elements, one obtains :
λ2 = κ t .
(4.3)
If growth occurs by the motion of A atoms only then :
κ = 2(DA0 /kT) · (∆G/m) · exp(−Q/kT) .
(4.4)
Here, ∆G for solid state reactions can be taken as the heat of formation of the compound AmBn per mole, and Q the activation energy for the diffusion of A atoms in AmBn. (Eq. 4.3 is identical to Eq. 1.37). Were we consider diffusion in an ideal solid solution rather than in some intermetallic compound with potentially very narrow limits of composition, Eq. 4.1 would become identical to Eq. 1.3 since : ∆GA/λ = dµA/dλ = kT ⋅ d(ln cA)/dλ = kT ⋅ (1/cA) ⋅ (dcA/dλ) .
(4.5)
Introduction of the last term on the right into Eq. 4.1 yields the usual Fick's equation. Quite often the atoms of only one atomic species are mobile under the experimental growth conditions (all the more true as the temperature is low, as is usually the case for thin film reactions). Marker experiments used to determine the moving species during silicide formation are described in [86H1]. In general, it is found that metal atoms constitute the dominant mobile species in metal-rich silicides, and Si atoms in silicon-rich ones. This is especially true of a series of silicides (TiSi2, VSi2, NbSi2, TaSi2, CrSi2, MoSi2 and WSi2), that are built in the same fashion with each metal atom surrounded by 10 Si atoms, and no metal nearest neighbors (as in L12 structures typified by Cu3Au). In all of these the Si atoms are greatly more mobile than the metal atoms [78Z1, 82H1, 86H1]. This observation has been generalized as the "Ordered Cu3Au Rule" [86H1, 95H1, see also 93Y1] according to which generally in AmBn compounds with m/n equal to or greater than 2, the majority atoms (A) are much more mobile than the atoms of the minority species (B). This is related to the structures where the A atoms can migrate on a continuous network of A lattice sites, whereas the migration of the B atoms requires that these occupy A sites with an increase in activation energy for diffusion that should be commensurate with the heat of ordering (or of compound formation, per B atom) [68E1]. Experimentally, one deposits a metal film on a silicon substrate and observes the change in the metal (and Si) profile(s) after various heat treatments. Rutherford backscattering spectrometry (RBS) is almost ideally suited for this purpose [78C1], at least for thicknesses between 10 nm and 1 µm. It yields at the
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-3
same time the composition of the phases that are formed and, provided one knows the crystallographic structure or the density, the thickness of the growing layers. Some ingenious experiments [84Z1] were conducted with adjacent interacting films, so that growth occurred laterally, in the plane of the films; analysis could be obtained by electron microprobe over diffusion lengths much larger than accessible by RBS. Because silicide formation is usually accompanied by significant changes in resistance, it is also possible to follow the course of a reaction by in-situ resistance measurements while a sample is heated at a constant heating rate [see e.g. 96C1], which makes it possible to rapidly explore large temperature regions. From measurements at different heating rates it is possible to obtain the activation energy [57K1, 95Z1, 96C1]. This latter mode of experimentation is much less time consuming than the previous ones, coupled with in-situ X-ray diffraction made possible by synchrotron radiation, it even allows simultaneous determination of the phases that are formed [e.g. 96C2]. It is tempting to follow the dynamic course of a reaction with radiotracers, but the experimental conditions under which this yields meaningful results are strictly limited [91Z1, 93M2]. Radiotracers (including Ge* instead of Si* that has an uncomfortably short half-life) have been used to determine the respective D*'s in bulk Ni and Co silicides (so to speak under equilibrium condition, not during phase growth). The main difference is found to be a matter of the grain size d, but the results can be unified through the well known relation : Deff = Dv + 2(δ /d) Dgb
(4.6)
where, as usual, δ is the thickness of the grain boundaries. This relation is similar to Eq. 1.38 but it assumes that the area occupied by grain boundaries is small with respect to the cross section of the grains. Evaluating the contribution of grain boundaries to reactive phase growth by independently determining the grain boundary diffusion coefficient is quite time consuming, but it seems to be the only one that provides reliable results. The use of radiotracers during phase growth is fraught with difficulties (see above). Another technique based on an ingenious evaluation of the redistribution of isotopes during phase formation [83S1, 84A1] was shown [90G1] to be beyond the accuracy of analysis by secondary ion mass spectrometry (SIMS). The kinetics themselves are not helpful since one expects to obtain thicknesses proportional to t1/2 independently of whether diffusion occurs through the lattice or along the grain boundaries. If, however, growth occurs via the boundaries of grains with increasing grain size the exponent of t should become smaller than 1/2: 1/3, or possibly 1/4 in the case of normal grain growth. Where the activation energies (Q 's) for volume and grain boundary diffusion could be determined [95B1, 96G1] the ratio Qgb/Qv is in the high range of what obtains in simple metals, between 0.7 and 0.8. That is thought to result from the special nature of grain boundaries in intermetallic compounds [94H1]. It is often remarked that in thin film experiments phases form sequentially, while in "bulk" they tend to form simultaneously. First of all, this is not always true, see e.g. MoSi2 and Mo5Si3 [53F1]. Secondly, the difference is unlikely to be fundamental, since it can be attributed to simple differences of scales. Bulk experiments are usually conducted on a scale of length much larger than obtains for thin film ones, so that phenomena occurring on a length scale smaller than that of the measurements fail to be detected. The difference in scales calls for differences in temperatures, so that again at high temperatures in bulk experiments one may not have the time to observe phenomena that occur slowly at low temperatures in thin film experiments. Since much of the work on silicides was motivated by semiconductor technology, the diffusion of the p and n dopants, B, P, As, Sb, and Ge (although the latter is not a dopant, it is used for auxiliary purposes, e.g. amorphization of silicon prior to dopant implantation in order to avoid channeling) has received much attention. The dopants are often implanted in silicides and annealed for different periods of time at different temperatures. The usual mode of analysis has been SIMS, but electrical measurements were also used to evaluate dopant diffusion along thin film conductors made from a variety of silicides [93C1]. In technical applications, changes in electrical characteristics due to dopant migration in silicide elements
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4-4
4 Diffusion in silicides
[Ref. p. 4-35
during processing are to be avoided, but they were used for measuring diffusion. Most of the data reported in the tables below were obtained by other means: − reactive growth and thickness measurements e.g. [82P1], − reactive growth and resistance measurements e.g. [96C1], − tracer measurements in bulk samples e.g. [90C1], − implantation and profiling by SIMS in thin films e.g. [88G1] or in bulk samples [90G2]. In reactive growth, it is impossible to stabilize the samples before proceeding with the experiments; that is true also for implantation in amorphous layers, e.g. [92S1].
Acknowledgements This work would not have been possible without the contributions of the many investigators whose names appear in the references. May they all accept a public expression of our gratitude. Beyond these, we are specially indebted to a number of colleagues, whose direct collaboration or advice, became incorporated in our own understanding of diffusion in silicides. Even those would be too numerous to be individually recognized. However, special mention should be made of T. Barge, C. Bergman, J. Bernardini, V. Dybkov, R. Ghez, J.H. Gulpen, D. Gupta, D. Mangelinck, A. Michel, J. Philibert, G. Scilla, B. Svensson, O. Thomas, F. J. van Loo, and S.-L. Zhang. They all deserve to some degree to be our coauthors.
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Ref. p. 4-35]
4 Diffusion in silicides
4-5
4.2 Diffusion controlled formation of silicide thin films (Diffusion measurements were made during the formation of the silicide by reaction of the metal with Si; DDS: Dominant Diffusing Species; Tm: melting temperature in K). 1 eV/atom = 96.485 kJ/mol
κ0 [10−4 m2/s]
Q [eV/at]
T - range [°C]
Remarks
Fig.
Ref.
Tb-Si TbSi1.7 Hexagonal - defect AlB2, Tm ≈ 1873 K a), DDS: Si 2.5·10−3
1.25
250-300
<100> Si - Irradiation of the interface a) by analogy with GdSi 2-x (1873K) and SmSi2-x (1873-2073K)
81B1 1
80T1
Er-Si ErSi1.7 Hexagonal - defect AlB2, Tm ≈ 1873 K a), DDS: Si 2.6
1.70
300-350
<100> Si - Irradiation of the interface a) by analogy with GdSi 2-x (1873K) and SmSi2-x (1873-2073K)
90T1 1
80T1
Ti-Si TiSi2 Orthorhombic - TiSi2, Tm = 1813 K, DDS: Si
74C1, 75C1
3.5·10−3
1.8±0.1
475-550
Amorphous Si (by evaporation)
2
83H1
3.3·101
2.5±0.25
550-650
On <100>Si - Linear growth on <111>Si
2
88P1
1.8·105
3.0±0.2
575-750
Conventional and Rapid Thermal Annealing (RTA) / <100> Si - TiSi is also observed
2
90P1
Zr-Si Zr5Si4 Tetragonal - Zr5Si4, Tm = 2583 K 2.8±0.2
670-730
Reaction with SiO2 - Formation of a surface Zr oxide. Parabolic variation of the thickness of consumed SiO2
88W1
Hf-Si HfSi Orthorhombic - FeB, Tm = 2373 K, DDS: Si 10 Lando lt -Börnst ein New Series III/33A
2.5
525-650
<111> and <100>
73K1 3
73Z1
4-6
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
[Ref. p. 4-35
Remarks
Fig.
Ref.
V-Si V3Si Cubic - βW 2.0·10−4
2.0±0.2
Tm = 2208 K 730-820
DDS: V
79S1
Reaction with SiO2
4
VSi2 Hexagonal - CrSi2, Tm = 1950 K, DDS: Si 5.8·102
2.9
600-700
74K1
75C1, 80B1, 89F1
<100>
4
73T1
Cr-Si CrSi2 Hexagonal - CrSi2, Tm = 1773 K, DDS: Si
7.5·10−1
1.4±0.1
85H1, 85A1, 90T1, 80M1
425
Cross sectional TEM κ = 6.2·10−17 m2/s
5
84N1
520-650
Lateral formation
5
84Z1
Mo-Si MoSi2 Hexagonal - CrSi2 T < 900°C, Tm = 2300 K, DDS: Si Tetragonal - MoSi2 T > 900°C
65G1, 78B1
3·102
5
2.4±0.2
474-550
1.9±0.2 1.8±0.3
1151-1366
80 nm on <111>Si - For thicker Mo films (400nm) linear growth is reported
78G1
Laser annealing
88L1
<100> - Laser annealing - Hexagonal MoSi2
82B1
W-Si WSi2 Tetragonal - MoSi2, Tm = 2453 K, DDS: Si
65G1, 79B1
3·103
3.4±0.2
675-760
<100>
5
86L1
1.1
2.2±0.2
1200-1400
<100> - Laser annealing
5
86L1
62
3.0±0.2
690-740
<100> - Implantation of P in the vicinity of the W/Si interface prior to annealing
5
88M1
<100>
6
82E1
2.4±0.3
Laser annealing
88L1
Mn-Si MnSi Cubic - FeSi, Tm = 1548 K 1.3
1.9
425-500
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35]
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
Remarks
Tm = 1683 K
DDS: Si
4-7 Fig.
Ref.
Fe-Si FeSi Cubic - FeSi 1.8·10−1
1.7±0.15
450-525
75C1
<100>
7
75L1
<100> - Reaction with a Ru alloy containing 33at% Rh
7
82P1
Ru-Si RuSi Cubic - CsCl 2.2·103
2.4±0.2
Tm = 2073 K 400-475
Ru2Si3 Orthorhombic - Ru2Si3, Tm = 1973 K, DDS: Si 1.35
1.8
375-450
<100>
87H1 7
82P1
Os-Si Os2Si3 Orthorhombic - Ru2Si3, DDS: Si 2.5·10−2
1.8
450-525
82P1 <100> - A Ru adhesion layer is used between Si and Os
7
82P1
Rh-Si RhSi Orthorhombic - MnP, Tm = 1723 K, DDS: Si 6.0
1.95
350-425
80P1, 79P1
<100>
80P1
2.3
1.9
375-450
<100>
0.9
1.9
375-450
Amorphous Si (by evaporation)
8
84P1 84P1
8.4·10−2
1.7
375-450
Poly Si
84P1
Ir-Si IrSi Orthorhombic - MnP, DDS: Si 3.4·10−2
Lando lt -Bö rnst ein New Series III/33A
1.9
400-550
87H1 <100>
8
79P1
4-8
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
Remarks
[Ref. p. 4-35 Fig.
Ref.
Co-Si Co2Si Orthorhombic - anti PbCl2, Tm = 1605 K, DDS: Co
78G2
2.5·10−3
1.5±0.1
375-486
<100> - Simultaneous growth of Co2Si and CoSi
9
78L1
1.3·10−1
1.75
400-555
<100> and <111> - Thicknesses deduced from XRD intensities and ball bevel
9
75G1
8.9·10−2
1.7±0.1
385-490
<100> - Simultaneous growth of Co2Si and CoSi. Values of Q and κ0 are deduced from an analysis of this simultaneous growth
9
85L1
7.4·10−1
1.85±0.1
385-490
Amorphous Si - Simultaneous growth of Co2Si and CoSi. Values of Q and κ0 are deduced from an analysis of this simultaneous growth
45
2.1±0.2
375-675
Conventional and RTA - Amorphous Si
9
87L1
83.5
2.1±0.1
380-560
Silicon single crystal on Sapphire In situ ramped resistance measurements
9
96C1
1.4·103
2.3±0.1
380-550
Poly Si - In situ ramped resistance measurements
85L1
96C1
CoSi Cubic - FeSi, Tm = 1688 K, DDS: Si
78G2
1.75
400-555
<100> and <111> - Thicknesses deduced from XRD intensities and ball bevel - No value for κ
0.55
1.9±0.1
375-490
<100> - Simultaneous growth of Co2Si and CoSi
10
78L1
2.85·10−2
1.8±0.1
385-490
<100> - Simultaneous growth of Co2Si and CoSi - Values of Q and κ0 are deduced from an analysis of this simultaneous growth
10
85L1
8.5·10−2
1.9±0.1
385-490
Amorphous Si - Simultaneous growth of Co2Si and CoSi - Values of Q and κ0 are deduced from an analysis of this simultaneous growth
10
85L1
7.3·103
2.4±0.1
425-600
Silicon single crystal on Sapphire - In situ ramped resistance measurements
10
96C1
1.2·107
2.8±0.1
425-475
Poly Si - In situ ramped resistance measurements
10
96C1
75G1
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35]
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
4-9
Remarks
Fig.
Ref.
Co-Si (cont.) CoSi2 Cubic - CaF2, Tm = 1600 K, DDS: Co
84L1, 85H4
2.2·102
2.3
405-500
11
84L2
1.6·103
2.6±0.3
550-700
11
86H2
1.5·104
2.8
500-600
11
85A2
2.3±0.3
Amorphous Si (by evaporation) <100> Laser annealing
88L1
1.2·107
3.2±0.1
475-600
Silicon single crystal on Sapphire - In situ ramped resistance measurements
11
96C1
9.7·108
3.3±0.1
450-600
Poly Si - In situ ramped resistance measurements
11
96C1
Ni-Si Ni2Si Orthorhombic - anti PbCl2, Tm = 1580 K, DDS: Ni 1.22
1.5±0.2
225-325
74C1, 75C1, 77T1, 85A1
<100>
12 12
76O1
2
1.6±0.2
225-325
<111>
2.3·10−2
1.3±0.2
225-325
Poly Si (CVD)
76O1
2.3
1.5±0.1
200-325
<100>
3.2·10−1
1.4±0.1
210-335
Amorphous Si (by evaporation)
1.8
1.5±0.1
210-335
<100>
12
86L2
1.0·10−2
1.3±0.1
300-430
<100> and <111>
12
76C1
3·10−2
1.4±0.1
420-700
Lateral growth
12
84Z1, 82Z1
1.1·10−1
1.5
500-700
Lateral growth on<100>
12
89S1
4.2·10−1
1.8
500-700
Lateral growth on<111>
12
89S1
9.1·10−2
1.4±0.1
240-325
Amorphous hydrogenated Si
12
85H2
24.6
1.7±0.1
250-375
Silicon single crystal on Sapphire. In situ ramped resistance measurements
12
96C1
5.4·10−1
1.5±0.1
250-320
Poly Si - In situ ramped resistance measurements
76O1 12
75T1 86L2
96C1
NiSi Orthorhombic - MnP, Tm = 1273 K, DDS: Ni
81F1
2
1.65
275-350
<100>
13
84H1
0.3
1.65
325-400
<111>
13
84H1
9.0·10−4
1.2±0.3
300-360
<100>
13
84M1
26
1.8±0.2
320-370
<111>
13
84M1
0.9
1.55±0.1
250-400
<100> and amorphous Si
13
86L2
400
1.8±0.1
275-425
Poly Si - In situ ramped resistance measurements
13
96C1
Lando lt -Bö rnst ein New Series III/33A
4-10
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
[Ref. p. 4-35
Remarks
Fig.
Ref.
Ni-Si (cont.) NiSi2 Cubic - CaF2, Tm = 1298 K, DDS: Ni
84L1, 82H2
1.4·10−1
14
1.65
350-425
Amorphous Si (by evaporation)
84L3
Pd-Si Pd2Si Hexagonal - Fe2P, Tm = 1670 K, DDS: Pd-Si
74C1, 78P1, 84Z2, 85L2, 85H3, 89C1
3.8
1.4±0.2
175-450
<111>
15
76F1
2.85·10−4
0.95±0.1
210-290
<100>
15-16
81C1
2.4·10−4
0.9±0.1
210-290
Amorphous Si (by evaporation)
16
81C1
3.1·10−2
1.2±0.1
240-300
Sputtered Si
16
81C1
1.5·101
1.5
240-300
Sputtered Pd - <100>
16
81C1
6.1·10−2
1.3
240-300
Sputtered Pd - Amorphous Si (by evaporation)
16
81C1
8.4·10−2
1.3
240-300
Sputtered Pd - Sputtered Si
16
81C1
1.0±0.1
190-300
<100> - <111> - Amorphous Si (by evaporation)
4.5·10−5
0.9±0.1
200-225
<100>
16
85H2
9·10−5
0.9±0.1
200-225
Amorphous hydrogenated Si
16
85H2
16
76N1
80C1
8·10−2
1.2±0.2
200-275
Undoped poly Si (CVD)
0.4
1.4±0.2
310-410
<100> - RTA - κ0 depends on power
7·10−2
1.3±0.4
250-400
<111> - Measurement of the time necessary to consume the Pd layer as a function of temperature
15
73H1
3.9·101
1.5±0.1
200-275
<100> and <111>
15
73B1
(5·1013
cm−3)
88W2
1.92
1.4±0.1
200-275
<100>, P doped
15-17
83W1
4.8·10−4
1.05±0.1
200-275
<100>, As doped (5·1020 cm−3)
17
83W1
0.72
1.35±0.1
200-250
<111>, P doped (4·6.1014 cm−3)
17
83W1
cm−3)
17
83W1
15
86C1
6.0·10−4
1.05±0.1
200-250
<111>, As doped
7·10−4
1.06
160-220
<111> - Kinetics measured by X-ray diffraction
(5·1020
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35]
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
4-11
Remarks
Fig.
Ref.
Pt-Si Pt2Si Tetragonal - ZrH2, Tm = 1372 K, DDS: Pt
90W1, 85A1
4.33
1.5±0.1
250-325
18
77C1
8.9
1.6±0.1
280-350
<100>- Comparable results on <111> and poly Si
18
74P1
1.5·10−3
1.05
200-500
Thick films (0.1 - 1 µm) - Simultaneous growth of Pt2Si and PtSi
18
72M1
4.3·10−2
1.27±0.1
210-280
<100>
18-19
85T1
1.2·10−1
1.32±0.1
210-280
Amorphous Si (by evaporation)
19
85T1
7.1·10−2
1.28±0.1
210-280
Poly Si
19
85T1
1.2·10−2
1.24±0.1
210-280
P doped (8·1020 at/cm3) poly Si
19
85T1
4.8·10−2
1.25±0.1
200-300
Poly Si
3.2·10−2
1.25±0.1
200-300
As doped
1.8
1.4±0.1
200-300
1.9
1.3±0.2
9.0·10−3
86W1 (1·1021
at/cm3)
poly Si
19
86W1
Amorphous Si (by evaporation) Rates on Si <100> are ≈ 25% smaller
18
86L2
200-300
<100> - Deposition , "in situ" heat treatment and "real time" RBS analysis under UHV conditions
18
80C2
1.3
460-720
Lateral formation - Kinetics followed by SEM - Samples containing 7at% Rh show a reduced growth rate and an activation energy of 2.0 eV
18
82Z2
0.7
1.38
300-375
<100> - RTA
18
92P1
21.5
1.6±0.1
275-425
Silicon single crystal on Sapphire - In situ ramped resistance measurements
18
96C1
12.2
1.6±0.1
250-425
Poly Si - In situ ramped resistance measurements
PtSi Orthorhombic - MnP, Tm = 1502 K, DDS: Pt-Si 1.81
1.5±0.1
300-360
0.63
1.6±0.1
350-410
2.5·10−1
1.47
5.4·10−1
96C1
80B1, 81P1 20
77C1
<100>- Comparable results on <111> and poly Si
20
74P1
300-540
Thick films (0.1 - 1 µm) - Simultaneous growth of Pt2Si and PtSi
20
72M1
1.5±0.1
300-375
<100>
20-21
85T1
1.47
1.56±0.1
300-375
Evaporated Si (aSi)
21
85T1
4.8·10−1
1.50±0.1
280-375
Poly Si
21
85T1
2.4·10−1
1.5±0.1
280-375
P doped (8·1020 at/cm3) poly Si
21
85T1
Lando lt -Bö rnst ein New Series III/33A
4-12
κ0 [10−4 m2/s]
4 Diffusion in silicides
[Ref. p. 4-35
Q [eV/at]
T - range [°C]
Remarks
Fig.
10.9
1.5±0.2
200-300
<100> - Deposition , "in situ" heat treatment and "real time" RBS analysis under UHV conditions
6.3·10−1
1.5±0.1
250-370
Amorphous Si (by evaporation) - Rates on Si <100> are ≈ 25% smaller
5.2
1.6±0.1
300-400
<111>
0.32
1.45±0.1
300-400
<100>
2.8·10−1
1.45±0.1
300-400
Poly Si
Ref.
Pt-Si (cont.) PtSi (cont.) 80C2
20
86L2 83W2
20
83W2 86W1
4.4·10−2
1.45±0.1
325-400
As doped
14.1
1.7
375-450
<100> - RTA
8.3·101
1.8±0.1
300-475
Silicon single crystal on Sapphire - In situ ramped resistance measurements
1.4·102
1.8±0.1
300-475
Poly Si - In situ ramped resistance measurements
(1·1021
at/cm3)
poly Si
21
86W1 92P1
20
96C1 96C1
4.3 Diffusion controlled formation of "bulk" silicides (The diffusion couple is given in parentheses) (1 eV/atom = 96.485 kJ/mol)
κ0 [10−4 m2/s]
Q [eV/at]
T - range [°C]
Remarks
Fig.
Ref.
1.8±0.4
950-1150
κ0 and Q take into account the simultaneous growth of the 5 titanium silicides
22
95C1
1.15±0.25
950-1150
κ0 and Q take into account the simultaneous growth of the 5 titanium silicides
22
95C1
1.7±0.4
950-1150
κ0 and Q take into account the simultaneous growth of the 5 titanium silicides
22
95C1
2.3±0.8
950-1150
κ0 and Q take into account the simultaneous growth of the 5 titanium silicides
22
95C1
1.7±0.2
950-1150
κ0 and Q take into account the simultaneous growth of the 5 titanium silicides
22
95C1
Ti-Si Ti3Si (Ti/Si) 2.2·10−5 Ti5Si3 (Ti/Si) 1.97·10−7 Ti5Si4 (Ti/Si) 2.28·10−4 TiSi (Ti/Si) 4.88·10−2 TiSi2 (Ti/Si) 3.58·10−4
Landolt -Bö rnst ein New Series III/33A
Ref. p. 4-35]
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
4-13
T - range [°C]
Remarks
Fig.
Ref.
1130-1465
Disilicide-coated Nb samples
23
66B1
1040-1465
Disilicide-coated Ta samples
23
66B1
Mo3Si (Mo5Si3/Mo) 0.2 3.2
1500-1715
Disilicide-coated Mo samples Mo3Si forms when the disilicide layer has been entirely consumed to form Mo5Si3
24
64B1
Mo5Si3 (MoSi2/Mo) 100 3.7
1192-1715
Disilicide-coated Mo samples
24
64B1
MoSi2 (Mo/Si) 0.90 2.2
855-1100
Mo rods submerged in a packed mixture of Si and NaF. Heat treated in H2-Ar
24
65G1
2.9·10−3
1.8
1200-1350
Simultaneous formation of Mo5Si3 and MoSi2. Mo5Si3 growth is linear with time. MoSi2 growth is linear parabolic. The linear term is: 2A = 1.0·104 exp (- 0.72/kT)
24
71Z1
2.4·10−4
1.4±0.1
1000-1200
Mo plates / Si vapour transport. Needle like crystals
24
76C2
1200
Mo5Si3 formation starts after 0.3 mm of MoSi2 are formed
24
53F1
W5Si3 (WSi2/W) 19 3.7
1355-1870
Disilicide-coated W samples
25
64B1
WSi2 (W/Si) 1.1·10−4 1.9
1040-1150
W deposition on <111> Si by CVD
25
67H1
7.7·10−2
1200-1350
25
68Z1
Nb-Si Nb5Si3 (NbSi2/Nb) 4.5·10−2 2.5
Ta-Si Ta5Si3 (TaSi2/Ta) 4.5·10−2 2.5
Mo-Si
κ = 1.1·10−9
W-Si
Lando lt -Bö rnst ein New Series III/33A
2.1
4-14
4 Diffusion in silicides
κ0 [10−4 m2/s]
Q [eV/at]
[Ref. p. 4-35
T - range [°C]
Remarks
Fig.
Ref.
W-Si (cont.) WSi2 (W/Si) (cont.) 0.62
2.2
855-1100
W rods submerged in a packed mixture of Si and NaF. Heat treated in H2-Ar
25
65G1
3.3·10−2
1.9±0.1
1000-1200
W plates / Si vapour transport. Needle like crystals
25
76C2
Co-Si Co2Si (Co/Si) 2.82
2.6
846-1000
Simultaneous growth of the 3 Co silicides
26
95B1
6·10−2
2.1
900-1050
Simultaneous growth of the 3 Co silicides
26
93J1
0.22
2.1
846-1000
Simultaneous growth of the 3 Co silicides
26
95B1
3.9·102
2.9
900-1050
Simultaneous growth of the 3 Co silicides
26
93J1
CoSi (Co/Si)
CoSi2 (Co/Si) 0.14
2.45
846-1000
Simultaneous growth of the 3 Co silicides
26
95B1
5.2·10−2
2.4
900-1050
Simultaneous growth of the 3 Co silicides
26
93J1
800-900
Simultaneous growth of Ni5Si2, δ-Ni2Si, ε-Ni3Si2, NiSi and NiSi2 The Arrhenius plot is curved and can be approximated by 2 linear parts (low and high temp.). This behaviour is related to the evolution of grain size with temp. Similar results are obtained with other diffusion couples (Ni/Si, Ni/δ-Ni2Si, Ni/Ni3Si2 )
27
95G2
Use of different diffusion couples. Values for the integrated diffusion coefficient (not κ)
27
95G2
Ni-Si (Ni/Si)
83T1, 95G2
Ni5Si2 (Ni3Si/δNi2Si) 7.4·10−4
1.0±0.3
600-900
1.0·102
2.2±0.3
900-1100
δ-Ni2Si (Ni/Si, Ni/Ni3Si2, Ni5Si2/Si) 2.6·10-1 2.0±0.5 800-900
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35]
κ0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
4-15
T - range [°C]
Remarks
Fig.
Ref.
Cu3Si (Cu/Si) 2.1 1.10±0.5
343-545
Observation of an incubation time before diffusion. W markers show that Cu is the DDS
28
68V1, 82W1
3.5 1.3·105
350-470 470-650
Incubation time below 470°C (attributed to a SiO2 layer) - A columnar microstructure is observed - The evolution of grain size with temp. supports the fact that the reaction proceeds by grain boundary diffusion at T < 470°C and by volume diffusion at T > 470°C. Addition of phosphorus to Cu modify low T behaviour (T < 530°C): no incubation time, grain size reduction, increase of κ, and decrease of Q (0.95 eV)
28
88B1
Cu-Si
1.1±1.0 1.8±0.5
4.4 Tracer diffusion in silicides (1 eV/atom = 96.485 kJ/mol) D0 [10−4 m2/s]
Q [eV/at]
T - range [°C]
Remarks
Diff. Fig. path
Ref.
Matrix: TiSi2 Ge 2.03
2.94
600-800
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
29
88G1
P 7.12·10−5
2.05
550-800
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
29
86G1
392
2.64
800-900
Electrical measurements - Thin film lines - Dgb Strong contribution of grain boundary and interface diffusion.
93C1
Dgb Amorphous thin film on a Si substrate Implanted source - SIMS - Recrystallisation during diffusion D (500°C) ≈ 2·10−17 m2/s
93H1
Lando lt -Börnst ein New Series III/33A
4-16 D0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
[Ref. p. 4-35
T - range [°C]
Remarks
Diff. Fig. path
Ref.
Dv
86G1
Matrix: TiSi2 (cont.) As 4.92·10−6
1.81
600-800
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Numerical solution of Fick's law including surface effects
4.8
2.13
750-950
Electrical measurements - Thin film lines - Dgb Strong contribution of grain boundary and interface diffusion.
29
93C1
Matrix: TaSi2 P 3.13·10−11
0.83±0.05 516-915
Polycrystalline thin film on a Si substrate - Dv 33P deposited source -Type B kinetic Sectioning method - Layer activity (1st part of penetration plots)
30
83P1
4.21·10−12
0.67±0.05 516-915
Polycrystalline thin film on a Si substrate - Dv 33P deposited source -Type B kinetic Sectioning method - Layer activity (1st part of penetration plots) - Residual activity Graphical method taking into account diffusion along grain boundary
30
83P1
2.6·10−8
0.52±0.15 516-915
Polycrystalline thin film on a Si substrate - Dgb 33P deposited source -Type B kinetic Sectioning method - Layer activity (1st part of penetration plots) - analysis of the penetration tail - Suzuoka solution: α ·δ taken as = 5·10−10 m to calculate D0
30
83P1
Bulk single crystal - 51Cr - Sectioning method
Dv
31
83J1
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Complementary error function
Dv Dgb
32
91S1
Matrix: Cr3Si Cr 1.03
3.58±0.45 1400-1550
Matrix: MoSi2 As 3.2·10−6
1.4
550-700
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35] D0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
4-17
T - range [°C]
Remarks
Diff. Fig. path
Ref.
Matrix: WSi2 B 1.0·10−3
1.17
850-1000
Electrical measurement - Thin film lines Strong contribution of grain boundary and interface diffusion.
Dgb
33
93C1
P 4.2
2.14
850-1000
Electrical measurement - Thin film lines Strong contribution of grain boundary and interface diffusion
Dgb
33
93C1
9.5·102
2.4
350, 400
Amorphous thin film on a Si substrate Dgb Implanted source - SIMS - Recrystallisation during diffusion - Only 2 temperatures
As 2.6
2.11
850-1000
Electrical measurement - Thin film lines Strong contribution of grain boundary and interface diffusion
4.5·101
2.4
450, 500
Amorphous thin film on a Si substrate Dgb Implanted source - SIMS - Recrystallisation during diffusion - Only 2 temperatures
Sb 4.5
2.4
500, 550
Amorphous thin film on a Si substrate Dgb Implanted source - SIMS - Recrystallisation during diffusion - Only 2 temperatures
33
92S1
Bulk silicides - 59Fe and 71Ge - Sectioning Dv technique - Two other compositions are studied (21 and 18 at% Si). It is shown that: i) for these compositions diffusion is affected by the magnetic order-disorder transition and ii) Fe diffusion increases with Si content.
34
96G2
Dgb
92S1
33
93C1
92S1
Matrix: Fe3Si (24%Si) Fe 1.3
Lando lt -Bö rnst ein New Series III/33A
1.64±0.04 366-851
4-18 D0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
T - range [°C]
Remarks
[Ref. p. 4-35 Diff. Fig. path
Ref.
Matrix: Fe3Si (24% Si) (cont.) Ge 0.19
3.24±0.04 732-1190
Bulk silicides - 59Fe and 71Ge - Sectioning Dv technique - Two other compositions are studied (21 and 18 at% Si). It is shown that: i) for these compositions diffusion is affected by the magnetic order-disorder transition and ii) Fe diffusion increases with Si content
34
96G2
35
91B1
Matrix: CoSi2 Co 0.15
2.78
700-1100
Polycrystalline bulk samples - 60Co Sectioning method
Dv
9.6·102
2.5
700-1100
Polycrystalline bulk samples - 60Co Sectioning method - Type B kinetic Suzuoka solution - δ = 5·10−10 m
Dgb
8.3
3.23
650-1100
Polycrystalline bulk samples - 68Ge Sectioning method
Dv
2.2·105
2.71
750-1000
Polycrystalline bulk samples - 68Ge Sectioning method - Type B kinetic Suzuoka solution - δ = 5·10−10 m
Dgb
95B1
1.4·102
3.46
600-800
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
88T1
8.5·10−3
2.05
400-600
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
0.01
2.0
450-700
Polycrystalline bulk samples - Implanted and evaporated B source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
90G2
0.016
2.05
450-900
Polycrystalline bulk samples - Implanted and evaporated B source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
96Z1
95B1
Ge 35
95B1
B 35
88T1
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35] D0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
4-19
T - range [°C]
Remarks
Diff. Fig. path
2.09
800-950
Electrical measurements - Thin film lines - Dgb Strong contribution of grain boundary and interface diffusion
1.7·10−2
2.66
600-800
Polycrystalline thin film on a Si substrate Implanted source - SIMS analysis Numerical solution of Fick's law including surface effects
Dv
1.0·103
2.86
800-950
Electrical measurements - Thin film lines Strong contribution of grain boundary and interface diffusion
Dgb
7.37
3.3
750-950
Single crystals - Implanted source - SIMS analysis - Numerical solution of Fick's law including surface effects
Dv
1.0·103
2.91
800-950
Electrical measurements - Thin film lines Strong contribution of grain boundary and interface diffusion.
Dgb
Ref.
Matrix: CoSi2 (cont.) B (cont.) 4.9
93C1
P 35
88T1
93C1
As 36
96P1
93C1
Matrix: Ni2Si Ni 3.54
2.48
650-910
Polycrystalline bulk samples - 63Ni Sectioning method
Dv
18.2
1.71
530-706
Polycrystalline bulk samples - 63Ni Sectioning method - Type B kinetic Suzuoka solution - δ = 5·10−10 m
Dgb
3.41
710, 850
Polycrystalline bulk samples - 68Ge Sectioning method - 2 Points
Dv
36
90C1 90C1
Ge 1.4·103
Lando lt -Bö rnst ein New Series III/33A
36
90C1
4-20 D0 [10−4 m2/s]
4 Diffusion in silicides Q [eV/at]
[Ref. p. 4-35
T - range [°C]
Remarks
Diff. Fig. path
Ref.
95G2
Matrix: Ni5Si2 Ni 4.2·10−2
1.68±0.1
490-900
Polycrystalline bulk samples - 63Ni Sectioning method
Dv
3.9·10−1
1.12±0.1
350-585
Polycrystalline bulk samples - 63Ni Sectioning method - Type B kinetic Numerical solution - δ = 5·10−10 m
Dgb
350-550
31Si
redistribution in a Pd231Si /Pd2Si polycrystalline thin film - Sectioning method: r.f. sputtering - Residual activity - Model taking into account the influence of grain boundary
Dv
38
89E1
480-570
31Si
Dv
38
81P1
37
95G2
Matrix: Pd2Si Si 5.0·10−10
0.8±0.1
Matrix: PtSi Si 3.59·10−1
2.1±0.2
redistribution in a Pt31Si /PtSi polycrystalline thin film - Sectioning method: r.f. sputtering
Landolt -Börnst ein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-21 Temperature T [°C]
Figures for 4
800
700
600
500
10-13
TiSi2
[90P1]
Growth const.
κ [m2/s]
10-14
Growth const.
κ [m2/s]
Temperature T [°C] 350
300
250
10-17
TbSi 1.7
10-18
10-15
10-16 [88P1] 10-17
10-18
[83H1]
ErSi1.7 10-19
10-19 1.6
1.7
0.9
1.8
2.0 1.9 -3 -1 Inv. temp. 1/T [10 K ]
Fig. 1. Growth constants κ of TbSi1.7 and ErSi1.7 thin films vs. inverse temperature 1/T [80T1]
1.0
1.1
1.3
1.2
Fig. 2. Growth constant κ inverse temperature 1/T .
of TiSi2 thin films vs.
Temperature T [°C] 600
500
10-16
Temperature T [°C]
κ [m2/s]
HfSi 10-17
Growth const.
Growth const.
κ [m2/s]
700
10-18
10-19 1.0
1.1
1.2
1.3
Inv. temp. 1/T [10-3K -1] Fig. 3. Growth constant κ of HfSi thin films vs. inverse temperature 1/T [73Z1].
Landolt-Börnstein New Series III/33A
1.4
Inv. temp. 1/T [10 -3K -1]
800
700
600
10-16
VSi 2 V3Si
10-17
[73T1] [74K1] 10-18 0.9
1.0
1.1
1.2
Inv. temp. 1/T [10 -3K -1] Fig. 4. Growth constants κ of V3Si and VSi2 thin films vs. inverse temperature 1/T.
4-22
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C] 1300
1100
900
700
500
10-10
10-11
WSi 2
Growth const.
κ [m2/s]
10-12
[86L1]
CrSi 2 [84Z1]
10-13
10-14
10-15
10-16
CrSi 2 [84N1]
10-17
MoSi 2 [78G1]
[88M1]
WSi 2
10-18
[86L1]
10-19 0.6
0.8
0.7
0.9
1.0
1.1
1.2
1.4
1.3
1.5
Inv. temp. 1/T [10 -3K -1] Fig. 5. Growth constants κ of CrSi2, MoSi2 and WSi2 thin films vs. inverse temperature 1/T.
Temperature T [°C] 500
400
Growth const.
κ [m2/s]
Temperature T [°C] 500
400
10-16
MnSi 10-17
Growth const.
κ [m2/s]
10-15
FeSi 10-16
[75L1]
Ru 2Si 3 10-17 [82P1]
10-18
RuSi [82P1]
10-19
10-18 1.2
1.3
1.5 1.4 -3 -1 Inv. temp. 1/T [10 K ]
Fig. 6. Growth constant κ inverse temperature 1/T.
of MnSi thin films vs.
[82P1]
Os2Si 3
1.2
1.3
1.4
1.5
1.6
Inv. temp. 1/T [10 -3K -1 ] Fig. 7. Growth constants κ of FeSi, Ru2Si3 and Os2Si3 thin films vs. inverse temperature 1/T.
Landolt-Börnstein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-23 Temperature T [°C] 600
500
400
10-13
10-14
κ [m2/s]
Temperature T [°C] 500
400
Growth const.
Growth const.
κ [m2/s]
10-16
RhSi 10-17
10-18
IrSi [84P1]
[79P1]
[96C1]
10-15 [75G1] 10-16 [85L1] [78L1] 10-17
10-18
[80P1]
10-19
Co 2Si
[87L1]
10-19
10-20 1.2
1.3
1.4
1.5
1.6 Inv. temp. 1/ T [10 -3K -1]
1.0
1.7
1.1
1.2
1.3
1.4 -3 Inv. temp. 1/T [10 K -1 ]
1.5
1.6
Fig. 8. Growth constants κ of IrSi and RhSi thin Fig. 9. Growth constant κ of Co2Si thin films vs. inverse films vs. inverse temperature 1/T. temperature 1/T. Temperature T [°C] 600
400
500
10-14 [96C1]
600
500
400
10-14
10-16
κ [m2/s]
CoSi 2 [96C1] poly
10-17
Growth const.
Growth const.
κ [m2/s]
10-15
Temperature T [°C] 700
CoSi
10-18 [78L1] 10-19
10-15 [86H2]
[96C1] poly
10-16
10-17 [85A2]
10-18
[96C1]
[85L1]
[84L2]
10-19
10-20 1.1
1.2
1.3
1.4
1.5
Inv. temp. 1/T [10 -3K -1]
1.6
1.0
1.1
1.2
1.3
1.4
Inv. temp. 1/T [10 -3K -1 ]
Fig. 10. Growth constant κ of CoSi thin films vs. Fig. 11. Growth constant κ of CoSi2 thin films vs. inverse temperature 1/T. inverse temperature 1/T.
Landolt-Börnstein New Series III/33A
1.5
4-24
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C] 700
10-12
600
500
400
300
[89S1] <100>
Ni 2Si
10-13
Growth const.
κ [m2/s]
10-14 [89S1] <111> 10-15
[76C1] [96C1] [84Z1]
10-16
10-17
10-18 [85H2] 10-19
[75T1]
<100> [76O1] <111>
[86L2]
10-20 1.0
1.1
1.2
1.3
1.4
1.5
1.6 Inv. temp. 1/T [10 -3K -1]
1.7
1.8
1.9
2.1
2.0
Fig. 12. Growth constant κ of Ni2Si thin films vs. inverse temperature 1/T.
Temperature T [°C] 400
300
10-14
NiSi
[84L2]
κ [m2/s]
10-16
Temperature T [°C] 400
[84M1] <100> 10-17
<111>
Growth const.
Growth const.
κ [m2/s]
[96C1] 10-15
10-18 [84H1] <111> <100> 10-19 1.4
1.5
1.6
1.7
1.8 Inv. temp. 1/T [10 -3K -1 ]
1.9
2.0
350
10-16
NiSi 2 10-17
10-18
10-19 1.4
1.5
1.7 1.6 -3 -1 Inv. temp. 1/T [10 K ]
Fig. 13. Growth constant κ of NiSi thin films vs. inverse Fig. 14. Growth constant κ of NiSi2 thin films vs. temperature 1/T. inverse temperature 1/T [84L3].
Landolt-Börnstein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-25
Temperature T [°C] 300
400
200
10-13 [76F1] <111>
Growth const.
κ [m2/s]
10-14
Pd 2Si
[73H1] <111>
10-15
10-16
[73B1] <111> and <100>
10-17 [81C1] <100> 10-18 [83W1] <100>
10-19
[86C1] <111> 10-20 1.3
1.5
1.4
1.6
1.7
1.8
1.9
2.1
2.0 -3 -1 Inv. temp. 1/T [10 K ]
2.2
Fig. 15. Growth constant κ of Pd2Si thin films vs. inverse temperature 1/T.
Temperature T [°C]
Growth const.
κ [m2/s]
300
Pd e / Si <100>
200
10-15
Pde / Sie
Pd 2Si [81C1]
10-16
Pde / Sis Pds / Si <100> Pds / Sie
10-17
Pds / Sis [76N1]
10-18 1.7
1.8
1.9
2.0
2.1
Inv. temp. 1/T [10 -3K -1]
2.2
[85H2]
Pde / Si poly Pde / Si <100> Pde / aSi-H
Fig. 16. Growth constant κ of Pd2Si thin films vs. inverse temperature 1/T: influence of Si and Pd purity and/or cristallinity (Pde: evaporated Pd, Pds: sputtered Pd, Sie: evaporated Si, Sis: sputtered Si, aSi-H: hydrogenated amorphous Si).
Landolt-Börnstein New Series III/33A
2.3
2.4
4-26
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C]
Growth const.
κ [m2/s]
250
200
10-16
Pd 2Si 10-17
<100>
P doped (5 1013 cm-3)
<100>
As doped (5 1020 cm-3)
<111> P doped (4.6 1014 cm-3)
10-18
As doped (5 1020 cm-3)
<111> 10-19 1.8
1.9
2.0
2.1 -3 Inv. temp. 1/ T [10 K -1 ]
2.2
Fig. 17. Growth constant κ of Pd2Si thin films vs. inverse temperature 1/T: influence of Si doping and crystallinity [83W1]. Temperature T [°C] 600
500
400
300
10-13
κ [m2/s] Growth const.
Pt 2Si
[72M1]
[82Z2]
10-14
[92P1]
[96C1]
10-15
[80C2] 10-16 [74P1]
10-17
[77C1]
10-18
[85T1] [86L2] <100> 10-19 1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
Inv. temp. 1/ T [10 -3K -1] Fig. 18. Growth constant κ of Pt2Si thin films vs. inverse temperature 1/T.
Temperature T [°C]
Growth const.
κ [m2/s]
300
200
10-16 poly -As doped
Pt 2 Si
poly
10-17
10-18 <100> aSi
poly - P doped 10-19 1.7
1.8
1.9
2.0
2.1
Fig. 19. Growth constant κ of Pt2Si thin films vs. inverse temperature 1/T: influence of Si doping and crystallinity [85T1, 86W1].
2.2
Inv. temp. 1/T [10 -3K -1]
Landolt-Börnstein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-27
Temperature T [°C] 500
400
300
200
10-13 [72M1]
PtSi
Growth const.
κ [m2/s]
10-14 [92P1] 10-15 [77C1] 10-16
10-17
[74P1]
[83W2] [85T1]
10-18
[96C1] [86L2]
[80C2]
10-19 1.2
1.3
1.4
1.5
1.7
1.6
1.8
1.9
2.0
Fig. 20.Growth constant κ of PtSi thin films vs. inverse temperature 1/T.
2.2
2.1
Inv. temp. 1/T [10 -3K -1] Temperature T [°C] 400
300
Growth const.
κ [m2/s]
10-15
PtSi
<100> 10-16
10-17 aSi
poly -As doped
poly
10-18
poly - P doped 10-19 1.4
1.5
1.6
1.7
1.8
Fig. 21. Growth constant κ of PtSi thin films vs. inverse temperature 1/T: influence of Si doping and crystallinity [85T1, 86W1].
1.9
Inv. temp. 1/T [10 -3K -1 ] Temperature T [°C]
Temperature T [°C] 1100
1600 1400 1200
900
10-15
Ti5Si 4 Ti5Si 3
10-16
Ti 3Si 10-17
κ [m2/s]
TiSi 2 TiSi
Growth const.
κ [m2/s] Growth const.
10-14
1000
10-12
10-13
10-13
Nb5Si 3 10-14
Ta 5Si 3 10-15
10-16 0.7
0.8
0.9 -3 Inv. temp. 1/T [10 K-1]
Fig. 22. Growth constants κ of "bulk" Ti silicides vs. inverse temperature 1/T [95C1]. Landolt-Börnstein New Series III/33A
0.5
0.6
0.7 0.8 -3 -1 Inv. temp. 1/T [10 K ]
Fig. 23. Growth constants κ of "bulk" Nb5Si3 and Ta5Si3 vs. inverse temperature 1/T [66B1].
4-28
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C] 1800
1000
1400
10-11
Temperature T [°C]
Growth const.
Mo 5Si 3 [64B1]
10-12 10-13
[64B1]
κ [m2/s]
κ [m 2/s]
10-11
WSi 2
1000
1400
MoSi 2
Growth const.
1800
[65G1 ]
[71Z1] [53F1] [76C2]
MoSi 2 10-14
10-12
W 5Si 3
[68Z1]
[64B1]
[76C2] WSi 2
10-13
[65G1]
10-14
WSi2
10-13
[67H1] 10-16
10-13 0.4
0.5
0.6
0.7
0.8
0.4
0.9
0.5
0.6
0.7
0.8
0.9
Inv. temp. 1/T [10 -3 K-1]
Inv. temp. 1/T [10 -3K -1]
Fig. 24. Growth constants κ of "bulk" Mo5Si3 and Fig. 25. Growth constants κ of "bulk" W5Si3 and WSi2 MoSi2 vs. inverse temperature 1/T. vs. inverse temperature 1/T.
Te mper ature T [°C] 1000
Temperature T [°C] 1100
10-10
10-10
[93J1]
10-11
10-11
Co 2Si 10-14
[95B1]
10-12
10-12
[93J1]
CoSi 2
[95B1] [95B1]
10-16
0.9 Inv. temp. 1/T [10 -3K -1] 0.8
Ni5S i2 10-13
10-13
δ Ni 2Si
10-14 0.7
0.8
0.9
1.0
1.1 Inv. temp. 1/T [10-3K -1]
Dint [m2/s]
CoSi
0.7
10-9
Int. diff. coeff.
κ [m2/s]
[93J1]
10-13
10-15
600
900
Growth c onst.
Growth const.
κ [m2/s]
10-12
800
10-9
10-14 1.2
Fig. 26. Growth constants κ of "bulk" Co Fig. 27. Growth constant κ of "bulk" Ni5Si2 and integrated silicides vs. inverse temperature 1/T. diffusion coefficient Dint in "bulk" δNi2Si vs. inverse temperature 1/T [95G2].
Landolt-Börnstein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-29
Temperature T [°C] 600
10-8
κ [m2/s]
400
Cu 3Si
[88B1]
10-9
Growth const.
500
10-10
10-11
[68V1]
10-12 [88B1]
10-13
Fig. 28. Growth constant κ of "bulk" Cu3Si vs. inverse temperature 1/T.
10-14 1.0
1.1
1.2
1.3
1.4
1.5 -3 -1 Inv. temp. 1/ T [10 K ]
1.6
1.7
Temperature T [°C] 900
800
700
Temperature T [°C]
600
10-13
10-11
800
700
600 33P in TaSi
TiSi 2
As [93C1]
10-12
900
2
10-14 gb
10-13
Diff. coeff. D [m 2/s]
10-15 P [93C1]
Diff. coeff. D [m 2/s]
10-14
10-15
10-16 P [93H1] As [93H1 ]
10-19
10-18
10-20 0.8
v-RA v-LA 0.9
1.0
1.1
1.2
1.3
Inv. temp. 1/T [10 -3K-1 ]
10-19
Fig. 30. Diffusion coefficients D of 33P in TaSi2 (volume and grain boundaries) vs. inverse temperature 1/T [83P1].
Asv [86G1] 10-20 Ge v [86G1] P v [86G1] 0.9
1.0
1.1
1.2
Inv. temp. 1/T [10 -3K-1]
Landolt-Börnstein New Series III/33A
10-17
10-18
10-17
10-21 0.8
10-16
1.3
Fig. 29. Diffusion coefficients D of Ge, P and As in TiSi2 vs. inverse temperature 1/T.
4-30
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C] 10-16 2 Diff. coeff. D [m /s]
Vol. diff. coeff. D v [m2/s]
Temperature T [°C] 1600 1400 10-13 51Cr in Cr Si 3 10-14
10-15 0.5
700
600
As in MoSi 2 10-17 10-18
10-19
0.7 -3 Inv. temp. 1/T [10 K -1] 0.6
1.0
1.1
1.2
1.3
Inv. temp. 1/T [10-3 K -1]
Fig. 31. Volume diffusion coefficient Dv of 51Cr in Fig. 32. Diffusion coefficient D of As in MoSi2 vs. Cr3Si vs. inverse temperature 1/T [83J1]. inverse temperature 1/T [91S1].
Temperature T [°C] 900
800
700
600
500
400
10-11 B [93C1 ]
WSi 2
10-12 P [93C1 ]
10-13
As [93C1]
Diff. coeff. D [m 2/s]
10-14
10-15
10-16
10-17
10-18 As [92S1]
Sb [92S1]
10-19
10-20 P [92S1 ] 10-21
0.7
0.8
0.9
1.0
1.1
1.2
1.3
Inv. temp. 1/ T [10-3 K -1]
1.4
1.5
1.6
Fig. 33. Diffusion coefficients D of B, P, As and Sb in WSi2 vs. inverse temperature 1/T.
Landolt-Börnstein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-31
Temperature T [°C] 1200
1000
800
600
400
10-11
Fe3Si 10-12 10-13
2 Vol. diff. coeff. D v [m /s]
10-14
10-15
10-16 Fev 10-17
10-18
10-19 Ge v
10-20
10-21 0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
Inv. temp. 1/T [10 -3K-1 ] Fig. 34. Volume diffusion coefficients Dv of 59Fe and 71Ge in Fe3Si (24 at% Si) vs. inverse temperature 1/T [96G2].
Landolt-Börnstein New Series III/33A
4-32
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C] 10-8
1100 1000 900
800
700
600
500
400
CoSi 2
10-9
10-10
10-11 Gegb [95B1]
B [93C1]
10-12
P [93C1 ] 10-13
As [93C1]
2 Diff. coeff. D [m /s]
Cogb [95B1] 10-14
10-15
10-16
10-17 10-18
10-19
Gev [95B1]
Asv [96P1]
Bv [96Z1]
10-20 Cov [95B1]
10-21
P v [88T1] Bv [88T1]
10-22 0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Inv. temp. 1/T [10 -3 K-1] Fig.35. Diffusion coefficients D of 60Co, 68Ge, B, P and As in CoSi2 (volume and grain boundaries) vs. inverse temperature 1/T.
Landolt-Börnstein New Series III/33A
Ref. p. 4-35]
4 Diffusion in silicides
4-33
Temperature T [°C] 900
800
700
600
500
10-11
Ni 2Si 10-12
Nigb
2 Diff. coeff. D [m /s]
10-13 10-14
10-15 Niv
10-16
10-17 Gev 10-18
Fig. 36. Diffusion coefficients D of 63Ni and 68Ge in Ni2Si (volume and grain boundaries) vs. inverse temperature 1/T [90C1].
10-19 0.8
1.2 -3 -1 Inv. temp. 1/T [10 K ]
0.9
1.0
1.1
1.3
Temperature T [°C] 900
800
700
600
500
400
10-10 63Ni in Ni Si 5 2
Diff. coeff. D [m 2/s]
10-11
10-12 Nigb 10-13 10-14
10-15 Niv 10-16
10-17 0.8
0.9
1.0
1.1
1.2
1.3
1.4 -3 -1 Inv. temp. 1/ T [10 K ]
1.5
1.6
1.7
Fig. 37. Diffusion coefficients D of 63Ni in Ni5Si2 (volume and grain boundaries) vs. inverse temperature 1/T [95G1].
Landolt-Börnstein New Series III/33A
4-34
4 Diffusion in silicides
[Ref. p. 4-35
Temperature T [°C] 600
500
400
2 Diff. coeff. D [m /s]
10-16 31Si
in PtSi
10-17
10-18 31
10-19
10-20 1.1
31Si
1.2
1.3
1.4
1.5 -3 Inv. temp. 1/ T [10 K -1]
in Pd 2Si
1.6
Fig. 38. Diffusion coefficients D of Si in Pd2Si [89E1] and PtSi [81P1] vs. inverse temperature 1/T.
1.7
Landolt-Börnstein New Series III/33A
4 Diffusion in silicides
4-35
4.5 References for 4 53D1 53F1
Darken, L., Gurry, R.W.: Physical Chemistry of Metals, New York: Mc Graw-Hill, 1953, p. 463. Fitzer, E., in: Plansee Seminar über Pulvermetallurgie, Benesovsky, F. (ed), Wien: SpringerVerlag, 1953, p. 244. 57K1 Kissinger, H.E.: Anal. Chem. 29 (1957) 1702. 64B1 Bartlett, R.W., Gage, P. R., Larssen, P.: Trans. Metall. Soc. AIME 230 (1964) 1528. 65G1 Gage, P.R., Bartlett, R.W.: Trans. Metall. Soc. AIME 233 (1965) 832. 66B1 Bartlett, W.: Trans. Metall. Soc. AIME 236 (1966) 1230. 67H1 Hashimoto, N.: Trans. Metall. Soc. AIME 239 (1967) 1109. 68E1 Ebeling, R., Wever, H. : Z. Metallkd. 59 (1968) 22. 68V1 Veer, F.A., Kolster, B.H., Burgers, W.G.: Trans. Metall. Soc. AIME 242 (1968) 669. 68Z1 Zmiy, V.I., Seryugina, A.S.: Zashch. Pokrytaya Met. 2 (1968) 195; Prot. Coat. Met. (English Transl.) 2 (1970) 158. 71Z1 Zmiy, V.I., Seryugina, A.S.: Izv. Akad. Nauk. SSSR Neorg. Mater. 7 (1971) 1730. 72G1 Gumen, M.N., Podus, L.P.: Fiz. Met. Metalloved 34 (1972) 98. 72M1 Muta, H., Shinoda, D.: J. Appl. Phys. 43 (1972) 2913. 73B1 Bower, R.W., Sigurd, D., Scott, R.E.: Solid State Electron. 16 (1973) 1461. 73H1 Hutchins, G.A., Shepela, A.: Thin Solid Films 18 (1973) 343. 73K1 Kircher, C.J., Mayer, J.W., Tu, T.N., Ziegler, J.F.: Appl. Phys. Lett. 22 (1973) 81. 73T1 Tu, K.N., Ziegler, J.F., Kircher, C.J.: Appl. Phys. Lett. 23 (1973) 493. 73Z1 Ziegler, J.F., Mayer, J.W., Kircher, C.J., Tu, T.N.: J. Appl. Phys. 44 (1973) 3851. 74C1 Chu, W.K., Kräutle, H., Mayer, J.W., Müller, H., Nicolet, M.-A., Tu, K.N.: Appl. Phys. Lett. 25 (1974) 454. 74K1 Kraütle, H., Nicolet, M.-A., Mayer, J.W.: J. Appl. Phys. 45 (1974) 3304. 74P1 Poate, J.M., Tisone, T.C.: Appl. Phys. Lett. 24 (1974) 391. 75C1 Chu, W.K., Lau, S.S., Mayer, J.W., Müller, H., Tu, K.N.: Thin Solid Films 28 (1975) 393. 75G1 van Gurp, G.J., Langereis, C.: J. Appl. Phys. 46 (1975) 4301. 75L1 Lau, S.S., Feng, J.S.Y., Olowolafe, J.O., Nicolet, M.-A.: Thin Solid Films 25 (1975) 415. 75T1 Tu, K.N., Chu, W.K., Mayer, J.W.: Thin Solid Films 25 (1975) 403. 76C1 Coe, D.J., Rhoderick, E.H.: J. Phys. D: Appl. Phys. 9 (1976) 965. 76C2 Celis, R.J.M.H.: Master Thesis, Eindhoven: University of Technology, 1976. 76F1 Fertig, D.J., Robinson, G.Y.: Solid State Electron. 19 (1976) 407. 76N1 Nakamura, K., Olowolafe, J.O., Lau, S.S., Nicolet, M.-A., Mayer, J.W., Shima, R.: J. Appl. Phys. 47 (1976) 1278. 76O1 Olowolafe, J.O., Nicolet, M.-A., Mayer, J.W.: Thin Solid Films 38 (1976) 143. 77C1 Canali, C., Catellani, C., Prudenziati, M., Wadlin, W.H., Evans jr., C.: Appl. Phys. Lett. 31 (1977) 43. 77O1 Ottaviani, G., Canali, C., Ferrari, G., Majini, G., Prudenziati, M., Lau, S.S.: Thin Solid Films 47 (1977) 187. 77T1 Tu, K.N.: J. Appl. Phys. 48 (1977) 3379. 78B1 Baglin, J.E.E, d'Heurle, F.M, Petersson, C.S.: Appl. Phys. Lett. 33 (1978) 289. 78C1 Chu, W.K., Mayer, J.W., Nicolet, M.-A.: Backscattering Spectrometry, New York: Academic Press, 1978. 78G1 Guivarc'h, A., Auvray, P., Berthou, L., Le Cun, M., Boulet, J.P., Henoc, P., Pelous, G., Martinez, A.: J. Appl. Phys. 49 (1978) 233. 78G2 van Gurp, G.J., van der Weg, W.F., Sigurd, D.: J. Appl. Phys. 49 (1978) 4011. 78L1 Lau, S. S., Mayer, J.W., Tu, K.N.: J. Appl. Phys. 49 (1978) 4005. 78P1 Pretorius, R., Ramiller, C.L., Nicolet , M.-A.: Nucl. Instrum. Methods 149 (1978) 629.
Lando lt -Bö rnst ein New Series III/33A
4-36
4 Diffusion in silicides
78W1 Wagner, R.J., Lau, S.S., Mayer, J.W., Roth, J.A., in: Thin film Phenomena, Interfaces and Interactions, Baglin, J.E.E., Poate, J.M. (eds), Princeton: Electrochemical Society, 78-2 (1978) 59. 78Z1 Zirinsky, S., Hammer, W., d'Heurle, F.M., Baglin, J.E.: Appl. Phys. Lett. 33 (1978) 76. 79P1 Petersson, C.S., Baglin, J., Hammer, W., d'Heurle, F.M., Kuan, T.S., Odhomari, I., de Sousa Pires, J., Tove, P.: J. Appl. Phys. 50 (1979) 3357. 79S1 Schultz, R.J., Testardi, L.R.: J. Appl. Phys. 50 (1979) 5573. 80B1 Baglin, J.E.E, d'Heurle, F.M., Hammer, W.M., Petersson, C.S.: Nucl. Instrum. Methods 168 (1980) 491. 80C1 Cheung, N., Lau, S.S., Nicolet, M.-A., Mayer, J.W., Sheng, T.T., in: Thin Films Interfaces and Interactions, Baglin, J.E.E., Poate, J.M. (eds), Princeton: Electrochemical Society, 80-2 (1980) 494. 80C2 Crider, C.A., Poate, J.M.: Appl. Phys. Lett. 36 (1980) 417. 80M1 Martinez, A., Esteve, D., Guivarc'h, A., Auvray, P., Henoc, P., Pelous, G.: Solid State Electron. 23 (1980) 55. 80P1 Petersson, C.S., Anderson, R., Baglin, J., Dempsey, J., Hammer, W., d'Heurle, F.M., LaPlaca, S.: J. Appl. Phys. 51 (1980) 373. 80T1 Tsaur, B.Y., Hung, L.S.: Appl. Phys. Lett. 37 (1980) 922. 81B1 Baglin, J.E.E, d'Heurle, F.M., Petersson, C.S.: J. Appl. Phys. 52 (1981) 2841. 81C1 Cheung, N.W., Nicolet, M.-A., Wittmer, M., Evans jr., C.A., Sheng, T.T.: Thin Solid Films 79 (1981) 51. 81F1 Finstad, T.: Phys. Status Solidi (a) 63 (1981) 223. 81P1 Pretorius, R., Botha, A.P., Lombaard, J.C.: Thin Solid Films 79 (1981) 61. 81S1 Scottland, D.M., Nicolet, M.-A.: Phys. Status Solidi (a) 66 (1981) 773. 82B1 Bomchil, G., Bensahel, D., Golanski, A., Ferrieu, F., Auvert, G., Perio, A., Pfister, J.C.: Appl. Phys. Lett. 41 (1982) 46. 82E1 Eizenberg, M., Tu, K.N.: J. Appl. Phys. 53 (1982) 6885. 82H1 d'Heurle, F.M., in: VLSI Science and Technology, Dell'Oca, C., Bullis, W.M. (eds.), Pennington, N.J.: Electrochemical Society, 1982, p. 194. 82H2 d'Heurle, F.M., Petersson, C.S., Stolt, L., Stritzker, B.: J. Appl. Phys. 53 (1982) 5378. 82P1 Petersson, C.S., Baglin, J.E.E., Dempsey, J.J., d'Heurle, F.M., La Placa, S.J.: Appl. Phys. 53 (1982) 4866. 82W1 Ward, W.J., Caroll, K.M.: J. Electrochem. Soc. 129 (1982) 227. 82Z1 Zheng, L.R., Hung, L.S., Mayer, J.W., Majini, G., Ottaviani, G.: Appl. Phys. Lett. 41 (1982) 646. 82Z2 Zheng, L.R., Hung, L.S., Mayer, J.W.: Mater. Res. Soc. Symp. Proc. 18 (1982) 207. 83B1 Bartur, M., Nicolet, M.-A.: J. Appl. Phys. 54 (1983) 5404. 83H1 Hung, L.S., Gyulai, J., Mayer, J.W., Lau, S.S., Nicolet, M.-A.: J. Appl. Phys. 54 (1983) 5076. 83J1 Jurisch, M., Bergner, D.: Diffus. Defect Monogr. Ser. 7 (1983) 465. 83N1 Nicolet, M.A., Lau, S.S., in: VLSI Electronics, Microstructure Science, Einspruch, N.G., Larrabee, G.B. (eds.), New York: Academic Press, 1983, p. 329. 83P1 Pelleg, J.: Thin Solid Films 110 (1983) 115. 83S1 Stark, J.P.: Acta Metall. 31 (1983) 2083. 83T1 Tu, K.N., Ottaviani, G., Gösele, U., Föll, H.: J. Appl. Phys. 54 (1983) 758. 83W1 Wittmer, M., Tu, K.N.: Phys. Rev. B 27 (1983) 1173. 83W2 Wittmer, M.: J. Appl. Phys. 54 (1983) 5061. 84A1 Aly, E.S.M., Stark, J.P.: Acta Metall. 32 (1984) 907. 84B1 Berti, M., Drigo, A., Cohen, C., Siejka, J., Bentini, G.G., Nipoti, R., Guerri, S.: J. Appl. Phys. 55 (1984) 3558. 84H1 d'Heurle, F.M., Petersson, C.S., Baglin, J.E.E., LaPlaca, S.J., Wong, C.Y.: J. Appl. Phys. 55 (1984) 4208. 84L1 Lien, C.-D., Bartur, M., Nicolet, M.-A.: Mater. Res. Soc. Symp. Proc. 25 (1984) 51. 84L2 Lien, C.-D., Nicolet, M.-A., Lau, S.S.: Appl. Phys. A34 (1984) 249.
Landolt -Börnst ein New Series III/33A
4 Diffusion in silicides 84L3 84M1 84N1 84P1 84Z1 84Z2 85A1 85A2 85H1 85H2 85H3 85H4 85L1 85L2 85M1 85T1 86C1 86G1 86H1 86H2 86L1 86L2 86W1 87H1 87L1 88B1 88C1 88G1 88L1 88M1 88P1 88R1 88T1 88W1 88W2 89C1 89E1 89F1 89H1 89S1 90B1 90C1 90F1 90G1
4-37
Lien, C.-D., Nicolet, M.-A., Lau, S.S.: Phys. Status Solidi (a) 81 (1984) 123. Majini, G., Della Valle, F., Nobili, C.: J. Phys. D: Appl. Phys. 17 (1984) L77. Natan, M., Duncan, S.W., Byer, N.E.: J. Appl. Phys. 55 (1984) 1450. Psaras, P.A., Thomson, R.D., Herd, S.R., Tu, K.N.: J. Appl. Phys. 55 (1984) 3526. Zheng, L.R., Zingu, E., Mayer, J.W.: Mater. Res. Soc. Symp. Proc. 25 (1984) 75. Zingu, E.C., Mayer, J.W., Comrie, C.M., Pretorius, R.: Phys. Rev. B 30 (1984) 5916. Affolter, K., Zhao, X-A., Nicolet, M.-A.: J. Appl. Phys. 58 (1985) 3087. Appelbaum, A., Knoell, R.V., Murarka, S.P.: J. Appl. Phys. 57 (1985) 1880. Hung, L.S., Mayer, J.W., Pai, C.S., Lau, S.S.: J. Appl. Phys. 58 (1985) 1527. Hung, L.S., Kennedy, E.F., Palmström, C.J., Olowolafe, J.O., Mayer, J.W., Rhodes, H.: Appl. Phys. Lett. 47 (1985) 236. Ho, K.T., Lien, C.-D., Shreter, U., Nicolet, M.-A.: J. Appl. Phys. 57 (1985) 227. d'Heurle, F.M., Petersson, C.S.: Thin Solid Films 128 (1985) 283. Lien, C.-D., Nicolet, M.-A., Pai, C.S., Lau, S.S.: Appl. Phys. A 36 (1985) 153. Lien, C.-D., Nicolet, M.-A., Pai, C.S.: J. Appl. Phys. 57 (1985) 224. Marshall, E.D., Pai, C.S., Scott, D.M., Lau, S.S.: Mater. Res. Soc. Sym. Proc. 47 (1985) 161. Takai, H., Psaras, P.A., Tu, K.N.: J. Appl. Phys. 58 (1985) 4165. Coulman, B., Chen, H.: J. Appl. Phys. 59 (1986) 3467. Gas, P., Deline, V., d'Heurle, F.M., Michel, A., Scilla, G.: J. Appl. Phys. 60 (1986) 1634. d'Heurle, F.M., Gas, P.: J. Mater. Res. 1 (1986) 205. van den Hove, L., Wolters, R. Maex, K., De Keershmaecker, R., Declerck, G.: J. Vac. Sci. Technol. B4 (1986) 1358. Lajzerowicz jr., J., Torres, J., Göltz, G., Pantel, R.: Thin Solid Films 140 (1986) 23. Lien, C.-D., Nicolet, M.-A., Lau, S.S.: Thin Solid Films 143 (1986) 63. Wittmer, M., Wetzel, J.T., Psaras, P.A.: Philos. Mag. B 54 (1986) 359. d'Heurle, F.M.: Thin Solid Films 151 (1987) 41. Lim, B.S., Ma, E., Nicolet, M.-A., Nathan, M.: J. Appl. Phys. 61 (1987) 5027. Becht, J.G.M., van Loo, F.J.J, Metselaar, R.: React. Solids 6 (1988) 45. Comrie, C.M., Egan, J.M.: J. Appl. Phys. 64 (1988) 1173. Gas, P., Scilla, G., Michel, A., LeGoues, F.K., Thomas, O., d'Heurle, F.M.: J. Appl. Phys. 63 (1988) 5335. Lee, H.S., Wolga, G.J., in: Selected Topics in Electronic Materials, Appleton, B.R., Biegelsen, D.K., Brown, W.L., Knapp, J.A. (eds.), Material Research Society, 1988 p. 27. Ma, E., Lim, B.S., Nicolet, M.-A., Alvi, N.S., Hamdi, A.H.: J. Electro. Mater. 17 (1988) 207. Pico, C.A., Lagally, M.G.: J. Appl. Phys. 64 (1988) 4957. Raaijmakers, I.J.M.M.: Ph. D. Thesis, Eindhoven: Technical University, 1988. Thomas, O., Gas, P., Charai, A., LeGoues, F.K., Michel, A., Scilla, G., d'Heurle, F.M.: J. Appl. Phys. 64 (1988) 2973. Wang, S.Q., Mayer, J.W.: J. Appl. Phys. 64 (1988) 4711. Wei, C.S., Van der Spiegel, J., Santiago, J.J.: J. Electrochem. Soc. 135 (1988) 446. Comrie, C.M. , Egan, J.M.: J. Vac. Sci. Technol. A 7 (1989) 1492. Egan, J.M., Comrie, C.M.: Phys. Rev. B 40 (1989) 11670. Finstad, T.J., Thomas, O., d'Heurle, F.M.: Appl. Surf. Sci. 38 (1989) 106. Hong, Q.Z., Mayer, J.W.: J. Appl. Phys. 66 (1989) 611. Singh, A., Khole, W.S., Prudenziati, M., Majini, G., Morten, B: J. Appl. Phys. 66 (1989) 1190. Bakker, H., in: Landolt-Börnstein, New Series III/26, Diffusion in Solid Metals and Alloys, Mehrer, H. (ed.), Berlin: Springer-Verlag, 1990, p. 213. Ciccariello, J.-C., Poize, S., Gas, P.: J. Appl. Phys. 67 (1990) 3315. Farmer, J., Wandt, M.A.E., Pretorius, R.: Appl. Phys. Lett. 56 (1990) 1643. Gas, P., Zaring, C., Svensson, B.G., Östling, M., Petersson, C.S., d'Heurle, F.M.: J. Appl. Phys. 67 (1990) 2390.
Lando lt -Bö rnst ein New Series III/33A
4-38 90G2 90M1 90P1 90T1 90W1 91B1 91E1 91S1 91T1 91Z1 92P1 92S1 93C1 93H1 93J1 93M1 93M2 93Y1 94H1 95B1 95C1 95G1
95G2 95H1 95M1 95Z1 96C1 96C2
96G1 96G2 96L1 96P1 96Z1
4 Diffusion in silicides Gas, P., Zaring, C., Svensson, B.G., Östling, M., Whitlow, H.J., Barge, T.: Mater. Res. Soc. Symp. Proc. 187 (1990) 131. Mehrer, H., in: Landolt-Börnstein, New Series III/26, Diffusion in Solid Metals and Alloys, Mehrer, H. (ed.), Bertlin: Springer-Verlag, 1990, p. 279. Ponpon, J.P., Saulnier, A.: Appl. Surf. Sci. 40 (1990) 315. Thomas, O., Finstad, T.J., d'Heurle, F.M.: J. Appl. Phys. 67 (1990) 2410. Wandt, M.A.E., Comrie, C.M., Mc Leod, J.E., Pretorius, R.: J. Appl. Phys. 67 (1990) 230. Barge, T., Poize, S., Bernardini, J., Gas, P.: Appl. Surf. Sci. 53 (1991) 180. Erlesand, U., Östling, M., Boden, K.: Appl. Surf. Sci. 53 (1991) 153. Solmi, S., Angelucci, R., Cicognani, G., Canteri, R.: Appl. Surf. Sci. 53 (1991) 186. Thomas, O., Scilla, G., Gas, P., Cotte, J., Joshi, R.V., Bakli, M., Göltz, G., d'Heurle, F.M.: Appl. Surf. Sci. 53 (1991) 165. Zhang, S.-L, Gas, P., d'Heurle, F.M.: Appl. Surf. Sci. 53 (1991) 103. Pant, A.K., Murarka, S.P., Shepard, C., Lanford, W.: J. Appl. Phys. 72 (1992) 1833. Stanis, C., Thomas, O., Gas, P., Cotte, J., Charaï, A., LeGoues, F.K., d'Heurle, F.M.: J. Vac. Sci. Technol. A10 (1992) 907. Chu, C.L., Saraswat, K.C., Wong, S.S.: IEEE Trans. Electron Devices 39 (1993) 233. d'Heurle, F.M., Cotte, J., Gas, P., Göltz, G., Stanis, C., Thomas, O.: Appl. Surf. Sci. 73 (1993) 167. Jan, C.-H., Chen, C.-P., Chang, Y.A.: J. Appl. Phys. 73 (1993) 1168. Maex, K.: Mater. Sci. Eng. R 11 (1993) 53. Mishin, Y.M., Borchardt, G.: J. Phys. III (France) 3 (1993) 863 and 945. Yasuda, H., Nakajima, H., Koiwa, M.: Defect Diffus. Forum 95-98 (1993) 823. d'Heurle, F.M., Gas, P., Philibert, J.: Mater. Res. Soc. Symp. Proc. 343 (1994) 181. Barge, T., Gas, P., d'Heurle, F.M.: J. Mater. Res. 10 (1995) 1134. Cockeram, B., Wang, G.: Thin Solid Films 269 (1995) 57. Gas, P., d'Heurle, F.M., in: Properties of Metal Silicides, Maex, K., van Rossum, M. (eds.), IEE, London: IEE, 1995, p. 279; Gas, P., Barge, T., d'Heurle, F.M.: same p. 293; Gas, P., Thomas, O., d'Heurle, F.M.: same p. 298. Gülpen, J. H., Thesis, Eindhoven: University of Technology, 1995. d'Heurle, F.M., Gas, P., Philibert, J.: Solid State Phenomena 5 (1995) 1707. Maex, K., van Rossum, M. (eds): Properties of Metal Silicides, London, IEE, 1995. Zhang, S.L., d'Heurle, F.M.: Thin Solid Films 256 (1995) 155. Colgan, E., d'Heurle, F.M.: J. Appl. Phys. 79 (1996) 4087. Clevenger, L.A., Cabral, C., Roy, R.A., Lavoie, C., Viswanathan, R., Saenger, K.L., JordanSweet, J., Morales, G., Ludwig, K.L., Stephenson, G.B.: Mater. Res. Soc. Symp. Proc. 402 (1996) 257. Gas, P., d'Heurle, F.M.: Mater. Res. Soc. Symp. Proc. 402 (1996) 39. Gude, A., Mehrer, H.: Philos. Mag. (1996) in print. Lange, H.: Mater. Res. Soc. Symp. Proc. 402 (1996) 307. Pisch, A., Cardenas, J., Svensson, B.G., Petersson, C.S.: Mater. Soc. Symp. Proc. 402 (1996) 51. Zaring, C., Pisch, A., Cardenas, J., Gas, P., Svensson, B.G.: J. Appl. Phys. 80 (1996) 2742.
Landolt -Börnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-1
3 Diffusion in compound semiconductors M.B. DUTT AND B.L. SHARMA
3.1 Introduction Although there exist more than 150 compound semiconductors whose physico-chemical, electrical and optical properties are known, but due to technological considerations the extensive diffusion studies of only one and a half dozen binary compounds are reported in literature [91S]. Many of the compound semiconductors have not only acquired unique place in optoelectronic device technology but have also become a firm contender for the high performance market in both digital and microwave areas. In addition, availability of a large number of II-VI and III-V ternary and quaternary alloys have allowed to bridge the gap of properties existing between these compound semiconductors and have thus paved the way for new device structures. Since diffusion plays directly or indirectly a crucial role in the formation of device structures and in the epitaxial growth, the diffusion studies have continued to arise considerable interest among the reserchers. It is still the front runner for creation of deep junctions and, inspite of ion implantation being an alternate approach, the role of diffusion in it [87S, 88G] is equally important. In compound semiconductors, a variety of native point defects (e.g. vacancies, interstitials, antisites) are present. In addition to these , foreign impurities also introduce defects by association with native defects or by occupying interstitial sites. The presence of all these native defects and their complexes and dominance of any one of them depend upon the deviation from stoichiometry during crystal or epitaxial growth and are influenced greatly by the temperature and partical over-pressure of the constituents during diffusion. It is mainly due to these reasons and the fact that all these above mentioned defects may also take various charge states that the diffusion in compound semiconductors (unlike in Si and Ge) are highly dependent on experimental conditions. Diffusion coefficients under different experimental conditions, however, have different theoretical and practical interest. For example, a study of the dependence of diffusion coefficient on component vapour pressure provides information on defect mechanisms for diffusion [88S1] whereas the information about diffusion coefficients obtained by using various types of diffusion sources and systems [89S1] may be important in the formation of junctions under different experimental conditions. In the past, several excellent reviews dealing with diffusion in III-V [68K1, 70S, 75C1, 78W, 89S1] and II-VI [67W1, 67W2, 68Y1, 70S, 73S2, 82H1, 89S2] compound semiconductors have been reported in literature. Here in this chapter an attempt is made not only to consolidate all the information available in them but also to up-date the experimental diffusivity data and understanding of diffusion processes in these compound semiconductors and their alloys. The scanty information available about diffusion in IV-VI and some other compound semiconductors are also included here. In order to make this review selfconsistent, the relevant theoretical background of diffusion, the experimental methods used for diffusion and the techniques used to evaluate diffusion profiles and diffusion coefficients are also presented mainly in tabular form in the text.
Landolt -B { rnst ein New Series III/33A
3-2
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.2 Use of tables In the tables all measurements are reported wherever possible in terms of pre-exponential factor D0 and activation energy Q. SI units are used for these values in the tables. Since in semiconductor literature activation energy is generally reported in eV, a conversion factor given below has to be used for these values to express them in eV. 1 eV = 96.485 kJ mol−1 and 1 kJ mol−1 = 0.0104 eV In a number of cases multiple branches are observed in the experimental concentration profiles of constant source diffusion in compound semiconductors. The erfc function may, however, be fitted with each branch indicating more than one diffusion mechanism prevailing in such cases. In the tables D0 and Q values generally observed for two branches are referred to as slow(s) and fast(f). For non cubic semiconductor crystals where anisotropy in diffusion coefficients is reported, the D0 and Q values along and perpendicular to c-axis is given as for D and DA. Because of the variety and complexity of the nature of the experimental conditions and methods in compound semiconductors, it is not always possible to provide all the details in the tables. The readers are, therefore, advised to refer to the original literature carefully before using these values. __
3.3 Experimental methods A large number of experimental methods are used to study diffusion and to determine diffusion coeffcients. All these methods require a suitable source and a diffusion system [70S, 89S1]. The systems employed for diffusion are broadly divided into two groups, namely, closed-tube and open-tube. Depending on the constraints imposed by diffusion sources and ambients, both these type of systems are used to carry out diffusion in compound semiconductors. For example, the closed-tube systems are widely used for diffusing radioactive tracers due to minimal radioactive contamination during experimentation while open-tube systems, being capable of easily controlling and varying diffusion ambients and handling more than one specimen at a time, are generally preferred for diffusing impurities in semiconductor industry. The most widely used methods for determining diffusion coefficients in compound semiconductors employ sources containing radioactive isotopes and, therefore, prefer closed-tube systems. Although results obtained by using them are the least ambiguous and easiest to interpret, but it is not always possible to find a suitable isotope whose half-life is neither too long nor too short. In addition, the conditions used for determining these parameters are seldom true representative of those encountered in fabricating device structures. The typical type of sources widely used are listed in Table 1. As can be seen from this table, the impurity can be presented to a semiconductor specimen for diffusion in a number of ways and as solid, liquid and gaseous sources. The major advantages and disadvantages are also briefly mentioned in this table. As it is not possible to introduce all impurities into semiconductors by thermal diffusion, the predeposition step by ion implantation prior to actual diffusion can be used as an alternative to diffusion sources. This technique often requires an additional step between predeposition and diffusion to repair the disorder and damage created by ion implantation in the crystal.
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Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-3
Table 1 Type of sources 1. 'Paint-on' sources
2. 'Spin-on' sources
3. CVD sources
4. High vapour pressure solid sources
Lando lt -B { rnst ein New Series III/33A
Relevant information (i)
Diffusion impurities coated on surface either by vacuum evaporation, electro or electroless plating, painting or spraying.
(ii)
Used for studying diffusion of certain impurities like Au, Ag, Cu, Ni, etc. and for many radioactive tracer studies [70S].
(iii)
Closed-tube systems generally used.
(iv)
Considerable surface damage and poor control of surface concentration.
(i)
Modification of ‘paint-on’ source. It (as an emulsion) normally consists of a mixture of diffusant salt, film former, a reactive component and a solvent [81N, 81A4, 84A]. Diffusion deposition by spinning.
(ii)
These sources not only improve reproducibility and achieve better control of concentration but also act as a protector of specimen surface against decomposition.
(iii)
Almost any dopant used for compound semiconductors have such sources commercially available.
(iv)
Both closed-tube and open-tube systems can be used.
(v)
An additional cap layer of undoped silica or of phosphosilicate glass is deposited to prevent out-diffusion of the diffusant.
(i)
Chemical vapour deposited (CVD) sources, in the form of a film, consist of a diffusant oxide in an inert binder such as silica, are deposited by simultaneous oxidation of gaseous Si compound and a diffusant alkyl or hydride [75Y, 82F2].
(ii)
Such sources allow a precise control of diffusion and preserve surfaces during diffusion.
(i)
Solid sources either in elemental form or as a mixture or compound having high diffusant vapour pressure at elevated temperatures are used as external vapour source for studying diffusion.
(ii)
To avoid the surface decomposition such sources must be a combination of the diffusant and one or more constituents of the compound semiconductor [68C1, 82P2].
(iii)
Main disadvantage with these sources is the difficuly in controlling the diffusant content in the gas-phase surrounding the specimen.
3-4
3 Diffusion in compound semiconductors
Type of sources
[Ref. p. 3-70
Relevant information
4. High vapour pressure solid sources (cont.)
(iv)
Widely used as a constant source for diffusion both in closed and open tube systems [70S, 82P1].
5. High vapour pressure liquid sources
(i)
In this case a carrier gas is bubbled thruogh or passed over the liquid source to take source molecules which decompose or react with the gas at elevated temperatures to provide a secondary vapour source for diffusion.
(ii)
Easy to control the surface concentration by adjusting the amount of diffusant transported to the specimen by the help of the bubbler temperature and flow of the gas through it.
(iii)
Diffusion process can be conveniently initiated or terminated.
(iv)
Used with open tube systems.
6. LPE type liquid sources (i)
Diffusion source consisting of the diffusant and specimen material dissolved in a solvent is placed in close proximity in a modified graphite liquid phase epitaxy (LPE) boat configurations [82P1, 83Y2].
(ii)
Such sources allow a precise control of diffusion and preserve surfaces during diffusion.
(iii)
Difficulties may arise in maintaining a critical balance between epitaxial growth and etching of the specimen.
(i)
Dilute gaseous diffusant sources are either connected directly or diluted in-situ by mixing with carrier gases at the entry end of an open tube system [89S1].
(ii)
Expensive approach of diffusing impurities which often requires elaborate arrangements and precautions due to toxic and/or explosive nature of gaseous sources and carrier gases.
7. Gaseous sources
3.4 Evaluation techniques Various analytical solutions of diffusion equations (refer chapter 1) can be used to evaluate diffusion coefficients in compound semiconductors. In addition to the analytical solutions considered by Boltaks [63B1] and Sharma [70S] the analytical solutions of some other cases such as drive-in diffusion after deposition of a dielectric encapsulating film at lower temperature on the surface of the specimen having known amount of diffusing atoms in a shallow region close to surface [74D2, 77H], constant source diffusion into semi-infinite specimen through a finite layer of dielectric film or an epitaxial layer [70S, 82S1], two-step diffusion (first step consisting of diffusing small quantity of impurity into extremely thin layer of specimen from constant source while the second amounting to drive-in at higher temperature) [83G1], diffusion dominated redistribution of implanted atoms during annealing or drive-in diffusion [84G1] and out-diffu-
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-5
sion of a ternary constituent of a semi-infinite semiconductor specimen with rate limitation at the surface [85O] are also reported in literature. A large number of evaluation techniques have been used to investigate diffusion in compound semiconductors. The selection of an appropriate technique is dictated by the nature of the investigation and by the expertise of the investigator. The technique used to determine diffusion profiles can broadly be divided into three groups, namely, radioactive tracer, electrical and non-electrical techniques [70S, 86R, 87S]. The first group includes the most widely used technique in which the radioactive isotope diffused specimen is sectioned perpendicular to the concentration gradient and radioactivity in each section or that remaining on the specimen after each section is counted. The thickness of the removed layer after each section is determined either directly by measuring the remaining thickness of the specimen by optomechanical indicators, dial gauges, etc or indirectly by successive weighings. Besides radioactive tracer techniques for obtaining such information, non-electrical techniques (e.g. secondary ion mass spectroscopy, Rutherford back scattering, high resolution Auger spectroscopy, ion induced x-ray analysis, etc.) are also available for obtaining the impurity-atom distributions in semiconductors. Diffusion studies in semiconductors are generally initiated to obtain useful electrical information about the doped layers and/or junctions created by diffusion. The electrical techniques utilize the appreciable change in some electrical properties with doping concentration to determine the electrical depth profile (or more precisely the majority carrier distribution) of the diffused layer. Among the reported electrical techniques, capacitance-voltage and Hall measurements are the two most widely used techniques to determine the doping profiles in compound semiconductors. In the former, the differential capacitance of a p-n junction or Schottky diode is measured as a function of reverse bias up to a bias just below breakdown [69C, 72M2, 75W]. In fact, commercial profilers are now available to process the signals and automatically plot the doping profile from zero bias depletion width to the depletion depth at which reverse breakdown takes place. The depth distribution imposed by reverse breakdown has been overcome by Ambridge and coworkers [75A, 79A, 79S] by combining insitu controlled dissolution (electrochemically) of the specimen with capacitance-voltage measurements. This has been achieved by using an electrolyte-semiconductor contact in place of liquid mercury contact in a commercial profiler. With the latter, namely, Hall effect measurement technique, it is possible to obtain both the carrier concentration as well as its mobility. In fact, with four-probe technique reported by Van der Pauw [58V] combined with etching-off of thin layers of the specimen one after the other [68A, 70J, 71A1, 74S1], it is possible to obtain carrier concentration and mobility profiles. The layer removal by anodic oxidation or chemical etching are discussed at length with this technique by Ryssel and Ruge [86R]. Most of the techniques used for obtaining diffusion profiles are destructive in nature (i.e. they use layer removal method for obtaining depth profiles). The problems encountered in the study of diffusion in compound semiconductors are so varied that one or another of these techniques will be better suited or will be the only one useable under given conditions. For example, van der Pauw Hall effect and sheet resistivity measurement technique in conjunction with layer removal chemical etching is the only one suitable to analyse electrical behaviour of doped layers (i.e. for obtaining carrier concentration and mobility profiles) while SIMS and radioactive techniques are the two most useful techniques to determine the impurity-atom distribution and diffusion coefficients in compound semiconductors. For interdiffusion studies in the vicinity of the interface of heterostructures and monitoring disordering in super lattice structures, the AES profiling technique along with SIMS measurements may find wider application. In addition to those techniques mentioned above some other techniques based on luminescence [80L, 82L], elctroluminescence [87K], cathodoluminescence [83C1], direct optical spectroscopy and light-stimulated spectroscopy [89T2], transmission electron microscopy [85B2], X-ray diffraction analysis [77B2, 78B1], etc. can also be used in special cases. Such techniques used by some workers will be referred while discussing diffusion data of impurities in compound semiconductors.
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3-6
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.5 Diffusion in III-V compounds and their ternary alloys Besides being very interesting compounds from scientific and technological points of view, it is comparatively easy to form junctions in III-V compound semiconductors. Since these compounds are covalently bonded with an ionic contribution of only few percent, various impurities are available to form reliable junctions in them by diffusion. It can be seen from the reported ionization/binding energies of group II, IV and VI impurities in some of these semiconductors (refer Table 2) that number of diffusants can be used for doping III-V compound semiconductors. In order to have an insight into diffusion mechanisms of impurities and analyze their effects on electrical and optical properties, it is necessary to have an understanding of defect equilibria and self-diffusion in these compounds. The defect equilibria in both chemically pure and impure compounds are discussed at length by Kendall [68K1] and the reported self-diffusion studies along with information pertaining to impurity-diffusion is presented here.
3.5.1 Self-diffusion In general, self-diffusion in compound semiconductors depends on stoichiometry and the types and concentrations of defects at diffusion temperature. Due to pronounced tendency of III-V compounds to combine in nearly exact stoichiometric proportion, the native defect concentrations are very small and self-diffusion in them depends on the defects produced and/or present near the surface during diffusion. The selfdiffusion studies reported in literature are limited to AlSb, GaAs, GaSb, InAs, InP and InSb. Almost all the self-diffusion data summarized in Table 3 are obtained by using radioactive tracer technique and appear to follow normal Arrhenius relationship. A close look at self-diffusion studies [81P1, 83P1], however, show the dependence of self-diffusion coefficients on volatile component pressure and/or on the types and concentration of defects present at diffusion temperatures. In order to understand the mechanisms which are involved in self-diffusion in III-V compound semiconductors, the diffusion of Ga and As in GaAs are briefly discussed here. As can be seen from Table 3, the only reported self-diffusion studies are by Goldstein [61G1] and Palfrey et al. [81P1, 83P1]. A comparison of their self-diffusion data (refer Fig. 1) indicates that As has a lower diffusion rate in GaAs than Ga. The diffusion coefficients of As, as calculated from D0 and Q values (refer Table 3) estimated from isolated data points of Harper and Kendall [in 68K1] are also plotted in Fig. 1. Their D values for As are few orders of magnitude higher than those obtained by Palfrey et al. [83P1]. Interestingly their estimated activation energy value compares well with the predicted value of Potts and Pearson [66P2] and the value obtained by Palfrey et al. [83P1] at an As2 pressure of 0.75 atm. Since earlier works of Goldstein and of Harper and Kendall were associated with formidable experimental difficulties, the data based on the work of Palfrey and coworkers appear to be reliable. However, it must be noted that for rigorous evaluation of the diffusion of Ga or As in GaAs, all possible diffusion mechanisms, such as various interstitial mechanisms and diffusion via vacancies on Ga and As sub-lattices should be considered. A comparison of different self-diffusion data of Ga and Sb is shown in Fig. 2 [84W2].
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-7
Table 2. Ionization/binding energies of various doping impurities in III-V compounds (1 kJmol−1 = 0.0104 eV) (d) donor and its ionization/binding energy (Ec−Ed)
(a) acceptor and its ionization/binding energy (Ea−Ev)
Ionization/binding energy [kJmol−1] GaAs
GaP
Doping 73M2, 91M 73M2, impurity 91M
GaSb
InAs
InP
InSb
AlAs
AlSb
70S, 91M
70S, 91M
72W1, 77B1, 91M
70S, 91M
91M
70S
Group II Be
(a) 2.89
(a) 5.40
(a) -
(a)
(a) 2.89
(a)
(a)
Mg
(a) 2.89
(a) 5.20
(a)
(a) <0.48 (a) 2.89
(a)
(d)? 4.82
(a)
Zn
(a) 2.31...2.99
(a) 6.17
(a) 5.78
(a) <0.48 (a) 4.53
(a) 0.723
(d)? 5.78
(a)
Cd
(a) 2.02...2.89
(a) 9.35
(a)
(a) <0.48 (a) 5.40
(a) 0.82
(a) 1.83
(a) 3.95
(a) 2.51
(a) 5.20
(a)
Group IV C
Si
Ge
Sn
(a) 3.95
(d) (d) 7.90 0.193...0.559
(a) 0.91
(a) 2.41...2.89
(a) 19.56
(a) 1.25...1.64
(d) 0.568
(d) 19.66 (a) 0.92
(a) 2.89...6.74
(a) 2.89
(d) 0.559
(d) 6.26
(a)
(a) 1.93
(d) shallow
(a)
(d) 6.74
(a)
(a) 1.35
(d) shallow
(a) 0.867
(a)
(d)
(d,a)
(a) 20.23 (a)
(a) 0.96
(d) shallow
(a) 19.27 Pb
(a) 11.56
(d)
Group VI S
(d) 0.59
(d) 10.02 (d) 7.23
(d) ~ zero
(d) shallow
(d) ~ zero
(d)
Se
(d) 0.57
(d) 9.83
(d) ~ zero
(d) shallow
(d) ~ zero
(d) 15.42
(d) <7.71 (d) ~zero
(d) shallow
(d) ~ zero
(d) 6.55
(d) ~zero (d) 19.27
Te
(d) 2.89
Lando lt -B { rnst ein New Series III/33A
(d) 8.62
3-8
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 3. Self-diffusion and impurity diffusion data of group III and V impurities in III-V compounds (1 kJmol−1 = 0.0104 eV) Diffusant
D0 Q T [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Al
2 . 100
181.1
843-893
Estimated from reactive diffusion results
59P
Sb
1 . 100
163.8
843-893
X-ray measurements
59P
Ga
4 . 10−5 1 . 107
250.5
1298-1373 Radiotracer
1
81P1
539.6
1398-1503 Radiotracer
1
61G1
As
5.5 . 10−4
289.1
1273-1348 Radiotracer, As pressure dependence
1
83P1
7 . 10−1
308.3
Radiotracer
1
68K1
4 . 1021 D = 7.10−11
982.8
1398-1503 Radiotracer
61G1
1273
64K1
Fig. Ref.
AlSb
GaAs
In P
D=
10−12-10−10
Radiotracer
1073-1423 Reflectance measurements
76J1
GaSb Ga
Sb
In
3.2 . 103
303.5 D = (1.09 - 60).10−16
931-973
Radiotracer
2
57E
867-973
For Sb-rich samples, Radiotracer
2
84W2
D = (3.75 - 264).10−17 3.4 . 104 332.4
867-971
For Ga-rich samples, Radiotracer
2
84W2
931-973
Radiotracer
2
57E
D = (5.34 - 370).10−17 D = (8.01 - 1620).10−18
867-973
For Sb-rich samples, Radiotracer
2
84W2
867-971
For Ga-rich samples, Radiotracer
2
84W2
1.2.10−7
51.0
593-923
Radiotracer
60B2
1 . 105 7 . 1010
370.9
1103-1263 Radiotracer
61G1
544.4
1173-1273 Radiotracer
61G1
6 . 105 3 . 107
385.4
Radiotracer
69K1
428.8
Radiotracer
69K1
5 . 10−2 1.8. 1013
175.4
Radiotracer
57E
414.3
748-790
Radiotracer
69K2
6 . 10−7 5 . 10−2
139.7
673-773
Radiotracer
94R
186.9
751-793
Radiotracer
57E
3.1 . 1013
414.3
748-790
Radiotracer
69K2
5.35 . 10−4
184.0
673-773
Radiotracer
94R
InP In P
InAs In As
InSb In
Sb
751-793
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-9
3.5.2 Diffusion of shallow donors The elements which are commonly used for obtaining n-type layers, by diffusion or ion implantation, in III-V compound semiconductors belong to group IV and VI of the periodic table. The reported diffusion data along with solid solubilities of group IV and VI impurities are listed in Table 4. 3.5.2.1 Group IV impurities As can be seen from Table 2, several group IV elements behave as amphoteric impurities in III-V compounds. Since they can occupy both group III and group V sites and can act as donor or acceptor, they pose unusual difficulties in predicting diffusion and dopant behaviour in these compound semiconductors. For example, it is observed that Si introduced in GaAs during crystal/expitaxial growth, ion implantation or diffusion tends to behave as amphoteric impurity depending on processing history and/or ambient conditions. Eventhough ion implantation is currently being used to form Si-doped n-type layers, a number of Si diffusion studies in GaAs [61V, 65A1, 71L1, 84G4, 87D2, 90L1] have been reported in literature. Since diffusion also takes place during annealing of implanted layers [77L1, 81A3, 83O], the continued interest in the studies relating to Si diffusion in GaAs and extent of compensation by Si in GaAs is quite relevant. Various mechanisms are proposed to explain the diffusion of Si in GaAs. Kahen [89K] proposed that the effective diffusion coefficient of Si in GaAs, Deff can be expressed as Deff = Dp[1 − (1+4[Si]/Kp)−1/2] ,
(3.6)
where Dp is the diffusion constant of Si Ga − VGa pairs, Kp is the equilibrium constant for pair diffusion and [Si] is the total concentration. By using two adjusting parameters Dp and Kp, Kahen was able to predict the then available diffusion data [84G4, 85G3, 85K1]. Later, Matsushita et al. [93M2] have investigated diffusion and doping of Si into GaAs under different conditions and found their results consistent with the model proposed by Kahen. Since it is desirable to relate the diffusion sources and conditions to ternary phase diagrams for better understanding of impurity diffusion mechanisms, Lee et al. [90L1] have lately investigated diffusion of Si in GaAs using sources from different ternary triangle regions of the Si-Ga-As ternary phase diagram. Since such sources precisely control the chemical potential of all three components in the ambient vapour under constant temperature conditions, the sources used in this study were classified as As-rich source (Si-SiAs-GaAs and SiAs-SiAs2-GaAs) and Ga-rich source (Ga-Si-GaAs). The Si concentration-depth diffusion profiles measured by SIMS differed significantly for different sources. They observed that Garich source incorporated Si as net acceptor with concentration independent diffusion coefficient while diffusion from As-rich sources resulted in donor diffusion for Si with concentration-dependent diffusion behaviour. The concentration-dependent diffusion coefficient of donor Si in the case of As-rich source diffusion were related to the net ionized donor concentration, showing three different regimes: intrinsic, intermediate and saturation regime. They found that diffusion coefficients of Si were constant in intrinsic regime, proportional to n in the intermediate regime and again constant in saturation regime. The diffusion coefficient versus 1/T in the temperature range of 1073 K to 1273 K for saturation regime using Si-SiAs0 0 GaAs source is shown in Fig. 3. They have proposed a VAs or VGa model for acceptor Si diffusion and a 0 VGa and/or VGa mechanism for intrinsic regime and a VGa related mechanism for the extrinsic and saturation regimes for donor Si diffusion. Among the group IV elements, apart from diffusion of Ge in GaAs (refer Table 4) an interesting aspect of its diffusion is the interdiffusion at the GaAs-Ge or Ge-GaAs interface at growth temperatures. In fact, diffusion at the interface places strict limits on growth temperatures during heteroepitaxy and it is often necessary to use a growth temperature which is significantly less than ideal in order to control diffusion at the interface [91A]. Several investigators have studied diffusion in Ge/GaAs heterostructure systems [80M4, 81S3, 82B2, 90S4, 91A]. Bauer and Mikkelson [82B2] reported photoemisson spectroscopic
Lando lt -B { rnst ein New Series III/33A
3-10
3 Diffusion in compound semiconductors
[Ref. p. 3-70
evidence of As segregating on the surface of Ge grown on GaAs at a growth temperature of 593 K and a low growth rate. They indicated that As remained on the surface and was not incorporated in the Ge film. Strite et al. [90S4] used X-ray photoemission spectroscopy to study both As and Ga out-diffusion into epitaxial Ge as well as Ge out-diffusion into epitaxial GaAs. These studies in conjunction with room temperature I-V measurements [90S5] and SIMS measurements [91A] carried out on devices indicated that diffusion which was occuring was primarily out-diffusion from the substrate material (i.e. for GaAs/Ge, Ge and Ga and As for Ge/GaAs). They also observed that Ge/GaAs devices showed various degrees of degradation when annealed upto 1073 K probably due to interdiffusion but if several monolayers of pseudomorphic Si were grown at the Ge/GaAs interface then there was significant reduction of diffusion both during growth and annealing upto 1073 K. 3.5.2.2 Group VI impurities Among the elements of group VI, S, Se and Te have been known to behave as shallow donors in III-V compounds (refer Table 2). In spite of this, the low donor efficiency and possibility of forming compounds such as Ga2Se3 and Ga2Te3 at higher concentrations have limited the use of Se and Te to form n-type GaAs layers by diffusion. Sulphur is the element of this group whose diffusion has been extensively studied in III-V compounds (refer Table 4). The diffusion coefficients of S in GaAs as a function of temperature obtained by various workers [61V, 61G1, 65F3, 68K1, 70Y, 74M1, 85P3] are shown in Fig. 4. The reason for their differences is primarily due to varied experimental conditions. Young and Pearson [70Y] have studied diffusion of S in GaAs as a function of As overpressure by using radioactive tracer technique in the temperature range of 1273 to 1473 K. The variation of the S diffusion coefficient with As overpressure at 1273 K and 1403 K are shown in Fig. 5. It can be seen from this figure that D increases with As overpressure upto about 0.5 atm and becomes independent of pressure beyond this. Young and Pearson explained this behaviour on the basis of the assumption that S existed in two + + forms, namely, a donor on As site, S As , and a complex, (VGa S As VGa). Diffusion, at low As overpressure, + was suggested to occur via vacancies on As sub-lattice and S being in the form of immobile S As gave rise to a low effective diffusion coefficient while an increase in As overpressure resulted in a decrease in V As + and an increase in VGa and diffusion via Ga divacancies (VGaVGa) dominated. This caused more S As to become mobile and showed an increase in diffusion coefficient and, finally at some high As pressure, + diffusion coefficient saturated as all of the S in the form (VGa S As VGa) became mobile. Diffusion profiles similar to Young and Pearson were also obtained by Tuck and Powell [81T2]. On the basis of the shape of profiles and their change with As overpressure, Zahari and Tuck [82Z] offered a different interpretation of S diffusion in GaAs. The salient features of their model are discussed in [85T]. From As pressure dependence of S, it is, however, clear that diffusion based on ternary phase diagram considerations will be necessary to interpret the diffusion behaviour and assignment of diffusion coefficients in GaAs. As regard Se and Te of this group, many studies to investigate the behaviour or these dopants in GaAs during growth of Czochralski ingots, during epitaxy and after ion implantation have been reported in literature, but very little have been said about their diffusion in this compound. Some workers [74M2, 74H2, 68K2, 67A1] have observed existence of Te precipitates and compounds such as Ga2Se3 and Ga2Te3 in Te-doped GaAs at high concentrations while others [71M2, 71L3, 79H], in their inability to observe such formation, preferred to explain their behaviour on the basis of the formation of complex defects of vacancies and impurity atoms. While studying the diffusion of Te in GaAs, Yeh [64Y] observed that a film of SiO (200-300 nm) was generally sufficient to avoid formation of Ga2Te3 on or near the GaAs surface during diffusion. Apart from diffusion of Se or Te through protecting layer deposited onto the surface of GaAs, compound formation on GaAs surface during diffusion can be avoided either by using a small concentration of diffusant in the gas phase [76K1] or by diffusion after ion implantation [75Z]. Morkoc et al. [80M5] have investigated the out-diffusion of Te from Te-doped GaAs substrate into undoped epilayers by SIMS and estimated the diffusion coefficient of Te to be 3.10−18 m2s−1 at 855 K which is rather high and could be explained, in the absence of thermal diffusion data at relatively lower Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-11
temperatures, as due to different diffusion mechanism operating at and near the interface during growth and/or annealing compared to usual thermal diffusion. Table 4. Diffusion data and solubility of group IV and VI impurities in III-V compound semiconductors. (1 kJmol−1 = 0.0104 eV) D0 Q T [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Fig. Ref.
Solubility [106 m−3]
Ref.
1.9.1019(1373 K)
91M
GaAs C
D = 1.04.10−16
1098
Si
0.11
240.9
1123-1323 SIMS, Hall
1.7
271.7
1073-1273 SIMS, C-V, Hall
211.0
1133-1213 SIMS, C-V, Hall
93M2
346.9
1373-1473 Equilibrium As pressure
66S3 > 2.1018 (melt growth)
3.10−5
178.3
1373-1473 1.5 atm of As overpressure
66S3
1.10−6 1.6.10−5
173.4
1273-11473 As overpressure
69L
198.5
923-1073
84S1
3.5
318.0
1123-1373 Radiotracer; undoped sample
78T1 ~ 1019 (1073 K)
1.10−5 3.8.10−2
192.7
1073-1273 Radiotracer
75Y
260.2
1173-1373 Radiotracer, junction depth
63F
6.10−4
240.9
1333-1473 Radiotracer
61G1
O
2.10−3
106.0
973-1173
69R1
S
4.10−3 1.1.101
250.5
1223-1323 RTA; C-V, Hall
4
85P3 1.6.1018 (1173 K)
284.2
1023-1173 Electrical
4
74M1
1.85.10−2
250.5
1173-1473 Radiotracer; high As overpressure
5
70Y
1.6.10−5
157.1
973-1273
4
68K1
2.6.10−5
179.2
1173-1373 p-n stain etching
4
65F3
Ge 7.5.10−5
Sn
SIMS
89C
3
SIMS
Mass spectrometry
Radiotracer, incremental sheet resistance
84G4 > 4.7.1018 (melt growth)
91M
90L1 ~ 1020 surface (1173 K)
90L1
91M
73P
91M
(cont.)
Lando lt -B { rnst ein New Series III/33A
3-12
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 4 (cont.) D0 Q T [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Fig. Ref.
Solubility [106 m−3]
Ref.
GaAs (cont.) S 4.103
389.3
1273-1473 Radioactive
1.2.10−4
173.4
1173-1348 p-n; 2 atm As overpressure
61V
400.8
1298-1473 Radiotracer
61G1 9.5.1023 exp(−1.23/kT) 91M
1273
78L4
Se
3.103 D ~ 2.8.10
Te
−15
337.2 1.5.10−1 −13 . D = 1 10 - 2.10−12
Post implant anneal, SIMS
4
61G1
1273-1423
74K
1273, 1373
68O
max. 4.1019 (1273 K) max. 1.1020
71C 73K1
(melt growth) D ~ 3.10−14
853
Out-diffusion; SIMS
80M5
GaP Ge
1173-1273 Radiotracer
75S1
452.9
1373-1573 Radiotracer
70Y
1.3.10−5
106.0
773-923
Radiotracer; p-type sample
75U
1.10−2
154.2
773-923
Radiotracer; n-type sample
75U
2.4.10−5
77.08
593-923
Radiotracer
60B2
Se
D~2.4.10−13-1.37.10−11 673-773
Radiotracer
60B2 1.5.1018 (973 K)
61H
Te
3.8.10−4
S
3.2.103
max. ~ 6.1019 (1313 K) 65T2
GaSb Sn
115.6
593-923
Radiotracer
60B2 4.1018 (973 K)
61H
112.7
873-1173
p-n junction
56S
> 1.1019
62S1
InAs Ge 3.74.10−6
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-13
Table 4 (cont.) D0 Q T [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Fig. Ref.
Solubility [106 m−3]
Ref.
62S1
InAs (cont.) Sn 1.49.10−6
112.7
873-1173
p-n junction
56S
> 1.1019
S
6.78
212.0
873-1173
p-n junction
56S
max. ~1.1021 (1173 K) 76G
Se
1.26.101
212.0
873-1173
p-n junction
56S
max ~6.1020 (1173 K) 76G
Te
3.43.10−5
123.3
873-1173
p-n junction
56S
max. ~1.1020 (1173 K) 76G
823
Etching and cathodoluminescence; out-diffusion
83C1
858-981
Hall measurements
88P1
D ~ (1-5).10−8
823
Etching and cathodoluminescence; out-diffusion
83C1
D ~ 2.10−8
823
Etching and cathodoluminescence; out-diffusion
83C1
Radiotracer
61S
InP Sn
D ~ 3.10−8
S
3.6.10−4
Se
186.9
InSb Sn
5.5.10−8
72.3
663-785
S
9.10−2
134.9
633-773
Se
1.6
180.2
653-773
C-V
69R2
Te
1.7.10−7
54.9
573-773
Radiotracer
57K
Lando lt -B { rnst ein New Series III/33A
71R
3-14
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.5.3 Diffusion of shallow acceptors Most important elements that are known to be shallow acceptors (refer Table 2) in III-V compound semiconductors are Zn and Cd. They are widely used for preparing p-n junctions in these compounds by diffusion. These two elements have also been widely used as p-type dopants, in liquid and vapour phase epitaxy but the attempt to dope with them during MBE growth has been unsuccessful [88I]. Since other two elements, namely Be and Mg, of group II are being used as p-type dopant during MBE growth and ion implantation, their diffusion in these compounds will require a fresh look in future. Typical reported diffusion data of group II impurities are tabulated in Table 5. Among all the diffusion systems investigated, so far, the most extensively studied one is Zn/GaAs. In fact, because of this and technological importance, the diffusion of Zn in GaAs is discussed here in detail. Early worker [60C2, 60G1] observed that diffusion profiles of Zn in GaAs did not correspond to well known solutions of diffusion equations and diffusion was concentration-dependent. Longini [62L] proposed an interstitial-substitutional mechanism could be used to account for the Zn/GaAs result. If one assumes that Zn diffuses by this mechanism, then the effective diffusion coefficient, Deff (Zn), can be expressed in a general form as [72B3, 73C1]
a f
Deff Zn = Di
F GH
F GH
I JK
∂N s ∂N i 1 ∂p 1 ∂rp 1 ∂p 1 ∂rp − Di N i + + Ds − Ds Ns + ∂N ∂N p ∂N rp ∂N p ∂N rp ∂N
I, JK
(3.7)
where Di is the diffusion coefficient of interstitial species and Ni its concentration, Ds and Ns are the diffusion coefficient of substitutional species and its concentration, respectively, p is the hole concentration, rp is the hole activity coefficient and N = Ni + Ns is the total Zn concentration. Considering a model in which Zn diffuses interstitially as an ionized donor Zn ir+ where r represents the charge state and can be 1 or 2 and react with Ga vacancy to form an ionized subtitutional Zn acceptor, Zn -Ga , according to the reaction Zn ir+ + VGa ¤ Zn Ga + 2h ,
(3.8)
where h is a hole. It can be seen from this that the controlling factor in Zn diffusion is the equilibrium concentration of Ga vacancies, Nv, since Zn interstitials react with them. Assuming Nv as constant throughout the crystal and applying law of mass action, Ni can be expressed as a function of Ns, Nv and pAs α as Ni =
d i
Ns rp p Nv
r +1
d i = K aT f p N s rp p
r +1
1/ α Asα
,
(3.9)
where K(T) is a function of temperature only and respresents the equilibrium constant and other releated constants associated with the reaction of Eq. (3.8) and can be 2 or 4. Eliminating Ni from Eq. (3.7) by Eq. (3.9) and assuming N = Ns = p for N < 1026 m−3, the expression for Deff(Zn) becomes for r = 1, i.e. Zn +i Deff ( Zn ) =
2 Di N s2 rp2 K (T ) p1As/ αα
F1 + N GH 2r
s p
I + D F2 + N GH 2r ∂N JK ∂rp
s
s
s
p
I, ∂N JK ∂rp
(3.10)
s
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-15
and for r = 2, i.e. Zn ++ i Deff ( Zn ) =
3 Di Ns3 rp3 K (T ) p1As/ αα
F1 + 2 N GH 3r
s
p
I + D F2 + N GH 2r ∂N JK ∂rp
s
s
s
p
I. ∂N JK ∂rp
(3.11)
s
∂rp ∂N i ∂N << Ds s , rp = 1 and = 0 , the effective diffusion ∂N ∂N ∂N coefficient Deff(Zn) ≈ 2Ds = constant and the diffusion profiles will follow an erfc type distribution. For T ≤ 1173 K and N ≤ 1025 m−3, Di
For T > 1173 K and N ≈ 1025-1026 m−3 (low Zn concentration), Di
∂rp ∂N i ∂N >> Ds s , rp = 1 and = 0, ∂N ∂N ∂N
the effective diffusion coefficient takes the form Deff (Zn) =
2 Di N 2 a K (T ) p1/ Asa
for
Zn +i
(3.12)
Deff (Zn) =
3 Di N 3 a K (T ) p1/ Asa
for
Zn ++ i
(3.13)
and
For T > 1173 K and N > 1026 m−3 (high Zn concentration), rp < 1 and
∂rp ∂N
is negative and Eq. (3.7) leads
to a decrease in Deff (Zn). Casey and co-workers [67C] have shown that the diffusion coefficient of Zn, derived by BoltzmannMatano analysis, versus Zn concentration at various temperatures indicated a concentration-squared dependence near 1025 Zn atoms m−3 in GaAs with a decrease in Deff (Zn) at higher concentrations (refer Fig. 6). This type of relationship also holds good for InAs, GaP and InP. This type of relationship was also confirmed by using an isoconcentration technique [64C2, 72K1]. By using this technique, Kadhim and Tuck [72K1] have shown (refer Fig.7) that above mentioned square law relationship is followed quite closely in the Zn concentration range of 1024-1026 m−3. Since the diffusion conditions control the Zn surface concentration and defect equilibrium of GaAs, Casey, Panish and their coworkers [73C1, 75C1] have pointed out that, if the Zn/GaAs diffusion system has to be interpreted in terms of a diffusion model, then the diffusion conditions have to be related to the Zn-Ga-As ternary phase diagram. For example, the measured concentration dependence of Deff (Zn) depends upon the diffusion conditions. That is, at very high arsenic pressures (pAs > 2 atm), Nv is so high that Ni becomes negligible and diffusion process reverts from an interstitial-substitutional one to a substitutional one, while, at low arsenic pressures and at lower diffusion temperatures, interstitial diffusion becomes predominant. Mehrer, Stolwijk and co-workers [90L2, 92L, 93J, 95B2] have recently studied diffusion of Zn in semi-insulating GaAs in presence and absence of As source. The fast diffusion of Zn in their recent study [95B2] of Zn diffusion in GaAs under As ambient has been attributed to a minor fraction of Zn interstitials changing over to Ga sites thereby producing Ga interstitials. This was not observed in their earlier studies due to generation of diffusion induced microstructural defects which acted as sinks for interstitial Ga. Apart from As vapour ambient, they have recently studied the influence of P and Sb vapour ambients on diffusion of Zn in GaAs [95B1]. Algora et al. [90A2] have studied Zn diffusion in GaAs using a liquid phase epitaxy technique from an isothermal liquid solution of Ga-As-Zn and observed that Zn concentration in solid depended on square root of Zn atomic fraction present in the liquid. They found by SIMS measurements that Deff (Zn) varied as D = 2.9 . 10−67 N3.05 at 1123 K indicating that diffusing Zn interstitials are Zni++. Lando lt -B { rnst ein New Series III/33A
3-16
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Apart from the model discussed above, Gosele and Morehead [81G] proposed a different mechanism for Zn diffusion in GaAs and described it as a ‘kick-out’ mechanism. According to this, the diffusing Zn interstitial occupies the Ga site by pushing the Ga atom off its site to become a Ga interstitial. Equation (3.8) in this case is replaced by: Zn +i + Ga Ga ¤ Zn Ga + Ga i + 2h .
(3.14)
Van Ommen [83V1] compared the two above-mentioned approaches by fitting numerically calculated profiles to the experimental results of Tuck and Kadhim [72T2] and Ting and Pearson [71T] and found that the ‘kick-out’ approch provided a markedly better fit to the experimental profiles. Further evidence in support of the ‘kick-out’ model has come from metallurgical studies of Zn diffused samples [82H2, 67B1, 66S1]. Shaw [84S3] has pointed out that diffusion via singly ionized donor associate (ZnGa VAs)+ gives rise to the same diffusion behaviour of Zn in GaAs as do models suggested by Longini [62L] and Gosele and Morehead [81G]. In conclusion it can be said that, although most of the experimental findings of Zn diffusion in GaAs can be explained on the basis of vacancy model, the diffusion mechanism of Zn in GaAs is still far from being fully understood as there does not appear to be any decisive means of distinguishing between the proposed models. Device processing considerations require a relatively low temperature open-tube diffusion with minimum surface degradation. Several approaches have been used for this purpose. Reynolds et al. [88R] used gaseous metalorganic sources to provide independent control of As and Zn vapour pressures for diffusion of Zn in GaAs. Although this system provided good control of diffusion parameters but it required complex gas handling system. Other alternative open tube sources were spin-on glasses [87A] and CVD films [82F2, 80S]. These techniques produced good diffussion profiles but required tight control of film deposition conditions. Another approach used was to utilize a permeable protection layer which allowed Zn diffusion in GaAs while reduced the out-diffusion of As[82E, 90B]. Edwards and Rodel [82E] used rf sputtered very thin (20-70Å) SiO2 protection layer on GaAs to study the diffusion of Zn in GaAs at 873 K to 973 K from elemental Zn source. Unfortunately the diffusion profiles and junction depths in this case were very sensitive to both SiO2 thickness and deposition parameter. Bisberg et al [90B] have investigated the diffusion of Zn in GaAs and ternary III-V epilayers using electron beam deposited yttriastabilized cubic zirconia permeable protection layer and elemental Zn or a GaAs/Zn2As3 mixture as diffusion source in the temperature range of 600 to 750oC. The diffusion coefficients in this temperature range were found to lie between 3.10−17 m2/s and 4.10−15 m2/s and the results illustrated the effectiveness of this protective layer as a barrier to out-diffusion of Ga and As form GaAs at temperatures upto 973 K. Because of the complex nature of the dependence of Zn diffusion coefficient on the Zn concentration, As overpressure and experimental conditions, it is difficult to select any particular data from the reported investigations for listing in Table 5. However, D0 and Q values of some earlier workers are included in this table for the sake of comparison. It can be seen from Table 5 that there exists large variation in activation energies. In fact, the activation energies for Zn diffusion in GaAs, reported in literature are found to vary from 57.81 to 289.1 kJ mol−1. In addition to diffusion of Zn in GaAs, its diffusion in nearly all other III-V compounds (refer Table 5) are reported in literature. A concentration dependent behaviour of Zn in GaP [64C1, 73L, 77T2], GaSb [72B2, 74D1], InAs [67B2, 67M], InSb [64G1, 68K1, 70M] and AlSb [69S1] has been observed. The conclusions of these workers indicate that diffusion mechanism in these compounds is similar to that of Zn in GaAs. However, Zn appears to diffuse differently in InP. Kundukhov et al [67K2] and Hooper et al [74H1] have reported a large discrepancy between concentration of holes and that of Zn atoms in Zndiffused InP. These findings were verified by Tuck and Zahari [77T3] from homogeneous Zn-doped InP specimens prepared by diffusing radioactive Zn for very long diffusion times. They found that at the highest concentrations the Zn atoms exceeded holes by almost two orders of magnitude. This suggested that most of the Zn exists in some form other than a simple acceptor on In site. Tuck and Hooper [75T] studied diffusion of radioactive Zn in InP over a wide range of experimental conditions in the temperature range 873-1173 K. Based on their observations, they proposed the following mechanism for Zn diffusion in InP. Most of the Zn occurs in the InP in the form of a complex (VPZnInVP), Zn atoms also occupy In Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-17
site, giving rise to the observed p type conductivity and, in addition, Zn atoms exist in fast diffusing insterstitial state. Yamada et al [83Y1] have investigated the diffusion of Zn in n-type undoped and Sdoped InP in the temperature range of 773-973 K. SIMS and electrical measurements revealed that there existed two fronts in specimens having electron carrier concentrations less than 5.1022 m−3 while a single front in other specimens. Recently Mehrer, Stolwijk and co-workers [95W1, 95W2, 95W3] studied Zn diffusion in undoped and Fe-doped semi-insulating InP to find out defect formation under various conditions. Typical Zn diffusion profiles by electron microprobe (EMP) and secondary ion mass spectrometry (SIMS) profiles in undoped and Fe-doped InP after diffusion at 973 K are shown in Figs. 8 and 9 [95W1]. They have concluded that indiffusing interstitial Zn can occupy In sublattice sites via a kick-out reaction. Under certain diffusion conditions defect formation results from saturation of In interstitials which are generated via kick-out reaction. They have also suggested that in the case of Fe doped InP Zn also replaced Fe on In sublattice sites leading to the redistribution and precipitation of Fe.
Table 5. Diffusion data of group II impurities in III-V compounds. (1 kJmol−1 = 0.0104 eV) D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
Remarks
Ref.
973-1073
Be-implanted undoped GaAs; SIMS
89D
998-1098
Be doping spikes sandwiched between undoped GaAs grown by MOCVD; SIMS
88T1
1173
Annealing of Be-doped MBE samples; SIMS
78M1
1073
Hall
GaAs Be
D0(C) = 6.10−22 C 67.45 where C is in 106 m−3 8.7 . 10−8 154.2 D = (0.15-1).10−13 D = (0.5-1).10−14
Mg
7.3.10−6
115.6
1073-1173 Be evaporated on the surface; incremental sheet resistance
66P1
4.10−5 2.6.10−2
117.5
1073-1473 p-n junction
69A1
260.1
1198-1373 p-n junction, incremental sheet resistance
65M
1.4.10−4
182.1
-
Incremental sheet resistance
68G
873-1023
Uncoated and YSZ-protected GaAs; p-n junction, C-V profile, AES;
90B, 88B1
Q = 154.2-173.4
Zn
Cd
Hg
2.5.10−1 1.5.101
289.1
1023-1273 Radiotracer; concentration-dependent
68K1
239.9
933-1253
64K1
3.10−7
96.35
1073-1373 Incremental sheet resistance; average D
64K1
5.10−2 5.10−2
234.1
1143-1423 Radiotracer
60G1
269.8
1173-1373 Incremental sheet resitance; average D
64K1
1273
68K1
D = 5.10−14
Radiotracer
Radiotracer
cont.
Lando lt -B { rnst ein New Series III/33A
3-18
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 5 (cont.) D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
Remarks
Ref.
GaP Be
D = 2.4.10−9 - 8.5.10−8 (max. values)
Mg
5.10−5
Zn
1.0
1173-1273 D varies non-monotonically with concentration and attains a maximum
72I
134.9
973-1323
Electrical methods
77S2
202.3 0.45 −8 . 240.9 D0(C) = 7.5 10 C where C is in 106 m−3
973-1573
Radiotracer
63A1
1073-1173 Radiotracer; concentration dependent D0
64C1
154.2
773-813
p-n junction
81K1
GaSb Zn
Cd
4.10−2
192.7
783-873
Radiotracer
72B2
3.3.10−5
106.0
783-953
Isoconcentration D; Radiotracer
72B2
1.5.10−6
69.37
913-1073
p-n junction
68B3
1.98.10−6 1.98.10−6
112.7
523-773
Mg implantation and annealing
92G
112.7
873-1173
p-n junction
56S
4.2.10−3 1.9.10−4
92.5
873-1173
Isoconcentration D; Radiotracer
67B3
89.61
873-1173
p-n junction
66S2
3.11.10−3
112.7
873-1173
p-n junction
56S
7.4.10−4
110.8
923-1173
Radiotracer
67A1
231.2
773-923
p-n junction
81H3
1.45.10−5
127.2
923-1123
Radiotracer
71S2
4.9.10−2 1.4.103
146.5
823-948
Undoped InP; SIMS, p-n junction
87M
225.5
823-948
S-doped InP; SIMS, p-n junction
87M
198.7
623-853
Undoped InP; p-n junction
82A1
973
D is for p+ region; SIMS, EBIC
83Y1
InAs Mg
Zn
Cd
Hg
InP Zn
D = 2.08.10−10
cont. Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-19
Table 5 (cont.) D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
Remarks
Ref.
1.8
183.1
973-1173
Radiotracer
67A2
1.1.10−7
69.4
973-1173
Cd source at 973 K; electrical method
67K2
1.1.10−1
163.8 623-853
p-n junction
82A1
773
D(C) concentration dependent; SIMS, C-V profile
90W1
InP (cont.) Cd
153.2 D(C) = 1.10−14 - 1.10−10
85K3
InSb Zn
Cd
Hg
D0(C) = 6.32.108.exp[2.47(C/C0−1)], where C is in 106 m−3 251.47 673-773 Radiotracer −1 . 5.4 10 144.5 673-728 Diffusion source NSb/NZn ≤ 5; SIMS −3 . 5.75 10 144.5 628-728 Diffusion source NSb/NZn ≥ 5; SIMS
64G1 83N
5.10−1 1.4.10−7
130.1
635-781
Radiotracer
60G2
82.86
673-785
Radiotracer
61S
5.5
154.2
633-773
p-n junction
62W1
1.0.10−5 1.3.10−4
106.0
523-773
Radiotracer
63B3
115.6
633-773
p-n junction
62W1
1.26
168.6
673-773
Radiotracer
64G3
4.10−6
112.7
698-773
Radiotracer
64G2
830
Estimation of D; AlAs/GaAs interdiffusion
82K
933-1133
Radiotracer
69S2, 62S3
1173
Radiotracer; D concentration dependent
69S1
AlAs Zn
D ~ 9.10−11
AlSb Zn
3.3.10−1
Cd
D(C) = 4.10−12 - 3.10−10
Lando lt -B { rnst ein New Series III/33A
186.0
3-20
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.5.4 Diffusion of group I impurities Since Ag and Au are major components of the metal systems used for making ohmic contacts in III-V compound semiconductors [81S1], there has been a great deal of interest regarding their behaviour in these compounds. The reported diffusion data and solid solubilities of group-I impurities in III-V compounds are tabulated in Table 6. It can be seen from this table that not only the electrical behaviour of Cu, Ag and Au has been found to vary differently (e.g. they behave as acceptors in GaAs but donors in InAs) but also their activation energies do not follow any set pattern with respect to their atomic radius (e.g. Q increases with atomic radius in GaAs while decreases in InP) in these compounds. It has been observed that most of these impurities diffuse rapidly in III-V compounds and that their diffusion is considerably influenced by the defects which are present in the semiconductor and or are formed during diffusion annealing. Normally their diffusion profiles did not correspond to any standard solution of the diffusion equation but had two different branches (a slower one and a faster one) giving rise to two different sets of diffusion coefficients (refer Table 6). The low values of activation energies are indicative of diffusion through the interstices of the crystal lattice. A typical diffusion profile of Ag in GaAs, obtained by Tuck and Adegboyega [80T] while investigating vapour diffusion from a radioactive metallic Ag source in GaAs having different concentration levels in sealed ampoules at 1273 K for a range of As overpressure, is shown in Fig. 10. A model, proposed by Tuck and Adegboyega for diffusion of Ag in GaAs, assumes that diffusion takes place via an interstitial mechanism but most of the Ag exist on susbstitutional sites (with a small fraction existing interstitially) and that the substitutional Ag is immobile. The mechanism near to the surface is different, since the surface is an infinite source of vacancies and vacancies lost by interaction with interstitials are thus replaced by vacancy diffusion from the surface. The ‘dip’ (i.e. a minimum near to the surface) in the diffusion profile, shown in Fig. 10, is associated with the escape of interstitial Ag atoms from the surface during cooling at the end of diffusion annealing. Although D0 and Q values for Ag diffusion in InP were not reported by Tuck and coworkers, but its diffusion has been investigated by them in lower (i.e. 523-823 K) [78T2] and higher (i.e. 773-1173 K) [83C2] temperature ranges under various experimental conditions. Chaoui and Tuck [83C2] proposed a model in which the very rapid diffusion of Ag is due to the charged interstitial donor, Agi+ . At higher diffusion temperatures, this can join the lattice but does so by forming a complex of the type (VPAgInVP). In the bulk, this occurs only slowly since large numbers of vacancies of both types are required to participate and, therefore, virtually all Ag atoms are in interstitial form. Since an equilibrium exists between gaseous Ag and interstitial atoms at the surface (Agvap = Agi+ + e), interstitial atoms, vacancies and electrons are available close to the surface and the complex can be easily formed. In fact, there is evidence that this type of complex exists in Cd and Zn diffused samples [75T, 88T2]. It can also be easily visualized that there will be reduction in complex formation at higher P vapour pressures due to reduction in VP. The ‘dip’, similar to the one observed in the case of Ag in GaAs, was considered as due to rapid out diffusion of interstitial Ag during cooling process.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-21
Table 6. Diffusion data and solubility of group I impurities in III-V compound semiconductors (1 kJmol−1 = 0.0104 eV) D0 Q T [10−4m2s−1] [kJmol−1] [K]
Remarks
Ref.
Solubility [106 m−3]
Ref.
Li (a)
5.3.10−1
96.35
523-773
Conductivity and Hall, flame analysis
62F
7.1021exp(−0.57/kT)
62F
Cu (a)
3.10−2
51.07
373-773
Radiotracer
6.10−2
94.42
723-1023 Undoped GaAs; nondestructive ultrasonic, Radiotracer
64H1 max. 7.1018 (1373 K) 69V 3.7.1023exp(−1.3/kT)
GaAs
1.5.10−3
57.81 . D = (1-3) 10−5
Ag (a) 2.5.10−3 4.10−4
1073-1273 Radiotracer
78S1
1273-1373 Radiotracer
58F
144.5
773-1433 Slow component of 64B1 7.1019- 4.1020 diffusion; Radiotracer (773-1433 K)
77.08
773-1433 Fast component of 64B1 diffusion; Radiotracer
106.0 Au (a) 1.10−3 . −13 D = 4 10 -1.10−12
1013-1293 Radiotracer
64S
673-873
78V2
(Au-Ge)/GaAs interface; SIMS
6.1022exp(−1.7/kT)
64H1 58F
64B1
64S
GaP 1273-1573 Radiotracer
81K2 (2-5).1016 (1273 K)
240.9
1323-1523 A(111)-type face; Radiotracer
78D
231.2
1373-1523 B(111)-type face; Radiotracer
78D
Ag (a)
Au (a) 8 2.101
5.1014 - 1.1016
81K2
78D
GaSb Li (d) D0 = 0.59 exp(0.695 .10−16C) where C is in 106 m−3
473-873
Q = 119.5 2.3.10−4
183.1
800-930
67B6 max. 1.75.1017 Diffusion in p-type (723 K) specimen; electrical conductivity as a function of successive layer removal Slow component diffusion; electrical, flame photometry
67B6
67V
cont.
Lando lt -B { rnst ein New Series III/33A
3-22
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 6 (cont.) D0 Q T [10−4m2s−1] [kJmol−1] [K] GaSb (cont.) Li (d) 1.2.10−1
Remarks
Ref.
Solubility [106 m−3]
Ref.
67.45
550-930
Fast component diffusion; electrical, flame photometry
67V
86.72
743-923
Te doped n-type; Radiotracer
73B1 1.1022 exp(−0.53/kT) (in Te doped) 1.1024 exp(−1/kT) (in undoped)
Cu (d) 2.2.10−2
52.03
798-1163 Radiotracer
3.6.10−3
50.10
615-1148 Radiotracer
68B1 2.5.1021exp(−0.69/kT) 68B1 (873-1073 K) 67F 4.1022 exp(−1/kT) 67F
Ag (d) 7.3.10−4
25.05
723-1173 Radiotracer
67B3 1.1019 exp(−0.4/kT)
Au (d) 5.8.10−3
62.63
873-1173 Radiotracer
67R
3.8.10−3
66.48
873-1173 Radiotracer
69A2 9.2.1020 exp(−0.94/kT)
69A2
Ag (a) 3.6.10−4
56.85
773-1173 Radiotracer
69A4 1.6.1018 exp(−0.31/kT)
69A4
Au (a) 1.32.10−5 1.37.10−4
46.25
873-1093 Radiotracer
69R3
70.34
873-1173 Radiotracer
69R3 ~1015(1073 K) 69A3 2.1019 exp(−0.7/kT)
(cont.)
Cu (d, a)4.7.10−3
73B1
InAs
2.1017 exp(−0.28/kT)
67B4 67R
InP Cu (a)
69A3
(873-1123 K)
InSb Li (d)
7.10−4
26.98
273-483
Electrical
66T
Cu (a)
10−4 - 10−3 104.1
473-773
Slower component; Radiotracer
63S2 1.5.1022exp(−0.76/kT) 63S2 (473-773 K) .
3.10−5
35.65
503-763
Faster component; Radiotracer
64B3
24.09 Ag (a) 1.10−7 −9 . D = 4 10
713-783
Radiotracer
62W1
663
Radiotracer
64B3 cont. Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-23
Table 6 (cont.) D0 Q T [10−4m2s−1] [kJmol−1] [K] InSb (cont.) Au (a) 7.10−4
Remarks
Ref.
Solubility [106 m−3]
30.83
413-783
Radiotracer
64B3 1.1015 - 4.1015 (573-773 K)
34.65
423-773
Radiotracer
60W
Ref.
64B3
AlSb Cu (a)
3.5.10−3
3.5.5 Diffusion of other impurities Among other impurities, transition elements (Cr, Mn, Fe, Co) give rise to deep acceptor levels (refer Table 2) in III-V compounds. In fact, some of these elements have been found to produce semi-insulating (i.e. resistivity as high as 108 Ωcm) GaAs and InP. Since semi-insulating substrates form the basis of highspeed device and integrated circuit technologies, their diffusion studies have aroused great deal of attention in the past. The reported diffusion data of transition elements in III-V compounds are tabulated in Table 7. It can be seen from this table that Cr diffusion in GaAs has been investigated by various workers under different conditions. These investigations can be broadly classified as in-diffusion from Cr source [86D2, 79T, 72K2] and out-diffusion from or redistribution in Cr doped substrate [86D2, 82M1, 81L2, 80K1, 80W]. Based on available experimental data (some of which are plotted in Fig. 11), Yu et al. [91Y] have proposed an integrated substitutional-interstitial-diffusion (SID) mechanism, which takes into account both kick-out and dissociative mechanisms, to explain the Cr-in- and out-diffusion in GaAs. On quantitative basis they have justified that kick-out mechanism dominates Cr in-diffusion while the dissociate mechanism dominates Cr out-diffusion. The observed Cr in-diffusion profiles were complex and contained two parts, namely, high- and low-concentration parts. In the high concentration part, which extended from the surface, the Cr concentration decreased very rapidly with distance, whilst in the other, which extended much deeper, there was little Cr concentration variation with distance. Yu et al. [91Y] have referred these profiles as the rotated - integral - sign shape ( ~) profiles. As can be seen from Fig. 11, the diffusivity values for near surface region were much smaller than those for deeper into the bulk. The Cr out-diffusion profiles from Cr-doped GaAs specimens were error-function type and corresponding diffusivity values were found to be 2-3 order less than the values for Cr in-diffusion into the bulk (refer Fig. 11). Morkoc et al. [80M5] have studied Cr redistribution (at comparatively lower temperature of 853 K) near to the Cr-doped GaAs substrate/epitaxial layer interface during epitaxial growth by MBE. Their SIMS results indicated that Cr accumulated at the interface to a degree which depended upon the pre-growth procedure. Among the transition elements reported in this section, Mn is a comparatively shallow acceptor in GaAs and InP (refer Table 7). It has also been demonstrated that Mn could be used to obtain moderately doped p-type GaAs and InP [82V2, 82B1]. A detailed radioactive tracer diffusion study of Mn in InP is, however, needed to understand its behaviour in InP. Of late, there has been considerable interest in the study of rare-earth doped semiconductors. Especially such III-V compound semiconductors continue to show promise and potential for opto-electronic applications. However, the available information regarding the diffusion of rare earth impurities in III-V compounds is at present very scanty (refer Table 7). Kozanecki et al. [88K2], while studying annealing of Yb implanted layers in GaAs and GaP, observed that Yb out-diffused to surface during annealing at 1273 K. This out-diffusion and non substitutional location of rare earth ions seem to be main difficulties
Lando lt -B { rnst ein New Series III/33A
3-24
3 Diffusion in compound semiconductors
[Ref. p. 3-70
in obtaining rare earth-doped III-V compounds by ion implantation. Further work is necessary to understand the behaviour of rare earth impurities in III-V compounds.
Table 7. Diffusion data of transition and rare earth elements in III-V compounds. (1 kJmol−1 = 0.0104 eV) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4m2s−1] [kJmol−1] [K]
Remarks
Fig. Ref.
GaAs Cr
(a) 76.12 73M2
2.04.10−6
80.0
1023-1273 Cr-rich Cr-Ga-As ternary alloy source; fast component; SIMS
86D2
(d) 90H 28.9- 38.5
-
163.8
1023-1273 Slow component near surface; SIMS
86D2
D = 2.10−13- 2.10−11
973-1173
86D2
7.9.10−3
1073-1373 Chemical analysis
212.0
(a) 9.15
73M2
72K2
D ~ 10−12- 10−15
1073-1373 Effective diffusivity in the near surface region; diffusion from radioactive metallic Cr
4.3.103
873, 1023
Cr redistribution during MOCVD and VPE grown layers; follow this diffusion data; SIMS
81L2
873
Out-diffusion from Crdoped substrate into epilayer; SIMS
80W
327.6
D = 6.7.10−12
Mn
Out-diffusion by annealing of Bridgman Cr-doped GaAs in an evacuated quartz ampoule; SIMS 11
91Y, 79T
6.3.105
327.6
973-1173
Out-diffusion from Crdoped SI GaAs; SIMS
80K1
8.53.104
340.12
1073-1173 Out-diffusion from Crdoped GaAs; SIMS
82M1
6.5.10−1
239.9
1123-1373 As overpressure; Radiotracer
65S1
3.9.10−2
216.8
1223-1373 Radiotracer diffusion in Sn doped n-type GaAs
86S2
7.3.10−5
119.5
1223-1373 Radiotracer diffusion in Zn doped p-type GaAs
86S2
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-25
Table 7 (cont.) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4m2s−1] [kJmol−1] [K]
Remarks
Fig. Ref.
GaAs (cont.) 4.2.10−2
173.4
1123-1423 Radiotracer
75B1
2.2.10−3 1.5.10−2
223.5
1023-1323 Radiotracer
72U
192.7
1223-1373
78P3
5.102 1.2.10−1
240.9
1073-1273 Radiotracer
79D2
254.4
1023-1323 Radiotracer
72U
1.9.101
192.7
853-1433
Fast bulk region component; Radiotracer
73K2
1.3.102
279.4
853-1433
Slow near surface region component; Radiotracer
73K2
Er
5.10−14
28.91
573-973
As overpressure; SIMS
89Z
Tm
2.3.10−16
96.35
1073-1273 Radiotracer
65C
Fe
(a) 35.65 68S3 (a) 0.52
Co
(a) 15.42 73M2
GaP Cr
(a) 90.57 78S3
6.2.10−4
115.62
1173-1403 Radiotracer, ESR
78K
Mn
(a) 38.54 78S3
2.1.109 − 1.1.10 6
452.85
< 1223
Radiotracer, ESR
80K3
86.72
1223-1403 Radiotracer, ESR
80K3
1.6.10−1
221.6
1253-1433 Radiotracer
76S1
2.8.10−3
279.4
1123-1373 Radiotracer
75D
1273
Estimated from outdiffusion; RBS measurements
88K2
183.07(I) 773-923
Radiotracer
78S2
221.61(II)773-923
Radiotracer
Fe
(a) 67.45 78S3 (a) 115.6
Co
(a) 39.50 73M2
Yb
D ~ 10−14
GaSb Fe
5.10−2 6.102
cont.
Lando lt -B { rnst ein New Series III/33A
3-26
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 7 (cont.) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4m2s−1] [kJmol−1] [K]
Remarks
Fig. Ref.
InP Cr
Mn
Fe
(a) 59.74 78S3
873-1173
Very rapid diffusion; due to non-erfc profile no diffusion coefficient obtained; Radiotracer, C-V measurement
82B4
(a) 96.35 81F1
773-1173
Out-diffusion from Crdoped InP; samples capped with Si3N4; SIMS
81O
D = 4.2.10−9
1173
Fast component; C-V measurement
84S5
D = 3.8.10−10
1173
Slow component; C-V measurement
84S5
279.4
923-1023
Implantation and annealing; SIMS
85C3
3
192.7
883-1223
Radiotracer, C-V measurement
77S3
6.8.105
327.6
853-993
Diffusion from Fe doped substrate into LPE layer, SIMS; photoluminescence
81H1
2.5.10−4
163.8
973-1173
Out-diffusion of Fe from Fe doped substrate; SIMS
84K1
998
Ion implantation and annealing; SIMS
85S1
873- 1223
Radiotracer, C-V measurement
77S3
873
P overpressure; SIMS
89Z
(a) 22.16 84S3
(a) 65.52 78S3 (a) 75.15 81F2
D ~ 10−13
Co
(a) 28.91 82S2
9.10−1
173.4
D = 2.7.10−14
Er
InSb Fe
(a)
78S3
1.10−7
24.1
713-783
Radiotracer
62W1
Co
(a)
78S3
2.7.10−11 1.10−7
37.6
693-773
Radiotracer
65G3
24.1
713-783
Radiotracer
62W1
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-27
3.5.6 Diffusion in III-V compound ternary alloys Although III-V compound semiconductor heterojunctions have been in use for many years [74S1], their heterostructures utilizing ternary and quaternary alloys and/or super lattices are now forming an integral part of newer semiconductor devices. This has been possible primarily due to availability of newer techniques for growing ultra-thin epitaxial layers and for their characterization. The interest in the diffusion of impurities in ternary alloys of III-V compounds started mainly from the fact that p-n junctions in them were prepared by diffusing group II elements into n-type material. Since then, various impurity diffusion studies in ternary alloys of their lattice-matched heterostructures with binary compounds have been undertaken. Some of these reported studies are tabulated in Table 8. As can be seen from this table, the diffusion of Zn in ternary alloys has been studied in detail by various workers. Apart from this, since AlxGa1−xAs is one of the few ternaries in which the whole composition range is available to form latticematched heterostructures with GaAs, diffusion of a number of impurities (refer Table 8) have been investigated in this material. It must, however, be noted from the table that it is not always possible to obtain quantitative diffusion data in these studies due to various experimental constraints. Arseni et al. [69A5] have theoretically discussed the case in which the impurities diffuse in an homogeneous solid solution, A1−xBx (where x is the atomic fraction of the component B in the solid solution), by substitutional or interstitial hopping. Although this simple analysis falls short (as expected) of providing a very satisfactory explanation of the diffusion of impurities in III-V compound ternary alloys, it helps to explain qualitatively the dependence of diffusion coefficient upon the composition and the energy gap in some cases. Based on this, Boltaks et al. [75B2] have tried to explain their experimental observations that effective diffusion coefficient and solubility of Zn decreases with increasing Al content. However, the observations of Lee et al. [78L3] and Matsumoto [83M1] (i.e. diffusion depth increases with increasing Al content) have been explained on the basis of an interstitial-substitutional model [68K1] in which Zn interstitials increase with increasing Al content. Looking closely to the results of other workers, the explanation provided by Matsumoto appears to be correct. In addition to diffusion in ternary alloys, diffusion of Zn and Cd in quaternary InxGa1−xAsyP1−y latticematched to InP have also been reported in literature [83M2].
Table 8. Diffusion of metals M in III-V compound ternary alloys (ternary alloy/substrate). (1 kJmol−1 = 0.0104 eV) x
M
T [K]
Diffusion data and remarks
Ref.
AlxGa1−xAs/GaAs 0.15-0.29 Li
573
Diffusion from Li deposited on surface in vacuum; C-V and SIMS measurements.
82Z
0.3-0.4 0.3-0.4 0.3-0.4
Cu Ag Au
1073-1273 1073-1273 1073-1273
Radiotracer diffusion from chemically deposited layer; impurity concentration found to peak at the AlxGa1−xAs/GaAs interface; diffusion temperature does not affect the overall pattern but increases the height of the peak at interface.
76D
0.3
Be
1073
Out-diffusion during MBE growth and during subsequent annealing; D < 1.10−19 m2s−1 at 1073 K.
77I
0.3
Be
973
Diffusion profiles determined by SIMS; diffusion coefficient in AlxGa1−xAs more than 3 times larger than 6.10−19 m2s−1 calculated for GaAs.
85M2
0.3
Mg
1073-1173
Diffusion during post growth heat treatment of Mg doped MOVPE layers; C-V and SIMS used to evaluate.
90N cont.
Lando lt -B { rnst ein New Series III/33A
3-28
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 8 (cont.) x
M
T [K]
Diffusion data and remarks
Ref.
AlxGa1−xAs/GaAs (cont.) 0-0.4
Zn
923-1223
Radiotracer diffusion studied; effective diffusion coefficient and solubility decreased with increasing Al content; D0 = 9.10−4 m2s−1 and Q = 231.2 kJmol−1 for x = 0.3.
75B2
0-0.71
Zn
913-973
Diffusion studied by junction-depth measurements; diffusion depth increases with Al content for x less than 0.5; for x greater than 0.6 rate of increase is slower.
78L2
0-0.4
Zn
839-999
83M1 Diffusion depth increased monotonically with increase in Al content; Q of diffusion depth = 99.2 kJmol−1 for x = 0.3, smaller than 115.6 kJmol−1 for GaAs; electrical and optical measurements used to evaluate.
0.38
Zn
923
Zn diffused into samples coated with yttria-stabilized cubic90B zirconia protection layer from Zn elemental source; p-n junction depth followed a square root of diffusion time dependence; D = 3.10−16 m2s−1 at 923 K; SEM used to measure junction depths stained chemically.
0.1-0.5
Zn
973
Open tube diffusion; diffusion depth followed a square root of diffusion time dependence and increase with increase in Al composition; chemical-staining and SEM used to evaluate.
83Y2
0.07-0.75 Zn
873
Radiotracer diffusion from Zn9GaAs10 source; marked difference between Zn diffusion profiles in AlxGa1−xAs compared to those in GaAs.
83B1
0.1-0.35
Zn
923
Uniform dependence of Zn diffusivity on Al content; diffusion from ZnAs2 source, p-n junction measurements used to evaluate.
88Q
0.24
C
1173
Annealing at 1173 K of C-doped Al0.24Ga0.76As epilayers grown 90A1 by metalorganic MBE; annealing produced decrease in free carrier concentration; Hall, SIMS, optical absorption used to evaluate.
0-0.4
Si
1123
Diffusion from sputtered Si film; diffusion rate and surface concentration decreased with increasing Al content; SIMS used to evaluate.
87O
0-0.76
Fe
998-1128
Diffusion carried out to obtain Fe-doped AlxGa1−xAs layers; optical properties determined.
84W1
Effective diffusion coefficients (2.5.10−15-1.5.10−14 m2s−1) in AlxGa1−xP are about 10-15 times larger than in GaP and have smaller Q.
76K2
Diffusion profiles determined by ion microprobe; Zn diffusion and solubility limit increase with increasing Al content; D0 = 8.10−4 m2s−1 and Q = 16.38 kJmol−1 for x = 0.2.
84J
AlxGa1−xP/GaP 0.35
Zn
973-1123
AlxGa1−xSb/GaSb < 0.35
Zn
783-873
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-29
Table 8 (cont.) x
M
T [K]
Diffusion data and remarks
Ref.
Si diffusion observed to enhance interdiffusion on both group III and group V sites; DSi = 1.1.10−17 m2s−1, DGa= 1.47.10−18 m2s−1, DAs = 1.3.10−20 m2s−1 at 1113 K; SIMS used to evaluate.
93T
78M2
AlxIn1−xP/GaAs 0.5
Si
1113
GaAs1−xPx/GaAs 0.4
Be
873-1173
Substantial diffusion of Be implants during annealing at 1173 K; out-diffusion of Be into Si3N4 encapsulant also observed during high dose implant annealing.
0.38
Be
873-1173
Si3N4 or SiO2 encapsulation before annealing implanted samples; 76C2 very little diffusion during annealing for a Be fluence of 6.1017 m−2 but anomalous diffusion for a fluence higher than 1018 m−2.
0.35-0.7
Zn
1173
Radiotracer technique used; diffusion coefficient and solubility decreased with increasing P content.
0.4
Zn
923
90B Zn diffused into samples coated with yttria-stabilized cubiczirconia protection layer; junction depth followed a square root of diffusion time dependence; D = 9.7.10−16 m2s−1 at 923 K; SEM and chemical-staining used to evaluate.
0.38
Zn
823-1123
Diffusion from implanted layer studied by ion microprobe; SiO2 or Si3N4 encapsulant used during annealing.
77M
< 0.5
Fe
973-1008
Fe-doped GaAs1−xPx prepared by diffusion of Fe from a thin evaporated Fe film; electronic properties studied.
85H
Anodic oxidation along with radiotracer technique used to obtain diffusion profiles; D ~ 8.9.10−17 m2s−1.
77V1
Radiotracer diffusion from chemically deposited layer; diffusion profiles showed a minimum in the central part of the epilayer and a maximum at the epilayer/substrate interface. Radiotracer diffusion from vapour phase; D0 = 1.9.10−9 m2s−1
78V1
D (x) = 3.935.10−12 exp (−6.84x) m2s−1 for 0.48 < x < 0.74 at 1123 K; Temperature dependence of D with composition having Q(x) = 96.35(1.28+2.38x) kJmol−1; junction depth measured by angle-lapping and chemical staining under illumination.
90K
69A5
GaAs1−xPx/GaP 0.9
Zn
948
GaxIn1−xP/GaAs 0.4-0.5 0.4-0.5
Cu Au
873-1073 873-1073
0.4-0.5
Zn
773-1173
and Q = 86.72 kJmol−1.
78V1
GaxIn1−xP (crystal wafers) 0.48-0.74 Zn
1023-1173
cont.
Lando lt -B { rnst ein New Series III/33A
3-30
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 8 (cont.) x
M
T [K]
Diffusion data and remarks
Ref.
Radiotracer technique used; diffusion coefficient decreases linearly with increasing P content.
69A5
InAs1−xPx (crystal wafers) 0.1-0.5 0.1-0.5
Zn Cd
1073 1073
InxAl1−xAs/InP 0.52
Fe
1073-1153
93M1 Significant redistribution and out-diffusion after rapid thermal annealing of implanted Fe ions; out-diffusion so pronounced that only about 50 % remains after annealing; SIMS and RBS used to evaluate.
InxGa1−xAs/GaAs 0.2-0.8
Zn
773-873
80Y Junction depth followed a square root of diffusion time dependence; and for the effective diffusion coefficient D0 = 9.38.10−52 (C02) m2s−1 ,Q = 96.35(0.72−0.39x) kJmol−1 where C0 is the surface concentration and x is the In content; junction-depth measured by cleaving and chemical staining under illumination.
0.26-0.4
Zn
902-1018
Composition and temperature dependence of effective diffusion coefficient reported; junction depth measured by cleaving and chemical staining.
76U
0.18
Zn
973-1173
p-n junction depth measurements and electron probe analysis; D0 = 2.1.10−7 m2s−1 and Q = 163.8 kJmol−1.
71L2
InxGa1−xAs/InP 0.53
Be
773-973
Diffusion from implanted layer during annealing; diffusion profile obtained by SIMS showed high pile-up near to surface and substantial in-diffusion.
84V
0.53
Zn
873-1073
Diffusion from spin-on films; concentration profiles obtained from C-V measurements.
84A
0.53
Cd
773-873
Diffusion profiles had a shallow and relatively flat portion of large concentration followed by a steep descent to a weaklydoped p-region extending to p-n junction.
83A
0.53
Cd
973-1073
Diffusion from implanted layer; diffusion profiles obtained by SIMS exhibited high surface pile up.
84A
0.53
Fe
973-1123
Considerable amount of redistribution of implanted Fe atoms after rapid thermal annealing; SIMS and RBS used to evaluate.
91G
p-n junction depth measurements; D0 = 1.6.10−8 m2s−1, Q = 103.1 kJmol−1.
88K1
InAs1−xSbx/GaSb 0.1-0.12
Zn
623-773
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-31
3.6 Diffusion in II-VI compounds and their ternary alloys It is observed that II-VI compounds have either zincblende or wurtzite structures and their band gap energies lie between 362.3 kJmol−1 to −13.49 kJmol−1. Inspite of the structural similarity of a number of these compounds to III-V compounds, they differ from the latter in several ways. Most of these have large band gap energies due to rather high ionicity and are invariably of either n-type or p-type due to high degree of compensation caused by interaction between impurity and native defects. The conductivity conversion (i.e. junction formation) by diffusion is, therefore, met with little success. It is for this reason that attention has now been shifted from diffusion to ion implantation or heterostructures to form junctions. Although, in many cases, one is able to form junctions in II-VI compound semiconductors by ion implantation but the annealing of the damage, which accompanies it, often severely impairs the required properties one is trying to achieve from them. Even from this point of view, the relevance of diffusion data and an understanding of self- and impurity-diffusion is of vital importance. Several reviews [89S2, 88S1, 82B3, 82H1, 73S2, 68Y1, 67W1, 67W2], dealing with self-diffusion and/or impurity diffusion in II-VI compound semiconductors, have appeared in literature from time to time. The present status related to diffusion in them is reported here.
3.6.1 Diffusion of group II and group VI elements A variety of simple native defects, such as vacancies, interstitials and anti-site defects, are always present in II-VI compounds. The dominance of any one of these depends upon deviations from stoichiometric composition during growth or upon the temperature and partial over-pressure of the constituents during diffusion. In fact, it is observed that not only small stoichiometric changes in composition caused by diffusion can have dramatic effect upon electrical properties of II-VI compounds but complementary metal (group II) or chalcogen (group VI) diffusion can lead to a change in the stoichiometry to such an extent so as to form a ternary alloy of these compounds. Self-diffusion, in absence of any concentration gradients, can be measured by radiotracer technique and self-diffusivity, D, (neglecting non-defect mechanisms of diffusion) can be expressed as [73S1]. D=
 f j Dj C j
,
(3.15)
j
where fj, Dj and [Cj] are the correlation factor, the diffusivity and the concentration of the jth native defect, respectively. In general, [Cj] will vary in a characteristic way determined by partial over-pressure imposed during diffusion anneal and also, if the defect is ionized, by the electroneutrality condition. The dominant defects contributing to D can be identified by measuring the D as a function of partial over-pressure and/or doping level and the information derived from Hall measurements. In II-VI compounds, selfdiffusion via substitutional mechanism requires a significant concentration of anti-structure defects under high-temperature equilibrium conditions but very little experimental evidence till to date is available to justify the existence of anti-structure defects of majority species under these conditions [82H1]. Self diffusion in these compounds is, therefore, considered to occur via movement through interstitial sites until a vacancy on its own sub-lattice is reached. In fact, it is generally useful to know the change in defect concentrations as a function of partial pressure (i.e. a defect equilibrium or Brouer diagram) [54B3] to interpret the self-diffusion behaviour in these compounds. If the self-diffusion is via a non-defect mechanism (i.e. ring or direct exchange) then the diffusivity, D, will be independent of doping level (for usual concentration ranges) and of partial pressures. As can be seen from the diffusion data in subsequent sections that some diffusivities do exhibit these features. From the metal and chalcogen self-diffusion data tabulated in Table 9 and discussion in subsequent sections, there is at present no firm basis to conclude whether a native defect or non-defect mechanism is responsible for it.
Lando lt -B { rnst ein New Series III/33A
3-32
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.6.1.1 Metal self-diffusion As can be seen from Table 9, metal self-diffusion does not follow a common pattern in its dependence upon partial pressure in II-VI compounds. For example, metal self-diffusion in Cd and Zn chalcogenides have shown that it is either independent of the metal partial pressure (as in the case of ZnSe, ZnTe and CdTe) or increases with increasing metal partial pressure (as in the case of ZnS, CdS and CdSe). Based on the above mentioned observations and high temperature Hall measurements of various workers, Shaw [88S1] has tried to explain the diffusion mechanisms responsible for metal self-diffusion in these compounds. In ZnSe, ZnTe and CdTe neutral native associates and ionized native donors and acceptors all play a role, whereas in CdSe the contribution is mainly from doubly and singly ionized native donors. In the case of CdS, the Cd self-diffusion is apparently dominated by doubly ionized native donors, at least at higher temperatures. In ZnS, however, the only available data is so limited in number of observations and the pressure range that no specific conclusion can be drawn concerning the dominant defect eqilibria [73S2]. Furthermore, the increase in diffusivity with increasing sample size suggest that the values were not observed under isoconcentration conditions. The metal self-diffusion in Hg compounds shows far more complex features and the mechanism for diffusion in them appears to be much less clear. 3.6.1.2 Chalcogen self-diffusion Chalcogen self-diffusion in CdS, CdSe, CdTe, ZnS, ZnSe and ZnTe (refer Table 9) have revealed a common behaviour (i.e., self diffusion coefficient increases with increasing chalcogen pressure). In the 1/ 2 case of Cd chalcogenides (CdX), the chalcogen self-diffusivity D(X)∝ pX 2 under chalcogen-rich 3 sat conditions and changes to a weak increase with pCd (approximately p1/ Cd ) as pCd
is approached [71K,
67W2, 75C1]. Variation of Se diffusivity in ZnSe [67W2, 71H] and the measurements of Te diffusivity at sat sat and DZn in ZnTe [69R4] are also consistent with the above-mentioned pattern. The aboveDTe 2 1/ 2
mentioned behaviour (i.e., D(X)∝ pX 2 ) and the observation that chalcogen self-diffusivity was independent of the donor doping level in CdS [71K] and CdSe [67W2] under chalcogen rich conditions indicated that chalcogen under these conditions diffuses via electrically neutral self interstitials. This, however, is not the mechanism for chalcogen self-diffusion under metal rich conditions. In this case, a different vacancy or vacancy-interstitial mechanism may be responsible for chalcogen self-diffusion. More 1/ 2 recently it has been pointed out that the D(X)∝ pX 2 relation could also arise for diffusion by the anti-site defects [84S2], but the evidence of anti-site defects in the II-VI compounds is meagre. 3.6.1.3 Complementary metal and chalcogen diffusion Complementary metal and chalcogen diffusion in II-VI compound semiconductors have been used to prepare solid solution overlayers and heterostructures. In most of these studies, if M, N and X, Y denote goup II and group VI elements, respectively, the diffusion from a complementary metal (M) or chalcogen (X) elemental source or from MX vapour source into NX or MY substrate is investigated. This type of investigation often involves chemical concentration gradients in M and N or X and Y leading to the growth of ternary M1−xNxX or MX1−xYx solid solution. The reported diffusion data of this category are tabulated in the Table 10.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-33
Table 9. Metal and chalcogen self-diffusion data for II-VI compounds. (1 kJmol−1 = 0.0104 eV) D0 [10−4m2s−1]
Q T [kJmol−1] [K]
3.10−4
146.45
1198-1213 Zn
1.5.104 1.1016
313.14
1213-1303
627.24
1303-1348
8.10−5
211.97
7.105
OverRemarks pressure pX [atm]
Fig.
Ref.
ZnS Zn
S
Radiotracer technique used; D(Zn)∝ p1Zn.5 between 0.25 atm < pZn < 2 atm at 1323 K
58S
1013-1373 S2: 0.5
Radiotracer technique used; diffusion along (111) direction of ZB type ZnS; D increased with increasing S2 pressure at 1143 K
67G1
327.59
973-1164
S2: 0.5
Radiotracer technique used; samples sliced at 45o angle to c-axis of wurtzite type
67B2
2.16.104
303.50
873-1073
Ar
Radiotracer diffusion in ZB type ZnS
72W2
9.8
289.05
1033-1423 Zn sat. or Se2 sat.
8.4.10−4
163.80
1073-1273 Zn: 10−2 Radiotracer diffusion in Al-doped ZnSe (1.7.1025 m−3); diffusion also in As-doped ZnSe reported
1.3.10−1
250.51
1133-1293 Se2 sat.
Radiotracer technique used; D increases with increasing Se2 overpressure
2.3.10−1
260.15
1273, 1423
Se2 sat.
Radiotracer technique used; diffusion also studied for Znsaturated condition
1.4.101
259.18
966-1304
Zn sat. or Te2 sat.
Radiotracer technique used; D identical (within experimental scatter) in Zn-saturated and Tesaturated cases; D independent of component partial pressure
ZnSe Zn
Se
Radiotracer diffusion independent of component overpressure
12, 13
71H
78R
14, 15
71H
67W3
ZnTe Zn
Lando lt -B { rnst ein New Series III/33A
16
69R4
cont.
3-34
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 9 (cont.) D0 [10−4m2s−1]
Q T [kJmol−1] [K]
OverRemarks pressure pX [atm]
Fig.
Ref.
ZnTe (cont.) Zn
Te
2.34 1.10−4
196.55
1033-1133 Zn: 0.1
Radiotracer technique used
71S1
168.61
933-1233
Radiotracer diffusion in Aldoped ZnTe (2.1025 m−3)
69R4
2.104
366.13
1200-1250 Te2 sat.
Radiotracer technique used; D increases with increasing Te pressure
3.4
192.7
973-1373
Cd sat.
Radiotracer diffusion with Cd or CdO source used
64W
6.72.102 5.8.10−2
257.25
773-973
Cd sat.
178.25
973-1123
Cd sat.
Radiotracer technique used
84S2
1.2
221.61
875-1528
Cd sat.
Radiotracer technique used
72J
3.3.10−2
194.63
973-1273
Cd sat.
Radiotracer; D as a function of temperature and pCd reported
71K
1.6.10−2
200.41
1073-1173 S2: 2
Radiotracer; D as a function of temperature and pS2 reported
71K
231.24
1023-1323
Radiotracer technique used
69S4
6.3.10−2 4.12.10−2
120.44
873-1173
Cd sat.
Radiotracer technique used
73Z2
210.04
873-1173
Se2 sat.
9.2.10−2
161.87
823-1151
Cd sat.
Radiotracer technique used; 0. 46 D ∝ pCd
67B5
3.3.10−1 1.6.10−3
260.15
1033-1212 Se2 sat.
144.53
973-1273
Radiotracer technique used
70D
2.6.10−3 8.83.10−3
149.34
973-1273
Se2 sat.
Radiotracer technique used
67W2
120.44
873-1173
Se2 sat.
Radiotracer technique used
73Z2
1.26
257.25
973-1273
Cd sat.
Radiotracer technique used; D independent of pCd
67W1
3.26.102
199.44
923-1173
Cd sat.
Radiotracer technique used; D essentially independent of pCd
Zn sat.
17
69R4
CdS Cd
S
D ~ 10−10-10−7
CdSe Cd
Se
CdTe Cd
18, 19
68B2 cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-35
Table 9 (cont.) D0 [10−4m2s−1] CdTe (cont.) Cd 1.58.101
Q T [kJmol−1] [K]
OverRemarks pressure pX [atm]
Fig.
Ref.
235.1
923-1173
Te2 sat.
20
68B2
873
Cd
Diffusion in p-type; intensity distribution of characteristic X-ray used to obtain diffusion profile Radiotracer; D increases with increasing Te2 pressure
D ~ 2.6.10−7
Te
94B
1.66.10−4
132.96
773-1073
Te2 sat.
8.54.10−7
136.82
923-1173
Cd sat. or Te2 min.
1073
Cd sat. Radiotracer technique used or Te2 min.
67W2
D ~ 1.8.10−13
21
68B2
HgSe Hg
5.6.10−9
48.18
473-673
Hg sat.
Radiotracer technique used
69K3
Se
2.10−7
73.23
473-673
Hg
Radiotracer technique used
69K3
1.8.10−8
55.88
473-623
Hg sat.
78B3
723
Hg: < 4
Radiotracer technique used Radiotracer; slow(s) and fast (f) components observed; 2/3 /3 D(s) ∝ pHg and D(f) ∝ p1Hg for pHg between 0.63 to 4 atm; for pHg < 0.63 atm power exponent change sign
HgTe Hg
Te
7.7.10−11
11.56 (s)
463-613
Hg sat.
5.2.10−9 1.10−6
18.31 (f)
463-613
Hg sat.
134.89
473-673
Lando lt -B { rnst ein New Series III/33A
78Z
Radiotracer; slow(s) and fast(f) components observed
78B3
Radiotracer technique used
73Z1
3-36
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 10. Complementary metal/chalcogen diffusion in II-VI compounds. (1 kJmol−1 = 0.0104 eV) T [K]
Conditions, Ternary p(X) [atm] system
Composition range
D, D0 [10−4 m2 s−1] Q [kJmol−1]
Ref.
Cd
1373
Metal rich
Zn1−xCdxS
0.1< x < 0.9
D = 5.02⋅10−12 exp (3.19x)
71B
Se
1343
Chalcogen rich Se2: 1.75 S2: 0.75
ZnS1−xSex
0 < x < 0.31
D = 5.10−13
78A
973-1223
Metal rich
Zn1−xCdxSe 0 < x < 0.36
D0 = 6.4.10−4, Q = 180.2
73M2
D = 8·10−12
78A
ZnS
ZnSe Cd
Cd sat. and Zn min. S
1333
Chalcogen rich S2: 0.57 Se2: 1.53
ZnS1−xSex
Mg
1273
Mg
Zn1−xMgxSe x = 0.039
Diffusion for 20-50 hrs produced 83L2 ternary alloy
1173
Chalcogen rich
Zn1−xCdxS
D = 2.4.10−11
0.4 < x < 1
CdS Zn
x > 0.99
D0 = 1.22.10−8, Q = 63.59 (fast) 71Z2 D0 = 1.27.10−9, Q = 82.86 (slow)
993-1273
Se
923-1273
Chalcogen rich
1063-1283 Te
73N2
973-1273
Te2: 50 Torr
873, 923
Chalcogen rich
CdSe1-xSex
x < 0.01
D0 = 1.6.10−4, Q = 144.5
67W2
CdS1−xSex
0 < x < 0.5
D0 = 1.7.10−1, Q = 375.8
82N
D0 = 1.3.10−7, Q = 100.2
71N
CdSe S
CdS1−xSex
0.19 < x < 0.91 D = 7.10−13, 1.6.10−12
72T1
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-37
Table 10 (cont.) T [K]
Conditions, Ternary p(X) [atm] system
Composition range
D, D0 [10−4 m2 s−1] Q [kJmol−1]
Ref.
CdTe Zn
673-1173
Zn sat. and Cd min.
ZnxCd1−xTe x ~ 0.8
D = 10−11 - 10−9
92A2
Hg
553-613
Metal rich
Cd1−xHgxTe x < 0.01
84T
963
Metal rich
Cd1−xHgxTe 0.1< x 0.7
D0 = 5.103, Q = 192.7 D = 2.04.10−10 exp (5.49x) (f) D0 = 2.65.10−6, Q = 76.0 (s) D0 = 2.84.10−13, Q = 25.53
92J2
296-733
823,873
Hg sat.
Hg (HgTe + Cd1-xHgxTe 0.1< x 0.9 Hg source)
80I
,T<573 K D0 = 1.7.10−2, Q = 151.3, T >573 K D =2.8.10−13 exp(8.2x) at 823 K 75S3 D =1.6.10−12 exp(8.27x) at 873 K pHg dependence of D for different x
O
473
Heated in air
O
473-923
Oxygen CdO, TeO2 atmosphere on surface
923-1173 Se
973-1283
Se2
Se
1073
Cd sat. Te2 sat.
D ~ 4.10−10 D0 = 5.6.10−9, Q = 117.5
60B1 70V
for n-type D0 = 2.10−9, Q = 77.1 for p-type D0 = 6.10−10, Q = 27.9 65K
CdSe1−xTex x > 0.99
D0 = 1.7.10−4, Q = 130.1 D = 5.4.10−13 D = 1.9.10−10
Cd1−xHgxSe x > 0.99
D0 = 4.10−6, Q = 57.81
72Z
Zn1−xHgxTe 0.3 < x < 1
D0 = 5.10−4 exp [-42x(1-x)], Q = 105-200 x(1-x) D0 = 5.10−8, Q = 57.81
86P3 73Z1
D0 = 3.1.10−4, Q = 63.59
70B2
67W2
HgSe Cd
523-673
HgTe Zn
673-873
Zn
523-623
Cd
523-623
Lando lt -B { rnst ein New Series III/33A
Chalcogen rich
Chalcogen rich
Cd1−xHgxTe x > 0.99
3-38
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.6.2 Diffusion of group I impurities The reported diffusion data of group I impurities in II-VI compounds are tabulated in Table 11. It can be seen from this table that Li is the only impurity of group IA whose diffusion in these compounds has been investigated to some extent. The diffusion profiles of Li in ZnTe [80M2] and CdTe [76S2, 82S3] were found to be complex and exhibited more than one region. Diffusion of donor Li interstitials and acceptor substitutional migration of Li atoms via metal vacancies simultaneously is considered to be the reason for such complex behaviour. Attempts are, however, going on to form p-type II-VI compounds by doping with group IA impurities. In fact, low resistivity p-type ZnSe [91Q] and ZnTe [93L] have been obtained by using Li. The dominant effect which limits acceptor doping by Li in ZnSe is that the solubility of acceptors is limited by formation of phases, such as Li2Se etc. In addition to this, the role of alkali interstitials (e.g. Li, Na) in the electrical and luminescent properties of II-VI compounds has attracted considerable attention lately. Systematic diffusion studies of these elements are, therefore, needed for a better understanding and their possible uses in these compounds. The elements of group IB (i.e. Cu, Ag, Au) are important impurities in II-VI compounds. It has been observed that they diffuse much faster in these compounds at relatively low temperatures than they do in Si, Ge, or III-V compounds. In spite of the fact that II-VI compounds doped with these impurities have been extensively studied with regard to their fluorescent and optical properties, very limited diffusion data for these elements are available in literature (refer Table 11).
Table 11. Diffusion data of group I impurities in II-VI compounds. (1 kJmol−1 = 0.0104 eV) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4m2s−1] [kJmol−1] [K]
Remarks
Ref.
883-1233
Microhardness measurements; D values showed no anisotropy.
68D
1073
Solubility 2.8.1024 m−3 at 1073 K.
67W2
CdS Li
(a) 15.90
82H1 3.10−6
65.52
Na (a) 16.28
82H1 D ~ 3.10−7 -
Cu (a) 96.35
70S
2.1.10−3
92.50
419-673
Diffusion parallel to c-axis; 69S3 capacitance measurements; solubility 6.6.1028 exp(−0.5/kT) m−3.
1.5.10−3 1.2.10−2
93.23
673-973
Radiotracer technique used.
101.2
573-973
Ultrasonic measurements used.
73S4
8.10−5
69.37
293-473
Capacitance measurement used.
79L2
373-873
Radiotracer diffusion from Cu2S layer.
69P2
D = (1-5).10−10
Ag (a) ≤ 96.35 70S
2.5.101
134.9 (s) 573-773
59C
Radiotracer: (s) and (f) correspond 65W to slow and fast component of diffusion. cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-39
Table 11 (cont.) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4m2s−1] [kJmol−1] [K]
Remarks
Ref.
Ultrasonic measurements used.
73S4 84S6
CdS (cont.) Ag (cont.)
Au
2.4.10−1 1.3.101
77.08 (f)
573-773
142.6
573-773
2.8.101
134.9 (s) 633-833
Radiotracer technique used.
1.09.10−4 2.6.10−5
65.52
673-1173
Luminescence measurements used. 82L
72.26
373-573
Diffusion from vaccum sprayed Ag 74S2 films; sensitive dielectric method used to obtain diffusion profiles.
2.102 9.1.101
173.4
773-1073
Radiotracer technique used.
68N
202.3
773-1073
Ultrasonic measurements used.
73S4
3.10−4
51.06
295-673
Ultrasonic measurements used.
75S2
(f) D ~ (1-5).10−10
573-623
Ion microprobe and SIMS measurements used; (f) fast component.
76S2, 82S3
D < 10−14
333
CdSe Ag (a)
CdTe Li
(a) 3.28 26.01
Cu (a) 8.67 33.72
70S
70S
6.65.10−5 54.92 (s) 473-673 (f) 473-573 D ~ 5.10−8
Radiotracer sectioning technique; solubility 1.56.1929 exp(−0.55/kT) m−3.
92J1
9.57.10−4 3.7.10−4
67.45
523-753
Radiotracer technique used.
75P1
64.55
370-573
Radiotracer diffusion from Cu2Te 68W film; solubility 2.1024 m−3 at 573 K.
8.2.10−8
61.66
563-723
Rutherford back scattering technique 72M1 used; diffusion from evaporated Cu layer.
973-1073
Electrical and photoluminescence measured.
82C2
873-1273
Radiotracer technique used.
62T
Ag (a) 10.41
72M1
Au
72M1 6.7.101
(a) 38.54
66Y2
192.7
cont.
Lando lt -B { rnst ein New Series III/33A
3-40
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 11 (cont.) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4m2s−1] [kJmol−1] [K]
Remarks
(a) 115.6
9.75.10−3 4.3.10−4
200.4
673-1073
Luminescence measurements used. 82L
61.66
523-1473
Electroluminescence measurements 67K1 used.
2.6.10−3
76.12
743-1023
Radiotracer technique used.
69N
1.75.10−4
111.8
773-1073
Radiotracer technique used.
72W2
47.2
1223-1253 Diffusion in p-type ZnSe; conductivity measurements used.
93K
1.7.10−5 1.10−4
53.96
473-843
Radiotracer technique used.
65A2
63.59
673-1073
Luminescence measurements used. 80L
2.2.102
113.7
673-1073
Luminescence measurements used. 80L
Ref.
ZnS Cu
70S
Au (a)
ZnSe Li
(a) 10.98
Cu (a) 72.26
Ag (a) 57.81
82H1 2.66.10−6
70S
70S
ZnTe Li
(a) 5.59
82H1 2.9.10−2 1.7.10−4
117.5 (s) 673-973 75.15 (f) 673-973
Nuclear analysis and chemical or ion beam etching techniques used.
80M2
77.07
Radiotracer technique used.
73Z1
HgTe Ag
6.10−4
523-623
3.6.3 Diffusion of donor impurities The impurities of group III behave as donors on metal sites while of group VII are donors on chalcogen sites in II - VI compounds. They diffuse slower in comparison to group I impurities but their diffusion is sufficiently rapid to form homogeneously doped single crystals within experimentally practical time frame. For example, Al has been used to dope ZnS [77O], ZnSe [79G1], and ZnTe [71S3] and In has been used to prepare doped CdS [79P1] by diffusion. It has, however, been noticed that, compared to group III donors which tend to out-diffuse from crystals during annealing, group VII donors are stable to heat treatment [71P, 76C1, 79P2]. The reported diffusion data of group III and group VII impurities are tabulated in Table 12.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-41
3.6.3.1 Group III impurities In general, an electrically active impurity will probably be dominated by the electroneutrality condition (ENC) if present at concentration > 1023 m−3 and will be involved in ENC at smaller concentrations [88S1]. At high concentrations, the possibility of pairing and complex formation also exists. As a consequence, the impurity diffusion profile is likely to span several regions with different ENC and, therefore, changing concentrations of ionized native defects in each region. In such cases, diffusivity of impurity is expected to be concentration dependent. An example of this in In diffusion in CdS [78J] which is concentration dependent (i.e.D ∝ [In] at high In concentrations and becomes independent of [In] at low concentrations). The diffusion of In in CdTe has been studied by various workers. Kato and coworkers [63K, 66Y1] studied its diffusion by n-p junction formation and radiotracer techniques in the temperature ranging between 723 K to 1273 K. Since the initial non-stoichiometry of the sample as well as the component partial pressures at annealing temperature often drastically affect the impurity diffusion in II-VI compounds, Maslova et al. [71M1] and Chern and Kroger [74C] studied Cd-rich and Te-rich In diffusion, respectively. The former using p-n junction technique observed that addition of Cd to the In diffusion source reduced the In diffusion coefficient at 1273 K while the latter (using radiotracer technique) found that the addition of Te (instead of Cd) resulted in an increase in the diffusion coefficient of In at 928 K and 973 K. They also indicated that the Arrhenius relationship obtained by Yokozawa et al. [66Y1] is valid only for diffusion under conditions where partial pressures of Cd and Te are both small. As can be seen from Table 12, Watson and Shaw [83W] have investigated in detail the diffusion, solubility and electrical properties of In in CdTe for a range of diffusion source compositions and temperature range of 473-1123 K. D was found to be independent of [In] throughout this temperature range. D was largely independent of pCd at least above 773 K until either saturation limit was approached such that D increased sat sat or decreased near to pCd or pTe , respectively. D, showing little variation with temperature, between 2 473-673 K was difficult to interpret. They concluded that In was present as donor on Cd site and acceptor complex (InCdVCd) and a mixture of diffusion mechanisms was operative for In on Cd site involving neutral native defects or both neutral and ionized defects for different conditions. The acceptor complex (InCdVCd) diffused without assistance from other defects. Among the reported In diffusion in Zn chalcogenides (refer Table 12), its diffusion in ZnS [69N] and ZnTe [68Y2] was investigated by radiotracer technique while in I-doped n-type ZnSe [76K3] by p-n junction and ion microprobe techniques. Yokozawa et al. [68Y2] have suggested that In diffused into ZnTe via a vacancy mechanism involving Zn vacancies while the diffusion experiments of Kun and Robinson [76K3] showed that concentration dependent, high conductivity p-type ZnSe layer was formed when In was diffused at 833 K for 5 minutes from an In-Zn alloy source in n-type ZnSe and was followed by drive-in diffusion at 1213 K in high pZn atmosphere. They also observed similar behaviour when Ga or Tl were diffused but not when Al was diffused in I-doped n-type ZnSe. This type of behaviour of Ga, In or Tl in ZnSe is certainly not due to diffusion of these impurities but are probably related to some acceptor complex formation with halogen impurity interaction near the surface during drive-in process under high Zn overpressure. In fact, group III impurities other than Al have been found to behave differently in II-VI compounds. For example, B has never been demonstrated to act electrically as shallow donor [67W1] while Ga and In act as deep donors in ZnS (refer Table 12). Jones and Mykura [80J] have investigated Ga diffusion in CdS and found that Ga metal is substantially more reactive than In and formed a reactive layer of CdGa2S4 on CdS surface at temperatures below 1240 K during annealing in an ampoule containing Ga metal. Above 1240 K, the reactive layer became liquid and resulted in rapid mass loss from the specimen. They, however, found that Ga diffusion in CdS was not only concentration dependent but also orientation dependent with faster diffusion occuring perpendicular to c-axis of CdS.
Lando lt -B { rnst ein New Series III/33A
3-42
3 Diffusion in compound semiconductors
[Ref. p. 3-70
3.6.3.2 Group VII impurities As can be seen from Table 12, very scanty information is available regarding the diffusion of group VII impurities in II-VI compounds. In fact, these impurities have been used to provide uniform n-type doping levels in these compounds, and the diffusion data reported in literature for chlorine in CdS and CdTe is estimated from such doping experiments. Woodbury [67W1, 67W2] has used diffusion-doping to prepare Cl-doped CdS and CdTe by firing them in CdCl2 at 1073 K and deduced the diffusion coefficients of Cl sat under an excess pS2 for CdS and under pCd for CdTe (refer Table 12). Later Shaw and Watson [84S4] investigated the diffusion of Cl in undoped CdTe at near saturation Cd overpressure and under minimum total pressure conditions in the temperature range of 793-1073 K by using radiotracer technique. they observed no significant difference in the diffusivities under the two different conditions and concluded that Cl was present as donor on Cd site and diffused via a natural native defect pair [i.e. (VCdVTe)x or (TeiVTe)x] whose concentration was independent of pCd.
Table 12. Diffusion data of group III and group VII impurities in II-VI compounds. (1 kJmol−1 = 0.0104 eV) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Ref.
CdS Al
(d) 3.18
82H1
Ga
(d) 3.18
82H1
In
(d) 3.28
82H1 6.101 1.101
F
(d) 3.37
82H1
Cl
(d) 3.18
82H1 D ~ 3.10−10
Br
(d) 3.18
82H1
I
(d) 3.08
82H1 D~5.10−12 (f) D~9.10−13 (s)
940-1240
221.6 (||c) 923-1203 195.6 (⊥c)
Diffusion anisotropy observed; 80J optical and microprobe techniques used to evalutate. Diffusion parallel (||c) and perpendicular (⊥c) to c-axis measured; optical, microprobe and radiotracer techniques used.
78J
1073
Electrical method used to evaluate.
67W2
1273
Radiotracer technique used; 67W2 (f) and (s) represent fast and slow components. cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-43
Table 12 (cont.) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Ref.
8.10−2 6.48.10−4
155.1
923-1273
Radiotracer technique used.
66Y1
110.8
773-1123
83W
1.17.102
212.9
773-1123
Radiotracer; D0 and Q at Te saturation. Radiotracer; D0 and Q at Cd saturation; D is largely independent of Cd pressure.
CdSe Al
(d) 18.31 82H1
F
(d) 1.83
82H1
CdTe In
(d) 2.12
70S
D ~ 2.10−13 Cl
(d) 2.89
70S
7.1.10−2
473-673 154.2
D ~ 10−8
83W
83W
793-1073
Radiotracer; D0 and Q values for diffusion in near-saturated Cd pressure.
84S4
1073
Electrical method used to evaluate.
67W2
(d) 0.96
70S
1.10−8
38.54
Al
(d) 7.13
70S
5.69.10−4
123.3
1073-1273 Luminescence measurements used..
82L
Ga
(d) 38.54 82H1
In
(d) 48.18 82H1 3.101
212
1023-1273 Radiotracer technique used.
69N
Cl
(d) 9.63
173.4
1073-1373 Luminescence measurements used.
80L
202.3
973-1273
70A3
289.1
1173-1373 Luminescence measurements used.
I
Conductivity measurements of ion 67G2 implanted CdTe after annealing.
ZnS
82H1
ZnSe Al
Ga
(d) 25.05 82H1 2.3.10−2
(d) 2.7
82H1 1.81.102
Electrical and optical measurements used.
82L cont.
Lando lt -B { rnst ein New Series III/33A
3-44
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 12 (cont.) Ionization Ref. energy [kJmol−1]
Q T D0 [10−4 m2 s−1] [kJmol−1] [K]
Remarks
Ref.
ZnSe (cont.) D = 1.8.10−11- 1.5.10−10
Ga
973-1123
Electron probe microanalysis; 81M ZnSe films on GaAs were n-type.
1213
Low temperature diffusion at 833 K followed by drive-in at 1213 K; p-n junctions and ion microprobe techniques used.
76K3
192.7
973-1273
Electrical and optical measurements used; D = 1.3.10-13 m2 s−1 at 1273 K.
70A3
4
188.8
1373-1573 Radiotracer technique used.
68Y2
6.10−6
86.72
473-573
73Z1
In
(d) 2.79
82H1 D = 2.10−12
F
(d) 2.79
82H1
Cl
(d) 18.31 70S (d) 2.60 82H1
Br
(d) 20.23 70S
125.3
ZnTe Al
(d) 1.73
82H1
In F
(d) 1.73
82H1
HgTe In
-
Radiotracer technique used.
3.6.4 Diffusion of other impurities Although P, As and Sb have been studied as dopants in II-VI compounds by various workers, but the diffusion studies are limited to that of P in cadmium chalcogenides and Sb in HgSe (refer Table 13). Since scanty information is also available about diffusion of some impurities other than those reported in earlier sections, their diffusion data are also included in the Table 13. Mandel and Morehead [64M1] diffused P into n-type CdTe crystals (melt-doped with Al) at 1123 K in order to observe efficient injection luminescence in CdTe diodes. They found that a p-n junction was formed at a depth of 30 microns from the surface by diffusing P under a Cd overpressure for two weeks. From this measurements, they estimated the D of P (refer Table 13). Later, Hall and Woodbury [68H] obtained P diffusion profiles in CdTe at 1173 K and 1223 K and in CdSe at temperatures ranging from Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-45
1073 K to 1273 K ( as a function of Cd partial pressures ) by using radiotracer technique and found that they could be fitted to two erfc functions having different diffusivity values ( a slow component and a fast component). Measurement of D of P at 1173 K and 1223 K showed that the values for slow component -2 / 3 were largely independent of pCd whereas for fast component were proportional to pCd at small pCd and sat became independent of pCd near pCd . As mentioned by Selim and Kroger [77S1], the dominant defects at these temperatures are acceptors Pi and PTe and neutral complex (PCdPi) and is quite possible to expect their contributions in the diffusion of P. Similarity of these results with those observed for chalcogen selfdiffusion also indicate that an interstitial mechanism was responsible for P diffusion. A detailed analysis is, however, needed to establish the mechanisms responsible for its diffusion. Nebauer [73N1] studied diffusion of P in CdS in the Cd-rich part of the existence region by radiotracer technique. As in the case of P diffusion in CdTe, the diffusion profiles exhibited two erfc parts (i.e. slow and fast) with usual temperature and time dependence. The D0 and Q values, associated with fast component and D values for slow component are given in Table 13. The only reported diffusion of As in II-VI compounds is in CdTe by Morehead and Mandel [64M2] by radiotracer technique. They have, however, not mentioned any diffusion coefficient. The diffusion of transition elements Fe, Mn and Ni in some II-VI compounds are also reported in literature. Lukaszewicz [82L] has investigated diffusion of Ni, considered to be luminescence ‘ Killer’ impurity, in CdS and ZnSe from vacuum sprayed Ni films in an atmosphere of the anion component of the compound in the range of temperatures from 843 K to 1183 K. It was noted that at temperatures below 843 K only surface diffusion took place. Two-sample luminescence measurement technique was used to determine the diffusion coefficient of Ni. The D0 and Q value for Ni in CdS and D values at two temperatures for Ni in ZnSe are listed in Table 13. Panchuk et al. [81P2] have observed that Fe has a high solubility in CdTe above 953 K (>1024 m−3) and it decreased with increasing pCd. Diffusion experiments between 793 K and 1333 K showed that D was independent of the concentration of Fe and, at 1103 K, was independent to pCd. It was suggested that Fe diffused by the dissociative mechanism based on the principal neutral defects FeCd and Fei. The existence of predominantly neutral states, however, seems unlikely as FeCd is a deep donor in CdTe [85L] and, for [Fe] > 1024 m−3, the formation of complexes can not be ignored. In addition to above studies, diffusion of Mn in ZnS and in HgTe are also reported and its D0 and Q values are given in Table 13.
Table 13. Diffusion data of other impurities in II-VI compounds. (1 kJmol−1 = 0.0104 eV) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
6.5.10−4
154.2 (f)
1073-1273
Radiotracer; dependence of D on
73N1
(s)
1073-1273
Cd and P pressures observed
CdS P (a)
D~
10−12-
10−11
Ni
6.75.10−3
105.0
843-1173
Luminescence measurements
82L
Yb
D = 1.3.10−9
-
1233
Luminescence measurements
69G2
Radiotracer technique used
68H
Radiotracer; diffusion under saturated Cd pressure
68H cont.
CdSe P (a)
D = 5.3.10−12 - 6.10−11 (f) 1173-1273 D = 2.8.10−13 - 9.10−12 (s) 1073-1273
Lando lt -B { rnst ein New Series III/33A
3-46
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 13 (cont.) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
6.9.10−11
36.31
973-1198
Radiotracer; Do and Q for maximum Cd -r pressure; D(Sn) ∝ pCd where r = 0 at 973 K and steadily increases to 0.67 at 1198 K
78P2
8.3.10−2
212.0
973-1198
Radiotracer; D0 and Q for minimum Cd pressure
78P2
D = 1.2.10−10 (f) D = 9.10−12 (s)
1173
Radiotracer; diffusion profiles have two fast (f) and slow (s) components; D at 1173 K -2 /3 and 1223 K showed for (f) D(P) ∝ pCd at small pCd and for (s) it is independent of pCd
68H
D ~ 4.1010
1123
Diffusion under Cd pressure
64M1
1123
Diffusion under Cd pressure
64M2
74.19
793-1333
Radiotracer diffusion studied under pCd
81P2
237.0
773-1173
Radiotracer technique used; diffused in Ar atmosphere
72W2
1013 1183
Luminescence measurements used
82L
CdTe Sn
P (a)
As (a) Fe (d) D = 4.10−8 (1103 K)
ZnS Mn
2.3.103
ZnSe Ni
D = 1.5.10−8 D = 1.3.10−7
HgSe 6.3.10−5
81.9
813-903
Radiotracer technique used
63B1
Sn
1.8.10−3 1.72.10−6
77.1(f) 63.59(s)
473-573 473-573
Radiotracer (f) fast and (s) slow components observed
71Z1
Mn
1.5.10−4
125.3
523-623
Radiotracer technique used
73Z1
Sb
HgTe
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-47
3.6.5 Diffusion in II-VI compound ternary alloys Among the II-VI ternary alloys, the diffusion studies have been centered around CdxHgi−xTe as it has emerged as an important infrared material. The energy band gap of this alloy is found to vary almost linearly with composition from HgTe to CdTe and impurities of group I and III are, respectively, acceptors and donors on metal sites and group V and group VII are, respectively, acceptors and donors on Te sites [83V2]. The reported self- and impurity- diffusion data for this alloy are tabulated in Table 14. Since composition of interest lies in the range of 0.16 < x < 0.25 and the partial pressure of Hg above CdHgTe is several orders of magnitude higher than that of other two elements (Cd,Te), most of the studies reported in this table are for composition close to x = 0.2 and annealings have been carried out in Hg overpressures. Recent tracer diffusion studies (refer Table 14) on self-diffusion of Cd, Hg and Te in Cd0.2Hg0.8Te have produced reasonably reproducible experimental findings, despite considerable inconsistency in the early experimental work. For example, a common feature of Hg profiles, which are unchanged by preannealing, is that they can be fitted by a sum of two erfc curves. The slower component appears to be independent of pHg while the the diffusion coefficient of the fast component is proportional to pHg at high -1 at low pressures [89T1, 84C]. Brown and Willoughby [82B3, 83B3] observed pressures and to pHg additional faster component after diffusion anneals at 498 K instead of the slow component seen by Tang and Stevenson [89T1] and Archer et al. [92A1] ( which may probably be too slow to observe at 498 K and annealing time used). Two components are also seen for Cd self-diffusion with an exception of only a single component observed by Shaw [86S1]. At temperatures greater than 623 K, Cd diffusin appears to be independent of pHg except for an increase near the maximum value of pHg. The behaviour of Cd in CdHgTe is similar to Cd self-diffusion in CdTe. As can be seen from Table 14, Gorshkov and coworkers have found that, at a given temperature and Hg overpressure, the diffusion of Sn, P and Sb can be expressed in terms of a single diffusion coefficient while that of Cu, Ag, Au and In follows a two component pattern having slow and fast diffusion coefficients. Gorshkov et al. [84G2, 84G3] have broadly classified the diffusants into three groups on the basis of the closeness of their Q values in CdxHg1−xTe (x = 0.2). The first group (43.36 to 61.66 kJmol−1) consists of Cu (s), Au (s), In (f), P and Sb, the second (67.45 to 72.26 kJmol−1) of Cu (f), Ag (f) and Au (f) and the third (91.53 to 96.35 kJmol−1) of In (s) and Sn. They have suggested that the slow diffusion of Cu, Ag and Au, the fast diffusion of In and the diffusion of P and Sb takes place via the dissociative or relay migration mechanism while the slow diffusion of In involves the vacancy mechanism and neutral vacancy pairs (VHgVTe)x. The diffusion of Sn is suggested to occur via vacancy mechanism involving neutral Hg vacancies and vacancy pairs (VHgVTe)x. A mechanism is also proposed for rapid diffusion of Cu, Ag and Au. Lately there has been considerable interest in the study of interaction of metal overlayers with CdHgTe surface. In fact, the overlayers can be classified into three groups: namely, reactive, intermediate and unreactive depending upon the relative heats of formation of HgTe and the overlying metal telluride [83B2] and upon the heat of alloying of Cd and Hg with overlying metal [85M1]. For example, deposition of metal such as Al [86D1], In [86D1], Ti [87D1] and Cr [85F] has resulted in the formation of metal tellurides while Pt [87F] has formed a Cd-Pt alloy at the interface. It is clear from such studies that, while considering migration and incorporation in interpreting experimental results, the possible changes in surface chemical composition during diffusion of reactive metals must also be considered in such studies with ternary alloys.
Lando lt -B { rnst ein New Series III/33A
3-48
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 14. Diffusion data for II - VI compound ternary alloys. (1 kJmol−1 = 0.0104 eV) x
D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
OverRemarks pressure p(X) [atm]
Ref.
H2
Alloying of Li metal at 563 K and annealing at 523 K.
77J
53.0 (s) 523-673 67.45 (f) 523-673
Hg sat.
Radiotracer; slow (s) and fast (f) components observed.
84G2
40.47
Hg sat
Optical transmission technique used.
87B1
Hg ~ sat.
2/3 Radiotracer; D(f) ∝ pHg
84G2
Cdx Hg1-xTe 0.2
Li (p)
0.2
Cu (p) 1.1.10−6 9.1.10−2
0.21-0.25
0.2
523
8.1.10−3
Ag (p) 1.1.10−7 3.1.10−1
323-573
43.36 (s) 473-723 72.26 (f) 473-723
whereas D(s)
/3 ∝ p1Hg
which
sat pHg
when is approached becomes independent of pHg at 573 K. 0.2
Au (p) 2.5.10−8 1.10−1
43.36 (s) 473-673 69.37 (f) 473-673
Hg ~ sat.
2/3 Radiotracer; D(f) ∝ pHg
whereas D(s)
84G2
/3 which ∝ p1Hg
sat when pHg is approached /4 becomes p1Hg dependent at 573 K.
0.18
0.2
0.2
D(s) = 4.5.10−13 D(f) = 2.7.10−11 Cd 1.48 (self) 3.84.101
7.10−1
498
Ar
Radiotracer and SIMS; evaporated Au source.
85P1
159.0 (s) 623-823 163.8 (f) 623-773
Hg: 0.02-6 Radiotracer diffusion from the electrodeposited thin layer; fast (f) and slow (s) components independent of pHg.
89T1
149.3 (s) 673-763
Hg sat.
84C
Radiotracer; D(s) independent of pHg.
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-49
Table 14 (cont.) x
D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
OverRemarks pressure p(X) [atm]
Hg sat.
Ref.
Cdx Hg1-xTe (cont.) 0.2
Cd 2.07.10−3 (self) (cont.)
110.8
503-773
0.2
D ~ 2.10−14 - 1.10−12
50.1
473-673
115.6
527-725
0.16-0.24 Hg 3.10−3 (self)
6.07 5.5.10−7
163.8 (s) 623-773 58.77 (f) 623-773
Radiotracer; D independent 86S1 of pHg at 773 K but largely independent of pHg at 573673 K except for a sharp rise sat . close to pHg Radiotracer technique used. 74Z
Hg sat.
Hg: 1
93A Radiotracer; D0 and Q for MOCVD grown material; strong composition dependence of D observed for 0 ≤ x ≤ 0.45. Radiotracer; 89T1 D(s) almost independent r of pHg while D(f)∝ pHg where r changes from −1 to 1 as stoichiometry changes from Te rich to Hg rich conditions.
0.2
9.8.10−9 2.5.10−9
33.72 (s) 473-573 14.45 (f) 473-573
Hg: 10−2
Radiotracer; 82G D(s) independent of pHg while /2 . D(f) ∝ p1Hg
4 3.1.101
144.5 (s) 673-748 144.5 (f) 673-748
1/ 3 Hg: 2.5.10−1 Radiotracer; D(s)∝ pHg while 84G2 1/ 2
D(f)∝ pHg for range near sat , the exponents change pHg sign for p < 6.5.104 Pa at Hg
723 K and < 2.5.104 Pa at 673 K. 0.2
9.9.10−1
144.5 (s) 623-763
Hg sat.
Radiotracer; D(s) independent of pHg .
84C
0.2
2.10−4
106.0
Hg sat.
Radiotracer; diffusion profiles have two components.
92A1
523-673
cont. Lando lt -B { rnst ein New Series III/33A
3-50
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 14 (cont.) x
D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
OverRemarks pressure p(X) [atm]
Ref.
923
Hg
Sputtered Al source; n-p junction used to evaluate.
77J, 82B3
498
Ar
Diffusion in MOVPE grown 86P1 layer; single component erfc profiles obtained.
Cdx Hg1-xTe (cont.) 0.4
Al (n) D ~ 8.10−10
0.2
Ga (n) D ~ 2.10−8
573
H2
Molten Ga used as source; 77J, n-p junction used to evaluate. 82B3
0.2
-
498
Ar
Diffusion in MOVPE grown 86P1 layer; single component erfc profiles obtained.
0.2
In (n) 1.5.10−4 2.10−6
91.53 (s) 573-723 53.0 (f) 573-723
Hg sat.
Radiotracer; 83G2 D(s) independent of both pHg and dopant oncentration 0 .7 while D(f)∝ pHg at 673 K.
0.22
2.4.10−4
106.0 (s) 523-623
Vacuum
85D ZnS encapsulated In implanted specimen annealed in vaccum; n+ electrical activity is related to radiation damage and partly to implanted In impurity; SIMS.
0.2
2.6.10−2
131.0 (s) 503-673
Hg
Radiotracer; D(s) independent of pHg.
0.2
D(s) = 4.10−15
498
Ar
Diffusion in MOVPE grown 86P1 layer; single component erfc profiles obtained.
0.21
5.25.10−6
353-423
no overpressure
Diffusion data obtained from 80M1 Hall measurements; same Q for x = 0.29.
523-723
Hg sat.
Annealing of In doped MBE 92M layer; D vs 1/T given; SIMS.
773-873
Hg
Sputtered Si source used; Hall measurements.
36.61
D ~ 10−17- 6.10−15
0.4
Si (n)
85S3
77J
cont. Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-51
Table 14 (cont.) x
D0 [10−4 m2 s−1]
Cdx Hg1-xTe (cont.) 0.2 Sn 1.10−4
Q T [kJmol−1] [K]
OverRemarks pressure p(X) [atm]
96.35
Hg sat.
523-773
Radiotracer; D independent of pHg for
Ref.
84G2
-1 pHg >2.5⋅103 Pa but D ∝ pHg for lower pHg at 573 K.
0.2
P (p) 4.9.10−10
53.0
573-673
Hg sat.
Radiotracer; D independent of pHg for
84G2
/2 pHg >2.5⋅103 Pa but D ∝ p1Hg for lower pHg at 573 K; heavy donor (In) or acceptor (Ag) doping causes substantial reduction in D.
*
As (p) D = 4.10−11 - 8.10−15
-
0.23
0.2
623
Hg: 0.11- 0.8
Annealing of double layer 93C heterostructure (*) formed by As-doped CdHgTe LPE grown layer on undoped CdHgTe layer in Hg pressure; -3 D ∝ pHg dependence observed; SIMS.
D = 8.10−17 - 6.10−14
523-673
Hg sat.
Annealing of As-doped MBE 92M layer; D vs 1/T given, As diffuses more rapidly than In; SIMS.
D~2.10−13
673
Hg sat.
Sample implanted with As at 87B2 373 K annealed in pHg; SIMS and differential Hall used to evaluate.
573-673
Hg
Radiotracer; D independent of pHg for
Sb (p) 1.1.10−8
61.66
84G2
/2 pHg >2.5·103 Pa but D ∝ p1Hg for lower pHg at 573 K; heavy donor (In) or acceptor (Ag) doping causes substantial reduction in D.
cont.
Lando lt -B { rnst ein New Series III/33A
3-52
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 14 (cont.) x
D0 [10−4 m2 s−1]
Q T [kJmol−1] [K]
OverRemarks pressure p(X) [atm]
Ref.
207.2 (s) 623-773
Hg: 1
Radiotracer diffusion from 89T1 electrodeposited layer; diffusion profiles showed two branches in non preannealed samples; for preannealed -1 samples D(s) ∝ pHg .
Hg
-1 Radiotracer; D ∝ pHg but
Cdx Hg1-xTe (cont.) 0.2
Te 8.86.101 (self)
D = 10−9- 6.10−11
x=0.2
400
80Z
sat /3 , D ∝ p1Hg near pHg .
0.22-0.24 I (n)
D < 1.10−13
673
Hg: 0.1
Annealing of I-doped 93M3 CdHgTe grown by MOCVD; SIMS.
HgSxSe1−x 0.2
Hg 4.10−9 (self)
28.9
473-673
S2 sat.
Radiotracer technique used. 69K3
0.2
S 8.8.10−10 (self)
28.9
473-673
S2 sat.
Radiotracer technique used. 70K
0.2
Se 3.14.10−6 (self)
61.66
473-673
Se2 sat.
Radiotracer technique used. 70K
HgSxTe1−x 0.2
Hg 2.10−10 (self)
57.81
473-673
Hg sat.
Radiotracer technique used. 69K3
0.2
S 1.10−6 (self)
48.18
473-673
S2 sat.
Radiotracer technique used. 70K
Zn
Phosphorus doped ZnSe0.5 Te0.5 used for diffusion, p-n junction and optical techniques used.
ZnSexTe1−x 0.5
Al (n) D = 1.2.10−9
192.7 973-1273 (1273 K)
70A3
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-53
3.7 Diffusion in IV-VI compounds Diffusion in IV-VI compounds have not been investigated as extensively as in other compounds discussed in earlier sections. One of the reasons being their limited device applications. Among these compounds, the diffusion studies have been mainly restricted to the lead chalcogenides as PbS was earlier used for infrared detectors while PbSe and PbTe were used for making thermoelectric devices. The available information pertaining to self and/or impurity diffusion in these Pb chalcogenides have been reviewed in the past by various workers [59S, 63B1, 70S, 73S2]. This information along with the one regarding dopants introduced during growth in IV-VI compounds are tabulated in Table 15.
3.7.1 Self-diffusion It has been observed [54B1, 54B2, 62B2, 64B4, 70B3] that PbS, PbSe and PbTe are homogeneous over a narrow range on either side of stoichiometric composition and annealing them in a controlled atmosphere of their components have a pronounced effect on their electrical properties. It is now well established (refer Table 15) that annealing them in high vapour-pressure of a group VI component leads to the formation of a p-type layer in n-type specimens while those heated in vaccum or in Pb-rich ambient form a n-type layer in p-type specimens. As can be seen from Table 15, Wagner and coworkers [62S2, 63S2, 65S2, 70B1, 71G1] have studied self-diffusion of Pb and chalcogen X in PbX. The lead chalcogenides, PbS, PbSe and PbTe, showed some general similarities in their diffusion behaviour. In all three compounds, self-diffusion of Pb is enhanced by the presence of both donor and acceptor impurities. This has been attributed as due to active participation of ionized Pb vacancies and Pb interstitials in the diffusion process. Further support to this interpretation is provided by the observed variation of the Pb diffusion coefficient with pS2 for PbS and pTe2 for PbTe [63S2, 71G1, 73S2]. The chalcogen self-diffusion have also shown similar behaviour in all lead chalcogenides. For example, increase in chalcogen self-diffusion coefficient with increasing chalcogen pressure has been observed in PbS [65S2], PbSe [70B1] and PbTe [71G2]. In the case of PbS and PbSe, diffusion isotherms have shown that there are distinct regions in which different defects dominate the diffusion process. The neutral chalcogen interstitials, however, appear to dominate near chalcogen saturation region. On the other hand, eventhough self-diffusion of Te in PbTe is found to increase with Te content in the specimens, the same activation energy Q for all compositions indicate that only one defect mechanism dominates over the entire range [71G1]. An interstitial or interstitialcy mechanism has been proposed by Stevenson [73S2] to explain the increase of self-diffusion coefficient of Te with Te content.
3.7.2 Impurity diffusion Although the type and concentration of carriers in lead chalcogenides could be controlled by the adjustment of the deviation from stoichiometry (refer section 3.7.1), but the search for better electrical properties has led to several impurity diffusion studies in them. It can be seen from Table 15 that dopants are either introduced in the melt or by diffusion during growth or more recently by ion implantation. Earlier thermoelectric applications have led to investigations of suitable acceptor and donor dopants as well as diffusion of metal contacts in IV-VI compounds. A detailed study of the effect of metallic impurities and halogens on electrical properties of PbTe dated back to 1956 in which Kovalchik and Maslakovets [56K] have shown that Mg, Ge, Sn, Bi, Nb, Fe, Co, Ni and Pt acted as donors while Cu, Ag, Au, Zn, Cd, Al and In behaved as acceptors in presence of halogen atoms. Later Strauss [73S3] has systematically investigated the effects of dopants in PbTe and concluded that In and Bi are donors, Tl is an acceptor and Cu, Ag, Sb and As are amphoteric. While studying self-diffusion in lead chalcogenides Wagner and coworkers (refer Table 15) have extensively used Bi as a donor and Ag as an acceptor dopant Lando lt -B { rnst ein New Series III/33A
3-54
3 Diffusion in compound semiconductors
[Ref. p. 3-70
in them. It can be seen from the investigations reported in literature that acceptor or donor character of impurities in lead chalcogenides often depend on the annealing procedure applied to the crystal (i.e. whether this annealing procedure is carried out under metal or nonmetal saturated conditions). With use of newer techniques, like MBE for growing thin epitaxial layers, the utilization of crystal stoichiometry deviations to form junctions in these compounds are no more practical as interdiffusion coefficients for them are in the range of 10−15 to 10−12 m2 s−1 [73S2]. Bi and Tl are, therefore, used as ntype and p-type dopants, respectively, as their doping behaviour is relatively unaffected by stoichiometry deviations. Partin [85P2, 83P3] has shown that rare earth elements, such as Dy, Ho and Yb, could be better n-type dopants in PbTe as their diffusion coefficients are relatively low at epitaxial growth temperatures (refer Table 15). However, further investigations are necessary to ascertain the role of their fast diffusion component in the formation of shallow junctions and hetero layers and to find out their behaviour in other IV-VI compounds. Apart from diffusion and epitaxial growth, impurity ion implantation is not only used as an alternate approach for doping thin layers but ion damage is also found to be an interesting method to convert certain p-type lead chalcogenides to n-type. Donnelley et al. [71D, 72D] were the first to report the conversion of p-type PbTe to n-type by energetic ion damage and used this effect to produce photovoltaic detectors and laser diodes by proton bombardment. Palmetshofer et al. [77P, 78P1] studied the carrier concentration and doping profiles in ion-bombarded PbTe and observed that after certain ion fluence the carrier concentration reached a constant value irrespective of the original carrier concentration and ion species (Pb, Te, Xe). Similar dose-independence of the carrier concentration of proton bombareded PbTe has been observed by Bryant and Staudte [82B5]. These above mentioned studies may, however, pose some difficulties in doping PbTe by impurity ion-implantation and in their analysis. Finally, some observations, such as, change in carrier concentration in n-type PbTe by room temperature annealing [77F, 82B5], room temperature diffusion of Ag and aging of contacts in p-type PbTe [81B] and influence of gamma-radiation on diffusion of Ag in p-type PbTe at 313 K [79D1], indicate that impurities and defects in PbTe are very much more mobile than is generally realized. Table 15. Self and impurity diffusion data along with information regarding dopants introduced during growth in IV-VI compounds. (1 kJmol−1 = 0.0104 eV) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
Doping with NaS; electrical properties measurement
80P
PbS Na (a) Cu (d) 4.6.10−4 5.10−3
34.69
423-723
n-p junction technique used to evaluate
63A2
29.86
373-673
n-p junction technique used to evaluate
57B1
Ag (a)
-
Defect concentration altered by addition of Ag solute; self-diffusion of Pb enhanced by addition of Ag.
63S2
Influence of Tl on the solubility of excess Pb and carrier concentration in PbS studied.
80B1
Tl (a)
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-55
Table 15 (cont.) D0 [10−4 m2 s−1] PbS (cont.) Pb 8.6.10−15
Q [kJmol−1]
T [K]
Remarks
Ref.
146.5
773-1073
Radiotracer; D0 and Q for minimum pS2
63S2
(self; d)
diffusion in inert gas and varying pS2 studied;
973
Bi (d) -
D enhanced with donor (Bi) and acceptor (Ag) additions and by excess Pb or S in pure samples. Radiotracer self-diffusion studied in undoped 63S1 PbS over the entire range of existence; D vs. pS2 showed four distinct regions.
973
Simultaneous radiotracer diffusion of Bi and Pb; D of Bi nearly same as that of Pb for both undoped and Bi-doped PbS for various pS2 .
68Z
773-1023
Radiotracer; D increased with pS2 and
65S2
S 4.56.10−5 (self; a)
117.5
Ni (d) 1.78.101
91.53
473-773
n-p junction technique used to study diffusion in p-type undoped and Ag-doped PbS.
57B2
Na (a) 5.6.10−6 1.5.101
38.54 (f) 167.6 (s)
673-1123
Radiotracer; fast (f) and slow (s) components of diffusion found.
65F1
Cu (a) 2.5.10−5
33.72
366-793
Radiotracer diffusion in Ar atmosphere; max. solubility 9.1024 m−3 at 1073 K.
66K1
Ag (a) 7.4.10−4
33.72
673-1123
slightly enhanced with Bi doping; D0 and Q for 1024 m−3 excess S.
PbSe
Cd (d) -
673
− Radiotracer, solubility 1.1024- 8.1024 m 3 in the range of 673-1123 K.
65F1
Doping during melt-growth; Hall measurements.
65R
Cd diffusion at 673 K with Cd source temperature varied from 423 to 573 K; Hall effect, conductivity and solubility studied.
77S4
Doping during melt-growth; Hall and solubility investigated.
65R cont.
. In (d)
Lando lt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors
3-56
[Ref. p. 3-70
Table 15 (cont.) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
Influence of Tl on the solubility of excess Pb and carrier concentrations in PbSe studied.
80B1
PbSe (cont.) Tl (a)
Pb 4.98.10−6 (self; d) 4.28.10−2
79.97
673-1073
Radiotracer diffusion in undoped samples.
62S2
155.1
673-1073
Radiotracer diffusion in Bi-doped samples; D enhanced by Bi-doping for T > 973 K and depressed for T < 973 K.
62S2
4.41.10−7
53.0
673-1073
Radiotracer diffusion in Ag-doped samples; D enhanced by Ag doping.
62S2
3.74.10−2 9.81.10−4
197.5
773-1073
Radiotracer diffusion in Pb saturated PbSe.
73G2
160.9
693-1073
Radiotracer diffusion in Se-saturated PbSe.
73G2
Sb (d) 3.4.10−1
192.7
923-1123
Radiotracer technique used.
64B2
Se 8.74.10−7 (self; a)
60.7
623-1123
Radiotracer diffusion in undoped and Ag-doped PbSe; D0 and Q for undoped samples.
70B1
8.13.10−4 5.53.10−1
128.1
693-1073
Radiotracer diffusion in Se-saturated PbSe.
73G2
213.9
773-1073
Radiotracer diffusion in Pb-saturated PbSe.
73G2
2.1.10−5
115.6
923-1123
Radiotracer diffusion in PbSe with composition 58B close to the congruent subliming composition.
43.4
673-1123
Radiotracer diffusion in n-type undoped, Na2Se-doped p-type PbSe; Q higher in doped samples.
Ni (d) D ~ 1.10−10
973
Radiotracer in n-type undoped and p-type Ag- 68S2 doped PbSe; anomalous behaviour observed.
Ga (d) D ~ 3.10−8
623
Radiotracer; D for fast diffusion component.
66K2
873-1123
Radiotracer diffusion in undoped and Na-doped PbTe; D0 and Q for undoped samples.
68C2
Cl (d) 1.6.10−8
65F2
PbTe Na (a) 1.7.10−1
Cu (a, d)
180.0
Cu is an acceptor in Te-saturated and a donor in 73S3 Pb-saturated PbTe; Hall measurements. cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-57
Table 15 (cont.) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
Ag is an acceptor in Te-saturated and a donor in Pb-saturated PbTe; Hall measurements.
73S3
313
Influence of γ-radiation on diffusion of Ag in p-type PbTe.
79D1
973, 1073
Cd-doped crystal prepared by diffusion from Pb-Cd alloy; solubility and electron concentration as a function of pCd measured.
76V1
673
Cd diffusion with source temperature varied 77S4 from 423 K to 583 K; Hall effect, conductivity and solubility measured.
573-673
81S2 Cd diffusion led to formation of Pb1-xCdxTe with x < 0.01; inter-diffusion due to formation of CdTe on the surface
PbTe (cont.) Ag (a, d) D ~ 10−14
Cd (d)
Ga (d)
Doping during growth; solubility measured.
77B4
In (d)
Hall coefficient and electrical conductivity measured.
71A2
Tl (a)
Electrical properties measured in the temperature range of 77-900 K; optical and thermoelectric properties also studied
79G3
Sn (d) 3.4.10−1 3.2.10−1
192.7
923-1123
Radiotracer technique used.
58B
171.5
823-973
Diffusion while doping from vapour phase; X-ray microanalysis used; formation of Pb1−xSnxTe on surface observed.
84B
57.81 Pb 2.9.10−5 (self; d) D = 3.6.10−11
523-773
Annealing in Pb-rich vapour; n-p junction measurements used to evaluate D.
57B3, 56B
973
Radiotracer diffusion under Pb saturation pressure condition.
71G1
973
Radiotracer diffusion under Te2 saturation pressure condition.
71G1
973
D for samples annealed in Ar atmosphere showed enhancement doping with Ag or Bi.
71G1
1.04
823-973
Radiotracer diffusion in Pb-rich crystal.
71G2
255.3
823-973
Radiotracer diffusion in Te-rich crystal.
71G2
D = 3.2.10−10
3.1.10−6 2.5.103
cont. Lando lt -B { rnst ein New Series III/33A
3-58
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 15 (cont.) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
As is an acceptor in Pb-saturated and a donor in Te-saturated PbTe; Hall measurements.
73S3
Radiotracer technique used.
58B, 56B
Amphoteric behaviour observed.
73S3
Bi-doped PbTe epitaxial layers grown on Pb0.8Sn0.2Te; diffusion of Bi and Sn observed during growth; electron microprobe profiling used.
79G2
PbTe (cont.) As (a, d) Sb (d) 4.9.10−2
148.4
773-1073
Bi (d)
Te 2.7.10−6 (self; a) 2.4.10−6
72.26
773-1073
Radiotracer technique used.
58B
100.2
833-993
Radiotracer diffusion in Te-rich crystal.
71G2
6.5.10−7
100.2
833-993
Radiotracer diffusion in Pb-rich crystal.
71G2
Thermoelectric properties studied.
79B
Cr (d) Cl (d) D > 2.3.10−10
973
Fe
Radiotracer Ni36Cl2 source used; simultaneous 69G1 diffusion of Ni and Cl studied. Fe-doped single crystal grown from melt; magnetic properties studied.
80A1
Ni (d) D > 1.10−6
973
Electroplated Ni or radiotracer 63NiCl2 vapour source used; diffusion in flowing Ar or in evacuated sealed amphoule; solubility 2.1023 m−3 at 973 K.
69G1
Dy (d)
643
Behaviour very similar to Ho observed.
85P2
Ho (d) D < 1.10−16
643
D value for high concentration (>1.1024 m−3); 85P2 at low concentration Ho diffused rapidly and is temperature insensitive; SIMS depth profiling used.
Yb (d) D < 3.10−17
643
SIMS depth profiling used to evaluate D.
83P3 cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-59
Table 15 (cont.) D0 [10−4 m2 s−1]
Q [kJmol−1]
T [K]
Remarks
Ref.
70.34
673-873
X-ray microanalysis used to evaluate D.
84D1
GeTe Ag (a) 7.10−6
3.8 Diffusion in other useful compounds The self-and impurity-diffusion in technologically important compound semiconductors (i.e. III-V, II-VI and IV-VI) have already been dicussed in earlier sections. Apart from these, the diffusion studies of some other useful semiconductor compounds have occasionally been reported in literature. Few such studies in selective group IV, group II-V and group V-VI compounds are discussed in the following sections.
3.8.1 Diffusion in SiC Large band gap compound semiconductor of group IV is SiC. Efficient luminescence, even at temperatures greatly exceeding room temperature, is observed in it. Depending on the impurity composition, the spectral region of luminescence may cover the whole visible and near infrared regions. Since both n- and p-type SiC can be easily realized, very intense electroluminescence can be generated in the p-n junctions of this compound [77T1]. One of the most interesting feature of this compound is that various multilayer periodic structures, polytypes, are produced in the process of its crystallization. The properties of p-type SiC are nearly similar in the different polytypes whereas in n-type they differ greatly [77T1]. The main SiC polytypes, in which diffusion studies have been carried out are 4H, 6H, 15R and 3C having energy gaps of 316, 297.7, 291.0 and 231.2 kJmol−1 ,respectively [80V2, 77V2, 71L4]. Earlier cubic SiC was reported as β-SiC while all hexagonal and rhombohedral polytypes were denoted as α-SiC. The reported self- and impurity-diffusion data and maximum solubility at different temperatures in different types of SiC are tabulated in Table 16. It can be seen from this table that some diffusion studies are mentioned as those pertaining to α-SiC instead of a specific polytype. The self-diffusion of Si and C in intrinsic, N-doped n-type and Al-doped p-tpye SiC have been studied by Hong and coworker [80H, 81H2] and Ghoshtagore and Coble [66G]. Hong et al. have observed that Si- diffusion in N-doped exceeded that in undoped SiC because of the increase in the concentration of the charged acceptor-type Si vacancies in the presence of N species while the reason for the difference in the self-diffusion coefficient of C in undoped and N-doped SiC is due to the decrease in the solubility of charged donor type C vacancies, and, therefore, in the total number of vacancies caused by the presence of donor N impurity. Ghostagore and Coble have observed that self-diffusion coefficient D for Si-diffusion in Al-doped p-type SiC was approximately an order of magnitude higher than that of C in N-doped n-type SiC between 2200-2290 K (refer Table 16). All these observations indicate that diffusion of host components in SiC is very much dependent on the impurity present in it.
3.8.2 Diffusion in some group II-V and V-VI compounds Apart from group IV-VI compounds, some group II-V and V-VI compounds have been used in the past for making thermoelectric devices. The available data pertaining to self- and impurity-diffusion in ZnSb, CdSb, Bi2Se3 and Bi2Te3 compound semiconductors are tabulated in Table 17. Some of this earlier
Lando lt -B { rnst ein New Series III/33A
3-60
3 Diffusion in compound semiconductors
[Ref. p. 3-70
information in Table 17 may be related to imperfect crystals as thermoelectric applications required cast samples rather than single crystals. Bi2Se3 and Bi2Te3 have rhombohedral structure with strong anisotropy of principal physico-chemical properties along and perpendicular to c-axis as is clear from the radiotracer diffusion studies of Cu, Ag and Cd in Bi2Te3 (refer Table 17). This type of diffusion data could be explained by assuming that the diffusion along the clevage plane (i.e. in the direction ⊥ to c-axis) proceeds through interstices along the layers of like atoms while at right angle to the clevage plane via interstices and/or Bi vacancies. Table 16. Self and impurity diffusion and max. solubility in different types of SiC. (1 kJmol−1 = 0.0104 eV) Q T Ionization D0 energy [77T1] − [kJmol 1] [10−4 m2 s−1] [kJmol−1] [K]
Max. solubility [77T1]
Remarks
Ref.
[106 m−3]
SiC (6H) Li
1.2.10−3
163.8
Be (a) 38.54 57.81
3.10−1 3.2.101
298.7 (f) 1973-2523 501.0 (s)
7.1017-5.1019 (2073-2573 K)
p-n junction technique 68M used; fast (f) slow (s) components.
B (a) 37.58
5.101
520.3
1973-2673
4.1019-2.5.1020 (2073-2573 K)
Surface concentration 77V2 by Neutron activation analysis; N-doped ntype samples; Hall and p-n junction techniques used.
3.2
491.4
1873-2823
Diffusion in N-doped n-type samples; conductivity and p-n junction technique used.
72M3
2423-2523
Diffusion in N-doped
69P1
1870-2470
85G2 1020exp(−1.4/kT) Radiotracer, (1870-2470 K) autoradiograph and ESR techniques used; diffusion in n-and ptype SiC; D0 and Q for p-type SiC.
n-type SiC. Al (a) ~26.01
8
587.7
2223-2673
2423-2523
(0.7-1.1).1021 (2573 K)
p-n junction technique 69M used; N-doped n-type specimens used. Diffusion in N-doped 69P1 n-type SiC; p-n junction LED formed. cont. Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-61
Table 16 (cont.) Q T Ionization D0 engergy [77T1] [kJmol−1] [10−4 m2 s−1] [kJmol−1] [K]
Max. solubility [77T1]
Remarks
Ref.
[106 m−3]
SiC (6H) (cont.) Ga (a) 27.94
D = 2.5.10−14- 3.10−12
2073-2573
C (self)
3.102
597.4
2126-2333
Radiotracer diffusion in Al-doped p-type samples.
66G
2.1017
1262
2250-2361
Radiotracer diffusion in N-doped n-type samples.
66G
Radiotracer diffusion 66G in Al-doped p-type SiC.
Si (self)
4.10−11 < D < 2.10−10
2200-2290
N (d) 9.15
D ~ 5.10−9
2723
D = 10−18-10−12 4.3-8.7.104 732-896
2073-2723
2.3.1018-7.1018 (2073-2573 K)
8.1020, 2.6.1020 (2023, 2723 K)
D = 1.5.10−16 - 5.10−13 2027-2527
Sc (a) 23.12
D < 10−13
2073-2573
Specimen placed inside isothermal SiC enclosure with an external pressure of 35 atm of N.
65S3
77T1
2273-2823
O
p-n junction technique 77T1 used.
3.1017 (2073 K)
Diffusion in p-type, Al-doped specimens; N partial pressures from 0.1-1atm used.
66K3
n-p junction technique used.
77T1
77T1
SiC (4H) B(a)
1.6.102
558.9
1973-2673
Surface concentration 77V2 by Neutron activation analysis; N-doped n-type samples; electrical and Hall measurements used. cont.
Lando lt -B { rnst ein New Series III/33A
3-62
3 Diffusion in compound semiconductors
[Ref. p. 3-70
Table 16 (cont.) Q T Ionization D0 engergy [77T1] [kJmol−1] [10−4 m2 s−1] [kJmol−1] [K]
Max. solubility [77T1]
Remarks
Ref.
Radiotracer diffusion in intrinsic α-SiC. Radiotracer diffusion in N-doped n-type α-SiC.
80H
[106 m−3]
SiC (α) C (self)
Si (self)
Cr (d)
8.62.105
714.0
2123-2453
3.32.107
790.0
2123-2453
5.01.102
695.6
2273-2573
1.54.105
788.1
2273-2573
2.28.10−1
462.5
1973-2173
Radiotracer diffusion in intrinsic α-SiC. Radiotracer diffusion in N-doped n-type α-SiC.
80H
81H2 81H2
Junction preparation 65G1 during crystal growth from Cr solution due to diffusion
Table 17. Diffusion data of some group II-V and group V-VI compounds. (1 kJmol−1 = 0.0104 eV) D0 [10−4 m2 s−1]
Q [kJmol−1] T [K]
Remarks
Ref.
Cd
2.8.10−10
16.38
543-658
Radiotracer technique used
60K
Sn
3.2.10−9
35.65
573-673
Radiotracer technique used
55B1
2.3
150.3
673-756
Radiotracer technique used
55B1
II-V ZnSb
Sb
Fe
4.10−11
19.27
573-673
Radiotracer technique used
55B1
30
172.5
673-756
Radiotracer technique used
55B1
2.23.10−9
25.05
543-658
Radiotracer technique used
60K
4.67.10−9
53.0
373-473
Radiotracer technique used
59K
CdSb Se
cont.
Landolt -B { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
3-63
Table 17 (cont.) D0 [10−4 m2 s−1]
Q [kJmol−1] T [K]
Remarks
Ref.
Zn (a)
5.10−9
73.23
573-673
Radiotracer technique used
59K
Cd (a)
1.39.10−3
88.64
573-673
Radiotracer technique used
60K
Sn (a)
4.10−9
39.50
633-813
Radiotracer technique used
55B2
Sb (a)
1.8.10−3
122.4
633-813
Radiotracer technique used
55B2
Se (self)
8.5.10−9
209.1
373-473
Radiotracer technique used
59K
Fe
1.25.10−7
46.25
573-673
Radiotracer technique used
60K
3.4.10−3 7.1.10−2
20.23 (D ||)
298-573
Radiotracer technique used
60C1
77.08 (D⊥)
473-773
Radiotracer technique used
60C1
2.2.10−3 2.3.10−1
40.47 (D ||)
373-773
Radiotracer technique used
62B1
112.73 (D⊥) 573-773
Radiotracer technique used
62B1
4.8.10−3 1.102
46.25 (D ||)
623-803
Radiotracer technique used
63B2
173.4 (D⊥)
623-803
Radiotracer technique used
63B2
Sn (a)
3.10−8
48.18
533-743
Radiotracer technique used
55B2
Sb (a)
4.3.10−4
104.1
543-773
Radiotracer technique used
55B2
V-VI Bi2Se3
Bi2Te3 Cu (d)
Ag (d)
Cd (a)
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Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-1
2 Diffusion in silicon, germanium and their alloys N.A. STOLWIJK AND H. BRACHT
2.1 Introduction Diffusion processes in semiconductors are of vital importance for the fabrication of electronic devices. For this reason, the diffusion behaviour of solute and self-atoms in the group-IV semiconductors germanium and silicon has been extensively studied since the early fifties. Stimulated by potential technological applications also atomic diffusion in Si1−xGex alloys and Si/Si1−xGex heterostructures of various compositions x has recently attracted much attention. This chapter contains data on silicon, germanium and Si1−xGex alloys. The silicon section presents an entirely new compilation also with respect to older data. Only limited use has been made of previous data collections [70sha1, 86wöh1, 89sch1, 90sha1]. The section on germanium is an up-dated version of an earlier Landolt-Börnstein compilation [89sto1]. Here, recently published data have been added to the rearranged tables and figures. The SiGe part mainly concerns very recent diffusion data which have been collected for the first time. Most of these data originate from thin Si1−xGex layers embedded in heterostructures or superlattices.
2.1.1 Characteristics of diffusion in semiconductors Compared with e.g. metallic materials group-IV semiconductors are characterized by the following diffusion-relevant properties: 1) The covalent bonding between the host atoms limits the maximum solubility of most solutes to ppm ranges. This implies that small amounts of solute substance already act as inexhaustible diffusion source imposing a timely constant boundary concentration. On the other hand, seemingly weak external influences may lead to exceeding the equilibrium solubility limit, which, in turn, is likely to initiate precipitation processes. 2) Commercially available semiconductor crystals are extremely pure since impurity levels are commonly below about 0.1 ppm. As a consequence, stringent precautions must be taken in order to reduce impurity contamination during sample preparation and high-temperature treatments. 3) Dislocation densities are extremely low. Commercially available silicon wafers are usually completely dislocation-free. Germanium crystals with dislocation densities in the range 103-105 cm−2 are quite common. 4) The open structure of the diamond lattice favours interstitial incorporation of self- and solute-atoms. For this reason interstitial diffusion and interstitial-substitutional exchange diffusion (via the kick-out or dissociative mechanism) are much more prominent in semiconductors than e.g. in metals. 5) Beside vacancies also self-interstitials may act as diffusion vehicles. There is general acceptance for the view that common shallow dopants in silicon exchange with both kinds of intrinsic point defects. This so-called dual mechanism gives rise to a variety of complex diffusion phenomena.
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2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
6) Electronic effects play an important role. The electric-field effect accounts for the diffusion drift component which is due to the electric field built-up by inhomogeneously distributed dopants. The Fermilevel effect describes changes in equilibrium concentrations of intrinsic point defects (or changes in solute solubilities) caused by shifts of the Fermi level. These shifts may be induced either by background doping or by the diffusing species itself. Ion-pairing effects arise from the coulombic attraction between oppositely charged solute atoms and intrinsic point defects. 7) Surface reactions proceeding under certain ambient conditions may strongly influence solute diffusion behaviour. Oxidation-enhanced or -retarded dopant diffusion in silicon is a striking example. The crucial role of self-interstitials injected by the oxidizing Si/SiO2 interface is widely accepted nowadays.
2.1.2 Expressions for the diffusion coefficient Atomic mechanisms of diffusion are presented in section 1.3 of the "General introduction". This section gives expressions for the diffusion coefficient(s) associated with individual mechanisms or combinations of different mechanisms. These expressions may be useful as background knowledge for interpreting some of the entries made in the tables containing diffusion data. The interstitial mechanism is not separately treated here since it can be characterized by a simple diffusion coefficient Di based on a single atomic jump frequency and a single jump length. Ring or direct-exchange mechanisms are ignored as they appear to be of minor importance in semiconductors. Dissociative mechanism The dissociative mechanism (DM) applies to so-called hybrid solute elements A which occupy both substitutional (As) and interstitial (Ai) lattice sites. These species may interchange with the aid of vacancies (V) according to Eq. (1.55). Considering the different solubilities or equilibrium concentrations (Cseq ,Cieq ,CVeq ) and diffusivities (Di , DV) the following proportions prevail: Cseq >> Cieq and CVeq DV << Cieq Di. Here the purely substitutional diffusion coefficient associated with the vacancy mechanism as given by Eq. (1.54) or (2.6) is neglected. In the vacancy-controlled case of the dissociative mechanism the diffusivity of the dominating solute component, i.e. As, reads V = DDM
CVeq DV . Cseq
(2.1)
This V-controlled diffusivity holds in crystals with low densities of dislocations and other extended defects. On the other hand, the Ai-controlled variant of the dissociative mechanism is characterized by i = DDM
Cieq Di Cseq
.
(2.2)
This Ai-controlled diffusion coefficient applies to highly dislocated crystals. In dislocation-free crystals it becomes significant for isoconcentration conditions or if Cieq Di << CVeq DV . Kick-out mechanism In the kick-out mechanism (KOM) interstitial-substitutional exchange involves self-interstitials (I) rather than vacancies as reflected by Eq. (1.56). The kick-out mechanism may play a prominent role under diffusion conditions characterized by Cseq >> Cieq and CIeq DI << Cieq Di. Similar as for the dissociative mechanism two extreme cases can be distinguished. In the self-interstitial-controlled mode of the kick-out mechanism the As diffusivity is given by
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
I = DKOM
F I GH JK
CIeq DI Cseq ⋅ Cs Cseq
2-3
2
,
(2.3)
where the factor in parentheses reflects the dependence on the actual local concentration Cs. This I-controlled diffusivity determines the As incorporation in virtually perfect, dislocation-free crystals. It is connected with diffusion-induced supersaturation of self-interstitials. By contrast, in dislocation-rich crystals, under isoconcentration conditions, or for Cieq Di << CIeq DI (in dislocation-poor crystals) the solute diffusion process is governed by the same Ai-controlled diffusion coefficient as that given in Eq. (2.2) for the dissociative mechanism, that is, i = DKOM
Cieq Di
.
Cseq
(2.4)
Vacancy mechanism In analogy to the dissociative and the kick-out mechanism, in the field of diffusion in semiconductors the vacancy mechanism (VM) is often represented by a quasi-chemical reaction [89fah1, 93sto1], i.e., As + V ↔ AV .
(2.5)
Here AV stands for the nearest-neighbour As-V pair. Comparison with Eq. (1.56) reveals that vacancy and As-V pair in the vacancy mechanism play similar roles as self-interstitial and Ai atom in the kick-out mechanism, respectively. Therefore, the As-V controlled diffusivity can be written as AV = DVM
eq CAV DAV
Cseq
.
(2.6)
eq denotes the equilibrium As-V pair concentration which usually establishes at the surface. The Here CAV pair diffusivity DAV is, however, a complex quantity that accounts for diffusion correlation effects and full or partly dissociation of As and V [90Sto1]. In fact, Eq. (2.4) is equivalent with Eq. (1.54) in the "General introduction". Therefore, interpretations of experimental data in terms of "migration via dopant-vacancy pairs" which are frequently found in the more recent literature on diffusion in semiconductors are usually not different from the conventional "vacancy mechanism" interpretation. Exploiting the analogy between vacancy and kick-out mechanism further, one may conceive of an isolated-vacancy-controlled diffusivity within the vacancy mechanism given by [90Sto1, 93sto1] V DVM
=
CVeq DV Cseq
FC I ⋅G H C JK eq s
2
.
(2.7)
s
eq DAV. It may This V-controlled diffusivity holds in virtually dislocation-free crystals if CVeq DV << CAV have practical significance for phosphorous in silicon [96Yos1]. For substitutional solute concentrations exceeding 2·1020 cm−3 the vacancy can migrate along uninterrupted chains of solute atoms. This so-called vacancy percolation model [84Mat1] accounts for the observed enhanced diffusivity of antimony and arsenic in silicon after high-dose implantation [93Nyl1].
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2-4
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
Interstitialcy mechanism In recent semiconductor literature the interstitialcy mechanism (IM) is frequently expressed as [89fah1, 93sto1] As + I ↔ AI .
(2.8)
In this reaction AI refers to an As-I pair or to an A atom and a self-interstitial sharing one lattice site. There are analogies with both the vacancy mechanism and the kick-out mechanism. Hence, the As-I controlled diffusivity reads C eq D AI = AI eq AI , (2.9) DIM Cs eq DAI << CIeq DI in dislocation-free crystals. Similar as DAV in the vacancy mechanism which holds for CAI DAI is a complex quantity which comprises correlation and dissociation effects. It must not be envisaged as the diffusivity of a tight pair that includes a labelled host atom. For solute diffusion in diamond lattices the interstitialcy mechanism is poorly elaborated theoretically in the literature. In common experiments the diffusivity of Eq. (2.9) cannot be distinguished from that of Eq. (2.4). Moreover, the As diffusivities via eq DAI and the interstitialcy and the kick-out mechanism are identical for CIeq DI << CAI I I = DKOM , where the latter diffusivity is given by Eq. CIeq DI << Cieq Di, respectively. To be specific, DIM (2.3). This may explain why high-concentration phosphorous diffusion into silicon leads to generation of excess self-interstitials [79Str1], which in turn gives rise to enhanced broadening of an underlying borondoped (base) region. This technologically important phenomenon is known as the emitter-push effect [77wil1, 78wil1].
Multiple charge states In semiconductors, solute elements and intrinsic point defects may occur in different electronic charge states depending on the position of the Fermi level. For instance, iron in silicon can be predominantly dissolved either as neutral ( Fe 0i ) or as singly positively charged (Fe +i ) interstitial atom. These configurations are characterized by dissimilar diffusivities denoted as Di0 and Di+ , respectively [92Hei1]. For solutes migrating via the vacancy mechanism the generalized expression for the diffusion coefficient comprises different charge states of the vacancy. As an example, gallium diffusion in silicon has been described as AV = D0 + D+ DVM
F pI , GH n JK
(2.10)
i
where D0 and D+ account for exchanges with neutral V0 and singly positively charged V+ vacancies, respectively [75sha1]. The factor in parentheses reflects that the V + contribution linearly increases with increasing electronic hole density p. The deviation of p from the intrinsic (defect) electron density ni may be either established by background doping or induced by the diffusing solute itself. In the latter case p varies with the actual local solute concentration which gives rise to concentration-dependent diffusion. This feature may be recognized from penetration profiles that deviate from the complementary error function. Multiple mechanisms In practice, solute elements may migrate via different mechanisms simultaneously. For instance, hybrid solutes like gold and zinc in silicon are reported to diffuse through both interstitial-substitutional exchange mechanisms at the same temperature, i.e., the dissociative mechanism in addition to the kick-out mechanism [83Mor1, 95Bra1]. In the Ai-controlled case the total diffusivity Di complies with the expression in Eq. (2.2) or (2.4). In the intrinsic-point-defect controlled case overall transport of As atoms is governed by the joint flux of vacancies and self-interstitials. Accordingly, one obtains for the total diffusivity [83Mor1] V I + DKOM , D VI = DDM
(2.11)
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-5
where the components on the right-hand-side are given by Eqs. (2.1) and (2.3). For solutes of more pronounced substitutional nature the total diffusive displacement may consist of simultaneous contributions of the vacancy mechanism (Eq. (2.6)) and the interstitialcy mechanism (Eq. (2.9)), i.e., AV D AV,AI = DVM
CV CVeq
AI + DIM
CI . CIeq
(2.12)
AV AI Here DVM and DIM are given by Eq. (2.6) and (2.9), respectively. The additional weighing factors eq eq CV / CV and CI / CI make allowance for deviations of the vacancy and the self-interstitial concentration from their equilibrium values. Hence, diffusion taking place under non-equilibrium conditions may be enhanced or retarded depending on the degree of super- or undersaturation of either intrinsic point defect and on the so-called fractional interstitial(cy) component fI in thermal equilibrium defined as
fI =
AI DIM . AI AV + DVM DIM
(2.13)
E.g. for antimony in silicon fI(1100°C) = 0.015 has been determined from diffusion experiments in oxidizing and nitridizing atmosphere [82Ant1]. Also joint diffusion by more than two mechanisms has been invoked to rationalize experimental observations [88Cow1, 92Van1]. Self-diffusion In general, constituent atoms of the host lattice may utilize both vacancies and self-interstitials as diffusion vehicles. Consequently, in thermal equilibrium the uncorrelated self-diffusivity DSD is written as D SD =
CVeq DV CIeq DI + , C0 C0
(2.14)
where C 0 designates the lattice-site concentration (or atomic density) of the host crystal. CVeq DV and CIeq DI can be determined from penetration profiles of solute elements diffusing via the dissociative mechanism (cf. Eq. (2.1)) and the kick-out mechanism (cf. Eq. (2.3)), respectively. For labelled self-atoms like e.g. radioactive isotopes the so-called tracer self-diffusion coefficient DT given by c D T = fVM
CVeq DV C0
c + fIM
CIeq DI C0
(2.15)
c c holds true. In this expression fVM = 0.5 and fIM = 0.73 stand for the atomic correlation factors for diffusion in the diamond lattice via the vacancy mechanism and the interstitialcy mechanism, respectively [56Com1, 58Com1]. There is evidence that in germanium vacancies are predominant for both self- and solute diffusion, i.e., CVeq DV >> CIeq DI. In contrast, silicon self-diffusion appears to be carried by selfinterstitials as well as vacancies [84fra1, 85tan1, 95Bra1].
2.1.3 Methods of measurement Methods for measuring diffusion coefficients are briefly presented in section 1.4 of the "General introduction". Diffusion source techniques and experimental methods of analysis that are preferentially applied in the field of semiconductors can be found in sections 3.3 and 3.4 of the chapter on "Diffusion in compound semiconductors''. A useful tool for studying diffusion in group-IV semiconductors which is not treated in the other chapters of this volume provides the spreading-resistance technique characterized below.
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2-6
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
Spreading-resistance technique This is a two-point probe technique for measuring the local electrical resistance on semiconductor surfaces [66Maz1, 92Paw1]. In principle, it is suitable to monitor diffusion-induced depth distributions of electrically active solutes. The probe tips usually made of tungsten-osmium alloy have a mutual separation of typically 100 µm. The contact areas with the semiconductor surface are roughly 5 µm in diameter. The current running between the probes spreads over a small space region near the semiconductor surface, which justifies the notion of "spreading resistance". The technique is commonly operated in an automaticstepping mode with probe-tip step widths varying from 5 to 25 µm in the case of depth profiling. For deep profiles extending over several hundreds of micrometers stepping is done on a perpendicular cross section of the sample. For shallow profiles down to total penetrations of 1 µm or so spreading-resistance measurements are performed on a bevel plane making a small angle against the original sample surface. In this way the depth resolution can be enhanced by a factor of 100 or more. However, steep profiles appear flattened off due to the finite sampling volume and therefore need elaborate numerical correction procedures [91Paw1]. To account for the barrier resistances between probe tips and semiconductor surface extensive calibration with the aid of homogeneously doped samples of known resistivity is required. The calculation of solute concentration is based on the known electronic levels introduced by the solute in the semiconductor bandgap. Lower limits for quantitative evaluation of concentrations are in favourable cases about 1013 cm−3 for silicon and 1014 cm−3 for germanium.
2.1.4 Notations and use of tables Order of solute elements In this chapter solute diffusion data of the group-IV semiconductors silicon, germanium and Si1–xGex are compiled successively. For each host crystal the data are ordered according to the position of the solute elements in the periodic table, that is, from hydrogen group elements to helium group elements. Within each group the order runs from light to heavy elements. Types of information In the tables, diffusion data are given whenever possible in terms of the pre-exponential factor D0 and the activation energy Q introduced by Eq. (1.61) of the "General introduction". In some cases D0 and/or Q are not reported in the original work but were calculated by the present authors from tabulated or plotted diffusion coefficients. Such cases are indicated as "recalculated" in the column "Methods and Remarks". In the field of diffusion in semiconductors numerous investigations do not aim at determining the temperature dependence of the diffusion coefficient but rather focus on some other important feature like concentration dependence or enhanced diffusion upon implantation. In these instances D0 and Q cannot be given. The "temperature range" (T-range) given in the third column of the tables refers to the interval over which D0 and Q were calculated. If these parameters are not provided "temperature range" pertains to the total range of temperatures at which diffusion experiments were performed. In many cases the ranges of parameter calculation and experiment are identical. In other cases, however, some low- or high-temperature have been omitted in the evaluation of pre-exponential factor and activation energy. Frequently, experiments were performed at a single temperature. Accordingly, only this temperature is indicated. Other experiments were solely carried out at two different temperatures. This may be recognized from the character "&" between the lower and higher temperature. The column "Methods and Remarks" usually contains information of the following kind: The type of host crystals employed. A distinction is made between single and poly-crystals. In the case of silicon the specification of the crystal-growth technique by FZ for "floating-zone" or CZ for "Czochralski" does imply that the specimens are single-crystalline. The main difference between FZ and CZ crystals concerns their oxygen content. Typical oxygen concentrations are 1016 cm−3 for FZ and 1018 cm−3 for CZ substrates. Other possible specimen arrangements are epitaxial layers or poly-crystalline layers grown on top of single-crystalline substrates. Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-7
Generally, crystal or surface orientation is not mentioned unless this parameter was (or could have been) significant for the experimental results reported. As a rule of thumb, type and/or degree of background doping are only indicated when they played a crucial role in the experiment under consideration. This is true for diffusion in heavily doped crystals imposing electronically extrinsic conditions. The key parameter for the degree of extrinsity in a particular case is the ratio of the shallow-dopant concentration to the intrinsic charge carrier density at the diffusion temperature ni(T). The latter quantity is plotted in Figs. A, B and C for pure silicon [54Mor2, 77Was1], pure germanium [54Mor1], and silicon-germanium alloys [60Bus1]. Fig. B shows that doping levels up to 1017 cm−3 lead to intrinsic conditions at common diffusion temperatures. At elevated temperatures even dopant concentrations as high as 1019 cm−3 may be considered as intrinsic. 1000 500
20
10
Temperature T [°C] 200 100 50 0
–50 –75
1400 1200 20 10
18
[60Bus1]
19
[54 Mor1] Ge
–3
12
10
10
10
[77Was1]
8
10
10
1
2 3 –3 –1 Inv. temp. 1/T [10 K ]
4
5
SixGe1-x
–3
Carrier conc. ni [cm ]
17
10
0.6
B 0.7
0.8 1.0 1.1 0.9 –3 –1 Inv. temp. 1/T [10 K ]
1.2
1.3
Figs. A, B and C. A: Intrinsic carrier concentration ni vs. inverse temperature 1/T of Si, Ge and Si12.8Ge87.2. The straight lines represent experimental data from the literature. Dashed lines show extrapolations based on the experimental results.
T = 1000 K
4 3
B: Intrinsic carrier concentration ni vs. inverse temperature 1/T of Si, Ge and Si12.8Ge87.2. The straight lines represent experimental data from the literature which are extrapolated up to the melting temperature for Ge and Si.
2
18 9 8 7 6
0 Ge
[60Bus1]
8 6
2
A
5
4⋅10
Si12.8Ge87.2
4
19
5 17
[54Mor2] Si
18
10
6
9 8 7 6
Ge [54 Mor1]
2
Si
0.5
8 6 4
10
10
500
2
Carrier conc. ni [cm ]
–3
Carrier conc. ni [cm ]
[54Mor2]
14
10
10
600
4
Si12.8Ge87.2
16
10
10
Temperature T [°C] 800 700
8 6
10
4
1000
C
Lando lt -Bö rnst ein New Series III/33A
0.2
0.4 0.6 Si molar fraction x
0.8
1.0 Si
C: Intrinsic carrier density ni of SixGe1-x alloys at T = 1000 K (= 727 °C) vs. composition x running from 0 (pure germanium) to 1.0 (pure silicon) [60Bus1].
2-8
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
The dislocation density of the semiconductor host. In several cases, like e.g. gold in silicon or copper in germanium, the presence of dislocations - even in low density - strongly affects the diffusion behaviour. Most experiments use commercially available FZ or CZ crystals which are nominally dislocation-free. Therefore, this dislocation-free standard situation is not explicitly mentioned. In rare instances concerning older publications (around 1970 or before) no specification of the dislocation density is given although the employed specimens most probably did contain dislocations. The chemical composition and physical condition of the diffusion source. In very common cases, like e.g. an evaporated elemental surface layer for gold in silicon, this information is usually omitted here. In many diffusion studies the solute element is introduced by ion implantation. Then it may be relevant for the subsequent diffusion behaviour whether the implantation treatment has generated an amorphous surface layer or not. Therefore the statement "implantation above (below) amorphization threshold'' is made whenever this information is available. More implicitly, such information may be deduced from the specification "high-(low-)dose implantation". The diffusion ambient conditions. Solute diffusion in semiconductors may depend on the environment in which the high-temperature treatment takes place. Oxidizing atmospheres lead to thermal oxidation of silicon surfaces which, in turn, may promote injection of self-interstitials into the diffusion zone underneath the growing oxide layer. Wellknown examples are oxidation-enhanced diffusion of phosphorous and oxidation-retarded diffusion of antimony in silicon. Nitridizing atmospheres appear to have the opposite effect which may be related to injection of vacancies or absorption of self-interstitials under thermally growing silicon nitride films. Standard diffusion ambients like "evacuated closed (quartz) ampoule" or "open tube system under argon flow" are not always indicated. The heating system. Furnace heating through electrical-resistance wire is considered as default technique. It is only explicitly indicated when used in addition to or comparison with some other annealing technique like e.g. "pulsedlaser annealing" or "electron-beam heating". Another frequently employed technique is known as "rapid thermal annealing" or RTA which indicates annealing periods in the range of a few seconds to several minutes and usually refers to heating by (tungsten-halogen) lamp radiation. The method(s) of measurement. A number of established experimental techniques is designated by frequently used abbrevations which are compiled in Table 1. In other cases a short self-explanatory description is given. Concerning serial removal of thin surface layers for concentration-depth profiling, a distinction is made between "mechanical sectioning" (by grinding or lapping techniques), "chemical sectioning" (using etching solutions), "electrochemical sectioning" (comprising anodic oxidation in conjunction with oxide-layer etching) and "sputter-sectioning" (utilizing ion beams). Sheet-resistance measurements are indicated by the frequently applied "4-point probe" technique whenever this specification is given by the original authors. The description "differential Hall effect" includes Hall-effect and sheet-resistance measurements in conjunction with some sectioning technique. In the case of junction space-charge capacitance techniques like capacitance-voltage (C-V) profiling or deep level transient spectroscopy (DLTS) the pn-junction arrangement is explicitly stated in contrast to the more common Schottky-contact arrangement (default). The major outcome of the investigation. This concerns the major outcome of the investigation other than the temperature dependence of the pertaining diffusion coefficient(s) represented by D0 and Q values. Frequently, diffusion research focuses on the dependence on boundary concentration, implantation dose, ambient conditions, background doping level, or substrate (defect) structure.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-9
The interpretation of the experimental data This refers to the interpretation of the experimental data made by the original authors in terms of diffusion mechanisms and other relevant physical processes. More or less trivial interpretations are often ignored. For instance, "vacancy mechanism" was frequently reported for shallow dopants in silicon until about the end of the 1970's in a rather standard fashion. On the other hand, in the case of pertinent experimental evidence or other meaningful circumstances such interpretation is reproduced here. Reference to other literature. This may concern either data from previous studies which were additionally used for fitting and modeling or publications which provide essential information required for a complete account of the given results. Accompanying investigations or observations. This kind of information links the diffusion data to other important physical phenomena.
The second last column of the tables refers the reader to figures in which reliable or typical data are graphically displayed. In the case that a certain publication is represented by more than one figure, the corresponding figure numbers are listed in increasing order without necessarily making reference to the D0 and Q values that may appear on the same line. In choosing figures from original articles or composing new survey plots the present authors were guided by the following ideas. Whenever possible, each solute element is represented by one or more characteristic diffusion profiles selected among the reported experiments. For each solute element one or more Arrhenius diagrams provide semi-logarithmic plots of the measured diffusion coefficients against inverse absolute temperature. In these diagrams, fits of the theoretical temperature dependence are shown as straight lines which are described by Eq. (1.61) and the pertaining D0 and Q value in the table. An Arrhenius plot associated with a particular solute element often contains data from various authors which usually cover different temperature ranges. Also other salient features characterizing the diffusion behaviour, like e.g. dependence on boundary concentration, ambient conditions or implantation dose, are graphically displayed in appropriate cases. For each group of the periodic table the most reliable or representative diffusion data of individual solutes are included in an Arrhenius survey plot which allows for a direct comparison between chemically related elements in one particular matrix. In several instances also other similarities among solute elements serve as a criterion to put their diffusivities together in one figure. The last column of the tables contains the references to the original publications. Usually one set of data is associated with one reference. Quite often, however, closely similar publications of (partly) the same authors are taken together. In these cases one data entry is provided with two or more references. The reader should further note the different citation codes for regular journal and conference articles on one hand, e.g. [77Fai2], and text books, data collections, and review papers on the other, e.g. [77fai1] Abbrevations It is common practice in the field of semiconductor technology and diffusion to use abbrevations or acronyms for physical parameters, crystal-growth techniques, experimental conditions, methods of measurement, etc. Abbrevations and acronyms appearing in the tables and figures are listed below. Abbrevation, acronym
Explanation
Ai As A1−xBx a/c ASL C
interstitial configuration of solute element A substitutional configuration of solute element A binary alloy of composition x in mole fraction amorphous-crystalline (interface) asymmetrically strained superlattice concentration
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2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
Abbrevation, acronym
Explanation
C0 C0 C eq Cieq
lattice-site concentration of host lattice 0 = 4.413·1022 cm−3) (silicon: CSi0 = 5.000·1022 cm−3, germanium: CGe boundary concentration (at zero penetration depth) thermal equilibrium concentration or solubility solubility on interstitial sites
CIeq Cmax Cseq
equilibrium concentration of self-interstitials maximum concentration solubility on substitutional sites
CVeq CA CPAA C-V CVD CZ D D0 Di Di DI DSD Ds DT DV DLTS E EC EV EBIC EPD EPR fI FZ 2H i I IR I-V kB MBE ML MOS n ni NAA p poly-Si PAC Q
equilibrium concentration of vacancies concentration of solute element A charged particle activation analysis capacitance-voltage (measurement) chemical vapour deposition Czochralski (crystal growth technique) diffusion coefficient or diffusivity pre-exponential factor (in Arrhenius expression of diffusivity) diffusivity under intrinsic conditions diffusivity of interstitial foreign atom diffusivity of self-interstitials uncorrelated self-diffusion coefficient diffusivity of substitutional foreign atom tracer self-diffusion coefficient diffusivity of vacancies deep level transient spectroscopy isotope effect parameter conduction band edge valence band edge electron-beam induced current etch pit density electron paramagnetic resonance fractional interstitial(cy) component of diffusion floating-zone (crystal growth technique) deuterium interstitial (as index) self-interstitial (as index) infrared (absorption, spectroscopy) current-voltage characteristic Bolzmann's constant molecular beam epitaxy monolayer metal-oxide-silicon (device structure) electron density electron density under intrinsic conditions neutron activation analysis density of electron holes polycrystalline silicon perturbated angular correlation activation energy (in Arrhenius expression of diffusivity) Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
Abbrevation, acronym
Explanation
RBS RTA s SIMS SL SSL t T Tm TEM V V Ω
Rutherford back scattering rapid thermal annealing substitutional (as index) secondary-ion mass spectroscopy superlattice symmetrically strained superlattice time temperature temperature of melting transmission electron microscopy vacancy (mostly as index) or vanadium activation volume atomic volume
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2-11
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
6-1
6 Grain-boundary and dislocation diffusion in semiconductors and silicides G. ERDÉLYI AND D.L. BEKE
6.1 Introduction 6.1.1 General remarks Internal surfaces (grain- or interphase boundaries) or line defects (dislocation “pipes”) are almost invariably present in real materials. Since they in general have less ordered atomic structures as compared to the ideal bulk material, they act as fast diffusion paths. Furthermore, in many cases they are places of segregation or desegregation in alloys. Thus the importance of diffusion and segregation in many solid state reactions (e.g. in thin films, microelectronic devices) can hardly be overemphasized. This chapter presents a collection of experimental data on the triple or double products of grain- or dislocation diffusion (see also Chaps. 1.2.2 and 1.2.3 of this volume). The results are presented in tables and Arrhenius diagrams.
6.1.2 Methods of measurements The most important method - serial sectioning in type-B kinetic regime - is described in Chaps. 1.2.2 and 1.2.3 and shall not be repeated here (see also Eqs. 1.49 and 1.52 there). From these measurements the product of the diffusion coefficient (D' or D" for grain boundaries or dislocations, respectively) the segregation factor (K', or K", respectively) and the grain boundary width δ (or the square of the pipe radius, a, for dislocation diffusion) can be determined. In some papers (especially in those published before the general acceptance of the above mentioned equations) the Fisher’s solution of Fisher’s model [88Kau] was used in the evaluation of grain boundary measurements: P = δD'K = 2(D/πt)1/2(-∂lnc/∂lny)−2.
(6.1)
From profiling measurements carried out in type-A or C kinetic regimes, the diffusion coefficient of the given short circuit can be estimated directly. However, experimental realization of measurements in typeC regime is complicated because usually very low concentrations should be measured with high accuracy. Similarly, in type-A regime the separation of the bulk and short circuit contributions is difficult and the knowledge of the grain-boundary volume fraction is also necessary (see Eq. 1.38). Some of the other methods - which were applied to get the experimental data collected here - are described shortly in the following sections.
6.1.2.1 Low angle grain boundary method If we suppose that a low angle boundary, with a structure of a linear array of dislocations with spacing λ, is equivalent to some uniform boundary slab (provided also that (Dt)1/2 >>δ ), then the usual methods for
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
[Ref. p. 6-24
the determination of the grain boundary products can be applied to give the value of the coefficient of dislocation diffusion D'' from the relation [90Lec] D"πa2 =D'δλ,
(6.2)
where D' is the grain boundary diffusion coefficient. 6.1.2.2 Defect annealing method From the rates of annealing of various defects, related to dislocations (i.e. pores, dislocation loops), the product D"a2 can also be determined [90Lec]. 6.1.2.3 Pavlov-Panteleev method Before the Le Claire-Rabinovitch solution of the dislocation diffusion problem [81Lec, 84Lec] (see also Eq. 1.52 in Chap. 1.2.3), Pavlov, Panteleev and Maiorov [64Pav] gave an expression for the slope of the penetration function in the form −∂lnc/∂y = [DI(t)/D"a2K"]1/2.
(6.3)
Here I(t) is a function of time and is given in tables (see e.g. [88Kau]). In early publications on dislocation diffusion this solution, or an other expression introduced by Panteleev [68Pan, 69Dud] were sometimes used in the evaluation of dislocation diffusion measurements. 6.1.2.4 Indirect methods in type-A kinetic regime In cases where the diffusion penetration depth and the density of short circuit paths are large enough to be in the type-A kinetic regime and the process is monitored by an indirect method, the grain boundary or dislocation diffusion coefficients can be estimated if the volume fraction of the given short circuit (see Eq. 1.38 in Chap. 1.2.2) is known. Such indirect method can be one of those listed in Chap. 1; the conductivity method in semiconductors and ionic systems (see also Chap. 2. in Subvolume B); the imaging of the displacement of p-n junctions at grain boundaries using either EBIC (electron beaminduced current) or chemical stain methods; see also this Chap. 6.1.2.6. 6.1.2.5 Determination of double products from creep and sintering experiments In fine-grained specimens, under certain conditions, the process of creep and sintering can be controlled by self-diffusion along grain boundaries [90Kau]. Accordingly, the determination of the double product D'δ is possible from the measurement of the creep rate, dε/dt [63Cob]; D'δ = (dε/dt) kTd3/14πσΩ,
(6.4)
or from the rate of fractional linear shrinkage, d(∆l/l0 )/dt [64Joh]; D'δ = [d(∆l/l0 )/dt] (∆l/l0 )2.12πkTr4/γ Ω.
(6.5)
Here k is the Boltzmann constant, T the temperature, d the grain size, σ the applied stress, Ω the atomic volume, r the particle radius, and γ the surface tension. 6.1.2.6 Isoconcentration contour method Mapping the concentration in a cross section perpendicular to the grain boundary yields isoconcentration contours as it is illustrated in Fig. 6 of Chap. 1. If one measures the contour angle ψ, the triple product can be obtained from [90Kau] P = 8t1/2D3/2cot3ψ /η0,
(6.6)
where η0 = y0 /(Dt)1/2 is the reduced penetration depth along the grain boundary.
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
6-3
These measurements can be carried out for example by autoradiography, metallographic techniques, microhardness measurements or by microanalysis in SEM. Especially, in semiconductors the isoconcentration contours of the doping atoms can be revealed by either the chemical stain (groove and stain technique) or the electron beam induced current method (EBIC). By grinding the specimen to a small angle against the original surface, deeper regions of the p-n (n-p) junction formed by the diffusion process, can be exposed. The electron beam scanning the surface creates electron-hole pairs which can recombine through an external circuit. The rate of pair generation is spatially imaged. By monitoring the recombination current, one can map the electric activity of the sections and the isoconcentration contours. Along grain boundaries the dopant penetration is deeper, which is reflected on the EBIC map as spikes or protrusions, showing that regions of deep penetrations have different charge collection efficiency. [81Joh, 83Buo].The isoconcentration contour corresponds to the minimum detectable diffusant concentration. It can be shown that if β > 10 (β has the usual meaning, see Chap. 1), one can estimate the grain boundary diffusivity from the experimentally measured penetration depth y0, i.e. from the position of the apex of the isoconcentration contour, using the relation [88Kau] P ∼ y02/t1/2
(6.7)
The (6.7) expression allows one to compare the diffusion rates for different specimens simply by comparing the penetration depth provided all the specimens are annealed for the same time and the same technique is used for mapping the isoconcentration contours. 6.1.2.7 Hwang-Balluffi method In this case the accumulation of the diffusant on one surface of a thin film is measured if there is a diffusion source on the other side of the film. If the surface diffusion is fast as compared to the grain boundary diffusion and if a steady-state is established in the grain-boundaries, the accumulation kinetics can be described by [79Hwa] cs /c0 = 1 − exp(−λD't/K'h).
(6.8)
Here cs is the average diffusant concentration at the accumulation surface, c0 is the diffusant concentration at the source surface, K' is the surface segregation coefficient, λ and h are the grain boundary length per unit area and the thickness of the film, respectively. This solution is valid in type-C kinetic regime provided h is much smaller than the grain boundary diffusion length. Fortunately, the solution is not sensitive to the boundary conditions and to the morphology of the grains. (i.e. it is the same for columnar or spherical grains) 6.1.2.8 First appearance method An other frequently used method for the estimation of grain boundary diffusion coefficient in thin films is the so-called first appearance technique. One can roughly estimate the D' coefficient by observing the time required for the first appearance of the diffusing atoms at the back side of a thin film. Such measurements can be carried out either in type-C or type-B kinetic regimes by means of AES or other surface sensitive analytical techniques. [76Hal,78Hol]. 6.1.2.9 Gilmer-Farrell method The analytical model of grain boundary diffusion in thin films, developed by Gilmer and Farrel describes the diffusion in type-B kinetic regime [76Gi1, 76Gi2]. According to their evaluation method, at y = h the log cs /c0λ(Dt)1/2 versus βη−2 (at1/2) function will be an "universal curve" for βη−1 > 25. From this curve β = P/2D(Dt)1/2 (see also Chap. 1.2.2) can be determined and thus P can be calculated.
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
[Ref. p. 6-24
6.2 Use of tables and figures 6.2.1 Some general remarks Diffusion processes in semiconductors proved to be more complex phenomena than the transport in metallic systems. In order to interpret the results, various defects, site preferences and mechanisms should be taken into account even for bulk diffusion [92Sto]. The importance of self interstitials, the kick-out and the dissociative mechanism, the role of sources and sinks (surfaces and dislocations) in the case of volume heterodiffusion in silicon was recognized only at the beginning of the eighties [80Gös, 86Sto]. The development of polycrystalline semiconductors as solar cells, interconnecting materials during the last two decades made it more important to get a better understanding of matter transport in polycrystalline semiconductors. It is understandable that grain boundary diffusion studies from earlier periods are relatively rare. The experimental data can not be considered to be as reliable as the grain boundary diffusivity data for example in metals. The following circumstances may explain the controversial data: (i)
Numerous experimental investigations were carried out before the general acceptance of the reliable evaluation methods. In many investigations non-adequate solutions were employed to evaluate the grain boundary diffusion data. (ii) Numerous factors affect the diffusion behavior: the purity of the samples, presence of hard to eliminate contaminants, dislocation density, segregation behavior, vapor pressure of the dopants, oxidation during the diffusion anneal. These parameters were not properly controlled in many investigations. (iii) Recent experimental findings show that diffusion behavior of some impurities in polycrystalline matrices can not be interpreted in the framework of the traditional models. For example, the diffusion of Au in polycrystalline Si shows the following characteristics: a) high diffusivity through the lattice, b) negligible diffusion along grain boundaries, c) strong segregation effects [96Sto, 96Poi]. Since D' > D was a basic supposition to get the classical solutions of the grain boundary diffusion problem (Chap. 1.2.2 ) these solutions can not be applied to analyze the profiles measured for Au diffusion in silicon. A new model developed recently may also apply to other systems in which high volume diffusion mobility is linked to strong segregation effects [96Sto].
6.2.2 Practical guide to the use of the tables In this chapter dislocation- and grain boundary diffusion data measured in semiconductors are compiled in tables and figures in the following order: (i) Dislocation diffusion in semiconductors. (ii) Grain boundary diffusion in semiconductors and in silicides. The matrix is given in the top row of the table. The diffusing element (diffusant) can be found in the first column of the table in alphabetical order. Data are given in the usual Arrhenius form D"a2K" = (D"a2K" )0 exp( − Q"/ RT ),
(6.9)
for dislocation diffusion and D'δK = (D'δK )0 exp( − Q'/ RT ),
(6.10)
for grain boundary diffusion. For self diffusion K = K" = 1, in the case of heterodiffusion K ≠ 1, and K" ≠ 1 and the temperature dependence of the segregation factor is included in the activation energies. In the majority of the publications on heterodiffusion K = K" = 1 was implicitly supposed. In order to calculate the triple
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
6-5
products we used δ = 0.5 nm unless in the original paper another value for the grain boundary width was supposed. The pre-exponential factor and the activation energy are given in the 2nd and 3rd columns, respectively. Occasionally, the 2nd and 3rd columns are merged in order to give the dislocation and grain boundary diffusivities directly. This kind of representation was used when the original data could not be analyzed in the usual terms of the Arrhenius equation, for example when data were measured only at one or two temperatures. In those cases where the authors do not extract grain boundary diffusivities from their measurements carried out in type-A kinetic regime, the pre-exponential factor of the effective diffusion coefficients (Deff)0 , or the effective diffusion coefficients themselves (Deff) are given. In those cases where the evaluation method used by the authors seems to be inadequate, “apparent diffusivities” (Dapp) or "apparent pre-exponential factors" (Dapp)0 are given. The temperature range of the experiments is given in the 4th column. When diffusivities are given instead of the activation energy and the pre-exponential factor, the temperatures of the individual diffusion anneals are given in this column. The 5th column contains information on the matrix and the experimental methods used for the measurement of the concentration profile. As for the matrix, the most important information on purity, doping level and some relevant data on the microstructure are given. The latter comprises the dislocation density nd and the grain size d. The meaning of the abbreviations used to characterize the matrix, sample preparation and the experimental methods are as follows: SC BC PC TF CVD LPCVD
Single crystal Bicrystal Polycrystalline Thin film Chemical vapor deposition Low pressure chemical vapor deposition
SAM RAM EBIC EPMA AES RBS
Section activity measurement Residual activity measurement Electron beam induced current Electron probe microanalysis Auger electron spectroscopy Rutherford backscattering spectroscopy
The abbreviation “Eq.“ indicates which equation or evaluation method was employed in the original publication. Here we used the following abbreviations: F S W
P P-P
Fisher’s equation, (Eq. 6.1) Suzuoka’s equation, (Eq. 1.44 see Chap.1, sect. 1.2.2.1) Whipple’s equation, (Eq. 1.44 see Chap.1, sect. 1.2.2.1)
H-B H
Panteleev’s equation, [68Pan] Pavlov-Panteleev equation, (Eq. 6.3)
EB
VD
Hwang-Baluffi equation, (Eq. 6.8) Hart’s equation, (Eq. 1.38, see Chap.1, sect. 1.2.2) equation analogous to volume diffusion (in the case of type-C or type-A kinetic regimes, see Chap.1, sect. 1.2.2) Eq. 6.7
In the majority of published works the measurements were carried out in type-B or type-A kinetic regimes. In order to extract the grain boundary diffusivities the corresponding volume diffusion data are necessary. In the 5th column these volume diffusion data (abbreviation: VDD) with references are given provided this information was available from the original publications. Occasionally, remarks on the reliability of the quoted results are also given in this column. In column 6 references are made to the figures. In the figures selected data are plotted. The temperature ranges of the diffusivities shown in the figures agree with those given in the tables. In column 7 the appropriate reference is listed.
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
[Ref. p. 6-24
6.3 Dislocation diffusion in semiconductors (1 kJ mol−1 = 0.0104 eV)
(K"a2D")0 [m4s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
133.9
1073-1273
n-type Si,SC, nd = 5·107 m−2 , serial sectioning, SAM; Eq.: P-P; VDD: D0 = 2.0 10−7 m2s−1 Q = 154.0 kJ/mol [60Bol]
1 67Ste
Al
(Deff)0 =1.4·10−2 m2 s−1 293.7
1273-1473
Si, SC, nd ≥ 1011 m−2 , metallography of the p-n junction, VDD: not given explicitly
- 69Dud
Al
K"a2D" = 3.3·10−29 K"a2D" = 1.6·10−27
1423 1488
Si, SC, nd = (107-1011)m−2 resistivity measurement, Eq.: H; VDD: D(1423K) = 2.25⋅10−16m2/s D(1488K) = 2.20⋅10−15m2/s [74Pav]
- 74Pav
(K"δ D")0 = 9.4·10−14 m3 s−1 Q" = 247.0 kJ mol−1
1223-1323
CVD Si, stair rod dislocations in epi-layer TF, nd = 4·1010 m−2, sectioning: anodizing and stripping, SAM, Eq.: W; d ≈ a VDD: D0 = 5.1⋅10−5m2/s Q = 340.6 kJ/mol [75Cam]
1 75Cam
B
(Deff)0 = 1.9·10−2 m2 s−1 316.3
1273-1473
Si SC, nd ≥ 1011 m−2 metallography of the p-n junction, VDD: not given explicitly
- 69Dud
Cu
D" = 10−10m2s−1
1273
Si, SC, nd = (1010-1011) m−2 metallography of the p-n junction, VDD: not given
- 67Dud
Matrix: Si 110
76
Ag
As
1.5·10−20
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Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
(K"a2D")0 [m4s−1]
Q" [kJ mol−1 ]
Matrix: Si (cont.) Ge K"a2D" = 4.5.0·10−36
6-7
T-range [K]
Method/Remarks
Fig. Ref.
1223
n-type Si, SC, dislocations along <110> nd = (5·107-5·108) m−2 , serial sectioning, RAM, Eq.: P-P; −21 −2 VDD: D = 8.0⋅10 m /s [74Pan]
- 74Pan
598-723
p-type Si, PC, EBIC-technique
- 84 Du2
H2
D" ≥ 10−12 m2s−1
114
In
1.0·10−16
322.2
1283-1543
p-type Si, SC, nd = 5·108 m−2, serial sectioning, SAM, Eq.: P-P; VDD: D0 = 1.65·10−3 m2s−1 Q = 376.6 kJ/mol [56Ful]
1 66Pav
114
In
1.0·10−17
307.5
1223-1473
n-type Si, SC, nd =5·107 m−2 , serial sectioning, SAM, Eq.:P-P, VDD: D0 = 1.65·10−3 m2s−1 Q = 376.6 J/mol [56Ful]
1 67Ste
114
In
K"a2D" = 2.25·10−35
1223
n-type Si, SC, dislocations along <110>, nd ≥ (5.107-5⋅108) m−2, serial sectioning, RAM, Eq.:P-P, VDD: D (1223) = 2.0⋅10−19 m2s−1 [74Pan]
- 74Pan
32
P
124
Sb
1.1·10−16 2.1·10−17 1)
329.7 295.9 1)
1173-1473
Si ,SC, nd ≥ 1011 m−2, serial sectioning, SAM, Eq.: P; VDD: D0 = 8.43⋅10−4 m2s−1 Q = 354.5 kJ/mol, 1) data recalculated in [89Kau]
1 69Dud
4.05·10−19
292.5
1023-1223
p-type Si, SC, nd = (1.1-3.8)⋅107m−2, serial sectioning, SAM, Eq.: P-P; VDD: D0 = 5.6 · 10−4 m2s−1 Q = 380.7 kJ/mol [56Ful]
1 64Pav
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6-8
6 Grain boundary and dislocation diffusion in semiconductors and silicides (K"a2D")0 [m4s−1]
Matrix: Si (cont.) Sb 7.0·10−16 8.0·10−17 2)
124
[Ref. p. 6-24
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
351.5 327.9 2)
1173-1473
Si ,SC, nd ≥ 1011 m−2, serial sectioning, SAM, Eq.:P;VDD: D0 = 1.81 10−2 m2 s−1 2) Q = 420.9 kJ/mol 2) [69Dud] 2) estimated graphically from the
1 69Dud
Arrhenius plot [89Kau] 124
Sb
K"a2D" = 9.0·10−36
124
Sb
3.82·10−19
125
Sb
Zn
D" = 8⋅10−10 m2s−1
1223
279.8
n-type Si, SC, dislocations along <110>, nd = (5·107-5·108) m−2 , serial sectioning, RAM, Eq.: P-P; −20 2 −1 VDD: D = 4.0⋅10 m s [74Pan]
- 74Pan
1438-1593
p-type Si, SC, nd = (1.1010-1012) m−2 , serial sectioning, SAM, RAM, Eq.: H; VDD: D0 = 5.6 10−4 m2s−1 Q = 381.1 kJ/mol [56Ful]
1 76Fah
1373
n-type Si, nd =3 1012 m−2, serial sectioning by sputtering, D"/D = 1200; estimated pipe radius a ≈ 1 nm
- 82Nei 82 Koh
1073
Si,SC, nd = (1010-1011 )m−2 metallogr. of p-n junction shift
- 67Dud
986
SC, deformed samples, nd = 6.7·1010 m–2, SIMS profiling, VDD: D = 1.66⋅10−19 m2s−1, 3 ) estimated in [84Lec]
Matrix: Ge Ga
D" = 2.39⋅10−13 m2s−1 3)
79Ahl
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
(K"a2D")0 [m4s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
6-9 Fig. Ref.
Matrix: Te 127
Te
99.9999 % Te, SC, nd = (4.7⋅108-7⋅1010 ) m−2 , 2 set of samples , containing edge or screw dislocations supposing C kinetic regime, sectioning,;
127
Te
(D"app)0 =9.67·10−10 m2/s 62.7 (D"app)0 =7.12·10−11 m2/s 94.6
526-674
for edge dislocations for screw dislocations, Eq.: VD; conditions of C regime are not fulfilled, see [89Kau]
127
Te
(2aD" )0app = 4.38·10−16 m3 s−1
64.6
526-674
matrix as above; Eq.: F; results - 67Gho evaluated for edge dislocations, supposing type-B kinetic regime
127
Te
(2aD" )0app = 9.45·10−14 m3 s−1
90.7
matrix as above, Eq.: F; results evaluated for screw dislocations supposing type-B kinetic regime
67Gho
- 67Gho
- 67Gho
6.4 Grain boundary diffusion in semiconductors and silicides 6.4.1 Grain boundary diffusion in elemental semiconductors (1 kJ mol−1 = 0.0104 eV) (KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
573
Si PC, TF, current-voltage and EMPA
- 77Nak
623-698
Si 99.9%, PC, TF, d = 40 nm, surface accumulation technique, combined with AES, Eq.: individual
3 80Hwa
Matrix: Si Al
KδD' ≈ 5·10−26 m2s−1
Al
6.5 10−7
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254.7
6-10
6 Grain boundary and dislocation diffusion in semiconductors and silicides (KδD')0 [m3s−1]
[Ref. p. 6-24
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
310.7
1223-1323
Si, PC, CVD, As was implanted, RBS profiling, Eq.: VD
2 77Tsu
1273
p-type Si, PC, TF, laserrecrystallized, d = (1-5) µm, EBIC technique and TEM; 1)data deduced in [83Buo]
- 81Joh
1073-1273
Si, PC, TF, As was implanted, 2 81Rys RBS-profiling, Eq.: VD; Deff depends on the surface treatment prior to the polysilicon deposition, 2) PC Si deposited on freshly-
Matrix: Si (cont.) As
(Deff)0 = 6.3⋅10−5 m2 s−1
As
KδD' = 4.45·10−25 1)
As
(Deff)0= 8.5.10−7 m2 s−1 1.66.10−4 m2 s−1
2) 3)
264.4
2)
310.7
3)
etched substrate,plotted data in Fig. 2. 3) PC Si deposited on silicon having oxide.
As
6.85.10−17 4)
221.9
1223-1523
p-type Si, PC, LPCVD, TF, 2 82Ba1 d = (6-10) µm, EBICtechnique, Eq.: EB; 4) estimated graphically in [89Kau]
As
(Deff )0 = 3.1.10−4 m2 /s 5)
293.6
973-1373
Si, PC, d ≤ 100 nm, optical microscopy and SIMS-profiling; 5) graphically estimated data
- 82Sat
from the Arrhenius plot
As
4.3.10−9
75
Deff = 2.5.10−15 m2 s−1
As
As
5⋅10−13
376.3
324.2
1023-1223
2 82Swa Si, PC, CVD, d = (210-510) nm, As was implanted, RBS profiling, Eq.: VD; conditions of the C-regime are not fulfilled
1373
Si, PC, LPCVD, EMPA, Deff time dependent; grain growth effect
- 83Lew
973-1123
Si, PC, TF, d = 80 nm, SIMS profiling; Eq.: VD; type-C regime was assumed
2 84Ari
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6 Grain boundary and dislocation diffusion in semiconductors and silicides
(KδD')0 [m3s−1] Matrix: Si (cont.) As 5.5.10−11
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
340.6
1073-1173
Si,PC, TF, d = 100 nm, SIMS 2 85Sak profiling, Eq.: individual; VDD: not given explicitly
1173-1373
Si, PC, TF, p-n junction metallography, Eq.: Gilmer-Farrel 6) evaluated in [83Buo]
3 72Kam
1173-1323
Si, PC, TF, resistivity measurement and staining technique, Eq.: VD; effects of diffusion sources were also investigated 7) B source: BN, 8) B source: B H 2 6
- 75Hor
1348
n-type solar grade Si, PC d = 50 µm, conductivity measurement and anodic sectioning, Eq.: W 9) evaluated in [83Buo]
- 81Jai
1073-1173
Si, PC, TF, d = 100 nm, SIMS 3 85Sak profiling, Eq.: individual; VDD: not given explicitly
B
3.3⋅10−17 6)
180.3 6)
B
(Dapp)0 = 1.51⋅10−7 m2 s−1 7) 6.01.10−7 m2 s−1 8)
230.6 7) 242.2 8)
B
KδD' = 1.05⋅10−21 9)
B
4.1.10−14
14
2
264.4
C
H
1626
KδD' = 4.25⋅10−24
H
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10)
6-11
p-type Si, PC, grinding sectioning and autoradiography, RAM, no gb preferential diffusion could be detected
Fig. Ref.
- 87Cha
523-673 623
- 82Joh Si, PC, LPCVD, TF, SIMS profiling, only depth profiles are given, 10) diffusivity deduced in [85Gin]
673
Si, PC, TF, EBIC-technique, Eq.: EB; D' ∼ (10−12-10−13) m2s−1 at 673K
- 84Du1
6-12
6 Grain boundary and dislocation diffusion in semiconductors and silicides (KδD')0 [m3s−1]
Q" [kJ mol−1 ]
[Ref. p. 6-24
T-range [K]
Method/Remarks
Fig. Ref.
673
P-doped Si, PC, CVD, conductivity measurement
- 85Gin
523
Si, PC, LPCVD, TF, SIMSprofiling, gbs act as efficient traps rather than as path for enhanced diffusion
- 92Jac
1323-1473
Si, BC, - 61Que <100>{010}7.5°,boron conc.: (1.7⋅1023-1.2⋅1024 ) m−3 isoconcentration contour angle measurement
1173-1373
Si, PC, TF, p-n junction metal- 4 72Kam lography, Eq.: Gilmer-Farrel 11) evaluated in [83Buo] .
1173-1473
B-doped Si, PC LPCVD, TF - 82Ba1 d = (5-10) µm, EBIC-technique, Eq.: EB; 12) estimated graphically from the
Matrix: Si (cont.) H
2
KδD' = 1.34.10−21 m3s−1
H
P
P
2.0⋅10−16
P
(D"app)0 = 4.2.10−10 m2 s−1
11)
165.0
157.3
11)
12)
Arrhenius plot
(Dapp)0 = 5.1⋅10−9 m2s−1
P
188.1
1173-1373
13)
matrix and method see above, Eq.: W; VDD: D0 = 1.05.10−3 m2/s Q = 353.1 kJ/mol [56Ful] regime of kinetics can not be identified; 13) estimated graphically from the
- 82Ba2
Arrhenius plot 32
P
5.9⋅10−17
135.1
1173-1573
intrinsic Si, PC, CVD-grown, recrystallised, d=(30-100)µm, chemical sectioning, SAM; Eq.: W; VDD: not given
4 82Lio
Landolt -Börnst ein New Series III/33A
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
(KδD')0 [m3s−1]
Q" [kJ mol−1 ]
6-13
T-range [K]
Method/Remarks
Fig. Ref.
1273
B-doped Si, BC, tilt, <111>{112}3°, chemical sectioning, SAM, Eq.: W; VDD: not given 14) as received, 15)preannealed, 16) carbon saturated specimens
- 82Lio
1273
BC, as above, p-n junction profiling; D' was dependent on diffusion. Annealing time: 17) t = 8.64.104 s 18) t = 2.59.105 s 19) t = 4.32.105 s
- 82Lio
1273
Si, BC, twist <011>{111}3° chemical sectioning, Eq.: W; 20) as received 21) preannealed 22) carbon-saturated specimens
- 82Lio
973-1373
CVD Si, BC, d ≤ 100 nm, optical microscopy and SIMS-profiling 23) graphically estimated data
- 82Sat
Matrix: Si (cont.) 32
P
P
32
P
P
KδD' = 6.02.10−23 KδD' = 5.08⋅10−23 KδD' = 4.80⋅10−23
14)
KδD' = 1.05.10−23 KδD' = 1.15⋅10−23 KδD' = 6.60⋅10−24
17)
KδD' = 3.2⋅10−23 KδD' = 3.3⋅10−23 KδD' = 2.6⋅10−23
15) 16)
18) 19)
20) 21) 22)
(Deff )0 =3.25 10−4 m2/s
23)
278.2
from the Arrhenius plot
P
KδD' = 1.3⋅10−22
P
-
P
2.55.10−13
Lando lt -Bö rnst ein New Series III/33A
24)
1313
cast Si, PC, metallography and EBIC measurement, Eq.: W 24) deduced in [83Buo]
- 82Hol
328.0
973-1173
Si PC, TF, SIMS profiling; gb diffusivity comparable with volume diffusivity
- 84Los
280.8
1073-1173
Si, PC, TF, d = 100 nm, SIMS profiling, Eq.: individual; VDD: not given; stress effects also investigated
4 85Sak
6-14
6 Grain boundary and dislocation diffusion in semiconductors and silicides (KδD')0 [m3s−1]
[Ref. p. 6-24
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
6.0⋅10−12
276.9
1173-1423
Si, PC, CVD-grown, recrystal- 4 86Spi lised, d = (5-50)µm, impurity conc. < 5.1017m−3 serial sectioning , SAM and autoradiography, Eq.: W; VDD: D0 = 8.0 · 10−7 m2s−1 Q = 277.9 kJ/mol [86Spi]
2.0⋅10−17
139.3
1023-1323
B-doped, Si; PC, groove and stain technique, Eq.: W; VDD: D0 = 1.6 10−9 m2 s−1 Q = 202.9 kJ/mol [89Hol]
Sb 2.2⋅10−19
80.1
1173-1373
intrinsic Si, PC, CVD-grown, 5 82Lio recrystallised, d = (30-100)µm chemical sectioning, SAM, Eq.: W; VDD: not given
1273
- 82Lio B-doped, Si, BC, tilt <111>{112}3°, p-n junction profiling, diffusivity depends on the annealing time, VDD: not given, 25) t = 1.21.106 s 26) t = 2.42.106 s
1273
B-doped, Si, BC, twist <011>{111}3°, p-n junction profiling, VDD: no information 27) t = 1.21.106 s 28) t = 2.42.106 s
- 82Lio
1203-1423
Si PC, CVD-grown, recrystallised, d = (5-50)µm impurity conc. < 5.1017m−3 mechanical sectioning, SAM and autoradiography, Eq.: W; VDD: D0 = 1.35· 10−3 m2s−1 Q = 376.3 kJ/mol 29) recalculated in [86Spi]
5 85Spi 86Spi
Matrix: Si (cont.) 32
P
P
124
Sb
Sb
125
KδD' = 6.5⋅10−23 KδD' = 3.9⋅10−23
25)
KδD' = 9.3⋅10−25 KδD' = 3.6⋅10−25
27)
Sb 4.87⋅10−10 1.9⋅10−11
26)
28)
279.8 29)
4 89Hol
Landolt -Börnst ein New Series III/33A
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
(KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
6-15 Fig. Ref.
Matrix: Ge 68
Ge
As
195
2.1⋅10−16
133.4
D' ≈ (105-106 ).D
Au 1.8⋅10−11
Ga
(D')0 = 2.1⋅105 m2s–1
110.0
30
)
405.1
910-1023
Ge PC, d = 1000 µm, serial sectioning, SAM, RAM, Eq.: W; VDD: D01 = 3.10−3m2s−1 Q1 = 310.0 kJ/mol, D02 = 1.1.10−4 m2s−1 Q2 = 276.0kJ/mol [85Wer]
1073-1193
Ge, BC, symmetrical tilt boundaries, 4 types of specimens: bc 1: <100>2°, bc 2: <100>11° bc 3: <010>2°, bc 4: <010>11° p-n junction metallography, a rough estimation of D'
814-949
Ge, PC, d = 1000 µm, serial sectioning, SAM, Eq.: W; VDD: D0 = 1.93.10−6m2 s−1 Q = 148.0 kJ/mol [89Alm]
30
) 953-1118
6 89Alm 97Alm
-
59Kar
6 89Alm
Ge BC, tilt gbs, symmetric with - 83Ahl respect to the <100> or <110> directions in both grains, SIMS profiling, Eq.: VD, results were interpreted as diffusion in a second phase, formed around dislocations 30 ) graphically estimated from the Arrhenius plot.
Sb
113
D' ≈ (105-106 ).D
Sn 7.0.10−12
Lando lt -Bö rnst ein New Series III/33A
169.5
1073-1193
matrix and method see As diffusion in Ge
- 59Kar
684-953
Ge, PC, d = 1000 µm, serial sectioning, SAM, Eq.: W; VDD: D0 = 3.66.10−4m2s−1 Q = 256.0 kJ/mol, [89Alm]
6 89Alm 97Alm
6-16
6 Grain boundary and dislocation diffusion in semiconductors and silicides (KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
[Ref. p. 6-24
Method/Remarks
Fig. Ref.
Matrix: Te Te (KδD' )0app = 1.11⋅10−14
127m
80.1
526-674
Te, PC, d = (75-120) µm, mechanical sectioning, Eq.: F; VDD: not given, results questionable, see [89Kau]
- 67Gho
6.4.2 Grain boundary diffusion in compound semiconductors 1 kJ mol−1 = 0.0104 eV (KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
Matrix: CuInSe2 Cd
5.3.10−13 1) 4.2.10−10 2)
144.7 111.0
500-800
PC TF, d = (1.8-2.4) µm "first - 79Kaz appearance" method , AES, different diffusion sources were used: 1) Cd source: CdS 2) Cd source: elemental Cd
164.0 106.1
not given
PC, TF, d = (0.8-1.2) µm, method see above 3) Cd source: CdS, 4) Cd source: elemental Cd
- 79Kaz
640
p-type, PC, Hg0.8Cd0.2Te, mechanical and chemical sectioning, RAM, EBICtechnique, enhanced diffusion only along large angle boundaries was observed
- 89Kli
Matrix: CuInS2 Cd
6.9.10−13 3) 3.1.10−9 4)
Matrix: HgCdTe 203
Hg
Landolt -Börnst ein New Series III/33A
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
(KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
6-17 Fig. Ref.
Matrix: In Sb 114m
5.85.10−20
124
6.6.10−18
In
Sb
80.1
107.1
8 94Ras
473-683
PC InSb, TF, d = (200-300) nm, tracer was produced by neutron activation, lateral diffusion of In was measured supposing type C-kinetics, Eq.: VD; VDD were also determined
473-623
8 94Ras PC InSb, TF, d = (200-300) nm, tracer was produced by neutron activation, lateral diffusion of Sb was measured supposing type Ckinetics, Eq.: VD; VDD were also determined
6.4.3 Grain boundary diffusion in silicides 1 kJ mol−1 = 0.0104 eV (KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
Matrix: CoSi2 60
Co
4.81.10−11
241.2
977-1373
CoSi2 bulk samples, d = 2 mm prepared by solidification from melt, chemical sectioning, SAM, Eq.: S; VDD: D0 = 2.1.10−5 m2/s Q = 273 kJ/mol [91Bar]
68
Ge
1.08.10−8
261.5
1025-1366
matrix, method as above, Eq.:S; 7 93Bar VDD: D0 = 8.3.10−4 m2/s Q = 311.6 kJ/mol [93Bar] 68 Ge tracer was used in lieu of a Si tracer.
Lando lt -Bö rnst ein New Series III/33A
7 93Bar
6-18
6 Grain boundary and dislocation diffusion in semiconductors and silicides (KδD')0 [m3s−1]
[Ref. p. 6-24
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
Fig. Ref.
164.0
803-1183
PC Ni2Si, prepared from 6N purity Ni and Si,chemical dissolution, RAM, Eq.: S; VDD: D0 – Q = 236.4 kJ/mol [89Cic]
- 89Cic
803-983
PC Ni2Si, d = (1-3)mm, chemical dissolution and mechanical abrasion, RAM, Eq.: S VDD: D0 = 3.54.10−4 m2/s Q = 239.8 kJ/mol [90Cic]
7 90Cic
983
matrix, method see above VDD: D (983K) = 5.03.10−19 m2/s [90Cic]
-
Matrix: Ni2Si 63
Ni
δD' = 14.5.10−22 3.0.10−22 1.2.10−22 1.4.10−23
m3/s m3/s m3/s m3/s
63
Ni
9.1.10−13
68
Ge
δD' = 1.7.10−22 m3/s
979 923 871 803 165.2
90Cic
Matrix: MoSi2 B
D' > 7.10−15 m2s−1
1333
MoSi2 TF, deposited by dc magnetron sputtering, SIMS profiling VDD: D (1333K) = 8.10−17 m2s−1
-
86Kat
603-673
- 84Zin PC Pd2Si, grown on <100>Si, accumulation rate of Ni on Pd2Si was measured by RBS, Eq.: a version of H-B
Matrix: Pd2Si Ni
115.8
Landolt -Börnst ein New Series III/33A
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
(KδD')0 [m3s−1]
Q" [kJ mol−1 ]
T-range [K]
Method/Remarks
6-19 Fig. Ref.
Matrix: TaSi2 33
P
(KδD')0app = 1.34.10−21
50.2
773-1173
sputtered TaSi2 TF grown on PC Si, d = (50-100) nm, sectioning: chemical dissolution, RAM, Eq.: W VDD: D0 = 4.21.10−16 m2/s Q = 64.6 kJ/mol [83Pe1]
- 83Pe1
33
P
(KδD')0app = 1.11.10−21
27.0
773-1173
sputtered TaSi2 TF grown on SiO2/Si, method see above, VDD: D0 = 3.50.10−16 m2/s Q = 60.8 kJ/mol [83Pe2]
- 83Pe2
Lando lt -Bö rnst ein New Series III/33A
6 Grain boundary and dislocation diffusion in semiconductors and silicides
6-20
[Ref. p. 6-24
Figures for 6
-24
X in Si -25 Ag, [67Ste] -26 In, [66Pav]
-28 P, [69Dud]
4
lg (K "a D "/[m /s])
-27
-29
2
Sb, [76Fah] -30 In, [67Ste]
Sb, [69Dud]
-31 As, [75Cam] -32 Sb, [64Pav] -33 -34 6
6.5
7
7.5
8
8.5 −4
9
9.5
10
−1
Inv. temp. 1/T [10 K ] Fig. 1. Si:Ag, As, In, P, Sb. Semilogarithmic plot of the dislocation diffusivity K"a2D" of different impurities in silicon vs. inverse temperature 1/T.
Landolt -Börnst ein New Series III/33A
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
-23
As in Si
[82Swa]
-24
[82Ba1]
-25 lg (K ' δ D '/ [m3/s])
[85Sak] -26 [77Tsu] -27 [81Rys] -28
-29
[84Ari]
-30 6
6,5
7
7,5
8
8,5
9
9,5
10
Inv. temp. 1/T . [10−4K−1] Fig. 2. Si:As. Semilogarithmic plot of the grain boundary diffusivity KδD' of arsenic in silicon vs. inverse temperature1/T.
-23
X in Si
B, [72Kam]
3
lg (K δ D '/[m /s])
-24 -25 B, [85Sak] -26 Al, [80Hwa] -27 -28 7
9
11
13 −4
15 −1
Inv. temp. 1/T [10 K
17
]
Fig. 3. Si:Al, B. Semilogarithmic plot of the grain boundary diffusivity KδD' of aluminium and boron in silicon vs. inverse temperature 1/T.
Lando lt -Bö rnst ein New Series III/33A
6-21
6-22
6 Grain boundary and dislocation diffusion in semiconductors and silicides
[Ref. p. 6-24
-20
P in Si -21 [82Lio]
[72Kam]
[86Spi]
3
lg (K 'δ D ' /[m /s])
-22
-23
-24 [89Hol] -25
-26 [85Sak] -27 6
6.5
7
7.5
8
8.5 −4
9
9.5
10
−1
Inv. temp. 1/T [10 K ] Fig. 4. Si:P. Semilogarithmic plot of the grain boundary diffusivity K'δD' of phosphorus in silicon vs. inverse temperature 1/T. -20
-16
Sb in Si
-17
X in Ge
-20.5 Au, [89Alm]
-18 -19 lg (K δ D '/[m /s])
3
[86Spi]
3
lg (K δ D '/[m /s])
-21
-21.5 [82Lio] -22
-20 -21 Sn, [89Alm] -22 -23
-22.5 Ge, [89Alm]
-24 -25
-23 7
7.5 8 8.5 4 1 Inv. temp. 1/T [10− K− ]
9
Fig. 5. Si:Sb. Semilogarithmic plot of the grain boundary diffusivity KδD'of antimony in silicon vs. inverse temperature 1/T.
9
10 11 12 13 14 4 1 Inv. temp. 1/T [10− K− ]
15
Fig. 6. Ge:Au, Ge, Sn. Semilogarithmic plot for the grain boundary self- and impurity diffusivity KδD' in germanium vs. inverse temperature 1/T. Landolt -Börnst ein New Series III/33A
Ref. p. 6-24]
6 Grain boundary and dislocation diffusion in semiconductors and silicides
6-23
-25
-18
X in InSb
Ge in CoSi2, [93Bar] -19
-26 In, [94Ras] lg (K δ D '/[ m /s])
3
Ni in Ni2Si, [90Cic]
3
lg (K δ D '/[m /s])
-20
-21
-27
-28 Sb, [94Ras]
-22 -29 -23 Co in CoSi2, [93Bar] -30
-24 7
8
9
10
11 −4
12
13
−1
Inv. temp. 1/T [10 K ] Fig. 7. CoSi2:Co, Ge; Ni2Si:Ni. Semilogarithmic plot for the grain boundary self- and impurity diffusivity KδD' in silicides vs. inverse temperature 1/T.
Lando lt -Börnst ein New Series III/33A
14 15 16 17 18 19 20 21 22 Inv. temp. 1/T [10− K− ] 4
1
Fig. 8. InSb:In, Sb. Semilogarithmic plot of the grain boundary diffusivity KδD' of In and Sb in InSb compound vs. inverse temperature 1/T.
6-24
6 Grain boundary and dislocation diffusion in semiconductors and silicides
6.5 References for 6 56Ful
Fuller, C.S., Ditzenberger, J.A.: J. Appl. Phys., 27 (1956) 544
59Kar
Karstensen, F.: Z. Naturforschung 14a (1959) 1031.
60Bol
Boltaks, B.I., Sue Si In: Fiz. Tverd. Tela 2 (1960) 2677.
61Que
Queisser, H.J, Hubner, K., Schockley, W.: Phys. Rev. 123 (1961) 1245.
63Cob
Coble, R.L.: J. Appl. Phys. 34 (1963) 1679.
64Joh 64Pav
Johnson, D.L., Clarke, T.M.: Acta Metall. 12 (1964) 1173. Pavlov, P.V., Panteleev, V.A., Maiorov, A.V.: Sov. Phys. Solid State 6 (1964) 305
66Pav
Pavlov, P.V., Lainer, L.V., Sterkhov, V.A., Panteleev, V.A.: Fiz. Tverd. Tel.,8 (1966) 725.
67Dud 67Gho 67Ste
Dudko, G.V., Kolegaev, M.A., Cherednichenko, D.I.: Elektron. Obrab. Mater. 6 (1967) 58. Ghoshtagore, R.R.: Phys. Rev. 155 (1967) 603. Sterkhov, V.A., Panteleev, V. A., Pavlov, P.V.: Sov. Phys. Solid State 9 (1967) 533.
68Pan 69Dud
Panteleev, V.A.: Collected Papers on Diffusion in Metals and Alloys, 3rd Federal Conf., Tula: Polytech. Inst. Tula , 1968, p. 223. Dudko, G.V., Kolegaev, M.A., Panteleev, V. A.: Sov. Phys. Solid State 11 (1969) 1097.
72Kam
Kamins, T.I., Manoliu, J., Tucker, R.N.: J. Appl. Phys. 43 (1972) 83.
74Pan 74Pav
Panteleev, V. A., Barysev, R.S., Lainer, L.V., Zinina, A.G., Pakutina, E.F.: Sov. Phys. Solid State 16 (1974) 320. Pavlov, P.V., Dobrokhotov, E.V.: Sov. Phys. Solid State 16 (1974) 1.
75Cam 75Hor
Campbell, D.R., Tu, K.N., Schwenker, R.O.: Thin Solid Films 25 (1975) 213. Horiuchi, S., Blanchard, R.: Solid State Electron. 18 (1975) 529.
76Gi1 76Gi2 76Hal
Gilmer, G.H., Farrell, H.H.: J. Appl. Phys. 47 (1976) 3792. Gilmer, G.H., Farrell, H.H.: J. Appl. Phys. 47 (1976) 4373. Hall, P.M., Morabito, J.M.: Surf. Sci. 59 (1976) 624.
76Fah
Fahrenholz, P., Mimkes, J.: Phys. Status Solidi (b) 78 (1976) K137.
77Nak 77Tsu
Nakamura, K., Kamoshida, M.: J. Appl. Phys. 48 (1977) 5349. Tsukamoto, K., Akasaka, Y., Horie, K.: J. Appl. Phys. 48 (1977) 1815.
78Hol
Holloway, P.H., McGuire, G.E.: J. Electrochem. Soc. 125 (1978) 2070.
79Ahl 79Hwa 79Kaz
Ahlborn, K.: J. Phys. (Paris) Colloq. C Suppl. 6 40 (1979) 185. Hwang, J.C.M., Balluffi , R.W.: J. Appl. Phys. 50 (1979) 1349. Kazmerski, L.L.: Thin Solid Films 57 (1979) 99.
80Gös 80Hwa
Gösele, U., Frank., W., Seeger, A.: Appl. Phys. A 23 (1980) 361. Hwang, J.C.M., Ho, P.S., Lewis, J.E., Campbell, D.R.: J. Appl. Phys. 51 (1980) 1576. Landolt -Börnst ein New Series III/33A
6 Grain boundary and dislocation diffusion in semiconductors and silicides
6-25
81Joh 81Jai 81Lec 81Rys
Johnson, N.M., Biegelsen, D.K., Moyer, M.D.: Appl. Phys. Lett. 38 (1981) 900. Jain, G.C., Chakravarty, B.C., Singh, S.N.: Appl. Phys. Lett. 38 (1981) 815. LeClaire A.D., Rabinovitch, A.: J. Phys. C 14 (1981) 3863. Ryssel, H., Iberl, H., Bleier, M., Prinke, G., Haberger, K., Kranz, H.: Appl. Phys. 24 (1981) 197.
82Ba1
82Hol 82Joh 82Koh 82Lio 82Nei 82Sat 82Swa
Baumgart, H., Leamy, H.J., Trimble, L.E., Doherty, C.J., Celler, G.K.: Grain Boundaries in Semiconductors, Leamy, H.J., Pike, G.E., Seager, C.H. (eds.), New York: North-Holland, 1982 p. 311. Baumgart, H., Leamy, H.J., Celler, G.K., Trimble, L.E.: J. Physique. C1 Suppl. No 10, 43 (1982) 363. Holloway, P.H.: J. Vac. Sci. Technol. 21 (1982) 19. Johnson, N.M., Biegelsen, D.K., Moyer, M.D.: Appl. Phys. Lett. 40 (1982) 882. Kohlbrecher, H., Peglow, H., Mimkes, J.: Thin Solid Films 92 (1982) 381. Liotard, J.L., Bibérian, R., Cabané, J.: J. Physique. C1 Suppl. No. 10, 43 (1982) 213. Neis, A., Mimkes, J.: Thin Solid Films 87 (1982) 53. Sato, Y., Murase, K., Harada, H.: J. Electrochem. Soc. 129 (1982) 1635. Swaminathan, B., Saraswat, K.C., Dutton, R.W.: Appl. Phys. Lett. 40 (1982) 795.
83Ahl 83Buo 83Lew 83Pe1 83Pe2
Ahlborn, K., Schröter, W.: Philos. Mag. A 48 (1983) 661. Buonaquisti, A.D., Carter, W., Holloway, P.H.: Thin Solid Films 100 (1983) 235. Lewis, N., Gildenblat, G., Ghezzo, M., Katz, W., Smith, G.A.: Appl. Phys. Lett. 42 (1983) 171. Pelleg, J.: Thin Solid Films 110 (1983) 115. Pelleg, J.: Thin Solid Films 110 (1983) 129.
84Ari 84Du1 84Du2 84Lec
Arienzo, M., Komem, Y., Michel, E.A.: J. Appl. Phys. 55 (1984) 365. Dubé, C., Hanoka, J.I.: Appl. Phys. Lett. 45 (1984) 1135. Dubé, C., Hanoka, J.I., Sandstrom, D.B.: Appl. Phys. Lett. 44 (1984) 425. LeClaire A.D., Rabinovitch, A.: in “ Diffusion in Crystalline Soilds”, Chap. 5, Murch, G.E., Nowick, A.S. (eds.), New York: Academic Press Inc. 1984. Losee, D.L., Lavine, J.P., Trabka, E.A., Lee, S.-T., Jarman, C.M.: J. Appl. Phys. 55 (1984) 1218. Zingu, E.C., Mayer, J.W.: Mater. Res. Soc. Symp. Proc. 25 (1984) 45.
82Ba2
84Los 84Zin 85Gin 85Sak 85Spi 85Wer 86Kat
Ginley, D.S., Hellmer, R.P.: J. Appl. Phys. 58 (1985) 871. Sakamoto, K., Nishi, K., Yamaji, T., Miyoshi, T., Ushio, S.: J. Electrochem. Soc. 132 (1985) 2457. Spit, F.H.M., Albers, H., Lubbes, A., Rijke, Q.J.A., v Ruijven, L.J., Westerveld, J.P.A., Bakker, H., Radelaar, S.: Phys. Status Solidi (a) 89 (1985) 105. Werner, M., Mehrer, H.: Phys. Rev. B 32 (1985) 3930.
86Sto 86Spi
Kato, J., Fujisawa, A., Asahina, M., Shimura, H., Yamamoto, Y.: J. Appl. Phys. 59 (1986) 4186 Stowijk, N.A., Hölzl J., Frank, W., Weber, E.R., Mehrer, H.É Appl. Phys. A 39 (1986) 37. Spit, F.H.M., Bakker, H.: Phys. Status Solidi (a) 97 (1986) 135.
87Cha
Chari, A., de Mierry, P., Menikh, A., Aucouturier, M.: Rev. Phys. Appl. 22 (1997) 655.
88Kau
Kaur, I., Gust, W.: Fundamentals of Grain and Interphase Boundary Diffusion, Stuttgart: Ziegler Press, 1988.
Lando lt -Bö rnst ein New Series III/33A
6-26 89Alm 89Cic 89Hol 89Kau 89Kli 90Cic 90Kau 90Lec
6 Grain boundary and dislocation diffusion in semiconductors and silicides Almazouzi, A.: Thèse, Université Aix-Marseille III, 1989. Ciccariello, J.C., Guelton, N., Poise, S., Gas, P.: Defect Diffus. Forum 66-69 (1989) 1377. Holloway, P.H., Abrantes, T.: J. Vac. Sci. Technol. A7 (1989) 1573. Kaur, I., Gust, W., Kozma, L.: Handbook of Grain and Interphase Boundary Diffusion Data,Vol.1-2, Stuttgart: Ziegler Press, 1989. Klimakow, A., Schenk, M.: Phys. Status Solidi (a) 115 (1989) K135. Ciccariello, J.C., Poise, S., Gas, P.: J. Appl. Phys. 67 (1990) 3315. Kaur, I., Gust, W.: in "Diffusion in Solid Metals and Alloys", Mehrer, H. (ed.), LandoltBörnstein New Series, Vol. III/26, Berlin: Springer-Verlag, 1990, p 630. LeClaire, A.D.: in "Diffusion in Solid Metals and Alloys", Mehrer, H. (ed.), Landolt-Börnstein New Series, Vol. III/26, Berlin: Springer-Verlag, 1990, p 627.
91Bar
Barge, T., Poise, S., Bernardini, J., Gas, P.: Appl. Surf. Sci. 53 (1991) 180.
92Jac 92Sto
Jackson, W.B., Johnson, N.M., Wu, I.-W., Chiang, A., Smith, D.: Appl. Phys. Lett. 61 (1992) 1670. Stolwijk, N.A.: in "Proceedings of the Int. Conf. on Diffusion in Materials", Kyoto, Japan 1992, Koiwa, M., Hirano K., Nakajima, H., Okada T. (eds.), Defect and Diffusion Forum, 95-98 ( 1993) 895.
93Bar
Barge, T.: Thèse, Université Aix-Marseille III, 1993.
94Ras
Rastogi, A., Reddy, K.V.: Semicond. Sci. Technol. 9 (1994) 2067.
95Bar
Barge, T., Gas, P., d'Heurle, F.M.: J. Mater. Res. 10 (1995) 1134.
96Poi 96Sto
Poisson, Ch., Rolland, A., Bernardini, J., Stolwijk, N.A.: J. Appl. Phys. 80 (1996) 6179. Stolwijk, N.A., Poisson, Ch., Bernardini, J.: J. Phys. Condens. Matter 8 (1996) 5843.
97Alm
Almazouzi, A., Moya, E.G., Bernardini, J.: Defect and Diffusion Forum Vols. 143-147 (1997) 1047.
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7 Surface diffusion on semiconductors E.G. SEEBAUER AND C.E. ALLEN
7.1 Introduction 7.1.1 General remarks Diffusion of adsorbates on surfaces plays an important role in a wide variety of physical processes, including crystal growth, sintering, corrosion, and heterogeneous catalysis. The present chapter concerns surface diffusion on semiconducting substrates; metallic substrates have been treated in a previous issue of this series [93Bon1] and insulating substrates are treated in subvolume B of this volume. Published data for semiconductors are far less numerous than for metals. Most work on semiconductors has been performed on Si, Ge, and GaAs and is comparatively recent (< 10 years old). The reasons for this stem both from the technological driver and from experimental difficulty. Semiconductor surfaces have sparked truly intense interest during the past 10 years because of the miniaturization of electronic devices and the corresponding importance of interfacial effects as the surface-to-volume ratio has increased. Semiconducting surfaces are also intrinsically more fragile than those of metals, effectively prohibiting the use of important surface diffusion techniques such as field ion microscopy and field emission microscopy.
7.1.2 Definitions of diffusion parameters Under most conditions, where tunneling is negligible, the diffusivity D typically obeys Arrhenius behavior with respect to temperature T: D = D0 exp (−Qdiff /kT) ,
(7.1)
where D0 represents the pre-exponential factor, Qdiff the activation energy for diffusion, and k Boltzmann's constant. Often, for comparison of activation energies between systems, the diffusion energy is scaled to the desorption energy Qdes through the definition of a corrugation ratio Ω = Qdiff /Qdes [90Gom1]. There exist several ways to distinguish surface diffusion coefficients. Here, data are subdivided according to whether the diffusion takes place by intrinsic or mass transfer diffusion. The mass transfer and intrinsic diffusion coefficients refer, respectively, to situations in which the number of mobile particles varies or remains constant as some system variable (almost always temperature) is varied [73Bon1]. Sometimes in the literature "intrinsic" refers to mass transport over short (atomic scale) distances, while "mass transfer" connotes motion over micrometers or more. However, these connotations are probably historical artifacts of the days when intrinsic diffusivities DI were measured experimentally by various probe tip methods (short length scale), while mass transfer diffusivities Dt were measured by profile decay methods (long length scale). Real surfaces are not perfectly flat but support various defect structures such as steps, kinks, and vacancies. Such structures are shown schematically in Fig. 1. Somewhat surprisingly, a growing body of evidence suggests that intrinsic diffusion parameters are relatively insensitive to small concentrations of surface steps, kinks or other defects. One could easily conceive of physical situations in which diffusion over long distances is limited primarily by motion over steps, which often bind adsorbates more strongly than do Lando lt -Bö rnst ein New Series III/33A
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[Ref. p. 7-18
terraces [73Bon1]. Indeed, for Ag on Ge(111), as shown in Fig. 2, minor variations in crystallographic orientations cause major changes in D0 and Qdiff [83Sul1]. However, in the relatively few systems for which direct comparisons are available between measurements made over short and long distances for the particular case where adsorbate incorporation into the surface is unlikely, no clear difference emerges. Fig. 3 compares diffusional activation energies of gases on solids measured by both short-range (2-20nm) and long-range (2-20µm) methods; the numbers are identical within experimental error. Unfortunately, almost no comparable data exist for D0. Furthermore almost all the data are for metals; only one semiconductor (Si) and no insulators are represented. Nevertheless, the data point to the usefulness of macroscopic measurements to probe microscopic processes. Dt and DI are formally related by [73Bon1]: Dt =
N DI , Ns
(7.2)
where N is the actual number of mobile particles, while Ns is a maximal number. For self-diffusion (A moving on A), Ns is the areal density of particles in the substrate, while for heterodiffusion (A moving on B), Ns is the areal density of adsorbed heteroatoms. In self-diffusion, typically N/Ns << 1, this quantity may be strongly temperature-dependent due to adatom-vacancy pair formation, for example. In heterodiffusion, often all adsorbate is mobile so that N = Ns implying that Dt = DI. However, in other cases, especially at low coverages, adsorbate may become trapped at kink or step sites on the surface, or even become incorporated substitutionally into terrace sites. In such cases, N/Ns may again become small and temperature-dependent. Good examples include Group III and V elements on Group IV semiconductors. Here, hard evidence obtained by scanning tunneling microscopy demonstrates that boron and phosphorous can substitute for toplayer silicon atoms [94Wan1, 95Wan1]. These considerations are usually ignored in experimental presentations of diffusion data. However, total mass transport across the surface is governed by Dt, with critical implications for applications involving particle sintering, scratch filling, and other practical situations. Since N/Ns can be such a strong function of temperature in practical applications, the distinction between Dt and DI cannot be casually dismissed.
7.2 Experimental techniques As mentioned above, effects of surface damage for semiconductors have eliminated several common experimental techniques used for metals such as field emission [83Gom1] and field ion [94Kel1] microscopies from the available repertoire. Instead, there has arisen a large collection of over 15 methods, most of which can be applied only to a very restricted set of adsorption systems that fortuitously have properties favorable to the detection of surface mobility. Below the salient features of these methods are outlined briefly. In some cases, diffusion methods have been utilized in ways not detailed here. This section will focus only on the usages listed in the tables of data.
7.2.1 Single-atom imaging Some techniques are capable of following the motion of individual adsorbed atoms, in which case intrinsic diffusion can be followed. Scanning tunnelling microscopy (STM) is most commonly used for this purpose. In STM [91Mo1, 95Swa1], a very sharp probe tip is placed within about 0.5 nm of the surface and electrically biased to yield a tunnelling current between the tip and surface. Although many forms of STM exist, a common method of imaging requires that the tunnelling current be held constant while the tip is slowly scanned across the surface. Because of the spatial corrugation in electronic potential, the scanning tip must be moved
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perpendicularly to the surface using a piezoelectric actuator in order to maintain constant current. A surface image can then be constructed by monitoring the required voltage on the actuator as a function of the lateral position of the tip. STM is limited for diffusion studies primarily by its restriction to relatively slow diffusion at low adsorbate coverages, since following single atoms becomes quite difficult when the mobility is large and when many diffusing atoms are present.
7.2.2 Electron diffraction Low-energy electron diffration (LEED) examines long-range surface periodicity by the diffraction of lowenergy electrons (~50-100 eV) from the surface onto an imaging screen [74Bed1]. Phase transitions involving surface reconstruction that affect the periodicity are easily followed in real time with LEED. To the extent that such transitions are mediated by surface diffusion, the diffusion coefficient can be estimated. However, surface reconstruction is a very complicated process whose dynamics are poorly understood. It is unclear how to relate the energetics of atomic motion through a fixed energy corrugation (classical surface diffusion) to reconstruction effects that induce dramatic changes in corrugation. Reconstructions can involve substantial collective motions and can be influenced by subsurface lattice strains, thereby introducing difficult complications. Reflection high-energy electron diffraction (RHEED) examines surface periodicity using much higher electron energies (10-20 keV). For surface diffusion studies, RHEED monitors primarily the atomic smoothness of the surface during deposition from the gas phase [90Gib1]. Generally the substrate is misoriented a few degrees from a low-index crystallographic plane in order to create a regular array of atomic steps. If diffusion during deposition is fast, atoms adsorbing on terraces incorporate at the steps, inducing "step-flow" growth. The surface remains smooth, and RHEED diffraction spots remain unchanged. If diffusion is too slow for motion over the length scale set by step separation in the time scale set by incident flux, two-dimensional island nucleation on the terraces occurs. As the surface roughens and smoothens repetitively (as new monolayers are completed), the RHEED pattern changes in oscillatory fashion. With extensive mathematical modeling of the growth, the onset of RHEED oscillations can then be used to extract the diffusivity. This method has been used mostly for diffusion of Ga on GaAs, but the results are quite scattered, probably due to the complexity of the physical situation and the consequent uncertainties in modeling. Reflection electron microscopy (REM) is used to observe denuded zones created at terrace edges. The diffusivity may be calculated by analyzing the denuded zones as a function of temperature and time. This technique is limited to studying surfaces where islands may be easily distinguished, as on the Si(100) surface where the (2x1) and (1x2) reconstructions alternating between successive layers are clearly visible [95Doi1]. Spatial resolution lies near 0.5µm.
7.2.3 Chemical state relaxation In this method a spectroscopy with sensitivity to chemical binding state is used to follow the evolution of an initially random adsorbate distribution into a preferred chemical state. Such techniques generally have quite limited application for surface diffusion because (a) two easily distinguished chemical states must exist, and (b) it must be established that the transformation is diffusively mediated. Perturbed γγ angular correlation (PAC) is a technique that examines the temporal coincidence of the two γ quanta emitted during the radioactive decay of 111In to 111Cd [92Kra1]. This coincidence is affected by the interaction of the electric quadrupole moment of an excited-state 111Cd nucleus with an extranuclear electric field gradient. The gradient varies with bonding site for In on Si (111). Thus, adsorbate present in an initially random distribution characterized by a variety of gradient fields can diffuse into a single well-defined state, and be followed by PAC during the process. Surface second harmonic generation (SHG) is an optical reflectance technique that employs pulsed lasers [88Ric1]. Because of the lack of inversion symmetry and the large electric field gradients present at a surface, Lando lt -Bö rnst ein New Series III/33A
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[Ref. p. 7-18
a nontrivial second-order optical susceptibility may exist there, leading to frequency doubling that can be detected in reflection. SHG is especially useful for substrates with high crystal symmetries, so that second harmonic contributions from the bulk can be completely suppressed. The surface second harmonic yield can be dramatically affected by adsorption, although quantitative coverage calibration requires a measurement by some independent technique. In the case of hydrogen adsorbed on silicon surfaces, SHG is sensitive to H bonded to terraces but not certain types of defects [96Han1]. Therefore, diffusion between the defects and the terraces may be monitored, generally during an adsorption experiment (in which adsorption is defectmediated).
7.2.4 Spin axis relaxation Atomic-spin sensitive techniques exist that monitor surface diffusion through changes in spin axis that occur during diffusion. Nuclear spin relaxation (NSR) measures nuclear spin depolarization occuring by coupling of the nuclear electric quadrupole moment of the adsorbate to fluctuations in the substrate electric field gradient as the atom moves [95Chr1]. The depolarization of an initially prepared set of nuclear spins is monitored by thermal desorption into a special detector. Mathematical modeling is complicated, and only a small set of substrates and adsorbate nuclei can avoid competing depolarization processes. Spatial resolution depends on the diffusion distance before desorption, but lies near 10 nm.
7.2.5 Profile evolution Numerous techniques exist in which adsorbate is deposited on some portion of a surface to yield a sharp initial concentration profile, which is then allowed to broaden diffusively. The deposition usually involves either a tightly focused molecular beam or a diffuse source together with a retractable mask. Sometimes spatially resolved pulsed laser desorption from a uniform adsorbed layer can yield the desired profile [91Rei1]. However, surface damage is a problem in many cases [86See1]. Profile evolution techniques measure only the chemical diffusivity for heterodiffusion, but in suitable profile geometries can do so very directly with a minimum of complicated mathematical modeling. The utility of a given method is generally limited by (a) the variety of adsorbates it can monitor without major surface perturbation, (b) the spatial resolution it can attain (including initial profile formation), and (c) the suitability of the initial profile geometry for quantitative analysis. Scanning electron microscopy (SEM) can be used when the adsorbate and substrate have good contrast for imaging by electron reflection. This generally holds only for metallic adsorbates on semiconductors and insulators, and even then only in special cases. For example, multilayers of adsorbate may be required, thereby complicating the diffusion process because multiple surface corrugations are present. Concentration calibration is difficult. Better results are obtained when the adsorbate strongly modifies the surface contact potential [94Mil1]. The maximum resolution for SEM is about 3 nm, although in practice results as poor at 15 µm have been reported. Electron beam damage is a possible problem. Scanning Auger microscopy (SAM) has better, more general sensitivity for a wide variety of adsorbates, but has somewhat poorer spatial resolution (~50 nm). This technique has been employed very effectively with a one-dimensional initial step suitable for analysis in the Boltzmann-Matano framework [83Sul1]. This technique is particularly suited for obtaining the concentration dependence of D. Again, however, electron beam damage can be an issue. Techniques based on spatially-resolved surface second harmonic generation (SHG) can sometimes better avoid the damage problem. Two such methods exist for measuring surface diffusion. One involves measuring second harmonic diffraction (SHD) from a regular adsorbate "grating" initially set up by laser desorption at the antinodes of a two-laser interference pattern [91Rei1]. As the profile decays by diffusion, the SH signal in first-order diffraction decreases. The technique has diffraction-limited resolution (~0.4µm), but measures the concentration dependence of D with difficulty. The method is also restricted to systems in which the
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adsorbate is bonded weakly enough to be desorbed without surface damage for grating formation. Second harmonic microscopy (SHM) is an alternate technique that images the profile in real space rather than reciprocal space [92Sch1]. Here, a one-dimensional profile (in the Boltzmann-Matano geometry) is set up by masked deposition, and the entire profile is illuminated and imaged at the second harmonic wavelength into a photodiode array. The concentration dependence of D is obtained easily, and the damage problems associated with laser desorption are avoided. However, the spatial resolution tends to be a bit poorer (~1-3 µm). Surface ion microscopy (SIM) can be used for species that desorb naturally as ions [92Sto1]. Therefore, its use has been restricted so far to highly electropositive elements such as potassium, rubidium, and cesium. The desorbing ions may be manipulated using appropriate ion optics to produce an enlarged image with a spatial resolution of about 10 µm.
7.2.6 Capillarity-driven effects Capillarity effects arise in physical situations where significant geometrical curvatures are present. Because of the existence of surface energy, the local chemical potential becomes a function of the local radius of curvature K according to the Gibbs-Thompson equation [93Bon1]:
µ (K) = µ0 + γ Ω K
(7.3)
where Ω is the atomic volume and γ the (orientation-dependent) specific surface energy. Spatial gradients in K and/or γ therefore give rise to gradients in µ, which in turn cause diffusion. These effects can form the basis for diffusion measurements when small scratches, grooves, voids, etc., are formed artificially on a surface and are then permitted to relax by diffusion. Scratch decay (SD) [94Kee1] and surface smoothing (SSm) [81Gav1] make use of this idea using the optical scattering pattern from a single scratch or a random array of scratches, respectively. Grain boundary grooving (GBG) [81Rob1] examines the widening of grain boundaries on the initially flat surface of a polycrystalline material. All of these methods work best for self-diffusion, and because of the relatively large amounts of mass transfer required, generally find use only at high temperatures. Thus, they are used extensively for studies of mass-transfer diffusion. The mathematical modeling is fairly extensive, and the results are generally averaged over a large range of crystallographic orientations. Modeling difficulties are most severe when the surface energy varies significantly (and often in unknown fashion) with orientation. However, the experiments are generally easy to set up. Spatial resolution varies with the detection technique, but ranges from about 10 nm (for SEM) to about 1 µm (for optical methods). An in-plane variant of the typical capillarity measurement involves examining the time-dependent shape fluctuations of monatomic steps. In this case, γ becomes a step energy, and K the local radius of curvature of a step. Fluctuations are diffusionally mediated, and in favorable cases can be monitored with electron microscopy. Low-energy electron microscopy (LEEM) involves forming a real image from a diffraction spot in a LEED experiment, and has been used on Si(100) where alternating terraces between steps have LEED patterns rotated 90° from each other, resulting in strong contrast in the resulting LEEM images [94Bar1]. Spatial resolution is about 15 nm.
7.2.7 Island growth Several methods rely on the diffusional formation of particle islands of adsorbate having poor wettability on the underlying substrate. Such systems often obey transformation kinetics governed by Ostwald ripening, in which large particles having large radii of curvature grow by virtue of Eq. 7.3 at the expense of small particles with small radii. The means of mass exchange between particles is surface diffusion. Rutherford backscattering/electron microscopy (RBS/EM) uses two methods to monitor particle growth [87Zin1]. RBS involves monitoring the scattering of high-energy helium nuclei off the surface. The backscattering can be used to obtain the average particle height, but electron microscopy is required to determine particle shape (from which the RBS data can yield volume) and to ensure that the shape is constant Lando lt -Bö rnst ein New Series III/33A
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[Ref. p. 7-18
during growth. With this method, fairly extensive mathematical modeling is required to obtain D, and the preexponential factor cannot be obtained. It is also generally unclear what adsorbate concentrations characterize the diffusional process.
7.2.8 Miscellaneous Molecular beam (M beam) techniques have been used to get activation energies for surface diffusion by examining adsorption [93Fel1] or desorption [75Fox1] kinetics. In either case, the beam is modulated. The adsorption or desorption must take place only at sites that are fairly widely spaced, with surface diffusion occurring to deliver adsorbate to or from the sites. Mathematical modeling then yields an expression for either a sticking probability or a desorption probability that contains the difference Qdes − Qdiff as a net activation energy. When Qdes can be obtained independently, as is usually possible, Qdiff can then be computed. Unfortunately, the physical situation is generally not defined well enough to determine D0; in fact, a value must generally be assumed to obtain Qdiff.
7.3 Physical picture It is useful to analyze the surface diffusion coefficient terms of enthalpies and entropies [91Lom1]: D = (νλ2/4) exp (∆S/k) exp (−∆H/kT) .
(7.4)
Here, ν is the attempt frequency for hopping, λ is the standard hop length, and ∆S and ∆H are entropy and enthalpy changes associated with hopping and possibly formation of the adsorbed particle. Comparison of Eq. 7.4 with Eq. 7.1 shows that D0 = (νλ2/4)exp (∆S/k) and that Qdiff = ∆H.
7.3.1 Intrinsic diffusion In intrinsic diffusion, ∆S and ∆H are associated with site-to-site hopping only. A first-principles estimate for D0 can be made by assuming ∆S = 0. Then with the attempt frequency ν ~ 1013s−1 (corresponding to a vibrational frequency), and λ ~ 0.3 nm (corresponding to an atomic diameter), D0 is estimated to be near 10−7 m2/s, broadly in accord with most experiments. The activation energy Qdiff, and therefore the corrugation ratio Ω, is not so easily estimated a priori.
7.3.2 Mass transfer diffusion As indicated in Eq. 7.2, the mass transfer diffusivity Dt equals the intrinsic diffusivity DI multiplied by the fractional coverage of the mobile adsorbate N/Ns. At equilibrium N/Ns is fixed by the affinity of free adatoms for kinks, steps and terraces, into which adatoms might be incorporated. An expression for the equilibrium of adatoms with these various bonding sites may be written in terms of enthalpies ∆Hf and entropies ∆Sf of formation [51Zen1]: N/Ns = exp(−∆Hf, kink/kT + ∆Sf, kink/k) + exp(−∆Hf, step/kT + ∆Sf, step/k) + exp(−∆Hf, terr/kT + ∆Sf, terr/k) .
(7.5)
At a given temperature, typically only one of three terms in this summation is likely to dominate. Combination of Eqs. 7.2 and 7.5 then yields simple relations between the activation energy and preexponential factor for intrinsic and mass-transfer diffusion:
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7 Surface diffusion on semiconductors
Qdiff, t = Qdiff, I + ∆Hf ,
a
f
D0t = DI0 exp D S f / k ,
7-7 (7.6) (7.7)
where the subscripts t and I refer to mass transfer and intrinsic diffusion, respectively. Let us now consider the sign and magnitude of ∆Hf and ∆Sf. Since ∆Hf is a positive quantity for adatom formation from all surface structures (i.e., kinks, steps, terraces), it is clear that Qdiff, t will generally be greater than Qdiff, I. In fact, because the energies for vacancy formation in terraces can be quite large [95See1], Qdiff, t may be much larger than Qdiff, I in this case. The effects are expected to be smaller for steps and kinks because fewer bonds need to be broken to form an adatom-vacancy pair. It also turns out that ∆Sf is generally a positive quantity as well. In the bulk, ∆Sf is known to be positive [51Zen1], and often fairly large [82Lan1,86Lan1], because of lattice mode softening near the vacancy. Similar effects seem to occur near terrace vacancies on surfaces [95See1], although the effects are probably smaller at steps and kinks. At low temperatures, experimental evidence on semiconductors indicates that the primary source of adatoms is from kink sites. New high-temperature STM experiments allow for the real-time measurements of step fluctuations due to rapid diffusion of kinks along the steps. The activation energy for this type of diffusional fluctuation can be readily obtained, although the corresponding pre-exponential factor cannot. On Si(100), two different groups have reported nearly identical activation energies for step rearrangement due to adatom formation and migration from kink sites (130 kJ/mol) [94Bar1, 95Swa1]. This energy falls between the intrinsic and higher temperature mass transfer results (Qdiff = ~85, 220 kJ/mol, respectively) [87Ich1, 93Voi1, 94Kee1]. At higher temperatures, the terraces appear to serve as the primary source of adatoms thereby leading to higher activation energies for mass transfer diffusion as just suggested. Molecular dynamics simulations for self-diffusion on Lennard-Jones solids [94Sun1] and on semiconductors [96Sun1, 96All1] show that the population of adatom-vacancy pairs on the surface increases dramatically, and that Dt scales directly with N. Direct experimental evidence comes from surface roughening measurements. The transition temperature between an atomically flat surface and one composed of many adatoms and vacancies is closely related to the roughening temperature [51Bur1, 94Con1]. In fact, the experimentally measured roughening temperatures occur in the general range of 60 to 75% of the substrate melting temperature Tmelt, coinciding very closely [94Con1, 94Lap1] with the transition temperature measured between the two mass transfer regimes in the case of self-diffusion as described below. Curiously, there exists no evidence that adatom creation from steps ever controls mass transfer diffusion. Only two temperature regimes can be discerned in the tables of data, suggesting that kinks and terraces can account for all mobile adatoms. This might be due to two causes. First, the energy of adatom creation from steps might be so close to that for kinks that the transition between the two is indistinguishable. Second, the combination of Qdiff and D0 for this regime might conspire in such a way that the contribution to mass transfer from the steps is always overshadowed by diffusion from either kinks or terraces. At temperatures approaching the melting point Tmelt of the substrate, it is reasonable to expect that the surface becomes so disordered that the adatom concentration N should approach Ns. Therefore, Dt should approach DI. That this situation occurs is shown in Fig. 4, which shows Dt [94Kee1] and DI [91Mo1] for selfdiffusion on Si(100) in Arrhenius form. The two lines, when extrapolated, cross very near Tmelt.
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[Ref. p. 7-18
7.4 General correlations 7.4.1 Intrinsic diffusion The data for intrinsic diffusion on semiconductors in Table 1 allow for some statistical analysis. A histogram plotting the frequency of reported values vs. log D0 is shown in Fig. 5. Each vertical bar represents the number of reports falling within the factor of 10 ranges demarked on the abscissa. Too few data exist to draw strong conclusions about patterns in D0. Several reports cluster about the "expected" value of about 10−7 m2/s. However, the significant outliers deserve some attention. In each of these cases, D0 is surprisingly low, near 10−14 m2/s for Pb/Si(111), 10−13 m2/s for Pb/Ge(111) [92Gan1] and 10−16 m2/s for H/Si(100) [96Han1]. It should be noted that in none of these cases does migration occur by simple site-to-site hopping; rather, diffusion involves complicated concerted motions. Since concerted motions can only occur when atoms are appropriately aligned, the attempt frequency in Eq. 7.9 decreased from a typical atomic vibrational frequency (typically 1013/s) to a much smaller value (here, 107/s or less), resulting in small values of D0. A corresponding histogram for Ω is shown in Fig. 6. More data exist than for D0, but the range of values is very broad. Interestingly, many of the data exceed Ω = 0.35, which is a rough upper limit for diffusion on metallic substrates [91Zhd1, 95See1]. The data for Ω on semiconductors in this temperature regime may be correlated more profitably with a simple relation based on bond counting. Using singly bonded H on Si(111) as a base case, where a corrugation ratio of Ω = 0.6 has been determined both experimentally [88Rei1, 96Han1] and theoretically [93Vit1] one finds:
Ω = 0.6/M ,
(7.8)
where M is the number of covalent bonds the adsorbed atom has to the surface. The correspondence between the data and this relation is shown in Fig. 7. Systems with the concerted diffusive motions described above are excluded. For monatomic adsorbates, determining M is straightforward. However, for dimers, it is a bit more difficult. In the case of Sb2/Si(100), for example [93Mo1] the Sb forms dimers that align themselves perpendicularly to the Si dimer rows. Diffusion was proposed to occur via a two-step process in which the Sb dimer first rotates parallel to the Si rows by pivoting about one of the Sb atoms, followed quickly by a second pivot, resulting again with the dimer perpendicular to the rows. In such a case, the dimer diffuses when one of the two bonds between a single Sb atom and the Si(100) surface is broken. Hence, for diffusion of a dimer on Si(100), M equals 2. Ga, which also forms dimers on the Si(100) surface, is treated in a similar manner. The desorption energy in Table 1 for the dimers was estimated to be that measured experimentally for single atoms with no correction associated with the dimerization. Data excluded from Fig. 7 include the study of benzene on Si(111), as the number of bonds to the surface is indeterminate, and studies where complicated concerted motions were found to occur. This correlation is expected to work only for species making strong directional bonds to the surface. There is no reason to expect that weakly bonded adsorbates, held by Van der Waals attraction, will obey this rule, as demonstrated by benzene on Si/(111). Further, if site-to-site hopping is not the mechanism of diffusion, deviations are expected, as evidenced by the concerted exchange studies.
7.4.2 Mass transfer diffusion For all nonmetallic substrates, Qdiff and D0 for mass transfer diffusion are greater than those for intrinsic diffusion. Two mass transfer diffusion regimes exist, dependent on substrate temperature. These regimes are divided by a critical temperature Tc that scales with the melting temperature of the substrate. Tc also appears to vary appreciably with substrate. However, values lying between 60 and 75% of Tmelt are typical. Tc is generally difficult to determine precisely, since any particular experiment rarely exhibits both regimes. A rare, clear example of this transition is shown in Fig. 8 for self-diffusion on the Si(100) surface.
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Below Tc, Qdiff lies at approximately twice the value for that of intrinsic diffusion while D0 lies very slightly above the intrinsic value. As mentioned above, adatom equilibrium with kinks probably governs this behavior. Reports in this regime on semiconductors typically involve self-diffusion. Above Tc, Qdiff and D0 increase dramatically in response to adatom formation from terraces. Reports in this regime include both selfdiffusion and heterodiffusion. Fig. 9 shows a histogram for D0 reports for mass transfer on semiconductors. The data taken at large T/Tmelt average to roughly D0 = 5.10−1 m2/s - a very high value. Only two reports exist for lower temperatures, and these are many orders of magnitude lower, near 10−9 m2/s. Fig. 10 shows data for Ω plotted in similar fashion. A fairly large data set exists, since values for Qdes are relatively abundant for both self-diffusion and heterodiffusion. Again, the data fall into two clear groups. At high T/Tmelt, Ω averages 0.75, while at low temperature, Ω is near 0.3.
7.4.3 Adsorbate concentration dependence In general, the diffusion coefficient often exhibits a strong dependence on surface concentration. Numerous examples of this behavior have been documented on metal surfaces [93Bon1]. Relatively few examples have been reported for nonmetals, and all extant measurements are for mass-transfer diffusion on semiconductors. The entire literature is summarized in Figs. 11 through 16. The data reported in the tables for these systems are quoted in the low-coverage limit. The behavior ranges from that of In on Si(111) [95All1], where both Qdiff and Do are independent of coverage over a wide range, to that of In on Ge(111) [94Sun1], where Qdiff varies by 40% and Do by six orders of magnitude. These variations can be strongly peaked, and in such cases are almost certainly the result of surface phase transitions. Since mass transfer diffusion is involved, it is unclear in general whether the variations result from changes in DI, N/Ns, or both. However, in the case of Sb on Ge(111) [92Sch1], changes in N/Ns were thought to be responsible, due to an adsorbate islanding mechanism. Small changes in crystallographic orientation can have enormous effects, as in the case of Ag on Ge(111) [83Sul1].
7.5 Commentary to tables The tables of diffusion parameters are divided as follows: intrinsic diffusion and mass transfer diffusion on semiconducting substrates (Table 1 and 2, respectively). In a few cases, D0 was not reported in the original work, but was readily obtained by the present authors by extrapolation of the data presented. Tables 1 and 2 do not contain all data available in the literature, but represent the results of a critical survey. Some words of caution are in order about the results presented. Deficiencies in methodology become particularly pronounced in the calculation of Qdiff and D0, which are derived, respectively, from the slope and intercept (extrapolation to infinite temperature) of an Arrhenius plot. In experiments where the rate of diffusion can be determined with only modest accuracy, gross errors in Qdiff and D0 may result. Moreover, in many cases D was not measured directly but was obtained from some other physical observable influenced by D. Nontrivial physical and mathematical modeling was then required to obtain D. Sometimes only the temperature dependence of D could then be retrieved. Thus, D0 was often not available. Furthermore, in other studies, the diffusivity could only be obtained at a single temperature. In these cases, either the literature report or the present authors assumed a value of D0 in order to estimate Qdiff. As a result of these various problems, the spread in reported diffusion results was found to be enormous for the several adsorption systems in which comparisons were possible. In such cases, particularly outlandish reports for the magnitudes of Qdiff and D0 were eliminated outright. For intrinsic diffusion, Qdiff and D0 (where available) are reported for each entry, together with Ω when the desorption energy could be determined. Where Qdes (for Ω) is taken from a reference not containing the
Lando lt -Bö rnst ein New Series III/33A
7-10
7 Surface diffusion on semiconductors
[Ref. p. 7-18
surface diffusion data, both references are given. The method and adsorbate coverage are indicated, together with the temperature range. As indicated in earlier sections, diffusion behavior is closely tied to Tmelt. Thus, the temperatures have all been reported as fraction T/Tmelt. For mass transfer diffusion, an indication is given of whether each system appears to be in the hightemperature or low-temperature mass transfer regime. Coverages are not reported because self-diffusion is often involved, or because coverages are often so poorly defined. In systems with well-defined coverages for heterodiffusion, the Qdiff and D0 are reported in the low-coverage limit.
7.6 Surface diffusion tables Index to method abbreviations: AES GBG LEED LEEM M beam NSR PAC RBS/EM REM RHEED SAM SD SEM SHD SHG SHM SIM SSm STM
Auger electron spectroscopy Grain boundary grooving Low energy electron diffraction Low energy electron microscopy Molecular beam Nuclear spin relaxation Perturbed γγ angular correlation Rutherford backscattering/electron microscopy Reflection electron microscopy Reflection high-energy electron diffraction Scanning Auger microscopy Scratch decay Scanning electron microscopy Second harmonic diffraction Second harmonic generation Second harmonic microscopy Scanning ion microscopy Surface smoothing Scanning tunneling microscopy
Table 1: Intrinsic Diffusion on Semiconductors (1 kJ/mol = 0.0104 eV) System
D0 [m2/s]
Qdiff [kJ/mol]
Ω
T/Tmelt
Method, Coverage
Ref.
H/Si(111)
7.10−8 8.10−8
145
0.6
0.4...0.43
SHD, 0.15
91Rei1
146
0.6
0.31...0.42
SHG, 0
96Han1
75
0.38
0.33...0.44
SHG, 0
96Han1, 89Sin1
Al/Si(111)
7.10−16 1.10−7
Si/Si(111) Si/Si(111)
H/Si(111) H/Si(100)
a
67
0.22 )
0.40...0.58
SEM, >1
78Nes1
−
106
0.23
0.48...0.53
LEED, −
74Bed1
−
71
0.16
0.38...0.47
93Voi1 87Zin1, 87Zin2
Si/Si(100)
10
65
0.14
0.2...0.33
STM, − STM, 0.07
Ga/Si(111)
−
46
0.24
0.37...0.48
RBS/EM, all
−7
91Mo1
Landolt -Börnst ein New Series III/33A
Ref. p. 7-18]
7 Surface diffusion on semiconductors
System
D0 [m2/s]
Qdiff [kJ/mol]
Ω
Ga/Si(100)
−
73
0.35
Ge/Si(100)
−
81
In/Si(111)
−
69
Sn/Si(111)
−
31
Sn/Si(100)
−
Sb2/Si(100)
−8
10
7-11
T/Tmelt
Method, Coverage
Ref.
0.37...0.48
RBS/EM, all
87Zin1, 87Zin2
0.20 )
0.47...0.56
RBS/EM, all
90Zin1
0.37
0.13...0.33
PAC, 0
92Kra1
0.09
0.37...0.48
RBS/EM, all
87Zin1, 87Zin2
96
0.23
0.37...0.48
RBS/EM, all
87Zin1, 87Zin2
117
0.35
0.24...0.32
STM, 0.02
93Mo1, 95All1
a
Ag/Si(111)
−
38
0.16
0.40...0.50
SEM, >1
92Ray1
Ag/Si(111)
32
0.16
0.29...0.47
84Han1
45
0.23
0.19...0.21
SEM, − SEM, 0.01
94Mil1
Pb/Si(111)
− 4.10−7 b) 3 . 10−14
62
0.36
0.18...0.21
STM, 0.01
96Gom1, 95Hib1
Pb/Si(111)
5 . 10−9
116
0.67
0.27...0.33
STM, 0.13
95Hib1
C6H6/Si(111)
−
90
1.0
0.175
STM, all
95Wol1
Ag/Ge(111)
− 5.10−13
44
0.18
0.52...0.64
94Ven1
52
0.40
0.25...0.29
SEM, − STM, 0
92Gan1, 83Met1
NO2/GaAs(110) −
25
0.67
0.17...0.30
M Beam, all
93Fel1
−
23
0.63
0.21...0.29
M Beam, −
75Fox1
Cs/Si(100)
Pb/Ge(111) As4/GaAs(100)
Table 2: Mass transfer diffusion on semiconductors (1 kJ/mol = 0.0104 eV) Surface
D0 [m2/s]
Qdiff [kJ/mol]
Ω
T-regime
T/Tmelt
Method
Ref.
Si/Si(100)
−
117
0.26
low
0.66...0.86
LEEM
94Bar1
Si/Si(100)
−
93
0.20
low
0.30...0.41
STM
95Pea1
Si/Si(100)
−
126
0.28
low
0.29...0.36
STM
95Swa1
Si/Si(100)
− 4.10−8 d)e)
109 )
0.24
low
0.42
STM
92Zan1
Si/Si(100)
135
0.28
low
0.46...0.61
REM
95Doi1
Si/Si(111)
−
125
0.28
low
0.37
RHEED 87Ich1
Ge/Ge(111)
−
106
0.28
low
0.35...0.38
RHEED 93Fuk1
Ga/GaAs(100)
8.5.10−10
126
0.36
low
0.47...0.50
RHEED 85Nea1, 90Gib1
Al/AlAs(100)
−
167
0.43
low
0.51...0.54
RHEED 93Shi1
In/Si(111)
0.3
176
0.64
high
0.43...0.51
SHM
96All1
Sb/Si(111)
1
251
0.75
high
0.52...0.57
SHM
95All1
Ge/Si(111)
6 . 10−2
238
0.58 )
high
0.57...0.66
SHM
96All2
Si/Si(poly)
94
298
0.66
high
0.86...0.98
GBG
81Rob1
Si/Si(100)
0.1
222
0.50
high
0.63...0.80
SD
94Kee1
Si/Si(100)
−
213
0.47
high
0.43...0.45
STM/ LEED
91Web1
Si/Si(100)
9.5.10−4
213
0.47
high
0.77...0.86
SSm
81Gav1
Lando lt -Bö rnst ein New Series III/33A
c
a
7-12
7 Surface diffusion on semiconductors
[Ref. p. 7-18
Surface
D0 [m2/s]
Qdiff [kJ/mol]
Ω
T-regime
T/Tmelt
Method
Ref.
Si/Si(100)
0.15 d)e)
258
0.53
high
0.61...0.66
REM
95Doi1
Si/Si(111)
0.9
347
0.77
high
0.51...0.57
LEED
78Ols1
Au/Si(111)
0.12 2.10−5
192
0.71
high
0.66...0.71
Auger
84Gav1
142
0.57
high
0.67...0.73
NSR
95Chr1
155
0.88
high
0.47...0.66
SIM
92Sto1
Rb/Si(111)
8 1.102
168
0.87
high
0.47...0.66
SIM
92Sto1
Cs/Si(111)
1.103
179
0.93
high
0.47...0.66
SIM
92Sto1
192
0.58
high
0.48...0.62
SAM
83Sul1, 79Ber1
Li/Si(111) K/Si(111)
f g
Ag/Ge(111) ) ) 10 −
368
0.98
high
0.38...0.41
RHEED 93Fuk1
f
Sb/Ge(111) )
0.87
199
0.73
high
0.68...0.76
SHM
92Sch1
In/Ge(111) f)
0.12
138
0.55
high
0.53...0.63
SHM
94Sun2
268
0.77
high
0.54...0.62
RHEED 89Oht1, 90Gib1
high
0.47...0.53
RHEED 90Shi1
Ge/Ge(111)
Ga/GaAs(100)
0.47 )
Ga/GaAs(100) − __________________ a) b) c) d) e) f) g) h) i)
h
272
i
0.78 )
Desorption energy estimated by present authors Pre-exponential factor estimated by present authors 7 Data recalculated assuming a pre-exponential factor for kink formation of 10 / s as measured in Refs. [95Pea1] and [95Swa1]. D0 calculated from original data by present authors. Diffusion on the 1x2 surface. D0 on the 2x1 surface is a factor of 10 slower. Data extrapolated to θ = 0. Surface cut 5 degrees off axis. Along [1 1 0 ] direction. D0 along [110] is a factor of 4 smaller. Qdiff determined assuming Qdes = 350 kJ/mol.
Landolt -Börnst ein New Series III/33A
Ref. p. 7-18]
7 Surface diffusion on semiconductors
7-13
Figures for 7 Terrace
Kink
–9
10
Step Adatom
Step-adatom
8 6
Ag on Ge (111) ϕ
4 2 –10
10
Terrace vacancy
175 O/W(100)
2 –1
–11
10
8 6 4
125
2
CO/Ni(111)
100
–12
H/Ni
10
8 6
CO/Pt(111)
25
–13
10
H/Pt
O/Pt CO/Rh 25
50 75 100 125 150 –1 Activ.energy Qmac [kJ mol ] Fig. 3. Diffusion activation energy Qmic obtained by microscopic methods measuring over a few atomic diameters, compared with energy Qmac obtained by macroscopic methods measuring over many atomic diameters. The results are nearly identical, falling on the 45° line. Data are for O/W(100) [80Bow1, 79Che1], H/Ni [57Wor1, 87Mul1], CO/Ni(111) [90Lin1, 88Zhu1], H/Pt [69Lew1, 86See2], CO/Pt(111) [92Kwa1, 82Poe1], O/Pt [68Lew1, 94Oer1], CO/Rh [88See1, 89Dun1], and H/Si(111) [91Rei1, 96Han1].
Fig. 4. Arrhenius plot for the intrinsic [91Mo1] and mass transfer [94Kee1] self-diffusivities DI and Dt, respectively, on Si(100), showing convergence near the melting temperature.
Lando lt -Bö rnst ein New Series III/33A
ϕ=0°
2
0
0.1
0.2
0.3 0.4 Coverage θ
0.5
0.6
Fig. 2. Variations in D as a function of step density for Ag/Ge(111) [83Sul1]. Inclination with respect to the (111) face is, 5.9o, 0.9o and 0o. –4
10
Tmelt
–6
10
Si on Si (100)
–8
10 2 –1
H/Si(111)
0
ϕ = 0.9 °
4
75 50
ϕ = 5.9 °
2
Diff.coeff. D [m s ]
–1
Activ.energy Qmic [kJ mol ]
150
4
Diff. coeff. D [m s ]
Adatom Fig. 1. Model of a surface showing various typical features, such as terraces, steps, kinks, vacancies, and adatoms.
8 6
–10
10
exp. extrapolated
–12
10
–14
10
Dt
–16
10
DI
–18
10
0
0.5
1.0 1.5 2.0 2.5 –3 –1 Inv. temp. 1/T [10 K ]
3.0
3.5
7 Surface diffusion on semiconductors
7-14
[Ref. p. 7-18
6
3
4
2
Frequency f
Frequency f
5
3 2
1
1 0 –16 10
–14
–12
–10
–8
–6
–4
10 10 10 10 10 2 –1 Pre-exp.factor D0 [m s ] Fig. 5. Frequency f of literature reports vs. D0 for intrinsic diffusion on semiconductors.
1.0
10
0.4 0.6 0.8 1.0 Corrugation ratio Fig. 6. Frequency f of literature reports vs. Ω for intrinsic diffusion on semiconductors.
–13 8 6 4
10
Semiconductors
Si on Si (100)
2
0.8
–14 8 6 4
10 2 –1
Diff.coeff. D [m s ]
Corrugation ratio
0.2
0
0.6
2 –15 8 6 4
10
0.4 0.2
b
–16 8 6 4
10 exp. theor.
2 3 Surface bonds M Fig. 7. Dependence of corrugation ratio Ω on number of adsorbate-surface bonds M for intrinsic diffusion on semiconductors. 0
a
2
1
2 –17
10
1.0 1.1 1.2 1.3 –3 –1 Inv.temp. 1/T [10 K ] Fig. 8. Arrhenius plot of the diffusivity D for the mass transfer self-diffusion of Si/Si(100) [95Doi1]. Two regimes appear, separated by the break in the plot near 1025K. Diffusion on the 1x2 and 2x1 terraces are represented by closed (b) and open (a) symbols, respectively.
0.8
0.9
Landolt -Börnst ein New Series III/33A
Ref. p. 7-18]
7 Surface diffusion on semiconductors
8
6 5
5 Frequency f
Frequency f
6
low T high T
4 3
1
3
1
0 –10 10
–8
220
10
–6
–4
–2
2
4
10 10 10 1 10 10 2 –1 Pre-exp.factor D0 [m s ] Fig. 9. Frequency f of literature reports vs. D0 for mass transfer diffusion on semiconductors. The data group into high and low temperature regions.
0.4 0.6 0.8 1.0 Corrugation ratio Fig. 10. Frequency f of literature reports vs. Ω for mass transfer diffusion on semiconductors. The data group into high and low temperature regions. 200
Sb on Ge (111)
210
180 –1
200 190 180 1 8 6
160
140 120
4
2 –1
0.2
0
Activ.energy Q [kJ mol ]
–1
4
2
2
Activ.energy Q [kJ mol ]
low T high T
7
7
Pre-exp.factor D0 [m s ]
7-15
2 –1
10
100 2 10
8 6 4 2
0
0.1
Fig. 11. D0 and Qdiff Ge(111) [92Sch1].
0.2
0.3 0.4 0.5 0.6 Coverage θ vs. coverage θ for Sb diffusion on
Fig. 12. D0 and Qdiff vs. coverage θ for In diffusion on Ge(111) [94Sun2] and Si(111) [95All1].
1
2 –1
10
Pre-exp.factor D0 [m s ]
–2
–2
10
–4
10
In on Si (111) In on Ge (111) –6
10
Lando lt -Bö rnst ein New Series III/33A
0
0.1
0.2
0.3 0.4 Coverage θ
0.5
0.6
7 Surface diffusion on semiconductors
7-16
55
Ge on Si (111)
–1
Activ.energy Q [kJ mol ]
–1
Activ.energy Q [kJ mol ]
260 250 240 230 220 –1 10
45 40
8
2 –1
Pre-exp.factor D0 [m s ]
2 –1
Pre-exp.factor D0 [m s ]
Cs on Si (100)
50
35 –5 10
8 6 4
2
6 4
2
–6
–2
10
[Ref. p. 7-18
0
0.2
Fig. 13. D0 and Qdiff Si(111) [96All2].
0.4 0.6 0.8 1.0 Coverage θ vs. coverage θ for Ge diffusion on
3.25
10
0
0.2
0.4 0.6 0.8 1.0 Coverage θ Fig. 14. D0 and Qdiff vs. coverage θ for Cs diffusion on Si(100) [94Mil1] calculated from the analytical expression given in that paper.
Ag on Ge (111) ϕ 3.00
3
10
10
2.50
–19
10
2.25 2 –1
Pre-exp.factor D0 [m s ]
1
2.00 1.75
ϕ = 5.9 ° ϕ = 0.9 ° ϕ=0°
1.50 1.25
Ag on Ge (111) ϕ
2
–1
Activ.energy Q [10 J atom ]
2.75
0
0.1
0.2
0.3 0.4 0.5 0.6 Coverage θ Fig. 15. Qdiff vs. coverage θ for Ag diffusion on Ge at several crystal orientations near (111) [83Sul1]. Inclination angle ϕ with respect to the (111) face is, 5.9o, 0.9o and 0o.
Fig. 16. D0 vs. coverage θ for Ag diffusion on Ge at several crystal orientations near (111) [83Sul1]. Inclination angle ϕ with respect to the (111) face is, 5.9o, 0.9o and 0o.
–1
10
–2
10
–3
10
–4
10
–5
10
ϕ = 5.9 ° ϕ = 0.9 ° ϕ=0°
–6
10
–7
10
0
0.1
0.2 0.3 Coverage θ
0.4
0.5
Landolt -Börnst ein New Series III/33A
7 Surface diffusion on semiconductors
7-17
7.7 Special references: review articles Gjostein, N.A.: Surface self-diffusion in FCC and BCC metals: a comparison of theory and experiment, in: "Surfaces and Interfaces I," chapter 11, Burke, J.J., Reed, N.L., and Weiss, V. (eds.), New York: Syracuse University Press, 1967. Robertson, W.M.: Surface diffusion of oxides, a review. J. Nucl. Mater. 30 (1969) 36. Bonzel, H.P.: A surface diffusion mechanism at high temperature. Surf. Sci. 21 (1970) 45. Neumann, G., Neumann, G.M.: Surface self-diffusion of metals. Diffusion Monograph Series 1 (1972) 1. Bonzel, H.P.: Surface diffusion of metals, in: "Structure and Properties of Metal Surfaces," Vol. 1, Shimodiara, S., (ed.), Tokyo: Maruzen, 1973. Rhead, G.E.: Diffusion on surfaces. Surf. Sci. 47 (1975) 207. Ehrlich, G., Stolt, K.: Surface diffusion. Annu. Rev. Phys. Chem. 31 (1980) 603. Gomer, R.: Surface diffusion. Vacuum 33 (1983) 537. Naumovets, A.G., Vedula, Yu.S.: Surface diffusion of adsorbates. Surf. Sci. Rep. 4 (1985) 365. Doll, J.D., Voter, A.F.: Recent developments in the theory of surface diffusion. Annu. Rev. Phys. Chem. 38 (1987) 413. Atkinson, A.: Surface and interface mass transport in ionic materials. Solid State Ionics 28-30 (1988) 1377. Rhead, G.E.: Atomic mobility at solid surfaces. Int. Mater. Rev. 34 (1989) 261. Gomer, R.: Diffusion of adsorbates on metal surfaces. Rep. Prog. Phys. 53 (1990) 917. Baetzold, R.: Surface diffusion of atomic and molecular adsorbates, in: "Metal-Surface Reaction Energetics," chapter 3, Shustorovich, E. (ed.), New York: VCH, 1991. Ehrlich, G.: Direct observations of the surface diffusion of atoms and clusters. Surf. Sci. 246 (1991) 1. Lombardo, S.J., Bell, A.T.: A review of theoretical models of adsorption, diffusion, desorption and reaction of gases on metal surfaces. Surf. Sci. Rep. 13 (1991) 1. Bonzel, H.P.: Landolt-Börnstein, New Series III/26, Madelung, O. (ed.), New York: Springer-Verlag, 1993, p. 717. Ehrlich, G.: Diffusion of individual adatoms. Surf. Sci. 299/300 (1994) 628. Kellogg, G.L.: Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces. Surf. Sci. Rep. 21 (1994) 1. Suni, I.I., Seebauer, E.G.: A new mechanism for surface diffusion at high temperatures. Surf. Sci. 301 (1994) L235. Seebauer, E.G., Allen, C.E.: Estimating surface diffusion coefficients. Prog. Surf. Sci. 49 (1995) 265.
Lando lt -Bö rnst ein New Series III/33A
7-18
7 Surface diffusion on semiconductors
7.8 References for 7 51Bur1 51Zen1
Burton, W.K., Cabrera, N., Franc, F.C.: Philos. Trans. R. Soc. London A 243 (1951) 299. Zener, C.: J. Appl. Phys. 22 (1951) 372.
57Wor1
Wortman, R., Gomer, R., Lundy, R.: Chem. Phys. 27 (1957) 1099.
68Lew1
Lewis, R., Gomer, R.: Surf. Sci. 12 (1968) 157.
69Lew1
Lewis, R., Gomer, R.: Surf. Sci. 17 (1969) 333.
73Bon1
Bonzel, H.P.: in "Structure and Properties of Metal Surfaces," Vol. 1, Shimodiara, S., (ed.), Tokyo: Maruzen Co., Ltd., 1973.
74Bed1
Bedair, S.M.: Surf. Sci. 42 (1974) 595.
75Fox1
Foxon, C.T., Joyce, B.A.: Surf. Sci. 50 (1975) 434.
78Nes1 78Ols1
Nesterenko, B.A., Zrazhevskii, V.A., Rozmnyuk, V.T.: Fiz. Tverd. Tela 20 (1978) 1901; Sov. Phys. Solid State (English Transl.) 20 (1978) 1099. Olshanetski, B.Z., Repinsky, S.M., Shklyaev, A.A.: Pisma Zh. Eksp. Teor. Fiz. 27 (1978) 403.
79Ber1 79Che1
Bertucci, M., Le Lay, G., Manneville, M., Kern, R.: Surf. Sci. 85 (1979) 471. Chen, J.R., Gomer, R.: Surf. Sci. 79 (1979) 413.
80Bow1 81Gav1 81Rob1
Bowker, M., King, D.A.: Surf. Sci. 94 (1980) 564. Gavrilyuk, Yu.L., Kaganovskii, Yu.S., Lifshits, V.G.: Kristallografiya 26 (1981) 561; Sov. Phys. Cryst. (English Transl.) 26 (1981) 317. Robertson, W.M.: J. Am. Ceram. Soc. 64 (1981) 9.
82Lan1 82Poe1
Lannoo, M., G. Allan: Phys. Rev. B 25 (1982) 4089. Poelsema, B., Veheij, L.K., Cosma, G.: Bull. Am. Phys. Soc. 49 (1982) 1731.
83Gom1 Gomer, R.: Surface Mobilities on Solid Materials, Binh, Vu Thien (ed.), NATO ASI Series B, 86, New York: Plenum Press, 1983, p. 1. 83Met1 Metois, J.J., Le Lay, G.: Surf. Sci. 133 (1983) 422. 83Sul1 Suliga, E., Henzler, M.: J. Phys. C 16 (1983) 1543. 84Gav1 84Han1
Gavrilyuk, Yu.L., Lifshits, V.G.: Phys. Chem. Mech. Surf. 2 (1984) 1091. Hanbücken, M., Futamoto, M., Venables, J.A.: Surf. Sci. 147 (1984) 433.
85Nea1
Neave, J.H., Dobson, P.J., Joyce, B.A., Zhang, J.: Appl. Phys. Lett. 47 (1985) 100.
86Lan1 86See1 86See2
Lannoo, M., Allan, G.: Phys. Rev. B. 33 (1986) 8789. Seebauer, E.G., Kong, A.C.F., Schmidt, L.D.: Surf. Sci. 176 (1986) 134. Seebauer, E.G., Schmidt, L.D.: Chem. Phys. Lett. 123 (1986) 129.
87Ich1 87Mul1 87Zin1 87Zin2
Ichikawa, M., Doi, T.: Appl. Phys. Lett. 50 (1987) 1141. Mullins, D.R., Roop, B., Costello, S.A., White, J.M.: Surf. Sci. 186 (1987) 67. Zinke-Allmang, M., Feldman, L.C.: Surf. Sci. 191 (1987) L749. Zinke-Allmang, M., Feldman, L.C., Nakahara, S.: Appl. Phys. Lett. 51 (1987) 975. Landolt -Börnst ein New Series III/33A
7 Surface diffusion on semiconductors
7-19
88Rei1 88Ric1 88See1 88Zhu1
Reider, G.A., Höfer, U., Heinz, T.F.: Phys. Rev. Lett. 66 (1988) 2883. Rice, B.M., Raff, L.M., Thompson, D.L.: J. Chem. Phys. 8 (1988) 7221. Seebauer, E.G., Kong, A.C.F., Schmidt, L.D.: J. Chem. Phys. 88 (1988) 6597. Zhu, X.D., Rasing, T., Shen, Y.R.: Phys. Rev. Lett. 61 (1988) 2883.
89Dun1 89Oht1 89Sin1
Duncan, T.M., Thayer, A.M., Root, T.W.: Phys. Rev. Lett. 63 (1989) 62. Ohta, K., Kojima, T., Nakagawa, T.: J. Cryst. Growth. 95 (1989) 71. Sinniah, K., Sherman, M.G., Lewis, L.B., Wienberg, W.H., Yates, J.T., Janda, K.C.: Phys. Rev. Lett. 62 (1989) 567.
90Gib1 90Gom1 90Lin1 90Shi1 90Zin1
Gibson, E.M., Foxon, C.T., Zhang, J., Joyce, B.A.: Appl. Phys. Lett. 57 (1990) 1203. Gomer, R.: Rep. Prog. Phys. 53 (1990) 917. Lin, T.S., Lu, H.J., Gomer, R.: Surf. Sci. 234 (1990) 251. Shitara, T., Kondo, E., Nishinaga, T.: J. Cryst. Growth 99 (1990) 530. Zinke-Allmang, M., Stoyanov, S.: J. Appl. Phys. 29 (1990) L1884.
91Lom1 91Mo1 91Rei1 91Web1
Lombardo, S.J., Bell, A.T.: Surf. Sci. Rep. 13 (1991) 1. Mo, Y.W., Kleiner, J., Webb, M.B., Legally, M.G.: Phys. Rev. Lett. 66 (1991) 1998. Reider, G.A., Höfer, U., Heinz, T.F.: Phys. Rev. Lett. 66 (1991) 1994. Webb, M.B., Men, F.K., Swartzentruber, B.S., Kariotis, R., Legally, M.G.: Surf. Sci. 242 (1991) 23. Zhdanov, V.P.: Surf. Sci. Rep. 12 (1991) 183.
91Zhd1 92Gan1 92Kra1
Ganz, E., Theiss, S.K., Hwang, I., Golovchenko, J.: Phys. Rev. Lett. 68 (1992) 1567. Krausch, G., Detzel, T., Fink, R., Lucksheiter, B., Platzer, R., Wöhrmann, U., Shatz, G.: Phys. Rev. Lett. 68 (1992) 377. 92Kwa1 Kwasniewski, V.J., Schmidt, L.D.: Surf. Sci. 274 (1992) 329. 92Ray1 Raynerd, G., Doust, T.N., Venables, J.A.: Surf. Sci. 261 (1992) 251. 92Sch1 Schultz, K.A., Seebauer, E.G.: J. Chem. Phys. 97 (1992) 6958. 92Sto1 Storch, R., Stolz, H., Wassmuth, H.W.: Ann. Phys. Leipzig 1 (1992) 315. 92Zan1 Zandvliet, H.J.W., Elswijk, H.B., van Loenen, E.J.: Surf. Sci. 272 (1992) 264. 93Bon1 93Fel1 93Fuk1 93Mo1 93Shi1 93Vit1 93Voi1
Bonzel, H.P.: Landolt-Börnstein, New Series III/26, Madelung, O. (ed.), New York: SpringerVerlag, 1993, p. 717. vom Felde, A., Bahr, C.C., Cardillo, M.J.: Chem. Phys. Lett. 203 (1993) 104. Fukutani, K.: Surf. Sci. 281 (1993) 285. Mo, Y.W.: Phys. Rev. Lett. 71 (1993) 2923. Shitara, T., Neave, J.H., Joyce, B.A.: Appl. Phys. Lett. 62 (1993) 1658. Vittadini, A., Selloni, A., Casarin, M.: Surf. Sci. 289 (1993) L625. Voigtländer, B., Zinner, A.: Surf. Sci. 292 (1993) L775.
94Bar1 94Con1 94Hwa1 94Kee1 94Kel1 94Lap1 94Mil1 94Oer1 94Sun1 94Sun2
Bartlet, N.C., Tromp, R.M., Williams, E.D.: Phys. Rev. Lett. 19 (1994) 1656. Conrad, E.H., Engel, T.: Surf. Sci. 299/300 (1994) 391. Hwang, I.S., Theiss, S.K., Golovchenko, J.A.: Science 265 (1994) 490. Keeffe, M.E., Umbach, C.C., Blakely, J.M.: J. Phys. Chem. Solids 55 (1994) 965. Kellogg, G.: Surf. Sci. Rep. 21 (1994) 1. Lapujoulade, J.: Surf. Sci. Rep. 20 (1994) 191. Milne, R.H., Azim, M., Persaud, R., Venables, J.A.: Phys. Rev. Lett. 73 (1994) 1396. von Oertzen, A., Rotermund, H.H., Nettesheim, S.: Surf. Sci. 311 (1994) 322. Suni, I.I., Seebauer, E.G.: Surf. Sci. 301 (1994) L235. Suni, I.I., Seebauer, E.G.: J. Chem. Phys. 100 (1994) 6772.
Lando lt -Bö rnst ein New Series III/33A
7-20 94Ven1
7 Surface diffusion on semiconductors
94Wan1
Venables, J.A., Persaud, R., Metcalfe, F.L., Milne, R.H., Azim, M.: J. Phys. Chem. Solids 55 (1994) 955. Wang, Y., Bronikowski, M.J., Hamers, R.J.: J. Phys. Chem. 98 (1994) 5966.
95All1 95Chr1 95Doi1 95Hib1 95Pea1 95See1 95Swa1 95Wan1 95Wol1
Allen, C.E., Seebauer, E.G.: Langmuir 11 (1995) 186. Chrost, J., Fick, D.: Surf. Sci. 343 (1994) 157. Doi, T., Ichikawa, M., Shigeyuki, S., Ninomiya, N.: Surf. Sci. 343 (1995) 24. Hibino, H., Ogino, T.: Surf. Sci. 328 (1995) L547. Pearson, C., Borovsky, B., Krueger, M., Curtis, R., Ganz, E.: Phys. Rev. Lett. 74 (1995) 2710. Seebauer, E.G., Allen, C.E.: Prog. Surf. Sci. 49 (1995) 265. Swartzentruber, B.S., Schacht, M.: Surf. Sci. 322 (1995) 83. Wang, Y., Hamers, R.J.: Phys. Rev. Lett. 74 (1995) 403. Wolkow, R.A., Moffatt, D.J., J. Chem. Phys. 103 (1995) 10696.
96All1 Allen, C.E., Ditchfield, R., Seebauer, E.G: J. Vac. Sci. Technol. A 14 (1996) 22. 96All2 Allen, C.E., Ditchfield, R., Seebauer, E.G: Phys. Rev. B 55 (1997) 13304. 96Gom1 Gomez-Rodriguez, J.M., Saenz, J. J., Baro, A. M., Veuillen, J. -Y., Cinti, R. C.: Phys. Rev. Lett. 76 (1996) 799. 96Han1 Hansen, D.A., Halbach, M.R. Seebauer, E.G.: J. Chem. Phys. 104 (1996) 7338. 96Sun1 Suni, I.I., E.G. Seebauer: Thin Solid Films 272 (1996) 229.
Landolt -Börnst ein New Series III/33A
2 Diffusion in silicon, germanium and their alloys
2-12
[Ref. p. 2-196
2.2 Diffusion in silicon 2.2.1 Tables for 2.2 2.2.1.1 Solute elements of group IA (hydrogen group). (See Figs. 1-7, p. 135) (1eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
9.4·10−3
0.48
967-1200 high-ohmic CZ crystals, H permeation through silicon cylinder, mass spectroscopy, interstitial mechanism
4.2·10−5
0.56
400-500
FZ crystals, B-doped (150 Ωcm), tritium outdiffusion, ionisation chamber measuring the amount of tritium evolved
250-400
B-doped CZ crystals (20-30 Ωcm), annealing in 2H or 2 H2 ambient, SIMS and EPR, D2H = 4·10−15 cm2s−1 at 350 oC, penetration depth of 2 H in polycrystalline films greater than in single crystals, 2H passivation of dangling bonds at grain boundaries
82Joh1
B-doped crystals (4·1014-7·1015 cm−3) and Al-, Ga-, or In-doped crystals, H plasma, spreading resistance, acceptor neutralization by hydrogenation of silicon dangling bonds
84Pan1 83Pan1
85Joh1
Methods and Remarks
Fig.
Ref.
H in Si
9·10−7
4 5
56Wie1
4
68Ich1
0.8
100-250
H diffusivity at B-doped (5·1018 cm−3) CZ crystals, Q decreases with decreasing B-doping, 18O2 in 2H plasma, SIMS, no 18O penetration observed, 2H penetration increases with decreasing B content, acceptor compensation involves Si-H bonding [85Joh2], no deep 2H penetration in P-doped (1017 cm−3) Si
0.45
130-250
n-type CZ crystals (4-10 Ωcm), Au doping, H plasma, spreading resistance, evaporated Al layers acting as diffusion barrier, Au neutralization
120
B-doped silicon (4·1018 cm−3) with and without As implanted layer, H plasma, spreading resistance, SIMS, As layer blocks H penetration, H is tied to one and B to three Si atoms [85Pan2]
85Pan1
50-250
B-doped FZ crystals (1-1000 Ωcm), n+p-diodes, H or 2 H plasma, C-V profiling, H-B pair formation, difference between hydrogenated and deuterated Si, field drift gives evidence for H+
85Tav1
2
5
85Mog1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Methods and Remarks
150
n-type crystals (2·1014-2·1019 cm−3) and P-implanted B-doped (2·1016 cm−3) crystals, 2H plasma, SIMS and Hall measurements, 2H diffusivity depends on P concentration, 2H diffusivity decreases with increasing P doping, chemical bonding model proposed
2-13
Fig.
Ref.
H in Si (cont.)
3.3 4.2·10−4
1.22 0.8
120-1200 H0 diffusivity, includes data of [56Wie1, 68Ich1] 120-250 H+ diffusivity, analysis of 2H profiles given by [85Joh1, 85Joh2, 85Pan1], H+ diffusivity enhancement by built-in electric field
87Cap1
87Cha1
150
P- or B-doped (1017 cm−3) crystals, H or 2H plasma, SIMS, TEM, photoluminescence spectroscopy (PL), DLTS, near-surface high 2H concentration correlates with H-stabilized platelets, hydrogenation generates electronic states
87Joh1
27-700
evaluation of literature data including[68Ich1, 85Mog1, 85Ben1, 85Pea1, 86Pea1, 87Cap1]
87Pea1
27
DH = 2·10−11 cm2s−1, B-doped ((1-2)·1015 cm−3) CZ crystal, wet chemical etching, C-V analysis of acceptor density, proposes ion bombardment-induced H injection from surface-adsorbed H2O or hydrocarbon
87Sea1
350-500
cast polycrystalline p-type Si (5-8 Ωcm), grain size 0.6-1.0 cm, H plasma, Schottky diodes, electronbeam-induced current mode of SEM, decrease of minority carrier trap center density indicates H diffusion from the bulk to the surface
88Kum1
27
DH = 10−10 cm2s−1, B-doped crystals (4·1015 cm−3), injection by low energy H+ ion beam, C-V profiling, positively charged H involved in H-B pair formation , ratio of H+ to Ho about 0.1
88Sea1
20
Lando lt -Bö rnst ein New Series III/33A
4
DH = 10−12 cm2s−1 DH = 10−11 cm2s−1 B-doped (6·1016 cm−3), P-doped (1018 cm−3) and undoped single crystals, 2H plasma, SIMS, complex profiles due to H-B interaction, strongly trapped H: DH = 10−10 cm2s−1, mobile H: DH = 10−9 cm2s−1, electrochemical permeation of H through Si membrane, under high fugacities small fraction of H diffuses fast
150 320
0.53
86Joh1
2-14
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
150
DH0 = 1.4·10−8 cm2s−1 consistent with [56Wie1] DH– = 3·10−10 cm2s−1, DH+ = 6·10−13 cm2s−1 includes SIMS results of [85Joh1, 86Joh1, 87Joh1] for deuterated n- and p-type Si, near-surface trapping and trapping by B and P, H2 formation
89Mat1 90Mat1
150 480
DH in p+-type film > DH in n+-type film DH in p+-type film = DH in n+-type film n+p- and p+p-structures by LPE, n+ doping by P (1.5·1018 cm−3), p+ doping by B (1.5·1018 cm−3), B-doped (1.3·1015 cm−3) substrate, 2H plasma, SIMS, H trapping by B or P at 150 oC, no trapping at 480 oC
89Ome1
100
DH+ = 10−12 cm2s−1, B-doped CZ crystals ( 8·1014 cm−3), H incorporation by mechano-chemical polishing, C-V profiling, H-B complexes
89Sch1
500 250
D2H =3·10−14 cm2s−1 re-estimated from 2H profile D2H =10−14 cm2s−1 [90Wu1] B-doped crystals, H and 2H plasma, nuclear resonance reaction for H and SIMS for 2H profiling, 2H trapping by B, 2H concentration equals B concentration, limited-flux model [90Wu1]
89Ton1
H in Si (cont.)
2.4·10−7
0.43
90-210
B-doped crystals (1019-1.2·1020 cm−3), H plasma, see also [90Her2], infrared reflectance spectroscopy for B-H profiling, diffusion limited by trapping, binding energy of B-H pairs 0.6 eV
5
90Her1 91Her1
2.00·10−5
0.49
95-279
n-type crystals (15-100 Ωcm), electron-radiation defects, Au incorporated during growth, dislocations induced by deformation, H plasma or boiling water, DLTS, decrease in concentration of Au-related level
5
90Kov1
2.5·10−1
0.58
11-48
CZ and FZ crystals or EFG ribbons, n- and p-type, H implantation, C-V measurements on Schottky diodes, H+ motion in p-type silicon, H0 trapped at sites other than shallow dopants, multihydrogen complexes, D0 recalculated from Arrhenius plot
5
90Sea1
60
DH– = 10−15 cm2s−1, P-doped CZ crystals (1.45·1017 cm−3), H plasma, Schottky diodes, annealing with or without reverse bias, C-V measurements, evidence for H−
90Zhu1
(−3)-157
B-doped crystals (3·1018 and 5·1018 cm−3), implantation of 111In+ and damage anneal, H and 2H plasma, PAC spectroscopy, local hopping of H and 2 H around Cd with 0.21 eV activation energy
91Geb1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Methods and Remarks
2-15
Fig.
Ref.
H in Si (cont.) evalution of literature data refering to the microscopic structure of H-related defects and H motion in silicon
91Hal1
7.75·10−4
0.81
125-200
P-doped CZ crystal (1017 cm−3) and P-doped FZ crystals (8·1017 cm−3) , 2H plasma, vacuum annealing, SIMS, mobile complex 2H2*, no dissociation under reverse bias, D0 recalculated from Arrhenius plot
5
91Joh1
7·10−2 5·10−3
0.54 0.49
(−53)-(−3) 1H diffusion (−53)-(−3) 2H diffusion CZ- and FZ-crystals with various concentrations of P, Oi, and Cs, etching with HNO3 or 2HNO3, 70-90 oC anneal to release H-P and to form H-C, DLTS, annihilation of H-C or 2H-C under illumination, H or 2 H diffusion to P is rate limiting step, see also [93Kam1]
5
91Kam1
1.70·102
1.2
225-350
B-doped CZ crystal (10 Ωcm), H gas, H plasma, uniaxial stress, IR absorption, relaxation of stressinduced dichroism, enhanced O diffusion, H migration suggested to be trap limited
5
91New1 92New1
8.40 6.00·10−1 1.20·10−4 1.30·10−2
1.12 1.03 0.60 0.80
120-185 120-1207 120-185 120-185
H0 diffusion H0 diffusion, including data of [56Wie1] H+ diffusion H− diffusion p- and n-type FZ crystals, various dopant concentrations, 2H plasma, SIMS, C-V measurements combined with chemical sectioning, D H0 < D H– < D H+
1 4
91Riz1
27-47
P-doped crystals (1016 cm−3), Schottky diodes on deuterated side, hole injection by illumination, capacitance transients due to H motion in depletion layer, D2H– = 2.8·10−12 cm2s−1 at 27 oC indirectly determined from recombination with P+, Q = 0.7 eV
60-140
B-doped FZ crystals (0.47 and 10 Ωcm), H plasma, C-V measurements, trap limited H diffusion, DHeff inversely proportional to B concentration, Q = 0.7 eV
75-250
B-doped FZ crystals (0.1-100 Ωcm), 2 H plasma, SIMS, limited multiple trapping of H at B sites, D value used from [56Wie1]
75-250
n-type FZ crystals (0.1-100 Ωcm), 2 H plasma, SIMS, four-point-probe spreading resistance, DH0, H– in n-type < DH+ in p-type Si, trapping mechanisms: platelet and molecule formation, dopant-H complexing
Lando lt -Bö rnst ein New Series III/33A
92Joh1
3
92Zun1
93Bor1 94Pea1 2
94Pea1
2-16
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Methods and Remarks
[Ref. p. 2-196
Q [eV]
T-range [oC]
Fig.
Ref.
9.4·10−3
0.78
450-1000 p-type single crystals, metallic Li on surfaces, annealing in He ambient, pn-junction method, Li acts as donor
6
53Ful1
2.3·10−3
0.66
360-860
p-type single crystals, initial Li pulse introduced at 800 oC, Li+ drift in external electric field, pn-junction method
6
54Ful1
2.3·10−3 2.2·10−3
0.72 0.7
0-877 420-800
given in [90sha1] also including data of[54Ful1, 60Pel1, 60Pel2, 66Pra1]
6
58Mai1 59Sha1
Li in Si
evaluation of literature data including [53Ful1, 54Ful1]
59rei1
2.5·10−3
0.655 25-1350
including data of [54Ful1, 59Pel1], p-type FZ crystals (1000 Ωcm), 6Li and 7Li outdiffusion, resistivity and Hall measurements, D6Li/D7Li = 1.07 at 800 oC, Li+ diffusion, interstitial mechanism
2.50·10−3
0.655 25-125
p-type crystals, Li+ drift in the electric field of a reverse biased pn junction, C-V measurements, ion pairing reactions considered, consistent with high temperature data [54Ful1]
60Pel2
2.65·10−3
0.63
400-500
p-type single crystals (4-1000 Ωcm), Li diffusion by decomposition of LiAlH4, four-point-probe combined with mechanical sectioning
66Pra1
0.83
27-137
68Hac1
1.03
27-57
neutron irradiation 1014-3·1014 n cm−2, D0 =7.0·1012/(n cm−2), electron irradiation 1016-2·1018 e cm−2, D0 =2.1·1018/(e cm−2), B-doped crystals (< 1014 cm−3), Li drift in an electric field of a reverse-biased diode, neutron and electron irradiation-induced vacancies provides sites for Li precipitation
(−73)-27
B-doped single crystals (1000-2000 Ωcm) Li diffusion under influence of X-ray irradiation, C-V measurement, enhanced Li drift
70Kli1
400
B- and P-doped crystals, resistivity measurement, D = 2·10−8 cm2s−1 in the presence of a B gradient, D = 8·10−9 and 2·10−8 cm2s−1 in the presence of a P gradient
70Mok1
6
60Pel1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Methods and Remarks
2-17
Fig.
Ref.
Li in Si (cont.) 3.8·10−3
0.66
300-550
single crystals, special diffusion experiment which prevents exposure to atmosphere, both pure Li and Li3N layers as source, four-point-probe resistivity measurement combined with mechanical sectioning, Li precipitation near the surface
1.1·103
1.13
36-100
recalculated from data given in [86wöh1], B-doped crystals, O concentration 4·1017 cm−3, Hall measurements performed during Li out-diffusion
800
D = 6·10−12 cm2s−1 attributed to Nai, p-type crystals (40 Ωcm), samples exposed to sodium vapour, NAA , no conductivity type inversion observed, amphoteric property of Na
65Cal1
500 600
DNai = 1.5·10−11 cm2s−1 DNai = 8·10−11 cm2s−1 p-type crystals (40 Ωcm), Na implantation at 460 oC, pn-junction method,
65Cal2
400 500
DNai = (1-5)·10−12 cm2s−1 DNai = (5-10)·10−11 cm2s−1 p-type crystals, Na implantation at 400 oC and 500 oC, no additional annealing, pn-junction method
66Rut1
71Lar1
6
74Les1
Na in Si
1.65·10−3
0.72
530-810
B-doped single crystals (100 Ωcm), about 103 dislocations/cm2 , diffusion from molten metal or during electrolytical deposition, pn-junction method, donor levels, interstitial mechanism
1.47·10−2
1.27
650-900
p-type single crystals, Na implantation, pn-junction method, deep penetration of interstitial Na at 600 oC when radiation-induced defects are annealed out
75Kor1
500-900
p-type CZ and FZ crystals, pn-junction method, Na implantation at 23 oC results in retardation of DNai for T < 650 oC, temperature dependence of DNai after Na implantation at 500 oC consistent with [75Kor1], retardation of DNai by radiation-induced defects
76Bel1
Lando lt -Bö rnst ein New Series III/33A
7
67Svo1
2-18
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
1.27
650-900
comprises data of [75Kor1, 76Bel1, 85Zas1], evaluation of literature data including [64Svo1, 65Cal1, 65Cal2, 66Rut1, 67Svo1, 69Par1], Na implantation in p-type or high resistivity crystals, additional annealing, pn-junction method, four-point-probe measurement combined with sectioning, Na loss after implantation due to out-diffusion, implantation-induced shallow donor Nai, Nas under equilibrium diffusion conditions
7
88Kor1
1.1·10−3
0.76
540-790
B-doped single crystals (100 Ωcm), dislocation density < 103 cm−2, diffusion from molten metal or during electrolytical deposition, pn-junction method, donor levels, interstitial mechanism
7
67Svo1
1.1·10−8
0.8
500-800
p-type single crystals, K implantation, pn-junction method and resistivity measurements
7
72Zor1
Na in Si (cont.) 1.5·10−2
K in Si
high resistivity p-type crystals, electrolytically deposited layer, incremental sheet resistance, Hall measurements, interstitial donor
86Ho1
Rb in Si 570-1100 p-type FZ crystals, Rb implantation at RT and 350 oC, Hall effect, sheet resistivity, channeling and backscattering measurements, out-diffusion, Rb not on substitutional or tetrahedral interstitial lattice sites to levels greater than 10%
70Mey2
Cs in Si p-type crystals, Cs implantation, sheet resistance, C-V analysis, donor centers observed 810-1160 p-type FZ crystals, Cs implantation at RT and 350 oC, Hall effect, sheet resistivity, channeling and backscattering measurements, out-diffusion, Cs not on substitutional or tetrahedral interstitial lattice sites to levels greater than 10%
63Cal1 65Cal3 70Mey1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-19
2.2.1.2 Solute elements of group IIA (beryllium group). (See Figs. 8-10, p.136) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [ °C]
Methods and Remarks
1050
D ≈ 10−7 cm2s−1, Be-doped crystal (1016 cm−3), out-diffusion, resistivity and Hall effect measurement, Be-related acceptor level, (see also [68Rob1, 81Hen1, 82Tom2, 86Kle2, 90Hen1, 91Hey1, 92Hey1] )
300-1100
D = 10−15-10−13 cm2s−1 , n- and p-type crystals (1 Ωcm), Be implantation also through thin SiO2 layers, SIMS, C-V profiling, higher implantation doses enhance Be out-diffusion.
Fig.
Ref.
Be in Si
10−2
2.0
70Taf1
8
75Hur1
collection of foreign-atom diffusion data including [82Tom1]
88Had1
450-950
p-type FZ crystals (50 Ωcm), Mg implantation, SIMS and Hall effect, Mg implanted layers show n-type conductivity, Mg-silicide formation between 500 °C and 800 °C, Mgi diffuse into the bulk between 900 °C and 950 °C, Mgi acts as double donor [72Ho1]
82Sig1
400-1000
p-type FZ crystals (10-100 Ωcm), 24Mg+ implantation, (p,γ) resonance broadening, radiation-damage enhanced out-diffusion suggested
Mg in Si
9
83Räi1
double donor Mgi [79Oht1, 82Lin1, 86Kle1, 94Häß1, 94Thi1], evidence for a substitutional Mg acceptor level [88Bab1]
Ca in Si
Lando lt -Bö rnst ein New Series III/33A
1412
D = 2.3·10−5 cm2s−1 at melting point, deduced from the distribution coefficient of Ca in Si
1100
D ≈ 6·10−14 cm2s−1, p- and n-type crystals (10 Ωcm, 50 Ωcm), closed ampoule annealing using high purity carbon crucible doped with Ca, SIMS and Hall effect, substitutional incorporation at T > 1020 °C deduced from solubility measurements
900
n-type CZ crystals, Ca implantation, RTA, DLTS and optically stimulated DLTS, Ca-related donor detected
69Den1 10
83Sig1
94Häß1
2-20
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
2.2.1.3 Solute elements of group IIIB (scandium group including rare earth elements) (See Figs. 11-16, p. 137) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig. Ref.
3.2
1100-1250
deposition of radioactive 46ScCl on Si plates, chemical sectioning, residual activity measurement, surface concentration ≈ 1018cm−3
11
1050
D = 3.9·10−13 cm2s−1, single crystals, vacuum deposition of Ce, SIMS analysis
1.74
1100-1280
D0 and Q recalculated from given data, P-doped crystals (15 Ωcm) radioactive 143Pr chloride, chemical sectioning, residual activity method
11
88Naz1
1.2 0.13
730-1270 730-1270
slow diffusing component fast diffusing component p-type single crystals, radiotracer 147Pm, solubility at 1200 oC about 6·1013 cm−3
12 13
70Fer1
1100-1320
D = 3·10−13- 10−11 cm2s−1 , single crystals
Sc in Si 8·10−2
89Azi1
Ce in Si 89Fu1
Pr in Si 2.5·10−7
Pm in Si 7.5·10−9 4.2·10−12
Dy in Si 94Lat1
Er in Si 1.6·104
5.0
1100-1250
recalculated from Arrhenius plot shown in [95Sob1]
15
77Age1
2·10−3
2.9
1100-1250
n-type single crystals (15 Ωcm), Er-chloride film containing radiotracer 169Er, chemical sectioning, residual β-activity, boundary concentration 3·1018-5·1019 cm−3, substitutional mechanism
15
91Naz1
5·10−4
2.7
900-1300
recalculated from Arrhenius plot shown in [95Sob1]
15
93Ren1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
Er in Si (cont.) 5·10−1 3.3
2 Diffusion in silicon, germanium and their alloys
2-21
T-range [oC]
Methods and Remarks
Fig. Ref.
1100-1250
n- and p-type CZ and FZ crystals (1-50 Ωcm), tetraethoxysilane with Er-oxide or Er-chloride, RBS, DLTS, four-point-probe combined with chemical sectioning, formation of acceptor centers, Er boundary concentration in Ar ambient higher than in O2 ambient, D0 and Q recalculated from the Arrhenius plot
15
93Sob1
1200
D = 1.3·10−12 cm2s−1, n-type CZ crystals (1-20 Ωcm), surface films of tetraethoxysilane with Er-oxide or Er-chloride, Er introduced at 1250 oC, deposition of nitride films, test structures by selectively etching, annealing in Ar and O2 ambient, pn-junction staining, four-point probe combined with chemical etching, interaction of Er with excess intrinsic point defects, Si3N4 is effective barrier for out-diffusion of Er
14
95Ale1 95Nai1
1315
D = 1-3·10−16 cm2s−1, single crystals, diffusion within a closed Si cavity, O2 and Ar ambient mixture, SIMS, erfc profiles
95Rob1
review about Er in Si, including diffusion data of [77Age1, 91Naz1, 93Ren1, 93Sob1]
95Sob1
Tm in Si 8·10−3
3.0
1100-1280
n-type single crystals (15 Ωcm), Tm-chloride film containing radiotracer 170Tm, residual βactivity combined with chemical sectioning, boundary concentration between 3·1018-5·1019 cm−3, substitutional mechanism
11
91Naz1
0.95
947-1097
n-type crystals (10 Ωcm), Yb-layer deposited, gas-phase diffusion is not reproducible, NAA combined with chemical sectioning, two donor levels, non-erfc profiles, solubility measurement, interstitial mechanism proposed
11 16
90Bak1
1100-1320
D = 10−12-4.2·10−12 cm2s−1, single crystals
Yb in Si 2.8·10−5
Lu in Si
Lando lt -Bö rnst ein New Series III/33A
94Lat1
2 Diffusion in silicon, germanium and their alloys
2-22
[Ref. p. 2-196
2.2.1.4 Solute elements of group IVB (titanium group). (See Figs. 17-20, p.139) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
1.5
1000-1250
p-type single crystals, radiotracer 44Ti, mechanical sectioning
Fig.
Ref.
Ti in Si 2·10−5
19
81Gra1
n- and p-type CZ and FZ crystals, deposition of Ti by evaporation, (differential) DLTS, two donor and one acceptor level, interstitial diffusion, no haze formation, includes literature data of 3d transition elements 1.5·10−3
1.64
825-1100
D0 and Q recalculated from given data, p- and n-type CZ crystals doped with Ti, DLTS on n+p-diodes, Ti out-diffusion due to POCl3 gettering
77Bol1
19
reviews of solubility, diffusion, and energy-level data found for 3d transition elements in Si, see also [83Web1, 85Web1, 89Utz2]
83Roh1
83web2 86Gra1 91sch1
1.45·10−2
1.79
950-1200
p-type CZ and FZ crystals (8-60 Ωcm), evaporation of Ti layer, capping with Si, formation of TiSi2 at 600 oC, DLTS and C-V measurement, chemical sectioning, erfc profiles, interstitial diffusion
19
88Hoc1
1.2·10−1
2.05
600-1150
P- and B-doped Si, evaporation of Ti, in-diffusion at 1050-1150 oC or out-diffusion at 600-800 oC after Ti saturation at 1200 oC, DLTS combined with chemical sectioning, one acceptor and two donor levels, interstitial impurity
17 18 19 20
91Kug1 92Nak1 94Nak1
P- and B-doped FZ crystals co-doped with Ti, DLTS and thermally stimulated capacitance measurements, one acceptor and two donor levels, review of energy levels and segregation coefficients of 3d-5d transition elements in Si
94Lem1
Zr- or Hf-doped FZ crystals, grown-in concentrations near 1012 cm−3, B or P co-doping 1013-1014 cm−3, DLTS, one acceptor and two donor levels, see also [94Lem1]
90Lem1
Zr, Hf in Si
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-23
2.2.1.5 Solute elements of group VB (vanadium group). (See Figs. 20-22, p. 139) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Method and Remarks
Fig.
Ref.
900-1100
D ≈ 10−7 cm2s−1, n- and p-type CZ and FZ crystals, V2O5 as diffusion source, DLTS on p+n- and n+pjunctions, two donor and one acceptor level
80Oht1
1075-1100
n- and p-type CZ and FZ crystals, V scratched on the surface, no haze formation, (differential) DLTS, one acceptor and two donor levels, interstitial diffusion, includes literature data of other 3d transition elements in Si
81Gra1
825
n- and p-type CZ crystals doped with V, DLTS on n+p diodes, out-diffusion due to POCl3 gettering
83Roh1
review of solubility, diffusion, and energy-level data found for 3d transition elements in Si, see also [83Web1, 85Web1]
83web2 86Gra1
V in Si
6.1·10−1
2.8
1100-1250
n-type and p-type single crystals, radiotracer 48V deposited as chloride, chemical sectioning, residual γ-activity, boundary concentration ≈ 2·1017 cm−3
22
89Azi2
9.0·10−3
1.55
600-1200
P- and B-doped Si, evaporation of V, in-diffusion at 1050-1200 oC or out-diffusion at 600-800 oC after V saturation at 1170 oC, DLTS combined with chemical sectioning, one acceptor and two donor levels, interstitial impurity
20 21 22
91Sad1 92Nak1 94Nak1
P- and B-doped FZ crystals co-doped with V, DLTS and thermally stimulated capacitance measurements, one acceptor and two donor levels, review of energy levels and segregation coefficients of 3d-5d transition elements in Si
94Lem1
P- and B-doped FZ crystals co-doped with Nb, DLTS and thermally stimulated capacitance measurements, one acceptor and two donor levels
94Lem1
D = 10−13-10−12 cm2s−1
67Smi1
P- and B-doped FZ crystals co-doped with Ta, DLTS and thermally stimulated capacitance measurements, one acceptor and two donor levels
94Lem1
Nb in Si
Ta in Si 1215-1294
Lando lt -Bö rnst ein New Series III/33A
2-24
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
2.2.1.6 Solute elements of group VIB (chromium group). (See Figs. 20, 23, 24, p. 139) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
Cr in Si 1·10
−2
1·10−2
T-range [oC]
Methods and Remarks
Fig.
Ref.
· 1.0
900-1250
B-doped CZ crystals (5-20 Ωcm), immersion in an aqueous solution of CrNO3, annealed in H stream, pn-junction method, precipitation kinetics studied by EPR
24
70Ben1
1.0
1100-1250
P- and B-doped FZ crystals, Cr evaporation, NAA, four-point probe and spreading resistance, pn-junction method, solubility increases from 2.2·1013 cm−3 at 900 oC to 2.5·1015 cm−3 at 1280 oC
23 24
74Wur1
1000-1150
D = 10−7-10−8 cm2s−1 , n- and p-type CZ and FZ crystals (1-200 Ωcm), Cr evaporation, haze formation, Cr-B pair formation, (differential) DLTS, one donor level, interstitial diffusion, includes literature data of diffusion and energy levels of other 3d transition elements in Si
81Gra1
825
n- and p-type CZ crystals doped with Cr, DLTS on n+p-diodes, POCl3 gettering reduces Cr concentration below DLTS detection limit ( ≤ 4·1011 cm−3)
83Roh1
900
D ≈ 4.4·10−7 cm2s−1, single crystals, NAA and EPR, estimation from diffusion time necessary to reach 50% saturation
83Web1
reviews of solubility, diffusion, and energy-level data found for 3d transition elements in Si, see also [83Web1, 85Web1]
83web2 86Gra1
3·10−2
1.1 0.85
850-1050 24-96
p-type CZ crystals, CB = (6-8)·1014 cm−3, Cr sputtered onto one side, RTA in mixed Ar/H2 ambient, Cri-Bs pair formation, DLTS, high temperature data from erfc fitting of Cri-Bs profiles, low temperature data from Cri-Bs association kinetics during annealing
24
89Zhu1
2.5·10−3
0.81
24-1200
simultaneous fit of high- and low-temperature data given by [70Ben1] and [89Zhu1], interstitial mechanism, summarizes diffusion and solubility data of other 3d transition elements in Si
24
91sch1
P- and B-doped FZ crystals co-doped with Cr, DLTS and thermally stimulated capacitance measurements, one donor level, review of energy levels and segregation coefficients of 3d-5d transition elements in Si
94Lem1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-25
T-range [oC]
Methods and Remarks
Fig.
Ref.
27-400
P- and B-doped FZ or CZ crystals, coating with CrCl3, annealing at 800-1200 oC, out-diffusion, DLTS profiling, one donor level, interstitial impurity, formation of Cr-B pairs, includes data of Ti, V, Mn, and Fe in Si
825
p- and n-type CZ crystals doped with Mo, DLTS on n+p-diodes, no POCl3 gettering, one energy level
83Roh1
1200
D ≥ 10−8 cm2s−1, Mo contamination in Si epitaxial layers and Si substrate wafers, DLTS
85Tob1
1000
D = 2·10−10 cm2s−1, B- and P-doped FZ crystals, Mo deposited by spincoating, (optical) DLTS combined with chemical sectioning
91Ham1
P- and B-doped FZ crystals co-doped with Mo, DLTS and thermally stimulated capacitance measurements, one donor level
94Lem1
D ≈ 10−12 cm2s−1 , P- or B-doped CZ or FZ crystals, sputtered W layer capped with Si, WSi2 formation at 850 oC, DLTS, three W-related energy levels, non-erfc profiles, occurrence of Wi and Ws suggested
91Bou1
P- and B-doped FZ crystals co-doped with W, DLTS and thermally stimulated capacitance, one donor level
94Lem1
Cr in Si (cont.) 6.8·10−4
0.79
20 24
94Nak1
Mo in Si
W in Si 1100
Lando lt -Bö rnst ein New Series III/33A
2-26
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
2.2.1.7 Solute elements of group VIIB ( manganese group). (See Figs. 25, 26, p. 141) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
1.3
1000-1350
D = 1·10−6-2·10−5 cm2s−1 attributed to Mni+, n-type single crystals, vapour phase diffusion with Mn source at 1000 oC, radiotracer 54Mn combined with mechanical sectioning, electrotransport and solubility measurements, interstitial mechanism
72Bak1
900-1100
n- and p-type CZ and FZ crystals (1-200 Ωcm), Mn scratched on the surface, haze formation, (differential) DLTS, one acceptor and two donor levels, interstitial diffusion, includes literature data of diffusion and energy levels of other 3d transition elements in Si
81Gra1
1100
D ≈ 2·10−6 cm2s−1, single crystals, NAA and EPR, estimation from diffusion time necessary to reach 50% saturation
83Web1
reviews of solubility, diffusion, and energy-level data found for 3d transition elements in Si, see also [83Web1, 85Web1]
83web2 86Gra1
Mn in Si
6.9·10−4
0.63
900-1200
As- or P-doped FZ crystals, radioactive 54Mn evaporated, mechanical sectioning, DLTS, interstitial mechanism
700-1038
CZ and FZ crystals, As-, B-, or P-doped to 1019-1020 cm−3 or virtually intrinsic, radioactive54MnCl2, mechanical sectioning, mobile species: Mni (charge 0 or +1), immobile species: Mns (charge ≤ -1) and Mni-B or Mns-P pairs
90Gil1
1200
n-type CZ crystals (5 Ωcm), saturation with radioactive 54Mn at 1200 oC, mechanical sectioning, DLTS, Mn out-diffusion and electrical active Mn not influenced by Ni layer on surface
91Abd1
25 26
86Gil1
2.4·10−3
0.72
14-90
B-doped FZ crystals, diffusion from MnCl2 source into n+p-junctions at 1000 oC, DLTS, association kinetics of Mni and Bs, interstitial mechanism, (MniBs)+ binding energy 1.03 eV
26
91Nak1 92Nak1
1.3·10−3
0.7
14-1200
simultaneous fit of high- and low-temperature data given by [86Gil1] and [91Nak1], interstitial mechanism, summarizes diffusion and solubility data of other 3d transition elements in Si
26
91sch1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-27
T-range [oC]
Methods and Remarks
Fig.
Ref.
1200
single crystals doped with O to 5·1015-1016 cm−3 and C to 1016-2·1017 cm−3, radioactive 54MnCl2, mechanical sectioning, DLTS, Mn profile not influenced by O and C, electrically active Mn affected by SiO2 particles
94Abd1
1050-1200
B-doped single crystals co-doped with S at 1250 oC, Mn diffusion from vapour phase, Hall measurement, NAA, IR, EPR, decrease of donor concentration, evidences for electrically inactive Mn-S complexes
94Bak1
P- and B-doped FZ crystals co-doped with Mn, DLTS and thermally stimulated capacitance measurements, three levels due to Mni or Mn-B pairs, review of energy levels and segregation coefficients of 3d-5d transition elements in Si
94Lem1
1200
n-type CZ crystals, Ni saturation at 1200 oC from radioactive 63NiCl2, Mn deposition, mechanical sectioning, Ni gettering
95Kul1
1200-1250
p- and n-type crystals, Re chloride source, photocapacitance, acceptor levels attributed to isolated Re and Re complexes, additional level found by photoconductivity measurements (see [76Leb2])
76Leb1
1200-1250
n-type crystals, solution of HReO4 on the surface, photocapacitance on pn-junction diodes, one Rerelated donor and four acceptor levels
77Yun1
P- and B-doped FZ crystals co-doped with Re, DLTS and thermally stimulated capacitance measurements, two levels in n-type Si, no level in p-type Si, low segregation coefficient (5·10−9)
94Lem1
Mn in Si (cont.)
Re in Si
Lando lt -Bö rnst ein New Series III/33A
2-28
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
2.2.1.8 Solute elements of group VIII (iron group). (See Figs. 20, 27-30, p. 141) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
1100
no effect of external electric field
Ref.
Fe in Si 6.2·10
−3
59
57Gal1
0.87
1100-1250
single crystals, radiotracer Fe from FeCl3 source + sectioning
27 30
56Str1
2.3·10−2
0.77
30-85
FZ crystals, B-doping (30Ωcm), high-temperature Fe saturation + quenching, (1-2)·105 dislocations/cm2, two-point resistivity, kinetics of Fe+-B− pairing, also precipitation kinetics at 100-200 oC, D0 and Q given by [91sch1]
27 30
62She1
6.3·10−4
0.58
100-500
single crystals, about 104 dislocations/cm2, annealing after high-temperature in-diffusion, resistivity and Hall effect, capturing of Fe by dislocations
30
72Bol1
1200
D = 4·10−6 cm2s−1, single crystals, 103-104 dislocations/cm2, out-diffusion after saturation, radiotracer 59Fe + chemical sectioning
75Usk1
1000-1200
1.5 Ωcm slices deposited with Au, annealing with 10−2 s pulses from xenon lamps, DLTS profiling, effective temperature calculated, prevalence of interstitial mechanism
76Ant1
1.3·10−3
0.68
20-1250
Overall fit to published data resulting from hightemperature radiotracer diffusion [56Str1] and lowtemperature DLTS [80Kim1], resistivity [62She1] and EPR [60Lud1] measurements
27
83Web1 83web2
4.5·10−2
1.1
600-700
polycrystals with different grain boundary orientations, single grains and single crystals, Fe diffusion after high-temperature Au saturation, 2- or 4-probe resistivity, conduction along Fe-decorated grain boundaries, D0 and Q recalculated from Arrhenius plot including [56Str1]
30
84Mir1
8.0·10−6
0.43
120-200
FZ crystals diffused with Fe and Au, DLTS on pnjunctions, kinetics of Au-Fe pair formation, D0 and Q recalculated from Arrhenius plot
30
85Bro1
3.3·10−1
0.81
0-72
FZ crystals, pairing of interstitial Fe with B after indiffusion and quenching, DLTS, Hall effect
30
88Nak1
9.5·10−4
0.65
800-1070
FZ crystals, in-depth DLTS by layer removal, interstitial Fe isolated and paired with B, erfc profiles
30
89Iso1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-29
T-range [oC]
Methods and Remarks
820
n-type single crystal, 59Fe deposition on surface, annealing in Cl-containing ambient, radiotracer technique with sectioning, charge carrier lifetime measurements, strongly reduced Fe incorporation
27-577
CZ crystals, RTA after 57Fe implantation, in-beam Mössbauer line broadening, agreement with [83web2]
700 & 920
FZ crystals, heavily B- or P-doped (ca. 1020 cm−3) and virtually intrinsic, radiotracer 59Fe + sectioning, mobile species: Fei (charge 0 or +1), immobile species: Fes (charge < −2) and FeiB and FesP pairs.
90Gil1
30-1070
review on 3d transition elements in Si [89Utz2]
91sch1
0.66
0-1070
comprises [88Nak1] and [89Iso1]
0.68 0.80
40-80 150-260
diffusivity of singly positively charged Fei diffusivity of neutral Fei FZ crystals, annnealing after 1300 oC saturation, electron spin resonance, precipitation of Fei0 in n-type Si, Fei+-acceptor pairing in p-type Si
1.4·10−3 1.0·10−2
0.69 0.84
77-137 127-197
diffusivity of singly positively charged Fei diffusivity of neutral Fei CZ and FZ crystals, annealing after high temperature in-diffusion, photocapacitance of Schottky diodes, drift of Fe ions in electric field
2 5·10−4
0.92 0.56
90-140 90-140
diffusivity of singly positively charged Fei diffusivity of neutral Fei B-doped single crystals, 4-9·1014 B/cm3 annealing after 950 oC in-diffusion in O2 ambient, DLTS and C-V analysis, D(Feo) > D(Fe+), D0 recalculated from Arrhenius plot
95Kov1
considers FeB pairing and carrier emission limited drift, no controversy between [95Kov1] and [92Hei1, 92Hei2, 92Tak1]
96Hei1
gives further evidences for D(Feo) > D(Fe+), see [95Kov1]
96Kov1
Fig.
Ref.
Fe in Si (cont.)
1.1·10−3
Lando lt -Bö rnst ein New Series III/33A
90Moi1
27
20
90Sch1
92Nak1 92Tak1
28 29 30
92Hei1 92Hei2 91Hei1 90Hei1
2-30
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
1000-1280
D = 5·10−7-5·10−6 cm2s−1, n-type single crystals, ca. 104 dislocations/cm2, resistivity, interstitial mechanism, also Hall effect, photoconductivity and IR absorption, acceptor and donor level attributed to different states
74Yun1
1000
single crystal, annealing at 100-450 oC after 1000 oC in-diffusion, DLTS, fast interstitial diffusion, transition to substitutional sites
91Jie1
1280
D = 2·10−6 cm2s−1 (fastest component) attributed to isolated atoms, single crystals, 4-point probe and photo-capacitance, compensation of shallow donors and acceptors, formation of complexes
78Azi1
Ru in Si
Os in Si
2.2.1.9 Solute elements of group VIII (cobalt group). (See Figs. 31-34, p. 142) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
1000-1300
D = 10−6- 10−4 cm2s−1, single crystals, 103 dislocations/cm2, radiotracer 56Co with sectioning, dissociative mechanism
70Bak2
950
single crystals, 104 dislocations/cm2, 57Co decaying to 57Fe, Mössbauer spectroscopy, tetrahedrally coordinated component and Co-vacancy complex
75Usk2
900-1200
B-doped wafers, radiotracer sectioning, erfc profiles
400-1000
samples diffusion-doped with P (ca. 1021 cm−3) or B (ca. 1020 cm−3) or lightly doped, radiotracer 60Co with chemical sectioning, reduced diffusivity due to enhanced Cos2− solubility and/or Cos− P+ pair formation in n-type Si: dissociative mechanism, only fast migrating Coi2+ in p-type Si
77Mal1
1000-1250
FZ crystals, 57Co Mössbauer spectroscopy and depth profiling, mainly interstitial diffusion and solubility, minor solubility of substitutional Cos
81Ber1
700-1300
review on 3d transition elements in Si
83web2
Co in Si
9.2·104
2.8
57
Co with mechanical
32 33
77Kit1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-31
T-range [oC]
Methods and Remarks
Fig.
Ref.
Co in Si (cont.) 1.0·10−9
1.5
700-1000
single crystal, thin Co surface film, Gaussian profiles, NAA with serial sectioning, SIMS, extremely low diffusivity
33
87App1
9.1·104
2.8
1000-1150
FZ crystals, 100 dislocations/cm2 after annealing (out-diffusion) following 1200 oC saturation, DLTS with sectioning, profiles of Cos (minority species), dissociative mechanism, includes data of [77Kit1, 84Nak1, 86Suw1]
32 33
88Has1
9·10−4
0.37
900-1100
FZ crystals, radiotracer 57Co with sectioning, erfc profiles, interstitial mechanism, reduced diffusivity at 760 and 820 oC due to SiO2 surface layer
31 32 33
89Utz1
700 & 800
FZ crystals, heavily B- or P-doped to ca. 1020 cm−3 or virtually intrinsic, radiotracer 57Co with sectioning, mobile species: Coi (charge 0 or +1), D(Coi+) / D(Coi0 ) = 1.0 ± 0.4, immobile species: Cos (charge < −2) and CoiB or CosP pairs, includes data of [86Gil1, 89Utz1]
90Gil1
700-1100
review on 3d transition elements in Si comprising [89Utz2]
91sch1
1000-1250
D = 10−6-10−4 cm2s−1, see also [86wöh1]
75Azi1
Rh in Si −7
2 −1
1100
D > ca. 3·10 cm s reestimated from 30 min saturation treatment, 500 µm- thick FZ crystals, DLTS + etching, incorporation as Rhs, diffusion via Rhi
89Cza1
Ir in Si 4.0·10−2
1.3
950-1250
single crystals, 103-104 dislocations/cm2, NAA and electrical methods, dissociative mechanism, minority of electrically detected atoms
33 34
76Azi1
7.2·10−3
1.2
700-900
CZ crystals, 3·104-4·105 dislocations/cm2, annealing after high-temperature saturation, resistivity + Hall effect, photo-capacitance, simultaneous occurrence of Iri and Irs suggested
33
77Azi1
Lando lt -Bö rnst ein New Series III/33A
2-32
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-196
2.2.1.10 Solute elements of group VIII (nickel group). (See Figs. 35-42, p. 143) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
1.3·10−2
1.4
700-900
vacancy-limited diffusivity of Nis via dissociative mechanism (CVeqDV/Cseq), FZ crystals, 104-105 dislocations/cm2, out-diffusion after Ni saturation, 4-point-probe
35
67Yos1
0.1
1.91
450-800
vacancy-limited diffusivity of Nis via dissociative mechanism (CVeqDV/Cseq), CZ crystals, 400-1000 dislocations/cm2, decrease of 63 Ni surface radioactivity, dislocation-induced vacancies
35
67Bon1
600-1250
D(1200 oC) = 5.2·10−5 cm2s−1, radiotracer 63Ni, autoradiography, co-diffusion with P retards Ni diffusivity
68Bab1
800
D = 1.57·10−7 cm2s−1 , Ni surface segregation, Auger spectroscopy
70Rid1
Ni in Si
0.5
1.53
251-350
(100) crystals, ion-sputtered Ni layer, electron-beam heating, Auger spectroscopy, interstitial mechanism suggested, only abstract given
75Yoo1
10−13
0.27
250-350
single crystals, Ni film by r.f. sputter-deposition, Auger spectroscopy + sputter-sectioning, large Ni concentrations, no lattice defects observed, interstitial mechanism
77Ber1
2.3·10−3
0.47
800-1300
radioactive analysis, interstitial mechanism, (only abstract given)
900
FZ crystals, both in-diffusion and annealing after saturation, 4-point-probe, change of bulk concentration linear in time, dissociative mechanism
82Kit1 83Kit1
700-1300
review on 3d transition elements in Si
83web2
−3
35
80Bak1
2.3·10 3.4·10−12
1.7 0.13
597-797 197-597
diffusivity at high Ni boundary concentrations diffusivity in amorphous Ni-Si interphase B-doped single crystals (7.5 Ωcm), ca. 103 dislocations/cm2, Ni-Si interdiffusion with amorphous transition layer, radiotracer 63Ni + autoradiography
35
84Usk1
1.68
2.16
450-540
35
85Tho1
6.3·10−4
0.76
450-540
solubility-diffusivity product normalized to atomic density of Si (C eqD/C 0) indirectly deduced diffusivity CZ crystals, permeation through wafers, RBS, NAA, interstitial mechanism
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-33
T-range [oC]
Methods and Remarks
Fig.
Ref.
1000
both RTA and furnace annealing, permeation through wafers, optical microscopy, SIMS, recombination of interstitial Ni with vacancies introduced by pre-heating
220-540
CZ crystals, permeation through wafers, radiotracer 63 Ni + autoradiography, D estimated from least arrival times, interstitial mechanism
800-1300
review on 3d transition elements in Si comprising [89Utz2]
91sch1
950
D = ca. 3·10−14 cm2s−1, CZ crystals spin-coated with Ni(NO3)2, oxidizing ambient, SIMS, diffusivity attributed to Nis
93Zho1
950-1150
D ≈ 4·10−5 cm2s−1, standard wafers, lateral profiles from line-shaped source, DLTS, gettering efficiency test, interstitial mechanism
85Gra1
705-1320
thick FZ crystals, NAA + sectioning, erfc profiles, interstitial mechanism
36 37 38
91fra1
550-1050
FZ crystals, ca. 104 dislocations/cm2, DLTS profiling of Pds on p+nn+ structure, in-diffusion 880-1050 oC: kick-out mechanism limited by selfinterstitials, 550 oC annealing of supersatured wafers: vacancy-limited dissociative mechanism
39
93Vic1
800-1000 800-1000
3000 Ωcm wafers 3 Ωcm wafers backside oxide layer, Pt sputter-deposition on front side, diffusion-induced charge accumulation underneath backside MOS structure, C-V measurement, erfc-profile assumed, both Pti and Pts suggested
42
69Bai1
600-800
FZ crystals, sequential diffusion: Pt after Au (875 oC), DLTS on p+nn+ structures, (partial) replacement of Aus by Pts via Pt-Au kick-out proces, also simultaneous diffusion investigated (820-870 oC)
Ni in Si (cont.)
6·10−4
0.76
88Spa1
35 36
89Spi1
Pd in Si
2.95·10−4
0.22
Pt in Si 1.7·102 1.5·102
2.15 2.22
Lando lt -Bö rnst ein New Series III/33A
85Sai1
2-34
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Methods and Remarks
700-850
n-type epitaxial layer, Pt Schottky contacts used as diffusion source, C-V measurements and DLTS, non-erfc profiles, kick-out mechanism, selfinterstitial-limited diffusivity, includes [84Man1]
1000-1250
self-interstitial-limited diffusivity of Pts via kick-out mechanism (CIeqDI/Cseq), FZ crystals, NAA + mechanical sectioning, spreading resistance, nonerfc profiles, dependence of bulk concentration on wafer thickness
700
FZ wafers, DLTS + step etching, inverse U-shaped profiles, influence of initial non-equilibrium vacancy concentration, dissociative mechanism
[Ref. p. 2-196
Fig.
Ref.
Pt in Si (cont.)
2.08·105
3.85
86Man1
36 40 42
89Hau1
91Zim2
5.07·10−2 1.82·10−2
0.604 700-950 2.52 700-950
interstitial diffusivity Di characterizing Pti solubility-diffusivity product of Pti normalized to atomic density of Si (CieqDi/C 0), recalculated, FZ crystals, spin-on Pt source, DLTS on bevel plane or after step etching, complex profiles, kick-out mechanism dominates above 900 oC, dissociative mechanism below 850 oC, numerical solution of diffusion-reaction equations
42
92Zim1 92Zim2 91Zim1
34
2.09
910-1210
42
93Cof1
4.6·105
3.58
910-1085
Pti-limited kick-out diffusivity of Pts (CieqDi/Cseq) recalculated from given Arrhenius plot self-interstitial-limited kick-out diffusivity of Pts (CIeqDI/Cseq), recalculated from Arrhenius plot further data from B-doped wafers implanted through SiO2 window, RTA , lateral profiles, twodimensional spreading resistance, CieqDi/Cseq (1200 oC) = 4.6·10−6 cm2s−1
2.1 1.45·10−1
1.79 3.10
950-1120 950-1120
Pti-limited kick-out diffusivity of Pts (CieqDi/Cseq) solubility-diffusivity product of Pti normalized to atomic density of Si (CieqDi/C 0) FZ crystals, 108 dislocations/cm2, RTA, spreading resistance, kick-out mechanism revealed by experiments on non- and moderately dislocated Si
36 41 42
95Ler1 94Ler2
700
n-type crystal with PtSi Schottky diode, low-dose implantation of O, F or Cl through silicide, annealing in N2 ambient, DLTS, enhanced accumulation of Pt in implantation damage layer, kick-out mechanism
95Hol1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-35
2.2.1.11 Solute elements of group IB (copper group). (See Figs. 43-55, p. 145) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
1000-1200
D (1120 oC) = 3.2·10−5 cm2s−1, effective diffusivity mainly attributed to Cui+, Si-64Cu-Si sandwich arrangement annealed in H2 ambient, drift in external electric field, permeation of radioactivity and quantitative autoradiography
57Gal1
900
D = 5·10−5 cm2s−1, single crystals, radiotracer 64Cu + mechanical sectioning
56Str1
800-1100
radiotracer 64Cu + sectioning, see also [63Bol1]
Cu in Si
4.0·10−3 5.0·10
−3
1.0 0.43
20
−3
64
400-680
B-doped (5·10 cm ) crystals, radiotracer Cu + sectioning or autoradiography, interstitial mechanism (Cui+), enhanced solubility due to Fermi-level effect, retardation in heavily P- or Asdoped crystals, [57Str1] included
1000
D = 10−6 cm2s−1, single crystals, 106-107 dislocations/cm2 induced by local electronbeam heating, pn-junction depth measurements
45
58bol1
44 45
64Hal1
67Dud1
5·104
0.665 (−53)-7
Cu-related effective diffusivity influenced by trapping (see [92Mes1, 94Mes1]), In-doped CZ crystals chemo-mechanically polished on back side, drift and diffusion in space charge region of frontside Schottky diode, C-V profiling, dissociation/association with In
43 45
88Zun1 89Pre1
1.5·10−2
0.86
900-1050
solar-grade polycrystals containing dislocations and SiC particles, radiotracer 64Cu + sectioning, electrotransport reveals migration as positive ion, accelerated diffusion due to extended defects
45
89Abd1
3·10−3
0.15
400-680
data of [64Hal1] corrected for (unscreened) Coulomb interaction with boron (Cu+-B- pairing), evidence from 111In PAC experiments in Cu-implanted B-doped FZ crystals
90Kel1
950
D = 9·10−14 cm2s−1 attributed to Cus, CZ crystals spin-coated with Cu(NO3)2, diffusion in oxygen ambient, SIMS, boundary concentration 1018cm−3, influence of oxidation-induced self-interstitials
93Zho1
(–93)-900
Overall fit including (corrected) data of [64Hal1, 94Mes1] In-doped CZ and Ga-doped FZ crystals, Cu saturation at 1062 oC, transient ion drift (Cui+) in depletion region of Schottky diode, capacitance measurement after reverse bias pulses
4.5·10−3
0.39
7-127
Lando lt -Bö rnst ein New Series III/33A
44 45 46
93Hei1
2-36
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
(−93)-7
CZ (In-, Ga- or B-doped) and FZ (Ga- or B-doped) crystals, Cu saturation at 1062 oC, Cui+-acceptor pairing in depletion region of Schottky diode, C-V profiling, effects of local electric field and trapping by oxygen
44
94Mes1
Cu in Si (cont.)
Ag in Si 2.0·10−3
1.60
1100-1350
single crystals, Ag deposition on ground surfaces, radiotracer 110Ag + sectioning, diffusion under external electric field reveals movement as positive ion
47
61Bol1
1.6·10−1 6.3·10−2
0.83 0.71
300-1000 300-1000
diffusivity on ground (100) surfaces diffusivity on polished (100) surfaces single crystals, 104 dislocations/cm2, radiotracer 110 Ag + quantitative autoradiography, similar data obtained for (110) and (111) orientations, negligible effect of external electric field, strong effect of high dislocation density, vacancy mechanism
47
64Bol1
1.5
1.39
800-1000
5·103 dislocations/cm2, radiotracer 110Ag + sectioning, vacancy mechanism, positive effective charge under external electric field, interpretation as diffusivity along dislocations
47
67Ste1
4.05
3.04
1000-1200
polycrystals, radiotracer technique, reports smaller DAg than for mono-Si, see [86wöh1]
47
70Pru1
1200-1250
D(1200 oC) = 6·10−4 cm2s−1, single crystals, 103-104dislocations/cm2, radiotracer 110Ag + chemical sectioning, out-diffusion after saturation, in-diffusion profile depends on lateral distance from Ag surface source
75Usk1
25
D = 5.1·10−16 cm2s−1, FZ crystals, uniform Ag doping by 1175 oC diffusion, motion of negatively charged centre in depletion zone of n+p-junction, DLTS profiling
84Pea1
1014-1154
FZ crystals, diffusion to saturation + quenching, NAA + mechanical sectioning, estimation based on measured Ag solubility and C eqD product of Aui [86Sto1], interstitial mechanism, enhanced Ag accumulation in dislocated Si
0.6
1.15
46 47
87Rol1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Methods and Remarks
450-500
D = (0.8-1.6)·10−15 cm2s−1, single crystals, epitaxially grown Ag layers, SIMS after surface removal of Ag, boundary concentrations > 1019 cm−3, slow diffusivity compared to [61Bol1]
2-37
Fig.
Ref.
Ag in Si (cont.)
Au in Si 1.1·10
−3
91Nas1
Diffusion in virtually perfect monocrystals 1.12
800-1200
single crystals, radiotracer 198Au with mechanical sectioning
900-1370
D = 5·10−10-4·10−6 cm2s−1, diffusion from surface layer or gas phase, radiotracer 198Au or non-active Au with pn-junction depth measurement, scattered data due to crystal imperfections, electrotransport also studied interstitial diffusivity Di characterizing Aui purely substitutional diffusivity via Aus-vacancy exchanges vacancy-limited diffusivity of Aus via dissociative mechanism (CVeqDV/Cseq) Aui-limited diffusivity of Aus via dissociative mechanism (CieqDi/Cseq) FZ crystals, zero or 104 dislocations/cm2, radiotracers 198Au and 199Au with mechanical sectioning, both erfc and non-erfc profiles
2.44·10−4 2.75·10−3
0.39 2.04
800-1200 700-1200
1.15·103
3.12
800-1300
2.8·10−2
2.92
800-1200
53
60Bol1 60Bol2
53
0.72
Lando lt -Bö rnst ein New Series III/33A
64Wil1
1000 & 1100
pulled crystals, Au plated on back side of wafers, radiotracer 199Au with etching and autoradiography, Au accumulation near front surface, dislocations and areas of high P concentration, slow increase of CAu in bulk regions, dissociative mechanism
65Spr1
1000-1200
CZ crystals, zero to 5·103 dislocations/cm2, various kinds of doping, AuCl3 source in Ar, X-ray topography, various kinds of diffusion-induced dislocation loops observed, dissociative mechanism
66Iiz1
850 & 1000 220-300 mm thick wafers, homogeneous redistribution of implanted Au, NAA with chemical sectioning, dissociative mechanism 9.8·10−5
56Str1
500-650
FZ crystals, 195Au radiotracer with chemical sectioning, erfc-like profiles, D0 and Q recalculated from given data
74Sch1
53
76Che1
2-38
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Au in Si (cont.)
218
2.1·10−2
3.02
1.7
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
Diffusion in virtually perfect monocrystals (cont.) 105-505
D = 4.4·10−13-2.1·10−9 cm2s−1, n-type epitaxial layer, Au Schottky contact as diffusion source, electronic compensation , C-V profiling, dissociative mechanism
76Obr1
270-670
dislocation-free FZ crystals, Au saturation at 1100 oC, loss rate from solution during annealing, diffusion-limited precipitation proposed
77Sch1
825-1100
evaluation of literature data [65Spr1, 72Lam1, 82Hil1] involving virtually dislocation-free and dislocated single crystals, first account of the kickout mechanism
80Gös1
810-1010
FZ crystals, spreading resistance, effects of preannealing and P pre-diffusion, kick-out mechanism, self-interstitial annihilation at the surface depends on surface conditions
82Hil1
800-1098
FZ crystals, NAA with mechanical sectioning, nonerfc profiles fitted by kick-out model, CAu in wafer centre increases with square root of time, selfinterstitial-limited diffusivity
1000-1098
numerical analysis of data from [83Sto1] revealing minor contribution of the dissociative mechanism beside major kick-out contribution
800-1200
self-interstitial-limited diffusivity of Aus via kickout mechanism (CIeqDI/Cseq) recalculated from given data, extension of [83Sto1], NAA and spreadingresistance, also out-diffusion at 900 oC after hightemperature saturation, C eqD product correlates with Si self-diffusion
800-1200
comparison between Au in Si (kick-out mechanism) with Cu in Ge (dissociative mechanism)
1200
FZ crystals, NAA with mechanical sectioning and spreading resistance, U- and W-shaped profiles, diffusion-induced stacking faults acting as selfinterstitial sinks, kick-out mechanism
800-1200
self-interstitial-limited diffusivity of Aus via kickout mechanism (CIeqDI/Cseq), standard wafers implanted with Au, RTA and furnace annealing, spreading resistance and RBS, non-erfc profiles fitted within kick-out model, similar diffusivity in n- and p-type Si
48
83Sto1
83Mor1
46 48 50 54
84Sto1 86Sto1 86Hau1
85Sto1 52
86Hau1
88Cof1 90Cof1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Au in Si (cont.)
Methods and Remarks
2-39
Fig.
Ref.
Diffusion in virtually perfect monocrystals (cont.)
1.74·10−4 2.9·10−2
0.29 2.97
800-1200 800-1200
interstitial diffusivity Di characterizing Aui solubility-diffusivity product of Aui normalized to atomic density of Si (CieqDi/C 0), recalculated FZ and CZ crystals, RTA, spreading resistance, numerical analysis of complex profiles within kick-out model, includes data of [83Sto1, 86Sto1]
54
90Boi1
0.46
1.7
950-1291
3.33
950-1291
46 54 55
91Küh1
3.48·10−1
Aui-limited kick-out diffusivity of Aus (CieqDi/Cseq), D0 and Q recalculated solubility-diffusivity product of Aui normalized to atomic density of Si (CieqDi/C 0), recalculated FZ crystals, 198Au diffusion after 197Au saturation at the same temperature, radiotracer technique with mechanical sectioning, kick-out mechanism
0.28
1.6
900-1200
Aui-limited diffusivity of Aus via kick-out mechanism (CieqDi/Cseq), boron-doped wafers, Au implantation through SiO2 windows, lateral diffusion near surface, spreading resistance, erfc profiles
54 55
91Cof1 93Cof1
1150
FZ and CZ crystals, resistivity of bulk region, Au-induced stacking-fault formation, kick-out (or dissociative) mechanism
9.31·10−4 2.70·10−5
6.07·106 57.7
0.261 800-1100 1.99 800-1100
2.59 2.15
Lando lt -Bö rnst ein New Series III/33A
interstitial diffusivity Di characterizing Aui solubility-diffusivity product of Aui normalized to atomic density of Si (CieqDi/C 0), recalculated FZ crystals, DLTS on bevel plane or after etching, numerical analysis within kick-out model includes data of [84Sto1, 86Sto1]
92Mor1
54
92Zim2
1150
FZ crystals, P-doping 1017 cm−3, DLTS and NAA with mechanical sectioning, agreement between electrical and chemical (non-erfc) profile, kick-out mechanism
94Tak1
900-1100 900-1100
interstitial diffusivity Di characterizing Aui Aui-limited kick-out diffusivity of Aus (CieqDi/Cseq), recalculated FZ crystals, RTA, spreading resistance, kick-out with dissociative mechanism including Frenkel pair reaction, analysis includes data of [84Sto1, 92Zim2]
95Gha1
2-40
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Au in Si
5·10–5
10
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
Diffusion in crystals containing dislocations or other extended defects 1000-1300
FZ and CZ crystals, dislocation density (EPD): zero to 103 cm-2, various Au sources, IR-light microscopy, etching, radiotracer 198Au + autoradiography, helical dislocations formed by diffusion-induced climb, CAu increases with EPD, dissociative mechanism
60Das1
720-900
FZ crystals, (2-8)·104 dislocations/cm2, NAA + mechanical sectioning, autoradiography, decoration of crystal defects, bulk concentration increases with square root of time
66Mar1
0.87
1000-1200
polycrystals, radiotracer technique, reports smaller D and larger C than for mono-Si, see also [86wöh1]
70Pru1
4.5
800-1200
FZ and CZ crystals, zero to 104 dislocations/cm2, NAA of bulk region (no profiles), effects of growth method, sample thickness and lattice defects, dissociative mechanism
70Yos1
1200
CZ crystals, (0.5-3.2)·103 dislocations/cm2, evaporated Au surface layer, X-ray topography, extrinsic stacking faults of Frank-type induced by diffusion, dissociative mechanism
71Brü1
550-700
n-type single crystals, 4·104 dislocations/cm2, Au saturation at 1140 oC, loss rate from solution during annealing, Hall effect and resistivity, precipitation at dislocations
72Bad1
1000
FZ crystals, zero to 104 dislocations/cm2 (grown-in), spreading resistance and 4-point probe, enhancement of bulk concentration in bent samples, dissociative mechanism
72Bro1
750-1100
FZ and CZ crystals, zero to 104 dislocations/cm2, NAA of bulk region (no profiles), CAu increases with square root of time, dissociative mechanism
72Lam1
900-1200
thin FZ crystals, zero or 104 dislocations/cm2, radiotracer 198Au + mechanical sectioning, dissociative mechanism, special vacancy generation model accounts for square root time dependence of bulk concentration
73Hun1
1.57
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Au in Si (cont.)
5.6
0.61
2.13
Ref.
D ≈ 3·10−7 cm2s−1: Aui-limited diffusivity of Aus via dissociative mechanism (CieqDi/Cseq) vacancy-limited diffusivity of Aus via dissociative mechanism (CVeqDV/Cseq) mainly from [73Hun1] thick FZ or other crystals, ca. 1 or 104 dislocations/cm2, radiotracer 198Au + mechanical sectioning
73Hun2
850-1200
FZ crystals, zero or 106-108 dislocations/cm2, NAA of bulk region, increase rate of CAu, dissociative mechanism, comparison of as-deformed with additionally annealed samples
74Käs1
900-1200
B-doped wafers (2-6 Ωcm), dislocation density (EPD): 2·103 to 2·105 cm-2, NAA + chemical sectioning, autoradiography, TEM, CAu increases with increasing EPD or heavy P doping, precipitation at dislocations and P+-Au– pairing suggested, no depth profiles
77Koh1
907-1150
FZ crystals, zero, 104 or 109 dislocations/cm2, spreading resistance, effect of dislocation density on profile shape and diffusion rate, kick-out mechanism, includes data of [84Sto1, 86Sto1]
85Sto2
Aui-limited kick-out diffusivity of Aus (CieqDi/Cseq), D0 and Q given by [91Grü1] solubility-diffusivity product of Aui normalized to atomic density of Si (CieqDi/C 0) FZ crystals, 107-109 dislocations/cm2, spreading resistance, erfc-type profiles, comparison with dislocation-free Si, kick-out mechanism
51 55
86Sto1
950-1200
FZ and (multiple oxidized) CZ crystals containing dislocations (zero to 5·104 cm−2), stacking faults and/or oxygen precipitates, spreading resistance + preferential etching, decoration of defects with Au, kick-out (and dissociative) mechanism
52
87Sto1
850
bicrystal, scanning minor carrier transient spectroscopy, enhanced Au incorporation near grain boundary due to grain boundary diffusion
89Hei1
950
ribbon-grown polycrystals, 105-107 dislocations/cm2, spreading resistance, kick-out mechanism, efficiency of dislocations for selfinterstitial annihilation: > 10%
91Yan1
900-1200
44
2.23
907-1154
64
3.93
907-1154
Lando lt -Bö rnst ein New Series III/33A
Fig.
Diffusion in crystals containing dislocations or other extended defects (cont.) 900-1100
1.94·10–7
Methods and Remarks
2-41
2-42
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Au in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
Diffusion in crystals containing dislocations or other extended defects (cont.) 960
FZ and CZ crystals, cantilever or 4-point bending, 3·104-5·108 dislocations/cm2, kick-out mechanism, self-interstitial annihilation efficiency of dislocations
92Pic1 93Pic1 94Pic1
2.47
1.94
897-1193
Aui-limited diffusivity of Aus via kick-out mechanism (CieqDi/Cseq) various polycrystals, grain size 25µm-25mm, ca. 107 dislocations/cm2, radiotracer 195Au + mechanical sectioning, erfc or Gaussian profiles, retarded diffusivity for 665 oC < T < 897 oC possibly due to grain boundary segregation
55
93Poi1
1.99 0.74
1.88 3.41
945-1119 945-1119
Aui-limited kick-out diffusivity of Aus (CieqDi/Cseq) solubility-diffusivity product of Aui normalized to atomic density of Si (CieqDi/C 0) deformed FZ crystals, 107-109 dislocations/cm2, RTA, spreading resistance
55
94Ler1 94Ler2
850-1000
FZ and CZ crystals, cantilever bending, 5·103-2·106 dislocations/cm2, DLTS on bulk region, CAu vs. dislocation density, kick-out mechanism, dislocation efficiency as sink for self-interstitials
Au in Si
95Yak1
Diffusion under special conditions 1100
no effect of external electric field
57Gal1
127
single crystals, diffusion under neutron + γ irradiation in nuclear reactor and 60Co γ irradiation, NAA with chemical sectioning, enhancing effect of γ's partly compensated by retarding influence of neutron-induced vacancies, dissociative mechanism
72Koi1
340
D ≈ 10−9 cm2s−1, high ohmic FZ crystals, diffusion in air ambient, SiO2 formation on top of Au surface layer, infrared photoconduction, abundance of Aui, interstitial mechanism
75Nak1
1000-1200
1.5 Ωcm slices deposited with Au, annealing with 10−2 s pulses from xenon lamps, DLTS profiling, effective temperature calculated, prevalence of interstitial mechanism
76Ant1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Au in Si (cont.)
Fig.
Ref.
Diffusion under special conditions (cont.) 20-200
FZ crystals, effects of radiation: white and IR light or electrons (0.015-1.5 MeV), radiotracer 195Au + chemical sectioning, penetration below 100 nm, evaluation of literature data: [70Zyu1, 71Kli1, 71Zai1, 72Koi1, 73Kan1, 73Zyu1] D = (1.4 -7.5)·10−14 cm2s−1, FZ crystals,195Au diffusion after 197Au pre-diffusion or pre-heating at 1000 oC, Gaussian-like profiles
76Che1
700-840
D = (0.5-70)·10−14 cm2s−1, monotonic increase, P-diffused crystals, doping level 1021 cm−3, radiotracer 198Au with chemical sectioning, formation of Au-P pairs in dynamical equilibrium
76Mal1
800-890
FZ crystals, influence of carbon concentrations up to 3·1017 cm−3, spreading resistance and 4-point probe
77Hil1
600-870
FZ crystals, sequential diffusion: Au after Pt (820-870 oC), DLTS on p+nn+ structures, (partial) replacement of Pts by Aus via Au-Pt kick-out process, also simultaneous diffusion
85Sai1
800-1200
CZ crystals, simultaneous Au and B diffusion, spreading resistance, RBS, kick-out mechanism
89An1
750-1000
CZ and FZ crystals, low or high (up to 5·1017 cm−3) carbon concentration, effects of C and O precipitates formed during pre-annealing, NAA with mechanical sectioning
89Ito1
550-1100
FZ crystals, (enhanced) Au diffusion after Rh saturation (1000-1100 oC), DLTS with step etching, Au-Rh kick-out process
89Cza1
≤ 627
CZ crystals with evaporated Au layer, pulsed heating by xenon lamps, effective temperature calculated, DLTS profiling, enhanced penetration, anomalous profiles, formation of O- and P-vacancy complexes
90Kap1
820
n-type single crystal,195Au deposition on surface, annealing in Cl-containing ambient, radiotracer technique with sectioning, charge carrier lifetime measurements, strongly reduced Au incorporation
90Moi1
877-1002
CZ crystals, diffusion in H2 ambient, resistivity from 4-point geometry, IR absorption, enhanced diffusivity compared to FZ crystals, further enhancement by pre-heating for Oi precipitation
90Vla1
200-400
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-43
2 Diffusion in silicon, germanium and their alloys
2-44
D0 [cm2s−1]
Q [eV]
T-range [oC]
Au in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
Diffusion under special conditions (cont.) 820-880
FZ crystals, Au diffusion after neutron irradiation, enhancement for furnace annealing (820 oC), shallow penetration for pulsed light annealing (880 oC), NAA with sectioning
91Svi1
20-100
CZ and Au-doped (8·1013 cm−3) FZ crystals, effect of reactive ion etching, differential DLTS, exponential profiles, enhanced in- and out-diffusion
93Kov1
800 & 900
p-type wafers P-diffused at back side to 3.3·1020 cm−3, Au diffusion at front side, DLTS on bevel planes, formation of Au-P pairs, gettering influence of P
94Zim1
600
P-doped wafers (1 Ωcm), diffusion under Ne+ bombardment of wafer back side, DLTS with chemical sectioning, IV and C-V measurements, reduced penetration due to implantation-induced acoustic wave
95Ant1
960
FZ crystals, effect of pre-annealing in air, diffusion in air, spreading resistance, subsurface humps in profile, dissolving vacancy clusters
95Mon1 95Mon2
2.2.1.12 Solute elements of group IIB (zinc group) (See Figs. 56-61, p. 149) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
1100-1300
D = 10−6-10−7 cm2s−1, single crystals, bulk resistivity by 2-point probe, scattered data, no Zn vapour pressure dependence, dissociative mechanism, effect of surface oxide, also out-diffusion studied
980-1270
single crystals, dislocation density > 104 cm−2, electrotransport, pn-junction localisation by thermal probe, diffusion as Zn2+ ion
800
D = 8·10−6 cm2s−1, single crystals, 106-107 dislocations/cm2 induced by local electronbeam heating, pn-junction depth measurements
67Dud1
1100-1300
D = 10−6-10−7 cm2s−1, single crystals, 103-104 dislocations/cm2, Zn source at 750-800 oC, radiotracer 65Zn + sectioning, non-erfc profiles, dissociative mechanism
70Bak1
Fig.
Ref.
Zn in Si
0.1
1.4
57Ful1
58
63Mal1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-45
T-range [oC]
Methods and Remarks
Fig.
Ref.
900-1100
D(1000 oC) = 4.4·10−8 cm2s−1 primarily characterizing Zns atoms, n- and p-type wafers, Zn source at 600-900 oC, spreading resistance, time lag due to SiO2 surface layer, non-linear Zn vapour pressure dependence, effect of surface treatment, also accelerated diffusion observed
70Zal1
127
single crystals, diffusion under neutron + γ irradiation in nuclear reactor, NAA + chemical sectioning, dissociative mechanism
72Koi1
1200
D = 2·10−6 cm2s−1, single crystals, 103-104 dislocations/cm2, out-diffusion after saturation, radiotracer 65Zn + chemical sectioning
75Usk1
700-900
D(700 oC) > 7·10−4 cm2s−1 attributed to Zni, P-doped wafers (7.5 Ωcm), high dose implantation at front (Zn) and back (Ar) side, Zn accumulation at back side upon annealing, RBS
82Mus1
redistribution of implanted Zn under pulsed laser annealing, segregation at liquid-solid interface due to fast solid-state diffusivity
83Cam1
989
CieqDi/Cseq = 4.6·10−8 cm2s−1: Zni-limited kick-out diffusivity of Zns, CIeqDI/Cseq = 5.9·10−10 cm2s−1: self-interstitial-limited kick-out diffusivity of Zns, FZ crystals, zero or (0.5-2)·108 dislocations/cm2, spreading resistance and Hall effect, first evidence for kick-out mechanism
89Per1
900-1200 902-1200
Zni-limited kick-out diffusivity of Zns (CieqDi/Cseq) self-interstitial-limited kick-out diffusivity of Zns (CIeqDI/Cseq) FZ crystals, zero or at least 108 dislocations/cm2, spreading resistance, NAA + mechanical sectioning, erfc and non-erfc profiles
1208
CIeqDI/Cseq = 8·10–8 cm2s–1: self-interstitial-limited diffusivity of Zns, CieqDi/Cseq = 4·10–7 cm2s–1: Znilimited diffusivity of Zns FZ crystals, zero or at least 108 dislocations/cm2, special RTA technique, spreading resistance, temporal evolution of diffusion profiles fitted within kick-out model
Zn in Si (cont.)
6.9 1.0·103
2.14 3.11
Lando lt -Bö rnst ein New Series III/33A
58
91Grü1
91Bra1
2-46
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
Zn in Si (cont.) 0.64 34
1.85 4.03
870-1208 870-1208
Zni-limited kick-out diffusivity of Zns (CieqDi/Cseq) solubility-diffusivity product of Zni normalized to atomic density of Si (CieqDi/C 0) FZ crystals, 107- 109 dislocations/cm2, furnacebased RTA + quenching, spreading resistance, dislocations act as sinks for self-interstitials and as traps for Zn, also Zni-Zns exchange rates determined
56 58 59
93Bra1 93Bra2
1.0·10−5
0.05
870-1208
interstitial diffusivity Di characterizing Zni, dislocation-free and highly dislocated FZ crystals, complex numerical analysis of Zns profiles [93Bra1,95Bra1] within theory of kick-out (and dissociative) mechanism
58
93Bra2
1200
D = 1.3·10−8 cm2s−1: Zni-limited kick-out diffusivity of Zns (CieqDi /Cseq), B-doped wafers implanted through SiO2 window, RTA, lateral profiles, twodimensional spreading resistance self-interstitial-limited kick-out diffusivity of Zns (CIeqDI/Cseq), D0 and Q recalculated vacancy-limited dissociative diffusivity of Zns (CVeqDV/Cseq), D0 and Q recalculated FZ crystals, zero or 107- 109 dislocations/cm2, furnace-based RTA + quenching, spreading resistance, kick-out and dissociative mechanism, full evolution of Zn incorporation
57 58 59
95Bra1 94Bra1 94Bra2
350-1100
D = (0.25-1)·10−15 cm2s−1, FZ crystals, redistribution of implanted layer, isochronal and isothermal annealing in Ar ambient, effects of recrystallization and surface proximity
60
70Mey1
1100-1250
single crystals, pn-junction depth and resistivity measurements, see [86wöh1]
59
72Spi1
1200
CZ crystals, DLTS, evidence for double acceptor Cds as major species, also implantation of 111In decaying to 111Cd
700-1000
polished wafers with amorphized layer due to Ar implantation, isochronal annealing after Hg implantation at RT, RBS, Hg content decreases at 700 oC and disappears at 1000 oC
56.1
2.77
870-1208
5.6·10−4
1.51
870-1000
93Cof1
Cd in Si
4.5
3.70
91Lan1
Hg in Si 61
93Hon1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-47
2.2.1.13 Solute elements of group IIIA ( boron group). (See Figs. 62-108, 170, 182, 183, p. 151) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
B in Si
Methods and Remarks
Fig.
Ref.
temperature dependence and mechanism of diffusion
0.001
2.51
1050-1250
single crystals, BCl3 source, pn-junction measurement, sheet resistance, Hall effect, C0(1250 oC) = (3-6)·1020 cm−3
85
54Ful2
10.5 1.00
3.69 3.39
950-1275 950-1275
joint fit to B and P data separate fit to B data by [94Rak1] As-doped single crystals, B2O3 source in closed ampoule, 4-point probe + mechanical sectioning, pn-junction staining, C0 = (1-10)·1021 cm−3
85
56Ful1
5
3.51
1058-1342
single crystals, B2O3 source in N2 flow, 4-point probe, pn-junction staining, thermal probe, C0 = 1.6·1017-7.0·1018 cm−3, see also [94Rak1]
85
60Kur1
3.2 6.5·10−2 1.28
3.63 3.15 3.23
1000-1280 1000-1280 1000-1280
C0 = 3.5·1019 cm−3, recalculated from plotted data C0 = (4 -8)·1019 cm−3, recalculated by [94Rak1] C0 = 1.4·1021 cm−3, recalculated by [94Rak1] CZ crystals, B-doped oxide film in N2, pn-junction staining, 4-point probe, C-dependence observed, effect of undoped oxide at Si interface
85 89
69Bar1
1.2
3.5
1000-1200
single crystals, C0 = 2-8·1019 cm−3, pn-junction method, see also [86wöh1]
5.1
3.69
1100-1250
C0 = 1019-1020 cm−3, single crystals, elemental B source in Ar, pn-junction staining, 4-point probe (also with sectioning), C0 depends on time, source mass and temperature, B transfer by B2O3 suggested
85
69Oka1
1.7·10−2 0.51
2.93 3.40
1040-1275 1040-1275
DB beneath (100) surface, recalculated DB beneath (111) surface, recalculated epitaxial layer, drive-in in O2 ambient after predeposition, 4-point probe, pn-junction staining, C0 = 4.3-4.7·1018 cm−3
90 90
70Cha1
2.1·10−3
2.85
1130-1405
B-doped epitaxial layers on FZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, B-vacancy pair mechanism, C0 < 3·1019 cm−3
87 92
71Gho3
2.46
3.59
1100-1250
CZ crystals, B-doped Si powder source in vacuum, spreading resistance, monotonic time-increase of C0, surface-limited intrinsic diffusivity
86
72Gho1
2·10−2
2.98
1000-1200
single crystals, B-doped oxide sources in N2, pnjunction staining, sheet resistance, D0 and Q recalculated
86
72Kam1
Lando lt -Bö rnst ein New Series III/33A
69Alv1
2-48
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
0.76 0.037 0.76
0.782
3.46 3.46 3.46
Fig.
Ref.
temperature dependence and mechanism of diffusion (cont.) model based on mobile neutral Bs-vacancy pairs and immobile Bs−
76And1
1000-1300
re-examination of data on oxidation- and radiationinfluenced diffusion and emitter-push effect
79Gös1
875-1230 1000-1100
total intrinsic DB = D0 + D+ D0 via neutral vacancies D+ via singly positively charged vacancies review and evaluation of literature data including [60Kur1, 72Wag1, 73Cro1, 75Fai2, 78Ant2]
850-1050
models based on interaction of B with selfinterstitials, fitting of data
86Mor1 86Mor2 87Mul1
600-900
MBE-grown B-modulated structure, Cmax = 2.8·1018 cm−3, annealing in inert or dry O2 ambient, SIMS, exponential-type broadening of B spikes, evidence for Bi as intermediate species, kick-out mechanism
90Cow2
600-900
see [90Cow2], evidence for kick-out mechanism, evaluation of kick-out reaction rates
450 & 550
MBE-grown double B-spike structure, low-dose Si implantation, RTA in dry N2, SIMS, long-range Bi migration, energy barriers for kick-out and dissociative reactions and Frenkel-pair recombination
3.397 950-1350
B in Si 16
Methods and Remarks
[Ref. p. 2-196
statistical analysis of literature data, pn-junction depth and sheet-resistance measurements, Q represents average of [56Ful1, 60Kur1, 61Wil1, 69Bar1, 70Usk1], ln D0 = −28 + 8.17Q
90
62
81fai1
91Cow1 92Cow1
85 86
94Rak1
85
61Wil1
effects of high concentration and heavy doping 3.69
1050-1350
FZ crystals, B2O3 layer source in air, 4-point probe, pn-junction staining, C0 = ca. 1021 cm−3, increase of DB(1250 oC) with increasing n-type background doping, see also [94Rak1]
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
Methods and Remarks
2-49
Fig.
Ref.
effects of high concentration and heavy doping (cont.)
5 15 40
3.5 3.7 3.7
1100-1300 1050-1300 1100-1250
C0 < 2·1019 cm−3, P background 9·1014 cm−3 C0 > 2·1019 cm−3, P background (9-115)·1014 cm−3 C0 > 2·1019 cm−3, P background 1.4·1014 cm−3 single crystals, B2O3/SiO2 source in Pt box, pnjunction method, CPAA, sheet resistance + chemical sectioning, DB enhancement depending on C0 and background CP, lattice strain effect suggested, D0 and Q recalculated by [71Gho3]
6.0·10−7
1.67
700-1151
diffusivity for C0 < 1018 cm−3, n-type wafers, B2O3 layer source in N2, 4-point probe + electrochemical sectioning, DB increases with increasing C0 > 1018 cm−3
140 95 8.2 120 3.0 1.9
4.09 4.04 3.65 4.04 3.57 3.48
1000-1200 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200
C0 = 8·1019 cm−3, (111) orientation C0 = 2·1020 cm−3, (111) orientation C0 = 1·1021 cm−3, (111) orientation C0 = 8·1019 cm−3, (100) orientation C0 = 2·1020 cm−3, (100) orientation C0 = 1·1021 cm−3, (100) orientation single crystals, pn-junction and resistivity methods, D100 > D111, see [86wöh1]
70Kat1
956-1250
modeling of enhanced DB at high CB based on plastic flow involving dislocation movement and vacancy generation, data of [66Rup1, 64Mae1]
70Tha1 70Tha2
1000-1250 1000-1250
D0 and Q given by [70Usk1] D0 and Q recalculated by [94Rak1] single crystals, 6·103 dislocations/cm−2, B2O3 source in Ar ambient, pn-junction staining, 4-point probe, C0(1200 oC) = 1018-1021 cm−3, DB increases with increasing C0
85
70Usk1
1000 & 1100
single crystals, 11B or As doping up to ca. 1020 cm−3, 10 B implantation, annealing in N2 flow, CPAA, DB depends linearly on hole density, CB-dependent DB for light background doping
63
73Cro1
900-1300
theoretical C-dependence of DB based on electric field and plastic deformation, extends and modifies [70Tha1, 70Tha2]
1050
single crystals, P or As doping 2·1019- 1.5·1020 cm−3 by implantation and/or diffusion, B implantation, annealing in N2, SIMS, DB decreases linearly with increasing electron density
162 1.44·10−3
4.04 2.57
Lando lt -Bö rnst ein New Series III/33A
64Mae1
86
69Vic1
73Jai1
63
75Fai2 81fai1
2-50
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of high concentration and heavy doping (cont.)
3.17
3.59
870-1150
intrinsic diffusivity including literature data single crystals, BN disk or B2O3 box source in N2, sheet resistance + sectioning, DB proportional to CB >> ni, generalized profile shape, charged vacancy model
64 87
75Fai3 81fai1
4.50·104 1.00·103 1.00·10−2 2.50·10−3
4.84 4.37 2.95 2.72
950-1200 950-1200 950-1200 950-1200
C0 = 3·1018 cm−3 C0 = 6·1019 cm−3 C0 = 1·1020 cm−3 C0 = 5·1020 cm−3 single crystals, borosilicate glass source by reactive plasma sputtering, air or N2 ambient, 4-point probe + electrochemical sectioning, pn-junction staining, O2 affects penetration depth
89
79Bag1
1.37
3.59
986-1132
intrinsic diffusivity single crystals, BN source in N2 flow, sheet resistance + electrochemical sectioning, profiles with near-surface plateaus, DB increases with CB
87
80Fro1
800-1100
single crystals, B-doped oxide film source in N2, sheet resistance + electrochemical sectioning, C-dependent diffusivity, more complex behaviour at 800-900 oC
80Mat1
925-1050
single crystals, drive-in in N2 after pre-deposition, sheet resistance + electrochemical sectioning, DB increases with CB
83An1
1050-1200
intrinsic DB deduced from extrinsic conditions: agreement with [75Fai3] single crystals, BN film source under nitride cap, N2 ambient, spreading resistance, pn-junction staining, retarded DB at diffusion front for C0 < ni
990-1200
see [84Kim1], also 4-point probe + sectioning, Cdependent diffusivity interpreted according to [68hu1], expressions for penetration depth and total amount of diffused B
84Kim2
1100
single crystals, BN source in N2 flow, 4-point probe and atomic emission spectroscopy + chemical sectioning, DB increases with CB, effect of B silicate glass on profile
85Gai1
870-1250 870-1250
D0 via neutral vacancies D+ via singly positively charged vacancies theoretically derived expressions using literature data, D+/D0 = ca. 25, test experiments at 950 oC on B-implanted Si with or without heavy As-doping
3.17
1.7 24.5
3.59
3.89 3.83
87
90 90
84Kim1
85Tso1 83Tso1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
0.76 0.015
11.46 3·10−4
3.45 2.62
3.75 2.1
Fig.
Ref.
effects of high concentration and heavy doping (cont.) 900-1100
standard wafers, heavy doping due to implantation + diffusion of 11B or As, low-dose 10B implantation, annealing with oxide cap, SIMS, DB enhancement under p-doping, retardation under n-doping, charged vacancy model
86Wil1
900
single crystals, high-dose B or BF2-implantation after pre-amorphization by Si implantation, SIMS, complex profiles interpreted within dissociative model
89Hol1
1000-1200 1000-1200
intrinsic diffusivity diffusivity of Bi-self-interstitial complex directly bonded (100) wafers: lightly B-doped FZ / heavily B-doped CZ, interdiffusion in N2, spreading resistance, fast-diffusing complex originates from heavily B-doped Si
860
D0 = 1.2·10−16 cm2s−1, D+ = 9.5·10−17 cm2s−1 , in-situ B-doped epitaxial ipi-structure, N2 ambient, SIMS, self-doping dependence
93Kuo1
750-900
CZ crystals, B doping 1.6-1.8·1019 cm−3, annealing in N2, SIMS, TEM, B accumulation near surface, extended-defect formation pointing to saturation with interstitials, B-O pairing
93Wij1
1000-1200 1000-1200
intrinsic diffusivity Bi-mediated enhanced tail diffusivity see [91Wij1]
1027 & 1157
neutron transmutation-doped FZ crystals, predeposition from liquid B source in N2 and drive-in, RTA, SIMS, 4-point-probe + chemical sectioning
B in Si 2.02
Methods and Remarks
2-51
65
65 87
91Wij1
93Wij3
95Nag2
effects of surface reactions or ambient 3.52
Lando lt -Bö rnst ein New Series III/33A
1035-1195
CZ crystals, pre-deposition from B2O3 source, drive-in under O2, 4-point probe + chemical sectioning, analysis includes segregation to growing oxide
66
64Kat1
1050 & 1100
(100) and (111) epitaxial crystals, pre-deposition from B2O3 source, drive-in under O2 or N2, pn-junction depth, enhanced DB for (100) orientation in O2 but not in N2
67
69Wil1
2-52
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1100-1250
single crystals, pre-deposition from BN source, drive-in in wet O2, 4-point probe + chemical sectioning, C-V measurement of C0, segregation to growing oxide layer observed
70Hua1
1150 & 1200
(100), (110) and (111) crystals, pre-deposition from B2O3, drive-in under Ar or dry O2, pn-junction staining, orientation-dependent depth in O2 due to differences in source depletion, segregation to growing oxide
70Kov1
975 1100
D = 2.9·10−14 cm2s−1 (pre-deposition) D = 2.4·10−13 cm2s−1 (drive-in) CZ (100) and (111) crystals, pre-deposition from BBr3 in N2/O2 flow, drive-in in Ar ambient, no orientation dependence observed, enhanced DB for (100) crystals in oxidizing drive-in ambient
71All1
900 1000 1100
D = 1.5·10−15 cm2s−1 D = 1.7·10−14 cm2s−1 D = 1.7·10−13 cm2s−1 B-implanted single crystals, annealing in Ar flow with residual O2, 4-point probe + electrochemical sectioning, segregation to growing oxide
72Wag1
1100
see [71All1], drive-in in dry O2 or Ar after predeposition, enhanced diffusivity in (100) Si connected with growing oxide, Q111 − Q100 = 0.58 eV
73All1
0.0322
3.02
1000-1200
B-implanted CZ crystals, annealing in steam ambient, 4-point probe + sectioning, analysis includes electric-field and Fermi-level effects beside segregation to oxide, DB enhancement for short times at 1000 oC
88
74Pri1
0.325 0.417 6.06·10−2
3.34 3.33 3.05
950-1200 950-1200 950-1200
D in inert ambient, D111 in dry O2 ambient D110 in dry O2 ambient D100 in dry O2 ambient CZ crystals, drive-in after pre-deposition from BBr3 source, sheet resistance, pn-junction depth
90
76Mas1
1000-1150
single crystals, pre-deposition from doped oxide in N2, drive-in in HCl-added dry or wet O2, pn-junction staining, sheet resistance, HCl reduces oxidation-enhanced DB, effect of surface orientation
76Nab1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.) 0.55
24 4.1·10−5 1.5·10−5 3.9·10−6 7.5·10−3 1.6·10−5
0.77
Methods and Remarks
2-53
Fig.
Ref.
68 80 87 93
78Ant2
effects of surface reactions or ambient (cont.)
3.42
900-1200
intrinsic diffusivity in N2 ambient, B-implanted CZ crystals, sheet resistance, spreading resistance, enhanced diffusivity in dry O2 ambient: D100 > D111
2.07
950-1150
activation energy of diffusivity enhancement, CZ (100) crystals, P pre-diffusion, annealing in various oxidizing ambients, pn-junction staining, 4-point probe, DB enhancement depends on concentration, junction depth and oxidation rate
3.87 2.34 2.30 2.22 2.85 2.28
840-1150 840-1200 840-1150 840-1100 840-1200 840-1100
intrinsic diffusivity under inert conditions ∆DB beneath (100) surface in dry O2 ambient ∆DB beneath (110) surface in dry O2 ambient ∆DB beneath (111) surface in dry O2 ambient ∆DB beneath (100) surface in steam ambient ∆DB beneath (111) surface in steam ambient single crystals with buried P-doped layer, selective area diffusion, pn-junction staining, spreading resistance
900-1200
CZ (100) crystals with oxide layer, low-dose P implantation, selective-area diffusion in dry O2, spreading resistance, DB enhancement factors depend on oxidation rate and temperature
1000
B-implanted CZ crystals, annealing in dry O2 vs. N2, C-V profiling, oxidation-enhanced diffusion, dependence on oxidation time, fI = 0.30
106 182
82Ant2
1000-1150
intrinsic diffusivity in N2 ambient CZ crystals, low-dose B implantation, annealing in O2, C-V profiling on MOS diode, enhanced diffusivity: D100 > D111 = D110, enhancement factors depend on time and temperature, effect of damage due to additional Ar implantation
87
82Miy1
950-1150
B-implanted (100) FZ and CZ crystals, selectivearea diffusion in dry O2, pn-junction staining, oxidation-enhanced DB, O precipitation in CZ crystals produces self-interstitial supersaturation below Si/Si3N4 interface
1100
B-implanted FZ (100) crystals, capping by Si3N4, selective-area oxidation of backside in dry O2, pnjunction staining, DB enhancement increases with time and decreasing wafer thickness
3.47
Lando lt -Bö rnst ein New Series III/33A
80Tan1
87 91
81Hil1 80hil1
81Lin1
82Miz3
183
82Miz2 83Miz2
2-54
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1010 & 1230
FZ crystals with B-doped buried layer, annealing in NH3, pn-junction staining, spreading resistance, DB retardation under bare surface, enhancement under oxide cap
83Fah1
1000-1150
B-implanted FZ or CZ crystals, annealing in NH3 or N2, pn-junction staining, retardation under bare surface, enhancement under SiO2 film, effect of surface orientation
83Miz1
920
CZ (100) crystals, low-dose B implantation, wet O2 ambient at pressures 1-20 bar, EBIC, SIMS, pnjunction staining, reduced lateral and in-depth diffusion under high pressure
84Der1
950 & 1000 CZ (100) crystals, 11B doping 1019-1020 cm−3 by implantation + diffusion, low-dose 10B implantation + damage anneal, drive-in under N2 or dry O2, SIMS, oxidation-induced enhancement ∆DB is 2-3.5 times larger for high CB than for intrinsic conditions
69
85Miy1
1000
CZ (100) crystals, P doping 2.7·1019-1.2·1020 cm−3 by implantation + diffusion, low-dose 10B implantation + damage anneal, drive-in under N2 or dry O2, SIMS, transient enhanced DB and oxidationinduced enhancement ∆DB decrease with increasing CP
69
85Miy1
1100
(100) single crystals with B-diffused layer, annealing in O2 flow under continuously increasing pressure, DB enhancement independent of time due to constant oxidation rate
85Miz1
950
single crystals with buried B-doped layer, sputterdeposition of TaSi2 film, annealing in N2, spreading resistance and pn-junction staining, enhanced diffusion during silicidation
87Hu1
950-1100
CZ crystals, pre-deposition from spin-on source, drive-in in dry O2 or N2, extrinsic conditions: C0 = 1020 cm−3, 4-point probe + electrochemical sectioning, oxidation enhancement of DB smaller than for intrinsic conditions
87Ish1
1000-1150
B-implanted (100) crystals, annealing in dry O2 with HCl, SIMS, spreading resistance, oxidationenhanced diffusion reduced by HCl
1000
model for oxidation-enhanced DB under extrinsic doping conditions, fitting of data [85Miy1, 85Miy2], fI = 0.25
70
87Sub1
87Tso1 89Tso1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
0.105 1.32·10−5
3.22 1.98
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-55
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1100
B-implanted CZ crystals, annealing in N2, O2 or O2/NF3, pn-junction staining, oxidation-retarded DB due to F addition to ambient
88Kim1
650-850
CZ crystals, BF2 implantation above amorphization threshold, annealing in dry O2 or N2, SIMS and pnjunction staining, transient enhanced diffusion independent of ambient
90Kim1
900-1100
FZ crystals, low-dose B implantation, annealing in Ar or dry O2, C-V profiling, DB enhancement by oxidation up to a factor of 11
90Pac1
800-1100
single crystals, B diffusion through windows in oxide layer, electrochemical C-V profiling, 4-point probe + sectioning, ultra-shallow profiles, effects of Cl in ambient and oxide thickness, non-equilibrium point defects
91Bag1 93Bag1
1000
single crystals, low-dose B implantation, SiO2 growth, RTA 950-1150 oC in NH3 ambient, enhanced diffusion during poly-Si deposition at 1000 oC, penetration of Ni into substrate suggested
91Bus1
1000
(100) crystals, 11B doping 5·1019 cm−3 by implantation and annealing, low-dose 10B implantation and damage anneal, SIMS, oxidationenhanced DB in extrinsic conditions, time dependence investigated, fI = 0.4
91Tso1
200
epitaxial film with B-doped buried layer, evaporated Pt layer, silicidation in Ar ambient, SIMS and RBS, enhanced diffusion preferentially towards surface
91Wit1 92Wit1 92Pic2
962-1157 962-1157
intrinsic DB under oxide layer in N2 ambient intrinsic DB under oxide layer in NH3 ambient B-diffused CZ crystals, second drive-in under oxynitridation conditions, 4-point probe, pnjunction staining, DB enhancement depends on NH3 pressure but not on depth and time
91
93Che1
750-900
MBE-grown B-doping superlattice, O2 ambient, SIMS, oxidation-enhanced broadening of B spikes depending on depth, kick-out mechanism
71
93Gos1
1100-1150
(111), (100) and (110) crystals, B implantation, annealing in wet H2, pn-junction staining, orientation dependence reduced by nitride/oxide surface layers
93Pas1
2-56
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si 85 100 5 23
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
anomalous diffusion after implantation 4.12 4.12 3.69 3.56
1000-1300 1000-1300 1000-1300 1000-1300
implanted dose: 1.6·1013 cm−2 implanted dose: 1.6·1014 cm−2 implanted dose: 1.6·1015 cm−2 implanted dose: 1.6·1016 cm−2 B-implanted single crystals, annealing in Ar flow, 4-point probe, pn-junction staining, effects of dislocations or electric field suggested, enhanced DB at 600-950 oC due to implantation damage and/or Bi
99
67Pav1
700-1100
(111), (110) and (763) FZ crystals with or without B doping 5·1018-1020 cm−3, 10B or 11B implantation, N2 or Ar ambient, SIMS, effects of time, doping and orientation, transient enhanced DB due to Bi, immobile B in precipitates
72
73Hof1
1050-1200
single crystals, high-dose B implantation below amorphization threshold, RTA, SIMS, TEM, no enhanced diffusion
83Nar1
925
single crystals, low energy implantation of B, BF or BF2, SIMS and C-V profiling, redistribution of F and B during 20 min annealing, effects of implantation dose and damage
83Wil1
1000-1100
CZ crystals, B implantation below amorphization threshold, RTA in air or N2, SIMS, TEM, transient enhanced DB outside dislocation network near Cmax, vacancy supersaturation suggested
84Fai1
1150
B-implanted CZ crystals, RTA by graphite heater, Hall effect + sheet resistance, RBS + channeling, SIMS, electrical activation accompanied by diffusion
84Wil1
1050 & 1150
CZ crystals, 11B implantation and RTA in N2 followed by same heat treatment after 10B implantation, SIMS, transient enhanced DB cannot be due to channeled Bi
85Cho1
1000-1150
evalution of literature data, RTA upon B implantation, modeling based on vacancies in multiple charge states
85Fai1
600-1200
FZ crystals, B implantation below amorphization threshold, flowing N2 ambient, SIMS, effects of channeling and implantation-induced defects, charged vacancy model fits data above 1000 oC
85Mar1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-57
Fig.
Ref.
anomalous diffusion after implantation (cont.) 850-900
FZ or CZ crystal, B implantation above amorphization threshold, epitaxial regrowth, precipitation annealing, TEM and RBS, no transient enhanced diffusion
85Pen1 86Pen1 87Pen1 88Pen1
1000-1100
review of literature data: RTA after B or BF2 implantation
85Sei1
1050
single crystals, implantation: B after Si or Ge, evacuated ampoules, differential Hall effect, retarded DB depending on Si/Ge pre-implantation dose, dual vacancy-interstitial(cy) mechanism, effect of elastic misfit stress suggested
85Ste1 85Ste2
700-1100
CZ crystals, B pre-diffusion, Si implantation above amorphization threshold, furnace annealing in N2 or electron-beam heating, pn-junction staining, SIMS, X-ray diffraction, kink-and-tail profiles, enhanced DB below a/c interface due to self-interstitials
800
B-implanted single crystals, selected area removal of implantation damage layer, N2 ambient, SIMS, spreading resistance, enhanced DB caused by damage and not by channeled Bi
800-1000
B-implanted single crystals, RTA or furnace annealing in N2, near-intrinsic conditions, Cmax below solubility, SIMS, time of and displacement by transient enhanced DB decrease with increasing temperature
73 75 76
87Mic1
800-1000
single crystals, Si implantation below or above amorphization threshold, B implantation, RTA or furnace annealing, SIMS, reduction of transient enhanced DB (TED) due to Si implantation damage, also reversed implantation order: TED observed
74 76
87Mic2
750-900
B-diffused CZ crystals, Si implantation above amorphization threshold, annealing in N2, pnjunction staining, X-ray diffraction, enhanced DB correlates with implantation-induced local strain
87Ser1
700-900
B-diffused single crystals, Si implantation above amorphization threshold, annealing in N2, simulation of strain profiles, enhanced DB in profile tail due to self-interstitial supersaturation
87Ser2
750-1100
see [87Ser1, 87Ser2], electron-beam RTA at 1100 oC, also SIMS
87Sol1
75 76 170
87Ang1 88Sol1
87Fan1
2-58
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.) 1.4·10−7
1.1
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
anomalous diffusion after implantation (cont.) 800-950
transient enhancement ∆DB at zero time limit, B-implanted CZ crystals, RTA in N2, SIMS, time τ of exponential ∆DB decay evaluated, dependence on implantation energy observed
950-1100
single crystals, B implantation through oxide film, also post- or pre-amorphization by Si implantation, RTA or furnace annealing in inert ambient, SIMS, transient enhanced DB in c-Si but not in a-Si
1000
single crystals, B implantation after shallow or deep Si pre-implantation below amorphization threshold, RTA, SIMS, TEM, anomalous DB correlates with damage distribution
89Bao1 89Guo1
900
B-implanted single crystals, SIMS, model of transient enhanced DB including clustering of B and self-interstitials, kick-out and dissociative mechanism, correlation with local solubility
89Cow1
750 & 950
CZ crystals, BF2 implantation above amorphization threshold, furnace annealing or/after RTA in N2 or O2, SIMS, TEM, both short- and long-time enhanced diffusion transients, Q reduced by 2.5 eV
89Kim1
1000 & 1150
single crystals, pre-amorphization by deep Si implantation, shallow B implantation, RTA, SIMS, TEM, enhancement (1150 oC) or reduction (1000 oC) of transient enhanced DB compared to crystalline Si
89Kim2
1050
B-implanted single crystals, Si or Ge implantation, furnace annealing or pulsed RTA, differential Hall effect, SIMS, X-ray diffraction, enhanced DB due to excess self-interstitials (low-dose implants) or elastic incompatibility stress (high-dose implants)
89Ste1
800 & 900
FZ crystals, low-to-high-dose B implantation, furnace annealing or RTA in dry N2, SIMS, spreading resistance, transient enhanced DB for CB < ni due to excess self-interstitials, clustering for CB > ni, pre-annealing and amorphization effects examined
75 76
90Cow1 90Cow3
650-900
CZ crystals, B implantation through SiO2 film, RTA and furnace annealing in N2, SIMS, transient enhanced DB up to certain concentration limits
75 76
90Fai1
88Miy1
75 76
88Sed1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.) 1.2·10−4
2.2·10−2
2.1
2.5
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-59
Fig.
Ref.
88
90Fan1
anomalous diffusion after implantation (cont.) 885-1105
FZ crystals, B implantation through oxide film, furnace annealing or RTA in N2, spreading resistance, TEM, transient enhanced DB due to recoil-implanted oxygen precipitation, interstitialtype dislocation loops observed, D0 recalculated
800-1000
FZ crystals, low-dose B implantation through oxide, low-dose Si implantation, C-V profiling, transient enhanced DB increasing with Si dose
90Pac2
900
p-type crystals, diffusion under in-situ implantation, differential Hall effect, depth-dependent enhanced diffusivity, trapping of point defects by B
91Ale1
1000
single crystals, Si implantation above amorphization threshold, B implantation, RTA, SIMS, spreading resistance, TEM, pre-amorphization reduces transient enhanced DB
91Bao1
885 & 900
FZ crystals with or without oxide film, B-implantation + annealing in N2/NF3 or B+2F implantation + annealing in N2, F suppresses O-precipitation enhanced DB in through-oxide implanted Si
91Fan1
800
CZ crystals, Si implantation near amorphization threshold, low-dose BF2 implantation, N2 ambient, SIMS, TEM, amorphous-island formation, lateral distribution of enhanced- and retarded-DB regions
91Kas1
1000 & 1150
single crystals, low- or high-dose Si implantation, B implantation, RTA in N2, SIMS, TEM, transient enhanced DB affected by pre-damaging and preamorphization
91Kim1
900
CZ crystals, low-dose B implantation, 1.0 MeV Si implantation, RTA in N2, SIMS, TEM, RBS + channeling, reduction of transient enhanced DB due to extended-defect formation
91Rai1
800-1050
transient enhanced DB including literature data, B-implanted single crystals, RTA or furnace annealing in N2, SIMS, differential Hall effect, time and concentration limits of DB enhancement evaluated, modeling includes B precipitation
900-1050
B-implanted single crystals, RTA or laser annealing, sheet resistance, pn-junction depth, suppression of transient enhanced DB by laser annealing
75 76 88
91Sol1
92Jua1
2-60
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
anomalous diffusion after implantation (cont.) 900-1050
92Jua2
single crystals, B or BF2 implantation above amorphization threshold, RTA, spreading resistance, 4-point probe, TEM, BF2 reduces transient enhanced DB and improves activation
950 & 1000 CZ crystals, pre-amorphization by Si implantation, implantation of B followed by C, transient enhanced DB in pre-amorphized Si eliminated by carbon
92Nis1
800-1000
CZ crystals, B implantation, SIMS, transient enhanced DB, slight (strong) suppression by preamorphization (+ regrowth) due to Ge implantation
92Pet1
950
Sb-doped wafer, continuous B implantation at 950 oC, SIMS, B accumulation at surface due to flux of B-self-interstitial pairs
800
CZ crystals, implantation of Si or Ge or C, low-dose BF2 implantation, SIMS, RBS, TEM, enhanced or retarded DB depending on pre-implantation element and dose (amorphization)
93Kas1
900-1100
single crystals, shallow B implantation, RTA in N2, SIMS, TEM, transient enhanced DB depends exponentially on time, multizone model based on dose-dependent defect/damage distribution
93Kin1
550 & 800
MBE-grown B-doped marker layers, Si implantation below amorphization threshold, furnace annealing or RTA in dry N2, SIMS, TEM, ultrafast initial and slower secondary transient enhanced DB, dose-dependent formation of {113} interstitial-type defects
94Cow2 93Cow1
B in Si
77
92Pic2
cooperative effects with other dopants 1020-1200
P-diffused CZ crystals, dislocation density < 2·103 cm−2, BBr3 source, pn-junction staining, TEM, anomalous P-base shifts in p+np structure, also enhanced B-base penetration in n+pn structure
66Law1
1250
FZ crystals, simultaneous B-Ga diffusion, elemental B source, pn-junction staining, 4-point-probe + mechanical sectioning, B-related effects on Ga diffusion
71Oka1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
Methods and Remarks
Fig.
Ref.
cooperative effects with other dopants (cont.) 1000
72Zie1
B-doped or B-diffused crystals, redistribution during As emitter diffusion, nuclear reaction activation, dip in B profile due to electric field, B out-diffusion observed B- and/or As-doped oxide source, simultaneous or sequential As-B diffusion vs. B alone, SIMS, emitter-push effect, temperature not indicated
Lando lt -Bö rnst ein New Series III/33A
2-61
78
73Bla1
1000 & 1100
B-diffused single crystals, As-doped oxide source, C-V measurements, pn-junction staining, retarded DB during As emitter diffusion, vacancy-As2 complexes cause vacancy undersaturation
73Fai3
1000
B-implanted single crystals, simultaneous or sequential As-B diffusion, N2 or O2 ambient, C-V measurements, comparison of implanted and doped-oxide As source
74Fai1
1025
D = 4.8·10−14 cm2s−1, n-type crystals, As + B implantation, annealing in vacuum, sheet resistance + electrochemical sectioning, formation of n-p-n structures by co-diffusion
74Hei1
950
CZ crystals with 102-103 dislocations/cm2 or epitaxial layer, sequential diffusion: P after B, predeposition from BBr3 and drive-in, pn-junction staining, 4-point probe and electrochemical sectioning, emitter-push effect depending on C0(P)
900
CZ crystals, sequential diffusion: P after B, B-doped oxide source, pn-junction staining, sheet resistance + electrochemical sectioning, emitter-push effect depending on C0(P) and C0(B)
74Nak1
700
single crystals, sequential pre-deposition of B and As, simultaneous As-B diffusion in N2 ambient, sheet resistance + electrochemical sectioning, enhanced B diffusion, emitter-push effect
75Shi1
1100 & 1260
single crystals, simultaneous B-Ga diffusion, Bdoped Si and elemental Ga source, suppression of dislocations due to strain compensation by Ga
77Yon1
700-1000
B-implanted FZ crystals, P diffusion in N2, SIMS, C-V profiling, TEM, P-emitter push effect depending on C0(P) and B implantation dose and depth, no dislocations, enhanced DB with Q lower by 1.3 eV
81
79 80 81
74Lee1
79Lec1 80Lec1
2-62
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
Methods and Remarks
Ref.
1070
B-doped single crystals, epitaxial layer growth after As- or Sb implantation, P diffusion in N2, pn-junction staining, enhanced B diffusion
83Har1
1000 & 1100
single crystals, BF2 implantation above amorphization threshold, furnace annealing or RTA in N2, TEM, SIMS, spreading resistance, complex redistribution of B and F observed
84Lun1
800-1200
CZ crystals, Au evaporation after B pre-deposition, simultaneous diffusion, spreading resistance, RBS, electron microscopy, enhanced DB due to Au, kick-out mechanisms for B and Au
89An1
900
Ge-implanted single crystals, high-dose BF2 implantation, annealing in neutral ambient, SIMS, spreading resistance, retarded Bi and enhanced Bs due to long-range interactions with Ge
91Aro1
3.426 1050 & 1100
intrinsic diffusivity into single crystal substrate, deposition of poly-Si layer, implantation of B and/or As, RTA in Ar ambient, SIMS, mutual retardation for As-B co-diffusion
3
3.426 1050 & 1100
single crystals, implantation of B and/or As through oxide film, RTA in Ar ambient, SIMS, effects of As-B co-diffusion examined
B in Si
11.5
Fig.
cooperative effects with other dopants (cont.)
2.6
0.15
[Ref. p. 2-196
88
91Gon1 93Gon1
92Gon1
special source conditions
4.25
3.77
1200
standard wafers, oxide source layer deposition from pre-mixed SiH4/B2H6/Ar gas, annealing in N2 or air, sheet resistance, reproducibility and uniformity examined, effect of SiO2 capping film
1000-1270
single crystals, B-doped oxide source by reactive sputtering, N2 ambient, 4-point probe + electrochemical sectioning, pn-junction staining, C0 = ca. 1016 cm−3
1000-1100
CZ crystals, B2O3-SiO2 glass film source, 4-point probe, pn-junction staining, C0-dependent diffusivity with maximum at C0 = 3·1020 cm−3, effect of undoped oxide at glass/Si interface
1180-1260
BN surface layer source, pre-deposition at 850-950 oC, drive-in under SiO2 cap, spreading resistance, C0 = 1018-1019 cm−3
68Fis1
89
68Nag1
71Bro1
86
71Sch2
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
2·10−4
2.3
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-63
Fig.
Ref.
special source conditions (cont.) 1000-1200
epitaxial layer, BN source wafer in He, Ar or N2, 4-point probe + electrochemical sectioning, ambient-dependent pn-junction depths, effect of borosilicate glass and Si-B phase formation
74Sta1
1000 & 1050
spin-on diffusion source containing carborane polymers, sheet resistance, pn-junction staining, C0 < 3·1020 cm−3
76Bey1
900-1100
CZ crystals, BBr3 source at 24 oC in N2/O2, TEM, differential Hall effect, formation of B-rich layer (BRL) depends on doping gas composition, BRL affects C0 and amount of B entering substrate
1200
single crystals, BN deposition, Si3N4 capping, N2 ambient, pn-junction staining, 4-point probe + dry plasma sectioning, analysis based on [75Fai3], also drive-in after pre-diffusion studied
80Sho1
1200
single crystals, pre-deposition from B2O3 source, drive-in in O2, 4-point probe with electrochemical and chemical sectioning
83Era1
800-1000
analysis of As-implanted poly-Si diffusion sources, SIMS, segregation to poly/mono interface
85Sch1
870-990
single crystals, BN source in dry Ar, pn-junction staining, SIMS, I-V measurement + chemical sectioning, analysis accounts for SiBx phase formation near surface
86
86Dom1
800-1000
single crystals, poly-Si layer deposition, B doping during deposition or by implantation, SIMS, DB depends on timely constant poly/mono interface concentration
83
86Gar1
1050-1150
single crystals with poly-Si layer, B implantation, RTA, SIMS, sheet resistance, TEM, extremely shallow pn-junctions, epitaxial realignment effect
87Böh1
900-1000
single crystals with B-implanted TaSi2 layer, annealing in N2 ambient, SIMS, shallow penetration into Si substrate, no crystal defects
87Gie1
850-1050
single crystals, (no) deposition of poly-Si layer heavily B-doped in situ or by implantation, annealing in ampoule with highly B-doped Si powder, DB depends on CB but not on source or time, profiles fitted by kick-out model [86Mor1]
88Orr1
82
78Neg1
2-64
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
special source conditions (cont.) 1250
FZ crystals, high energy B implantation 15-50 MeV, projected range 15-80 µm, spreading resistance, enhanced DB in O2 vs. N2 ambient
89LaF1
900-1050
CZ crystals, borosilicate glass layer source, RTA or furnace annealing in N2, 4-point probe, SIMS, enhanced DB correlates with source strength
91Miy1
800-1150
single crystals with B-implanted poly-Si layer, RTA and furnace annealing, SIMS, TEM, various effects observed
91Par2
1.285·10−3 2.695 800-950 0.336 3.426 800-950
CB < 5.0·1018 cm−3 CB > 1.0·1020 cm−3 single crystals with poly-Si layer, high-dose BF2 implantation, capping oxide, SIMS, spreading resistance, Boltzmann-Matano analysis, D0 and Q also vary for 5.0·1018 cm−3 < CB < 1.0·1020 cm−3, dose independence
B in Si
other effects or conditions
89
93Sul1
84
61Que1
1150
single crystals, B2O3 source in N2 ambient in Pt box, preferential etching, C0 = 5.0·1020 cm−3, diffusion-induced dislocation patterns
1100
CZ crystals, diffusion in Pt box, X-ray topography, C0 = 1021 cm−3, rectangular arrays of diffusioninduced dislocations
62Sch1
1200
single crystals also after plastic deformation, BBr3 diffusion through oxide windows, preferential etching, TEM, X-ray topography, lateral patterns of diffusion-induced dislocations
66Law1
956-1100
single crystals, diffusion in Pt box [60DAs2], 4-point probe + electrochemical sectioning, X-ray diffraction, diffusion-induced dislocation density decreases with B penetration depth
66Rup1
1050
melt-grown oxygen-free single crystals, P or Sb doping up to 2·1019 cm−3, B2O3 source in vacuum, sheet resistance, TEM, optical microscopy, diffusion-induced precipitates including rods, platelets and stacking faults
68Dob1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
3.5
Methods and Remarks
Fig.
Ref.
other effects or conditions (cont.) 1100-1200
CZ crystals, drive-in after pre-deposition through oxide windows, 4-point probe and NAA + sectioning, X-ray topography, dislocations generated outside diffused areas, effects of O2 ambient and surface orientation
68Fai1 66Sch1
1000-1300
epitaxial layer, B2O3 or BBr3 source, pn-junction and sheet-resistance measurements, no difference between epitaxial and bulk Si, see [86wöh1]
70Sla1
950 & 1120 CZ crystals, pre-deposition from BN source, drivein in O2, sheet resistance, pn-junction staining, DB retardation due to diffusion-induced dislocations
70Yos2
1100
CZ crystals with stacking faults, B-doped oxide source in dry N2, preferential etching, sheet resistance + electrochemical sectioning, stackingfault annihilation only near surface
76Has1
766-843
B-implanted single crystals, isochronal annealing in dry N2 flow at 800-1100 oC, TEM, Q deduced from isothermal shrinkage rate of rod-shaped defects
77Wu1
1150
CZ crystals with stacking faults, B-doped oxide layer under undoped oxide, also B2O3 as source, N2 or O2 ambient, preferential etching, stackingfault growth due to B diffusion and/or oxidation, reduced growth in Cl-containing ambient
78Cla2
600-900
CZ crystals with B-doped buried layers, annealing in vacuum under proton irradiation, intrinsic conditions, spreading resistance, pn-junction staining, flux-dependent enhanced DB due to excess vacancies
78Mas1
700
plates with B doping 1.5·1017-2.5·1019 cm−3, annealing under proton irradiation, SIMS, B-peak (dip) formation at projected proton range for CB below (above) 1018 cm−3, electrostatic interaction of B with radiationinduced defects suggested
82Koz1
900 & 1000 CZ crystals with stacking faults, epitaxial layer, predeposition (1000 oC) and drive-in (900 oC) from B-doped oxide in N2, sheet resistance + electrochemical sectioning, no annihilation of stacking-faults
Lando lt -Bö rnst ein New Series III/33A
2-65
83Mat1
2-66
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
B in Si (cont.)
33.7
0.58
3.93
Fig.
Ref.
other effects or conditions (cont.) single crystals, low-to-high-dose B or BF2 implantation, RTA by arc lamp, sheet resistance, SIMS, TEM, less residual damage with decreasing dose and increasing temperature
84Hod1
900 & 1000 single crystals with buried oxide layer, high-dose B implantation through SiO2 windows, diffusion annealing, pn-junction staining, no lateral diffusion near buried oxide observed
85Kam1
700
platelets purified by electron-beam melting, low or high oxygen concentration, B implantation + damage anneal, annealing under proton irradiation, SIMS, proton-stimulated DB via vacancy-O complexes
85Koz1
(−68)-(−48) interstitial diffusivity Di of Bi , FZ and CZ crystals, B doping 1-5·1019 cm−3 compensated by P or As, electron irradiation below −163 oC, isothermal or isochronal annealing at −108 - +27 oC, IR absorption, Di deduced from loss kinetics of radiation-induced Bi
87Tip2
900
CZ crystals, B-doped spin-on source, long-time lamp annealing in N2, intrinsic conditions, electrochemical C-V profiling, enhanced diffusion attributed to radiation heating
89Ish2
800 & 1050
MBE-grown superlattices / pipi-structures, RTA or UHV furnace annealing, SIMS, electrochemical C-V profiling, TEM, DB depends on growth temperature but hardly on CB
89Jac1
600-700
MBE-grown npnip-structure, smearing of B profile under in-situ Si bombardment during growth, SIMS, spreading resistance, transient enhanced DB
89Puk1
850-1150
FZ and CZ crystals, shallow B implantation, SIMS on 10B and 11B, Gaussian profiles, isotope effect E = 0.39 ± 0.03, also diffusion under high pressure 0-16 kbar, relative activation volume V/Ω = 0.27 ± 0.13, intersticialcy mechanism
1150
B-implanted CZ crystals, annealing in N2, O2 or N2/O2 flow, comparison between spreadingresistance and SIMS profiles, complete electrical activation observed
850-1280
0.04
Methods and Remarks
[Ref. p. 2-196
88 102
90Söd1 89Söd1
90Cla1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
B in Si (cont.)
Methods and Remarks
2-67
Fig.
Ref.
other effects or conditions (cont.) 800-1000
single crystals pre-amorphized by Si implantation, shallow B implantation, furnace annealing or RTA in N2, SIMS, differential Hall effect, TEM, dopant activation followed by precipitation observed, diffusion simulation includes precipitation phenomena
90Sol1
800
CZ crystals, heating in H2 to remove oxide, diffusion in B2H6/H2, electrical activation by RTA using graphite strip heater, SIMS, differential Hall effect, ultra-shallow p+ layer
91Ina1
500-800
in-situ B implantation during wafer heating by lamp radiation, SIMS, enhanced DB due to radiationinduced point defects
91Sch2
850 & 1000
B-implanted single crystals, scanning tunneling microscopy + chemical etching vs. SIMS and spreading resistance, electrically active B detected
91Tak1
1420
D = 2·10−14 cm2s−1 in the melt, epitaxial layer on B-doped wafers, local melting by laser annealing, spreading resistance, diffusion from substrate into epi-layer
92Kim1
800-900
epitaxial layers with B-doping spikes, dry O2 ambient, depth dependence of DB characterizes epi-layer growth technique
92Oos1
700-1100
directly bonded identical (100) CZ wafers, moderate B doping, annealing in dry O2, SIMs, spreading resistance, X-ray diffraction, stress-enhanced DB at bonding interface
93Ish1
3.84 3.33 2.73
900-1025 900-1025 900-1025
intrinsic DB under furnace annealing intrinsic DB under RTA intrinsic DB in Si substrate of SiGe heterostructure under RTA in-situ B-doped epitaxial layers, SIMS, enhanced diffusivity due to RTA
88
93Loe1
8.0
3.47
1085-1375
As-doped single crystals, Al oxide source in low-pressure air ambient, pn-junction staining, C0 = (0.1-4)·1017 cm−3, vacancy mechanism
97
56Ful1
2.8·103
3.8
1200-1400
single crystals, Al surface layer, pn-junction method, C0 around 1017 cm−3, only abstract given, further data reported by [56Mil1]
97
56Gol1
14.17 0.38 3.2·10−3
Al in Si
Lando lt -Bö rnst ein New Series III/33A
2-68
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
Al in Si (cont.) 4.8
3.36
1050-1380
As-doped single crystal, elemental Al source, Ta tube used for impurity gettering, pn-junction and CV measurement, C0 = (0.15-2.7)·1019 cm−3
98
56Mil1
2.9
3.23
800-1250
n-type wafers, elemental Al or Al-Si source, 4-point-probe + pn-junction staining, C0 = (0.2-1.3)·1019 cm−3, effects due to amount and composition of source studied
97
67Kao1
800
single crystals, Al implantation above amorphization threshold, vacuum annealing, 4-point probe + sectioning, photo-e.m.f., enhanced DAl attributed to excess vacancies
1119-1390
Al-doped epitaxial layers on CZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, Al-vacancy pair mechanism
1150 & 1215
D(1150 oC) = (2.25-2.5)·10−12 cm2s−1, D(1215 oC) = (2.2-3.6)·10−11 cm2s−1, P-doped crystals (10-15 Ωcm), deformation by bending to 103-107 dislocations/cm2, pure Al source, 4-point-probe + chemical sectioning, C0 = 1016-1017 cm−3, diffusivity along dislocations also given
74Pav1
1175-1245
FZ crystals, elemental Al source in Ar or vacuum, spreading resistance, Hall effect + resistivity, C0 = 1.5·1016-8.0·1017 cm−3, Al-O reactions studied in Al-doped CZ crystals at 400-1270 oC
77Rai1
1025-1175
FZ wafers, elemental Al or Al-Si source, evacuated open tube with Al-coated walls, 4-point-probe and spreading resistance, C0 = 1018-1019 cm−3, various wafer/source arrangements investigated
1250
single crystals, elemental Al source, bare Si surface vs. masking by SiO2-Si3N4-SiO2 sandwich, spreading resistance, thermal probe, C0 = 2·1016 cm−3
1000-1250 800-1000
recalculated from Arrhenius plot recalculated from Arrhenius plot standard wafers, elemental Al vs. Al-coated or Al-doped wafers as source, Ar or N2 ambient, spreading resistance, C0 = ca. 2·1018 cm−3
1.385
1.8
0.41 6.3·10−6
3.41
3.2
2.98 1.76
68Ito1 70Ito1
92 94 97
98
71Gho1
78Ros1
79Bal1
97
81Cha1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-69
T-range [oC]
Methods and Remarks
Fig.
Ref.
900-1250 1119-1390
total intrinsic DAl = D0 + D+ D0 via neutral vacancies D+ via singly positively charged vacancies review and evaluation of literature data including [67Kao1, 71Gho1, 77Rai1, 78Ros1]
98
81fai1
950-1150
FZ and CZ crystals, Al implantation and damage anneal, diffusion in O2 with and without Si3Ni4 capping, pn-junction staining, oxidation enhanced DGa for (100) orientation, reduced /reverse effects for CZ (111), HCl in ambient suppresses O2 effect
95
82Miz1
1250
D = 3.1·10−11 cm2s−1, single crystals, Al-doped spin-on oxide source in air, spreading resistance, Gaussian profiles, statistical analysis
83Nis1
1060 & 1240
FZ crystals, pre-deposition in vacuum, drive-in under N2/O2 atmosphere, reduction of processinduced defects, various experimental techniques
89Sch2
900-1250
FZ crystals, Al implantation through SiO2 film, annealing in N2 ambient, spreading resistance, SIMS, low electrical activity due to Al-O precipitation, out-diffusion suppressed by SixNy-SiO2 capping
91Wat1
1000-1290
FZ crystals, deep Al implantation and activation anneal, diffusion annealing, spreading resistance
1200
Al-implanted FZ and CZ crystals, annealing in N2, spreading resistance, SIMS, formation of Al-O complexes reduces electrical activity
1000-1290
Al-implanted FZ crystals, RTA and SiC-furnace annealing in N2, SIMS, spreading resistance, profile fitting accounts for out-diffusion
800-1000
gettering effect of Al-P co-diffusion, surface photovoltage technique measuring minority carrier diffusion length
93Har1
1200
FZ crystals, Al implantation, out-diffusion and precipitation during annealing, SIMS, spreading resistance, effect of capping films investigated
93Sca1
962-1240
FZ crystals, Al pre-deposition and drive-in diffusion, spreading resistance, D0 and Q recalculated from tabulated data
Al in Si (cont.) 1530 1.385 2480
7.4
8.88
11.7
4.1 3.41 4.20
3.42
3.44
3.46
Lando lt -Bö rnst ein New Series III/33A
98
93LaF1 93LaF2
98
93 97 98
93Gal1
94Mit1
2-70
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
1000-1200
FZ crystals, Al implantation through SiO2 windows, annealing in N2 ambient, spreading resistance, pnjunction staining, two-dimensional profiles, numerical analysis based on neutral vacancies and self-interstitials
95Gal1
1020
FZ crystals, special Al-on-Si source arrangement, RTA, SIMS, C-V and spreading resistance, also sequential diffusion: P after Al promotes Al tail und near-surface up-hill diffusion, Al after P leads to Al retardation suggesting Al-P complex formation
95Nag1
1017 1047 1197
D = 7·10−13 cm2s−1, pre-deposition in vacuum D = 1.5·10−12 cm2s−1, pre-deposition in vacuum D = 7·10−12 cm2s−1, drive-in under N2 neutron transmutation-doped FZ crystals, Alevaporated source wafers, RTA, SIMS, 4-pointprobe + chemical sectioning, also sequential diffusion: Al after P and P after Al
96
95Nag2
Al in Si (cont.)
Ga in Si 3.6
3.51
1105-1360
As-doped single crystals, Ga oxide source in low-pressure air ambient, pn-junction staining, C0 = (0.15-2.1)·1020 cm−3
103
56Ful1
270
4.15
1130-1358
recalculated from given Arrhenius plot, n-type single crystals, Ga vapour source carried by Ar flow, pn-junction determination, 4-point probe + mechanical sectioning, C0 = 1.4·1017-4.3·1018 cm−3, intrinsic conditions
103
58Kur1
2.1
3.52
1180-1340
n-type crystals (15 Ωcm), Ga vapour source, pnjunction determination, C0 = (1-5)·1019 cm−3, also enhanced DGa in Sb-pre-diffused crystals due to electric-field and Fermi-level effect
103
64Bol2
1100-1250
P-doped single crystals, diffusion through thermally grown SiO2 layer into Si, Ga2O3 source in N2/H2 mixture, pn-junction staining
64Gro1
1200
D = 2.9·10−12 cm2s−1 for C0 = 4·1019 cm−3 low-dislocated CZ crystals with thermal oxide layer, elemental Ga source in evacuated ampoule, sheet resistance and radiotracer + electrochemical sectioning, all Ga on substitutional sites, erfc profile
64Kre1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-71
T-range [oC]
Methods and Remarks
Fig.
Ref.
1250
D = (9.6-11.3)·10−12 cm2s−1, n-type FZ crystals, simultaneous Ga-As or Ga-P diffusion through SiO2 windows, pn-junction staining, 4-point-probe + mechanical sectioning, Ga retardation in n+-layer due to electric field, enhancement for short times in case of Ga + P
68Oka1
1256
D = 9.0·10−12 cm2s−1, high-ohmic P-doped crystals, Ga pre-deposition in Ar ambient, drive-in diffusion in air, resistivity and pn-junction measurements, out-diffusion to surface
70Con1
70Pru1
Ga in Si (cont.)
6·10–3
2.08
1000-1200
polycrystals, radiotracer technique, reports larger DGa than for mono-Si, see also [86wöh1]
0.374
3.39
1143-1393
Ga-doped epitaxial layers on CZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, Ga-vacancy pair mechanism
92 103
71Gho1
60 8·10−3
3.89 2.49
900-1050 900-1050
intrinsic DGa in as-grown CZ crystals extrinsic DGa in B-pre-diffused CZ crystals dislocation density below 4·103 cm−2, Si(Ga) powder source in vacuum, NAA + chemical sectioning, DGa proportional to hole density, CB = 1.59·1019-8·1020 cm−3
99 100 103
71Mak1
1150
D = 1.6·10−12 cm2s−1, n-type crystal, amorphous layer source containing Ga2O3, see [86wöh1]
1250
n-type single crystals, light or heavy background doping (P, As), pure Ga source, also simultaneous diffusion with As or B, also double diffusion: P after Ga, NAA + chemical sectioning, 4-pointprobe, DGa retardation by n+-doping, enhancement by p+-doping
1280
crystals doped with P or B up to 1020 cm−3, Ga2O3 source, NAA + sectioning, C0 = 3·1017 cm−3, doping-dependent diffusivity, see [86wöh1]
72Hei1
1000
(100), (111) and (110) crystals, thermal oxidation and window etching, elemental Ga source, pn-junction staining and 4-point probe, enhanced DGa in SiO2-covered regions
72Nak1
Lando lt -Bö rnst ein New Series III/33A
71Mer1 100
71Oka1
2-72
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
1100
n-type crystals (5-8 Ωcm), Ga2O3 powder source, sequential diffusion: P at 1050 oC after Ga, radiotracer 67Ga + chemical sectioning, 4-pointprobe, DGa enhancement during P diffusion leads to push-out of base-collector junction
74Jon1
800-1050
steam oxidized wafers, diffusion through SiO2 layer into Si, Ga2O3 source in H2/H2O gas ambient, C-V profiling on MOS capacitor
74Wag1
900-1050 900-1050
diffusivity via neutral vacancies diffusivity via positively charged vacancies evaluation of [71Mak1]
75sha1
1100
P-doped crystals (1 Ωcm), Ga2O3 powder source in mixed H2/N2 ambient, sequential diffusion: P at 900 oC or 1050 oC after Ga, 4-point-probe + chemical sectioning, push-out of Ga tail, dip in Ga profiles under P emitter zone
75Jon1
1100
see [75Jon1], radiotracer 67Ga + chemical sectioning
76Jon1
1100
see [75Jon1, 76Jon1], sequential diffusion: P at 900 oC or As at 1000 oC after Ga, large (P) or small (As) push-out of Ga tail, dip in Ga profiles
77Jon1
1260
single crystals, simultaneous Ga-B diffusion, elemental Ga and B-doped Si source, suppression of dislocations due to strain compensation
77Yon1
1035 & 1100
single crystals with oxide layers 0 -1.0 µm, elemental Ga source in vacuum, 4-point-probe + chemical sectioning, little effect of SiO2 layer
78Jai1
1250
single crystals, elemental Ga source, bare Si surface vs. masking by SiO2-Si3N4-SiO2 sandwich, spreading resistance, thermal probe, C0 = 1·1019 cm−3
79Bal1
Ga in Si (cont.)
124 0.716
3.96 3.46
5·10−3
2.70
700-1100
FZ crystals, elemental Ga source, SIMS, NAA + electrochemical sectioning, vacancy mechanism, influence of surface oxide considered, C0 = 7.32·1018-3.26·1019 cm−3
103
80Har1
13.1 0.374 28.5
3.70 3.39 3.92
900-1360 1143-1393
total intrinsic DGa = D0 + D+ D0 via neutral vacancies D+ via singly positively charged vacancies review and evaluation of literature data including [56Ful1, 58Kur1, 64Bol2, 71Gho1, 71Mak1, 71Oka1]
93 103
81fai1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-73
T-range [oC]
Methods and Remarks
Fig.
Ref.
1000 & 1075
modeling of sequential diffusion: As after Ga, includes Fermi-level and electric-field effects and excess point-defect generation by As diffusion, see [77Jon1]
101
81Mal1
1150-1250
n-type wafers, Ga-doped oxide film as spin-on source, 4-point-probe and pn-junction determination, C0 = (0.1-2.7)·1019 cm−3, D0 represents average of erfc- and Gaussian analysis
103
85Dan1
680-740
Ga implantation above amorphization threshold, precipitation annealing after epitaxial regrowth at 600 oC, TEM analysis of precipates beneath a/c interface, DGa enhancement due to excess selfinterstitials
85Pen1 86Pen1 86Pen2 88Pen1
1050
D = 1.45·10−13 cm2s−1 (erratum considered), buried Ga-doped epitaxial layer, bare or SiO2-covered surface, annealing in NH3 ambient, SIMS, spreading resistance, fractional vacancy component < 0.05
89Fah1
850-1150
FZ crystals, evaporated Ga layer, SIMS on 69 Ga and 71Ga, erfc profiles, isotope effect E = 0.51 ± 0.04, also diffusion under high pressure 0-16 kbar, relative activation volume V/Ω = −0.7 ± 0.1, intersticialcy mechanism
900
high-dose Ge implantation and damage anneal, Ga and BF2 implantation, annealing in N2 ambient, SIMS and spreading resistance, simultaneous retardation of Ga and B diffusion
91Aro1
900-1250
FZ crystals, Ga implantation into Si or surface oxide, annealing in N2 ambient, spreading resistance, SIMS, out-diffusion prevented by SiO2-SixNy-SiO2 capping film
92Wat1
1105-1360
As-doped single crystals, In oxide source in low-pressure air ambient, pn-junction staining, C0 = (0.28-67)·1018 cm−3
106
56Ful1
1150-1306
crystals doped by diffusion or during growth up to 1021 cm−3 (n-type) or 5·1018 cm−3 (p-type), elemental In vapour source, radiotracer 114In + mechanical sectioning, doping-dependent DIn, interchange mechanism via interstitial activated complex
104
66Mil1
Ga in Si (cont.)
2.3
6.5
3.4
3.59
102 103
90Söd1 89Söd1
In in Si 16.5
3.91
Lando lt -Bö rnst ein New Series III/33A
2-74
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
In in Si (cont.) 1·103
3.19
900-1200
5·103 dislocations/cm2, radiotracer 114In + sectioning, interpretation as diffusivity along dislocations, vacancy mechanism, electrotransport at 900 oC, positive effective charge due to hole drag
106
67Ste1
0.785
3.63
1180-1398
In-doped epitaxial layers on CZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, In-vacancy pair mechanism
92 106
71Gho1
950
D = 2·10−15 cm2s−1, single crystals, 5·103-5·104 dislocations/cm2, elemental vapour source, radiotracer + sectioning, analysis accounts for diffusion along dislocations
74Pan1
1150-1246
D0(1215 oC) = 1.7·10−12 cm2s−1 D+(1215 oC) = 3.2·10−12 cm2s−1 evaluation of [66Mil1] in terms of In diffusion via neutral and positively charged vacancies
75sha1
1105-1360 1180-1398
total intrinsic DIn = D0 + D+ D0 via neutral vacancies D+ via singly positively charged vacancies review and evaluation of literature data including [56Ful1, 66Mil1, 71Gho1]
93 106
81fai1
1000
D = 6.7·10−15 cm2s−1 under inert conditions, CZ crystals, In implantation after gettering and oxidation treatments, damage anneal, enhanced DIn in O2 vs. N2 ambient, C-V profiling on MOS diodes, fI = ca. 0.35
105
82Ant1
1000-1200 1000-1200
regular DIn after implantation: dose 1013 cm−2 enhanced DIn after implantation: dose 1014 cm−2 P-doped crystals, In implantation through SiO2 layer, damage anneal, diffusion in N2 ambient, pnjunction determination, sheet resistance + Hall effect, enhancement due to Inx-Siy precipitation
93 106
83Cer1
450-600
In implantation above amorphization threshold, also pre-amorphization by Si implantation, epitaxial regrowth under flowing N2, TEM, transient enhanced DIn
88Pen1
25-800
In incorporation during molecular beam epitaxy, SIMS, complex model accounts for incorporation rate, surface segregation, and bulk diffusion
89Sun1
269 0.785 415
1.7·102 1.4·104
4.19 3.63 4.28
4.2 4.56
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
2-75
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
16.5
3.91
1105-1360
As-doped single crystals, Tl oxide source in low-pressure air ambient, pn-junction staining, C0 = (0.9-3.7)·1017 cm−3
108
56Ful1
1.37
3.70
1244-1398
Tl-doped epitaxial layers on CZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, Tl-vacancy pair mechanism
92 108
71Gho1
269 1.37 351
4.19 3.70 4.26
1105-1360 1244-1398
total intrinsic DTl = D0 + D+ D0 via neutral vacancies D+ via singly positively charged vacancies review and evaluation of literature data including [56Ful1, 66Mil1, 71Gho1]
93 108
81fai1
15
3.75
1070-1300
high-ohmic FZ crystals, elemental Tl vapour source, 4-point-probe + sputter-sectioning, C0 = 1·1016-7·1017 cm−3, intrinsic conditions
107 108
89Sel1
Tl in Si
2.2.1.14 Solute elements of group IVA (carbon group). (See Figs. 109-128, p. 166) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
3.3·10−1
2.92
1070-1400
CZ crystals, 10 dislocations/cm2, radiotracer 14C with mechanical sectioning, Ba14CO3 or radioactive acetylene in closed ampoule, DC unchanged in plastically deformed samples
110 111
61New1
3.3·101
2.94
950-1100
P-doped FZ crystals, 5·104 dislocations/cm2 radioactive Ba14CO3 source, sectioning technique
110 111
73Gru1
0.88
(−65)-(−51) interstitial diffusivity characterizing Ci , B-doped FZ crystals, carbon doping 1017 cm−3, 1.5 MeV electron irradiation, EPR, Ci motion followed by formation of Ci-Cs pairs
76Wat1
B-doped CZ crystals, 104-105 dislocations/cm2, carbon doping 8.5·1017 cm−3; Si ribbons obtained by edge-defined film-fed growth, 106-107 dislocations/cm2, < 1016 oxygen/cm3, carbon doping 9·1017 cm−3; out-diffusion, N2 or O2 ambient, SIMS, outdiffusion enhancement due to P-diffusion, C precipitation, no difference between CZ and ribbon samples
84Kal1 85Lad1
C in Si
900
Lando lt -Bö rnst ein New Series III/33A
2-76
2 Diffusion in silicon, germanium and their alloys
D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
C in Si (cont.) 4.4
0.88
(−65)-(−51) interstitial diffusivity characterizing Ci, estimation including data of [76Wat1]
111
86gös1
6.5
3.00
1155-1365
reanalyzed from given data, B-doped poly-Si, radioactive Ba14CO3 source in closed ampoule, mechanical sectioning, no grainboundary diffusion, carbon segregation to grain boundaries
110 111
87Cha1
4.4·10−1
0.87
(−65)-58
interstitial diffusivity characterizing Ci, includes EPR data of [76Wat1], p-type FZ crystals, carbon doping 2·1017 cm−3, oxygen doping 5·1014 cm−3, electron irradiation, decay of Ci-related IR absorption, Ci motion followed by formation of Ci-Cs pairs, no dependence of DC on Ci charge state
111
87Tip1
9.5·10−1
3.04
903-1385
FZ crystals, carbon doping < 5·1014 cm−3, oxygen doping < 3·1015 cm−3, CZ crystals, defect-free or 2·105 stacking faults/cm2, plastically deformed samples with about 109 dislocations/cm2, elemental C or BaCO3 source, radioactive 14C combined with mechanical sectioning, no effect of crystal defects, proposes Ci-controlled incorporation of Cs by interstitial-substitutional diffusion mechanisms
109 110 111 112
89Rol1
94dav1
(–65)-1385 review of diffusion data and other carbon-related features, interpretations involve Cs, Ci, mutual pairs, and complexes with point defects and/or other impurities
Si in Si
direct self-diffusion measurements
3
4.73
1178-1300
p-type (400 Ωcm) and P- or B-doped (0.001 Ωcm) single crystals, 103- 5·104 dislocations/cm2, evaporated 30Si source, closed ampoule annealing in Ar ambient, chemical sectioning combined with NAA, enhanced self-diffusion in P-doped samples, divacancy mechanism for self-diffusion proposed
115
66Gho1 67Gho1
1.8·103
4.77
1200-1400
FZ crystals (p-type, 6000 Ωcm), evaporation of radiotracer 31Si, closed ampoule annealing in Ar ambient, mechanical sectioning
115
66Pea1
9.0·103
5.13
1100-1300
CZ and FZ crystals, intrinsic and As-, P-, or Bdoped ( ≤ 2·1020 cm−3) samples, closed ampoule containing HCl, radiotracer 31Si combined with chemical etching, erfc-profiles, enhanced diffusion in n-type and to a minor extent in p-type Si, single vacancy mechanism assumed
112 113 115
67Fai1 66Mas1
1.2·10
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Si in Si (cont.)
Methods and Remarks
2-77
Fig.
Ref.
direct self-diffusion measurements (cont.) evaluation of doping effect on Si self-diffusion, experimental data from [67Fai1], interstitialcy mechanism, amphoteric nature of self-interstitials
70Chi1
75sha1
1.57·104 1.48·102 1.9·10−2
5.23 4.84 3.91
1090-1190 1090-1190 1090-1190
D0 via neutral vacancies, D− via single negatively charged vacancies D+ via single positively charged vacancies analysis of doping dependence, data given by [67Fai1]
1.46·103
5.02
1047-1387
B-doped (260-360 Ωcm) FZ crystals, radiotracer 31Si, thin film deposited by sputtering and annealing in Ar ambient, sectioning by ion beam sputtering, Gaussian profiles, diffusion via self-interstitials assumed
114 115
77May1
3.2·102
4.78
1034-1244
enhanced diffusivity in B-doped CZ crystals (0.6- 1.6·1019 cm−3), radiotracer 31Si, thin film deposited by sputtering and annealing in H2 ambient, sectioning by ion beam sputtering, Gaussian profiles, diffusion via self-interstitials
115
79Het1
8.0
4.1
900-1100
p-type FZ crystals, 30Si implantation, annealing in Ar ambient, 30Si (p,γ) 31Si resonance broadening method
115
79Hir1
1.54·102
4.65
855-1175
p-type FZ crystals (1200-1400 Ωcm), 30 Si evaporation, annealing in open tube or closed ampoules filled with NH4Cl, SIMS, Gaussian profiles, no change in self-diffusion mechanism from high to low temperature observed
115
80Kal1 79Kal1
2.0·101
4.4
830-1200
n-type single crystals (10 kΩcm), 30Si implantation, vacuum annealing,30Si (p,γ) 31Si resonance broadening method, two concurrent mechanisms or one anharmonic diffusion process suggested
112 115
83Dem1
1000
n-type single crystals, 30Si implantation, annealing under 21-35 kbar hydrostatic pressure, SIMS, selfdiffusion increases with pressure, negative activation volume indicates diffusion via selfinterstitials
Si in Si 1.81·104
85Azi1
metal diffusion experiments 4.88
Lando lt -Bö rnst ein New Series III/33A
800-1300
vacancy component CVeqDV/C 0 deduced from Au diffusion within dissociative model, FZ crystals, zero or 104 dislocations/cm2, radiotracer 198Au and 199 Au with mechanical sectioning
117
64Wil1
2 Diffusion in silicon, germanium and their alloys
2-78
D0 [cm2s−1]
Q [eV]
T-range [oC]
Si in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
metal diffusion experiments (cont.)
3.0·101
4.5
700-900
vacancy component CVeqDV/C 0 deduced from Ni diffusion within dissociative model, FZ crystals, 104-105 dislocations/cm2, out-diffusion after Ni saturation, 4-point-probe
117
67Yos1
1·103
4.23
450-800
vacancy component CVeqDV/C 0 deduced from Ni diffusion within dissociative model, CZ crystals, 400-1000 dislocations/cm2, decrease of 63Ni surface radioactivity, vacancy migration energy of 1.91 eV estimated
117
67Bon1
2.26·102
5.0
450-800
vacancy component CVeqDV/C 0, reanalysis of Ni diffusion experiments by [67Bon1], additional self-interstitial component suggested
117
68see1
1.94·10−7
0.61
900-1200
vacancy component CVeqDV/C 0 deduced from Au diffusion within dissociative model, includes [73Hun1], thick FZ or other crystals, ca. 1 or 104 dislocations/cm2, radiotracer 198Au with mechanical sectioning
117
73Hun2
1000
CVeqDV/C 0 ≈ CIeqDI/C 0 = 6.3·10−17 cm2s−1, numerical analysis of Au diffusion profiles of [83Sto1]
83Mor1
83Sto1
9.14·102
4.84
800-1098
self-interstitial component CIeqDI/C 0 deduced from Au diffusion within kick-out model, FZ crystals, NAA with mechanical sectioning
6.40·102
4.80
800-1200
self-interstitial component CIeqDI/C 0 deduced from Au diffusion within kick-out model, FZ crystals, NAA and spreading-resistance
116
84Sto1 86Sto1
6·10−1
4.03
700-1000
1·10−5
900-1412
117 118 119
85tan1 83Tan1
0.4
1·10−1
2
900-1200
vacancy component CVeqDV/C 0 estimated, includes data of [64Wil1,83Mor1] self-interstitial diffusivity DI estimated, based on experiments of [79Lec1] and CIeq>CVeq at T=Tm , vacancy diffusivity DV estimated from Au solubilty results review of intrinsic point defects including oxidation enhanced/retarded dopant diffusion, Au diffusion, swirl defect formation
1.40·103
5.01
700-850
self-interstitial component CIeqDI/C 0 deduced from Pt diffusion within kick-out model, n-type epitaxial layer, Pt Schottky contacts used as diffusion source, C-V measurements, DLTS, non-erfc profiles, includes [84Man1]
116
86Man1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Si in Si (cont.)
Methods and Remarks
2-79
Fig.
Ref.
metal diffusion experiments (cont.)
6.0·102
2.44
700 & 800
self-interstitial diffusivity DI, analysis of Arimplantation gettering of Au-diffused dislocationfree Si, gettering profiles taken from [81Lec1], kick-out model
118
87Bro1
6.0·10−3
3.3
800-1200
self-interstitial component CIeqDI/C 0 deduced from Au diffusion within kick-out model, RTA and furnace annealing of Au-implanted Si, spreading resistance and RBS
116
88Cof1
4.0·103 4.0·101 2.0·10−1
5.0 4.6 1.2
700-1250 700-1250 700-1250
self-interstitial component CIeqDI/C 0 vacancy component CVeqDV/C 0 self-interstitial diffusivity DI approximate numerical analysis of Au and Pt diffusion profiles of [83Sto1, 84Sto1, 86Man1, 89Hau1], kick-out and dissociative model
116 117 118
88Mor1
1.00·103
4.94
1000-1250
self-interstitial component CIeqDI/C 0 deduced from Pt diffusion within kick-out model, FZ crystals, NAA with mechanical sectioning, spreading resistance, non-erfc profiles
116
89Hau1
989
CIeqDI/C 0 = 2.1·10−17 cm2s−1 , self-interstitial component deduced from Zn diffusion within kickout model, FZ crystals, zero or (0.5-2)·108 dislocations/cm2, spreading resistance, Hall effect
800-1200
self-interstitial diffusivity DI , FZ and CZ crystals, Au surface layer by evaporation or sputtering, RTA, spreading resistance, numerical analysis within kick-out model
1208
self-interstitial component CIeqDI/C 0 = 1.12·10−13 cm2s−1 self-interstitial diffusivity DI = 8·10−5 cm2s−1 evaluation of Zn diffusion within kick-out model, FZ crystals, zero or at least 108 dislocations/cm2, spreading resistance, temporal evolution of diffusion profiles
91Bra1
900-1200
self-interstitial component CIeqDI/C 0 deduced from Zn diffusion within kick-out model, FZ crystals, zero or at least 108 dislocations/cm2, spreading resistance, NAA with mechanical sectioning
91Grü1
770
vacancy component CVeqDV/C 0 = 2.58·10−20 cm2s−1 vacancy diffusivity DV = 2.2·10−11 cm2s−1 numerical analysis of Pt diffusion within dissociative model, FZ crystals, DLTS
91Zim3
1.03·106
6.0·102
3.22
4.79
Lando lt -Bö rnst ein New Series III/33A
89Per1
118
90Boi1
2-80
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Si in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
metal diffusion experiments (cont.) 700
vacancy component CVeqDV/C 0 = 7.14·10−22 cm2s−1 vacancy diffusivity DV = 2.1·10−12 cm2s−1 numerical analysis of Pt diffusion within dissociative model, FZ wafers, DLTS with step etching, inverse U-shaped profiles, influence of initial non-equilibrium vacancy concentration
91Zim2
2.58·10−2 1.0·103 1.1·103 4.0·10−1
0.965 4.80 2.84 4.00
800-1100 800-1100 700-950 700-950
self-interstitial diffusivity DI self-interstitial component CIeqDI/C 0, recalculated vacancy diffusivity DV vacancy component CVeqDV/C 0 recalculated numerical analysis of Au profiles within kick-out model includes [84Sto1, 86Sto1], simulation of Pt profiles within kick-out and dissociative model, FZ crystals, DLTS on bevel plane or after etching
3.15·104
4.89
910-1085
self-interstitial component CIeqDI/C 0, recalculated data taken into account Pt solubility data of [89Hau1], B-doped wafers Pt-implanted through SiO2 window, RTA, lateral profiles, two-dimensional spreading resistance
3.0·103 8.6·10−2 5.1·101 3.0·10−2
4.95 3.8 1.77 1.8
870-1208 870-1000 870-1208 870-1000
self-interstitial component CIeqDI/C 0 vacancy component CVeqDV/C 0 self-interstitial diffusivity DI vacancy diffusivity DV numerical analysis of Zn diffusion within kick-out and dissociative model, FZ crystals, zero or at least 108 dislocations/cm2, furnace-based RTA combined with quenching, spreading resistance, full evolution of Zn incorporation with time
116 117 118 119
95Bra1 94Bra1 94Bra2
2.65·1011 2.64·106
4.44 4.00
900-1100 900-1100
self-interstitial diffusivity DI vacancy diffusivity DV numerical analysis of Au diffusion within kick-out and dissociative model, includes data of [84Sto1, 92Zim2], FZ crystals, RTA, spreading resistance
118 119
95Gha1
1100
DI = 2.47·10−3 cm2s−1, self-interstitial diffusivity, reanalysis of Zn diffusion profiles given by [93Bra2, 94Bra2], kick-out mechanism, includes trapping of self-interstitials due to substitutional carbon
118 119
92Zim1 92Zim2 91Zim1
93Cof1
95Gos1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Si in Si
Methods and Remarks
2-81
Fig.
Ref.
enhanced/retarded dopant diffusion experiments 600
DV = 3.5·10−4 cm2s−1, vacancy diffusivity, n-type single crystals, p-type layer by B diffusion, annealed under proton or H2 beam bombardment, pn-junction staining, vacancy mechanism, enhanced DB
72Min1
1.47
600-900
migration enthalpy of neutral vacancy, CZ crystals pre-diffused with As, B and P, annealing in vacuum under proton irradiation, intrinsic conditions, spreading resistance and pnjunction staining, flux-dependent enhanced diffusion due to excess vacancies
78Mas1
2.08·10−2 4.7
3.89 4.40
850-1100 850-1100
self-diffusivity CVeqDV/C 0 via neutral vacancies self-diffusivity CIeqDI/C 0 via neutral self-interstitials numerical analysis of B diffusion profiles given by [72Quo1], includes various vacancy and selfinterstitial assisted mechanisms
84Mat1
3.75·10−9
0.13
700 & 800
self-interstitial diffusivity DI , CZ and FZ crystals, P implantation and annealing at 900 oC, epitaxial layer growth, selected area Ar implantation, annealing in N2, spreading resistance, pn-junction staining, enhanced P diffusion, Ar implant damage is source of self-interstitials
120
85Bro2
2.8·101
2.3
950-1200
lower bound on self-interstitial diffusivity DI , recalculated from given data, FZ crystals, P- or Sb implantation, epitaxial layer growth, wet oxidation of selected areas, spreading resistance, selfinterstitial injection causes enhancement of DP and retardation of DSb
120
85Gri1
1100
self-interstitial diffusivity DI = 2·10−9 cm2s−1, modeling of oxidation-retarded Sb diffusion, experimental data of [83Miz2], physical model for oxidation-enhanced and retarded diffusion
86Sch1 85Sch1
1100
self-interstitial diffusivity DI = 9·10−10 cm2s−1 probably affected by traps, FZ crystals, P implantation, etching of membranes, selective capping with SiO2/Si3N4, dry oxidation, pn-junction staining, spreading resistance, enhanced DP due to self-interstitial injection
87Ahn1
Lando lt -Bö rnst ein New Series III/33A
2-82
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Si in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
enhanced/retarded dopant diffusion experiments (cont.) 1100
self-interstitial diffusivity DI = 2.62·10−9 cm2s−1 vacancy diffusivity DV = 4.5·10−8 cm2s−1 numerical analysis of oxidation-enhanced diffusion of P (self-interstitial supersaturation) and oxidationretarded diffusion of Sb (vacancy undersaturation), experimental data from [81Miz1, 83Miz2]
87Bra1
1100
FZ and CZ crystals, etching of membranes, P implantation, capping with SiO2/Si3N4, backside oxidation in dry O2, pn-junction staining, different results in CZ and FZ crystals, DI retardation by traps suggested
87Gri2
1100
enhanced vacancy diffusivity DV = 3·10−10 cm2s−1 due to nitride-film stress, Sb-implanted FZ crystals, SiNx capping by chemical vapour deposition, annealing in Ar, pn-junction staining
88Ahn1
1100
self-interstitial diffusivity DI = 6.0·10−9 cm2s−1 vacancy diffusivity DV = 5.3·10−9 cm2s−1 numerical analysis of oxidation-enhanced (B, P) and -retarded (Sb) diffusion, data of [82Miz1,83Miz1]
90Bud1
3.35·10−1
1.86
460-1200
self-interstitial diffusivity DI : includes [85Gri1], B-doped CZ single crystals, 1.3·1018 oxygen/cm3, 2·1017 or < 3·1015 carbon/cm3, oxygen thermal donor formation at 460 °C and 500 oC in N2 ambient, spreading resistance, oxygen out-diffusion due to self-interstitial diffusion suggested, no carbon effect
120
90Wij2
3.60·102
4.8
700-1050 800
self-interstitial component CIeqDI/C 0 self-interstitial diffusivity DI ≤ 10−11 cm2s−1 epitaxial wafers with heavy B or As background doping , P or Sb implantation, RTA and furnace annealing, SIMS, transient enhanced DP , no transient enhanced DSb , modeling includes excess self-interstitials due to implantation
120
91Gil1
2.04 4.6 3.00·102
4.40 4.43 4.77
900-1100 900-1100 800-1098
self-diffusivity CVeqDV/C 0 via neutral vacancies self-diffusivity CVeqDV/C 0 including all charge states self-diffusivity via neutral self-interstitials deduced from CIeqDI/C 0 given by [83Sto1] numerical analysis of B and P profiles and reanalysis of Au profiles from [84Sto1, 86Sto1]
120
92Mat1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Si in Si (cont.)
1.0·102
3.1
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-83
Fig.
Ref.
enhanced/retarded dopant diffusion experiments (cont.) 1100
self-interstitial diffusivity DI = 4.1·10−8 cm2s−1 P-doped FZ crystals, P implantation, epitaxial layer growth, selective capping with SiO2/Si3N4, dry O2 ambient, spreading resistance, decrease of oxidation-enhanced DP with epi-layer depth, self-interstitial supersaturation
750-900
self-interstitial diffusivity DI, B-doped superlattices grown by low-temperature MBE, annealing in dry O2, SIMS, B-spike width decreases with increasing depth, low DI probably due to trapping not caused by B atoms (see [95Gos1])
900
self-interstitial component CIeqDI/C 0 ≈ 1.72·10−18 cm2s−1 analysis of reduced oxidation-enhanced DB in samples containing extended defects, data from SIMS and TEM measurements of buried B layers by [93Rot1]
93Hua1
1100
self-interstitial diffusivity DI = 4.2·10−10 cm2s−1 vacancy diffusivity DV = 2.1·10−10 cm2s−1 analysis of oxidation-enhanced (P) and -retarded (Sb) diffusion from [82Miz1, 81Miz1]
93Oki1
1100
self-interstitial diffusivity DI = 2.4·10−9 cm2s−1 vacancy diffusivity DV = 2.1·10−10 cm2s−1 analysis of oxidation-enhanced (P) and -retarded (Sb) diffusion from [82Miz1, 81Miz1]
93Oki2 94Oki1
analysis of oxidation-enhanced DB decreasing with depth in MBE-grown films, modeling of selfinterstitial diffusion affected by immobile traps
94Cow1
750-900
vacancy diffusivity DV(850 °C)=2.5·10−13 cm2s−1 Sb- and B-doped buried layers grown by MBE, vacuum annealing, RBS for Sb and SIMS for B profiling, grown-in vacancy supersaturation causes enhanced DSb , retarded DB due to self-interstitial undersaturation
94Gos1
670 730 790
self-interstitial diffusivity DI ≈ 6.4·10−15 cm2s−1 self-interstitial diffusivity DI ≈ 1.1·10−13 cm2s−1 self-interstitial diffusivity DI ≈ 1.3·10−12 cm2s−1 B-doped superlattices grown by MBE, damage by Si implantation, vacuum annealing, SIMS, enhanced B diffusion and B clustering caused by self-interstitial injection, DI affected by traps, binding energy about 2eV
93Aga1
120
93Gos1
95Sto1
2-84
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Si in Si
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
investigations of growth/shrinkage of extended defects 4.1
970-1070
CZ crystals, P-doping (0.005-200 Ωcm) or B-doping (0.005-5 Ωcm), dislocation loops formed by Ne-ion radiation damage, TEM, shrinkage of dislocation loops during annealing, intrinsic point defects responsible for self-diffusion act as acceptors
5.2
1100-1200
activation energy for stacking-fault shrinkage, P- and B-doped CZ crystals, dry oxidation at 1200 oC to grow stacking faults, annealing in dry N2, preferential etching, assumes stacking-fault shrinkage due to self-diffusion via vacancies, enhanced shrinkage by dopant diffusion
≥ 2·10−3
3.6
1120-1370
FZ crystals deformed by compression, measures the stress at the beginning of stage III of the strain-hardening curve, dynamical recovery controlled by self-diffusion via a vacancy mechanism
121
78Sie1 79Bri1
8.6·105
4.0
1100-1200
self-interstitial diffusivity DI, CZ crystals, optical microscopy, B implantation introduces nucleation sites for stacking faults, front surface capped with Si3N4/poly-Si/SiO2, growth of stacking faults at the front surface during backside oxidation
121
83Tan2
2.2·102
4.4
850-1200
vacancy component CVeqDV/C 0, CZ crystals, 8·1015 carbon/cm3, two-step annealing to nucleate and grow stacking faults, TEM, diffusional growth driven by vacancies in undersaturation
121
83Wad1
4.3
950-1100
slow shrinkage of oxidation-induced stacking faults (OSF) attributed to Si self-diffusion, CZ crystals, Si implantation for OSF nucleation, dry oxidation, annealing in N2, etching to reveal OSF lengths, also fast OSF shrinkage observed
2.86
1080-1270
vacancy diffusivity DV, CZ crystals, 7-10·1017 oxygen/cm3, 2·1016 carbon/cm3, two-step annealing for oxide precipitation and nucleation/growth of stacking faults, successive etching, optical microscopy, depth profile of stacking fault radius, growth induced by vacancies in undersaturation
5.8
2.57·102
121
74San1
76Has1
85Nis1
121
85Wad2
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Si in Si (cont.)
1.46·103
1.2·1013 7.0·105 4.84·105 4.37·10−2
Methods and Remarks
2-85
Fig.
Ref.
investigations of growth/shrinkage of extended defects (cont.) 1000
self-interstitial diffusivity DI ≥ 0.5·10−6 cm2s−1, CZ crystals, 14.7-15.6·1017 oxygen/cm3, 0.1-0.23·1017 carbon/cm3, pre-annealing at 650 oC, thermal oxidation in different ambients, preferential etching, oxygen precipitation decreases with increasing SiO2 growth rate due to self-interstitial injection, decrease of bulk microdefects by increasing carbon concentration
4.96
900-1400
self-interstitial component CIeqDI/C 0, modeling of aggregation of intrinsic point defects during CZ crystal growth, includes [90Wij1]
4.8
800-1290
self-interstitial component CIeqDI/C 0 deduced from stacking-fault shrinkage, FZ crystals, Au diffusion from dried solution of HAuCl4 to grow stacking faults, etching techniques, X-ray topography
7.2 4.45 2.8 0.45
900-1000 900-1000 900-1000 900-1000
self-interstitial component CIeqDI/C 0, recalculated vacancy component CVeqDV/C 0 , recalculated self-interstitial diffusivity DI vacancy diffusivity DV numerical analysis of the distribution of grown-in defects in CZ crystals, Cu-decoration method, assumes entropy barrier against pair annihilation of self-interstitials and vacancies
1000
self-interstitial diffusivity DI = 5.9·10−6 cm2s−1, CZ crystals, pre-annealed at 650 oC, thermal oxidation, RTA, etching to reveal depth profiles of oxygen precipitates, self-interstitial injection suppresses oxygen precipitation
90Yam1
121
92Wij1
93Vys1
121
94Hab1
94Yam1
Ge in Si 6.26·105
5.28
1150-1350
radiotracer 71Ge, mechanical sectioning
125
57Pet1
1.54·103
4.65
1200-1380
CZ crystals, radiotracer 71Ge with mechanical sectioning, strain energy due to Ge incorporation < 0.013 eV
125
73Vay1 75Vay1
950
bulk diffusivity D = 8·10−17 cm2s−1 pipe diffusivity D = 5·10−15 cm2s−1 dislocated single crystals, radiotracer combined with serial sectioning
Lando lt -Bö rnst ein New Series III/33A
74Pan1
2-86
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
Ge in Si (cont.) 6.2·104
5.16
1100-1265
Dge for C0 < 1022 cm−3, radiotracer 71Ge, enhanced Dge for C0 above dislocation generation threshold (1022 Ge/cm3), retarding effect of simultaneous B diffusion, dislocation model proposed
125
74Pav2
1.54·103 2.7·10–2 4.6·10–2
4.65 3.0 3.0
1200-1380 1208-1380 1208-1380
intrinsic diffusivity diffusivity under B doping (4.5·1019 cm–3) diffusivity under P doping (1.1·1020 cm–3) CZ crystals, radiotracer 71Ge with mechanical sectioning, enhanced DGe both in n- and p-type Si, interstitialcy mechanism, amphoteric nature of Si self-interstitials
125
75Vay1
2.505·103 3.5·10−1
4.97 3.93
1030-1300 855-1010
B-doped ((0.6-1.6)·1019 cm−3) FZ crystals As-doped ((2-6)·1019 cm−3) CZ crystals annealing in H2 ambient, radiotracer 71Ge with sputter-sectioning, Gaussian profiles, DGe enhanced by B- and As-doping for T > 900 oC, DGe retarded by B-doping for T < 900 oC, energy levels for selfinterstitials evaluated, at T > 1000 oC interstitialcy mechanism, at T < 1000 oC vacancy mechanism
112 123 125
79Het1
7.55·103
5.08
1100-1300
P-doped CZ crystals, Ge-doped SiO2 film source, annealing in N2 or O2/N2 ambient, SIMS
122 125
82Ogi1
989-1225
single crystals, Ge surface layer, SIMS profiling of various Ge isotopes, isotope effect compatible with both vacancy and interstitialcy mechanism
876-1388
P-doped (3-10 Ωcm) FZ crystals, evaporated thin Ge films, SIMS, DGe independent of vacuum or H2 annealing, single diffusion mechanism proposed
1050-1300
p-type CZ crystals, Ge implantation above amorphization threshold, RTA, RBS, TEM, no enhancement of DGe during RTA, Ge precipitation in the amorphous region
1050-1200
DGe in lightly B-doped samples, lightly (~1016 cm−3) or heavily (~1018 cm−3) B-doped mono- and polycrystalline crystals, Ge deposition by sputtering, annealing in H2 ambient, SIMS, enhanced DGe in lightly doped Si and in heavily doped Si at 1000 oC, singly charged and neutral vacancies suggested
1.03·105
1.38·105
5.33
5.39
83Söd1
112 125
84Dor1 83Dor1 86Hol1
125
86Bou1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-87
T-range [oC]
Methods and Remarks
Fig.
Ref.
1050
DGe = (5.3 ± 0.4) ·10−16cm2s−1, p-type (50 Ωcm) CZ crystals, buried Ge-doped epitaxial layer grown by MBE, annealing in NH3 with or without SiO2 capping, SIMS, spreading resistance, DGe enhanced by self-interstitial and vacancy injection, fI = 0.30-0.40
124
89Fah1
1050-1230
FZ crystals, evaporated Ge layer, SIMS, Gaussian profiles, isotope effect E = 0.25 ± 0.03, also diffusion under high pressure, activation volume V/Ω = −0.52 ± 0.15, intersticialcy mechanism
102
89Söd1
1000-1100
FZ crystals, P doping ≤ 5·1020 cm−3 by implantation, Ge implantation, RTA, SIMS, RBS, Hall effect, enhanced diffusivity for P doping >1020 cm−3
93Nyl1
1215-1294
crystals doped by diffusion or during growth up to 1021 cm−3 (n-type) or 3.9·1018 cm−3 (p-type), electroplated layer source, radiotracer 113Sn with mechanical sectioning, DSn nearly independent of doping, interchange mechanism via interstitial activated complex or formation of Sn-neutral vacancy pairs
66Mil1
Ge in Si (cont.)
Sn in Si
3.2·101
4.25
1050-1294
includes data of [66Mil1] single crystals, Sn-, P-, and B-doped powder sources, closed ampoule annealing, NAA of Sn and P, chemical sectioning, DSn not affected by B co-diffusion but enhanced by P co-diffusion, vacancy mechanism
127
68Yeh1
5.4·10−2
3.5
1100-1200
P-doped epitaxially grown Si crystals, Sn-doped oxide source, RBS + channeling, mainly on substitutional site (89-98%), Sn diffusion enhanced by P diffusion, solubility limit 6-8·1019 cm−3
126 127
74Aka1
1200
D = 2·10−13 cm2s−1 (undoped sample), undoped, B-doped (1·1020 cm−3), and P-doped (1.5·1020 cm−3) single crystals, deposition of metallic Sn film, ampoule annealing, radiotracer 119mSn with serial sectioning, Mössbauer spectroscopy, substitutional impurity, no doping dependence observed, Sn nearly behaves like host atoms
Lando lt -Bö rnst ein New Series III/33A
76Ser1
2-88
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Methods and Remarks
1215
D0 = 4.6·10−14 cm2s−1 D− = 6.7·10−14 cm2s−1 D+ = 7.2·10−15 cm2s−1 evaluation of [66Mil1] in terms of Sn diffusion via neutral, negatively and positively charged vacancies
75sha1
700-1050
p-type FZ crystals, Sn implantation, Cmax = 1·1020 cm−3, RTA in N2 ambient, Mössbauer and RBS analysis, no redistribution of as-implanted profiles, precipitation for CSn > 1·1021 cm−3
86Wey1
1000 & 1050
FZ crystals, P doping 1.7·1020 cm−3 and 4.2·1020 cm−3 by implantation and drive-in at 1075 °C, 119Sn implantation, RTA in Ar ambient, Hall and resistivity measurements, RBS, D increases with about (n/ni)4, Mössbauer spectrum for CP > ca. 2·1020 cm−3 indicates new Sn defect complex
1100
FZ crystals, evaporated Sn surface with capping, drive-in, removal of capped layers, additional annealing of repeatedly capped and bare samples in NH3, SIMS, enhanced DSn during nitridation, vacancy component of DSn increased by vacancy injection
89Mar1
1000-1100
FZ crystals, P doping ≤ 5·1020 cm−3 by implantation, Sn implantation, RTA, SIMS, RBS, Hall effect, enhanced diffusivity above vacancy-percolation limit
93Nyl1 89Nyl1
1000-1200
n-type single crystals, Sn implantation, RTA to recrystallize armorphous layer, RTA or furnace annealing in Ar ambient, SIMS, Gaussian profiles
750
single crystals, Pb implantation up to 180 keV, RBS analysis of implanted and annealed samples, Pb accumulation near the surface, in-diffusion depth correlated to thickness of reordered layer
78Chr1
565
single crystals, Pb implantation, RBS analysis of Pb redistribution, out-diffusion correlated to recrystallization of amorphous layer
78Hsi1
Pb implanted Si, RTA, RBS, Pb precipitates and local stress retard recrystallization, polycrystalline structure, grain boundaries as diffusion paths mediate Pb redistribution
87Shi2
Sn in Si (cont.)
5.0·103
4.91
[Ref. p. 2-196
Fig.
128
112 127
Ref.
88And1
94Kri1
Pb in Si
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2-89
2.2.1.15 Solute elements of group VA (nitrogen group). (See Figs. 129-191, p. 171) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
0.87
3.29
around 1200
single crystals, annealing after implantation, pn-junction staining, Hall effect
130
68Cla1
3.0·10−2
2.63
700-850
p-type FZ crystals, diffusion in N2 flow, repeated Ne-ion bombardment with defect anneal, n-type inversion-layer depth measurement, thermoprobe + electrochemical sectioning, interstitial diffusion of N2 molecule, see review [76Pav1]
130
75Den1
1000
single crystals, N2 implantation through SiO2 layer, annealing in N2 ambient, CPAA, N accumulation at Si/SiO2 interface
83Jos1
> 1200
single crystals, high-dose N implantation, furnace and pulsed-laser annealing, RBS + channeling, TEM, IR absorption, Si3N4 formation
85Smi1
1025-1075
FZ crystals, high-dose N implantation, annealing in dry N2, broadening of implanted layer, SIMS, defect formation observed
86Bod1
800-1200
homogeneously N-doped FZ crystals, out-diffusion in N2 ambient, SIMS, IR absorption, migration as N-N pairs
1270
D = 2·10−6 cm2s−1, FZ and CZ crystals, diffusion from N2 ambient, quenching vs. slow cooling, shallow donor formation upon isochronal annealing 600-700 oC due to N-O complexes, spreading resistance, 4-point probe
89Har1
800-1050
FZ crystals, N implantation, RTA in Ar ambient, SIMS, anomalous profile broadening, coimplantation with C and/or O also investigated
89Hoc1
900-1200
CZ crystals: annealing in O2 or oxide precipitation treatment, FZ crystals: B implantation, diffusion from N2 ambient, SIMS, N accumulation at SiO2/Si interface, O precipitates or implantation damage, migration as N-N pairs
89Ito2
ca. 1410
D = ca. 1·10−6 cm2s−1, CZ crystals capped with Si3N4, high-speed laser melting, SIMS, out-diffusion from an exponential-type N profile
93Wil1
N in Si
2.7·103
2.8
Lando lt -Bö rnst ein New Series III/33A
129 130 131
88Ito1
2-90
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
temperature dependence and mechanism of diffusion
0.001
2.51
1050-1250
single crystals, elemental P source, pn-junction measurement, sheet resistance, Hall effect, C0(1250 oC) = (3-6)·1020 cm−3
153
54Ful2
10.5
3.69
950-1235
B-doped single crystals, P2O5 source in closed ampoule, 4-point probe + mechanical sectioning, pn-junction staining, C0 = 0.6-9·1021 cm−3
153
56Ful1
1185-1300
D(1250 oC) = 3·10−12 cm2s−1, elemental P source in Ar ambient, radiotracer + mechanical sectioning, influence of oxygen dissolved in Si investigated, see [74har1]
59Har1
1.85·10−4
2.23
800-1300
P2O5 source in oxidizing ambient, sheet resistance, C0 = ca. 1021 cm−3, D0 and Q recalculated by [74har1]
153
59Sah1
1·10−2
2.73
927-1310
C0 > 6·1020 cm−3, D0 and Q recalculated by [74har1]
153
62Wil1
0.12
2.96
1180-1330
elementary P source, radiotracer + electro-chemical sectioning, C0 = (2-9)·1019 cm−3, see also [74har1]
153
62Yan1
1175
D = 2.5·10−12 cm2s−1 for C0 < 2.6·1019 cm−3, predeposition from doped oxide and drive-in under Ar, radiotracer + electrochemical sectioning
64Sch1
1000
D = 2.9·10−14 cm2s−1 for C0 = ca. 1021 cm−3, P3N5 source in N2 flow, sheet resistance + electrochemical sectioning
66Nic1
1200
D = 2.65·10−12 cm2s−1 for C0 = ca. 4·1020 cm−3, P-doped Si source in closed ampoule, NAA + chemical sectioning
68Yeh1
49.3 2.49·10−5
3.77 2.0
820-1100 820-1100
slow diffusivity component, molecular SiP fast diffusivity component, vacancy mechanism single crystals, POCl3 source in N2/O2 flow, 4-point probe + electrochemical sectioning, transition region connects constant CP near surface with normal tail region
155
69Tsa1
2.0·10−2
2.93
1100-1275
single crystals, drive-in under O2 atmosphere after pre-deposition, 4-point probe, pn-junction staining, no effect of surface orientation, C0 = (1.08-8.5)·1019 cm−3, D0 and Q from [74har1]
154
70Cha1
6·10−6
1.90
850-1150
single crystals, PH3 source in Ar/N2/O2 flow, 4-point probe, pn-junction measurement
153
70Hsu1
2.9
975-1100
PH3 source in oxidizing ambient, see [74har1]
70Kes1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
2-91
Fig.
Ref.
temperature dependence and mechanism of diffusion (cont.)
1.1
3.4
900-1200
test wafer placed between neutron-activated Pdoped source wafers, evacuated closed ampoule, radiotracer 32P and 4-point probe + chemical sectioning, SiO2 and Si3N4 masking investigated
132 154
71Frä1
7.4·10−2
3.30
1130-1405
P-doped epitaxial layers on FZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, radiotracer 32P + chemical sectioning, P-vacancy pair mechanism, C0 < 8·1018 cm−3, also isoconcentration diffusion
154 161
71Gho3 70Gho2
20.23
3.87
1100-1250
CZ crystals, P-doped Si powder source in vacuum, spreading resistance, monotonic time-increase of C0, surface-limited intrinsic diffusivity
133 154
72Gho1
1·10−2
2.87
1000-1200
single crystals, P-doped oxide sources in N2, pnjunction staining, sheet resistance, D0 and Q recalculated by [74har1]
154
72Kam1
950
D = 8·10−15 cm2s−1, single crystals, 5·103-5·104 dislocations/cm2, elemental vapour source, radiotracer + sectioning, analysis accounts for diffusion along dislocations
74Pan1
1154-1252
D0(1215 oC) = 1.4·10−12 cm2s−1 D−(1215 oC) = 2.4·10−12 cm2s−1 evaluation of [66Mil1] in terms of P diffusion via neutral and negatively charged vacancies
75sha1
950-1200 950-1200
diffusivity D0 via neutral vacancies diffusivity D− via negatively charged vacancies evaluation of [73Mak1]
75sha1
1100
D = 1.33·10−13 cm2s−1, annealing after low-dose implantation, profile broadening agrees with theoretical predictions, see [86wöh1]
76Sat1
875-1290 800-1100 875-1200
D0 via neutral vacancies equals total intrinsic DP D− via singly negatively charged vacancies D2− via doubly negatively charged vacancies single crystals, POCl3 source in N2/O2 or Ar/O2 flow, 4-point probe + electrochemical sectioning, SIMS, model based on dissociating P+-vacancy pairs, fitting includes [72Gho1, 73Mak1, 74Mat1]
81 131 134 135 136 159
77Fai2 77fai1 81fai1
1000-1300
re-examination of data on oxidation- and radiationinfluenced diffusion and emitter-push effect
151
79Gös1
900-1100
model based on dissociating P-vacancy pairs and P2-vacancy complexes, data fitting includes [74Mat1, 74Yos1, 79Yos1]
137
83Yos1 95Yos1 95Yos2
4.5·10−2 92
3.85 4.44 44.2
3.19 4.14
3.66 4.0 4.37
Lando lt -Bö rnst ein New Series III/33A
2-92
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
1.89
3.64
Fig.
Ref.
temperature dependence and mechanism of diffusion (cont.) 877-1100
analytical model based on similarity methods, data fitting includes [69Tsa1, 77Fai2]
86Jep1
850-900
models based on interaction of P with self-interstitials, data fitting includes [74Yos1, 82Nob1]
86Mor1 86Mor2 87Mul1
900-1000
model based on pairs of P with self-interstitials and vacancies, fitting of data: [74Yos1, 79Yos1, 76Mat1]
92Dun1
911-1227
CZ crystals, P implantation through oxide, RTA for activation, furnace annealing in Ar flow, SIMS, comparison with Si-TaSi2 eutectic crystals
900-1200
model based on pairs of P with self-interstitials and vacancies, fitting of data: [74Gho1, 74Mat1, 76Mat1, 74Yos1, 79Yos1]
P in Si
4.8 0.6 5·10−2 3·10−3 0.7 0.44 3·10−2 8.7·10−4
Methods and Remarks
[Ref. p. 2-196
154
93Pel1
95Gha2
effects of high concentration and heavy doping
3.7 3.4 3.0 2.6 3.4 3.3 2.9 2.4
1200-1250
solar-grade crystals, sheet resistance and Hall effect + sectioning, C-V measurements, C0 = 5·1020 cm−3, non-erfc profiles
61Sub1
800-1114
D(1000 oC) = 4·10−13 cm2s−1 for C0 < 1020 cm−3, CZ crystals, pre-deposition from P2O5, also drive-in, 4-point probe and NAA + electrochemical sectioning, C-dependent diffusivity, flat profile near surface
61Tan1
1200-1300 1200-1300 1200-1300 900-1300 1200-1300 1200-1300 1200-1300 900-1300
C0 = 3·1018 cm−3, CB = 5·1014 cm−3, drive-in C0 = 3·1019 cm−3, CB = 5·1014 cm−3, drive-in C0 = 3·1020 cm−3, CB = 5·1014 cm−3, drive-in C0 = 1.1·1021 cm−3, CB = 5·1014 cm−3, pre-deposition C0 = 3·1018 cm−3, CB = 1·1017 cm−3, drive-in C0 = 3·1019 cm−3, CB = 1·1017 cm−3, drive-in C0 = 3·1020 cm−3, CB = 1·1017 cm−3, drive-in C0 = 9.5·1020 cm−3, CB = 1·1017 cm−3, pre-deposition B-doped crystals, pre-deposition from P2O5/CaO glass, drive-in under dry O2, 4-point probe, pnjunction staining, for D0 see [71Gho3]
156
62Mac1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
2-93
Fig.
Ref.
effects of high concentration and heavy doping (cont.)
6 3.2·10−5 6·10−5 2.4·10−4 6.8·10−5
3.7 2.28 2.0 2.0 1.8
1100-1250 1100-1250 1150-1200 1100-1250 1100-1250
C0 = (2-8)·1018 cm−3, CB = 1·1016 cm−3, 4PP C0 = ca. 1021 cm−3, CB = 1-40·1016 cm−3, 4PP C0 = ca. 1021 cm−3, CB = 4.2·1019 cm−3, 4PP C0 = ca. 1021 cm−3, CB = 3.8·1020 cm−3, 4PP C0 = ca. 1021 cm−3, various CB or CP, radiotracer single crystals, H4P2O7 source in N2 flow, 4-point probe (4PP) or radiotracer 32P + chemical sectioning, pn-junction method, D0 and Q recalculated, see [71Gho3]
140 157
62Mae1
2.8 9.3 2.9·109 4.1·1013 7.6 77.8 3.6·104
3.46 3.74 5.94 7.22 3.61 3.86 4.63
1100-1285 1100-1285 1100-1285 1100-1285 1112-1320 1112-1320 1112-1320
B background doping 3·10 17 cm−3 B background doping 4.4·1018 cm−3 B background doping 1.2·1019 cm−3 B background doping 3·1019 cm−3 Ga background doping 2·1017 cm−3 Ga background doping 2·1018 cm−3 Ga background doping 1.4·1019 cm−3 elementary P or P2O5 source, radiotracer method, C0 = (5-7)·1020 cm−3, see [74har1]
158
63Moc1
1154-1252
crystals doped by diffusion or during growth up to 6.3·1019 cm−3 (n-type) or 5.0·1018 cm−3 (p-type), compound vapour source, radiotracer 32P + mechanical sectioning, doping-dependent DP, vacancy mechanism
66Mil1
970
CZ crystals, annealing in O2 after pre-deposition, pn-junction staining, NAA + electrochemical sectioning, TEM, X-ray topography, precipitate and dislocation formation at high C0, retarded DP in tail region
68Duf1 68Duf2
1000-1200 1000-1200
C0 = 5·1018 cm−3, see also [74har1] C0 = 2·1020 cm−3, see also [74har1] CZ crystals, P-doped oxide source in N2, 4-point probe + electrochemical sectioning, pn-junction staining, high-concentration effects
970-1250
modeling of enhanced DP at high CP based on plastic flow involving dislocation movement and vacancy generation, data of [68Duf1, 64Mae1]
1000-1200
single crystals, 4·103 dislocations/cm−2, P2O5 source in Ar ambient, radiotracer 32P + chemical sectioning, C0(1200 oC) = 2.5·1018-1021 cm−3, DP increases with increasing C0
6.7 1.82·10−4
1·103
3.74 2.31
4.28
Lando lt -Bö rnst ein New Series III/33A
155
70Bar1
70Tha1 70Tha2 153
70Usk1
2-94
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of high concentration and heavy doping (cont.) 450-900
CZ crystals, pre-deposition from POCl3, annealing in N2 or H2, sheet resistance + electrochemical sectioning, Hall effect, flat near-surface zone, fast penetration of tail region, temperature dependence of kink concentration
71Sch1 72Sch1
1069 & 1152
D(1069 oC) = 4.8·10−13 cm2s−1 for C0 = 6·1018 cm−3, P2O5 source in carrier gas flow, NAA, DP increases with increasing C0 and background donor level, see also [86wöh1]
72Hei1
1091
D = 4·10−14 cm2s−1 at low concentration, single crystals, P-doped epitaxial layer, annealing in N2 with oxide cap, spreading resistance, weak C-dependence observed
72Mat1
900-1300
theoretical C-dependence of DP based on electric field and plastic deformation, extends and modifies [70Tha1, 70Tha2]
73Jai1
5.3 0.39
3.69 3.12
950-1300 950-1200
intrinsic diffusivity including [62Mac1, 62Mae1] isoconcentration diffusivity at CP = 4.5·1020 cm−3 CZ crystals untreated or long-time P pre-diffused, Si(P) powder source in vacuum, NAA or radiotracer 32 P + electrochemical sectioning, extrinsic DP proportional to electron density
135 154 155 159 160
73Mak1
3.4·10−5
2.03
700-1200
Boltzmann-Matano analysis of literature data, lowconcentration diffusivity in the presence of high C0 values
81 159
74Lee1
700-1100
single crystals, P-doped oxide source in N2, sheet resistance + electrochemical sectioning, enhanced DP due to high C0, no dislocations
136 137
74Mat1
900
CZ crystals, oxide layer source with various P doping levels, annealing in N2, 4-point probe or NAA + electrochemical sectioning, C0-dependent DP, enhancement due to dissociating P-vacancy pairs extends at least 20 µm deep
79 136 137
74Yos1 77Yos1 79Yos1
900 & 1100 P-diffused CZ crystals with epitaxial layer, Cmax = 5·1019 cm−3, annealing in N2, NAA + chemical sectioning, pn-junction staining, Fermilevel and electric-field effects
75Mat1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.) 4.00 2.49 2.24 2.14
Fig.
Ref.
effects of high concentration and heavy doping (cont.) 900-1150 900-1150 900-1150 900-1150
C0 = 3.5·1018 cm−3, intrinsic conditions C0 = 7.0·1019 cm−3, extrinsic conditions C0 = 1.8·1020 cm−3, extrinsic conditions C0 = 5.0·1020 cm−3, extrinsic conditions single crystals, oxide layer source with various P-doping levels, annealing in N2, 4-point probe + electrochemical sectioning, excess vacancies due to Fermi-level effect
1086-1132
numerical analysis of high-concentration profiles, includes data of [70Tha1, 70Tha2]
850-1000
P-implanted CZ crystals, damage anneal by laser, furnace annealing in N2, differential Hall effect, flat carrier density near surface, precipitation leading to enhanced tail penetration, P solubility from [77Mas1] included
138
82Nob1
900 900 1100 1100
D0 = 7.33·10−16 cm2s−1, D− = 2.93·10−17 cm2s−1, D2− = 3.73·10−16 cm2s−1 D0 = 1.43·10−13 cm2s−1, D− = 9.31·10−15 cm2s−1, D2− = 3.64·10−14 cm2s−1 CZ crystals, B doping (3-40)·1019 cm−3 or As doping 2·1014-3·1019 cm−3, low-dose P implantation + damage anneal, diffusion in N2, SIMS, DP via neutral, negative, and double-negative defects
143
93Joh2
D0 via neutral vacancies D− via singly negatively charged defects FZ crystals, heavy doping by diffusion: CB = 1.6-5.0·1019 cm−3 or CAs = 3.1-18·1019 cm−3, low-dose P implantation through oxide film + activation anneal, diffusion in N2, SIMS, B-P pairing for n < ni included D0 via neutral vacancies D− via singly negatively charged defects analysis based on same extrinsic data [95Wit1] but combined with intrinsic DP from [86Dun1, 92Jen1, 81fai1]
2.1·10−4 4.7·10−1
2.65 3.50
915-1105 915-1105
1.0·102 3.6·10−2
4.10 3.22
915-1105 915-1105
P in Si 2.2
Methods and Remarks
2-95
137
76Mat1
79Ara1
95Wit1
effects of surface reactions or ambient 3.5 2.5
Lando lt -Bö rnst ein New Series III/33A
1000-1200 1000-1200
drive-in diffusivity in N2 ambient drive-in diffusivity in oxidizing ambients CZ (111) crystals, pre-deposition from POCl3 source, pn-junction staining, sheet resistance + electrochemical sectioning, C0 = ca. 5·1019 cm−3, oxidation-enhanced DP
154
73Mas1
2-96
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
6
0.6 3.7·10−5
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1100
CZ (111) crystals, pre-deposition from POCl3, drive-in under N2, N2/O2, dry O2, or steam, pn-junction staining, sheet resistance, enhancement ∆DP depends on oxidation rate and ambient but not on depth, interstitialcy mechanism
142
76Mas2
1000-1150
single crystals, pre-deposition from doped oxide in N2, drive-in under HCl-added dry or wet O2, pn-junction staining, sheet resistance, HCl reduces oxidation-enhanced DP, effect of surface orientation
141
76Nab1
900-1200
DP in inert ambient agreeing with [62Mae1] CZ crystals, low-dose P implantation, annealing in inert or dry O2 ambient, spreading resistance, oxidation-enhanced DP
139 140 157 184
78Ant1
1000-1270
single crystals with P-doped epitaxial layers, annealing in inert or oxidizing ambients, pn-junction staining, spreading resistance, intrinsic conditions, oxidation-influenced DP depending on temperature, surface orientation, and oxide thickness
184
79Fra1
2.07
950-1150
activation energy of enhancement ∆DP, CZ (100) crystals, P pre-diffusion, annealing in various oxidizing ambients, pn-junction staining, 4-point probe, ∆DP depends on concentration, junction depth, and oxidation rate
3.51 2.39
840-1150 840-1150
intrinsic diffusivity under inert conditions diffusivity enhancement in dry O2 ambient single crystals (100) with buried P-doped layer, selective area diffusion, pn-junction staining, spreading resistance
155
81Hil1 80hil1
900-1200
CZ (100) crystals with oxide layer, low-dose P implantation, selective-area diffusion in dry O2, spreading resistance, DP-enhancement factors depend on oxidation rate and temperature
142 184
81Lin1
1000
P-implanted CZ crystals, annealing in dry O2 vs. N2, C-V profiling, oxidation-enhanced DP, dependence on oxidation time, fI = 0.38
105 182
82Ant2
1000-1200
review of data on oxidation-influenced diffusion including [78Ant1], fI(1100 oC) = 0.53-0.57
82Ant3
950-1150
CZ crystals, pre-deposition from P-doped SiO2 film, drive-in under dry O2, 4-point probe + electrochemical sectioning, intrinsic conditions, oxidation-enhanced DP, effects of surface orientation and time
82Ish1
3.7
80Tan1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
Fig.
Ref.
183
82Miz2 83Miz2
effects of surface reactions or ambient (cont.) 1100
P-implanted FZ (100) crystals, capping by Si3N4, selective-area oxidation of backside in dry O2, pn-junction staining, DP enhancement increases with time and decreasing wafer thickness
950-1150
P-implanted (100) FZ and CZ crystals, selectivearea diffusion in dry O2, pn-junction staining, oxidation-enhanced DP, O precipitation in CZ crystals produces self-interstitial supersaturation below Si/Si3N4 interface
82Miz3
1010 & 1230
FZ crystals with P-doped buried layer, annealing in NH3, pn-junction staining, spreading resistance, DP retardation under bare surface, enhancement under oxide cap
83Fah1
1000-1150
P-implanted FZ or CZ crystals, annealing in NH3 or N2, pn-junction staining, retardation under bare surface, enhancement under SiO2 film
83Miz1
900-1270
combined evaluation of oxidation-enhanced DP and oxidation-retarded DSb data including [78Ant1, 79Fra1, 81Lin1, 81Miz1]
1100
P-diffused CZ crystals, C0 < 3·1019 cm−3, Cl implantation, annealing in steam or N2, differential Hall effect, pn-junction staining, Cl reduces oxidation-enhanced DP
85Arm1
1100
P-implanted FZ crystals, annealing in NH3 ambient, spreading resistance, time dependence of nitridation and oxynitridation effect, fI > 0.93
85Fah1
1100
(100) single crystals with P-diffused layer, annealing in O2 flow under continuously increasing pressure, DP enhancement independent of time due to constant oxidation rate
85Miz1
892-1092
P-diffused FZ crystals with patterned capping, annealing in dry O2, pn-junction staining, lateral extent of oxidation-enhanced DP
85Tan2
900 & 1000 D(900 oC) = 1.25·10−14 cm2s−1 in N2 ambient, CZ (100) crystals, low-dose P implantation, annealing in dry O2 or mixed Ar/O2 ambient, spreading resistance, enhanced DP depending on oxidation rate and Ar/O2 ratio
Lando lt -Bö rnst ein New Series III/33A
2-97
184
142
83Tan3
86Dun1
2-98
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
3.5
3.67
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1100
CZ wafers with buried oxide layers, P implantation, annealing with various cappings in NH3 or O2, pn-junction staining, reduced (oxy)nitridation effects and similar oxidation effects with respect to bulk wafers
86Fah2
1000
model based on self-interstitial injection transient during oxidation, data fitting includes [82Ant2]
86Mat1 86Mat2
1100
simultaneous evaluation of various literature data concerning oxidation-influenced DP and stackingfault growth
86Yos1
1100
numerical analysis of oxidation-retarded diffusion, data from [81Miz1, 83Miz2]
87Bra1
1250
FZ crystals, pre-deposition from POCl3, drive-in under O2, NAA + chemical sectioning, up-hill diffusion near Si/SiO2 interface, no loss of P
88Mas1
200-700
review of silicidation-influenced diffusion data
88Wit1
650-850
CZ crystals, As implantation above amorphization threshold, annealing in dry O2 or N2, SIMS, pn-junction staining, transient enhanced DP depends on ambient, stress effect suggested
90Kim1
900-1100
FZ crystals, low-dose P implantation, annealing in Ar or dry O2, C-V profiling, DP enhancement up to a factor of 17 by oxidation
90Pac1
800-950
single crystals, P diffusion through windows in oxide layer, electrochemical C-V profiling, 4-point probe + sectioning, ultra-shallow profiles, effects of Cl in ambient and oxide thickness, non-equilibrium point defects
91Bag1 93Bag1
1000
single crystals, low-dose P implantation, SiO2 layer growth, RTA 950-1150 oC in NH3 ambient, enhanced DP during poly-Si deposition at 1000 oC, penetration of Ni into substrate suggested
91Bus1
1150
FZ crystals, low-dose P implantation, annealing in mixed N2/O2 ambient, spreading resistance, enhanced diffusion, effect of surface orientation
91Dun1
900-1150
intrinsic DP under nitride/oxide capping, FZ (100) crystals, low-dose P implantation, deposition of oxide film of variable thickness, annealing in steam diluted with N2, spreading resistance, oxidationenhanced DP, self-interstitial supersaturation vs. oxidation rate investigated
154
92Jen2
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1100
analysis of oxidation-influenced diffusion data [82Miz3], fI = 0.93
1000-1150
P- implanted CZ crystals with oxide layer, annealing in dry O2, pn-junction staining, spreading resistance, enhanced or retarded DP depending on oxide thickness and temperature
1100
analysis of nitridation-influenced diffusivities [85Fah1] including interstitialcy, vacancy, dissociative, and dissociation mechanism
900 & 1100 (100) crystals with heavy B or As doping, low-dose P implantation, annealing in N2 or dry O2, SIMS, oxidation-enhanced DP depends on Fermi level, fI = ca. 1
P in Si
Lando lt -Bö rnst ein New Series III/33A
2-99
92Oki1 142
92Shi1
92Van1
143
93Joh1
136
70Tit1
anomalous diffusion after implantation 600-900
single crystals, P implantation through oxide layer, annealing in vacuum or air, sheet resistance + electrochemical sectioning, pn-junction measurement, enhanced DP depending on time, ambient, cooling rate, and depth
650 & 750
FZ crystals, channeled + random P implantation , furnace annealing in N2, differential Hall effect, enhanced DP, also electron-beam annealing for electrical activation
700-1150
P-implanted single crystals, RTA in Ar, SIMS, transient enhanced DP only for low-dose implantation
1000-1350
P-implanted CZ crystals, RTA by graphite heater, Hall effect + resistivity, SIMS, effect of crystal orientation
84Wil1
905-1050
evaluation of literature data, RTA upon P implantation, modeling based on vacancies in multiple charge states
85Fai1
950
single crystals, low-dose P implantation, furnace annealing under oxide cap in N2, SIMS, transient enhanced DP: time and dose dependence, stronger effects than in RTA studies
86Cow1
82Gal1
144
84Oeh1
2-100
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
1.41·10−5
1.8
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
170
87Ang1 88Sol1
anomalous diffusion after implantation (cont.) 700-1100
CZ crystals, P pre-diffusion, Si implantation above amorphization threshold, furnace annealing in N2 or electron-beam heating, pn-junction staining, SIMS, X-ray diffraction, enhanced DP below a/c interface due to self-interstitials
600-800
single crystals, P implantation above amorphization threshold, epitaxial regrowth, precipitation annealing, TEM, transient enhanced DP due to excess self-interstitials
87Pen1 88Pen1
750-900
P-diffused CZ crystals, Si implantation above amorphization threshold, annealing in N2, pnjunction staining, X-ray diffraction, enhanced DP correlates with implantation-induced local strain
87Ser1
600-750
P-diffused single crystals, Si implantation below amorphization threshold, annealing in N2, SIMS, simulation of strain profiles, enhanced DP correlates with self-interstitial supersaturation
87Ser2
750 & 900
CZ crystals, P implantation above amorphization threshold, furnace annealing or/after RTA in N2 or O2, SIMS, TEM, both short- and long-time enhanced diffusion transients, Q reduced by 2.5 eV
89Kim1
950-1150
interstitial diffusivity Di characterizing Pi, model based on simultaneous diffusion via vacancy and dissociative mechanism, fitting of data from [84Oeh1]
600-1000
single crystals with dislocation loops, P implantation, furnace and electron-beam heating, X-ray diffraction, SIMS, TEM, reduced enhanced DP due to dislocations
89Ser1 89Zau1
950
FZ crystals with buried B-doped layer, P and/or As implantation above amorphization threshold, SIMS, spreading resistance, TEM, P-As co-diffusion suppresses transient enhancement of P alone
90Dea1 93Kon1
650-900
CZ crystals, P implantation through SiO2 film, RTA and furnace annealing in N2, SIMS, transient enhanced DP up to P kink concentration
90Fai1
1050
CZ crystals, P implantation through oxide windows, RTA or furnace annealing, pn-junction staining, measured depth and lateral profiles compared with simulations
90Sub1
159
89Nan1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
Fig.
Ref.
anomalous diffusion after implantation (cont.) 900
p-type crystals, diffusion under in-situ implantation, differential Hall effect, depth-dependent enhanced DP
700-1050
epitaxial wafers with heavy B or As doping, P implantation below amorphization threshold, RTA and furnace annealing, SIMS, transient enhanced DP depends on implantation energy, dose, background doping, and temperature
145 146
91Gil1
850
single crystals, P implantation in pre-amorphized layer, annealing in wet O2, SIMS, up-hill diffusion near a/c interface due to dislocation loops, interstitialcy mechanism
147
91Orl1 90Kim2
800-1100
single crystals, implantation below amorphization threshold: Si after P, RTA and furnace annealing, spreading resistance, transient enhanced DP depending on temperature, see [92Bac1]
91Par1
800
p-on-p+ epitaxial layers, P implantation and damage anneal, low-dose Si or Ar implantation, annealing in N2, SIMS, transient DP enhancement due to second implantation
93Gil1
900 & 1000 single crystals, high-dose As implantation + damage anneal, low-to-high-dose P implantation, annealing in mixed N2/O2 ambient, SIMS, differential Hall effect, As reduces transient enhanced DP
P in Si
91Ale1
148
93Sol1
cooperative effects with other dopants 805-1070
B-diffused CZ crystals, dislocation density < 2·103 cm−2, POCl3 or P2O5 source, pn-junction staining, TEM, enhanced B-base penetration in n+pn-structure, also anomalous P-base shifts in p+np-structure
66Law1
1250
FZ crystals, simultaneous and sequential P-Ga diffusion, pn-junction staining, NAA and 4-pointprobe + mechanical sectioning, P-related effects on Ga diffusion
68Oka1 71Oka1
single crystals, P-As co-diffusion, RBS, radioactive analysis, X-ray topography, C0(P) = 1021 cm−3, suppression of P-induced dislocations
72Fuj1
900-1050
Lando lt -Bö rnst ein New Series III/33A
2-101
Ga-diffused single crystals, POCl3 source in N2/O2, radioactive analysis (Ga) and 4-point probe (P) + chemical sectioning, effect of P diffusion on Ga profile
81
74Jon1 76Jon1 77Jon1
2-102
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
cooperative effects with other dopants (cont.) 950
CZ crystals with 102-103 dislocations/ cm2 or epitaxial layer, sequential diffusion: P after B, POCl3 source or P-doped oxide layer, pn-junction staining, 4-point probe or NAA + electrochemical sectioning, emitter-push effect depending on C0(P)
74Lee1
900
B-diffused CZ crystals, POCl3 source or P-doped oxide layer in N2/O2, pn-junction staining, sheet resistance + electrochemical sectioning, emitterpush effect on B base depending on C0(P)
74Nak1
900 & 1100 single crystals with P-doped buried layers, P-doped oxide source in N2, pn-junction staining, DP enhancement in buried-layer decreases with increasing distance (5-25 µm) from surface
149
77Mat1
1000-1200
single crystals, P + As-doped oxide source in N2/O2 ambient, P-induced dislocations suppressed by As co-diffusion
77Yon1
1100
CZ crystals, P-Ge co-diffusion from POCl3/GeCl4, sheet resistance + electrochemical sectioning, pn-junction staining, etch pit counting, reduction of P-induced dislocations due to Ge strain compensation
78Mat1
700-1000
B-implanted FZ crystals, P-doped spin-on oxide source in N2, SIMS, C-V profiling, TEM, P-emitter push effect depending on C0(P) and B implantation dose and depth, no dislocations
1070
B-doped single crystals, P diffusion from P2O5 source in N2 ambient, pn-junction staining, effects on As- or Sb-doped buried layers and redistribution of B
1000-1200
FZ crystals, POCl3 or implanted source in lowoxygen ambient , SIMS, spreading resistance,TEM, effects on As- or Sb-doped buried layers
900
Ge-implanted single crystals, high-dose P implantation, annealing in neutral ambient, SIMS, spreading resistance, retarded DP due to long-range P-Ge interactions
90Aro1
1020 & 1150
FZ crystals, spin-on P source, RTA, SIMS, C-V, spreading resistance, sequential diffusion: P after Al promotes Al tail und near-surface up-hill diffusion, Al after P leads to DAl retardation suggesting Al-P complex formation
95Nag1
79 80 81
79Lec1 80Lec1
83Har1
185
87Tsa1 87Tsa2
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
2-103
Fig.
Ref.
cooperative effects with other dopants (cont.) 1017 & 1147
P in Si
95Nag2
neutron transmutation-doped FZ crystals, predeposition from liquid P source in N2 and drive-in, RTA, SIMS, 4-point-probe + chemical sectioning, also sequential diffusion: Al after P and P after Al
special source conditions 1200
standard wafers, oxide source layer deposition from pre-mixed SiH4/PH3/Ar gas, annealing in N2 or air, sheet resistance, reproducibility and uniformity examined, effect of SiO2 capping film
68Fis1
7·10−2 6·10−1 7.4
3.3 3.54 3.74
1160-1315 1160-1315 1160-1315
P-doped epitaxial or poly-Si layer source in H2 P-doped Si powder vapour source in H2 P2O5/SiO2 layer source in air FZ (111) crystals, radiotracer 32P + chemical sectioning, C0 = 2-7·1018 cm−3, enhanced diffusion due to surface oxidation, D0 and Q from [74har1]
157
70Gho1
15.7
3.82
1100-1257
low-dislocated FZ (111) crystals, P-doped oxide layer source in Ar flow, radiotracer 32P + chemical sectioning, analysis accounts for finite P-transfer rate from SiO2 to Si
153
74Gho1
1100 & 1200
CZ crystals, pre-deposition from POCl3, drive-in under N2/O2, 4-point probe and NAA + electrochemical sectioning, TEM, agreement between electrical and chemical profiles, precipitation observed
75Neg1
1050
spin-on source containing triphenylphosphate, sheet resistance, pn-junction staining, C0 < 8·1019 cm−3
76Bey1
1100
single crystals, P2O5 source in N2, 4-point probe with electrochemical and chemical sectioning
83Era1
1147-1247
single crystals, P-doped spin-on oxide source in air, 4-point probe, C0 depends on oxide doping level
84Nis2
single crystals with P-doped Ni film, diffusion during Ni-silicide formation, enhanced DP due to excess vacancies beneath silicide layer
84Pit1
800-1000
analysis of P-implanted poly-Si layer sources, SIMS, segregation to poly/mono interface
85Sch1
900-1000
single crystals with P-implanted TaSi2 layer, annealing in N2 ambient, SIMS, shallow penetration into Si substrate, no crystal defects
87Gie1
0.906 380-630
Lando lt -Bö rnst ein New Series III/33A
2-104
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
special source conditions (cont.) 685 & 785
P in Si
94Lou1
thermally oxidized wafers with poly-Si layer, PH3 source in H2/N2, RTA at 1000 oC for activation, SIMS, Hall effect, effects of grain-boundary segregation
other effects or conditions 1100
CZ crystals, diffusion in Pt box, X-ray topography, C0 = 1021 cm−3, rectangular arrays of diffusioninduced dislocations
62Sch1
1000-1300
CZ crystals, P2O5 source in N2 flow, TEM, crossed grid of diffusion-induced edge dislocations
64Was1
1150
P-diffused CZ crystals, sheet resistance + electrochemical sectioning, TEM, C0 > 1021 cm−3, diffusion-induced dislocations and precipitates
65Jos1
1175 & 1200
single crystals, P-doped anodic oxide film, radiotracer 32P and sheet resistance + electrochemical sectioning, SiP precipitate formation depending on surface orientation
65Oke1
1000-1200
single crystals, drive-in after P2O5 pre-deposition or P-doped oxide film, X-ray diffraction, TEM, formation of SiP precipitates
66Bec1
1070
single crystals also after plastic deformation, POCl3 diffusion through oxide windows, preferential etching, TEM, X-ray topography, lateral patterns of diffusion-induced dislocations
66Law2
970-1200
CZ crystals, drive-in after pre-deposition through oxide windows, 4-point probe and NAA + sectioning, X-ray topography, dislocations generated outside diffused areas, effects of O2 ambient and surface orientation
68Fai1 66Sch1
1100
B-doped CZ crystals, diffusion from P2O5 source through oxide windows of varying shape, X-ray topography, lateral interjunction strain gradients observed
68Jun1
0.015
2.7
1000-1200
epitaxial layers, NAA, erfc profiles, enhanced DP due to structural imperfections, see also [86wöh1]
155
70Lyu1 71Sta1
1.5
3.16
1000-1200
polycrystals, radiotracer techniques, reports larger DP than for mono-Si, see also [86wöh1]
160
70Pru1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
1.93
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-105
Fig.
Ref.
other effects or conditions (cont.) 1000
CZ crystals, pre-deposition from POCl3 source, drive-in under O2, sheet resistance, pn-junction staining, DP retardation due to diffusion-induced dislocations
70Yos2
900
epitaxial layer on P-doped substrate, annealing under proton irradiation, C-V profiling, enhanced diffusion depending on dose
72Ohm1
600-900
P-doped single crystals, in-situ diffusion into growing epitaxial films, see also [86wöh1]
74Ari1
1200
FZ crystals, diffusion leading to C0 > 6·1020 cm−3, X-ray topography, TEM, diffusion-induced dislocations investigated
75Gri1
1100
CZ crystals with stacking faults, P-doped oxide source in dry N2, preferential etching, sheet resistance + electrochemical sectioning, stackingfault annihilation only near surface
76Has1
1000
CZ crystals, POCl3 source in N2 or N2/O2, NAA, resistivity, TEM, X-ray topography, diffusioninduced dislocations, stacking-fault and SiPprecipitate length vs. diffusion time
77Arm1 77Mas1
1150
CZ crystals with stacking faults (SF), P-doped oxide layer under undoped SiO2, annealing in N2 or dry O2, preferential etching, diffusion-induced SF growth increasing with P-doping level, reducing effect of Cl in ambient
600-900
CZ crystals, P drive-in after implantation, annealing in vacuum under proton irradiation, intrinsic conditions, spreading resistance, pn-junction staining, flux-dependent enhanced DP due to excess vacancies
600 & 700
P-diffused epitaxial layer without extended defects, annealing in dry O2 or vacuum, spreading resistance, TEM, extrinsic stacking faults and misfit dislocations observed
152
78Tse1
950
npn-transistor structure, P-emitter diffusion, pnjunction staining, TEM, formation of interstitialtype dislocation helices and loops, push-out of B-doped base
151
79Str1 80Str1
150
78Cla1
78Mas1
2-106
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
P in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
other effects or conditions (cont.) 850-1410
CZ crystals, P implantation above amorphization threshold, multiscanning electron-beam annealing, RBS, TEM, X-ray topography, differential Hall effect, residual damage after epitaxial regrowth, complete activation
81Ben1
400-600
FZ and CZ crystals, P implantation + anneal, in-situ Ar implantation, spreading resistance, SIMS, anomalous profiles depending on oxygen concentration, migration via O-vacancy and P-vacancy complexes suggested
81Bor1
900 & 1000 CZ crystals with stacking faults, epitaxial layer, predeposition (1000 oC) and drive-in (900 oC) from P-doped oxide in N2, sheet resistance + electrochemical sectioning, annihilation of stacking faults observed
83Mat1
1092
84Nis1
CZ crystals with near-surface stacking faults (SF), pre-deposition from P2O5 at 850-1100 oC, drive-in under N2 or Ar, 4-point probe, pn-junction staining, preferential etching, P-diffusion-induced SF growth
900 & 1000 single crystals with buried oxide layer, predeposition from POCl3 through SiO2 windows, drive-in annealing, pn-junction staining, no lateral diffusion near buried oxide observed
85Kam1
950-1100
CZ crystals with near-surface stacking faults, predeposition from P2O5 at 950 oC, drive-in under N2, pn-junction staining, TEM, stacking-fault growth increases with P dose
86Nis2
0.2 0.008
3.27 2.88
900-1150 900-1150
polycrystals with grain size 0.1-3 mm polycrystals with grain size 5-50 µm H3PO4/H2O source in closed ampoule, radiotracer 32 P + mechanical sectioning, analysis accounts for grain-boundary diffusion effects
160
86Spi1
1.8·10−4
2.53
920-1120
solar-grade poly-Si, doped-oxide source, NAA + mechanical sectioning, absence of grain-boundary diffusion, D0 and Q recalculated
160
87Cha1
1.9
3.3
1015-1200
solar-grade poly-Si with various extended defects, drive-in after pre-deposition, NAA + chemical sectioning, erfc profiles
160
88Abd1
1100
P-implanted FZ crystals, SiNx capping by chemical vapour deposition, annealing in Ar, pn-junction staining, retarded DP due to nitride-film stress
88Ahn1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
P in Si (cont.)
Methods and Remarks
2-107
Fig.
Ref.
other effects or conditions (cont.) 900
CZ crystals, P-doped spin-on source, long-time lamp annealing in N2, intrinsic conditions, electrochemical C-V profiling, enhanced DP attributed to radiation heating
89Ish2
1150 & 1240
FZ crystals, diffusion from POCl3 or drive-in after implantation, reduction of process-induced defects, various experimental techniques
89Sch2
800-1000
single crystals, P implantation above amorphization threshold, annealing under high pressure in Ar, sheet resistance + electrochemical sectioning, enhanced DP due to pressure effect
89Vas1
800-1000
CZ crystals, P-doped spin-on glass, RTA in Ar ambient, 4-point probe, differential Hall effect, comparison of RTA with furnace annealing
92Har1
As in Si
temperature dependence and mechanism of diffusion
0.32
3.56
1095-1380
B-doped single crystals, As oxide source in lowpressure air ambient, pn-junction staining, C0 = 5.8·1017-4.5·1018 cm−3
174
56Ful1
68.6
4.24
1100-1350
single crystals, As2O3 source in mixed N2/O2 flow, 4-point-probe and pn-junction staining, C0 = 1017-1019 cm−3
174
62Arm1
2.564
3.87
1125-1312
single crystals, As2O3 source in N2 flow, sheet resistance, pn-junction staining, C0 = 7·1017-7·1018 cm−3, also elemental As source in closed ampoule
174
64Raj1
8.3·104
5.20
1164-1280
single crystals, AsH3 source in O2 flow, 4-point probe, pn-junction staining, C0 = 1-2·1019 cm−3
174
68Hsu1
1100-1200
crystal with As doping 1·1019 cm−3, out-diffusion in dynamic vacuum, NAA + (electro)chemical sectioning, evaluation of As evaporation velocity
70Ara1
1.5·103
4.65
1100-1275
single crystals, drive-in under O2 atmosphere after pre-deposition, 4-point probe, pn-junction staining, no effect of surface orientation, C0 = (0.44-2.8)·1018 cm−3, D0 and Q recalculated
174
70Cha1
24
4.08
1000-1200
intrinsic diffusivity from low-C0 profiles, also extrinsic diffusion, NAA + sectioning, analysis based on double acceptor-level vacancies, electricfield effect, and As-cluster formation
166 175
71Chi1
Lando lt -Bö rnst ein New Series III/33A
2-108
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
As in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
temperature dependence and mechanism of diffusion (cont.)
6.55·10−2
3.44
1167-1394
As-doped epitaxial layers on FZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, As-vacancy pair mechanism
161 174
71Gho2
2870
4.57
950-1150
intrinsic diffusivity from profile tail, NAA + sectioning, Boltzmann-Matano analysis, C-dependent diffusivity, C0 = 8·1020-1021 cm−3
164 175
71Ken1
110 25 44
4.1 4.0 4.2
1000-1200 1000-1200 1000-1200
C0 = 4·1019 cm−3 C0 = 1·1019 cm−3 C0 = 4·1018 cm−3 single crystals with arsenosilicate glass film, diffusion in Ar ambient, pn-junction staining, 4-point probe + electrochemical sectioning, enhanced DAs in O2 ambient observed
1000-1058
single crystals, various As sources, NAA and resistivity, C-dependent diffusivity, C0 = 1020-1021 cm−3, As+ in equilibrium with As2vacancy complexes, includes [71Ken1, 71San1]
162
73Fai1
700-1100
intrinsic diffusivity, single crystals, elemental As source, 4-point probe + electrochemical sectioning, RBS, C0 = 1-3·1020 cm−3 weakly dependent on temperature and As pressure
175
75Ohk1
900-1050
evaluation of data from [78Mur1, 79Mur1], model includes As-vacancy pairs and As2-vacancy complexes
1167-1394 900-1275
D0 via neutral vacancies D− via singly negatively charged vacancies D2− via doubly negatively charged vacancies review and evaluation of literature data including [69Mas1, 70Cha1, 71Gho2, 73Bal1]
1050 & 1150
D(1050 oC) = 1.5·10−13 cm2s−1, 4-point-probe and radiotracer 125Sb + sectioning
969
0.066 12.0
4.45
3.44 4.05 4.32
As in Si 60 7.3
72Won1
80Yos1 96Yos1 166
81fai1 75Fai1
82Nei1
effects of high concentration and heavy doping 4.20 3.54
953-1350 853-1148
intrinsic diffusivity including data of [62Arm1] extrinsic diffusivity for CAs = 2.7·1020 cm−3 CZ crystals heavily As-doped or virtually intrinsic, Si(As) powder source in vacuum, radiotracer 76As + electrochemical sectioning, erfc profiles, isoconcentration DAs proportional to electron density, see [75sha1]
163 174 176
69Mas1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
As in Si (cont.) 0.51
3.53
Methods and Remarks
2-109
Fig.
effects of high concentration and heavy doping (cont.) 950-1050
extrapolated intrinsic lattice diffusivity, epitaxial layers with As doping 2·1018 cm−3 and dislocations, elemental As in evacuated ampoule, radiotracer 76As + electrochemical sectioning, DAs increases with C0
174
75Cam1
850-1100
single crystals with As-doped poly-Si layer, annealing in N2, 4-point probe and NAA + electrochemical sectioning, SIMS, BoltzmannMatano analysis, C-dependent DAs, mobile (Ass+) and immobile atoms
164 167
78Mur1 79Mur1
85Ang1
900 & 1000 CZ crystals, high-dose As implantation and laser annealing, precipitation annealing in N2, differential Hall effect, pn-junction staining, X-ray scattering, C-controlled diffusivity not affected by precipitation
5.85·10−6
1.65
Ref.
mathematical analysis of As high-concentration diffusion
87Kin1
850-1050
single crystals, As implantation or As-doped polySi layer: 1019-1021 cm−3, precipitation annealing, TEM, differential Hall effect, NAA, dislocationloop formation
90Hir1
1000-1100
FZ crystals, P doping < 5·1020 cm−3 by implantation, As implantation, RTA in Ar ambient, SIMS, RBS, Hall effect, enhanced DAs above vacancypercolation limit
As in Si
165 176
93Nyl1 90Gai1 89Nyl1
effects of surface reactions or ambient
24
4.08
975-1200
DAs in inert ambient agreeing with [71Chi1], CZ (100) crystals, low-dose As implantation, annealing in inert or dry O2 ambient, spreading resistance, oxidation-enhanced DAs
165 175
78Ant1
13 1.9·10−6
4.05 2.34
840-1150 840-1150
intrinsic DAs in inert ambient enhancement ∆DAs in dry O2 ambient single crystals (100) with buried As-doped layer, selective area diffusion, pn-junction staining, spreading resistance
131 175 176
81Hil1 80hil1
1090
As-implanted CZ (100) crystals, annealing in dry O2 vs. N2, C-V profiling, oxidation-enhanced DAs, dependence on oxidation time, fI = 0.35
182
82Ant2
950-1150
CZ crystals, pre-deposition from As-doped SiO2 film, drive-in under dry O2, 4-point probe + electrochemical sectioning, intrinsic conditions, enhanced DAs, effects of surface orientation and time
167
82Ish1
Lando lt -Bö rnst ein New Series III/33A
2-110
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
As in Si (cont.)
1.5
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1070
As-implanted single crystals with epitaxial layer, P diffusion from P2O5 source in N2 ambient, pn-junction staining, enhanced As diffusion
950-1100
see [82Ish1], extrinsic conditions after predeposition: C0 = 5-7·1019 cm−3, C-dependent DAs retarded by oxidation at 1000-1100 oC
167
83Ish1
1100
As-implanted FZ crystals, annealing in NH3 ambient, spreading resistance, time dependence of nitridation and oxynitridation effect, fI = 0.3-0.4
168
85Fah1
1000-1150
As-implanted single crystal, annealing in dry O2 with HCl, SIMS, spreading resistance, oxidationenhanced DAs reduced by HCl
1000-1150
FZ crystals with As-doped buried layer, P diffusion in mixed O2/N2 ambient from POCl3 or implanted source, spreading resistance, SIMS, TEM, enhanced DAs
1100
evaluation of literature data [81Miz1, 82Ant2, 85Fah1] also including dissociative and direct exchange mechanism, generalized fractional interstitial component equals 0.4
88Cow1
200-700
review of silicidation-influenced diffusion data, snowplow effect for As
88Wit1
650-850
CZ (100) crystals, As implantation above amorphization threshold, annealing in dry O2 or N2, SIMS, pn-junction staining, transient enhanced DAs independent of ambient, see [89Kim1]
90Kim1
1000
single crystals, low-dose As implantation, SiO2 growth, RTA 950-1150 oC in NH3 ambient, enhanced DAs during poly-Si deposition at 1000 oC, penetration of Ni into substrate suggested
91Bus1
850-1050
wafer with As doping 4·1019 cm−3, low-dose Sb implantation, epitaxial layer growth, annealing in dry O2, SIMS, enhanced As diffusion, fI = 0.45-0.52
92Per1
1100
analysis of nitridation-influenced DAs from [85Fah1] based on interstitialcy, vacancy, dissociative and dissociation mechanism
83Har1
87Sub1
185
168
87Tsa1
92Van1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
As in Si
22.9
Methods and Remarks
2-111
Fig.
Ref.
anomalous diffusion after implantation 500-900
D(900 oC) = 5·10−16 cm2s−1, single crystals, As implantation below amorphization threshold, annealing in dry N2, NAA + electrochemical sectioning, differential Hall effect, DAs enhanced by factor of 10
900-1200
intrinsic diffusivity via vacancy mechanism, bulk wafers or epitaxial layers, high-dose As implantation, annealing in O2 or N2, SIMS, 4-point probe, Hall effect, comparison with chemical source diffusion, no ambient dependence
1000-1200
single crystals, analysis of profile parameters characterizing diffusion upon implantation, SIMS and differential resistance data, C0 > 1019 cm−3
76Fai1
900-1100
single crystals, high-dose As implantation through oxide, annealing in N2, resistivity + sectioning, TEM, knock-on oxygen effects
80Wad2
1050-1200
single crystals, As implantation above amorphization threshold, RTA, RBS + channeling, TEM, enhanced DAs
83Nar1
2.1
1000-1150
transient enhanced diffusivity, CZ crystals, As implantation above amorphization threshold, RTA in air or N2, SIMS, enhancement suppressed by 550 oC furnace pre-anneal
84Fai1
1.8
1000-1200
single crystals, As implantation above amorphization threshold, RTA, RBS, SIMS, TEM, transient enhanced DAs
84Kal2
1000-1100
single crystals, As implantation above amorphization threshold, xenon-lamp RTA in air, RBS + channeling, 4-point probe, C-dependent DAs
84Nyl1
1100-1300
As-implanted CZ crystals, RTA by graphite heater, Hall effect + sheet resistance, RBS, C-dependent DAs, effect of crystal orientation
84Wil1
900-1200
evaluation of literature data, RTA upon As implantation, modeling based on vacancies in multiple charge states
85Fai1
1000
As implantation, annealing in N2, calculation of profile based on C-dependent diffusivity
85Ghe1
1000-1100
single crystals, As implantation above amorphization threshold, 550 oC pre-anneal and RTA in N2, differential Hall effect, RBS, TEM, little effect of pre-anneal observed
85Kwo1
4.1
Lando lt -Bö rnst ein New Series III/33A
73Bal1
167 175
75Fai1
2-112
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
As in Si (cont.) 2.0
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
anomalous diffusion after implantation (cont.) 85Pen1 86Pen1 86Pen2 88Pen1
800
FZ or CZ crystal, As implantation above amorphization threshold, epitaxial regrowth, precipitation annealing, TEM, RBS, transient enhanced DAs due to excess self-interstitials, includes [80Lie1]
700-1150
single crystals, low-to high-dose As implantation, RTA in N2, SIMS, C-enhanced but no transient enhanced DAs, no effect of recrystallization preannealing
850-1200
review of literature data: RTA after implantation
700-1100
CZ crystals, As implantation + damage anneal, Si implantation above amorphization threshold, furnace annealing in N2 or electron-beam heating, pn-junction staining, SIMS, X-ray diffraction, enhanced DAs below a/c interface due to selfinterstitials
750-900
As-implanted CZ crystals, Si implantation above amorphization threshold, annealing in N2, pnjunction staining, X-ray diffraction, enhanced DAs correlates with implantation-induced local strain
87Ser1
800-1100
FZ crystals, high-dose As implantation, RTA in air, RBS, TEM and Hall effect, C-dependent diffusivity, no transient enhancement
87Shi1
modeling of As diffusion from an delta-shaped implanted source
87Jep1
169
85Sed
85Sei1 170
87Ang1 88Sol1
750 & 900
CZ crystals, As implantation above amorphization threshold, furnace annealing or/after RTA in N2 or O2, SIMS, TEM, both short- and long-time enhanced DAs transients, Q reduced by 2.5 eV, see [90Kim1]
780-1100
single crystals, high-dose As implantation, shorttime furnace annealing in N2, differential Hall effect, transient enhanced DAs, temperaturedependent time constant
89Sas1
850-1050
single crystals, As-implantation through oxide, annealing in Ar flow, NAA + electrochemical sectioning, TEM, X-ray fluorescence, near-surface accumulation due to stress-induced dislocations, effect of knock-on oxygen
89Yok1 89Yok2
171
89Kim1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
As in Si (cont.)
Fig.
Ref.
anomalous diffusion after implantation (cont.) 950
FZ crystals with buried B-doped layer, P and/or As implantation above amorphization threshold, SIMS, spreading resistance, TEM, P-As co-diffusion suppresses transient enhancement of As alone
90Dea1
650-900
CZ crystals, As implantation through SiO2 film, RTA and furnace annealing in N2, SIMS, transient enhanced DAs up to As solubility limit
90Fai1
800-1100
single crystals, implantation below amorphization threshold: Si after As, RTA and furnace annealing, spreading resistance, no transient enhanced DAs
91Par1
900 & 1000 single crystals, As and P implantation, annealing in mixed N2/O2 ambient, SIMS, Hall effect + resistivity, no influence of P on DAs
93Sol1
800-1100
CZ crystals with oxide layer, low-dose As implantation, annealing in N2 ambient, SIMS, retarded diffusion in tail region, segregation to Si/SiO2 interface
94Aok1
800-1050
single crystals, high-dose As implantation, annealing in N2 ambient, secondary neutral atom mass spectroscopy, TEM, precipitation and dissolution of SiAs precipitates
94Nob1
As in Si
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-113
cooperative effects with other dopants 1250
FZ crystals, simultaneous Ga-As diffusion, pnjunction staining, 4-point-probe + mechanical sectioning, retarded DGa in n+-layer
68Oka1
1250
single crystals, simultaneous Ga-As diffusion, NAA + chemical sectioning, 4-point-probe, Ga retardation by As doping
71Oka1
single crystals, As-P co-diffusion, RBS, radioactive analysis, X-ray topography, C0(As) = 7·1019 cm−3, C0(P) = 1021 cm−3, As prevents P-induced dislocation generation, temperature not given
72Fuj1
1000
B-doped or B-diffused crystals, Si(As) powder source, nuclear reaction activation, NAA, RBS, effect of As diffusion on B redistribution
72Zie1
1000-1200
As- and/or B-doped oxide source, simultaneous or sequential As-B diffusion vs. As alone, SIMS, emitter-push effect
78
73Bla1
2-114
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
As in Si (cont.)
35
4.0
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
cooperative effects with other dopants (cont.) 1000 & 1100
B-diffused single crystals, As-doped oxide source, C-V measurements, pn-junction staining, retarded DB during As emitter diffusion, vacancy-As2 complexes cause vacancy undersaturation
73Fai3
1000
B-implanted single crystals, As-doped oxide or implanted source, N2 or O2 ambient, C-V measurements, simultaneous vs. sequential As-B diffusion discussed
74Fai1
1025
D = 8.4·10−15 cm2s−1, n-type crystals, As + B implantation, annealing in vacuum, sheet resistance + electrochemical sectioning, formation of n-p-n structures by co-diffusion
74Hei1
700
single crystals, pre-deposition from As-doped oxide layer, drive-in under N2, sheet resistance + electrochemical sectioning, enhanced DAs, also As emitter-push effect in B-pre-diffused crystals
75Shi1
1000
Ga-diffused single crystals, elemental As source in vacuum, radioactive analysis (Ga) and 4-point probe (As) + chemical sectioning, effect of As diffusion on Ga profile
77Jon1
1000
modeling of sequential diffusion: As after Ga, includes Fermi-level and electric-field effects and excess point-defect generation by As diffusion, see [77Jon1]
1050-1200
FZ crystals with As-doped buried layer, P implantation with Cmax below solubility limit, annealing in low-oxygen ambient, spreading resistance, pn-junction staining, enhanced DAs
87Tsa2
1050 & 1100
single crystals, implantation of As and/or B through oxide film, RTA in Ar ambient, SIMS, effects of As-B co-diffusion examined
92Gon1
As in Si
101
81Mal1
special source conditions 950-1050
single crystals, As-doped Si powder or singlecrystal source in closed ampoule, sheet resistance + sectioning, C0-dependence on source and time investigated
71San1
1150 & 1200
spin-on diffusion source containing arsenosiloxane, sheet resistance, pn-junction staining, C0 < 3·1020 cm−3
76Bey1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
As in Si (cont.)
32
4.1
Fig.
Ref.
special source conditions (cont.) 77Tsu1
1000 & 1100
single crystals with As-implanted poly-Si layer, annealing in N2 or O2, RBS, sheet resistance + electrochemical sectioning, effects of ambient, segregation and snowplowing
800-1000
analysis of As-implanted poly-Si sources, SIMS, segregation to poly/mono interface
950-1100
porous layers on single crystal substrate, As spin-on emulsion source, RTA in air, RBS, diffusion into substrate varies with time but not with temperature
86Bon1
1050-1150
single crystals with poly-Si layer, As implantation, RTA, SIMS, sheet resistance,TEM, extremely shallow pn-junctions, epitaxial realignment effect
87Böh1
900-1000
single crystals with As-implanted TaSi2 layer, annealing in N2 ambient, SIMS, shallow penetration into Si substrate, no crystal defects observed
87Gie1
1097-1207
single crystals, As-doped spin-on oxide film, annealing in O2 ambient, 4-point probe, little variation of C0 with temperature and time
90Nis1
800-1150
single crystals with As-implanted poly-Si layer, RTA and furnace annealing, SIMS, TEM, various effects observed
91Par2
1050 & 1100
intrinsic diffusivity into single crystal substrate, deposition of poly-Si layer, implantation of As and/or B, RTA in Ar ambient, SIMS, As segregation to poly/mono interface, mutual retardation for As-B co-diffusion
91Gon1 93Gon1
As in Si
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-115
173
85Sch2
other effects or conditions 1150
As-diffused CZ crystals, sheet resistance + electrochemical sectioning, C0 = 5·1020 cm−3, few diffusion-induced dislocations
65Jos1
1200
single crystals, As-doped Si powder source in evacuated ampoule, 4-point probe + sectioning, TEM, diffusion-induced extrinsic stacking faults and dislocation loops, vacancy undersaturation due to Asi diffusion component
70Das1
1000-1100
As-doped oxide or As-implanted layer source, evacuated ampoules, NAA, sheet resistance, comparison of electrically active with total As concentration, vacancy-As2 complexes suggested
73Fai2
2-116
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
As in Si (cont.)
4.6
Methods and Remarks
[Ref. p. 2-196
Fig.
other effects or conditions (cont.) 1100
CZ crystals with stacking faults, elemental As vapour source, preferential etching, sheet resistance + electrochemical sectioning, no stacking fault annihilation for high C0
76Has1
600-900
CZ crystals, As drive-in after implantation, annealing in vacuum under proton irradiation, intrinsic conditions, spreading resistance, pnjunction staining, proton-flux-dependent enhanced DAs due to excess vacancies
78Mas1
1000-1200
single crystals, As-doped spin-on oxide source, xenon-lamp RTA in air, RBS + channeling, 4-point probe, enhanced diffusion
83Bor1
83Mat1
900 & 1000 CZ crystals with stacking faults, epitaxial layer, predeposition (1000 oC) and drive-in (900 oC) from Asdoped oxide in N2, sheet resistance + electrochemical sectioning, annihilation of stacking faults observed 4.5 4.1 3.6
Ref.
850-1000 850-1000 850-1000
diffusivity under vacuum diffusivity under 20 kbar pressure diffusivity under 30 kbar pressure As-implanted single crystals, annealing under high pressure, RBS, TEM, negative activation volume pointing to interstitials, see [92Sug1]
172
85Nyg1
900 & 1000 single crystals with buried oxide layer, high-dose As implantation through SiO2 windows, furnace annealing, pn-junction staining, no lateral diffusion near buried oxide observed
85Kam1
450-850
in-situ As-doping of epitaxial Si during growth, SIMS, Hall effect, RBS and TEM
88Hou1
900
CZ crystals, As-doped spin-on source, long-time lamp annealing in N2, intrinsic conditions, electrochemical C-V profiling, enhanced DAs attributed to radiation heating
89Ish2
900-950
single crystals with buried oxide layer, As implantation above amorphization threshold, annealing in N2 with SiO2 cap, SIMS, spreading resistance, TEM, As pile-up at Si/SiO2 interface
89Nor1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Sb in Si
Methods and Remarks
2-117
Fig.
Ref.
temperature dependence and mechanism of diffusion 3.5
900-1300
D(1100 oC) = ca. 10−13 cm2s−1, pn-junction and radiotracer method
5.6
3.95
1095-1380
B-doped single crystals, Sb oxide source in low-pressure air ambient, pn-junction staining, C0 = 1.4·1018-2.7·1021 cm−3
188
56Ful1
0.112
2.86
940-1300
see [71Gho2]
188
57Pet1
12.9
3.98
1190-1398
single crystals, Sb2O5 source in low-pressure air, radiotracer 124Sb + mechanical sectioning, erfc profiles, C0 = 1019-1020 cm−3,
188
59Roh1
14.3
4.2
1200-1300
C0 = 1·1018-1.3·1019 cm−3, see [71Gho2]
188
60Dri1
188
62Thu1
6.3·10
9
20
−3
6.6
1125-1290
C0 = 1·10 cm , see [71Gho2]
2·107
5.85
ca.1200
liquid Sb(C2H5O)3 source, D0 and Q given by [71Gho2]
3.63·102
4.4
1150-1255
Sb-diffused CZ crystals with epitaxial layer, annealing in N2, pn-junction staining, sheet resistance + chemical sectioning, Cmax = 4.4·1018-1.2·1019 cm−3, C-independent diffusivity
1220 & 1275
single crystals, drive-in under O2 after predeposition, 4-point probe, pn-junction staining, no effect of surface orientation, C0 = (8.2-10.3)·1018 cm−3
54Dun1
67Git1 188
68Nak1
70Cha1
10.5
3.48
1000-1200
epitaxial layer, activation analysis techniques, DSb enhancement by factor 10-15 due to structural imperfections, see [86wöh1]
188
70Lyu1
0.214
3.65
1190-1405
Sb-doped epitaxial layers on FZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, Sb-vacancy pair mechanism
161 188
71Gho2
7.9 4.4
3.98 3.76
977-1227 977-1227
dislocation density 103-104 cm−2 dislocation density 3-6·106 cm−2 epitaxial layer, radiotracer 124Sb + sectioning, see [86wöh1]
188
72Usk1
950
D = 4·10−16 cm2s−1, single crystals, 5·103-5·104 dislocations/cm2, elemental vapour source, radiotracer + sectioning, analysis also accounts for diffusion along dislocations
Lando lt -Bö rnst ein New Series III/33A
74Pan1
2-118
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Sb in Si (cont.)
0.214 15
3.65 4.08
Fig.
Ref.
temperature dependence and mechanism of diffusion (cont.) 1192
D0 = 6·10−14 cm2s−1 D+ = 2.2·10−13 cm2s−1 evaluation of [66Mil1] in terms of Sb diffusion via neutral and positively charged vacancies
75sha1
1190-1405 950-1200
D0 via neutral vacancies D− via singly negatively charged vacancies review and evaluation of literature data including [71Gho2]
81fai1
1000
D = 1.25·10−14 cm2s−1, 4-point-probe and radiotracer 125Sb + sectioning
1150
D = 1.8·10−13 cm2s−1 for C0 = 2·1018 cm−3, single crystal, Sb vapour deposition + Si capping, radiotracer 125Sb + sputter sectioning
Sb in Si
177
82Nei1 82Nei2
effects of high concentration and heavy doping 3.91 1.43 2.39
9.70·103 3.65·102 1.43·102
Methods and Remarks
[Ref. p. 2-196
4.87 4.44 4.30
1215-1300 1215-1300 1215-1300
Al background doping: 2·1017 cm−3 Al background doping: 2·1018 cm−3 Al background doping: 1019 cm−3 FZ crystals, pn-junction method, see [63bol1]
1192-1290
crystals doped by diffusion or during growth up to 1021 cm−3 (n-type) or 2.4·1018 cm−3 (p-type), electroplated layer source, radiotracer 124Sb + mechanical sectioning, doping-dependent DSb, vacancy mechanism
180
66Mil1
1200
D = 2·10−13 cm2s−1, p-type single crystals, 7·103 dislocations/cm2, Sb2O5 source in Ar ambient, radiotracer 124Sb + chemical sectioning, C0 = 1017-4·1019 cm−3
180
70Usk1
1000-1150 1000-1150 1000-1150
C0 = 5.0·1018 cm−3 C0 = 1.0·1019 cm−3 C0 = 4.5·1019 cm−3 p-type single crystals, Sb-doped surface oxide, N2 ambient, 4-point-probe + electrochemical sectioning, Bolzmann-Matano analysis, Sb-vacancy pair mechanism
189
79Son1
58Pet1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Sb in Si (cont.) 17.5 0.01 659 122 18.4 0.07 0.52 7.2 0.02 1.57
5.85·10−6
4.05 3.75 4.58 4.39 4.19 3.22 3.48 3.83 2.96 3.66
1.65
Fig.
Ref.
effects of high concentration and heavy doping (cont.) 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200 1000-1200
D0 via neutral vacancies equals total intrinsic DSb D2− via doubly negatively charged vacancies B background doping ca. 1.0·1020 cm−3 B background doping ca. 1.3·1020 cm−3 B background doping ca. 1.8·1020 cm−3 As background doping 1.1·1020 cm−3 As background doping 9.0·1019 cm−3 As background doping 7.2·1019 cm−3 As background doping 1.8·1020 cm−3 As background doping 4.3·1019 cm−3 CZ crystals, As or B background doping by implantation, Sb implantation, annealing in N2 ambient, SIMS, Sb+B− pairing effects suggested
1100
CZ crystals, Sb implantation and damage anneal, P implantation or thermal pre-deposition, annealing in N2 ambient, SIMS, CP < 2·1020 cm−3, enhanced DSb
1000 & 1050
FZ crystals, heavy P doping by implantation and diffusion, 121Sb or 119Sb implantation, RTA in Ar ambient, differential Hall effect, RBS, Mössbauer spectroscopy, DSb increases with (n/ni)4 for n/ni > 20, new Sb-containing complex observed
1000 & 1050
enhanced diffusivities for CSb > 2.5·1020 cm−3 from [88And1] interpreted within vacancy-percolation model
89Mat2
700-1050
FZ crystals with heavy P, As, or Sb doping, 119Sb implantation, RTA, Mössbauer spectroscopy, RBS, differential Hall effect, Sb-vacancy-donor complex as moving entity suggested
92Nyl1
800-1100
FZ crystals, P doping up to 5·1020 cm−3 by implantation, Sb implantation, RTA, SIMS, RBS, Hall effect, enhanced DSb above vacancypercolation limit
Sb in Si
128 131 178 179 180 181 188 189
86Fai1
86Nis1
128
88And1
181 189
93Nyl1 90Gai1 89Nyl1
184
81Miz1
effects of surface reactions or ambient 1000-1200
Lando lt -Bö rnst ein New Series III/33A
Methods and Remarks
2-119
Sb-diffused CZ crystals with undoped epitaxial layer, annealing in O2 ambient, pn-junction staining, spreading resistance, oxidation-retarded DSb, vacancy undersaturation
2-120
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Sb in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
182
82Ant2
effects of surface reactions or ambient (cont.) 1100
Sb-implanted CZ crystals, annealing in dry O2 vs. N2, C-V profiling, oxidation-enhanced DSb, dependence on oxidation time, fI = 0.015
1070
Sb-implanted single crystals with epitaxial layer, P2O5 source in N2 ambient, pn-junction staining, retarded DSb
83Har1
1000-1150
Sb-diffused FZ or CZ crystals, annealing in NH3 or N2, pn-junction staining, DSb enhancement under bare surface, retardation under SiO2 film, effect of surface orientation
83Miz1
1100
Sb-diffused FZ or CZ (100) crystals, backside oxidation in dry O2, pn-junction staining, retarded diffusion under Si3N4 capping at front side, effects of oxygen precipitation
183
83Miz2
1160
CZ crystals with buried Sb-doped layer, annealing in dry O2, pn-junction staining, DSb retardation for (100) orientation, enhancement for (111) after long times
184
83Tan3
1100-1250
D(1250 oC) = 6.75·10−13 cm2s−1, p-type wafer, Sb-doped glass layer in O2/Ar or O2/N2 ambient, SIMS, spreading resistance, RBS, retarded diffusion
84Pin1
1100
Sb-implanted FZ crystals, annealing in NH3 ambient, spreading resistance, time dependence of nitridation and oxynitridation effect, fI < 0.32
85Fah1
1100
Sb-implanted CZ crystals, annealing with bare or capped surfaces in N2, spreading resistance, pnjunction staining, nitridation-enhanced DSb, also out-diffusion observed
85Koo1
1100
CZ wafers with buried oxide layers, Sb implantation, annealing with various cappings in NH3 or O2, pn-junction staining, reduced (oxy)nitridation and similar oxidation effects with respect to bulk wafers
86Fah2
1000-1100
Sb-implanted FZ crystals with undoped epitaxial layer, annealing in dry O2, SIMS, retarded DSb, fI = 0.01 at 1000 oC
86Gue1
1100
simultaneous evaluation of literature data concerning oxidation-influenced DSb and stacking fault growth
86Yos1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Sb in Si (cont.)
6.6
Methods and Remarks
2-121
Fig.
Ref.
effects of surface reactions or ambient (cont.) 1100
numerical analysis of oxidation-retarded diffusion, data from [81Miz1, 83Miz2]
950
single crystals with buried Sb-doped layer, sputterdeposition of TaSi2 film, annealing in N2, spreading resistance, pn-junction staining, enhanced DSb during silicidation
1100-1200
FZ crystals with Sb-doped buried layer, POCl3 or implanted source in mixed O2/N2 ambient, spreading resistance, SIMS, TEM, retarded DSb
1050
CZ crystals with Sb-doped buried layers, annealing in NH3 with or without SiO2 capping, SIMS, spreading resistance, (oxy)nitridation effects, fI < 0.02
200
epitaxial film with Sb-doped buried layer, evaporated Pt layer, silicidation in Ar ambient, SIMS, RBS, enhanced DSb preferentially towards surface
700-800
wafer with Sb-doped buried layer, Co or Ti evaporation, silicidation by RTA, SIMS, pnjunction staining, enhanced DSb preferentially towards surface
91Hon1 92Hon1
1100
analysis of oxidation-retarded diffusion, data from [81Miz1], fI = 0.029
92Oki1
850-1050
wafer with As doping 4·1019 cm−3, low-dose Sb implantation, epitaxial layer growth, annealing in dry O2, SIMS, oxidation-retarded DSb, fI(850 oC) < 0.0035
92Per1
1100
analysis of nitridation-influenced DSb data [85Fah1] including interstitialcy, vacancy, dissociative, and dissociation mechanism
92Van1
Sb in Si
87Bra1 87Hu1
185
87Tsa1
89Fah1
186
91Wit1 92Wit1 92Pic3
anomalous diffusion after implantation
1.8
Lando lt -Bö rnst ein New Series III/33A
500-800
single crystals, annealing after room-temperature or high-temperature in situ implantation, NAA + electrochemical sectioning, enhanced DSb depending on dose rate
660-850
FZ or CZ crystal, Sb implantation above amorphization threshold, epitaxial regrowth, precipitation annealing, TEM and RBS, transient enhanced DSb due to excess self-interstitials
70Gam1 70Gam2 70Nam1 187
85Pen1 86Pen1 86Pen2 88Pen1
2-122
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
Sb in Si (cont.)
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
anomalous diffusion after implantation (cont.) 86Nyl1
580-840
Sb-implanted FZ crystals, RTA in N2 ambient, Mössbauer spectroscopy on 119Sb, RBS, TEM, Hall effect, formation of Sb-vacancy complexes and Sb precipitates depending on temperature and implantation dose
700-1100
CZ crystals, Sb implantation + damage anneal, Si implantation above amorphization threshold, furnace annealing in N2 or electron-beam heating, pn-junction staining, SIMS, X-ray diffraction, no enhanced DSb
750-900
Sb-implanted CZ crystals, Si implantation above amorphization threshold, annealing in N2, pnjunction staining, X-ray diffraction, enhanced DSb correlates with implantation-induced local strain
87Ser1
1000
single crystal implanted through oxide layer, precipitation annealing, SIMS, TEM, modeling of precipitation process
89Bra1
1100
single crystals, high-dose Sb implantation, annealing in N2/O2 mixture, differential Hall effect, TEM, profile broadening and precipitation
89Nob1
700-1050
epitaxial wafers with heavy B or As doping, Sb implantation, RTA and furnace annealing, SIMS, no transient enhanced DSb
91Gil1
950
Sb-doped wafer, continuous B implantation at 950 oC, SIMS, Sb accumulation at surface due to flux of Sb-vacancy pairs
92Pic2
Sb in Si
170
87Ang1 88Sol1
special effects or conditions
1.53
1200
Sb drive-in after pre-deposition from mixed (CH3)3Sb/SiH4 ambient, sheet resistance, pn-junction measurement
70Git1
600-900
diffusion from Sb-doped substrates into growing epitaxial films, see [86wöh1]
74Ari1
900
epitaxial layer on Sb-doped substrate, annealing under proton irradiation, C-V profiling, enhanced DSb independent of dose
72Ohm1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Sb in Si (cont.)
13.6
3.9
Methods and Remarks
2-123
Fig.
Ref.
special effects or conditions (cont.) 1050 & 1150
single crystals, dislocations density < 5·102 cm−2, Sb-doped oxide source in N2 ambient, 4-point-probe + electrochemical sectioning, pn-junction staining, DSb enhancement due to diffusion-induced dislocations
180
81Son1
1050-1150
polycrystals, grain size 5-50 µm, dried aqueous SbCl3 source in Ar ambient, radiotracer 125Sb + mechanical sectioning, C0 < 5·1018 cm−3, dislocation-enhanced lattice diffusivity, also DSb-induced dislocations in coarse-grained crystals
189
85Spi1 86Spi1
1050-1200
FZ crystals with Sb-doped buried layer, P implantation with Cmax below solubility limit, annealing in low-oxygen ambient, spreading resistance, pn-junction staining, retarded DSb
87Tsa2
1100
Sb-implanted FZ crystals, SiNx capping by chemical vapour deposition, annealing in Ar, pn-junction staining, enhanced DSb due to nitride-film stress
88Ahn1
550-950
Sb-doped delta layer within epitaxial film, annealing in N2/H2 mixture, SIMS, asymmetric redistribution and oxide interface segregation, enhanced C-dependent DSb
91Fuk1 91Fuk2
625-725
Sb-doped delta layer within epitaxial film, precipitation upon annealing, RBS, TEM, modeling of vacancy-percolation diffusion and precipitation
92Opd1
Bi in Si 1030
4.64
1220-1380
B-doped single crystals, Bi oxide source in low-pressure air ambient, pn-junction staining, C0 = (0.1-2.4)·1018 cm−3
131 191
56Ful1
896
4.12
1150-1350
FZ crystals, dislocation density < 3·104 cm−2, Bi-metal or -oxide source in Ar flow, sheet resistance + step etching, pn-junction staining
191
65Pom1
1.08
3.85
1190-1394
Bi-doped epitaxial layers on FZ substrate, capping by amorphous Si3N4, flowing H2 ambient, intrinsic conditions, spreading resistance, Bi-vacancy pair mechanism
161 190 191
71Gho2
1.08 896
3.85 4.12
1190-1394 1150-1350
D0 via neutral vacancies D− via singly negatively charged vacancies review and evaluation of literature data including [65Pom1, 71Gho2]
Lando lt -Bö rnst ein New Series III/33A
81fai1 77fai1
2-124
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
2.0
755-800
FZ or CZ crystal, Bi implantation above amorphization threshold, epitaxial regrowth, precipitation annealing, TEM, RBS, transient enhanced DBi due to excess self-interstitials
187
85Pen1 86Pen1
2.50
1050-1200
CZ crystals, spin-on Bi source under SiO2 capping, N2 ambient, 4-point probe + electrochemical sectioning, C0 < 4.0·1017 cm−3, Bi-vacancy pairs
191
89Ish1
1100
CZ crystals, spin-on Bi source under SiO2 capping, pre-diffusion in N2 ambient, drive-in under O2 or N2 atmosphere, 4-point probe + electrochemical sectioning, oxidation-retarded DBi
Bi in Si (cont.)
2.00·10−4
90Ish1
2.2.1.16 Solute elements of groupVIA (oxygen group). (See Figs. 192-202, p. 190) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
O in Si
Methods and Remarks
Fig.
Ref.
Diffusion under regular conditons 2.55
1250-1400
CZ crystals, internal friction measurements 25-1100 oC, relaxation maximum at 1030 oC, motion between adjacent interstitial sites
57Sou1 60Sou1
FZ crystals, diffusion in air or O2 ambient, thermal donor formation at 450 oC, resistivity by 2-pointprobe, no effect of 108 dislocations/cm2
59Log1
evaluation of internal friction data [57Sou1] with relaxation maximum at 1030 oC
60Haa1
135
3.5
0.21
2.55
0.23
2.56
377-1090
CZ crystals, annealing in molten-salt bath at 377 oC, recovery of stress-induced dichroism, IR absorption, local hopping of Oi between bent Si-O-Si bonds, includes internal friction data [60Sou1]
64Wat1 82Wat1
9.1·10−2
2.4
1100-1200
FZ (111) and (100) crystals, diffusion from wet O2 ambient, X-ray diffraction, depth analysis of lattice strain due to oxygen incorporation, no essential dependence on surface orientation
73Tak1
1150
D = 1.2·10−10 cm2s−1, out-diffusion from CZ crystals, spreading resistance after 450 oC thermal donor formation
77Hu1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
O in Si (cont.)
Methods and Remarks
2-125
Fig.
Ref.
Diffusion under regular conditons (cont.) 1100 & 1150
D(1100 oC) = 1.3·10−10 cm2s−1, out-diffusion from CZ crystals, spreading resistance after 450 oC thermal donor formation
78Rui1
22.6
3.15
1000-1280
FZ crystals, grown surface oxide enriched in 18O, nuclear reaction analysis + mechanical sectioning, erfc profiles, effects due to shallow dopants investigated
1.5
2.77
1110-1300
single crystals, 102-104 dislocations/cm2, indiffusion, IR absorption and charged particle activation analysis, interstitial oxygen
7.0·10−2
2.44
700-1240
FZ crystals, diffusion under 1atm H218O steam pressure, SIMS, erfc profiles
193
82Mik1
0.17
2.54
330-400
CZ crystals pre-heated at 1350 oC, recovery kinetics of stress-induced dichroism, IR absorption, D0 and Q include [82Mik1], enhanced Oi reorientation rate in crystals pre-heated at 900 oC
193 195
83Sta1 83Ben1
2.0·10−2
2.42
650-1050
CZ crystals, kinetics of oxygen precipitation, IR absorption, etch pitch counts, optical and neutron scattering
0.11
2.51
350-1250
compilation of literature data including in-diffusion [82Mik1], precipitation [83Bin1] and stressrecovery [83Sta1, 83New2] studies
193
84Liv1 83New2
3.2
2.91
1150-1375
out-diffusion from CZ crystals in O2 ambient, indiffusion into FZ crystals in Ar ambient, charged particle activation analysis, enhanced diffusion below 1150 oC observed
193
85Ito1
1200
D = ca. 6·10−10 cm2s−1, out-diffusion from CZ crystals, comparison between profiling techniques: CPAA, X-ray lattice parameter analysis and spreading resistance after thermal donor formation
0.14
2.53
700-1160
out-diffusion from CZ crystals, SIMS, erf-type profiles, interstitial mechanism, little effect of ambient conditions (N2, wet O2 or P-indiffusion)
3.3·10−2
2.43
750-1050
CZ crystals, annealing in Ar ambient, growth kinetics of square-shaped oxide precipitates, high-voltage TEM
0.13
2.50
700-1100
FZ crystals, redistribution of implanted 18O, SIMS, interstitial mechanism, no dependence on implanted dose
Lando lt -Bö rnst ein New Series III/33A
193
80Gas1
82Vak1
83Bin1 84Liv1 83New3
85Sug1
192 193
85Lee1
85Wad1 80Wad1 193
86Lee1
2-126
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
O in Si (cont.) 0.13
2.53
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
193 195 196
86Mik1
Diffusion under regular conditons (cont.) 330-1375
Overall fit to literature data including SIMS [82Mik1, 85Lee1, 86Lee1], CPAA [80Gas1, 85Itoh1] and dichroism [83Sta1, 83New2]
20-1375
review of oxygen diffusion under regular and special conditions: experimental data and theoretical modeling
O in Si
94new1
enhanced diffusion under virtually regular conditions 450-1230
D(450 oC) = 2.7·10−14 cm2s−1 (enhanced), out-diffusion from CZ crystals, spreading resistance after 450 oC thermal donor formation, normal diffusivities above 900 oC, no effect of ambient (N2, O2, Ar, H)
195
81Gaw1
485
CZ crystals, oxygen precipitation leading to ribbonlike defects (coesite), TEM and IR spectroscopy, enhancement by 3-4 orders of magnitude
195
85Ber1
0.17 3.3·10−8
0.54 0.88
700-1160 400-525
normal diffusivity of atomic Oi fast Oi diffusivity component via O2 molecules out-diffusion from CZ crystals, redistribution of implanted 18O in FZ crystals, SIMS, also vacancy-O and self-interstitial-O complexes considered
194 195
86Lee2 86Lee3
3·10−5
1.85
250-400
D0 recalculated from Arrhenius plot, CZ crystals: undoped or Ge-doped (1019 cm−3), loss of stressinduced dichroism, IR absorption, enhancement by O-vacancy interactions suggested, effect of cooling rate, influence of pre-heating involving metalllic contamination
195
86Tip1
500-600
CZ crystals, precipitation loss of Oi, IR absorption, particle growth explained by normal O diffusion
500-1000
out-diffusion from CZ crystals, SIMS and IR absorption, enhanced diffusion below 650 oC, enhancement factor up to 1000 depending on temperature, time and wafer
425-700
review of literature data with emphasis on enhanced diffusion at low temperatures, molecular oxygen (O2) suggested as fast-diffusing species
87Mes1 195
88Lee1
89Gös1 82Gös1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
O in Si
3·10−10
Methods and Remarks
2-127
Fig.
Ref.
Diffusion under special conditions
0.16
1150
out-diffusion from CZ crystals, no impeding effect of various surface coverings: SiO2, Si3N4 or combined
80Hu1
1250
103-104 dislocations/cm2, diffusion in dry air with various surface coatings: B2O3, P2O5 or SiO2, CPAA + chemical sectioning, retardation due to O accumulation at diffusion-induced dislocations
81Vak1
1100
out-diffusion from CZ crystals, effect of various processing conditions, SIMS, retardation under oxidizing ambient suggests vacancy-dominant mechanism
83Hec1
27
D = 10−21 cm2s−1, CZ crystals, annealing under electron irradiation, loss of stress-induced dichroism, IR absorption, radiation-enhanced diffusivity, interstitialcy mechanism suggested
83New2
27-84
B-doped FZ crystals, subsequent exposure to H2 and O2 plasma, formation kinetics of B-OH complexes, fast diffusing O species different from bond-centered Oi, see [85Joh1]
84Han1
100-400
CZ crystals, boron doping 5·1019 cm−3, exposure to 18 O and 2H from gas discharge, SIMS, absence of 18 O penetration conflicts with [84Han1]
85Joh1
797-1047
D = (0.93-4.46)·10−9 cm2s−1, evaluation of Oi loss from CZ crystals with high carbon content [81Ler1], enhanced out-diffusion via Ci-Oi complexes
85Bab1
20-350
CZ crystals, diffusion under electron irradiation, IR absorption, enhanced diffusivity above 300 oC possibly due to dissociation of transient O-vacancy defects
86Oat1
350-450
low-carbon CZ crystals, light B doping, annealing in H plasma, IR absorption, 4-point probe, enhanced thermal donor formation, H-enhanced D0 suggested, no enhancement in Ar or air ambient
88Bro2
750 & 1000 CZ crystals, light or heavy carbon doping, outdiffusion of O and C in O2 ambient, SIMS, enhanced or retarded O diffusivity depending on carbon content and temperature 1100
Lando lt -Bö rnst ein New Series III/33A
D = 1.1·10−10 cm2s−1, CZ crystals, light or heavy Sb doping, out-diffusion in wet O2 ambient, SIMS, no influence of Sb or intrinsic point defects
88Shi1
88Wij1
2-128
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [oC]
O in Si (cont.)
1.0
7.1·10−4
1.41·102
Methods and Remarks
[Ref. p. 2-196
Fig.
Ref.
Diffusion under special conditions (cont.) 350-450
CZ crystals nominally undoped, annealing in H or 2 H plasma, IR absorption and 4-point probe resistivity, enhanced rates of both thermal donor production and loss of Oi from solution, enhanced O diffusion
89Mur1
950-1100
CZ crystals, Sb doping (0.23-2.1)·1018 cm–3, out-diffusion in N2 ambient, SIMS, no significant effect of Sb
90Pag1
460-800
out-diffusion from CZ crystals, carbon doping 2·1017 cm−3, SIMS and IR absorption, enhanced diffusivity below 690 oC attributed to Ci-Oi complexes
90Wij1
2.0
270-340
CZ crystals, pre-heated at 900 oC in 10% H2 ambient, loss of stress-induced dichroism, IR absorption, enhancement caused by hydrogen
2.0 2.2
347-397 347-397
virtually undoped CZ crystals Ge-doped CZ crystals: 1020 cm−3 kinetics of thermal donor formation, Hall effect, enhanced diffusivity due to vacancy-O clusters, reduced effect from vacancy trapping by Ge
91Kor1
1100
thick epitaxial layer grown on CZ substrate, outdiffusion during growth process from substrate into epi-layer, microscopic transversal IR spectroscopy
92Ged1 90Ged1
980-1200
out-diffusion from CZ crystals, RTA and furnace annealing in various gas ambients, CPAA + sectioning, radiation-enhanced diffusivity by RTA, maximum effect in H-containing ambient
93Mad1
750-900
out-diffusion from heavily B-doped CZ crystals, SIMS and TEM, retarded diffusivity due to B-O pairing
93Wij1
1150
out-diffusion from CZ substrate during epitaxial layer growth, SIMS, no effect of heavy doping of substrate with B or Sb
93Wij2
1000-1200
out-diffusion from CZ crystals, 1 atm H 2 ambient, SIMS, hydrogen enhancement effect observed, direct Oi-H interactions suggested
93Zho2
2.68
3.1
195
91McQ1 91New1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
2-129
Q [eV]
T-range [oC]
Methods and Remarks
Fig.
Ref.
0.92
2.20
1050-1370
FZ and CZ crystals, pn-junction depth measurement, Hall effect + resistivity, major energy level EC −0.18 eV, major incorporation as Ss, diffusion as Si
198
59Car1
5.95·10−3
1.82
1000-1200
FZ crystals, 5·104 dislocations/cm2, elemental vapor source, radiotracer 35S + sectioning, analysis accounts for Si-S compound formation on surface
198
74Gru1
0.22
2.1
994-1234
Si-limited kick-out diffusivity of Ss (CieqDi/Cseq), FZ crystals, ca.108 dislocations/cm2, elemental vapour source, spreading-resistance and Hall effect, pre-dominance of Ec−0.318 eV level attributed to Ss, first evidence for kick-out mechanism from nonerfc profiles in dislocation-free Si
197 198
89Sto1
4.70·10−2
1.80
1055-1398
Si-limited diffusivity of Ss (CieqDi/Cseq) via kick-out and dissociative mechanism, FZ crystals, low-pressure vapour source, radiotracer 35S + mechanical sectioning, erfc profiles
196 198
93Rol1
600-1100
FZ crystals, isochronal annealing after Se implantation, RBS and channeling, time evolution of Ses energy level, trapping at Si-SiO2 interface suggested
1050-1250
vapour phase source, sheet resistance + sectioning, donor level EC −0.23 eV
600-700
D(700 oC) = 2·10−13 cm2s−1, epitaxial layer, low-dose Se-implantation, differential DLTS, Gaussian distributions, double donor: EC −0.225 and EC −0.485, complete recovery of implantation damage at 700 oC
S in Si
Se in Si
0.95
2.60
70Mey1
200
76Zhd1 77Ric1
2.47
2.84
800-1250
single crystals, quenching after diffusion from vapour phase, spreading resistance and Hall effect, donor levels EC −0.2 eV and EC −0.3 eV, erfc profiles
200
78Vyd1
0.11
2.42
1000-1250
FZ crystals, quenching after diffusion from SeO2 source, differential Hall effect and pn-junction depth measurements, donor level EC −0.26 eV
200
79Kim1
900-1050
D = (0.46-7.3)·10−11 cm2s−1: monotonic increase with temperature, epitaxial layers, Se-diffused p+n-junctions, space-charge capacitance techniques and SIMS, double donor levels EC −0.30 eV and EC −0.57 eV
199 200
80Gri1 80Gri2
Lando lt -Bö rnst ein New Series III/33A
2-130
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
Se in Si (cont.) 0.3
2.6
1000-1265
FZ crystals, quenching after diffusion from vapour phase, 4-point probe + mechanical sectioning, Hall effect, donor level EC −0.30 eV, complete ionization at 20 oC assumed
200
88Stü1
9.54·10−2
2.50
840-1282
FZ crystals, quenching after diffusion from vapour phase, spreading resistance, Sei-limited diffusivity of Ses via kick-out or dissociative mechanism
196 200
90Grü1
0.50
3.34
900-1250
CZ crystals, Si powder added to Te source, SIMS, erfc profiles, substitutional mechanism
202
82Jan1
1.9·10−4 2.1·108
2.33 5.92
917-1356
two-exponential fit reproducing Tei-limited kick-out diffusivity of Tes (CieqDi/Cseq), FZ crystals, radiotracer 121Te from decay of implanted 121Xe + mechanical sectioning, spreading resistance based on donor level EC −0.199 eV after diffusion from inactive Te vapour
0.9
3.3
1045-1305
FZ crystals, quenching after diffusion from vapour phase, 4-point probe + mechanical sectioning, Hall effect, donor level EC −0.20 eV, complete ionization at 20 oC assumed
202
88Stü1
4.8·10−2 6.3·104
3.04 4.86
876-1380
two-exponential fit representing simultaneous diffusion via vacancy mechanism (3.04 eV) and Tei-limited kick-out mechanism (4.86 eV), FZ crystals, radiotracer 121Te from decay of implanted 121Xe + mechanical sectioning, Gaussian profiles, extremely low concentrations
196 201 202
93Rol2
Fig.
Ref.
Te in Si
86Sto2
2.2.1.17 Solute elements of group VIIA (fluorine group). (See Figs. 203-205, p. 193) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
400-1100
P-doped single crystals, low- and high-dose BF2 implantation at RT and −110 oC, isochronal annealing in forming gas, SIMS, no diffusion below 600 oC observed, F accumulation in damaged region beyond c/a interface
F in Si 79Tsa1 78Tsa1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Methods and Remarks
2-131
Fig.
Ref.
F in Si (cont.) n-type single crystals, high-dose BF2 implantation, pulsed laser annealing, CPAA, F redistribution and Si recrystallization depend on laser energy density, only diffusion toward surface, no trapping at residual defects
82Nyl1
925
single crystals, low energy implantation of F, BF or BF2, SIMS and C-V profiling, redistribution of F and B during 20 min annealing, effects of implantation dose and damage
83Wil1
1000
P-doped wafers with oxide layers 0-30 nm, BF2 implantation and epitaxial regrowth at 550 oC, RTA, SIMS and 4-point probe, segregation of F at Si/SiO2 interface
87Ozt1
calculations within local-density-functional theory, hopping of Fi– between tetrahedral sites through hexagonal sites, Si-F-Si bond-center formation near surface proposed
88Wal1
ca. 25
P-doped crystals, exposition to F2 or SF6 plasma at RT, CPAA and X-ray photoelectron spectroscopy, F penetration into plasma-induced pores
91Bra2
700-1000
single crystals, 30 min annealing after F implantation, CPAA and SIMS, migration towards surface and out-diffusion, accumulation to implantation-induced vacancies
91Yu1
300-1050
single crystals (n-, n+-, p-type), F implantation below amorphization threshold, isochronal annealing in He ambient, SIMS, thermal desorption spectrometry, preferential migration towards surface starting at 550 oC, out-diffusion depends on concentration but not on electric field
50-750
CZ crystals (n-, n+-, p-type), F implantation below amorphization threshold, isochronal annealing in He ambient, SIMS, thermal desorption spectrometry, positron-beam profiling of vacancytype defects, F-diffusion stage at 700 oC, dissociative mechanism
< 0.7
Lando lt -Bö rnst ein New Series III/33A
203
92Jen1
94Sze1 95Sze1
2-132
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
1100-1150
single crystals, annealing after 35Cl implantation through SiO2 film, accelerator mass spectroscopy after neutron activation, preferential diffusion towards front surface, little out-diffusion for highdose implants, similarities with F
204
95Dat1
600-1010
FZ crystals, I implantation above amorphization threshold, isochronal annealing, RBS and channeling, recrystallization above 600 oC, no out-diffusion barrier at surface
205
70Mey1
Fig.
Ref.
Cl in Si
I in Si
2.2.1.18 Solute elements of group VIIIA (helium group). (See Figs. 206-210, p. 194) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [oC]
Methods and Remarks
1.65·10−10
1.45
967-1207
0.11
1.26
1174-1207
solubility-diffusivity product normalized to atomic density of Si (C eqD/C0), recalculated from Arrhenius plot (vs. stated Q value: ca.1.74 eV) diffusivity deduced from permeation behaviour high ohmic CZ crystals, permeation measurement, mass spectrometry, migration enthalpy from response to temperature change
5.1·10−4
0.581 467-977
B-doped crystals (1020 cm−3), high dislocation density, He produced by neutron activation of 10 B dopant or exposure to plasma, He release kinetics, mass spectrometry, little influence of radiation damage, He bubble formation, doping or dislocations
1.28·10−3
1.8
extended Hückel theory calculations including lattice relaxations, interstitial mechanism, hopping between tetrahedral sites through hexagonal site
79Kap1
samples pre-thinned by Ar-ion milling, He implantation at RT, TEM, thermal desorption spectroscopy, He release from bubbles completed around 900 oC, agreement with permeation data [56Wie1]
87Gri1
He in Si
20-1000
56Wie1
207 208
64Lut1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [oC]
Methods and Remarks
2-133
Fig.
Ref.
He in Si (cont.) D(1198 oC) = 7·10−5 cm2s−1 (estimated), ab initio molecular dynamics calculations, interstitial mechanism, hopping between tetrahedral sites through hexagonal site, He atom inside vacancy not stable
0.82
7.6·10−3 1.6·10−2
0.80 0.90
92Ala1
360-800 300-900
diffusivity from in-situ desorption diffusivity from post-implantation desorption 280 µm-thick single crystals, thermal desorption spectroscopy after He implantation at RT or during implantation at high temperature, reduced diffusivity for high concentrations, low temperatures and large migration distances
206 207 208
94Jun1
20-650
(111) wafers, high-dose Ne implantation, isochronal annealing in Ar flow, RBS + channeling, some outdiffusion at 650 oC observed
76Wil1
525-575
1-10 Ωcm wafers, surface layer amorphization by Si implantation, 20Ne implantation at −180 oC, isothermal vacuum annealing, TEM, CPAA, Ne out-diffusion during recrystallization
78Wit1
20-650
(111) wafers, high-dose Ar implantation, isochronal annealing in Ar flow, RBS + channeling, profile broadening below 520 oC observed
76Wil1
250-1200
single crystals (1000 Ωcm), Kr radiotracer implantation at high energy, isochronal vacuum annealing, radioactivity of released gas, retarded and anomalous behaviour observed
70Mat1
20-850
(111) wafers, low-to-high-dose Kr implantation, isochronal annealing in Ar flow, RBS + channeling, profile broadening and out-diffusion depending on dose and temperature
76Wil1
200-900
n-type crystals, implantation of 84Kr + 85Kr at RT, isochronal vacuum annealing, radiotracer technique, RBS, dose-dependent loss of Kr at 550-900 oC connected with recrystallization
77Wel1
Ne in Si
Ar in Si
Kr in Si
Lando lt -Bö rnst ein New Series III/33A
2-134
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-196
T-range [oC]
Methods and Remarks
Fig.
Ref.
525-1000
1-10 Ωcm wafers, surface layer amorphization by Si implantation, 84Kr implantation at −180 oC, isothermal vacuum annealing, TEM, RBS, Kr out-diffusion at 900-1000 oC after recrystallization
250-980
single crystals (1000 Ωcm), Xe radiotracer implantation below amorphization threshold, isochronal annealing in N2 ambient, radioactivity measurement of released gas
700
D = 10−15-10−14 cm2s−1: effective diffusivity during recrystallization, p-type wafers Xe-implanted above amorphization threshold, vacuum annealing, TEM, nuclear backscattering
75Mad1
20-850
(111) wafers, low-to-high-dose Xe implantation, isochronal annealing in Ar flow, RBS + channeling, profile broadening and out-diffusion depending on dose and temperature
76Wil1
350
n-type wafers, Xe implantation above amorphization threshold, recrystallization assisted by Ar-ion irradiation, RBS + channeling, Xe redistribution towards surface suppressed by co-implantation of As
93Has1
Kr in Si (cont.) 78Wit1
Xe in Si 5·10−5
1.70
210 209
70Mat1
Landolt -Börnst ein New Series III/33A
3 Diffusion in compound semiconductors
3-64
[Ref. p. 3-70
Figures for 3 –15 8 6 4
10
–12
10
GaAs
–13
10
2 –16 8 6 4
–14
10
–15
10
–17 8 6 4
Ga
10
2
As
As
–18 8 6 4
10
2 –19 10 8 6 4 2 –20
10
2 –1
2
Diff.coeff. D [m s ]
2 –1
Diff.coeff. D [m s ]
10
–16
10
–17
10
Ga [57E] Sb
–18
10
–19
10
Ga
–20
Ga
10 [61G1] [81P1,83P1] pAs2 = 0.75 atm [68K1]
0.66
0.70
[84W2]
–21
10
As
0.74 0.78 0.82 –3 –1 Inv. temp. 1/T [10 K ] Fig. 1. GaAs self diffusion coefficients D vs. inverse temperature 1/T.
Sb
–22
10
1.2 1.3 1.4 1.5 –3 –1 Inv. temp. 1/T [10 K ] Fig. 2. GaSb self diffusion coefficients D vs. inverse temperature 1/T.
–14
1.0
1.1
–14
10
10
[61G1]
S in GaAs
Si in GaAs
[61V]
–15
–15
10
2 –1
2 –1
Diff.coeff. D [m s ]
10 Diff.coeff. D [m s ]
Sb [60B2]
GaSb
–16
–16
10
10
[85P3] [68K1] [70Y]
–17
–17
10
10
[74M1] –18
–18
10
0.70
[65F3]
0.75
0.80 0.85 0.90 0.95 1.00 –3 –1 Inv. temp. 1/T [10 K ] Fig. 3. Diffusion coefficient D of Si in GaAs vs. inverse temperature 1/T. [90L1].
10
700
800
900 1000 1100 1200 Temperature T [°C] Fig. 4. Diffusion coefficients D of S in GaAs vs. temperature T.
Landolt - { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
–14
–11
10
10
T = 1130 °C
1000 °C
–16
T = 900 °C
2 –1
2 –1
–12
10 Diff.coeff. D [m s ]
–15
10 Diff.coeff. D [m s ]
T = 1000 °C
Zn in GaAs
S in GaAs
T = 800 °C
–13
10
10
T = 700 °C
–14
–17
10
10
–15
–18
10
3-65
–4
–3
10
–2
10
–1
10 10 1 10 Ambient As pressure pAs [atm] Fig. 5. Diffusion coefficient D of S in GaAs as a function of ambient As pressure pAs at T = 1000 °C and 1130 °C [70Y].
10
24
25
26
27
10 10 10 –3 Zn conc. NS (Zn) [m ] Fig. 6. Diffusion coefficient D of Zn in GaAs vs. Zn concentration NS(Zn) at various temperatures as derived from Boltzmann-Matano analysis [67C].
–10
10
26
10
10
Zn in GaAs
Zn in undoped InP
T = 1273 K
–11
10
25
Zn conc. N (Zn) [m ]
10
2 –1
Diff.coeff. D [m s ]
T = 973 K , EMP SIMS
–3
–12
10
–13
10
–14
24
10
23
10
10
–15
10
22
10
–16
10
24
10
25
26
27
10 10 10 –3 Zn conc. NS (Zn) [m ] Fig. 7. Diffusion coefficient D of Zn in GaAs at T = 1273 K as a function of Zn concentration NS(Zn) [72K1].
Landolt - { rnst ein New Series III/33A
0
20
40 60 80 100 Depth x [µm] Fig. 8. Zn concentration profiles measured by EMP and by SIMS after diffusion at T = 973 K into undoped InP [95W1].
3 Diffusion in compound semiconductors
3-66
24
26
10
Zn in Fe-doped InP
25
10
Ag in GaAs
T = 973 K , EMP SIMS
T = 1273 K
–3
–3
Ag conc. N (Ag) [m ]
10
Zn conc. N (Zn) [m ]
[Ref. p. 3-70
24
10
23
10
23
10
22
10
22
10
0
20
40 60 80 100 Depth x [µm] Fig. 9. Zn concentration profiles measured by EMP and by SIMS after diffusion at T = 973 K into Fe-doped InP [95W1].
60 80 100 120 Depth x [µm] Fig. 10. Typical concentration profile of Ag in GaAs at T = 1273 K [80T].
–13
10
10
Cr in GaAs
D = 9.8 ⋅ 10–4 exp (–3.0 eV/kT) 2 –1
Diff.coeff. D [m s ]
–15
–15
10 2 –1
Zn in Zn-saturated ZnSe
–14
10
Diff.coeff. D [m s ]
40
10
–14
–16
10
–17
[91Y,79T] near surface [86D2] bulk-diffusion [86D2] out-diffusion [82M2] out-diffusion [80K1] out-diffusion
10
–18
10
–19
10
10
–16
10
–17
10
–18
10
–20
10
–21
10
–19
10
–22
10
20
–13
–12
10
0
0.7
0.8
0.9 1.0 1.1 –3 –1 Inv.temp. 1/T [10 K ] Fig. 11. Diffusion coefficients D of Cr in GaAs vs. inverse temperature 1/T at various conditions.
0.66
eagle pitcher material vapor-grown material
0.74
0.82 0.90 0.98 1.06 –3 –1 Inv. temp. 1/T [10 K ] Fig. 12. Radiotracer self-diffusion coefficient D of Zn in Zn-saturated ZnSe vs. inverse temperature 1/T [71H].
Landolt - { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
–13
–13
10
Zn in Se-saturated ZnSe
–14
10
10
–4
D = 9.8 ⋅ 10 exp (–3.0 eV/kT)
2 –1
–15
10
–16
10
eagle pitcher material vapor-grown material
–17
10
D = 0.13 ⋅ 10–4 exp (–2.6 eV/kT)
–15
10
–16
10
–17
10
[71H] [67W4]
–18
–18
0.66
0.82 0.90 0.98 1.06 –3 –1 Inv. temp. 1/T [10 K ] Fig. 13. Radiotracer self-diffusion coefficient D of Zn in Se-saturated ZnSe vs. inverse temperature 1/T [71H].
0.74
10
0.82 0.90 0.98 1.06 –3 –1 Inv. temp. 1/T [10 K ] Fig 14. Radiotracer self-diffusion coefficient D of Se in Se-saturated ZnSe vs. inverse temperature 1/T.
Se in ZnSe
maximum Se2 pressure
0.74
Zn in ZnTe
–14
10 2 –1
Diff.coeff. D [m s ]
10
10
T = 1294 K
minimum Se2 pressure
–15
2 –1
–16
10
–15
10
–16
10
–17
10
–18
minimum total vapor pressure
10
–17
10
0.66
–13
–15
4⋅10
Diff.coeff. D [m s ]
Se in Se-saturated ZnSe
–14
Diff.coeff. D [m s ]
2 –1
Diff.coeff. D [m s ]
10
10
3-67
–12
10
–10
10
–8
10
–6
–4
–2
10 10 10 Se2 pressure pSe2 [atm]
1
2
10
Fig. 15. Dependence of radiotracer self-diffusion coefficient D of Se in ZnSe vs. Se2 vapour pressure p Se 2 at T = 1294 K [71H].
Lando lt - { rnst ein New Series III/33A
0.75
at Zn saturation 3 at Zn saturation + 2 ⋅ 1025 Al at/m at Te saturation congruently subliming composition 0.80
0.85 0.90 0.95 1.00 1.05 1.10 –3 –1 Inv. temp. 1/T [10 K ] Fig. 16. Self-diffusion coefficient D of Zn in ZnTe vs. inverse temperature 1/T at various saturation conditions [69R4].
3 Diffusion in compound semiconductors
3-68
–12
–14
10
10
Te in ZnTe
–15
10 2 –1
Diff.coeff. D [m s ]
2 –1
Diff.coeff. D [m s ]
Cd in Cd-saturated CdTe
–13
10
–16
10
–17
10
D = 3.26 ⋅ 10–3 exp (–2.67 eV/kT) pCd = max
–14
10
–15
10
–16
–18
10
10
at Te saturation at Zn saturation maximum possible values
–19
10
[Ref. p. 3-70
0.70
–17
0.75
0.80 0.85 0.90 0.95 1.00 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 17. Self-diffusion coefficient D of Te in ZnTe vs. inverse temperature 1/T at Te saturation and Zn saturation [69R4].
10
0.98 1.06 1.14 1.22 1.30 –3 –1 Inv. temp. 1/T [10 K ] Fig. 18. Radiotracer self-diffusion coefficient D of Cd in Cd-saturated CdTe vs. inverse temperature 1/T [68B2].
–13
0.82
0.90
–13
10
10
Cd in CdTe
Cd in Te-saturated CdTe
T = 998 K
10
2 –1
Diff.coeff. D [m s ]
2 –1
Diff.coeff. D [m s ]
–14
10
–14
–15
10
minimum obtainable pCd
–16
10
–4
10
–3
10
maximum obtainable pCd –2
–1
10 10 1 10 Cd pressure pCd [atm] Fig. 19. Radiotracer self-diffusion coefficient D of Cd in CdTe vs. partial vapour pressure of Cd pCd at T = 998 K [68B2].
D = 1.58 ⋅ 10–3 exp (–2.44 eV/kT) pCd = min
–15
10
–16
10
–17
10
–18
10
0.85
0.95
1.05 1.15 1.25 1.35 –3 –1 Inv. temp. 1/T [10 K ] Fig. 20. Radiotracer self-diffusion coefficient D of Cd in Te-saturated CdTe vs. inverse temperature 1/T at minimum partial pressure of Cd [68B2].
Landolt - { rnst ein New Series III/33A
Ref. p. 3-70]
3 Diffusion in compound semiconductors
–13
10
Te in CdTe
[67W4] [68B2]
–14
2 –1
Diff.coeff. D [m s ]
10
–15
10
pTe2 = max
–16
10
–17
10
pTe2 = min
–18
10
0.85
1.05 1.15 1.25 1.35 –3 –1 Inv. temp. 1/T [10 K ] Fig. 21. Radiotracer self-diffusion coefficient D of Te in CdTe vs. inverse temperature 1/T at maximum and minimum partial pressure of Te2 [68B2].
Lando lt - { rnst ein New Series III/33A
0.95
3-69
3 Diffusion in compound semiconductors
3-70
3.9 References for 3 54B1 54B2 54B3
Brady, E.L.: J. Electrochem. Soc. 101 (1954) 466. Brebick, R.F., Scanlon, W.W.: Phys. Rev. 96 (1954) 598. Brower, G.: Philips Res. Rep. 9 (1954) 366.
55B1 55B2
Boltaks, B.I.: Dokl. Akad. Nauk SSSR 100 (1955) 901. Boltaks, B.I.: Zh. Tekh. Fiz. 25 (1955) 767.
56B 56K 56S
Boltaks, B.I., Mokhov, Yu. N.: Zh. Tekh. Fiz. 26 (1956) 2448. Kovalchik, T.L., Maslakovets, Yu. P.: Zh. Tekh. Fiz. 26 (1956) 2417. Schillman, E.: Z. Naturforsch. 11a (1956) 472.
57B1 57B2 57B3 57E 57K
Bloem, J., Kroger, F.A.: Philips Res. Rep. 12 (1957) 281. Bloem, J., Kroger, F.A.: Philips Res. Rep. 12 (1957) 303. Boltaks, B.I., Mokhov, Yu. N.: Sov. Phys. Tech. Phys. (English Transl.) 1 (1957) 2366. Eisen, F.H., Birchenall, C.E.: Acta Metall. 5 (1957) 265. Kulikov, G.S., Boltaks, B.I.: Sov. Phys. Tech. Phys. (English Transl.) 2 (1957) 67.
58B 58F 58S 58V
Boltaks, B.I., Mokhov, Yu. N.: Sov. Phys. Tech. Phys. (English Transl.) 3 (1958) 974. Fuller, C.S., Whetan, J.M.: J. Phys. Chem. Solids 6 (1958) 173. Secco, E.A.: J. Chem. Phys. 29 (1958) 406. Van der Pauw, L.J.: Philips Res. Rep. 13 (1958) 1.
59C 59K 59P 59S
Clarke, R.L.: J. Appl. Phys. 30 (1959) 957. Kuliev, A.A., Abdullaev, G.B.: Sov. Phys. Solid State (English Transl.) 1 (1959) 545. Pines, B.Y., Chaikovskii, E.F.: Sov. Phys. Solid State (English Transl.) 1 (1959) 864. Scanlon, W.W.: Solid State Phys. 9 (1959) 83.
60B1
60K 60W
Bodakov, Y.A., Lomakins, G.A., Naumov, C.P.: Sov. Phys. Solid State (English Transl.) 2 (1960) 49. Boltaks, B.I., Gutorov, J.A.: Sov. Phys. Solid State (English Transl.) 1 (1960) 930. Carlson, R.O.: J. Phys. Chem. Solids 13 (1960) 65. Cunnell, F.A., Gooch, C.H.: J. Phys. Chem. Solids 15 (1960) 127. Goldstein, B.: Phys. Rev. 118 (1960) 1024. Goldstein, B.: Properties of Elemental and Compound Semiconductors, New York: Interscience (1960) 155. Kuliev, A.A.: Sov. Phys. Solid State (English Transl.) 1 (1960) 1076. Wieber, R.H., Gorton, H.C., Peet, C.S.: J. Appl. Phys. 31 (1960) 608.
61G1 61G2 61H 61L 61S 61V
Goldstein, B.: Phys. Rev. 121 (1961) 1305. Goldstein, B., Keller, H.: J. Appl. Phys. 32 (1961) 1180. Hall, R.N., Racette, J.H.: J. Appl. Phys. 32 (1961) 856. Lehovec, K., Slobod-soy, A.: Solid State Electron. 3 (1961) 45. Sze, S.M., Wei, L.Y.: Phys. Rev. 124 (1961) 84. Vieland, L.J.: J. Phys. Chem. Solids 21 (1961) 318.
62B1 62B2 62F 62L
Boltaks, B.I., Fedorovich, N.A.: Sov. Phys. Solid State (English Transl.) 4 (1962) 400. Brebrick, R.F., Gubner, E.: J. Chem. Phys. 36 (1962) 1238. Fuller, C.S., Wolfstirn, K.B.: J. Appl. Phys. 33 (1962) 2507. Longini, R.L.: Solid State Electron. 5 (1962) 127.
60B2 60C1 60C2 60G1 60G2
Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors 62S1 62S2 62S3 62T 62W1 62W2 63A1 63A2 63B1 63B2 63B3 63F 63K 63S1 63S2 63S3 64A 64B1
3-71
Schillman, E., in: Compound Semiconductors - Preparation of III-V Compounds, Vol. 1, Willardson, R.K., Goering, H.L. (eds.), New York: Van Nostrand Reinhold, 1962, p. 358. Seltzer, M.S., Wagner jr., J.B.: J. Chem. Phys. 36 (1962) 130. Shaw, D., Jones, P., Hazelby, D.: Proc. Phys. Soc. (London) 80 (1962) 167. Teramoto, I., Takayanagi, S.: J. Phys. Soc. Jpn. 17 (1962) 1137. Watt, L.A.K., Chen, W.S.: Bull. Am. Phys. Soc. 7 (1962) 89. Wilson, R.B., Heasell, E.L.: Proc. Phys. Soc. (London) 79 (1962) 403. Allison, H.W.: J. Appl. Phys. 34 (1963) 231. Andramonov, V.S., Baryshev, N.S., Averyanov, I.S.: Sov. Phys. Solid State (English Transl.) 4 (1963) 1626. Boltaks, B.I.: Diffusion in Semiconductors, London: Infosearch, 1963. Boltaks, B.I., Fedorovich, N.A.: Sov. Phys. Solid State (English Transl.) 5 (1963) 691. Boltaks, B.I., Sokolov, V.I.: Sov. Phys. Solid State (English Transl.) 5 (1963) 785. Fane, R.W., Goss, A.J.: Solid State Electron. 6 (1963) 383. Kato, H., Takayanagi, S.: Jpn. J. Appl. Phys. 2 (1963) 250. Seltzer, M.S., Wagner jr., J.B.: J. Phys. Chem. Solids 24 (1963) 1525. Simkovich, G., Wagner jr., J.B.: J. Chem. Phys. 38 (1963) 1368. Stocker, H.J.: Phys. Rev. 130 (1963) 2160.
64M1 64M2 64S 64W 64Y
Anselmo, R.A., Woodbury, H.H.: Bull. Am. Phys. Soc. 9 (1964) 248. Boltaks, B.I., Fedorovich, N.A., in: Thermoelectric Properties of Semiconductors, Kutusov, V.A. (ed.), New York: Consultant Bureau, 1964. Boltaks, B.I., Shishiyanu, F.S.: Sov. Phys. Solid State (English Transl.) 5 (1964) 1680. Boltaks, B.I., Sokolov, V.I.: Sov. Phys. Solid State (English Transl.) 6 (1964) 600. Butler, J.F.: J. Electrochem. Soc. 111 (1964) 1150. Butler, J.F., Calawa, A.R., Phelan, R.J., Harman, T.C., Strauss, A.J., Rediker, R.H.: Appl. Phys. Lett. 5 (1964) 75. Chang, L.L., Casey, H.C.: Solid State Electron. 7 (1964) 481. Chang, L.L., Pearson, G.L.: J. Appl. Phys. 35 (1964) 374. Chang, L.L., Pearson, G.L.: J. Appl. Phys. 35 (1964) 1960. Gusev, I.A., Murin, A.N.: Sov. Phys. Solid State (English Transl.) 6 (1964) 932. Gusev, I.A., Murin, A.N.: Sov. Phys. Solid State (English Transl.) 6 (1964) 1229. Gusev, I.A., Murin, A.N., Seregin, P.P.: Sov. Phys. Solid State (English Transl.) 6 (1964) 1491. Hall, R.N., Racette, J.H.: J. Appl. Phys. 35 (1964) 379. Howard, R.E., Lidiard, A.B.: Rep. Prog. Phys. 27 (1964) 161. Kendall, D.L.: Appl. Phys. Lett. 4 (1964) 67. Kogan, L.M., Meskin, S.S., Goikhman, A. Ya.: Sov. Phys. Solid State (English Transl.) 6 (1964) 882. Mandel, G., Morehead, F.F.: Appl. Phys. Lett. 4 (1964) 143. Morehead, F.F., Mandel, G.: Phys. Lett. 10 (1964) 5. Sokolov, V.I., Shishiyanu, F.S.: Sov. Phys. Solid State (English Transl.) 6 (1964) 265. Woodbury, H.H.: Phys. Rev. A 134 (1964) 492. Yeh, T.H.: J. Electrochem. Soc. 111 (1964) 259.
65A1 65A2 65B 65C 65F1 65F2 65F3
Antell, G.R.: Solid State Electron. 8 (1965) 943. Aven, M., Halsted, R.E.: Phys. Rev. 137 A (1965) 228. Butler, J.F., Calawa, A.R., Rediker, R.H.: IEEE J. Quantum. Electron. 1 (1965) 4. Casey jr., H.C., Pearson, G.L.: J. Appl. Phys. 35 (1965) 3401. Fedorovich, N.A.: Sov. Phys. Solid State (English Transl.) 7 (1965) 1289. Fedorovich, N.A.: Sov. Phys. Solid State (English Transl.) 7 (1965) 1291. Frieser, R.G.: J. Electrochem. Soc. 112 (1965) 697.
64B2 64B3 64B4 64B5 64C1 64C2 64C3 64G1 64G2 64G3 64H1 64H2 64K1 64K2
Lando lt -B { rnst ein New Series III/33A
3-72 65G1 65G2 65G3 65K 65M 65R 65S1 65S2 65S3 65T1 65T2 65W 66G 66K1 66K2 66K3 66P1 66P2 66S1 66S2 66S3 66S4 66T 66Y1 66Y2 67A1 67A2 67A3 67B1 67B2 67B3 67B4 67B5 67B6 67C 67F 67G1 67G2 67K1
3 Diffusion in compound semiconductors Griffiths, L.B.: J. Appl. Phys. 36 (1965) 571. Grove, A.S., Roder, A., Sah, C.T.: J. Appl. Phys. 36 (1965) 802. Gusev, I.A., Murin, A.N.: Sov. Phys. Solid State (English Transl.) 6 (1965) 2274. Kato, H., Yokozawa, M., Takayanagi, S.: Jpn. J. Appl. Phys. 4 (1965) 1019. Moore, R.G., Belasco, M., Strack, N.: Bull. Am. Phys. Soc. 10 (1965) 731. Rosenberg, A.J., Wald, F.: J. Phys. Chem. Solids 26 (1965) 1079. Seltzer, M.S.: J. Phys. Chem. Solids 26 (1965) 243. Seltzer, M.S., Wagner jr., J.B.: J. Phys. Chem. Solids 26 (1965) 233. Slack, G.A., Scace, R.I.: J. Chem. Phys. 42 (1965) 805. Takeda, Y., Hirai, T., Hirao, M.: J. Electrochem. Soc. 112 (1965) 363. Trumbore, F.A., White, H.G., Kowalchik, M., Logan, R.A., Luke, C.L.: J. Electrochem. Soc. 112 (1965) 782. Woodbury, H.H.: J. Appl. Phys. 36 (1965) 2287. Ghoshtagore, R.N., Coble, R.L.: Phys. Rev. 143 (1966) 623. Kharakhorin, F.F., Gambarova, D.A., Aksenov, V.V.: Sov. Phys. Solid State (English Transl.) 7 (1966) 2813. Kharakhorin, F.F., Gambarova, D.A., Absenov, V.V.: Inorg. Mater. (English Transl.) 2 (1966) 1371. Kroko, L.J., Milnes, A.G.: Solid State Electron. 9 (1966) 1125. Potoratskii, E.A., Stuchebnikov, V.M.: Sov. Phys. Solid State (English Transl.) 8 (1966) 770. Potts, H.R., Pearson, G.L.: J. Appl. Phys. 37 (1966) 2098. Schwuttke, G.H., Rupprecht, H.: J. Appl. Phys. 37 (1966) 167. Sharma, B.L.: J. Inst. Telecommun. Eng. 12 (1966) 209. Sokolov, V.I.: (unpublished 1966) : in: F.S. Shishiyanu, Diffusion and Degradation in Semiconductor Materials and Devices (Russian) shtiintsa, Kishinev (1978) 70. Szeto, W., Somorjai, G.A.: J. Chem. Phys. 44 (1966) 3490. Takabatake, T., Ikari, H., Uyeda, Y.: Jpn. J. Appl. Phys. 3 (1966) 839. Yokozawa, M., Kato, H., Takayanagi, S.: Denki Kagaku oyobi Kogyo Butsuri Kagaku 34 (1966) 828. Yul, B.M., Chapnin, V.A.: Sov. Phys. Solid State (English Transl.) 8 (1966) 206. Abrahams, M.S., Buiocchi, C.J., Tietjen, J.J.: J. Appl. Phys. 38 (1967) 760. Arseni, K. A., Boltaks, B.I., Rembeza, S.I.: Sov. Phys. Solid State (English Transl.) 8 (1967) 2248. Arseni, K.A., Boltaks, B.I., Gordin, V.I., Ugai, J.A.: Izv. Akad. Nauk SSSR Neorg. Mater. 3 (1967) 1679. Black, J.F., Jungbluth, E.D.: J. Electrochem. Soc. 114 (1967) 181; 188. Blount, R.H., Marlor, G.A., Bube, R.H.: J. Appl. Phys. 38 (1967) 3795. Boltaks, B.I., Rembeza, S.I.: Sov. Phys. Solid State (English Transl.) 8 (1967) 2177. Boltaks, B.I., Rembeza, S.I., Sharma, B.L.: Sov. Phys. Semicond. (English Transl.) 1 (1967) 196. Borsenberger, P.M., Stevenson, D.A., Burmeister, R.A., in: II-VI Semiconducting Compounds, Thomas, D.G. (ed.), New York: Benjamin, 1967, p. 439. Bougnot, J., Monteil, E., Linares, C.: Phys. Status Solidi 21 (1967) K 31. Casey jr., H.C , Panish, M.B., Chang, L.L.: Phys. Rev. 162 (1967) 660. Fuller, C.S., Wolfstirn, K.B.: J. Electrochem. Soc. 114 (1967) 856. Gobrecht, H., Nelkowski, H., Baars, J.W., Weigt, M.: Solid State Commun. 5 (1967) 777. Gorodetskii, A.E., Kachurin, G.A., Smirnov, L.S.: Diffz. Polupov. Pub. 1969, Russian (1967) 72. Korsun, V.M., Nemchenko, A.M.: Sov. Phys. Solid State (English Transl.) 8 (1967) 2988.
Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors 67K2 67M 67R 67V 67W1 67W2 67W3 67W4 68A 68B1 68B2 68B3 68C1 68C2 68D 68G 68H 68K1 68K2 68M 68N 68O 68S1 68S2 68S3 68W 68Y1 68Y2 68Z 69A1 69A2 69A3 69A4 69A5 69C 69G1 69G2 69K1 69K2
3-73
Kundukhov, R.M., Metreveli, S.G., Siukaev, N.V.: Sov. Phys. Semicond. (English Transl.) 1 (1967) 765. Mozzhorin, Y.D., Stapeev, V.I.: Sov. Phys. Semicond. (English Transl.) 1 (1967) 690. Rembeza, S.I.: Sov. Phys. Semicond. (English Transl.) 1 (1967) 516. Van Maaren, M.H.: Phys. Status Solidi 24 (1967) K 125. Whelan, R.C., Shaw, D., in: II-VI Semiconducting Compounds, Thomas, D.G. (ed.), New York: Benjamin, 1967, p. 451. Woodbury, H.H., in: Phys. and Chem. of II-VI Compounds, Aven, M., Prenner, J.S. (eds.), North Holland (1967) 223-264. Woodbury, H.H.: in: II-VI Semiconducting Compounds, Thomas, D.G. (ed.), New York: Benjamin, 1967, p. 244. Woodbury, H.H., Hall, R.B.: Phys. Rev. 157 (1967) 641. Arizumi, T., Nishinaga, T., Kakehi, M.: Jpn. J. Appl. Phys. 7 (1968) 468. Boltaks, B.I., Rembeza, S.I., Bakhadyrkhanov, M.K.: Sov. Phys. Solid State (English Transl.) 10 (1968) 432. Borsenberger, P.M., Stevenson, D.A.: J. Phys. Chem. Solids 29 (1968) 1277. Bougnot, J., Szepessy, L., Dacunka, S.F.: Phys. Status Solidi 26 (1968) K 127. Casey, H.C., Panish, M.B.: Trans. Metall. Soc. AIME 242 (1968) 406. Crocker, A.J., Dorning, B.F.: J. Phys. Chem. Solids 29 (1968) 155. Dobrovinskaya, E.R., Krainyukov, N.I., Obukhouski, J.A., Sysoev, L.A.: Ukr. Fiz. Zh. (Russ. Ed.) 13 (1968) 861. Gupta, D.C., Shortes, S.R.: in Reference 68K1. Hall, R.B., Woodbury, H.H.: J. Appl. Phys. 39 (1968) 5361. Kendall, D.L., in: Semiconductors and Semimetals Vol. 4, Willardson, R.K., Beer, A.C. (eds.), New York: Academic Press, 1968, p. 163. Kressel, H., Hawrylo, F.Z., Abrahams, M.S., Buiocchi, C.J.: J. Appl. Phys. 39 (1968) 3139. Maslakovets, Yu. P., Mokhov, E.N., Vodakov, Yu.A., Lomakina, G.A.: Sov. Phys. Solid State (English Transl.) 10 (1968) 634. Nebauer, E.: Phys. Status Solidi 29 (1968) 269. Osborne, J.F., Heinen, K.G., Riser, H.: in: Reference 68K1. Shih, K.K., Allen, J.W., Pearson, G.L.: J. Phys. Chem. Solids 29 (1968) 379. Swaroop, B., Wagner jr., J.B.: Appl. Phys. Lett. 12 (1968) 267. Sze, S.M., Irvin, J.C.: Solid State Electron. 11 (1968) 599. Woodbury, H.H., Aven, M.: J. Appl. Phys. 39 (1968) 5485. Yarbrough, D.W.: Solid State Technol. 11 (1968) 23. Yokozawa, M., Kato, H., Takayanagi, S.: Denki Kagaku oyobi Kogyo Butsuri Kagaku 36 (1968) 282. Zanio, K.R., Wagner jr., J.B.: J. Appl. Phys. 39 (1968) 5686. Andrievskii, E.I., Mashkin, S.B., Khludkov, S.S.: Diffusion in Semiconductors (Russian), Gorkii (1969). Arseni, K.A.: Sov. Phys. Solid State (English Transl.) 10 (1969) 2263. Arseni, K.A.: Sov. Phys. Semicond. (English Transl.) 2 (1969) 1464. Arseni, K.A., Boltaks, B.I.: Sov. Phys. Solid State (English Transl.) 10 (1969) 2190. Arseni, K.A., Boltaks, B.I., Dzhafarov, T.D.: Phys. Status Solidi 35 (1969) 1053. Copeland, J.A.: IEEE Trans. Electron Devices 16 (1969) 445. George, T.D., Wagner jr., J.B.: J. Electrochem. Soc. 115 (1968) 956; 116 (1969) 848. Girton, D.G., Anderson, W.E.: Trans. Metall. Soc. AIME 245 (1969) 465. Kato, H., Yokozawa, M., Kohara, R., Okabayashi, Y., Takayanagi, S.: Solid State Electron. 12 (1969) 137. Kendall, D.L., Huggins, R.A.: J. Appl. Phys. 40 (1969) 2750.
Lando lt -B { rnst ein New Series III/33A
3-74 69K3 69L 69M 69N 69P1 69P2 69R1 69R2 69R3 69R4 69S1 69S2 69S3 69S4 69V
70A1 70A2 70A3 70B1 70B2 70B3 70D 70J 70K 70M 70S 70V 70Y 71A1 71A2 71B 71C 71D 71G1 71G2 71H 71K 71L1
3 Diffusion in compound semiconductors Kharakhorin, F.F., Zaitov, F.A., Gambarova, D.A., Petrov, V.M., Lutsiv, R.V.: Inorg. Mater. (English Transl.) 5 (1969) 1893. Lavrishchev, T.T., Vasylyeva, L.P., Zayatynov, R.K., Khludkov, S.S.: Izv. Tomsk Un-ta 2 (1969) 129. Mokhov, E.N., Vodakov, Yu. A., Lomakina, G.A.: Sov. Phys. Solid State (English Transl.) 11 (1969) 415. Nelkowski, H., Bollman, G : Z. Naturforsch. A 24 (1969) 1302. Potter, R.M., Blank, J.M., Addamiano, A.: J. Appl. Phys. 40 (1969) 2253. Purohit, R.K., Sharma, B.L., Sreedhar, A.K.: J. Appl. Phys. 40 (1969) 4677. Rachmann, J., Biermann, R.: Solid State Commun. 7 (1969) 1771. Rekalova, G.I., Shakov, A.A., Gaurushko, V.V.: Sov. Phys. Semicond. (English Transl.) 2 (1969) 1452. Rembeza, S.I.: Sov. Phys. Semicond. (English Transl.) 3 (1969) 519. Reynolds, R.A., Stevenson, D.A.: J. Phys. Chem. Solids 30 (1969) 139. Shaw, D., Showan, S.R.: Phys. Status Solidi 34 (1969) 475. Showan, S.R., Shaw, D.: Phys. Status Solidi 32 (1969) 97. Sullivan, G.A.: Phys. Rev. 184 (1969) 796. Sysoev, L.A., Gelfman, A.J., Kovaleva, A.D., Kravchenko, N.G.: Izv. Akad. Nauk SSSR Neorg. Mater. 5 (1969) 2208. Vasilev, V.S., Kamevoskii, I.N., Osvenskii, V.B.: Sov. Phys. Semicond. (English Transl.) 2 (1969) 1495. Antcliffe, G.A., Wrobel, J.S.: Mater. Res. Bull. 5 (1970) 747. Antcliffe, G.A., Wrobel, J.S.: Appl. Phys. Lett. 17 (1970) 290. Aven, M., Kreiger, E.L.: J. Appl. Phys. 41 (1970) 1930. Ban, Y., Wagner jr., J.B.: J. Appl. Phys. 41 (1970) 2818. Belov, V.V., Zaitov, F.A., Popovyan, G.E.: Sov. Phys. Solid State (English Transl.) 11 (1970) 1627. Brodersen, R.W., Walpole, J.N., Calawa, A.R.: J. Appl. Phys. 41 (1970) 1484. Dmitrieva, N.V., Vanyukov, A.V., Yakovlev, S.G.: Elektron. Tekh. Nauk - Tekh. Sb. Mater. 5 (1970) 150. Johansson, N.G.E., Mayer, J.W., Marsh, D.J.: Solid State Electron. (English Transl.) 13 (1970) 317. Kharakhorin, F.F., Gambarova, D.A., Zaitov, F.A., Lutsiv, R.V.: Izv. Akad. Nauk SSSR Neorg. Mater. 6 (1970) 564. Mozzi, R.L., Lavin, J.M.: J. Appl. Phys. 41 (1970) 280. Sharma, B.L.: Diffusion in Semiconductors, Trans Tech Publications, Germany, 1970. Vodovatov, F.F., Indenbaum, G.V., Vanyukov, A.V.: Sov. Phys. Solid State (English Transl.) 12 (1970) 17. Young, A.B., Pearson, G.L.: J. Phys. Chem. Solids 31 (1970) 517. Arizumi, T., Kakehi, M., Shimokawa, R.: J. Cryst. Growth 9 (1971) 151. Averkin, A.A., Kaidanov, V.I., Melnik, R.B.: Sov. Phys. Semicond. (English Transl.) 5 (1971) 75. Biter, W.J., Williams, F.: J. Lumin. 3 (1971) 395. Casey, H.C., Panish, M.B., Wolfstirn, K.B.: J. Phys. Chem. Solids 32 (1971) 571. Donnelly, J.P., Harman, P.C., Foyt, A.G.: Appl. Phys. Lett. 18 (1971) 259. George, T.D., Wagner jr., J.B.: J. Appl. Phys. 42 (1971) 220. Gomez, M.P., Stevenson, D.A., Huggins, R.A.: J. Phys. Chem. Solids 32 (1971) 335. Henneberg, M.M., Stevenson, D.A.: Phys. Status Solidi (b) 48 (1971) 255. Kumar, V., Kroger, F.A.: J. Solid State Chem. 3 (1971) 387. Lavrishchev, T.T., Khuldkov, S.S.: Izv. Akad. Nauk SSSR Neorg. Mater. 7 (1971) 2079. Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors 71L2 71L3 71L4 71M1
71M2 71N 71P 71R 71S1 71S2 71S3 71T 71Z1 71Z2 72B1 72B2 72B3 72D 72I 72J 72K1 72K2 72M1 72M2 72M3 72T1 72T2 72U 72W1 72W2 72Z 73B1 73B2 73C1 73C2 73G2 73G3 73K1
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Lavrishchev, T.T., Abramov, B.G., Khludkov, S.S.: Izv. Akad. Nauk SSSR Neorg. Mater. 7 (1971) 2081. Logan, R.M.: J. Phys. Chem. Solids 32 (1971) 1755. Lomakina, G.A., Vodakov, Yu. A., Mokhov, E.N., Oding, V.G., Kholuyanov, G.F.: Sov. Phys. Solid State (English Transl.) 12 (1971) 2356. Maslova, L.V., Matveev, O.A., Rud, J.V., Sanin, K.V., in: Physics of p-n Junctions and Semiconductor Devices, Ryvkin, S.M., Shmartsev, J.V. (eds.), New York: Consultant Bureau, 1971. Mitchell, I.V., Mayer, J.W., Kung, J.K., Spitzer, W.G.: J. Appl. Phys. 42 (1971) 3982. Nebauer, E., Lautenbach, J.: Phys. Status Solidi (b) 48 (1971) 657. Parker, S.G.: J. Cryst. Growth 9 (1971) 177. Rekalova, G.I., Shakov, A.A., Gaurushko, V.V.: Sov. Phys. Semicond. (English Transl.) 5 (1971) 685. Secco, E.A., Yeo, R.S.C.: Can. J. Chem. 49 (1971) 1953. Sharma, B.L., Purohit, R.K., Mukerjee, S.N.: J. Phys. Chem. Solids 32 (1971) 1389. Smith, F.T.J.: Solid State Commun. 9 (1971) 957. Ting, C.H., Pearson, G.L.: J. Electrochem. Soc. 118 (1971) 454. Zaitov, F.A.: Sov. Phys. Solid State (English Transl.) 13 (1971) 219. Zmija, J., Sados, L.: Biul. Wojsk. Akad. Tech. 20, No. 4 (1971) 105. Bjerkeland, H., Holwrch, I.: Physica Norvegica 6 [3-4] (1972) 139. Blashku, A.I., Boltaks, B.I., Burdiyan, I.I., Dzhafarov, T.D., Rzaev, M.A.: Sov. Phys. Semicond. (English Transl.) 6 (1972) 402. Boltaks, B.I.: Diffusion and Point Defects in Semiconductors (Russian), Nauka, 1972. Donnelly, J.P., Calawa, A.R. Harman, P.C., Foyt, A.G., Lindley, W.T.: Solid State Electron. 15 (1972) 403. Ilegems, M., O’Mara, W.C.: J. Appl. Phys. 43 (1972) 1190. Jones, E.D.: J. Phys. Chem. Solids 33 (1972) 2063. Kadhim, M.A., Tuck, B.: J. Mater. Sci. 7 (1972) 68. Khludkov, S.S., Prikhodko, G.L., Karchina, T.A.: Izv. Akad. Nauk SSSR Neorg. Mater. 8 (1972) 1044. Mann, H., Linker, G., Meyer, D.: Solid State Commun. 11 (1972) 475. Miller, G.L.: IEEE Trans. Electron Devices 19 (1972) 1103. Mokhov, E.N., Vodakov, Yu. A., Lomakina, G.A., Oding, V.G., Kholuyanov, G.F., Semenov, V.V.: Sov. Phys. Semicond. (English Transl.) 6 (1972) 414. Taylor, H.F., Smiley, V.N., Marton, W.E., Pawka, S.S.: Phys. Rev. B 5 (1972) 1467. Tuck, B., Kadhim, M.A.: J. Mater. Sci. 7 (1972) 585. Uskov, V.A., Sorvina, V.P.: Izv. Akad. Nauk SSSR Neorg. Mater. 8 (1972) 758. White, A.W., Dean, P.J., Fairhurst, K.M., Bradsley, W., Williams, E.W., Day, B.: Solid State Commun. 11 (1972) 1099. Williams, V.A.: J. Mater. Sci. 7 (1972) 807. Zaitov, F.A., Lutsiv, R.V., Maltsev, M.B., Khodakov, G.S.: Fiz. Elektron. ( Lvov) 5 (1972) 26. Blashku, A.I., Dzhafarov, T.D.: Sov. Phys. Solid State (English Transl.) 15 (1973) 536. Blomer, F., Leute, V.: Z. Phys. Chem. (Frankfurt) 85 (1973) 47. Casey, H.C., in: Atomic Diffusion in Semiconductors, Shaw, D. (ed.), New York: Plenum Press, 1973, p.351. Cookson, J.A., Pilling, F.D.: Thin Solid Films 19 (1973) 381. Gray, T.J., Lear, R., Dexter, R.J., Schwettman, F.N., Wimer, K.C.: Thin Solid Films 19 (1973) 103. Guldi, R.L., Walpole, J.N., Rediker, R.H.: J. Appl. Phys. 44 (1973) 4896. Kulikov, G.S., Nikulista, I.N.: Sov. Phys. Solid State (English Transl.) 14 (1973) 2335.
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3-76 73K2 73L 73M1 73M2 73N1 73N2 73P 73S1 73S2 73S3 73S4 73Z1 73Z2 74C 74D1 74D2 74H1 74H2 74K 74L 74M1 74M2 74S1 74S2 74T 74V 74Z
75A 75B1 75B2 75C1 75C2 75D 75K 75P1 75P2 75S1
3 Diffusion in compound semiconductors Kuznetsov, G.M., Pelevin, O.V., Barasukov, A.D., Olenin, V., Saueleva, I.A.: Izv. Akad. Nauk SSSR Neorg. Mater. 9 (1973) 847. Luther, L.C., Wolfstirn, K.B.: J. Electron. Mater. 2 (1973) 375. Martin, W.E.: J. Appl. Phys. 44 (1973) 5639. Milnes, A.G.: Deep Impurities in Semiconductors, Chapter 3, John Wiley (1973). Nebauer, E.: Phys. Status Solidi (b) 60 (1973) K 57. Nebauer, E.: Phys. Status Solidi (a) 19 (1973) K 183. Panish, M.B.: J. Appl. Phys. 44 (1973) 2659. Shaw, D., in: Atomic Diffusion in Semiconductors, Chapter 1, Shaw, D. (ed.), New York: Plenum Press, 1973. Stevenson, D.A., in: Atomic Diffusion in Semiconductors, Chapter 7, Shaw, D. (ed.), New York: Plenum Press, 1973. Strauss, J.: Electron. Mater. 2 (1973) 553. Sullivan, J.L.: J. Phys. D 6 (1973) 552. Zaitov, F.A., Stafeev, V.I., Khodakov, G.S.: Sov. Phys. Solid State (English Transl.) 14 (1973) 2628. Zmija, J.: Acta Phys. Pol. A 43 (1973) 345. Chern, S.S., Kroger, F.A.: Phys. Status Solidi (a) 25 (1974) 215. DaCunha, S.F., Bougnot, J.: Phys. Status Solidi (a) 22 (1974) 205. Douglas, E.C., Dingwall, A.G.F.: IEEE Trans. Electron Devices 21 (1974) 324. Hooper, A., Tuck, B., Baker, A.J.: Solid State Electron. 17 (1974) 531. Hutchinson, P.W., Bastow, B.D.: J. Mater. Sci. 9 (1974) 1483. Karelina, T.A., Lavrishchev, T.T. Prokhodko, G.L., Khuldkov, S.S.: Izv. Akad. Nauk SSSR Neorg. Mater. 10 (1974) 228. Leute, V., Blomer, F.: Z. Phys. Chem. (Frankfurt) 89 (1974) 15. Matino, H.: Solid State Electron. 17 (1974) 35. Morgulis, L.M., Osvenskii, V.B., Milvidskii, M.G.: Sov. Phys. Solid State (English Transl.) 16 (1974) 142. Sharma, B.L., Purohit, R.K.: Semiconductor Heterofunctions, Pergamon Press, 1974. Sorbier, J.P., Sanguinetti, N.: Rev. Phys. Appl. 9 (1974) 973. Tuck, B.: Introduction to Diffusion in Semiconductors, Peter Peregrinus Ltd. U.K., 1974. Vodakov, Yu. A., Mokhov, E.N., in: Silicon Carbide - 73, Marshall, R.C., Faust jr., J.W., Ryan, C.E. (eds.), Columbia, SC: University of South Carolina Press, 1974, p. 508. Zaitov, F.A., Shalyapina, G.M., Shalyapina, L.M., Mukhim, D.V.: Sov. Phys. Solid State (English Transl.) 16 (1974) 774. Ambridge, T., Faktor, M.M.: J. Appl. Electrochem. 5 (1975) 319. Boltaks, B.I., Kulikov, G.S., Nikulista, I.N., Shishiyanu, F.S.: Inorg. Mater. (English Transl.) 11 (1975) 292. Boltaks, B.I., Dzhafarov, T.D., Demakov, J.P., Maronchuk, I.E.: Sov. Phys. Semicond. (English Transl.) 9 (1975) 545. Casey H.C., Pearson, G.L., in: Point Defects in Solids, Crawford, J.H., Slifkin, L.M. (eds.), New York: Plenum Press, 1975, p. 201. Chern, S.S., Kroger, F.A.: J. Solid State Chem. 14 (1975) 44. Dzhafarov, T.D., Demakov, Yu. P., Pribylov, N.N.: Fiz. Tverd. Tela. 17 (1975) 3110. Kato, Y., Katayama, Y., Kobayashi, K.L.I., Komatsubara, K.F.: J. Appl. Phys. 46 (1975) 4614. Panchuk, O.E., Grytsiv, V.I., Belotskii, D.P.: Inorg. Mater. (English Transl.) 11 (1975) 1510. Park, Y.S., Shin, B.K., Look, D.C., Downing, D.L., in: Ion Implantation in Semiconductors, Namba, S. (ed.), New York: Plenum Press, 1975, p. 245. Schneider, M., Nebauer, E.: Phys. Status Solidi (a) 32 (1975) 333. Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors 75S2 75S3 75T 75U 75W 75Y 75Z
76B 76C1 76C2 76D 76G 76J1 76J2 76K1 76K2 76K3 76L 76S1 76S2 76U 76V1 76V2 77B1 77B2 77B3 77B4 77F 77H 77I 77J 77L1 77L2 77M 77O 77P 77S1 77S2 77S3 77S4
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Sullivan, J.L.: Thin Solid Films 25 (1975) 245. Svob, L., Marfaing, Y., Triboulet, R., Bailly, F., Cohen-Solal, G.: J. Appl. Phys. 46 (1975) 4251. Tuck, B., Hooper, A.: J. Phys. D 8 (1975) 1806. Uskov, V.A.: Sov. Phys. Semicond. (English Transl.) 8 (1975) 1573. Wu, C.P., Douglas, E.C., Mueller, C.W.: IEEE Trans. Electron Devices 22 (1975) 319. Yamazaki, H., Kawasaki, Y., Fujimoto, M., Kudo, K.: Jpn. J. Appl. Phys. 14 (1975) 717. Zalevinskaya, V.M., Kachurin, G.A., Smirnov, L.S.: Fiz. Tekh. Poluprovodn. (Leningrad) 9 (1975) 1627. Bis, R.F., Houston, B.: IEEE Trans. Nucl. Sci. 23 (1976) 1546. Catano, A., Kun, Z.K.: J. Cryst. Growth 33 (1976) 324. Chatterjee, P.K., McLevige, W.V., Streetman, B.G.: Solid State Electron. 19 (1976) 961. Dzhafarov, T.D., Demakov, J.P.: Phys. Status Solidi (a) 36 (1976) 439. Glazov, V.M., Akopyan, R.A., Shvedkov, E.I.: Sov. Phys. Semicond. (English Transl.) 10 (1976) 378. Jain, G.C., Sadana, D.K., Das, B.K.: Solid State Electron. 19 (1976) 731. Jensen, J.D., Schoolar, R.B.: J. Vac. Sci. Technol. 13 (1976) 920. Khuldkov, S.S., Lavrishchev, T.T.: Izv. Akad. Nauk SSSR Neorg. Mater. 12 (1976) 1163. Kleinknecht, H.P., Widmer, A.E.: Solid State Electron. 19 (1976) 1005. Kun, A.K., Robinson, R.J.: J. Electron. Mater. 5 (1976) 23. Lo, W.: Appl. Phys. Lett. 28 (1976) 154. Shishiyanu, F.S., Georgin, V.G.: Sov. Phys. Semicond. (English Transl.) 10 (1976) 1301. Svob, L., Grattepain, C.: Colloq. Metall. 19 (1976) 725. Urisu, T., Kajiyama, K., Yamaguchi, M.: Jpn. J. Appl. Phys. 15 (1976) 1607. Vydyanath, H.R.: J. Appl. Phys. 47 (1976) 4993. Vydyanath, H.R.: J. Appl. Phys. 47 (1976) 5003. Bachman, K.J., Beuhler, E., Miller, B.I., McFee, J.H., Thiel, F.A.: J. Cryst. Growth 39 (1977) 137. Bicknall, R.W.: Infrared Phys. 17 (1977) 57. Bleicher, M., Wurzinger, H.D., Maier, H., Preier, H.: J. Mater. Sci. 12 (1977) 317. Bushmarina, G.S., Gruzinov, B.F., Drabkin, I.A., Lev, E.Y., Nelson, I.V.: Sov. Phys. Semicond. (English Transl.) 11(1977)1098. Foley, G.M.T., Langenberg, D.N.: Phys. Rev. B 15 (1977) 4830. Hirao, T., Inoue, K., Takayanagi, S., Yaegashi, Y.: Ion Implantation in Semiconductors 1976, Chernow, F., Borders, J.A., Brice, D.K. (eds.), New York: Plenum Press, 1977, p.1. Ilegems, M.: J. Appl. Phys. 48 (1977) 1278. Johnson, E.S., Schmit, J.L.: J. Electron. Mater. 6 (1977) 25. Lee, D.H., Malbon, R.H., Whelan, J.M., in: Ion Implantation in Semiconductors, Chernow, F., Borders, J.A., Brice, D.K. (eds.), New York: Plenum Press, 1977, p. 115. Leute, V., Stratmann, W.: Ber. Bunsen-Ges. Phys. Chem. 81 (1977) 761. Muller, G., Haubold, M., Schimko, R., Richter, C.E., Schwarz, G.: Phys. Status Solidi (a) 42 (1977) 579. Oda, S., Kukimoto, H.: IEEE Trans. Electron Devices 24 (1977) 956. Palmetshofer, L., Heinrich, H., Benka, O., Rescheneder, W.: Appl. Phys. Lett. 30 (1977) 557. Selim, F.A., Kroger, F.A.: J. Electrochem. Soc. 124 (1977) 401. Shishiyanu, F.S., Shontya, V.P. (1977) : in: F.S. Shishiyanu, Diffusion and Degradation in Semiconductor Materials and Devices (Russian), Shtiintsa, Kishinev (1978) 77. Shishiyanu, F.S., Georgiu, V.G., Palazov, S.K.: Phys. Status Solidi (a) 40 (1977) 29. Silberg, E., Zemel, A.: Appl. Phys. Lett. 31 (1977) 807.
Lando lt -B { rnst ein New Series III/33A
3-78 77T1 77T2 77T3 77V1 77V2
78A 78B1 78B2 78B3 78D 78J 78K 78L1 78L2 78L3 78L4 78M1 78M2 78P1 78P2 78P3 78R 78S1 78S2 78S3 78S4 78T1 78T2 78V1 78V2 78W 78Z
79A 79B 79D1
3 Diffusion in compound semiconductors Tairov, Y.M., Vodakov, Y.A., in: Electroluminescence, Pankove, J.I. (ed.), Berlin: SpringerVerlag, 1977, p. 31. Tuck, B., Jay, P.R.: J. Phys. D 10 (1977) 1315. Tuck, B., Zahari, M.D.: J. Phys. D 10 (1977) 2473. Verplanke, J.: J. Electrochem. Soc. 124 (1977) 469. Vodakov, Yu. A., Lomakina, G.A., Mokhov, E.N., Oding, V.G.: Sov. Phys. Solid State (English Transl.) 19 (1977) 1647. Asami, S., Ebina, A., Takahashi, T.: Jpn. J. Appl. Phys. 17 (1978) 779. Bicknall, R.W.: Infrared Phys. 18 (1978) 133. Bublik, V.T.: Phys. Status Solidi (a) 45 (1978) 543. Buda, M.J., Zmija, J.: J. Electron. Technol. 11 (1978) 85. Dzhafarov, T.D., Litvin, A.A., Khudyakov, S.V.: Sov. Phys. Solid State (English Transl.) 20 (1978) 152. Jones, E.D., Mykura, H.: J. Phys. Chem. Solids 39 (1978) 11. Kirillov, V.I., Pribylov, N.N., Rembeza, S.I., Spirin, A.I.: Sov. Phys. Semicond. (English Transl.) 12 (1978) 1342. Lanir, M., Levinstein, H.: Infrared Phys. 18 (1978) 259. Lanir, M., Lockwood, A.H., Levinstein, H.: Solid State Commun. 27 (1978) 313. Lee, C.P., Margalit, S., Yariv, A.: Solid State Electron. 21 (1978) 905. Lidow, A., Gibbons, J.F., Deline, V.R., Evans, C.A.: Appl. Phys. Lett. 32 (1978) 15; J. Appl. Phys. 51 (1980) 4130. McLevige, W.V., Vaidyanathan, K.V., Streetman, B.G., Ilegems, M., Comas, J., Plew, L.: Appl. Phys. Lett. 33 (1978) 127. McLevige, W.V., Vaidyanathan, K.V., Streetman, B.G., Comas, J., Plew, L.: J. Electron. Mater. 7 (1978) 547. Palmetshofer, L., Vierlinger, E., Heinrich, H., Hass, L.D.: J. Appl. Phys. 49 (1978) 1128. Panchuk, O.E., Shcherbak, L.P., Feichuk, P.I., Savitskii, A.V.: Inorg. Mater. (English Transl.) 14 (1978) 41. Prikhodko, G.L., Tarasova, L.K., Khludkov, S.S.: Izv. Akad. Nauk SSSR Neorg. Mater. 14 (1978) 1378. Ray, A.K., Kroger, F.A.: J. Electrochem. Soc. 125 (1978) 1348. Shishiyanu, F.S.: Diffusion and Degradation of Semiconductor Materials and Devices (Russian) Shtiintsa, Kishinev (1978) 39. Shishiyanu, F.S.: Diffusion and Degradation in Semiconductor Materials and Devices (Russian), Shtiintsa, Kishinev (1978) 55. Shishiyanu, F.S.: Diffusion and Degradation of Semiconductor Materials and Devices (Russian) Shtiintsa, Kishnev (1978) 155. Smith, D.L., Pickhardt, V.Y.: J. Electrochem. Soc. 125 (1978) 2042. Tuck, B., Badawi, M.H.: J. Phys. D 11 (1978) 2541. Tuck, B., Jay, P.R.: J. Phys. D 11 (1978) 1413. Volkov, L.A., Demakov, J.P., Dzhafarov, T.D., Kesamanly, F.P.: Sov. Phys. Solid State (English Transl.) 20 (1978) 345. Vyas, P.D., Sharma, B.L.: Thin Solid Films 51 (1978) L 21. Willoughby, A.F.W.: Rep. Prog. Phys. 41 (1978) 1665. Zaitov, F.A., Gorshkov, A.V., Shalyapina, G.M.: Sov. Phys. Solid State (English Transl.) 20 (1978) 927. Ambridge, T., Ashen, D.J.: Electron. Lett. 15 (1979) 647. Borisova, L.D.: Phys. Status Solidi (a) 53 (1979) K 19. Didik, V.A., Malkovich, R.Sh., Savin, E.P.: Sov. Phys. Solid State (English Transl.) 21 (1979) 1427. Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors 79D2 79G1 79G2 79G3 79G4 79H 79L1 79L2 79P1 79P2 79S 79T 79V 79Z
80A1 80A2 80B1 80B2 80C 80F1 80F2 80H 80I 80J 80K1 80K2 80K3 80L 80M1 80M2 80M3 80M4 80M5 80P 80S 80T 80V1
3-79
Dzhafarov, T.D., Skoryatina, E.A., Guds, E.S., Moronchuk, I.E.: Phys. Status Solidi (a) 51 (1979) K 221. Ged, P.: J. Phys. Chem. Solids 40 (1979) 439. Gorina, Yu. I., Kalyuzhnaya, G.A., Kiseleva, K.V., Salman, V.M., Strogankova, N.I.: Sov. Phys. Semicond. (English Transl.) 13 (1979) 175. Gruzinov, B.F., Drabkin, I.A., Zakharyugina, G.F., Matveenko, A.V., Nelson, I.V.: Sov. Phys. Semicond. (English Transl.) 13 (1979) 190. Gruzinov, B.F., Drabkin, I.A., Eliseeva, Y.Y., Lev, E.Y., Nelson, I.V.: Sov. Phys. Semicond. (English Transl.) 13 (1979) 767. Hurle, D.: J. Phys. Chem. Solids 40 (1979) 627. Lashkarev, G.V., Kikodze, R.O., Radchenko, M.V., Slynko, E.I., Marchuk, I.Z.: Sov. Phys. Semicond. (English Transl.) 13 (1979) 902. Lepley, B., Nguyen, P.H., Boutrit, C., Ravelet, S.: J. Phys. D 12 (1979) 145. Partain, L.D., Sullivan, G.L., Birchenall, C.E.: J. Appl. Phys. 50 (1979) 551. Poindessault, R.: J. Electron. Mater. 8 (1979) 619. Sharpe, C.D., Lilley, P., Elliot, C.R., Ambridge, T.: Electron. Lett. 15 (1979) 623. Tuck, B., Adegboyega, G.A.: J. Phys. D 12 (1979) 1895. Veis, A.N., Kaidanov, V.I., Nemov, S.A., Lashkareva, L.S., Semenov, S.I., Soroko, Z.N.: Sov. Phys. Semicond. (English Transl.) 13 (1979) 975. Zaitov, F.A., Gorshkov, A.V., Shalyapina, G.M., Susov, E.V., Terekhovich, T.F.: Izv. Akad. Nauk SSSR Neorg. Mater. 15 (1979) 2077. Andrianov, D.G., Belokon, S.A., Lakeenkov, V.M., Pelevin, O.V., Savelev, A.S., Fistul, V.I., Tsiskarishvili, G.P.: Sov. Phys. Semicond. (English Transl.) 14 (1980) 102. Arnold, N., Dambkas, H., Heime, K.: J. Appl. Phys. 19 (1980) 361. Bublik, V.T., Milvidskii, M.G., Osvenskii, V.B.: Fizika 1 (1980) 7. Bytenskii, L.J., Kaidanov, V.I., Melnik, R.B., Nemov, S.A., Ravich, Yu. I.: Sov. Phys. Semicond. (English Transl.) 14 (1980) 40. Chevier, J., Armand, M., Huber, A.M., Linh, N.T.: J. Electron. Mater. 9 (1980) 745. Fewster, P.F., Willoughby, A.F.W.: J. Cryst. Growth 50 (1980) 648. Fleming, R.M., MoWhan, D.B., Gossard, A.C., Wiegmann, W., Logan, R.A.: J. Appl. Phys. 51 (1980) 357. Hong, J.D., Davis, R.F.: J. Am.Ceram. Soc. 63 (1980) 546. Ivanov-Omskii, V.I., Mironov, K.E., Ogorodnikov, V.K.: Phys. Status Solidi (a) 58 (1980) 543. Jones, E.D., Mykura, H.: J. Phys. Chem. Solids 41 (1980) 1261. Kasahara, J., Watanabe, N.: Jpn. J. Appl. Phys. 19 (1980) L 151. Kinoshita, H., Fujiyasu, H.: J. Appl. Phys. 51 (1980) 5845. Kirillov, V.I., Pribylov, N.N., Rembeza, S.I., Spirin, A.I.: Sov. Phys. Solid State (English Transl.) 22 (1980) 1945. Lukaszewicz, T., Zmija, J.: Phys. Status Solidi (a) 62 (1980) 695. Margalit, S., Nemirovsky, Y.: J. Electrochem. Soc. 127 (1980) 1406. Martin, P., Bontemps, A.: J. Phys. Chem. Solids 41 (1980) 1171. Mokhov, E.N., Vodakov, Yu. A., Lomakina, G.A., Oding, V.G., Semenov, V., Sokolov, V.I., in : Proc. All-Union Conf. on Wide-gap Semiconductors (Russian), Leningrad, 1980, p. 164. Monch, W., Gant, H.: J. Vac. Sci. Technol. 17 (1980) 1094. Morkoc, H., Hopkins, C., Evans, C.A., Cho, A.Y.: J. Appl. Phys. 51 (1980) 5986. Prokofeva, L.V., Vinogradova, M.N., Zarubo, S.V., Nikulin, Yu. A.: Sov. Phys. Semicond. (English Transl.) 14 (1980) 1304. Shealy, J.R., Baliga, B.J., Gandhi, S.K.: IEEE Electron Device Lett. 1 (1980) 119. Tuck, B., Adegboyaga, G.A.: J. Phys. D 13 (1980) 433. Veis, A.N., Kaidanov, V.I., Nemov, S.A.: Sov. Phys. Semicond. (English Transl.) 14 (1980) 628.
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3 Diffusion in compound semiconductors Vodakov, Yu. A.: Sov. Phys. Semicond. (English Transl.) 14 (1980) 222. Wilson, R.G., Vasudev, O.K., Jamba, D.M., Evans jr., C.A., Deline, V.R.: Appl. Phys. Lett. 36 (1980) 215. Yamamoto, Y., Kanbe, H.: Jpn. J. Appl. Phys. 19 (1980) 121. Zaitov, F.A., Gorshkov, A.V., Shalyapina, G.M.: Izv. Akad. Nauk SSSR Neorg. Mater. 16 (1980) 930.
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Abryutina, T.P., Geiman, K.I., Girich, B.G., Gureev, D.M., Zasavitskii, I.I., Matveenko, A.V., Matsonashvili, B.N., Nikolaev, M.I., Pelevin, O.V., Shotov, A.P.: Sov. Phys. Semicond. (English Transl.) 15 (1981) 543. Aitikeeva, T.D., Lebedev, A.I., Yunovich, A.E., Herrmann, K., Jalyschko, A.W., Schafer, P.: Phys. Status Solidi (a) 67 (1981) 171. Alexander, R.B., Dorenbush, W.E., Lo, W.: J. Appl. Phys. 52 (1981) 4593. Arai, M., Nishiyama, K., Watanabe, N.: Jpn. J. Appl. Phys. 20 (1981) L 124. Aytac, S., Schlachetzki, A.: Solid State Electron. 24 (1981) 87. Bryant, F.J., Staudte, D.M.: Solid State Electron. 24 (1981) 675. Fung, S., Nicholas, R.J.: J. Phys. C 14 (1981) 2135. Fung, S., Nicholas, R.J., Stardling, R.A.: J. Phys. C 14 (1981) 5069. Gosele, U., Morehead, F.: J. Appl. Phys. 52 (1981) 4617. Holmes, R.E., Wilson, R.G., Yu, P.W.: J. Appl. Phys. 52 (1981) 3396. Hong, J.D., Davis, R.F., Newbury, D.E.: J. Mater. Sci. 16 (1981) 2485. Horikoshi, Y., Saito, H., Takanashi, Y.: Jpn. J. Appl. Phys. 20 (1981) 437. Ishii, Y., Kawasaki, Y.: Electron. Lett. 17 (1981) 22. Kagawa, T., Motosugi, G.: Jpn. J. Appl. Phys. 20 (1981) 597. Khudyakov, S.V.: Sov. Phys. Semicond. (English Transl.) 15 (1981) 4. Kyutt, R.N., Mokhov, E.N., Tregubova, A.S.: Sov. Phys. Solid State (English Transl.) 23 (1981) 2034. Leute, V., Schmidtke, H.M., Stratmann, W., Winking, W.: Phys. Status Solidi (a) 67 (1981) 183. Linh, N.T., Huber, A.M., Etienne, P., Morrillot, G., Duchemin, P., Bonnet, M.: Semiinsulating III-V Materials, Rees, G.J. (ed.), Kent: Shiva, 1981, p. 211. Muranoi, T., Furukoshi, M.: Thin Solid Films 86 (1981) 307. Nissim, Y.I., Gibbons, J.F., Gald, R.B.: IEEEE Trans. Electron Devices 28 (1981) 607. Oberstar, J.D., Streetman, B.G., Baker, J.E., Williams, P.: J. Electrochem. Soc. 128 (1981) 1814. Palfrey, H.D., Brown, M., Willoughby, A.F.W.: J. Electrochem. Soc. 128 (1981) 2224. Panchuk, O.E., Fesh, R.N., Savitskii, A.V., Shcherbak, L.P.: Inorg. Mater. (English Transl.) 17 (1981) 1004. Sharma, B.L.: Semiconductors and Semimetals, Vol. 15, Willardson, R.K., Beer, A.C. (eds.), New York: Academic Press, 1981, p. 1. Silberg, E., Sternberg, Y., Yeliln, N.: J. Solid State Chem. 39 (1981) 100. Stall, R.A., Wood, C.E.C., Board, K., Dandekar, N., Eastman, L.F., Devlin, J.: J. Appl. Phys. 52 (1981) 4062. Tang, H.G., Lunn, B., Shaw, D.: J. Mater. Sci. 16 (1981) 3508. Thomas, C.B., Reehal, H.S., Warren, A. J., Collego, J.M.: Appl. Phys. Lett. 38 (1981) 736. Tuck, B., Powell, R.G.: J. Phys. D 14 (1981) 1317. Vorobev, V.M., Muravev, V.A., Panteleev, V.A.: Sov. Phys. Solid State (English Transl.) 23 (1981) 653. Zemel, A., Eger, D., Shrikman, H., Tamari, N.: J. Electron. Mater. 10 (1981) 301.
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Ando, H., Susa, N., Kanbe, H.: IEEE Trans. Electron Devices 29 (1982) 1408. Arnold, N., Heime, K.: Inst. Phys. Conf. Ser. 63 (1982) 371.
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Bestaev, M.V., Dedegkaev, T.T., Mashnikov, V.A.: Sov. Phys. Solid State (English Transl.) 27 1985) 1122. Brooker, G.R.: Inst. Phys. Conf. Ser. 76 (1985) 201. Chambon, P., Berth, M., Prevat, B.: Appl. Phys. Lett. 46 (1985) 162. Chang, S.Y., Pearson, G.L.: Appl. Phys. Lett. 46 (1985) 2986. Chaplin, R., Gaunear, M., L’Haridon, H.H.: J. Appl. Phys. 58 (1985) 1803. Destefanis, G.L.: J. Vac. Sci. Technol. A 3 (1985) 171. Franciosi, A., Phillip, P., Peterman, D.J.: Phys. Rev. B 32 (1985) 8100. Gavilovic, P., Deppe, D.G., Meehan, K., Holonyak jr., N., Burnham, R.D., Thornton, R.L.: Appl. Phys. Lett. 46 (1985) 75. Goncharov, E.E., Zubatov, A.G., Lomakina, G.A., Mokhov, E.N., Ryabova, G.G.: Sov. Phys. Solid State (English Transl.) 27 (1985) 2098. Greiner, M.E., Gibbons, J.E.: J. Appl. Phys. 57 (1985) 5181. Haung, Q., Grimmeiss, H.G., Samuelson, L.: J. Phys. C 18 (1985) 5445. Ishida, A., Aoki, M., Fujiyasu, H.: J. Appl. Phys. 58 (1985) 1901. Kavanagh, K.L., Mayer, J.W., Magee, C.W., Sheets, J., Tong, J., Woodall, J.M.: Appl. Phys. Lett. 47 (1985) 1208. Kawabe, M., Shimizu, N., Hasegawa, F., Nannichi, Y.: Appl. Phys. Lett. 46 (1985) 849. Kim, S.T., Moon, D.C.: New Phys. (Seoul) 25 (1985) 27. Lischka, K., Brunthaler, G., Jantsch, W.: J. Cryst. Growth 72 (1985) 355. McGilp, J.F., McGovern, I.T.: J. Vac. Sci. Technol. 83 (1985) 1641. Miller, J.N., Collins, D.M., Moll, N.J.: Appl. Phys. Lett. 46 (1985) 960. Opyd, W.G., Dimiduck, K.C., Sigmon, T.W., Gibbons, J.F.: J. Vac. Sci. Technol. A 3 (1985) 276. Palfrey, H.D., Blackmore, G.W., Courtney, S.J.: J. Appl. Phys. 58 (1985) 1404. Partin, D.L.: J. Appl. Phys. 57 (1985) 1997. Pearton, S.J., Cummings, J.: J. Appl. Phys. 58 (1985) 1500. Rao, E.V.K., Thibierge, H., Brillouet, F., Alexandre, F., Azoulay, R.: Appl. Phys. Lett. 46 (1985) 867. Schwarz, S.A., Schwartz, B., Sheng, T.T., Singh, S., Tell, B.: J. Appl. Phys. 58 (1985) 1698. Shah, J., Tell, B., Bridges, T.J., Burkhardt, E.G., DiGiovanni, A.E., Brown-Goebeler, K.: Appl. Phys. Lett. 47 (1985) 146. Shaw, D.: Phys. Status Solidi (a) 89 (1985) 173. Tuck, B.: J. Phys. D 18 (1985) 557. Zubatov, A.G., Zaritskii, I.M., Lukin, S.N., Mokhov, E.N., Stepanov, V.G.: Sov. Phys. Solid State (English Transl.) 27 (1985) 197. Davis, G.D., Beck, W.A., Niles, D.W., Colavita, E., Margaritondo, G.: J. Appl. Phys. 60 (1986) 3150. Deal, M.D., Stevenson, D.A.: J. Appl. Phys. 59 (1986) 2398. Faurie, J.: IEEE J. Quantum Electron. 2 (1986) 1656. Favennec, P.N., L’Haridon, H., Roquais, J.M., Salvi, M., LeCleach, X., Gouskov, L.: Appl. Phys. Lett. 48 (1986) 154. Kobayashi, J., Nakajima, M., Fukunaga, T., Takamori, T., Ishida, K., Nakashima, H.: Jpn. J. Appl. Phys. Part 2, Lett. 25 (1986) L 736. Palfrey, H.D., Willoughby, A.F.W., in: Extended Abstracts, 1986 Workshop on Physics and Chemistry of CdHgTe, 1986. Petukhova, N.N., Chesnokova, D.B., Yaskov, D.A.: Sov. Phys. Semicond. (English Transl.) 20 (1986) 1048. Pobla, C., Granger, R., Rolland, S., Triboulet, R.: J. Cryst. Growth 79 (1986) 515. Ryssel, H., Ruge, I.: Ion Implantation, Chapter 5, New York: John Wiley, 1986. Shaw, D.: Philos. Mag. A 53 (1986) 727.
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Skoryatina, E.A.: Sov. Phys. Semicond. (English Transl.) 20 (1986) 1177. Zanio, K., Massopust, T.: J. Electron. Mater. 15 (1986) 103.
87A 87B1
Amann, M.C., Franz, G.: J. Appl. Phys. 62 (1987) 1541. Bogoboyashchii, V.V., Elizarov, A.I., Petryakov, V.A., Stafeev, V.I., Severtsev, V.N.: Sov. Phys. Semicond. (English Transl.) 21 (1987) 893. Bubulac, L.O., Lo, D.S., Tennant, W.E., Edwall, D.D., Chen, J.C., Ratusnik, J.: Appl. Phys. Lett. 50 (1987) 1586. Davis, G.D., Beck, W.A., Mo, Y.W., Kilday, D., Margaritondo, G.: J. Appl. Phys. 61 (1987) 5191. Deppe, D.G., Holonyak jr., N., Kish, F.A., Baker, J.E.: Appl. Phys. Lett. 50 (1987) 1823. Deppe, D.G., Holonyak jr., N., Hsieh, K.C., Gavrilovic, P., Stutius, W., Williams, J.: Appl. Phys. Lett. 51 (1987) 581. Friedman, D.F., Carey, G.P., Lindau, I., Spicer, W.E.: Phys. Rev. B 35 (1987) 1188. Guido, L.J., Holonyak jr., N., Hsieh, K.C., Kaliski, R.W., Plano, W.E., Burnham, R.D., Thornton, R.L., Epler, J.E., Paoli, T.L.: J. Appl. Phys. 61 (1987) 1372. Guido, L.J., Hsieh, K.C., Holonyak jr., N., Kaliski, R.W., Eu, V., Feng, M., Burnham, R.D.: J. Appl. Phys. 61 (1987) 1329. Kaliski, R.W., Nam, D.W., Deppe, D.G., Holonyak jr., N., Hsieh, K.C., Burnham, R.D.: J. Appl. Phys. 62 (1987) 998. Marek, H.S., Serreze, H.B.: Appl. Phys. Lett. 51 (1987) 2031. Omura, E., Wu, X.S., Vawter, G.A., Hu, E.L., Coldren, L.A., Merz, J.L.: Appl. Phys. Lett. 50 (1987) 265. Pearton, S.J., Williams, J.S., Short, K.T., Johanson, S.T., Gibson, J.M., Jacobson, D.C., Poate, J.M., Boerma, D.O.: Mater. Res. Soc. Symp. Proc. 93 (1987) 59. Rao, E.V.K., Ossart, P., Alexandra, F., Thibierge, H.: Appl. Phys. Lett 50 (1987) 588. Razeghi, M., Archer, O., Launay, F.: Semicond. Sci. Technol. 2 (1987) 793. Sharma, B.L.: Diffus. Defect Data 51/52 (1987) 1. Tang, M.F.S., Stevenson, D.A.: J. Vac. Sci. Technol. A 5 (1987) 3124.
87B2 87D1 87D2 87D3 87F 87G1 87G2 87K 87M 87O 87P 87R1 87R2 87S 87T 88B1 88B2 88D1 88D2 88G 88I 88K1 88K2 88P1 88P2 88Q 88R 88S1 88S2 88T1 88T2
Bisberg, J.E., Dabkowski, F.P., Chin, A.K.: Appl. Phys. Lett. 53 (1988) 1729. Borg, R.J., Dienes, G.J.: An Introduction to Solid State Diffusion, San Diego: Academic Press, 1988, p. 173. Deppe, D.G., Holonyak jr., N., Baker, J.E.: Appl. Phys. Lett. 52 (1988) 129. Deppe, D.G., Plano, W.E., Dallesasse, J.M., Hall, D.C., Guido, L.J., Holonyak jr., N.: Appl. Phys. Lett. 52 (1988) 825. Gill, S.S.: Diffus. Defect Data Pt. B 1-2 (1988) 281. Ilegems, M., in: Epitaxial Electronic Materials, Baldereschi, A., Paorici, C. (eds.), Singapore: World Scientific, 1988, p. 223. Khald, H., Mani, H., Joullie, A.: J. Appl. Phys. 64 (1988) 4768. Kozanecki, A., Groetzschel, R.: J. Appl. Phys. 64 (1988) 3315. Parat, K.K., Gandhi, S.K.: Solid State Electron. 31 (1988) 1053. Pearton, S.J.: Diffus. Defect Data Pt. B 1-2 (1988) 247. Quintana, V., Clemencon, J.J., Chin, A.K.: J. Appl. Phys. 63 (1988) 2454. Reynolds, S., Vook, D.W., Gibbons, J.F.: J. Appl. Phys. 63 (1988) 1052. Shaw, D.: J. Cryst. Growth 85 (1988) 778. Shieh, C., Mantz, J., Colvard, C., Alavi, K., Engelmann, R., Smith, Z., Wagner, S.: Superlattices Microstruct. 4 (1988) 597. Tejwani, M.J., Kanber, H., Paine, B.M., Whelan, J.M.: Appl. Phys. Lett. 53 (1988) 2411. Tuck, B., Matsui, T.: Jpn. J. Appl. Phys. 27 (1988) 253.
Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors 89A 89C 89D 89H1 89H3 89H4 89K 89M 89P1 89P2 89P3 89S1 89S2 89S3 89T1 89T2 89Z 90A1 90A2 90B 90H 90I 90K 90L1 90L2 90N 90S1 90S2 90S3 90S4 90S5 90W1 90W2 90X 90Y
3-85
Abernathy, C.R., Pearton, S.J., Caruso, R., Ren, F., Kovalchik, J.: Appl. Phys. Lett. 55 (1989) 1750. Cunningham, B.T., Guido, L.J., Baker, J.E., Major, J.S., Holonyak jr., N., Stillman, G.E.: Appl. Phys. Lett. 55 (1989) 687. Deal, M.D., Robinson, H.G.: Appl. Phys. Lett. 55 (1989) 1990. Harrison, I., Ho, H.P., Tuck, B., Henini, M., Hughes, O.H.: Semicond. Sci. Technol. 4 (1989) 841. Hsieh, K.Y., Lo, Y.C., Lee, J.H., Kolbas, R.M.: Inst. Phys. Conf. Ser. 96 (1989) 393. Hwang, D.M., Schwarz, S.A., Mei, P., Bhat, R., Venkatasan, L., Nazar, L., Schwartz, C.L.: Appl. Phys. Lett. 54 (1989) 1160. Kahen, K.B.: J. Appl. Phys. 66 (1989) 6176. Mei, P., Schwarz, S.A., Venkatesan, T., Schwartz, C.L., Colas, E.: J. Appl. Phys. 65 (1989) 2165. Pape, I.J., Wa, P.L.K., Roberts, D.A., David, J.P.R., Claxton, P.A., Robson, P.N.: Inst. Phys. Conf. Ser. 96 (1989) 397. Park, H.H., Lee, K., Nam, E.S., Lee, Y.T., Kim, J.H., Kang, B.K., Kwon, O.: J. Korean Phys. Soc. 22 (1989) 435. Pearton, S.J., Abernathy, C.R., Hobson, W.S., Von Neida, A.E.: Mater. Res. Soc. Symp. Proc. 144 (1989) 433. Sharma, B.L.: Defect Diffus. Forum 64/65 (1989) 1. Sharma, B.L.: Defect Diffus. Forum 64/65 (1989) 77. Sharma, B.L.: Defence Sci. J. 39 (1989) 353. Tang, M.S., Stevenson, D.A.: J. Vac. Sci. Technol. A 7 (1989) 544. Tatarkiewicz, J.: Phys. Status Solidi (b) 153 (1989) 11. Zhao, X., Hirakawa, K., Ikoma, T.: Inst. Phys. Conf. Ser. 96 (1989) 277. Abernathy, C.R., Pearton, S.J., Manasreh, M.O., Fischer, D.W., Taboar, D.N.: Appl. Phys. Lett. 57 (1990) 294. Algora, C., Araujo, G.L., Marti, A.: J. Appl. Phys. 68 (1990) 2723. Bisberg, J.E., Chen, A.K., Dabkowski, F.P.: J. Appl. Phys. 67 (1990) 1347. Hennel, A.M.: Properties of GaAs, EMIS Datareviews Series, No. 2, Inst. Elect. Engrs. (1990) 196. Iwata, N., Nakahara, Y., Hirosawa, I.: Inst. Phys. Conf. Ser. 106 (1990) 459. Kim, S.T., Moon, D.C.: Jpn. J. Appl. Phys. 29 (1990) 627. Lee, K.H., Stevenson, D.A., Deal, M.D.: J. Appl. Phys. 68 (1990) 4008. Luysberg, M., Jager, W., Urban, K., Perret, M., Stolwijk, N.A., Mehrer, H.: Mater. Res. Soc. Symp. Proc. 163 (1990) 659. Nordell, N., Ojala, P., Van Berlo, W.H., Landgren, G., Linnarsson, M.K.: J. Appl. Phys. 67 (1990) 778. Sharma, B.L.: J. Inst. Electron. Telecommun. Eng. (New Delhi) 6 (1990) 149. Shotov, A.P., Selivanov, Yu. G.: Semicond. Sci. Technol. 5 (1990) 527. Soon, J.Y., Asahi, H., Sumida, H., Emura, S., Gonda, S., Tanoue, H.: Inst. Phys. Conf. Ser. 106 (1990) 527. Strite, S., Unlu, M.S., Adomi, K., Gao, G.B., Agarwal, A., Rockett, A., Morkoc, H., Li, D., Nakamura, Y., Otsuka, N.: J. Vac. Sci. Technol. B 8 (1990) 1131. Strite, S., Unlu, M.S., Adomi, K., Markoc, H.: Appl. Phys. Lett. 56 (1990) 1673. Wheeler, C.B., Roedel, R.J., Nelson, R.W., Schauer, S.N., Williams, P.: J. Appl. Phys. 68 (1990) 969. Whitehead, N.J., Gillin, W.F., Bradley, I.V., Weiss, B.L., Claxton, P.: Semicond. Sci. Technol. 5 (1990) 1063. Xiong, F., Tombrello, T.A., Schwartz, C.L., Schwarz, S.A.: Appl. Phys. Lett. 57 (1990) 896. Young, E.W.A., Fontijn, G.M.: Appl. Phys. Lett. 56 (1990) 146.
Lando lt -B { rnst ein New Series III/33A
3-86
91A 91G 91H 91M 91Q 91S 91Y 91Z
92A1 92A2 92G 92H 92J1 92J2 92K1 92K2 92L 92M 92O 92R 92Z 93A 93C 93F 93J 93K 93L 93M1 93M2 93M3 93O1 93O2 93R
3 Diffusion in compound semiconductors
Adomi, K., Chyi, J.I., Fang, S.F., Shen, T.C., Strite, S., Morkoc, H.: Thin Solid Films 205 (1991) 182. Gulwadi, S.M., Rao, M.V., Simons, D.S., Holland, O.W., Hong, W.P., Caneou, C., Dietrich, H.B.: J. Appl. Phys. 69 (1991) 162. Harrison, I., Ho, H.P., Baba-Ali, N.: J. Electron. Mater. 20 (1991) 449. Madelung, O. (ed.): Landolt-Börnstein, New Series Volume III/17a, Semiconductors Group IV and III-V Compounds, Berlin: Springer-Verlag, 1991. Qiu, J., DePuydt, J.M., Cheng, H., Hasse, M.A.: Appl. Phys. Lett. 59 (1991) 2992. Sharma, B.L., in: CRC Handbook of Chemistry and Physics, 71st Edition, Lide, D.L. (ed.), 1991, p. 12. Yu, S., Tan, T.Y., Gosele, V.: J. Appl. Phys. 70 (1991) 4827. Zogg, H., Maissen, C., Masek, J., Hoshino, T., Blunier, S., Tiwari, A.N.: Semicond. Sci. Technol. 6 (1991) C 36. Archer, N.A., Palfrey, H.D., Willoughby, A.F.W.: J. Cryst. Growth 117 (1992) 177. Aslam, N., Jones, E.D., Noakes, T.C.Q., Mullin, J.B., Willoughby, A.F.W.: J. Cryst. Growth 117 (1992) 249. Gerasimenko, N.N., Myasnikov, A.M., Obodnikov, V.I., Safronov, L.N.: Sov. Phys. Semicond. (English Transl.) 26 (1992) 926. Hsieh, K.C., Wu, C.H., Hofler, G.E., EL-Zein, N., Holonyak jr., N.: Inst. Phys. Conf. Ser. 120 (1992) 219. Jones, E.D., Stewart, N.M., Mullin, J.B.: J. Cryst. Growth 117 (1992) 244. Jones, E.D., Thambipillai, V., Mullin, J.B.: J. Cryst. Growth 118 (1992) 1. Kerkow, H., Quang, V.X., Selle, B.: J. Cryst. Growth 117 (1992) 677. Konstantinov, A.O.: Sov. Phys. Semicond. (English Transl.) 26 (1992) 151. Luysberg, M., Jager, W., Urban, K., Hettwer, H.-G., Stolwijk, N.A., Mehrer, H.: Mater. Sci. Eng. B 13 (1992) 137. Myers, T.H., Harris, K.A., Yanka, R.W., Mohnkern, L.M., Williams, R.J., Dudoff, G.K.: J. Vac. Sci. Technol. B 10 (1992) 1438. Olmsted, B.L., Houde-Walter, S.N.: Appl. Phys. Lett. 60 (1992) 368. Robinson, H.G., Deal, M.D., Stevenson, D.A., Jones, K.S.: Mater. Res. Soc. Symp. Proc. 240 (1992) 715. Zazoui, M., Feng, S.I., Bourgoin, J.C., Powell, A.L., Rockett, P.I., Grattepain, G., Friant, A.: J. Appl. Phys. 71 (1992) 4337. Archer, N.A., Palfrey, H.D., Willoughby, A.F.W.: J. Electron. Mater. 22 (1993) 967. Chandra, D., Goodwin, M.W., Chen, M.C., Dodge, J.A.: J. Electron. Mater. 22 (1993) 1033. Francis, C., Bradley, M.A., Boucaud, P., Julien, F.H., Razeghi, M.: Appl. Phys. Lett. 62 (1993) 178. Jager, W., Rucki, A., Urban, K., Hettwer, H.-G., Stolwijk, N.A., Mehrer, H., Tan, T.Y.: J. Appl. Phys. 74 (1993) 4409. Krasnov, A.N., Vaksman, Yu. F., Purtov, Yu. N.: Sov. Phys. Semicond. (English Transl.) 27 (1993) 287. Laks, D.B., Van de Walle, C.G., Newmark, G.F., Pantelides, S.T.: Appl. Phys. Lett. 63 (1993) 1375. Martin, J.M., Nadella, R.K., Rao, M.V., Simons, D.S., Chi, P.H., Caneou, C.: J. Electron. Mater. 22 (1993) 1153. Matsushita, S., Terade, S., Fuji, E., Harada, Y.: Appl. Phys. Lett. 63 (1993) 225. Murakami, S., Okamoto, T., Maruyama, K., Takigawa, H.: Appl. Phys. Lett. 63 (1993) 899. Olmsted, B.L., Houde-Walter, S.N.: Appl. Phys. Lett. 62 (1993) 1516. Olmsted, B.L., Houde-Walter, S.N.: Appl. Phys. Lett. 63 (1993) 530. Rao, E.V.K., Juhel, M., Krauz, P.H., Gas, Y., Thibierge, H.: Appl. Phys. Lett. 62 (1993) 2096. Landolt -B { rnst ein New Series III/33A
3 Diffusion in compound semiconductors
3-87
93T 93Z
Thornton, R.L., Ponce, F.A., Anderson, G.B., Endicott, F.J.: Appl. Phys. Lett. 62 (1993) 2060. Zimmermann, H., Gosele, V., Tan, T.Y.: Appl. Phys. Lett. 62 (1993) 75.
94A
Abrosimov, V.N., Avetisyan, L.F., Vyatkin, A.F., Dubrovskii, Yu.V., Pustovit, A.N.: Sov. Phys. Semicond. (English Transl.) 28 (1994) 1118. Babentsov, V.N., Kletskii, S.V., Tarbaev, N.V.: Semiconductor (formerly Sov. Phys. Semicond. (English Transl.) ) 28 (1994) 1194. Rastogi, A., Reddy, K.V.: J. Appl. Phys. 75 (1994) 4984.
94B 94R 95B1 95B2 95W1 95W2 95W3
Bosker, G., Hettwer, H.-G., Rucki, A., Stolwijk, N.A., Mehrer, H., Jager, W., Urban, K.: Mater. Chem. Phys. 42 (1995) 68. Bosker, G., Stolwijk, N.A., Hettwer, H.-G., Rucki, A., Jager, W., Sodervall, U.: Phys. Rev. B 52 (1995) 11927. Wittorf, D., Jager, W., Rucki, A., Urban, K., Hettwer, H.-G., Stolwijk, N.A., Mehrer, H.: Mater Res. Soc. Symp. Proc. 378 (1995) 183. Wittorf, D., Rucki, A., Jager, W., Dixon, R.H., Urban, K., Hettwer, H.-G., Stolwijk, N.A., Mehrer, H.: J. Appl. Phys. 77 (1995) 2843. Wittorf, D., Rucki, A., Jager, W., Urban, K., Hettwer, H.-G., Stolwijk, N.A., Mehrer, H.: Inst. Phys. Conf. Ser. 146 (1995) 417.
Lando lt -B { rnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2.2.2 Figures for 2.2
Si : 2H
21
10
19
19
10
–3
18
10
1 Ω cm
17
10
18
10
10 Ω cm 100 Ω cm
16
17
10
10
16
10
15
10
15
0
0.5
1.0
1.5 2.0 2.5 3.0 Depth x [µm] Fig. 1. Si:H. Concentration of deuterium C vs. depth x in B-doped and Al-doped silicon after indiffusion for temperatures and times as indicated. The solid curves are calculated, the symbols are experimental results [91Riz1].
1.0
Si :B :H
1.0 1.5 2.0 2.5 Depth x [µm] Fig. 2. Si:H. Concentration of deuterium C vs. depth x in n-type silicon samples of different resistivity as indicated. The samples were exposed to a 2H plasma for 1h at 125C. The lines represent the profiles obtained with SIMS [94Pea1]. Temperature T [°C] 700 500 300 200 100 –3 1200 10 [56 Wie1] –4 10 Si : H
0.5
–5
10
0.8
–6
10
initial 1h 3h 9h
–7
10
2 –1
Diff.coeff. D [cm s ]
0.6
0
–8
10
[68 Ich1]
–9
10
–10
10
0.4
–11
10
–12
10
0.2 0 0.2
16
–3
NA = 3.8 ⋅10 cm 16 –3 N0 = 2.1 ⋅10 cm 0.3
0.4
0.5 0.6 Depth x [µm]
0.7
H+ H0
–14
10
0.8
Fig. 3. Si:H. Normalized concentration of inactive BH pairs C vs. depth x after zero bias annealing at 100 C and times as indicated. The initial profile was formed prior by reverse-bias annealing. The symbols NA and N0 denote the acceptor concentration and the normalization value. The solid lines represent the fits obtained by a H diffusion model taking into account H trapping at B sites [92Zun1]. Lando lt -Bö rnst ein New Series III/33A
[87 Cap1]
–13
10
H+ H– H0
[91 Riz1]
10
Norm. BH pairs conc. C
0.1 Ω cm
2
–3
H concentration C [cm ]
10 H concentration C [cm ]
20
10
2
19
–3
Si :B 10 cm (185 °C/2.5 h) 18 –3 Si :B 2.5 ⋅10 cm (150 °C/2 h) 18 –3 Si :Al 10 cm (185 °C/2 h)
Si : 2H
2-135
–15
10
–16
10
0.6
1.0
1.4 1.8 2.2 2.6 3.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 4. Si:H. Diffusion coefficient D of hydrogen in silicon vs. inverse temperature 1/T. The straight lines are representative data from the literature for H (without specification of charge state [68Ich1]), neutral + – H0, and ionized H and H as indicated.
2 Diffusion in silicon, germanium and their alloys
2-136
–31500
10
Temperature T [°C] 200 100 50 0
500 [56 Wie1]
–4
10
–4 1200
–50
10
–6
10
–7
10
2 –1
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
[91 New1]
–9
10
–10
10
–9
–10
10
[85 Mog1]
–11
10
[90 Kov1]
–14
2
10
–16
1
2 3 4 5 –3 –1 Inv. temp. 1/T [10 K ] Fig. 5. Si:H. Diffusion coefficient D of hydrogen and deuterium in silicon vs. inverse temperature 1/T, from various authors as indicated. 1000
–7
Si : Na Si : K
–15
10
Temperature T [°C] 800 700 600
1.8 2.2 2.6 3.0 3.4 3.8 –3 –1 Inv. temp. 1/T [10 K ] Fig. 6. Si:Li. Diffusion coefficient D of lithium in silicon vs. inverse temperature 1/T, from various authors.
500
3.0
K [67 Svo1]
–8
–10
10
–11
10
1.0
–12
K [72 Zor1]
–13
10
1.5
0.8
0.9 1.0 1.1 1.2 1.3 –3 –1 Inv. temp. 1/T [10 K ] Fig. 7. Si:Na, K. Diffusion coefficient D of sodium and potassium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
Be Si (at 300 °C) –2 13 3 ⋅10 cm 6 keV anneal 2 h H2
T = 600 °C 500 °C 400 °C 300 °C
0.5
500 750 1000 1250 Depth x [Å] Fig. 8. Si:Be. Concentration of beryllium C implanted into silicon vs. depth x as measured by SIMS after annealing at different temperatures. Diffusion temperatures and times as well as the conditions for implantation are indicated in the insert [75Hur1]. 0
–14
9
2.0
1.0
10
1.4
Si :Be
2.5
Be conc. C [a.u.]
Na [88 Kor1]
–9
10
0.6
3.5
Na [67 Svo1]
10
[74 Les1]
–16
–15
–6
10
H
10
0.7
[60 Pel1]
–14
[91 Kam1]
[91 Joh1]
10
10
[58 Mai1]
10
H
[91 Her1]
–13
10
10
–12
10
–13
10
10
–11
10
[90 Sea1]
–12
2 –1
[54 Ful1]
–8
10
Diff.coeff. D [cm s ]
[53 Ful1]
–7
10
–8
0
–6
10
10
50
Si : Li
10
10 10
Temperature T [°C] 300 200 100
–5
Si :H
–5
10
500
[Ref. p. 2-196
250
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
15.0
19
Si : Mg
10
as implanted T = 800 °C 700 °C 600 °C 500 °C
12.5
Si : Ca 18
10 –3
Ca conc. C [cm ]
10.0
Mg conc. C [at%]
2-137
7.5 5.0
17
10
16
10
15
10
2.5
14
0
40
80
–8
1300
1200
120 160 200 240 280 Depth x [nm] Fig. 9. Si:Mg. Concentration of magnesium C implanted into silicon vs. depth x after annealing at different temperatures for 0.5 h as indicated in the insert. The symbols represent experimental results, the solid lines guide the eye [83Räi1].
10
–9
10
Temperature T [°C] 1100 1000
Si : X
0.1
0.2
4
Si : Pm
X = Yb [90Bak1]
T = 1227 °C t = 285 h 877 °C 300 h
3
10
Rel.conc.of Pm
2 –1
0
10
–10
Diff.coeff. D [cm s ]
0.3 0.4 0.5 0.6 Depth x [µm] Fig. 10. Si:Ca. Concentration of calcium C vs. depth d as measured by SIMS after in-diffusion at 1100 C for 1 h [83Sig1]. The dashed line represents the experimental result indicated by the symbols.
900
10
–11
10
Sc [89Azi1]
–12
10
–13
10
Tm [91Naz1]
1
Pr [88Naz1] 0.60
0.65
0.70 0.75 0.80 –3 –1 Inv. temp. 1/T [10 K ]
0.85
0.90
Fig. 11. Si:Sc, Pr, Tm, Yb. Diffusion coefficient D of scandium, praseodymium, thulium, and ytterbium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
Lando lt -Bö rnst ein New Series III/33A
2
10
10
–14
10
10
0
4
8 12 16 20 24 2 –6 2 Squared depth x [10 cm ] Fig. 12. Si:Pm. Concentration profiles of radioactive promethium-147 in silicon after diffusion at different temperatures vs. squared depth x2. The solid lines represent best fits of Gaussian functions [70Fer1].
2 Diffusion in silicon, germanium and their alloys
2-138
19
–11
10
10
1 2 3 4
Si : Er
Si : Pm 18
10 –3
Er conc. C [cm ]
2 –1
–12
10
Diff.coeff. D [cm s ]
[Ref. p. 2-196
–13
10
17
10
16
10
15
–14
10
0.6
0.8 0.9 1.0 1.1 –3 –1 Inv. temp. 1/T [10 K ] Fig. 13. Si:Pm. Diffusion coefficient D of promethium in silicon vs. inverse temperature 1/T revealing a slow (closed circles) and a fast (open circles) diffusion component [70Fer1].
–11
10
0.7
1300
1200
Temperature T [°C] 1100 1000
10
3 4 5 6 Depth x [µm] Fig. 14. Si:Er. Concentration profiles C of erbium vs. depth x in silicon measured by incremental sheet resistance after annealing at 1200 C for 3 h in Ar (1,2) and O2 (2,3) for nitride-covered (2) and uncovered (1,3) regions. Concentrations indicated by (4) correspond to junction depths measured by the staining method [95Ale1].
900
0
1
2
19
10
Si : Er
Si :Yb
18
10
–12
[93Sob1]
17
–3
Yb conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
10
[91Naz1]
–13
10
T = 947 °C / 3 h 997 °C / 3 h 1047 °C / 3 h 1097 °C / 3 h
10 16 10 8 6 4 2 15
10
–14
10
[77Age1]
[93Ren1]
8 6 4 2
–15
10
0.60
0.65
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 15. Si:Er. Diffusion coefficient D of erbium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
14
10
0
40
80 120 160 200 Depth x [µm] Fig. 16. Si:Yb. Concentration of ytterbium C vs. depth x after in-diffusion for 3 h at different temperatures as indicated [90Bak1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
14
14
10
4⋅10
Si :Ti
8
2
4
Ti conc. C [cm ]
1.4 –3
2
–3
Ti conc. C [cm ]
T = 700 °C
Si :Ti
T = 1150 °C, t = 48 h, d = 1160 µm
6
T = 1100 °C, t = 72 h, d = 1170 µm
13
10
2-139
8
t=0h
14
10
8
2.5 h
6
8.5 h
4
6
T = 1050 °C, t = 108 h, d = 1030 µm
4
2 2
13
10
12
10
0
0.2
0.4 0.6 0.8 1.0 Norm.depth x/d Fig. 17. Si:Ti. Concentration profiles C of electrically active titanium in silicon wafers vs. normalized depth x/d (d=sample thickness) measured by DLTS. Diffusion of titanium into silicon was carried out at different temperatures T for diffusion times t and sample thicknesses d as indicated. Solid lines represent best fits obtained with the solution of Fick's equation assuming a constant boundary concentration at x = 0 and x = d [91Kug1].
1200
–7
10
Temperature T [°C] 1000 800
2.0 2.5 3.0 3.5 4.0 4.5 Depth x [µm] Fig. 18. Si:Ti. Concentration profiles C of electrically active titanium in silicon vs. depth x measured by DLTS. Silicon samples were first in-diffused with titanium at 1200C for 15h. Out-diffusion of titanium was carried out at 700 C for times t as indicated. Solid lines represent best fits obtained with the appropriate solution of Fick's equation [91Kug1].
600
–5
10
1.0
1.5
1000
500
Temperature T [°C] 200 100 50
–6
10
Si :Ti
–8
0.5
Si : X
–7
10
0
10
–8
2 –1
2 –1
Diff.coeff. D [cm s ]
[88Hoc1]
–9
10
Diff.coeff. D [cm s ]
10
–10
–11
10
–12
10
Fe
–13
10 [91Kug1]
–12
V
–11
10
[77Bol1]
10
–10
10
[83Roh1]
10
–9
10
–14
10
X = Ti Cr
–15
Mn
10
–16
10 –13
10
0.6
0.7
0.8 0.9 1.0 1.1 1.2 –3 –1 Inv. temp. 1/T [10 K ] Fig. 19. Si:Ti. Diffusion coefficient D of titanium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
Lando lt -Bö rnst ein New Series III/33A
–17
10
0.5
1.0
1.5 2.0 2.5 4.0 3.0 3.5 –3 –1 Inv. temp. 1/T [10 K ] Fig. 20. Si:Ti, V, Cr, Mn, Fe. Diffusion coefficient of titanium, vanadium, chromium, manganese, and iron in silicon vs. inverse temperature 1/T [94Nak1].
2 Diffusion in silicon, germanium and their alloys
2-140
14 8 6
Si :V
4
–3
4 2 12
10
8 6 4
3
1150
5
1100
4
1100
6
1050
7
1050
2
0
–11
10
0.2
1200 700
–5
10
1.1
1.2
Temperature T [°C] 400 200 100
[70Ben1,74Wur1,89Zhu1]
–6
10
–7
Si :Cr
10
–9
2 –1
T = 1250 °C t = 6 min
10
Diff.coeff. D [cm s ]
–3
Cr conc. C [cm ]
0.8 0.9 1.0 –3 –1 Inv. temp. 1/T [10 K ]
Fig. 22. Si:V. Diffusion coefficient D of vanadium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
–10
10
–11
10
–12
10
–13
2
10
14
10
[91sch1]
–14
8 6
[94Nak1]
–15
10
4
–16
10
–17
2
10
0.7
10
Si : Cr
8 6
13
0.6
–8
4
10
[89Azi2]
–12
15
10
–10
10
15
2
[91Sad1]
10
0.4 0.6 0.8 1.0 Norm.depth x/d Fig. 21. Si:V. Concentration profiles C of electrically active vanadium in silicon vs. normalized depth x/d measured by DLTS. Diffusion was carried out at different temperatures for times and sample thicknesses d as follows: (1) 1200 °C, 8h, d = 1170 µm; (2) 1200 °C, 4 h, d = 1170 µm; (3) 1150 °C, 12 h, d = 1210 µm; (4) 1100 °C, 8 h, d = 1090 µm; (5) 1100 C, 16 h, d = 1110 µm; (6) 1050 °C, 24 h, d = 1180 µm; (7) 1050 °C, 12 h, d = 1180 µm; (8) 1000 °C, 38 h, d = 1110 µm. Solid lines represent best fits obtained with the solution of Fick's equation assuming a constant surface concentration at x/d = 0 and x/d = 1 [91Sad1]. 4⋅10
–9
10
8
1000 °C
11
10
–8
10
2 –1
V conc. C [cm ]
8 6
600
Si :V
2
1200
13
Temperature T [°C] 1000 800
1 T = 1200 °C
2
10
1200
–7
10
Diff.coeff. D [cm s ]
10
[Ref. p. 2-196
10
750 1000 1250 1500 Depth x [µm] Fig. 23. Si:Cr. Concentration profile C of chromium in silicon vs. depth x measured radiochemically [74Wur1]. 0
250
500
0.6
1.0
1.4 1.8 2.2 2.6 3.0 3.4 –3 –1 Inv. temp. 1/T [10 K ] Fig. 24. Si:Cr. Diffusion coefficient D of chromium in silicon vs. inverse temperature 1/T. Data from the literature as indicated. Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
–5 1200
700
–6
[86Gil1]
10 10
400
Temperature T [°C] 200 100
0
–16
4⋅10
Si :Mn
–7 –8
10
–3
Mn conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
[91sch1]
–10
10
–11 –12
10
–13
10
Si : Mn
2
10
15
10
8 6 4 2
14
10
[91Nak1,92Nak1]
–14
10
8 6 4
–15
10
2
–16
10
13
–17
10
1.8 2.2 2.6 3.0 3.4 3.8 –3 –1 Inv. temp. 1/T [10 K ] Fig. 26. Si:Mn. Diffusion coefficient D of manganese in silicon vs. inverse temperature 1/T. Data from the literature as indicated. Temperature T [°C] 1000 600 400 200 000 30 –4 10
0.6
1.0
1.4
–5
10
10 -1.0
0 0.5 1.0 Norm.depth x/a Fig. 25. Si:Mn. Concentration profiles of manganese in silicon vs. normalized depth x/a determined by the radiotracer method after diffusion from both surfaces into specimens of thickness 2a as indicated. Diffusion temperature T and time t are also indicated [86Gil1].
Si :Fe
–6
-0.5
2.0
10
Si : Fe
–7
10
1.6
–8
2 –1
8 6 4
–9
10
Diff.coeff. D [cm s ]
T = 1200 °C, t = 17 min,2a = 419 µm T = 1078 °C, t = 35 min,2a = 419 µm T = 992 °C, t = 33 min,2a = 398 µm T = 920 °C, t = 90 min,2a = 375 µm
16
10
10 10
2-141
–9
10
–10
Fe conc. C [a.u.]
10
–11
10
–12
10
–13
10
radiotracer [56Str1] DLTS [90Kim1] resistivity [62She1] EPR [60Lud1] Mössbauer [90Sch1]
–14
10
–15
10
–16
10
0.5
1.0
1.5 2.0 2.5 3.0 3.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 27. Si:Fe. Diffusion coefficient D of interstitial iron in silicon vs. inverse temperature 1/T obtained by radiotracer diffusion experiments at high temperatures and DLTS, resistivity, and EPR measurements at low temperatures. The least-squares fit has been performed using all these results (continuous line). [83web2]. Recent Mössbauer data covering some intermediate temperatures are in line with this fit.
Lando lt -Bö rnst ein New Series III/33A
1.2
0.8 t=
0.4
0
2
0 min 120 min annealing 250 min at 650 min T = 177 °C
4 6 8 10 Depth x [µm] Fig. 28. Si:Fe. Concentration C of interstitial iron in silicon vs. depth x for various annealing times t at 177 °C as indicated. The profiles were measured in the space charge region of a Schottky diode made on Fe-saturated samples [91Hei1, 92Hei1].
2 Diffusion in silicon, germanium and their alloys
2-142
2
+
D /D 0 ≈ 2
p-type Si
1
–11
10
Fe 0 [92Hei1] Fe 0 [90Sch1] Fe + [92Hei1] Fe+ [90Hei1]
10
10
10
–13
Si : Fe
[84Mir1]
–9
10
–10
[85Bro1]
–11
10
10
Fei+[92Hei1,92Hei2]
–12
10
Fei0[92Hei1,92Hei2]
–13
–14
10
10
0
[72Bol1]
–8
10
–12
Temperature T [°C] 200 100
[89Iso1]
–7
2 –1
–10
10
n-type Si
400
[56Str1]
–6
10
Diff.coeff. D [cm s ]
10
2 –1
10
Si : Fe
–9
Diff.coeff. D [cm s ]
1200 700
–5
–8
10
[Ref. p. 2-196
[88Nak1]
–14
–15
+
10
10
0
D /D ≈ 50
–16
10
1.0
1.5
2.0 2.5 3.0 3.5 4.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 29. Si:Fe. Diffusion coefficient D of interstitial iron in silicon vs. inverse temperature 1/T. Summary of data at low and moderate temperature from Mössbauer line broadening (closed triangles) or drift and diffusion in the space charge region of Schottky diodes. Curves (1) and (2) are described, respectively, by 2 D(Fei0) = 10− exp[-(0.84 eV)/kT] cm2s–1 [91Hei1] and D(Fe +) = 1.4.10−3 exp[-(0.69 eV)/kT] cm2s–1 [83web2].
–16
10
0.5
1.5 2.0 2.5 3.0 3.5 4.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 30. Si:Fe. Diffusion coefficient D of iron in silicon vs. inverse temperature 1/T. Data including diffusion constants for neutral and positively charged interstitial iron from various references as indicated.
–3
10
i
–4
8
Si :Co
6
T = 900 °C t = 600 s
Temperature T [°C] 1100 1000
1200
900
Si : Co
–5
2 –1
Diff.coeff. D [cm s ]
2
–3
Co conc. C [cm ]
4
13
10
1.0
10
14
10
[62She1]
–15
10
8 6
10
–6
10
–7
10
4 –8
10
1 2 3
2 –9
10
12
10
3.0 1.5 2.0 2.5 Depth x [mm] Fig. 31. Si:Co. Concentration C of cobalt in silicon vs. inverse temperature 1/T as measured by means of the radiotracer 57Co in conjunction with mechanical sectioning. Diffusion temperature T and time t as indicated. The erfc-fit yields D = 2.2·10−5 cm2/s [89Utz1]. 0
0.5
1.0
0.65
0.70
0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 32. Si:Co. Diffusion coefficient D of cobalt in silicon vs. inverse temperature 1/T. Data result from radiotracer experiments (1 [89Utz1], 2 [77Kit1] or DLTS measurements (3 [88Has1]. Solid line: interstitial Co [89Utz1], dashed line: substitutional Co [77Kit1, 88Has1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
1300
–4
10
2 Diffusion in silicon, germanium and their alloys
1100
Temperature T [°C] 900
10
4
Si :Co Si :Ir
–9
10
2 –1
–8
10
Diff.coeff. D [cm s ]
Ir [76Azi1] Ir [77Azi1]
–10
10
–11
10
Si :Ir
4 2 –7 10 8 6
–12
4
–13
2
–14
–8
10
10
10
–15
10
Co [87App1]
–16
10
–17
0.6
0.65
0.70
Temperature T [°C] 700 400
–5
10
–6
–6
2 –1
10
–7
10
–8
2 –1
Si : X
Si :Ni
Nii [80Bak1]
–9
10
eq
eq
Ci Di /Cs :Pts [95Ler1]
–7
–8
10
Nis [67Yos1]
–10
10
10 10
Nii [85Tho1]
10
300
Di :Pdi [91fra1]
–5
10
Diff.coeff. D [cm s ]
1200
Temperature T [°C] 700 500
1300 1100
–4
–4
0.85
0.7
10
10
0.75 0.80 –3 –1 Inv.temp. 1/T [10 K ]
Fig. 34. Si:Ir. Diffusion coefficient D of iridium in silicon vs. inverse temperature 1/T [76Azi1].
0.8 0.9 1.0 1.1 –3 –1 Inv. temp. 1/T [10 K ] Fig. 33. Si:Co, Ir. Diffusion coefficient D of cobalt and iridium in silicon vs. inverse temperature 1/T. Data from various references as indicated.
Diff.coeff. D [cm s ]
950
–6 10 8 6
10
10
Temperature T [°C] 1050
2
–7
10
2 –1
6
Co [77Kit1,88Has1]
–6
1150
10 8
Co [89Utz1]
–5
10
Diff.coeff. D [cm s ]
–5 1250
700
2-143
Di :Nii [89Spi1]
–11
10
Nii [89Spi1]
–12
10
–13
10
[84Usk1]
eq
[75Yoo1]
–14
10
Nis [67Bon1]
–15
10
–16
10
0.6
1.2 1.5 1.8 2.1 –3 –1 Inv. temp. 1/T [10 K ] Fig. 35. Si:Ni. Diffusion coefficient D of nickel in silicon vs. inverse temperature 1/T. Interstitial diffusion and vacancy-limited dissociative diffusivity (CVeqDV/Cseq) of nickel indicated as Nii and Nis, respectively. Data from various references as indicated. Lando lt -Bö rnst ein New Series III/33A
0.9
–9
10
–10
10
0.6
eq
CI DI /Cs :Pts [89Hau1] 0.8
1.0 1.2 1.4 1.6 1.8 –3 –1 Inv. temp. 1/T [10 K ] Fig. 36. Si:Ni, Pd, Pt. Diffusion coefficient D of nickel, palladium, and platinum in silicon vs. inverse temperature 1/T. Interstitial diffusion Di of mainly interstitially dissolved nickel and palladium as well as the effective diffusion coefficients of mainly substitutionally incorporated platinum which are termed the Pti-limited kick-out diffusivity of Pts (CieqDi/Cseq) and the self-interstitial-limited kick-out diffusivity of Pts (CIeqDI/Cseq). Data from the literature as indicated.
2 Diffusion in silicon, germanium and their alloys
2-144
–4
18
10
10
Si :Pd
T = 1103 °C t = 58 min
17
Si :Pd
6 5
2 –1
Diff.coeff. D [cm s ]
–3
9 8 7
10
Pd conc. C [cm ]
[Ref. p. 2-196
16
10
4 3
15
10
2
14
10
–5
10
13
10
25 10 15 20 Depth x [mm] Fig. 37. Si:Pd. Concentration C of palladium in silicon vs. depth x as measured by means of neutron activation analysis. Diffusion temperature T and time t as indicated. The solid line represents a fit of the complementary error function [91fra1]. 0
5
0.8 0.9 1.0 1.1 –3 –1 Inv. temp. 1/T [10 K ] Fig. 38. Si:Pd. Diffusion coefficient D of palladium in silicon vs. inverse temperature 1/T as measured by means of NAA [91fra1].
15
10
8 6
6
Norm.Pt conc. C/C eq
14
–3
Si :Pt
8
2
Pds conc. Cs [cm ]
0.7
1
Si :Pd
4
10
0.6
8 6 4
∝ t1/2
T = 1200 °C t =1h
4
2
2 13
10
–1
10
8 6
8
T = 1050 °C 955 °C 900 °C 880 °C
4 2
–2
6⋅10
12
10
2
10
3
4
8 10 2 4 6 8 10 Time t [min] Fig. 39. Si:Pd. Concentration Cs of substitutional palladium in the center of 250 µm-thick silicon wafers vs time t. Diffusion temperatures are as indicated. The dashed line represents t behaviour [93Vic1]. 2
4
6
0
0.2
0.4 0.6 0.8 1.0 Depth x [mm] Fig. 40. Si:Pt. Normalized concentration C/C eq of platinum in silicon vs. depth x as measured by neutron activation analysis. Diffusion temperature T and time t as indicated. C eq denotes equilibrium solubility. Solid line: kick-out model; dotted line: dissociative model [89Hau1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
15
10
8 6
–3
10
Si : Pt
1300
Temperature T [°C] 900
1100
Si : Pt
–4
4
2-145
10
700
Di [92Zim1,92Zim2]
2
2 –1
8 6
Diff.coeff. D [cm s ]
–3
Pt conc. Cs [cm ]
–5
10
T = 1201 °C t = 120 s
14
10
1120 °C 240 s
4 2 13
10
8 6 4
eq
–6
–7
10
[69Bai1]
–9
10
eq
12
0
100
200
300 400 500 Depth x [µm]
600
700
Fig. 41. Si:Pt. Concentration Cs of substitutional platinum in highly dislocated silicon wafers vs. depth x. Diffusion temperatures T and times t as indicated. Data points: spreading-resistance measurement. Solid lines: fits based on the complementary error function [95Ler1].
Si :Cu
–10
10
eq
CI DI /Cs [89Hau1]
0.6
0.7
eq
eq
CI DI /Cs [93Cof1]
0.8 0.9 –3 –1 Inv. temp. 1/T [10 K ]
1.0
1.1
Fig. 42. Si:Pt. Diffusion coefficient D of platinum in silicon vs. inverse temperature 1/T. Interstitial diffusivity Di of Pti, Pti-limited kick-out diffusivity CieqDi/Cseq of Pts, and self-interstitial-limited kick-out diffusivity CIeqDI/Cseq of Pts. CieqDi/Cseq data from [95Ler1] were obtained from Pt diffusion into dislocated silicon. Data from other references are based on diffusion into virtually perfect silicon crystals.
T = –13 °C initial
1.0
Norm.acceptor conc. C/Cinitial
eq
Ci Di /Cs [95Ler1]
10
10
2
10
eq
–8
1000 °C 960 s
950 °C 960 s
eq
Ci Di /Cs [93Cof1]
4 min
16 min
0.8 1h 0.6
16 min
0.2
experimental fit
4 min 0
Fig. 43. Si:Cu. Normalized inactive acceptor concentration C/Cinitial vs. depth x. The profiles arise from an initially unknown mobile defect after 50V reverse bias annealing at 20C (initial), and subsequent zero-bias annealing at −13C for the times t indicated [88Zun1]. In later studies the mobile defect has been identified as copper [89Pre1, 92Mes1, 94Mes1].
initial
t =1h
0.4
1
3
Lando lt -Bö rnst ein New Series III/33A
4
5 6 Depth x [µm]
7
8
2 Diffusion in silicon, germanium and their alloys
2-146
10
10
10
–6
–6
10
–7
10
10
2 –1
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
–8
10
–9
10
Si :Cu
[89Abd1]
–8
10
[58Bol1] [88Zun1,89Pre1]
–9
10
–10
–10
10
10
–11
10
–11
10
corrected radiotracer data [64Hal1,92Mes1] C-V on FZ Si [94Mes1] TID on Ga doped Si [93Hei1] TID on In doped Si [93Hei1] –3 D = 4.5⋅10 exp [– 0.39 eV/kT]
–12
10
–13
10
–14
1
–4
–13
10
–14
10
2
1200
–5
10
Temperature T [°C] 900 600 Di :Ag [87Rol1]
–6
10
[93Hei1]
–12
10
3 4 5 6 –3 –1 Inv. temp. 1/T [10 K ] Fig. 44. Si:Cu. Diffusion coefficient D of copper in silicon vs. inverse temperature 1/T [93Hei1]. The straight line was fitted to all data including corrected radiotracer data ([64Hal1, 92Mes1], C-V measurements on FZ silicon ([94Mes1] and transient ion drift (TID) experiments on Ga-doped or In-doped silicon [93Hei1].
10
1
2
3 4 5 6 –3 –1 Inv. temp. 1/T [10 K ] Fig. 45. Si:Cu. Diffusion coefficient D of copper in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
400
Di :Cu [93Hei1]
Si : X
–7
10 2 –1
–100
–7
10
Diff.coeff. D [cm s ]
[64Hal1,56Str1]
–5
Si :Cu
–5
10
10
Temperature T [°C] 400 200 100 0 –50
–4 1200
–4
[Ref. p. 2-196
eq
–8
eq
Ci Di /Cs :Au [91Küh1]
10
–9
10
–10
10
eq
eq CI DI /Cs :Au [84Sto1]
–11
10
–12
10
–13
10
–14
10
0.5
0.7
0.9 1.1 –3 –1 Inv. temp. 1/T [10 K ]
1.3
1.5
Fig. 46. Si:Cu, Ag, Au. Diffusion coefficient D of copper, silver, and gold in silicon vs. inverse temperature 1/T. Data represent diffusivities of the most abundant impurity species: the interstitial diffusivity Di for Cu and Ag, the Aui-limited kick-out diffusivity CieqDi/Cseq of Aus, and the self-interstitial-limited kickout diffusivity CIeqDI/Cseq of Aus, as indicated beside the references.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys Temperature T [°C] 1000
1200
–4
10
–5
[64Bol1]
[87Rol1]
10
1
800 [64Bol1]
Norm.Au conc. C /C eq
4
–7
2 –1
Diff.coeff. D [cm s ]
[67Ste1]
–8
10
–9
10
[61Bol1]
–10
10
4.27 2
4.27 –1
10
9 8 7
–12
10
0.6
0.8 0.9 1.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 47. Si:Ag. Diffusion coefficient D of silver in silicon vs. inverse temperature 1/T. Data from various references as indicated.
0.7
8
0.4 0.6 0.8 1.0 Norm.depth x/d Fig. 48. Si:Au. Normalized concentration of gold C/C eq vs. normalized depth x/d measured by neutron activation analysis (NAA) after in-diffusion at 1000 C. C eq denotes gold solubility. d refers to the thickness of the dislocation-free FZ silicon samples being ca. 500 µm thick except for the upper curve of the 4.27 h anneals for which d ≈ 300 µm holds [83Sto1].
0
1
Si : Au
6
T = 1098 °C
Norm. Au conc. C/C eq
Norm. Au conc. C m/C eq
8
–1
1000 °C
6
2 –1
10
8 6
4
4
2
2
–2
10 –1 4⋅10 6
T = 1050 °C t = 1.07 h
Si : Au
4
8
0.2
6
4
10
0.467 h
5 –2
4⋅10
–14
2
1.03
6
[70Pru1]
–13
10
26.8
3
10
–11
1
Si : Au
5
10
10
t = 100.6 h
6
Si :Ag
–6
10
9 8 7
2-147
–2
8
1
2
4
6
8 10
2
2 10
4 6 8 10 –2
2
2
4⋅10
Red. time t/d 2 [10 sm ] Fig. 49. Si:Au. Normalized concentration of gold Cm/C eq in the centre of a dislocation-free FZ silicon wafer vs. reduced diffusion time t/d2 [84Sto1]. C eq: gold solubility, d: wafer thickness being ca. 500 µm (triangels and full circles) or ca. 300 µm (open circle). The solid lines have slope 0.5 predicted by the kick-out model. The dashed curve represents the dissociative model. Lando lt -Bö rnst ein New Series III/33A
10
1
2
4
6 8 10
2
4
2 6 8 10
2
4
3 6 8 10
Depth x [µm] Fig. 50. Si:Au. Normalized concentration C/C eq of gold in dislocation-free FZ silicon vs. depth x in double-logarithmic representation. Diffusion temperature T and time t as indicated. Data: neutron activation analysis. Solid curve: kick-out model. Dashed curve: dissociative model [84Sto1].
2 Diffusion in silicon, germanium and their alloys
2-148
40
5
10
Si :Au
9 8 7 6
20
T = 1200 °C t = 45 min
–3
Subst.Au conc. Cs [10 cm ]
4
Resistance Rs [Ω]
15
10 8 6 4
1
0
0.2
0.4 0.6 Norm.depth x/d
9 8 7 6
0.8
Temperature T [°C] 900 700
–5
10
–6
Di [64Wil1]
[70Prn1]
10
–7
10
1.0
600
500
Si : Au
[77Bad1]
–8
10
–9
[77Koh1]
10
[56Str1]
10
–11
10
eq
eq
CV DV /Cs [64Wil1]
–12
10
–13
10
Ds [64Wil1]
–14
10
–15
10
eq
eq
Ci Di /Cs [64Wil1]
–16
10
–17
0.6
0.7
5 3
4⋅10 a
0
0.3
0.6
0.9 1.2 Depth x [mm]
1.5
1.8
2.1
b Fig. 52a, b. Si:Au. (a) W-shaped profile after gold diffusion in a virtually defect-free FZ silicon wafer of initially 1 Ω cm (p-type) resistivity. Spreading resistance RS, vs. penetration depth x. The peak in the resistance (scaling with gold concentration) is located at the depth where the optical micrograph (b) of the plane across which the profile has been measured shows many diffusion-induced stacking faults (short strokes) [86Hau1, 87Sto1].
[76Che1]
–10
10
2
4
1300 1100
–4
10
3
10
T = 1154 °C t = 900 s 1101 °C 1050 s 1049 °C 900 s
Fig. 51. Si:Au. Diffusion profiles in FZ silicon wafers with dislocation densities of 107 to 109 cm−2 as recorded by the spreading-resistance technique. Concentration of substitutional gold Cs vs. penetration depth x normalized to the wafer thickness d [86Sto1]. The solid lines were obtained by adjusting erfc-type profiles. The dashed line represents the 900s profile at 1050C in a dislocation-free specimen.
2 –1
Si :Au
5
2
Diff.coeff. D [cm s ]
[Ref. p. 2-196
0.8 0.9 1.0 1.1 –3 –1 Inv. temp. 1/T [10 K ]
1.2
1.3
Fig. 53. Si:Au. Diffusion coefficient D of gold in virtually perfect silicon (solid lines) and silicon containing dislocations (dashed lines) vs. inverse temperature 1/T. The diffusion coefficients are attributed to interstitial diffusivity Di of Aui, purely substitutional diffusivity Ds of Aus, vacancy-limited dissociative diffusivity CVeqDV/Cseq of Aus, and Auilimited dissociative diffusivity CieqDi/Cseq of Aus as indicated. Solid lines represents literature data which are based on diffusion analysis carried out before the kick-out mechanism was considered.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
Temperature T [°C] 1100 900
1300
10
–6
6
eq
eq
–8
10
8 6 4
[91Ler1] eq
eq
Cl Dl /Cs [84Sto1] 0.60
Si : Au
[93Poi1]
–7
–10
–12
[91Cof1]
10
10
10
[91Küh1]
900
2
2 –1
eq Ci Di /Cs [91Küh1]
Temperature T [°C] 1100
4
Ci Di /Cs [91Cof1]
eq
1300
8
Di [90Boi1]
10 2 –1
–6
Di [92Zim2]
Si : Au
Diff.coeff. D [cm s ]
800
Diff.coeff. D [cm s ]
–4
10
2-149
0.65
0.70 0.75 0.80 0.85 –3 –1 Inv. temp. 1/T [10 K ]
2
0.90
0.95
Fig. 54. Si:Au. Diffusion coefficient D of gold in virtually perfect silicon vs. inverse temperature 1/T. Within the theory of the kick-out mechanism the diffusion coefficients are attributed to the interstitial diffusivity Di of Aui, the Aui-limited diffusivity CieqDi/Cseq of Aus, and the self-interstitial-limited diffusivity CIeqDI/Cseq of Aus as indicated. Solid lines represent various literature data.
–8
10
0.60
[86Sto1] 0.65
0.70 0.75 0.80 –3 –1 Inv. temp. 1/T [10 K ]
0.85
0.90
Fig. 55. Si:Au. Diffusion coefficient D of gold in silicon vs. inverse temperature 1/T. The diffusion coefficient represents the Aui-limited kick-out diffusivity CieqDi/Cseq of Aus obtained from diffusion experiments in virtually perfect crystals ([91Cof1, 91Küh1]) and in crystals containing extended defects ([86Sto1, 93Poi1, 94Ler1]).
16
4⋅10
Si : Zn 16
–3
Subst.Zn conc. Cs [cm ]
10
15
t = 720.0 s 240.0 s 120.0 s 60.0 s 19.5 s 10.0 s 5.0 s 2.8 s
10
14
10
13
10 0
Lando lt -Bö rnst ein New Series III/33A
100
200 300 Depth x [µm]
400
500
Fig. 56. Si:Zn. Pentration profiles of zinc in highly dislocated silicon measured by the spreading-resistance technique after diffusion at 1115oC for different times t as indicated. Concentration of substitutional zinc Cs vs. depth x. Solid lines: erfc-fits [93Bra1].
2 Diffusion in silicon, germanium and their alloys
2-150
1
10
Si : Zn 12
Di [93Bra2]
10
10
[63Mal1]
8 3
7
10
eq
–8
10
eq
eq
Ci Di /Cs [95Bra1]
eq
2
6
eq
10
0
–10
5 0.2
0.4 0.6 0.8 1.0 Norm.depth x/d Fig. 57. Si:Zn. Penetration profiles of zinc in dislocation-free silicon wafers measured by the spreading-resistance technique after diffusion at 1115oC for different times t and wafer thicknesses d. Numbers indicate order with respect to diffusion time (1: t = 2.8 s, d = 1310 µm; 2: t= 5.0 s, d = 1430 µm; 3: t = 10.0 s, d = 1340 µm; 4: t = 19.5 s, d = 1420 µm; 5: t = 60.0 s, d = 1800 µm; 6: t = 120 s, d = 1445 µm; 7: t = 240 s, d = 1435 µm; 8: t = 720 s, d = 1400 µm; 9: t = 720 s, d = 910 µm; 10: t = 2880 s, d = 1415 µm; 11: t = 2880 s, d = 915 µm; 12: t = 11520 s, d = 545 µm). Normalized concentration of substitutional zinc Cs/Cseq vs. depth x. Solubility Cseq (1115oC)=3.47·1016 cm−3. Solid lines represent the theoretical best fits obtained with the kick-out diffusion model [95Bra1].
eq
–11
10
eq
CI DI /Cs [91Grü1] 0.60
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 58. Si:Zn. Diffusion coefficient D of zinc in silicon vs. inverse temperature 1/T. The diffusion coefficient represents the interstitial diffusivity Di of Zni, the Zni-limited kick-out diffusivity CieqDi/Cseq of Zns obtained from diffusion into dislocated silicon, the self-interstitial-limited kick-out diffusivity CIeqDI/Cseq of Zns , or the vacancy-limited dissociative diffusivity CVeqDV/Cseq of Zns as indicated along with the references.
–6
10
–7
10
–8
0.65
Temperature T [°C] 1100 1000
1300
Si : Zn Si : Cd
eq
900 eq
Ci Di /Cs [93Bra1] Zn
10 2 –1
Diff.coeff. D [cm s ]
eq
Fig. 59. Si:Zn, Cd. Diffusion coefficient D of zinc and cadmium in silicon vs. inverse temperature 1/T. The diffusion coefficient represents the Zni-limited kick-out diffusivity CieqDi/Cseq of Zns or the self-interstitiallimited kick-out diffusivity CIeqDI/Cseq of Zns. Data from the literature as indicated.
eq
CV DV /Cs [95Bra1]
10
1
–4
10
4
eq
Ci Di /Cs [91Grü1]
–9
–3
10
eq
Ci Di /Cs [93Bra1]
2 –1
Norm. Zn conc. Cs /Cseq
–2
10
Diff.coeff. D [cm s ]
–7
9
900
Si :Zn
–6
11
–1
10
Temperature T [°C] 1100
1200
–5
[Ref. p. 2-196
–9
10
eq
CI DI /Cs [95Bra1] Zn
–10
10
–11
10
–12
10
[72Spi1] Cd
–13
10
–14
10
0.60
0.65
0.70 0.75 0.80 –3 –1 Inv. temp. 1/T [10 K ]
0.85
0.90
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
1.0
21
Si : Cd
RT
15
T = RT 700 °C 800 °C 900 °C
–3
Hg conc. C [10 cm ]
20
Rel.number of Cd N/NO
0.6 Cd, N/N0 0.4 0.2
Lattice disorder σ
4
5
5
10 10 2⋅10 Anneal. time t [s] Fig. 60. Si:Cd. Normalized total number N/N0 of implanted cadmium atoms in silicon (closed circles, solid line) and degree of lattice disorder σ (open circles, dashed line) vs. duration t of isothermal annealing at 500C. The solid line was calculated for an effective (recrystallization-enhanced) Cd diffusivity of 2.5.10−16 cm2s−1 [70Mey1].
9 6
0 820
900 860 880 Channel number NCh Fig. 61. Si:Hg. Concentration of mercury C in silicon vs. detector channel number NCh. The profiles arise from RBS analysis after Hg implantation at room temperature into preamorphized Si surface layers and subsequent annealing for 30 min at different different temperatures as indicated. The surface is located at the right hand side [93Hon1]. 840
10
18
2⋅10
18
12
3
0 3 10
10 8
300 keV + Hg Si
Si :Hg
18
0.8
2-151
T = 700 °C
Si : B
Si :B
6
Norm. diff. conc. D /D
i
4
–3
B conc. C [cm ]
2 17
10
8 6 4
1
EV + = 0.35 eV (1000 °C)
–1
10
EV + = 0.05 eV (1000 °C)
2 16
10
as grown t= 3h 10 h 30 h
8 6 4
15
2⋅10 65
–2
10
–2
10
–1
10 1 Norm.hole conc. p/ni
10 20 i
115 140 165 190 Depth x [nm] Fig. 62. Si:B. Concentration C of boron in silicon vs. depth x. Data arise from SIMS profiling after epitaxial growth of a B-doping spike and subsequent annealing in dry O2 ambient at 700C for times t as indicated. The observed profile broadening from exponential-type to Gaussian-type provides evidence for the kick-out mechanism involving interstitial Bi as mobile species [91Cow1].
Lando lt -Bö rnst ein New Series III/33A
T = 870 °C 950 °C 1000 °C 1050 °C 1100 °C 1150 °C 1250 °C
90
Fig. 63. Si:B. Normalized diffusion coefficient D/D of boron in silicon vs. normalized hole concentration p/ni. Data originate from B diffusion in heavily doped n-type Si (p/ni < 1) as well as in lightly and heavily doped p-type Si (p/ni > 1) at various temperatures T as indicated [73Cro1, 75Fai2]. The solid and dashed lines are calculated with the vacancy donor level at different energies EV+ above the valence band edge as indicated [81fai1].
2 Diffusion in silicon, germanium and their alloys
2-152
1
19
10
1 – 0.87y – 0.45y 2 1–y 1 – y 2/3
Si : B
18
10
Si : B
17
10 –3
Hole conc. p [cm ]
Norm. B conc. C /CO
–1
10
erfc y
T = 700 °C t = 870 °C 870 °C 1050 °C 1250 °C 1150 °C 1018 °C 1000 °C
–2
10
42 h 16 h 2h 1h 34 h 35 min 105 min 5 min
0
0.2
16
10
15
10
t = 16 h T = 1200 °C 1150 °C
14
10
FZ Silicon
–3
10
[Ref. p. 2-196
0.4 0.6 Norm.depth x/xj or y/yj
0.8
1.0
Fig. 64. Si:B. Normalized concentration C/C0 of boron in silicon vs. normalized depth x/xj or normalized variable y/yj. Data arise from incremental sheet resistance measurements after B diffusion with boundary concentration C0 > 2·1019 cm−3 in nonoxidizing ambients at various temperatures T as indicated. The junction depth xj is taken at C ≈ 0.01C0. Solid lines and dashed line are different functional forms of a variable y = y(x, t, T) as indicated (t = diffusion time) [75Fai3, 81Fai1].
1000 °C
CZ
13
10
45
30 15 0 15 Distance from interface x [µm] Fig. 65. Si:B. Hole concentration p due to boron in silicon vs. distance x from the interface of directly bonded (100)-oriented wafers. Data arise from spreading-resistance measurements after 16h of interdiffusion between a lightly B-doped FZ wafer and a heavily B-doped CZ wafer in N2 ambient at temperatures T as indicated. Profile shapes reveal enhanced tail diffusivity [91Wij1, 93Wij3].
–1
2⋅10
SiO2/Si :B
–1
10
8 6
at k = 10 at k = 3 at k = 1
Norm.B conc. C/C0
4 2 –2
10
8 6 4 2
–3
10
0
0.5
1.0 1.5 2.0 2.5 Distance from interface x [µm]
3.0
3.5
Fig. 66. Si:B. Normalized concentration C of boron in silicon vs. distance x from the Si/SiO2 interface. Data arise from incremental sheet resistance measurements after B predeposition and drive-in diffusion under dry oxygen atmosphere at about 1195 C for 3100 s. Solid curves are based on a diffusivity of 2.0·10−12 cm2s−1 and different SiO2/Si segregation coefficients k as indicated [64Kat1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
0.5
2.0
Time t [h] 1.0 2.0
3.0
4.0 5.0
–12
2⋅10
Junction depth xj [µm]
900
–12
10
Si : B 1.6
Temperature T [°C] 1100 1000
1200
2-153
Si : B
(100) –13
10 2 –1
Diff.coeff. D [cm s ]
1.2 (111) 0.8
–14
10
0.4
100 111 inert.ambient dry O2 ambient
–15
10
0
0.5
1.0 1.5 2.0 2.5 1/2 Square root of time t1/2 [h ] Fig. 67. Si:B pn-junction depth xj due to boron in epitaxial silicon vs. square root of diffusion time t½. Data arise from B predeposition from a B2O3 source and subsequent drive-in diffusion at 1050 C in O2 ambient. Different surface orientations of the samples as indicated show enhanced B diffusion for (100) crystals [69Wil1].
–16
10
0.65
0.70
0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 68. Si:B. Diffusion coefficient of boron in silicon vs. inverse temperature 1/T. Data arise from annealing of B-implanted CZ crystals of given surface orientation in different ambients as indicated. Comparison with the solid line representing intrinsic diffusion reveals oxidation-induced enhancement of the B diffusivity [78Ant2].
–13
10
2 –1
Enhancement ∆D [cm s ]
Si : B
–14
10
measured calculated B doping [85Miy1] P doping [85Miy2] –15
10
–2
4⋅10
–1
10
Lando lt -Bö rnst ein New Series III/33A
1 Norm.hole conc. n/ni
10
20
Fig. 69. Si:B. Diffusivity enhancement ∆D of boron in silicon due to oxidation vs. normalized hole concentration p/ni. Data arise from 10B implantation in heavily 11B-doped and heavily P-doped CZ crystals with (100) orientation as indicated and subsequent annealing in dry O2 and N2 ambient at 1000 C for 30 min. Solid line has been calculated based on oxidationinduced excess self-interstitials [85Miy2].
2 Diffusion in silicon, germanium and their alloys
2-154
3.5
19
10
Si (100) : B –3
–3
4 % HCl 17
10
as deposited T = 800 °C, t = 15 min
2.5
19
0 % HCl B conc. C [cm ]
3.0
B conc. C [10 cm ]
T = 1150 °C
18
10
Si(100) :B
[Ref. p. 2-196
2.0 1.5 1.0 0.5
16
10
SIMS 0 %, 4 % HCl 0 % HCl 4 % HCl
simulation
15
0.5
1.0
1.5 2.0 2.5 3.0 3.5 Depth x [µm] Fig. 70. Si:B. Concentration C of boron in silicon vs. depth x showing the reducing effect of chlorinecontaining ambient on the oxidation-enhanced B diffusivity. Continuous lines result from SIMS profiling after annealing of B-implanted, (100)-oriented Sicrystals in dry O2 ambient with or without HCl as indicated. Discrete data originate from numerical simulation [87Sub1].
2
200
300 400 Depth x [µm]
500
600
B diffusivity I supersaturation
–16
2 –1
0
–16
100
3⋅10
10
Diff.coeff. D [cm s ]
10
0
a
8 6 4
2
–17
10
–18
7⋅10
0 100 200 300 400 500 600 Depth x [µm] b Fig. 71a, b. Si:B. (a) Concentration C of boron in silicon vs. depth x. Data show a SIMS-resolved Bmodulated epitaxial (100) Si structure before and after annealing in O2 ambient at 800 C during 15 min (b). Diffusion coefficient D of boron in silicon vs. depth x. Data result from the depth-dependent B-spike broadening depicted in (a). Solid line represents average Si self-interstitial (I) concentration (in arbitrary units) based on a constant oxidation-enhanced selfinterstitial boundary concentration and a constant selfinterstitial diffusivity DI of 1.4·10−13 cm2s−1 [93Gos1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
19
20
2⋅10
10
Si :B
2-155
Si :B
19
10
T = 1100 °C 20
19
10
1000 °C
–3
B conc. C [cm ]
–3
B conc. C [cm ]
10
17
20
19
10
10
t=
–3
B conc. C [cm ]
10
18
10
900 °C
0 min 35 min 65 min 118 min 180 min
16
10
10 800 °C
19
10
0
0.4
0.8 1.2 1.6 Depth x [µm] Fig. 72. Si:B. Concentration C of boron in silicon vs. depth x. Data originate from SIMS analysis of the 10B background component of heavily B-doped (111)oriented FZ crystals after 11B implantation with dose − 1016 cm 2 and energy 70 keV and subsequent annealing in inert ambient at temperatures T as indicated. The observed up-hill diffusion is interpreted in terms of B precipitation in the implanted zone [73Hof1].
Fig. 74. Si:B. Concentration C of boron in silicon vs. depth x. Data originate from SIMS analysis after 11B implantation (2·1014 cm−2, 60 keV) and RTA damage annealing (950C, 30s) followed by 28Si implantation (1·1014 cm−2, 50 keV) or none, and with subsequent furnace annealing at 800C for 35 min in either case. Anomalous profile broadening reveals transient enhanced B diffusion due to Si implantation [87Mic2].
Lando lt -Bö rnst ein New Series III/33A
10
3000 4000 5000 6000 7000 Depth x [Å] Fig. 73. Si:B. Concentration C of boron in silicon vs. depth x. Data arise from SIMS analysis after 11B implantation (2·1014 cm−2, 60 keV) and subsequent furnace annealing in N2 ambient at 800 C for times t as indicated. Near coincidence of the B profiles after annealing shows the phenomenon of transient enhanced diffusion [87Mic1].
0
1000 2000
19
2⋅10
Si :B
19
10
–3
19
B conc. C [cm ]
20
Si implant B;without Si implant B;with Si implant
18
10
17
10
16
10
0
1500
3000 4500 Depth x [Å]
6000
7500
2 Diffusion in silicon, germanium and their alloys
2-156
1000
5
10
Temperature T [°C] 900 800
700
21
10
10
20
10 –3
B conc. CTED [cm ]
Time length tTED [s]
Temperature T [°C] 1100 1000 900 800 700 Solubility
Si :B
4
3
10
2
10
[87Mic1] [88Sol1] [88Sed1] [90Fai1] [90Cow1, 90Cow3]
10 1 0.75
[Ref. p. 2-196
Si :B
600
[91Sol1] [87Mic1,87Mic2] [87Ang1] [88Sed1] [90Fai1] [90Cow1,90Cow3]
19
10
18
10
17
0.80
0.85 0.90 0.95 1.00 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 75. Si:B. Time length tTED of transient enhanced diffusion of boron in silicon vs. inverse temperature 1/T. Data from the literature as indicated originate from annealing of Si single crystals after B implantation [91Sol1].
10
0.7
0.8
0.9 1.0 1.1 1.2 –3 –1 Inv. temp. 1/T [10 K ] Fig. 76. Si:B. Concentration CTED below which transient enhanced diffusion (TED) occurs for boron in silicon vs. inverse temperature. Data from the literature as indicated arise from annealing of Si single crystals after B implantation. Arrows indicate that all boron underwent TED in experiments which concentrations higher than the B solubility given by the upper solid line. The lower solid line is described by an activation energy of 0.75 eV and a pre-exponential factor of 1.6·1022 cm−3 [91Sol1].
20
10
Si :B
Experiment Simulation RT profile
19
–3
B conc. C [cm ]
10
18
Fig. 77. Si:B. Concentration C of boron in silicon vs. depth x showing up-hill diffusion near surface. Data arise from SIMS profiling after continuous 120 keV B implantation at 950C at a dose rate of ca. 3·1011 cm−2s−1 until a total dose of 1015 cm−2 was reached. Dotted line represents corresponding B implantation at room temperature. Solid line results from numerical simulation based on fluxes of B-selfinterstitial and B-vacancy pairs [92Pic2].
10
17
10
16
10
0
0.5
1.0
1.5 2.0 Depth x [µm]
2.5
3.0
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
3
21
2⋅10 21 10
10
Si :B Si :As
10 –3
B (alone) 19
10
18
10
Si :B Si :P
1
B (+ As)
Norm. enhancement factor DB /DBeq
As (+B)
20
B, As conc. CB , CAs [cm ]
2-157
front side P emitter back side diffusion [74Yos1]
2
10
2
10
17
10
16
10
0
3000 4500 6000 7500 Depth x [Å] Fig. 78. Si:B, As. Concentrations CB and CAs of arsenic and boron in silicon vs. depth x. Data arise from B diffusion alone and from simultaneous B-As diffusion as indicated. Details about the diffusion conditions are not given [73Bla1].
–12
10
1500
Temperature T [°C] 900
1000
800
Si :B,P
1
0
25
50 75 100 125 150 Distance from surface x [µm] Fig. 79. Si:B, P. Diffusivity enhancement factor DB/DBeq of boron in silicon vs. distance x from surface where phosphorous diffusion takes place. Data arise from 1012 cm−2 B implantation at the front side of a FZ silicon wafer and subsequent 1021 cm−3 P-diffusion at 900 C for 30 min at front or back side as indicated. Solid lines are theoretical curves based on P-diffusioninduced excess point defects with diffusion length of 30 µm: surface ignored (curve 1) or surface acting as a perfect sink (curve 2) [79Lec1, 80Lec1].
–13
2 –1
B diff.coeff. DB [cm s ]
10
–14
10
B –15
10
–16
10
0.75
Lando lt -Bö rnst ein New Series III/33A
intrinsic
0.80
Si 12
–2
φ = 10 cm 14 –2 [80Lec1] φ = 10 cm 15 –2 φ = 10 cm [78Ant2]
0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ]
1.00
Fig. 80. Si:B, P. Diffusion coefficient DB of boron in silicon vs. inverse temperature 1/T. Data arise from deep B implantation at various doses φ as indicated and subsequent P diffusion to a boundary concentration of 1021 cm−3. Comparison with the intrinsic B diffusivity [78Ant2] shows the dose-dependent enhancement of the B marker layer broadening beneath a P-diffused surface region [80Lec1].
2 Diffusion in silicon, germanium and their alloys
2-158
1000
3
10
8
Temperature T [°C] 900
800
20
4⋅10
Si :B,P
6
[Ref. p. 2-196
Si :B
2
4
solubility
20
2
8 6 4
–3
B conc. C [cm ]
Norm. diff. conc. D /D
eq
10
2
10
8 6
P [77Fai2] P [74Lee1] B [79Lec1,80Lec1] B [74Jon1,77Fai2]
4
2
2 19
10
8 6 4
10 0.75
0.80
0.85
0.90
0.95
1.00
BBr3 [%] O2 [%] 0.04 7.2 0.04 1.8 0.32 1.8
2
–3 –1
Inv. temp. 1/T [10 K ]
18
10
Fig. 81. Si:B, P. Diffusivity enhancement factor D/Deq of boron and phosphorous in silicon vs. inverse temperature 1/T [79Lec1, 80Lec1]. Comparison of B marker layer broadening under surface P diffusion [79Lec1, 80Lec1] with P tail diffusivity [77Fai2, 74Lee1] and B base shift by the emitter-push effect [74Jon1, 77Fai2]. The solid line corresponds to an activation energy of −1.3 eV.
0
0.1
0.2 0.3 Depth x [µm]
0.4
0.5
Fig. 82. Si:B. Concentration C of boron in silicon vs. depth x. Data arise from differential Hall and sheetresistance measurements after a 20 min diffusion treatment at 1000C in mixed N2/O2/BBr3 gas ambients of different composition as indicated. Dashed line represents the B solubility limit at 1000C [78Neg1].
20
10
Si :B 20
–3
B conc. C [cm ]
10
19
10
18
10
as deposited annealed 17
10
0
150
300
450 600 Depth x [nm]
750
900
Fig. 83. Si:B. Concentration C of boron in silicon vs. depth x showing pile-up at the amorphous/crystalline interface.. Data arise from SIMS analysis after deposition of an in-situ B-doped poly-Si layer on top of (100)-oriented Si with or without subsequent annealing at 900C for 2h and 950C for 45 min as indicated [86Gar1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
–10
10
1300
1200
2-159 Temperature T [°C] 1100 1000
[61Wil1]
2 –1
Diff.coeff. D [cm s ]
10
–12
10
[54Ful1] [69Oka1]
–13
10
Fig. 84. Si:B. Optical micrograph of the (100) surface of a silicon bicrystal after boron diffusion with a boundary concentration of 5.0·1020 cm−3 (B2O3 source, N2 ambient). Subsequent preferential etching reveals a diffusion-induced dislocation network. The grain boundary with 11 misfit angle in the (010) plane is also shown [61Que1].
–10
10
[70Usk1]
–14
[94Rak1]
–15
10
0.70 0.75 0.80 0.85 –3 –1 Inv. temp. 1/T [10 K ] Fig. 85. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. The solid lines are early data from the literature. The dashed line represents an average of [56Ful1, 60Kur1, 61Wil1, 69Bar1, 70Usk1] given by [94Rak1].
0.60
–10
10
0.65
1400
Temperature T [°C] 1200 1000
Si :B 10
10
[71Gho3] Diff.coeff. D [cm s ]
–12
2 –1
2 –1
Diff.coeff. D [cm s ]
[71Sch2] 10
–13
[72Gho1]
–12
10
[75Fai3,84Kim1]
–13
10
[80Fro1]
[72Kam1] –14
10
[69Vic1]
0.8 0.9 1.0 1.1 –3 –1 Inv. temp. 1/T [10 K ] Fig. 86. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. The straight lines are data from the literature. The diffusivity given by [94Rak1] represents an average of [56Ful1, 60Kur1, 61Wil1, 69Bar1, 70Usk1].
Lando lt -Bö rnst ein New Series III/33A
[78Ant2] [81Hil1]
–15
0.7
[82Miy1]
10
[94Rak1] [86Dom1]
0.6
[93Wij3]
–14
–15
10
Si :B
[93Wij3]
–11
–11
10
[56Ful1]
[69Bar1]
10
Temperature T [°C] 1000 800
1200
Si :B
[60Kur1]
–11
10
0.55
0.60
0.65 0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 87. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. The solid lines show data from the literature for intrinsic conditions. The dashed line represents enhanced diffusivity attributed to a Bi-self-interstitial complex.
2 Diffusion in silicon, germanium and their alloys
800
d
–11
10
–12
10
[67Pav1] c b a
–11
–12
–13
[90Fan1]
f
–14
e
–15
10
–14
g e
d c [79Bag1]
–16
10
f [93Loe1]
–15
10
–17
[90Söd1]
[93Sul1]
0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 88. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. Data from [74Pri1] and [91Gon1] (solid lines) represent diffusivities for Bimplanted silicon samples annealed in steam and by RTA in Ar ambient, respectively. Data from [90Söd1] (solid line) give diffusivities after shallow Bimplantation. Data from [91Sol1] and [90Fan1] (solid lines) show transient enhanced diffusion of Bimplanted silicon upon RTA or furnace annealing in N2. Data from [67Pav1] (dashed lines) show enhanced diffusion for B-implantation doses increasing from a to d. Data from [93Loe1] (dashed lines) compare intrinsic diffusion under furnace annealing (e) and RTA (f, g) of silicon samples (e, f) and silicon substrates of SiGe heterostructures (g) all covered with B-doped epitaxial layers.
10
0.60
h
[68Nag1]
–18
0.65
g
10
–16
0.60
–13
10 10
10
10
Si :B
[69Bar1] a
10
[74Pri1] [91Sol1]
10
800
b
10
[91Gon1]
[Ref. p. 2-196
Temperature T [°C] 1000
1200
–10
10
Si :B
2 –1
Diff.coeff. D [cm s ]
Temperature T [°C] 1000
2 –1
1200
–10
10
Diff.coeff. D [cm s ]
2-160
0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 89. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. Data from [69Bar1] (solid lines) show diffusivities for boundary concentrations C0 = 3.5·1019 cm−3 (a) and C0 = 1.4·1021 cm−3 (b). Data from [79Bag1] (dashed lines) compare diffusion with C0 increasing from c to f. Data from [68Nag1] (solid line) represent diffusivities for C0 = ca. 1016 cm−3. Data from [93Sul1] (solid lines) give diffusivities for (implanted) boron concentrations CB < 5.0·1018 cm−3 (g) and CB > 1.0·1020 cm−3 (h).
–11
10
–12
10
0.65
(100)
1200
Temperature T [°C] 1000
Si :B
(111) [70Cha1]
–13
[76Mas1]
2 –1
Diff.coeff. D [cm s ]
10
Fig. 90. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. Data from [70Cha1] (solid lines) show diffusivities affected by oxidation of (100) and (111) surfaces. Data from [76Mas1] (dashed lines) represent diffusivities for silicon samples with variously oriented surfaces annealed in dry O2 ambient. Data from [81fai1] and [85Tso1] (solid lines) show diffusion via neutral (D0) and singly positively charged vacancies (D+) derived from literature data.
(100) (110) (111)
–14
10
D 0 [81fai1]
[81fai1]
–15
10
D+ D+ [85Tso1]
–16
10
–17
10
0.60
0.65
0.70 0.75 0.80 –3 –1 Inv. temp. 1/T [10 K ]
D0 0.85 0.90
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
1200
–11
10
2 Diffusion in silicon, germanium and their alloys
1100
Temperature T [°C] 1000 900
800
–10
10
1400
2-161
Temperature T [°C] 1300 1200
Si :X
Si :B –12
–11
10
[93Che1]
Tl
2 –1
–13
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
10
10
(100) –14
10
[93Che1]
[81Hil1,80hil1]
Al
–12
10
(111) –15
10
(100) (110)
[81Hil1,80hil]
In
(111)
B
–13
–16
10
0.60
0.65
0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 91. Si:B. Diffusion coefficient D of boron in silicon vs. inverse temperature 1/T. Data from [81Hil1, 80hil1] show diffusivities for intrinsic conditions (lower solid line) and for annealing in dry O2 (solid lines) and steam (dashed lines) ambient of variously oriented silicon samples as indicated. Data from [93Che1] (solid lines) represent diffusion under an oxide layer in N2 (lower solid line) and NH3 (upper solid line) ambient. Temperature T [°C] –10 1300 1200 1100 1000 900 10
10
0.58
Ga
0.60
0.62 0.64 0.66 0.68 0.70 0.72 –3 –1 Inv. temp. 1/T [10 K ] Fig. 92. Si:B, Al, Ga, In, Tl. Intrinsic diffusion coefficient D of boron, aluminum, gallium, indium and thallium in silicon vs. inverse temperature 1/T. Data result from spreading-resistance measurements after annealing of doped epitaxial Si layers on FZ or CZ substrates in flowing H2 ambient [71Gho1, 71Gho3].
Si :X –11
2 –1
Diff.coeff. D [cm s ]
10
–12
10
In,Tl [81fai11] Al [94Mit1]
–13
10
Ga [81fai1]
–14
10
In [83Cer1] B [78Ant2]
–15
10
0.60
0.65
Lando lt -Bö rnst ein New Series III/33A
0.70 0.75 0.80 –3 –1 Inv. temp. 1/T [10 K ]
0.85
0.90
Fig. 93. Si:B, Al, Ga, In, Tl. Diffusion coefficient D vs. inverse temperature 1/T of group III elements in silicon. The straight lines are data from the literature.
2 Diffusion in silicon, germanium and their alloys
2-162
Si :Al
18
2⋅10
18
Si3N4
T = 1230 °C, t = 2 h
10
[Ref. p. 2-196
SiO2 + Si3N4
bare Al diffused layer
17
substrate
a
16
10
b
0
4
20
10
Si :Al
20
10 8 6
T = 1017 °C 1032 °C 1047 °C
O-area ON-area N-area
4 60
100 200 400 600 1000 2000 Oxidation time t [min] c Fig. 95a, b, c. Si:Al. (a) Cross-sectional view of an aluminum-prediffused silicon sample before selective oxidation. (b) Idem, after selective oxidation. (c) pnjunction depth xj vs. oxidation time t at 1100C in dry O2 for (100)-oriented FZ substrates. Different areas are as indicated [82Miz1].
19
10
–3
Al conc. C [cm ]
Junction depth xj [µm]
8 12 16 20 Depth x [µm] Fig. 94. Si:Al. Concentration C of aluminum in silicon vs. depth x. Data were measured by the spreadingresistance technique after diffusion from an Al-doped epitaxial layer into a CZ substrate. Diffusion temperature T and time t as indicated [71Gho1].
18
10
Fig. 96. Si:Al. Concentration C of aluminum in silicon vs. depth x. Data result from SIMS profiling after diffusion in vacuum for 300s at different temperatures T as indicated. Heat treatments were performed in a RTA system using Al-evaporated Si wafers as diffusion source [95Nag2].
17
10
16
10
O-area
40
15
10
ON-area
xjO
N-area
xjON
10
xjN
–3
Al conc. C [cm ]
Si :Al
0
0.2
0.4 0.6 Depth x [µm]
0.8
1.0
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys Temperature T [°C] 1200 1100 1000 900
1300
–8
10
10
1000
Si :Al [56Mil1]
[56Gol1]
–10
10 2 –1
Diff.coeff. D [cm s ]
[56Ful1]
–10
10 2 –1
Temperature T [°C] 1200 1100
1300
–9
Si :Al
–9
10
Diff.coeff. D [cm s ]
800
2-163
–11
10
[71Gol1]
–12
10
[81Cha1]
[81Cha1]
[94Mit1]
–13
10
–11
10
[81fai1]
[78Ros1]
–12
10
[93LaF1,93Gal1]
–14
10
[67Kao1]
–15
10
[94Mit1]
–13
0.60
0.65
0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 97. Si:Al. Diffusion coefficient D of aluminum in silicon vs. inverse temperature 1/T. The straight lines are data from the literature.
10
0.68 0.72 0.76 0.80 –3 –1 Inv. temp. 1/T [10 K ] Fig. 98. Si:Al. Diffusion coefficient D of aluminum in silicon vs. inverse temperature 1/T. The straight lines are data from the literature. Data from [81fai1] represents intrinsic diffusivity based on an evaluation of [67Kao1, 77Rai1, 78Ros1].
0.64
10
19
10
0.60
Si :Ga
8
intrinsic extrinsic intrinsic extrinsic
Si :Ga Si :Al
6 4
Al T = 1200 °C
Norm. diff. coeff. D /D
i
T = 1000 °C, t = 67 h T = 1000 °C, t = 67 h T = 1050 °C, t = 50 h T = 1050 °C, t = 50 h
18
–3
Ga conc. C [cm ]
10
950 °C
2
Ga
1
8
1250 °C
6 4
17
10
[71Mak1] (950 °C) [71Oka1] (1250 °C)
2
Ga
–1
10
16
10
0
0.8 1.2 1.6 2.0 Depth x [µm] Fig. 99. Si:Ga. Concentration C of gallium into intrinsic and extrinsic silicon vs. depth x. Diffusion temperatures, diffusion times and doping conditions are as indicated. Extrinsic silicon originated from boron pre-diffusion to a concentration of 8·1020 cm−3 [71Mak1].
Lando lt -Bö rnst ein New Series III/33A
0.4
–1
6 8 1 2 6 8 10 4 Norm.hole conc. p/ni Fig. 100. Si:Al, Ga. Normalized diffusion coefficient D/Di of aluminum and gallium in silicon vs. normalized hole concentration p/ni (Di and ni refer to intrinsic conditions). Data originate from Ga diffusion in heavily doped n-type Si (p/ni < 1) at 1250 C [71Oka1] and in heavily doped p-type Si (p/ni > 1) at 950 C [71Mak1] as indicated. Solid and dashed lines represent results calculated for Al and Ga, respectively, for different temperatures T as indicated [81fai1].
10
2
4
2 Diffusion in silicon, germanium and their alloys
2-164
–12 8 6 4
20
4⋅10
As (electrical) Ga (tracer) Ga (electrical) As Ga
Si :X Ga
2 –13 8 6 4
10
19
10
2 –1
Diff.coeff. D [cm s ]
–3
As,Ga conc. C [cm ]
10
Si : As : Ga
20
10
[Ref. p. 2-196
18
10
B
2 –14
10
8 6 4 2
Ge
–15
10
17
10
8 6 4 2
16
10
80 2 4 6 8 Depth x [µm] Fig. 101a, b. Si: Ga, As. Concentration C of Ga and As vs. depth x in Si [81Mal1]. (a) 1072 °C/5 min Ga predeposition followed by 1000 °C/15 min Ga drive-in diffusion and subsquent 1000 °C/15 min As diffusion in oxidizing ambient. (b) Computer simulation of the experimental situation of (a).
–10
10
2
4
6
b
Temperature T [°C] 1200 1000
1300 [56Ful1]
3
10
–1
2 –1
Diff.coeff. D [cm s ]
–13
Si : In
3
[71Gho1]
10
2.5
4⋅10
–12
10
5.0 7.5 10.0 12.5 Pressure p [kbar] Fig. 102. Si:B, Ga, Ge. Diffusion coefficient D of boron, gallium and germanium in silicon at 1050C vs. hydrostatic pressure p [89Söd1]. The accuracy of the individual data is of the order of 15%.
800
0
–1
10
10
Si : Ga
[64Bol2] [85Dan1]
–11
–16
In activity As [counts min mg ]
0
a
[71Mak1]
[58Kur1] [81fai1]
–14
10
[71Mak1]
[80Har1]
2
10
10
intrinsic n-type p-type
1
–15
10
[90Söd1] –16
10
0.6
0.7
0.8 0.9 –3 –1 Inv. temp. 1/T [10 K ]
1.0
Fig. 103. Si:Ga. Diffusion coefficient D of gallium in silicon vs. inverse temperature 1/T. The straight lines are data from the literature. Data from [81fai1] are based on an evaluation of [56Ful1, 58Kur1, 64Bol2, 71Mak1]. The dashed line shows gallium diffusion coefficients in boron-diffused extrinsic silicon.
–1
10
1
2
4
6 8 10
2
4
2 6 8 10
2
2
4⋅10
Depth x [µm] Fig. 104. Si:In. Specific activity As of 114In in silicon vs. depth x. The profiles were measured after diffusion at 1246C from the vapour phase into intrinsic, n-type (n = 6.0·1019 cm−3) and p-type (p = 4.2·1018 cm−3) samples as indicated [66Mil1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
7
5
0.30
[67Ste1]
–10
10
3
[81fai1] [56Ful1]
–11
10
2
–12
10
In [82Ant1] P [82Ant2] B [82Ant2] theory [82Ant2]
–13
10
10
20 30 40 50 60 Oxidation time t [min] Fig. 105. Si:In, B, P. Mean diffusivity enhancement /D of boron, indium and phosphorous in silicon vs. oxidation time t at 1000C. Data result from comparing the diffusivity Dox in dry O2 ambient to the corresponding diffusivity D in inert ambient [82Ant1, 82Ant2]. 0
–10
10
Temperature T [°C] 1300 1200
140
1100
Si :Tl
[81fai1]
[83Cer1]
–14
[83Cer1]
–15
10
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 106. Si:In. Diffusion coefficient D of indium in silicon vs. inverse temperature 1/T. The straight lines are data from the literature. Data from [81fai1] are based on an evaluation of [56Ful1, 66Mil1]. The dashed line shows enhanced diffusivity after high-dose implantation [83Cer1].
0.60
0.65
1 0.9 0.8 0.7
[71Gho1] –12
10
[89Sel1] [56Ful1]
10
Norm. sheet conduct. s/sO
10 2 –1
[71Gho1]
10
–11
–13
900
–9
2 –1
4
Temperature T [°C] 1000
Si : In
–8
10
fI = 0.38
1
Diff.coeff. D [cm s ]
1200
10
Diff.coeff. D [cm s ]
Norm. Au conc. Dox /D
10
Si : X
6
Si :Tl
0.6 0.5 0.4 0.3
–14
10
1300
–7
2-165
0.56
0.64 0.68 0.72 0.74 –3 –1 Inv. temp. 1/T [10 K ] Fig. 108. Si:Tl. Diffusion coefficient D of thallium in silicon vs. inverse temperature 1/T. The straight lines are data from the literature. Data from [81fai1] are based on an evaluation of [56Ful1, 66Mil1].
Lando lt -Bö rnst ein New Series III/33A
0.60
0.2
0
1
2
3 4 5 6 7 Depth x [µm] Fig. 107. Si:Tl. Normalized sheet conductivity s/s0 of silicon vs. depth x after diffusion of thallium for 24 h 33 min at 1180 C. The solid line represents an erfc-fit yielding the diffusion coefficient D = 1.77·10−12 cm2s−1 [89Sel1].
2 Diffusion in silicon, germanium and their alloys
2-166
–8
18
10
10
Si : C
[Ref. p. 2-196
Temperature T [°C] 1200 1000
1400
900
Si : C
[87Cha1] –9
10
17
10
–10
–3
C conc. C [cm ]
2 –1
16
10
–13
–14
40 60 80 100 Depth x [µm] Fig. 109. Si:C. Concentration profiles C of carbon in silicon vs. depth x after diffusion at temperatures T as indicated utilizing radioactive Ba14CO3 as diffusion source. The solid lines represent fits of the complementary error function [89Rol1].
–10
10
–11
10
–12
10 2 –1
1200
500 Cs [87Cha1] Cs [73Gru1]
Temperature T [°C] 200 100 50 0
–14
10
10
0.60
1300 1200
Temperature T [°C] 1100 1000 900
800
Si :X
–10
10
–11
10
Cs [61New1] Cs [89Rol1]
0.55
–9
Si :C
–12
10 Ci [87Tip1]
–15
10
Si [67Fai1]
C [89Rol1]
–13
10
–14
10
–16
10
–15
10
–17
10
Ge [79Het1]
–16
–18
10
10
–19
10
Sn [94Kri1]
–17
10
–20
10
Ci [86Gos1]
–21
10
–22
10
0.65 0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 110. Si:C. Diffusion coefficient D of carbon in silicon vs. inverse temperature 1/T. The straight lines represent literature data for substitutionally dissolved carbon Cs .
–50
–13
10
Diff.coeff. D [cm s ]
20
2 –1
10
0
10
Diff.coeff. D [cm s ]
–9
–12
10
13
10
–11
[89Rol1]
14
–8
[73Gru1]
10
10
10
[61New1]
10
1016 °C
15
10
10
Diff.coeff. D [cm s ]
T = 1385 °C
2 3 4 5 –3 –1 Inv. temp. 1/T [10 K ] Fig. 111. Si:C. Diffusion coefficient D of carbon in silicon vs. inverse temperature 1/T. The solid and dashed lines are data from the literature for interstitially (Ci) and substitutionally (Cs) dissolved carbon, respectively. 1
Ge [84Dor1,83Dor1]
–18
10
Si [83Dem1]
–19
10
0.60
0.65
0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 112. Si:C, Si, Ge, Sn. Diffusion coefficient D vs. inverse temperature 1/T of group IV elements in silicon. The straight lines are data from the literature.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
1
2 Diffusion in silicon, germanium and their alloys
8 6
Fig. 113. Si:Si. Normalized silicon self-diffusion profiles vs. depth x after diffusion at 1200C for times t as indicated. The profiles were measured by means of the radiotracer 31Si in conjunction with chemical etching. Solid lines represent best fits of the complementary error function to self-diffusion profiles in intrinsic (open circles) and extrinsic (n-type, closed circles) silicon [67Fai1]. C (= 5.1022 cm−3) represents
Si :Si
4 2
Norm. Si conc. C /CO
–1
10
2-167
8 6
0
the silicon atom density.
4
t = 60 min
2
Si :Si
T = 1047 °C
60 min
–2
10
8 6 4
1101 °C
20 min
2 –3
10
0
0.1
0.2
0.3 0.4 Depth x [µm]
0.5
0.6 1146 °C
–11
10
1400
–12
10
–13
Temperature T [°C] 1200 1000
900
800
Si : Si
[66Pea1] [67Fai1]
2 –1
Diff.coeff. D [cm s ]
10
–15
a
[66Gho1]
–14
10 10
Logarithm of Si activity A
1201 °C
[77May1] [79Hir1]
–16
10
–17
10
T = 1247 °C [79Het1]
[79Kal1,80Kal1]
–19
10
0.55 0.60 0.65 0.70 0.75 0.08 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 115. Si:Si. Diffusion coefficient D of silicon in silicon vs. inverse temperature 1/T. The straight lines are diffusivities from the literature as measured by using radioactive or stable silicon tracers. The dashed line shows tracer self-diffusion coefficients in heavily boron-doped silicon [79Het1].
Lando lt -Bö rnst ein New Series III/33A
1302 °C
[83Dem1]
–18
10
b
1385 °C 2
1337 °C
Squared depth x Fig. 114. Si:Si. Activity profiles of the radiotracer 31Si in silicon vs. squared depth x2 as measured by the ion beam sputtering technique after diffusion at different temperatures T as indicated. Solid lines represent best fits based on Gaussian profiles [77May1].
2 Diffusion in silicon, germanium and their alloys
2-168
–12
10
Temperature T [°C] 1000 900 800
1200
–13
10
700
–8
10
[Ref. p. 2-196
Temperature T [°C] 800 600
1300 1200
[73Hun2]
Si :Si
–14
10
–13
500
Si : Si
[64Wil1]
10
–15
10
10
[95Bra1] [85Tan1]
[88Mor1]
[67Yos1]
2 –1
10
–18
[88Cof1]
[89Hau1]
–17
Diff.coeff. D [cm s ]
Diff.coeff. D [cm s ]
2 –1
–16
10
–18
10
[95Bra1]
–19
10
[84Sto1]
–20
10
[88Mor1]
–21
10
[67Bon1]
–23
10
–28
10
–22
10
10
[68see1]
[86Man1]
–23
0.65 0.70
0.75 0.08 0.85 0.90 0.95 1.00 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 116. Si:Si. Diffusion coefficient D of silicon in silicon vs. inverse temperature 1/T. The straight lines are data from the literature representing the selfinterstitial component CieqDI/C 0 of the uncorrelated self-diffusion coefficient DSD deduced from metal diffusion experiments in silicon.
1400
–3
10
1200
Temperature T [°C] 1000
–33
10
1.0 1.2 1.4 –3 –1 Inv. temp. 1/T [10 K ] Fig. 117. Si:Si. Diffusion coefficient D of silicon in silicon vs. inverse temperature 1/T. The straight lines are data from the literature representing the vacancy component CVeqDV/C 0 of the uncorrelated selfdiffusion coefficient DSD deduced from metal diffusion experiments in silicon.
800
0.6
–7
10
Si : Si
–4
10
–8
[88Mor1]
[85Tan1] –7
2 –1
[92Zim1]
–6
10
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
Si : Si
[85Tan1] [95Bra1]
10
10
Temperature T [°C] 1000 800
1200
10
[95Bra1]
–5
0.8
–9
10
–10
10
[95Gha1]
–8
10
[90Boi1]
–9
10
[87Bro1]
0.55
[92Zim1,92Zim2] –12
–10
10
[95Gha1]
–11
10
0.65
0.75 0.85 0.95 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 118. Si:Si. Diffusion coefficient D of silicon selfinterstitials (I) in silicon vs. inverse temperature 1/T deduced from metal diffusion experiments in silicon. The straight lines are data from the literature referred to as DI in the tables.
10
0.65
0.75
0.85 0.95 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 119. Si:Si. Diffusion coefficient D of vacancies (V) in silicon vs. inverse temperature 1/T deduced from metal diffusion experiments in silicon. The straight lines are data from the literature referred to as DV in the tables.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys Temperature T [°C] 1000 800
1200
–5
10
DI [85Gri1]
–7
10
–13
–15
eq
DV [85Wad2]
–10
DI [83Tan2]
10
eq
CV DV /C 0 [92Mat1]
–19
10
–16
10
eq
CV 0 DV 0 /C 0 [92Mat1]
–21
10
eq
eq
–18
0
–23
0.75 0.08 0.85 0.90 0.95 1.00 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 120. Si:Si. Diffusion coefficient D in silicon vs. inverse temperature 1/T representing the silicon selfinterstitial diffusion coefficient DI, the self-interstitial component CIeqDI/C 0 or the vacancy component CVeqDV/C 0 of the uncorrelated self-diffusion coefficient DSD. Neutral charge states of vacancies and selfinterstitials are indicated as V0 and I0, respectively. The straight lines are representative data from the literature which were deduced from dopant diffusion experiments.
10
eq
0
0
CI DI /C [92Wij1] eq
–20
0.65 0.70
0
CV DV /C [83Wad1]
[78Sie1,79Bri1]
10
CI DI /C [91Gil1]
eq
[74San1]
–14
10
–17
DI [94Hab1]
CV DV /C [94Hab1]
–12
10
10
10
–8
10
CI0 DI0 /C 0 [92Mat1]
10
DV [94Hab1]
–6
2 –1
DI [93Gos1]
10
800
10 Diff.coeff. D [cm s ]
–11
Temperature T [°C] 1200 1000
–4
DI [90Wij2]
10
1400
10
DI [85Bro2]
–9
2 –1
10
Si :Si
10
Diff.coeff. D [cm s ]
–2
2-169
0
CI DI /C [94Hab1]
0.55 0.60
0.65 0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 121. Si:Si. Diffusion coefficient D in silicon vs. inverse temperature 1/T representing silicon selfdiffusion [78Sie1, 79Bri1], the silicon self-interstitial diffusion coefficient DI, the vacancy diffusion coefficient DV, the self-interstitial component CIeqDI/C 0 or the vacancy component CVeqDV/C 0 of the uncorrelated self-diffusion coefficient DSD. The straight lines are representative data from the literature which were deduced from the growth or shrinkage of extended defects in silicon.
22
10
Si : Ge
T = 1100 °C, t = 8 h T = 1200 °C, t = 2 h T = 1250 °C, t = 1 h T = 1300 °C, t = 0.5 h
21
–3
Ge conc. C [cm ]
10
20
10
19
10
Fig. 122. Si:Ge. Concentration C of germanium in silicon vs. depth x determined by SIMS after diffusion at different temperatures as indicated. Solid lines represent best fits of the complementary error function [82Ogi1].
18
10
17
10
0
0.25
Lando lt -Bö rnst ein New Series III/33A
0.50
0.75 1.00 Depth x [µm]
1.25
1.50
2 Diffusion in silicon, germanium and their alloys
2-170
Temperature T [°C] 1100 1000
1200
5 4
Si :Ge 1
3
[Ref. p. 2-196
22
10
900
Si :Ge
As-doped
as-deposited (MBE)
21
10
Ratio of diff. coeff. r
–3
Ge conc. C [cm ]
2
T = 1050 °C, t = 80 min
1 3
a
V injection I injection reference
B-doped
2
1 0.8
20
10
19
10
18
10
b
0.6 0.65
0.70
0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 123a, b. Si:Ge. Ratios r of the germainium diffusion coefficient in doped silicon to that in intrinsic silicon vs. inverse temperature 1/T. Arsenic-doped (a) and boron-doped (b) samples have concentrations of about 4.1019 cm−3 and 1019 cm−3, respectively [79Het1].
0
0.1
0.2 0.3 0.4 0.5 Depth x [µm] Fig. 124. Si:Ge. Concentration C of an initial buried germanium epitaxial layer in silicon vs. depth x as determined by SIMS before (dashed curve) and after (solid curves) diffusion for 80 min at 1050 C under boundary conditions which cause either self-interstitial or vacancy injection, or no injection of intrinsic point defects [89Fah1].
1300
–10
10
10
8 6
2 –1
[82Ogi1]
–14
–15
10
19 8
[74Pav2]
[86Bou1]
–16
[79Het1]
10
6
[79Het1]
–17
4
10
2
10
18
10
10
Si :Ge
[73Vay1]
–13
10
Diff.coeff. D [cm s ]
2
10
–12
900
10
–3
Sn conc. C [cm ]
4
b a [75Vay1]
10
Si :Sn
Temperature T [°C] 1100 1000
[57Pet1]
–11
10 20
1200
[84Dor1,83Dor1]
–18 –19
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 Depth x [µm] Fig. 126. Si:Sn. Concentration C of tin in silicon vs. depth x obtained from Rutherford backscattering analysis after diffusion for 3 h at 1200 C. Solid line represents best fit of a complementary error function yielding D = 5.4.10−14 cm2 s–1 [74Aka1].
0.60
0.65
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 125. Si:Ge. Diffusion coefficient D of germanium in silicon vs. inverse temperature 1/T. The solid lines are data from the literature for intrinsic conditions. The dashed lines shows diffusion coefficients of germanium in heavily arsenic-doped [79Het1], boron-doped (a) and phosphorous-doped (b) [75Vay1] silicon.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
1000
–11 8 6 4
10
Si :Sn
2
2
–13 10 8 6 4
–12 10 8 6 4
2 –1
[74Aka1]
2 –14
10
Diff.coeff. D [cm s ]
2 –1
Temperature T [°C] 1200 1100
1300
–12 8 6 4
10
Diff.coeff. D [cm s ]
2 Diffusion in silicon, germanium and their alloys
8 6 4
[68Yeh1]
2
10
0.60
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 127. Si:Sn. Diffusion coefficient D of tin in silicon vs. inverse temperature 1/T. The straight lines are data from the literature.
0.65
16
10
8
Si :N
6 4
10
8 6 4
Sb slope = 1.7
Sb slope = 2.4
8 6 4
Sn slope = 4.1
Sn slope = 4.8
2 –15
10
10
2
2
6 8 10 10 2 4 6 8 10 Norm. el.conc. n/ni Fig. 128. Si:Sn, Sb. Diffusion coefficient D of tin and antimony in silicon vs. electron concentration n normalized to its intrinsic value ni. Data originate from RBS measurements on samples with a high phosphorous background concentration after implantation of Sn or Sb and subsequent diffusion at temperature T as indicated [88And1]. Data for Sb from [86Fai1] are also shown. 2
4
2
–3
N conc. C [cm ]
2
[94Kri1]
–16
10
Sb slope = 3.6
–13
10
2
T = 1050 °C
Sb slope = 4.6
–14
8 6 4
T = 1000 °C
Si :Sn Si :Sb
2
–15
2-171
15
10
10
8 6
1100
Temperature T [°C] 900
700
Si : N
–7
10
4
detection limit
–8
10
14
0
10
20
30 40 50 60 70 80 Depth x [µm] Fig. 129. Si:N. Concentration C of nitrogen in silicon vs. depth x. Profiles result from homogeneously Ndoped samples which were annealed in dry N 2 ambient for 15 min at the temperatures indicated [88Ito1].
Fig. 130. Si:N. Diffusion coefficient D of nitrogen in silicon vs. inverse temperature 1/T. Data from the literature as indicated. The dashed line represents data around 1200 oC for which no temperature range is given by [68Cla1].
Lando lt -Bö rnst ein New Series III/33A
–9
10 2 –1
T = 1000 °C 1100 °C
Diff.coeff. D [cm s ]
2
10
1300
–6
[88Ito1]
–10
10
–11
10
–12
10
[68Cla1]
–13
10
–14
10
[75Den1]
–15
10
–16
10
0.6
0.7
0.8 0.9 –3 –1 Inv. temp. 1/T [10 K ]
1.0
1.1
2 Diffusion in silicon, germanium and their alloys
2-172
1300 1200
–6
10
Temperature T [°C] 1100 1000 900
–7
10
800
19
10
6
N [88Ito1]
–10
2 –1
Diff.coeff. D [cm s ]
10
–11
10
–12
10
–13
10
P [77Fai2]
Bi [56Ful1]
–14
10
4
–3
–9
P surface conc. CO [cm ]
10 10
2
18
10
polished surface T = 1150 °C lapped surface polished surface lapped surface T = 1100 °C
8
Sb [86Fai1]
6
–15
10
17
4⋅10
–16
10
–17
10
As [81Hil1]
0.60
2
2
2 4 6 8 10 2⋅10 10 Annealing time t [h] Fig. 133. Si:P. Boundary concentration C0 of phosphorous in silicon vs. annealing time t. Data show the slow monotonic increase of C0 during P diffusion in vacuum from a Si powder source with P concentration of 1.665·1019 cm−3 at temperatures T as indicated. Surface conditions of the Si wafers are also indicated The solid lines are based on theory [72Gho1].
–18
10
Si :P
8
Si :X
–8
[Ref. p. 2-196
0.65
0.70 0.75 0.80 0.85 0.90 0.95 –3 –1 Inv. temp. 1/T [10 K ] Fig. 131. Si:N, P, As, Sb, Bi. Diffusion coefficient D vs. inverse temperature 1/T of group V elements in silicon. The straight lines are data from the literature.
1
2
4
6
8
20
10
Si :P T = 1000 °C t = 20 h
19
–3
P conc. C [cm ]
10
T = 1100 °C t = 5.5 h
T = 1200 °C t = 45 min
18
10
17
10
16
10
32
P 4PP 15
10
0
1
2
3
4
5 0
1
2 3 4 Depth x [µm]
5 0
1
2
3
4
5
Fig. 132. Si:P. Concentration C of phosphorous in silicon vs. depth x. Data arise from 32P radiotracer and 4-point probe (4PP) measurements as indicated after annealing of 500Ωcm p-type Si test wafers placed between neutron-activated P-doped source wafers inside evacuated closed ampoules. The P concentration of the source wafers is 1020 cm−3. Temperature and time of diffusion are as indicated [71Frä1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
21
–11
10
8 6 4 2
e-profile
–12
10
kink
4 2
tail
19
10
4
–13 8 6
0
0.25
0.75 1.00 1.25 1.50 Depth x [µm] Fig. 134. Si:P. Concentrations C and n of phosphorous and electrons, respectively, in silicon vs. depth x. Data show the total P profile and the corresponding electron profile measured by SIMS and the 4-point resistivity probe (4PP), respectively, after 60 min of diffusion at 1000C from a POCl3 source in oxidizing ambient. The kink marks the inflection beyond which the profile tail region appears. ne indicates the highest concentration for which electron and P concentration are equal [77Fai2, 81fai1].
surface region (D ∝ n2) ne
4 2
18
10
transistion region (D ∝ n–2)
2
SIMS 4PP
2
kink
4
10
8 6
tail region (D = const.)
8 6
2 –1
–3
P,e conc. C,n [cm ]
2
ne
8 6
Si :P
[73Mak1] [77Fai2]
4
20
10
8 6
Si :P
total P
Diff.coeff. D [cm s ]
10
2-173
–14
10
0.50
18
10
2
4
19 6 8 10 2
4
20 6 8 10 2 –3
4
21 6 810
e conc. n [cm ] Fig. 135. Si:P. Diffusion coefficient D of phosphorous in silicon vs. electron concentration n. Data originate from different regions of P diffusion profiles in highly doped Si [77Fai2] and from isoconcentration measurements in heavily-doped Si [73Mak1]. Solid and dashed lines reflect dependences on the electron concentration as indicated. Tail region, kink and ne are indicated in Fig. 134 [77Fai2, 81Fai1]. –11
10
8 6 4
Si : P T = 1100 °C
2 –12 8 6 4
2 –1
Diff.coeff. D [cm s ]
10
Fig. 136. Si:P. Diffusion coefficient D of phosphorous in silicon at a concentration of 1018 cm−3 in the profile tail region vs. electron concentration n0 at the surface. Data for temperatures T as indicated are from the literature given. Solid curves are based on theory [77Fai2, 81Fai 1].
Lando lt -Bö rnst ein New Series III/33A
2 –13
10
8 6 4
T = 900 °C
2 –14 8 6 4
10
2 –15 8 6 4
[74Yos1] [77Fai2] [74Mat1] [70Tit1]
10
2 –16
10
18
10
2
4
19 6 8 10 2
20
4 6 8 10 e surface conc. n0 [cm–3]
2
4
21 6 810
2 Diffusion in silicon, germanium and their alloys
2-174
22
22
10
Si :P
s
20
10
10
Si :P
2
–3
21 10 8 6 4
double kink
solubility [77Mas1]
2
–3
e conc. n [cm ]
–3
P+ conc. CP+ [cm ]
plateau
single kink
6 4
CP + [cm ] 20 3.0 ⋅10 20 1.0 ⋅10 19 5.5 ⋅10 19 1.6 ⋅10 18 2.5 ⋅10
10
19
10 8
T = 900 °C
21
20
10 8 6 4 2
19
10 8 6 4
LA alone LA + FA
2 18
10
18
10
tail 17
10
[Ref. p. 2-196
0
2.5 5.0 7.5 10.0 12.5 –17 –1/2 Time red. depth x/t 1/2 [10 cm s ]
15.0
Fig. 137. Si:P. Concentration CP+ of singly positively charged phosphorous in silicon vs. diffusion-time reduced depth x/t½. Data originate from 4-point probe resistivity measurements after P diffusion at 900 °C from variously doped oxide sources as reported by [74Mat1, 74Yos1, 76Mat1]. The profiles reveal different boundary concentrations as indicated. Solid lines represent a theoretical model based on dissociating (mobile) P-vacancy pairs and P2-vacancy complexes [95Yos1, 83Yos1, 79Yos1].
0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 Depth x [µm] Fig. 138. Si:P. Electron concentration n due to phosphorous in silicon vs. depth x. Data arise from laser (damage) annealing (LA) after P implantation of lower or higher dose (open symbols) and subsequent furnace annealing (FA) for 30 min at 850C in nitrogen ambient (closed symbols). The flat profile regions correspond to the solubility limit of electrically active P (dashed line) reflecting equilibrium with precipitated (inactive) P. Precipitation during 850C annealing also leads to enhanced diffusion in the profile tail [82Nob1]. 5
10
8 6 4
Si :P
2
Fig. 139. Si:P. Spreading resistance R induced by phosphorous in silicon vs. depth x. Data originate from P diffusion into (100)-oriented CZ crystals for 10 min at 1200C in dry O2 ambient. The profile under an initially bare Si surface is compared to that under a Si3N4/SiO2-capped surface [78Ant1].
Resistance R [Ω]
4
10
8 6 4 2 3
10
8 6 4
capped surface bare surface
2 2
10
0
0.5
1.0 1.5 Depth x [µm]
2.0
2.5
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
–11
10
2 Diffusion in silicon, germanium and their alloys
Temperature T [°C] 1100 1000
1200
900
1.0
Si :P –12
–6
Diff.coeff. D 1/2 [10 cm s
Diff.coeff. D [cm s ]
–13
2 –1
10
–14
10
dry O2 ambient inert ambient [62Mae1] [78Ant1]
–15
–16
0.65
[78Ant1]
0.70
in N2
0.6 0.4
1000 °C
in N2 1000 °C in N2
2
–12
T = 1000 °C dry O2 (100)
Si(100) :P
Si(100) :P
T = 1100 °C
–13
10
[92Shi1] [86Dun1] [81Lin1] [76Mas1]
2 –1
4
1100 °C
4 6 8 10 Volume ratio (HCl/O2) r [%] Fig. 141. Si:P. Square root of diffusion coefficient D of phosphorous in (100)-oriented silicon vs. volume ratio r of HCl to O2 in the drive-in diffusion ambient. Data result from pn-junction and sheet resistance measurements and show the reducing effect of HCl on oxidation-enhanced P diffusion at various temperatures as indicated. The P diffusivity under inert ambient (N2) conditions is also given [76Nab1].
Diff.coeff. D [cm s ]
eq
6
0
1100 °C
10
10 8
1150 °C
T = 1150 °C
0
0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 140. Si:P. Diffusion coefficient D of phosphorous in (100)-oriented silicon vs. inverse temperature 1/T. Data originate from spreading-resistance measurements following P diffusion in inert or dry O2 ambient as indicated [78Ant1]. The solid line represents the intrinsic P diffusivity from [62Mae1].
Norm.diff.coeff. D /D
0.8
0.2
10
10
Si :P
–1/2
]
10
2-175
2
–14
10
900 °C
–15
10
O2 data N2 data 1 –8 10
–16
–7
10
–6
–5
–4
–3
–2
10 10 10 10 10 –1 Oxidation rate R [µm min ] Fig. 142. Si:P. Average oxidation-induced diffusivity enhancement /Deq of phosphorous in (100)oriented silicon vs. oxidation rate R. Data from the literature as indicated refer to diffusion at 1000C in dry O2 ambient. Deq reflects the P diffusivity under inert ambient conditions [92Shi1].
Lando lt -Bö rnst ein New Series III/33A
10
–3
10
–2
10
–1
10 1 10 Norm.e conc. n/ni Fig. 143. Si:P. Diffusion coefficient D of phosphorous in (100)-oriented silicon vs. normalized election concentration n/ni showing oxidation-enhanced diffusivity depending on background doping. Data arise from SIMS measurements after P diffusion at temperatures T as indicated in heavily B- or As-doped Si crystals under dry O2 or N2 ambient as indicated [93Joh1, 93Joh2].
2 Diffusion in silicon, germanium and their alloys
2-176
19
19
2⋅10
10
Si :P
19
10
8 6
2
18
10
P conc. C [cm ]
–3
–3
P conc. C [cm ]
8 6 4 2
8 6
2 17
T = as implanted T = 950 °C, t = 10 s T = 1050 °C, t = 10 s T = 1150 °C, t = 10 s
4 2
8 6 4
13
0.1
0.2 0.3 0.4 Depth x [µm] Fig. 144. Si:P. Concentration C of phosphorous in silicon vs. depth x showing transient enhanced diffusion. Data result from SIMS profiling after low-dose P implantation (1.0·1014 cm−2, 50 keV) and rapid thermal annealing in Ar ambient for 10 s at temperatures T as indicated [84Oeh1].
16
10
–2
φ = 2⋅10 cm 13 –2 7⋅10 cm 14 –2 1.2⋅10 cm
2
16
0
8 6 4
10
17
10
Si :P
2
18
10
8 6 4
4
10
[Ref. p. 2-196
0
0.2
0.4 0.6 0.8 Depth x [µm] Fig. 145. Si:P. Concentration C of phosphorous in silicon vs. depth x. Data originate from SIMS profiling after P implantation at various doses φ as indicated and subsequent furnace annealing at 800C during 75 min. Solid lines are based on model simulations involving excess Si self-interstitials induced by implantation [91Gil1].
19
10
8 6
Si :P
4 2
intrinsic background 20 –3 B background 1⋅10 cm 20 –3 As background 3⋅10 cm
18
–3
P conc. C [cm ]
10
8 6 4 2
Fig. 146. Si:P. Concentration C of phosphorous in silicon vs. depth x. Data originate from SIMS profiling after P implantation at a dose of 7·1013 cm−2 in Si samples with B or As background doping as indicated and subsequent furnace annealing at 800C during 75 min. Solid lines are based on model simulations involving excess Si self-interstitials induced by implantation [91Gil1].
17
10
8 6 4 2
16
10
0
0.2
0.4 0.6 Depth x [µm]
0.8
1.0
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys 900
20
10
a/c interface
Si :P
18
[90Kim2] [91Orl1] 2
10
10
Norm. I conc. CI /CI eq
Oxide I 17
10
700
600 simulation
10
16
1 0.15 0.20 0.25 0.30 Depth x [µm] Fig. 147. Si:P. Concentration CP of phosphorous in silicon vs. depth x. Data result from SIMS profiling after P implantation in Si with a preamorphized surface layer and subsequent annealing for 60 min at 850C in wet O2 ambient. Uphill diffusion near the amorphous/crystalline (a/c interface is correctly reproduced by simulation (solid line) based on the interstitialcy mechanism. The calculated self-interstitial supersaturation CI/CIeq is given by the dotted line using the right ordinate as reference scale [91Orl1]. 10
Junction depth xj [nm]
–3
P conc. CP [cm ]
CP
Si :P
P alone 15 –2 P + As (2⋅10 cm ) 16 –2 P + As (1⋅10 cm )
800
19
10
2-177
0
0.05
0.10
500
0
1
2 3 4 5 1/2 Anneal time t1/2 [h ] Fig. 148. Si:P. pn-junction depth xj due to phosphorous in p-type silicon vs. square root of annealing time t½. Data result from implantation of P alone or with different doses of As as indicated and subsequent annealing at 900C. Comparison with simulation based on the standard diffusion coefficient (dashed line) reveals transient enhanced P diffusion reduced by the presence of As [93Sol1].
P-doped SiO2 P-diffused layer
xjp l
SiO2
Si epitaxial layer xj
P buried layer
Si substrate a 12
Si : P
Fig. 149a, b. Si:P (a) Schematic diagram of sample structure with junctions depths xj and xjp due to phosphorous diffusion and with thickness l of the epitaxial silicon layer (b). Diffusion coefficient D of phosphorous in buried layers at 1100C vs. epitaxial layer thickness l. Data originate from pn-junction staining after annealing in N2 ambient using dopedoxide sources deposited at low temperature in mixed PH3/SiH4 vapour of different molar ratio as indicated [77Mat1].
6 4
PH3/SiH4 ,0.36 PH3/SiH4 ,0.07 PH3/SiH4 ,0.005
2
b
Lando lt -Bö rnst ein New Series III/33A
8
–13
2 –1
Diff.coeff. D [10 cm s ]
10
0
5
10 15 20 Layer thickness l [µm]
25
30
2 Diffusion in silicon, germanium and their alloys
2-178
60
1.8 µm
Si :P
emitter base
40 30
p
O2 (Cl) a
20 O2 (Cl)
10
electron beam
1.3 µm
O2
0.2 µm
Stacking fault length LSF [µm]
50
N2
[Ref. p. 2-196
E
B
C
collector
n p
substrate E B
C
N2 0
2
4
6
8
10 Time t [h] Fig. 150. Si:P. Stacking-fault length LSF in silicon vs. time t of phosphorous diffusion at 1150C from a doped oxide layer in nitrogen, dry oxygen or chlorinecontaining ambient as indicated. Solid lines refer to oxide layers deposited from vapour ambients with a 0.12 molar ratio of phosphine to silane. Dashed curves represent samples without phosphorous [78Cla1].
b
Fig. 151a, b. Si:P. (a) Schematic of a silicon-based bipolar transistor. The specimens of about 2.5 µm thickness investigated in an electron microscope contained phosphorous emitter, boron base and part of the collector. (b) Schematic of climbed screw dislocations formed during P-emitter diffusion at 950C indicating P-induced supersaturation of Si selfinterstitials [79Str1, 79Gös1, 80Str1].
Fig. 152a, b. Si:P. TEM micrographs of (111)-oriented epitaxial silicon after phosphorous drive-in diffusion at 700C in vacuum showing (a) extrinsic stacking faults or (b) misfit dislocations. Observations are interpreted in terms of diffusion-induced self-interstitials [78Tse1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
1300 1200
–10
10
Temperature T [°C] 1100 1000 900
800
Si :P
[62Yan1]
[71Gho3]
2 –1
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
–12
10
–12
10
[59Sah1] [74Gho1]
10
800
Si :P
[72Gho1]
[54Ful2]
–13
Temperature T [°C] 1100 1000 900 [70Cha1]
–11
10
1300 1200
–11
10
2-179
[70Hsu1]
[72Kam1] –13
10
[73Mas1] [93Pel1]
[70Usk1]
–14
10
[71Frä1]
–14
[62Wil1]
10
[73Mak1]
[56Ful1] –15
10
0.60
0.70 0.75 0.80 0.85 0.90 1.00 –3 –1 Inv. temp. 1/T [10 K ] Fig. 153. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T. The straight lines are early data from the literature.
0.65
1300 1200
–11
10
Temperature T [°C] 1100 1000 900
–12
0.55
0.60
0.65 0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 154. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T. The straight lines show data from the literature for intrinsic conditions.
800
Si : P
[70Lyu1] 10
[92Jen2]
–15
10
[73Mak1]
2 –1
Diff.coeff. D [cm s ]
[70Bar1] –13
10
[73Mak1]
Fig. 155. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T. Data from [69Tsa1] show slow (solid line) and fast (dashed line) diffusivities. Data from [70Bar1] represent diffusivities under low (solid line) and high boundary concentrations (dashed line). Data from [73Mak1] give diffusivities for intrinsic (solid line) and isoconcentration (dashed line) conditions. Data from [81Hil1] compare intrinsic (solid line) and enhanced (dashed line) diffusion in dry O2. Data from [70Lyu1] show enhanced diffusion due to structural imperfections.
[81Hil1]
–14
10
[69Tsa1]
–15
10
–16
10
0.60
0.65
Lando lt -Bö rnst ein New Series III/33A
0.70 0.75 0.80 0.85 –3 –1 Inv. temp. 1/T [10 K ]
0.90
1.00
2 Diffusion in silicon, germanium and their alloys
2-180
–10
10
1300 1200
Temperature T [°C] 1100 1000
900
1300
–10
10
[Ref. p. 2-196
Temperature T [°C] 1200 1100
Si :P
e
–11
–12
[62Mac1]
–13
0.65
1300
–9
10
Temperature T [°C] 1200
1100
Si : P
c
b
a [62Mae1,78Ant1] [62Mae1]
10
0.60
0.64
0.68 0.72 0.76 0.80 –3 –1 Inv. temp. 1/T [10 K ] Fig. 157. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T. Solid lines represent data from [62Mae1] for boron-doped silicon with increasing boron concentration from a to d which arise from 4-point probe measurements and further data (e) for various boron- and phosphorous doping which arise from radiotracer measurements. Dashed lines show results from [70Gho1] for different diffusion sources used (f: epitaxial or poly-silicon layer; g: doped silicon powder; h: P2O5+SiO2).
g f e
2 –1
Diff.coeff. D [cm s ]
[62Mae1]
–14
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 156. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T given by [62Mac1]. The diffusivity increases with increasing boundary concentration C0 in silicon boron-doped to 5·1014 cm−3 (solid lines) or 1·1017 cm−3 (dashed lines).
–10
Si :P
f
10
–14
10
–12
10
–13
10
0.60
d
[70Gho1] g
2 –1
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
10
10
10
h
–11
10
1000
[63Moc1]
–11
10
c
–12
10
a b –13
10
0.60
0.62
0.64 0.66 0.68 0.70 –3 –1 Inv. temp. 1/T [10 K ]
0.72
d 0.74
Fig. 158. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T given by [63Moc1]. Solid lines represent data for boron-doped silicon with increasing boron concentration from a to d. Dashed lines represent data for gallium-doped silicon with increasing gallium concentration from g to e.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
–11
10
1400
2 Diffusion in silicon, germanium and their alloys
1200
Temperature T [°C] 1000
[73Mak1]
800
–10
10
–11
10
–15
10
V 0[77Fai2,81fai] V 2– [77Fai2,81fai]
2 –1
Diff.coeff. D [cm s ]
[74Lee1]
2 –1
Diff.coeff. D [cm s ]
Temperature T [°C] 1100 1000
900
Si :P
10
10
[73Mak1] [70Pru1]
–12
10
[88Abd1]
–13
10
[87Cha1] [86Spi1]
–14
10
–19
10
1200
Si :P Pj [89Nan1]
–13
–17
1300
2-181
0.55
V – [77Fai2,81fai] 0.65
0.75 0.85 0.95 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 159. Si:P. Diffusion coefficient D of phosphorus in silicon vs. inverse temperature 1/T. Results deduced by [77Fai2, 81fai1] are based on neutral (V0), singly (V−) and doubly (V2−) negatively charged vacancies as indicated. Data given by [74Lee1] result from Boltzmann-Matano analysis of diffusion profiles with high phosphorus boundary concentration. P i indicates the interstitial diffusivity calculated by [89Nan1]. The intrinsic diffusivity given by [73Mak1] is shown for comparison.
[86Spi1]
–15
10
0.60
0.65
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 160. Si:P. Diffusion coefficient D of phosphorus in silicon polycrystals vs. inverse temperature 1/T. The straight lines are data from the literature. Data given by [86Spi1] represent results for grain sizes of 0.1-3 mm (dashed line) and 5-50 µm (solid line). The intrinsic diffusivity in silicon single crystals given by [73Mak1] is shown for comparison.
–11
10
1400
Temperature T [°C] 1300 1200
8 6
Si :X
4 2
2 –1
Diff.coeff. D [cm s ]
–12
Fig. 161. Si:P, As, Sb, Bi. Intrinsic diffusion coefficient D of phosphorous, arsenic, antimony and bismuth in silicon vs. inverse temperature 1/T. Data result from spreading-resistance measurements after annealing of doped epitaxial Si layers on FZ or CZ substrates in flowing H2 ambient [71Gho2, 71Gho3].
Lando lt -Bö rnst ein New Series III/33A
10
8 6 4 2
Sb
–13
10
8 6
P
As Bi
4 2 –14
10
0.58
0.60
0.62 0.64 0.66 0.68 –3 –1 Inv. temp. 1/T [10 K ]
0.70
0.72
2 Diffusion in silicon, germanium and their alloys
2-182
–21
[Ref. p. 2-196
–21
10
10
Si :As
Si :As 75 As in intrinsic Si 75
–20
10
As in As-doped extrinsic Si total As in extrinsic Si
–3
As conc. C [cm ]
–3
As conc. C [cm ]
–20
10
–19
10
–19
10
–18
10
neutron activation analysis resistivity measurements empirical calculation
–18
10
0
xJ
–17
0.1
0.2 0.3 0.4 Depth x [µm] Fig. 162. Si:As. Concentration C of arsenic in silicon vs. depth x. Data result from neutron activation analysis (total As concentration) and resistivity measurements (electrically active As concentration) as indicated after 60 min of As diffusion at 1000C from a doped oxide source. The solid line is based on an empirical equation [73Fai1].
10
0.4 0.6 0.6 0.8 Depth x [µm] Fig. 163. Si:As. Concentration C of arsenic in silicon vs. depth x. Profiles originate from 4 h of 75As radiotracer diffusion at 948C into virtually intrinsic and extrinsically As-doped silicon samples as indicated. The total As distribution as measured by NAA after the latter (isoconcentration) experiment is also given [69Mas1].
10
8
Si :As
6
Si :As
2
2 –1
2
10
8
T = 850 °C 900 °C 950 °C [79Mur1] 1000 °C 1050 °C [79Mur1] [71Ken1]
6 4
2
1
4
6
8
8 6 4 2
–13
10
8 6 4
[93Nyl1] [81fai1]
2 –14
2
4 6 8 10 2 10 Norm.As conc. C /ni Fig. 164. Si:As. Normalized diffusion coefficient D/Di of arsenic in silicon vs. normalized total As concentration C/ni, respectively. Data arise from As diffusion in nitrogen ambient at various temperatures T as indicated [79Mur1, 78Mur1]. Solid and dashed lines represent empirical expressions given by [79Mur1] and [71Ken1], respectively. 2
–12
10
Diff.coeff. D [cm s ]
i
8 6 4
4
Norm.diff.coeff. D /D
0.2
–11
2
10
1
0
10
19
10
20
21
10 4 2 6 8 10 –3 Donor conc. CD [cm ] Fig. 165. Si:As. Diffusion coefficient D of arsenic in silicon at 1050C vs. donor background concentration CD. Data are from the literature as indicated. The dashed line represents the vacancy-percolation model [93Nyl1]. 2
4
6
8
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
Temperature T [°C] 1100 1000
1200
–12
10
900
–12
10
Si(100) :As
8 6
–13
[83Ish1]
2
[82Ish1]
2 –1
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
–13
10
–14
10
8 6
A B C D
4 2 –14
10
–15
10
8 6
E F G
4
dry O2 ambient [78Ant1] inert ambient [71Chi1] [78Ant1]
–16
2
0.65
10
4
2000 1000
3
10
10
18 8 10
19
20
2 4 6 8 10 10 –3 As conc. C [cm ] Fig. 167. Si:As. Diffusion coefficient D of arsenic in silicon vs. As concentration C showing retardation in oxidizing ambient for temperatures above 950C. A: 1100C, 1 h, dry N2 and 1100C, 6.5 h, dry N2. B: 1100C, 6.5 h, dry O2. C: 1100C, 1 h, dry O2. D: 1050C, 6 h, dry N2 and 1050C, 29.5 h, dry N2. E: 1050C, 29.5 h, dry O2. . F: 1050C, 6 h, dry O2. G: 1000C, 5.5 h, dry N2 and 1000C, 30 h, dry N2 H: 1000C, 30 h, dry O2. I: 1000C, 5.5 h, dry O2 J: 950C, 30 h, dry N2, 950C, 54 h, dry N2, 950C, 30 h, dry O2, and 950C, 54 h, dry O2 [83Ish1]. Data from the literature as indicated including intrinsic diffusivities from [82Ish1]. 6
2
4
6
8
4 10
1
5
400 900
10
40 100
10
Si:As
−1
2
3
0.8
10
17
4⋅10
7
1
4 3 2 1
Norm.vacancy conc. CV/CV
10
100
4
30
10 30
100
eq
10
4
400 2
10
10
0.70
4⋅10
I
J
–16
0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 166. Si:As. Diffusion coefficient D of arsenic in (100)-oriented silicon vs. inverse temperature 1/T. Data originate from spreading-resistance measurements following As diffusion in inert or dry O2 ambient as indicated [78Ant1]. The solid line represents the intrinsic As diffusivity from [71Chi1].
10
H
–15
–17
10
Si :As
[75Fai1] [79Mur1]
4
10
10
2-183
−2
−3
−4
10
−4
10
Lando lt -Bö rnst ein New Series III/33A
−3
−2
−1
10 10 10 10 1 eq Norm.interstitial conc. CI/CI
10
10
4
Fig. 168. Si:As. Contours of the diffusivity enhancement D/Deq of arsenic in silicon vs. normalized vacancy concentration CV/CVeq and normalized selfinterstitial concentration CI/CIeq. Calculation of the contours involves four different diffusion mechanisms [92Van1]. Data result from As diffusion at 1100 C under nitridizing ambient (D, CV, CI) compared to that under inert ambient conditions (Deq, CVeq, CIeq) [85Fah1].
2 Diffusion in silicon, germanium and their alloys
2-184
21
10
175
Si : As Junction depth step ∆xj [nm]
–3
As conc. C [cm ]
10
as implanted
19
t = 100 s
30 s t = 10 s
18
10
1000 B P Sb As
150
20
10
1100
125
[Ref. p. 2-196
Temperature T [°C] 900 800
700
Si :X
100 75 50 25
17
10
0 0.70
16
10
0
500
1000
1500 2000 2500 3000 Depth x [Å] Fig. 169. Si:As. Concentration C of arsenic in silicon vs. depth x. Data result from As implantation (dose 2·1015 cm−3, energy 50keV) and subsequent rapid thermal annealing in N2 ambient at 1100C for various times t as indicated. Calculation of the solid lines includes concentration-enhanced diffusion (Fermi-level and electric-field effects) but no transient enhanced diffusion due to implantation-induced defects [85Sed1].
0.75
0.80 0.85 0.90 0.95 1.00 1.05 –3 –1 Inv. temp. 1/T [10 K ] Fig. 170. Si:As, B, P, Sb. Saturation value of the pnjunction depth step ∆xj due to diffusion of arsenic, boron, phosphorous or antimony in silicon vs. inverse temperature 1/T. Data arise from dopant pre-deposition followed by Si implantation above the amorphization threshold and subsequent furnace (700-900C) or electron-beam (1100C) annealing in N2 ambient. The annealing times have been chosen so that transient enhanced diffusion is completed: 24 h for 700C, 4 h for 725C, 13 h for 750C, 0.8 h for 800C, 10 min for 900C, and 20 s for 1100C [87Ang1].
22
10
Si :As 21
10
20
–3
As conc. C [cm ]
10
19
10
t = 30 min as implanted
18
10
t = 60 min t = 240 min
17
10
16
10
0
0.03
0.06
0.09 0.12 Depth x [µm]
0.15
Fig. 171. Si:As. Concentration C of arsenic in silicon vs. depth x showing transient enhanced diffusion. Data arise from SIMS profiling after As implantation (dose 2·1015 cm−2, energy 40 keV) and subsequent furnace annealing in N2 ambient at 750C for various times t as indicated [89Kim1].
0.18
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
–12
10
2 Diffusion in silicon, germanium and their alloys Temperature T [°C] 950 900
1000
850
Si :As
22
10
p = 0 kbar 20 kbar 30 kbar
21
–14
standard interface –3
As conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
10
10
Mono-Si
Poly-Si
10
–13
p = 30 kbar (3.6 ± 0.4 eV)
2-185
20
10
19
10
oxidized interface
p = 0 kbar (4.5 ± 0.4 eV) –15
10
18
10
p = 20 kbar (4.0 ± 0.6 eV)
17
–16
10
0.77
0.79
0.81 0.83 0.85 0.87 0.89 0.91 –3 –1 Inv. temp. 1/T [10 K ] Fig. 172. Si:As. Diffusion coefficient D of arsenic in silicon vs. inverse temperature 1/T for different hydrostatic pressures p as indicated. Associated activation energies Q are given in parentheses [85Nyg1].
1300
–11
10
8 6
Temperature T [°C] 1200
0 0.1 0.2 -0.1 Distance from interface x [µm] Fig. 173. Si:As. Concentration C of arsenic in polyand monocrystalline silicon vs. distance x from the poly/mono interface. Data arise from SIMS profiling after As implantation in the poly-Si layer and subsequent annealing at 900C. Differences are observed between interfaces originating from standard cleaning treatments before poly-Si deposition and those covered with about 2.5nm of thermally grown oxide [85Sch2].
1100
–14
2 –1
[71Gho2]
4
[64Raj1]
2 –13
10
8 6
[56Ful1]
4
[68Hsu1]
0.60
[75Cam1]
–15
10
–16
10
[81Hil1]
–17
10
–18
10
[75Ohk1]
–19
[70Cha1]
–14
10
0.62
0.64 0.66 0.68 0.70 0.72 0.74 –3 –1 Inv. temp. 1/T [10 K ] Fig. 174. Si:As. Diffusion coefficient D of arsenic in silicon vs. inverse temperature 1/T. Data from the literature as indicated. [69Mas1] represents intrinsic diffusivity. Lando lt -Bö rnst ein New Series III/33A
Si :As
[75Fai1]
10
2
800
[71Ken1]
10 Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
8 6
Temperature T [°C] 1000 900
[71Chi1,78Ant1]
–13
10
[62Arm1]
–12
1200 1100
10
2
10
-0.2
–12
Si :As
[69Mas1]
4
10
–20
10
0.65
0.70
0.75 0.80 0.85 0.90 0.95 1.00 –3 –1 Inv. temp. 1/T [10 K ] Fig. 175. Si:As. Diffusion coefficient D of arsenic in silicon vs. inverse temperature 1/T. The straight lines are data from the literature for the intrinsic diffusivity.
2 Diffusion in silicon, germanium and their alloys
2-186
1300
–11
10
1200 [69Mas1]
–12
10
Temperature T [°C] 1100 1000
900
18
2⋅10
Si :As
4
–3
Sb conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
8 6
–13
10
–14
10
–15
10
2 17
10
8 6
[81Hil1]
sheet resistance radiotracer
4
–16
10
2 16
10
–17
10
–18
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 176. Si:As. Diffusion coefficient D of arsenic in silicon vs. inverse temperature 1/T. The solid lines are data from literature for the intrinsic diffusivity [69Mas1, 81Hil1]. The dashed lines represent enhanced diffusion by oxidation [81Hil1] and under extrinsic conditions [69Mas1]. Data given by [93Nyl1, 90Gai1, 89Nyl1] shows the diffusivity above the vacancy-percolation limit.
0.60
0.65
0.50 0.75 1.00 1.25 1.50 Squared depth x 2 [µm2] Fig. 177. Si:Sb. Concentration C of antimony in silicon vs. square of penetration depth x2. Data originate from 4-point probe sheet-resistance and 125Sb radiotracer measurements as indicated after diffusion at 1000C [82Nei1].
0
0.25
Si :Sb
19
10
–11
10
Sb implant As background,C0 =1.1⋅1020 cm–3 B background,C0 = 8 ⋅1019 cm–3
18
+
17
10
2 –1
Diff.coeff. D [cm s ]
–3
Si :Sb
n doping
–12
10
anneal: T = 1200 °C, t = 20 min
10 Sb conc. C [cm ]
Si :Sb
18
10
[93Nyl1,90Gai1,89Nyl1]
10
[Ref. p. 2-196
Background doping 20 3 1.8 ⋅10 As/cm 20 3 1.1 ⋅10 As/cm 19 3 9 ⋅10 As/cm 19 3 7.2 ⋅10 As/cm 19 3 4.3 ⋅10 As/cm 20 3 1 ⋅10 B/cm 20 3 1.2 ⋅10 B/cm 20 3 1.8 ⋅10 B/cm
–13
10
–14
10
16
10
–15
10
+
p doping 15
10
–16
0
0.4
0.8 1.2 1.6 Depth x [µm] Fig. 178. Si:Sb. Concentration C of antimony in silicon vs depth x. Data originate from SIMS profiling after implantation (1014 cm–2, 150 keV) and subsequent diffusion of Sb in samples with high arsenic or boron background concentration as indicated. Diffusion temperature T and time t are also indicated [86Fai1].
10
0.66
0.68
0.70 0.72 0.74 0.76 0.78 0.80 –3 –1 Inv. temp. 1/T [10 K ] Fig. 179. Si:Sb. Diffusion coefficient D of antimony in silicon vs. inverse temperature 1/T. Data originate from SIMS profiling after implantation and diffusion of Sb in samples with high arsenic or boron background concentration as indicated. The dashed line represents the Sb diffusivity Di under intrinsic conditions [86Fai1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
2
–11
10
10
[86Fai1] (B doping) [66Mil1] [86Fai1] (As doping) [66Mil1] (P doping) [81Son1][70Usk1] (Sb doping)
10
Si :Sb
(1000 °C) –12
10 2 –1
i
charged vacancy model
Diff.coeff. D [cm s ]
Si :Sb
Norm. diff. coeff. D/D
2-187
–13
10
(1200 °C)
–14
10
1 T = 1000 °C
–2
–1
10
2
1 10 10 Norm.e conc. n/ni Fig. 180. Si:Sb. Diffusion coefficient D of antimony in silicon normalized to its intrinsic value Di vs. electron concentration normalized to its intrinsic value ni. Data are from the literature as indicated. The solid and dashed lines represent best fits to the data based on Sb diffusion via neutral and doubly negatively charged vacancies with (n/ni < 1) or without (n/ni > 1) additional influence of ion pairing between antimony (Sb+) and boron (B−) [86Fai1].
2
4
6
20
8
21
, , ,
Si :X
6 5
P
exp. theory
T = 1000 °C, fI = 0.38
4 B
3
T = 1000 °C, fI = 0.30
2
T = 1090 °C, fI = 0.35 As
1
Sb 0
Lando lt -Bö rnst ein New Series III/33A
10
7
Norm. diff. coeff. D /D
Fig. 182. Si:As, B, P, Sb. Normalized time-averaged diffusion coefficient /Deq of arsenic, boron, phosphorous and antimony in silicon vs. diffusion time t in oxidizing ambient. Diffusion temperatures T are as indicated. Normalization involves diffusion coefficients Deq holding under inert ambient conditions. The solid lines represent the dual vacancy-interstitialcy mechanism with fractional interstitialcy component fI as indicated [82Ant2].
19
10 2 4 6 810 –3 Donor conc. CD [cm ] Fig. 181. Si:Sb. Diffusion coefficient D of antimony in silicon at 1050C vs. donor background concentration. Data are from the literature as indicated. The dashed line represents the vacany-percolation model [93Nyl1].
eq
10
[93Nyl1] [86Fai1]
–15
10
1100 °C
–1
10
ion pairing calculations
10
20
T = 1100 °C, fI = 0.015
30 40 Time t [min]
50
60
70
2 Diffusion in silicon, germanium and their alloys
2-188
BN-area
BO-area
1.8
Si3N4 diffused layer
Si :Sb Si :P
L
Si :X
substrate
1.2
SiO2 Si3N4
∆D
xjBO
xjBN
a
P Sb P P P
[81Miz1] [78Ant1] [81Lin1] [79Fra1]
fI = 0.7
0.6
fI = 0.5
0
b
1.4
t = 500 min 1000 min 2000 min 4000 min
1.2 1.0 0.8 0.6
T = 1100 °C dry O2
– 0.6 –1.2
fI = 0.02
0.6 1.2 1.8 2.4 δS Fig. 184. Si:Sb, P. Incremental average diffusivity enhancement ∆D of antimony and phosphorous in silicon vs. incremental average self-interstitial surpersaturation δs [83Tan3]. Curves represent theoretical calculations for different fractional selfinterstitial components fI as indicated. Data are from the literature on oxidation-retarded diffusion of Sb and oxidation-enhanced diffusion of P in silicon as indicated.
– 0.6
0
B P Sb
0 100 200 300 400 500 c Distance L [µm] Fig. 183a, b, c. Si:B, P, Sb. (a) Schematic cross section of a boron-, phosphorous- or antimony-diffused silicon sample before selective backside oxidation (BSO). (b) Idem, after selective BSO. (c) Ratio xjBO/xjBN of the pn-junction depth under oxidized backside areas to that under non-oxidized backside areas vs. distance L between front surface and bare back surface before oxidation. Data result from annealing at 1100C in dry O2. Solid lines serve to guide the eye [83Miz2]. Fig. 185. Si:Sb, As. Diffusion coefficient D of antimony and arsenic in silicon vs. inverse temperature 1/T. Data marked by Di refer to diffusion under intrinsic conditions. Also shown is the retarded diffusivity Dr of Sb and the enhanced diffusivity De of As in Sb- and Asdoped buried layers, respectively, in the presence of high-concentration phosphorous diffusion near the surface [87Tsa1]. Activation energies connected with the slope of dashed (Sb) and solid (As) lines are indicated in parentheses.
–12
10
Temperature T [°C] 1200 1100 1000
1300
Si :Sb Si :As 2 –1
Si :X
Diff.coeff. D [cm s ]
1.6
Depth ratio xjBO /xjBN
[Ref. p. 2-196
–13
10
De (As) (1.5 eV) De (Sb) (6.6 eV)
–14
10
i
D (Sb) (4.08 eV)
As Sb
i
D (As) (4.05 eV)
–15
10
0.60
0.65
0.70 0.75 –3 –1 Inv. temp. 1/T [10 K ]
0.80
0.85
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
19
19
10
10
Si :Sb
as-deposited
Pd2Si formation T = 200 °C, t = 35 min
18
18
10 –3
–3
Sb conc. C [cm ]
10 Sb conc. C [cm ]
2-189
17
10
17
10
16
16
10
10
15
10
15
10 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 Depth x [µm] Depth x [µm] a b Fig. 186a, b. Si:Sb. Concentration C of antimony in silicon vs. depth x. (a) Buried Sb marker layer in as-grown epitaxial silicon. (b) Asymmetric broadening of the Sb marker layer induced by Pd2Si formation at 200C for 35 min at the surface. The profile is shifted to the left due to the consumption of Si by the silicide formation [91Wit1]. 0
0.2
–101400
–14
10
10
Si :Sb Si :Bi
[68Nak1]
–12
Sb tracer
–17
10
–18
10
121
+
Sb Si (100) 20 11.1 ⋅10 RT 20 8.8 ⋅10 RT 20 5.9 ⋅10 RT 20 9.3 ⋅10 LN2 20 5.0 ⋅10 LN2 20 3.7 ⋅10 LN2 20 2.8 ⋅10 LN2
209 +
Bi Si(100) 20 1.3 ⋅10 LN2
–19
10
0.85
0.95 1.00 1.05 1.10 –3 –1 Inv. temp. 1/T [10 K ] Fig. 187. Si:Sb, Bi. Diffusion coefficient D of antimony and bismuth in (100)-oriented silicon vs. inverse temperature 1/T. Data show transient enhanced diffusivities deduced from RBS and TEM analysis after implantation above the amorphization threshold, epitaxial regrowth, and precipitation annealing at temperature T. Implant conditions are indicated by the Sb or Bi peak concentration (in cm−3) and the implantation temperature (RT = room temperature, LN2 = liquid nitrogen temperature). The lower solid line represents the Sb tracer diffusion coefficient [85Pen1, 86Pen2].
Lando lt -Bö rnst ein New Series III/33A
0.90
2 –1
–16
10
10
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
10
–13
10
1000
Si :Sb
[59Roh1] [56Ful1]
–11
10
–15
Temperature T [°C] 1200 1100
1300
[71Gho2]
[57Pet1]
[70Lyu1]
[60Dri1] [72Usk1]
[62Thu1]
–14
10
–15
10
[72Usk1]
[86Fai1]
–16
10
0.59
0.64
0.69 0.74 0.79 0.84 –3 –1 Inv. temp. 1/T [10 K ] Fig. 188. Si:Sb. Diffusion coefficient D of antimony in silicon vs. inverse temperature 1/T. Data from the literature as indicated. [86Fai1] represents the total intrinsic diffusivity.
2 Diffusion in silicon, germanium and their alloys
2-190
–11
10
1200
1100
Temperature T [°C] 1000 900
800
16
10
–3
Bi conc. C [cm ]
2 –1
4
[85Spi1,86Spi1]
–14
10
c b [79Son1] a
–15
10
0.66
0.74 0.78 0.82 0.86 0.90 0.94 –3 –1 Inv. temp. 1/T [10 K ] Fig. 189. Si:Sb. Diffusion coefficient D of antimony in silicon vs. inverse temperature 1/T. Solid lines of [79Son1] show diffusivities for C0 increasing from a to c. The dashed lines of [86Fai1] and [93Nyl1] represent the diffusivity via doubly negative vacancies and the diffusivity above the vacancy-percolation limit, respectively. The solid line given by [85Spi1] shows diffusion coefficients in silicon polycrystals.
–9
10
1300
8 6
n-layer before diffusion n-layer after diffusion p-layer before diffusion p-layer after diffusion
14
10
0.70
Temperature T [°C] 1200
15
10
2
[86Fai1]
–17
2
4
–16
10
T = 1286 °C t = 12 h
8 6
[93Nyl1,90Gai1,89Nyl1]
–13
10
Si :Bi
2
[86Fai1]
10
Diff.coeff. D [cm s ]
16
4⋅10
Si :Sb
–12
10
[Ref. p. 2-196
8 6
13
4⋅10
0
2
4
6 8 10 12 Depth x [µm] Fig. 190. Si:Bi. Concentration C of bismuth in silicon vs. depth x. Data were measured by the spreadingresistance technique after diffusion from a Bi-doped (n-type) epitaxial layer into a FZ p-type substrate. Diffusion temperature T and time t as indicated [71Gho2]. 1.2
Si :O 1.0
1100
Si :Bi
Cb = 1 ⋅10 cm
2 –1
Diff.coeff. D [cm s ]
18
–3
10
–3
0.8
O conc. C [10 cm ]
–10
T = 900 °C t = 14.2 h 18
–11
10
0.2
[56Ful1]
–13
10
18
[89Ish1]
–14
0.64
0.68 0.72 0.76 –3 –1 Inv. temp. 1/T [10 K ] Fig. 191. Si:Bi. Diffusion coefficient D of bismut in silicon vs. inverse temperature 1/T. The straight lines are data from the literature.
–3
C0 = 0.06 ⋅10 cm
9 12 15 18 Depth x [µm] Fig. 192. Si:O. Concentration C of oxygen in Czochralshi-grown silicon vs. depth x. Out-diffusion profile measured by SIMS after an annealing treatment in nitrogen ambient characterized by temperature T and time t as indicated. Bulk (Cb) and surface (C0) concentrations are also indicated. The solid curve is the best fit based on the error function [85Lee1]. 0
[71Gho2] 0.60
0.4
[65Pom1]
–12
10
10
0.6
3
6
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys
900
–8
10 –9 10
Temperature T [°C] 800 600 500
400
20
10
Si : O
–10
10
–11
18
–13
10
10
–14
10
–3
O conc. C [cm ]
2 –1
Si :O
19
10
10 –12 10
Diff.coeff. D [cm s ]
2-191
–15
10
–16
10
–17
10 –18 10
[82Mik1] [85Lee1, 86Lee1] [80Gas1] [85Ito1] [83Sta1] [83New2]
–19
10
–20
10
–21
10
17
10
d 16
10
c
b
a
15
10
–22
10
0.5
0.7
0.9 1.1 1.3 –3 –1 Inv. temp. 1/T [10 K ]
1.5
1.7
Fig. 193. Si:O. Diffusion coefficient D of oxygen in silicon vs. inverse temperature 1/T [86Mik1]. Data result from investigations by means of SIMS [82Mik1, 85Lee1, 86Lee1], CPAA [80Gas1, 85Ito1] and infrared dichroism [83Sta1, 83New2]. All diffusion data obtained under regular conditions (see table 2.2.1.16) are close to the solid line.
–8
10 –9 10
800
Temperature T [°C] 600 500 400
0
2
4
6 8 10 12 14 Depth x [µm] Fig. 194. Si:O. Concentration C of oxygen-18 in floating-zone silicon vs. depth x as measured by SIMS after (a) implantation and subsequent annealing for 67 h at (b) 525C, (c) 480C and (d) 425C. The samples associated with (c) and (d) had a preheat of 900C for 10 s. The sample of (d) had a lower implantation dose and its concentration is multiplied by 17 for display clarity [86Lee2].
300
Si :O
–10
10
–8
2 –1
Deff = 3.3 ⋅10 exp(–0.88 eV/kT ) cm s
–11
10 –12 10 –13
10
Diff.coeff. D [cm s ]
2 –1
14
10
–14
10
–15
10
–16
10
[81Gaw1] [83Sta1] [85Ber1] [86Lee2] [86Mik1] [86Tip1] [88Lee1] [91McQ1]
–17
10 –18 10 –19
10
–20
10
–21
10
–22
10
0.7
0.9
Lando lt -Bö rnst ein New Series III/33A
1.1 1.3 1.5 –3 –1 Inv. temp. 1/T [10 K ]
1.7
1.9
Fig. 195.Si:O. Diffusion coefficient D of oxygen in silicon vs. inverse temperature 1/T. Data originate from various authors as indicated. The solid line represents diffusion under regular conditions [86Mik1]. Data points reveal enhanced diffusion which in some cases has been attributed to effects of ambient hydrogen [83Sta1, 83New3] or to O2 molecules operating as fast migrating intermediate vehicles (shaded line [86Lee2]).
2 Diffusion in silicon, germanium and their alloys
2-192
Temperature T [°C] 1300 1200 1100 1000 900
–6
10
800
17
10
Si :S
Si :X
–7
10
S [93Rol1]
–8
16
2 –1
Diff.coeff. D [cm s ]
I-limited
–3
–9
10
–10
10
15
10
–11
10
14
–13
10
13
10
Te [93Rol2]
O [86Mik1]
–14
10
–15
10
0.60
0.65 0.70 0.75 0.80
0.85 0.90 0.95 1.00 –3 –1
Inv. temp. 1/T [10 K ] Fig. 196. Si:O, S, Se, Te. Diffusion coefficient D of oxygen, sulfur, selenium, and tellurium in silicon vs. inverse temperature 1/T. Solid lines represent literature data as indicated, the dashed line illustrates the result of [86Mik1].
–6 10 8 6 4
1400
Temperature T [°C] 1300 1200 1100
150 200 250 300 Depth x [µm] Fig. 197. Si:S. Concentration of substitutional sulfur Cs vs. depth x. Data result from spreading-resistance profiling after a diffusion treatment characterized by temperature T and time t as indicated. The concave erfc-tail (solid line) together with the convex nearsurface part suggest diffusion via the kick-out mechanism limited by interstitial sulfur (Si) and Si selfinterstitials (I), respectively [89Sto1].
1000
0
10 –3
Se conc. C [cm ]
2 –1
Si :Se
–11
2 –1
D = 1.7 ⋅10 cm s
2
[93Rol1]
–8 8 6 4
[89Sto1]
[59Car1]
p+
8 6 4 2
15
10 8 6 4
2 –9
2
8 6 4
14
[74Gru1]
2 –10
0.55
100
16
2
10
8 6 4
2
10
50
17
10
Si :S
–7 10 8 6 4
10
Si-limited
10
Se [90Grü1]
–12
10
Diff.coeff. D [cm s ]
T = 986 °C, t = 3.05 h
10
S conc. Cs [cm ]
10
[Ref. p. 2-196
0.60
0.65 0.70 0.75 0.80 –3 –1 Inv. temp. 1/T [10 K ] Fig. 198. Si:S. Diffusion coefficient D of sulfur in silicon vs. inverse temperature 1/T. Data result from experiments on dislocation-free [93Rol1], moderately dislocated [74Gru1] and highly dislocated [89Sto1] specimens, or from silicon with a non-specified dislocation density [59Car1].
10
0
2
4
6 8 10 12 Depth x [µm] Fig. 199. Si:Se. Penetration profile measured by SIMS on a silicon p+n-diode Se-diffused for 1 h at 960C. Concentration of selenium C vs. depth x. The arrow indicates the beginning of the n-region. Concentrtion calibration is uncertain within one order of magnitude [80Gri1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
2 Diffusion in silicon, germanium and their alloys Temperature T [°C] 1100 1000 900
1200
–8
10
16
10
Si :Se
[76Zhd1]
–9
800
2-193
Si :Te
15
10
10
[79Kim1]
[88Stü1]
–3
–10
10
Te conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
14
10
[90Grü1]
–11
10
[80Gri1]
13
10
T = 1207 °C, t = 4.98 d
12
10
11
10
T = 1092 °C, t = 10.0 d
–12
10
10
10
[78Vyd1]
–13
10
0.64
0.76 0.82 0.88 0.94 –3 –1 Inv. temp. 1/T [10 K ] Fig. 200. Si:Se. Diffusion coefficient D of selenium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
–9
10
0.70
1300
1200
Temperature T [°C] 1100 1000
9
10
4 6 8 2 –5 2 Squared depth x [10 cm ] Fig. 201. Si:Te. Penetration profiles of radioactive 121 Te in silicon measured after implantation of its rapidly decaying grandmother nuclide 121Xe and subsequent heat treatment as indicated by temperature T and time t. Concentration of tellerium C vs. squared depth x2. The solid lines represent best fits based on an instantaneous diffusion source and a reflecting boundary at x = 0 [93Rol2].
900
0
2
18
10
8
Si :Te
Si :F
6
–10
10
4
as implanted –11
2
T = 350 °C
–3
F conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
10
–12
10
[88Stü1]
8 6
–13
10
550
4
[82Jan1]
–14
10
–15
10
500
17
10
0.60
[93Rol2]
650 2
0.65
0.70 0.75 0.80 0.85 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 202. Si:Te. Diffusion coefficient D of tellurium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
Lando lt -Bö rnst ein New Series III/33A
16
10
700
850 °C 0
0.05
0.10 0.15 0.20 0.25 Depth x [µm] Fig. 203. Si:F. Concentration C of fluor in silicon vs. depth x. Data result from SIMS profiling after implantation of 1.1013 F+ atoms/cm2 at 30 keV and subsequent annealing for 30 min at different temperatures T as indicated [92Jen1].
2 Diffusion in silicon, germanium and their alloys
2-194
175
18
10
8 6
17
125 Number of counts NI
10 8 6
–3
Cl conc. C [cm ]
150
non-annealed T = 1100 °C, t = 2 h T = 1100 °C, t = 4 h T = 1100 °C, t = 8 h
2
35
Si :I
Si :Cl
4
4 2 16
10
8 6
2
100 34 kV 75
34 kV
25
15
10
8 6 14
450 600 750 900 Depth x [nm] Fig. 204. Si:Cl. Concentration C of chlorine in silicon vs. depth x. Data were obtained by accelerator mass spectroscopy after neutron activation of Si single crystals that had been implanted with 1013 35Cl atoms/cm2 at 200 keV and subsequently annealed at 1100C for various times t as indicated [95Dat1].
0
1
150
300
0 150
46 kV 155
160 165 170 175 180 Channel number NCh Fig. 205. Si:I. Number of counts NI related to iodine in silicon vs. detector channel number NCh. Data result from RBS analysis of a FZ sample that was implanted with I atoms at RT (2.1014 cm–2, 50 keV) and annealed in subsequent steps of 15 min at different temperatures TA as indicated. In this sample recrystallization occurred above 600C [70Mey1].
1 2
Si :He
3
–1
10
Fract. release (C0 – C )/C0
TA = 600 °C, t = 15 min TA = 760 °C, t = 15 min TA = 1010 °C, t = 15 min
50
4
4⋅10
[Ref. p. 2-196
4
Fig. 206. Si:He. Fractional release (C0-C)/C0 of helium from silicon vs. time t in double logarithmic representation. Data result from isothermal desorption experiments on homogeneously implanted 280 µmthick Si wafers at temperatures T and concentrations x (in atomic fractions) as indicated below. The dashed lines reproduce a t dependence [94Jun1]. − − 1: T = 897 °C, x = 1.8·10 7, 2: T = 602 °C, x = 39·10 6, −7 3: T = 500 °C, x = 2.1·10 , 4: T = 300 °C, x = 1.3·10−7 5: T = 351 °C, x = 5.8·10−5.
–2
10
5
–3
10
–4
10
10
2
10
3
Time t [s]
10
4
10
Landolt -Börnst ein New Series III/33A
Ref. p. 2-196]
–5
10
1000
2 Diffusion in silicon, germanium and their alloys
800
Temperature T [°C] 600
8 6
500
–5
10
2 –1
Diff.coeff. D [cm s ]
2 –1
Si :He
10
–6
Diff.coeff. D [cm s ]
[56Wie1]
8 6 4 2
[64Lut1]
–7
10
–8
10
[94Jun1]
–7
10
8 6
–9
10
4
[94Jun1]
2
–10
10
–8
10
0.95 1.05 1.15 1.25 1.35 1.45 –3 –1 Inv. temp. 1/T [10 K ] Fig. 207. Si:He. Diffusion coefficient D of helium in silicon vs. inverse temperature 1/T. Data result from thermal desorption measurements on dislocated B-doped samples in which He was introduced either by neutron activation of B (open symbols) or by plasma exposure (closed circles) [64Lut1].
0.75
–5
10
0.85
900
700
Temperature T [°C] 500
–7
10
He [94Jun1]
–9
2 –1
1.0 1.2 1.4 1.6 1.8 –3 –1 Inv. temp. 1/T [10 K ] Fig. 208. Si:He. Diffusion coefficient D of helium in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
300
Si :He Si :Xe
–11
10
–13
10
–15
10
0.6
0.8
1.0 2
1011 Xe ions/cm
0.8
Fract. release (C0 – C )/C0
10 Diff.coeff. D [cm s ]
300
–6
2
10
Temperature T [°C] 700 500
1300 1000
Si :He
4
2-195
Ge :Xe
0.6
GaAs :Xe Si :Xe
0.4 0.2
–17
10
Xe [70Mat1]
–19
10
–21
10
0.8
1.0
1.2 1.4 1.6 1.8 2.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 209. Si:He, Xe. Diffusion coefficient D of helium and xenon in silicon vs. inverse temperature 1/T. Data from the literature as indicated.
Lando lt -Bö rnst ein New Series III/33A
0 200
400
600 800 1000 Temperature T [°C] Fig. 210. Si, Ge, GaAs:Xe. Fractional release (C0-C)/C0 of xenon from silicon, germanium and GaAs vs. temperature T. Data result from 5 min isochronal desorption experiments following bombardment with 40 keV Xe ions to a dose of 1.1011 cm−2 [70Mat].
2 Diffusion in silicon, germanium and their alloys
2-196
2.2.3 References for 2.1 and 2.2 2.2.3.1 Textbooks 63bol1 74tuc1
Boltaks, B.I.: Diffusion in Semiconductors. London: Infosearch Ltd., 1963. Tuck, B.: Introduction to Diffusion in Semiconductors. Stevenage: Peter Peregrinus, 1974.
2.2.3.2 Data collections 70sha1 84lan1
86wöh1 89sch1
90sha1
Sharma, B.L.: Diffusion in Semiconductors, Clausthal-Zellerfeld: Trans. Tech. Publications, 1970, p. 110. Langheinrich, W., Haberle, K.: Technology of Si, Ge, and SiC, in: Landolt-Börnstein, New Series, Vol. III/17c, Schulz, M., Weiss, H. (eds.), Berlin, Heidelberg, New York: Springer Verlag, 1984, p. 118. Wöhlbier, F.H. (ed.): Diffusion and Defect Data - Solid State Data, Vol. 47 (Focus: Diffusion in Silicon), Switzerland: Trans. Tech. Publications, 1986. Schulz, M: Diffusion of Impurities in Silicon: Impurities and Defects in Group IV Elements and III-V Compounds, in: Landolt-Börnstein, New Series, Vol. III/22b, Schulz, M. (ed.), Berlin: Springer Verlag, 1989, p. 230. Sharma, B.L.:Diffusion in Silicon and Germanium. Defect Diffus. Forum 70 (1990) 1.
2.2.3.3 Review papers 59rei1 68hu1 68see1 69ken1 70gla1 73hu1 73sha1 74har1
74hu1 75sha1 77fai1 77wil1
Reiss, H., Fuller, C.S.: Diffusion Processes in Germanium and Silicon, in: Semiconductors, Chap. 6, Hannay, N.B. (ed.), New York: Reinhold, 1959, p. 222. Hu, S.M., Schmidt, S.: Interactions in Sequential Diffusion Processes in Semiconductors. J. Appl. Phys. 39 (1968) 4272. Seeger, A., Chik, K.P.: Diffusion Mechanisms and Point Defects in Silicon and Germanium. Phys. Status Solidi 29 (1968) 455. Kendall, D.L., DeVries, D.B.: Diffusion in Silicon: Semiconductor Silicon, Haberecht, R.R., Kern, E.L. (eds.), New York: The Electrochem. Soc., 1969, p.358. Glasow, W.M., Sanshow, W.S.: Die Germanium- und Silizium-Zweistofflegierungen. Berlin: VEB Deutscher Verlag der Wissenschaften, 1970. Hu, S.M.: Diffusion in Silicon and Germanium, in: Atomic Diffusion in Semiconductors, Shaw, D. (ed.), London, New York: Plenum Press, 1973, p. 217. Shaw, D.: Atomic Diffusion in Semiconductors, Shaw, D. (ed.), London, New York: Plenum Press, 1973. Hartmann, U.: Die Diffusion von Phosphor in Silizium - Diffusionsprofile und Diffusionskoeffizienten. Wiss. Z. TH Ilmenau 20 [2] (1974) 75. Hu, S.M.: Formation of Stacking Faults and Enhanced Diffusion in the Oxidation of Silicon. J. Appl. Phys. 45 (1974) 1567. Shaw, D.: Self- and Impurity Diffusion in Ge and Si. Phys. Status Solidi (b) 72 (1975) 11. Fair, R.B.: Recent Advances in Implantation and Diffusion Modeling: Semiconductor Silicon. The Electrochem. Soc. (1977) 968. Willoughby, A.F.W.: Interactions between Sequential Dopant Diffusions in Silicon - a Review. J. Phys. D 10 (1977) 455.
Landolt -Börnst ein New Series III/33A
2 Diffusion in silicon, germanium and their alloys 78wil1 79hil1 79see1
80fai1 80hil1 81fai1 81fra1
81wil1 83ant1
83hu1 83tan1
83web2 84fai1 84fra1
85bou1 85fai1 85pan1 85tan1
86gös1
86wol1 87fra1
2-197
Willoughby, A.F.W.: Atomic Diffusion in Semiconductors. Rep. Prog. Phys. 41 (1978) 1665. Hill, A.C., Bradley, R., Allen, W.G.: Redistribution of dopant impurities in oxidizing ambients. Solid State Electron. 22 (1979) 633. Seeger, A., Frank, W., Gösele, U.: Diffusion in Elemental Semiconductors: New Developments. Inst. Phys. Conf. Ser. 46 (1979 148. Fair, R.B.: On the Role of Self-interstitials in Impurity Diffusion in Silicon. J. Appl. Phys. 51 (1980) 5828. Hill, C.: Diffusion Behaviour Modified by Processing Conditions, in: Device Impact of New Microfabrication Technologies, Leuven: Summer Course, 1980, p. 988. Fair, R.B.: Concentration Profiles of Diffused Dopants in Silicon: Impurity Doping Processes in Silicon, Wang, F. (ed.), Amsterdam: North Holland, 1981, p. 315. Frank, W.: Self-interstitials and Vacancies in Elemental Semiconductors Between Absolute Zero and the Temperature of Melting. Adv. Solid State Phys. 21 (1981) 221. Willoughby, A.F.W.: Double-diffusion Processes in Silicon: Impurity Doping Processes in Silicon, Wang, F. (ed.), Amsterdam: North Holland, 1981, p. 1. Antoniadis, D.A., Moskowitz, I.: Modeling of Impurity Diffusion in Silicon during Oxidation, in: Aggregation Phenomena of Point Defects in Silicon, Sirtl, E. (ed.). The Electrochem. Soc. 1983, p. 1. Hu, S.M., Fahey, P., Dutton, R.W.: On Models of P-diffusion in Silicon. J. Appl. Phys. 54 (1983) 6912. Tan, T.Y., Gösele, U., Morehead, F.F.: On the Nature of Point Defects and the Effect of Oxides on Substitutional Dopant Diffusion in Silicon. Appl. Phys. A 31 (1983) 97. Weber, E.R.: Transition Metals in Silicon. Appl. Phys. A 30 (1983) 1. Fair, R.B.: The Role of Vacancies and Self-interstitials in Impurity Diffusion in Silicon. Mater. Sci. Forum 1 (1984) 109; Diffus. Defect Data 37 (1984) 1. Frank, W., Gösele, U., Mehrer, H., Seeger, A.: Diffusion in Silicon and Germanium, in: Diffusion in Crystalline Solids, Murch, G., Nowick, A.S. (eds.), New York, London, Orlando: Academic Press, 1984, p. 63. Bourgoin, J.C.: On Diffusion Mechanisms, Kimmerling, L.C. (ed.), Proc. Defect Conf. Coronado, 1985, p. 167. Fair, R.B.: Observations of vacancies and Self-interstitials in Diffusion Experiments in Silicon, Kimmerling, L.C. (ed.), Proc. Defect Conf. Coronado, 1985, p. 173. Pantelides, S.T.: Atomic Diffusion in Silicon: What theory hath wrought, Kimmerling, L.C. (ed.), Proc. Defect Conf. Coronado, 1985, p. 151. Tan, T.Y., Gösele, U.: Point Defects, Diffusion Processes, and Swirl Defects Formation in Silicon. Appl. Phys. A 37 (1985) 1. Gösele, U.: The Role of Carbon and Point Defects in Silicon, in: Oxygen, Carbon, Hydrogen, and Nitrogen in Crystalline Silicon, Mikkelsen jr., J.C., Pearton, S.J. Corbett, J.W., Pennycook, S.J. (eds). Mater. Res. Soc. Symp. Proc. 59 (1986) 419. Wolf, S., Tauber, R.N.: Silicon Processing for the VLSI Era, Vol. 1: Process Technology. Sunset Beach, California: Lattice Press, 1986, p. 242. Frank, W., Stolwijk, N.A.: Diffusion Mechanisms and Thermal-equilibrium Defects in Silicon and Germanium. Mater. Sci. Forum 15-18 (1987) 369.
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2 Diffusion in silicon, germanium and their alloys Pearton, S.J., Corbett, J.W., Shi, T.S.: Hydrogen in Crystalline Semiconductors. Appl. Phys. A 43 (1987) 153. Barraclough, K.G., Ashby, P.J., Wilkes, J.G., Canham, L.T.: Oxygen, Carbon, and Nitrogen in Silicon, in: Properties of Silicon. London and New York: INSPEC, The Institution of Electrical Engineers, 1988. Brown, A.A., Rosser, P.J., Moynagh, P.B., Godfrey, D.J., de Cogan, D., Nobili, D.: Diffusion, Solid Solubility, and Implantation of Group III and Group V Impurities, in: Properties of Silicon. London and New York: INSPEC, The Institution of Electrical Engineers, 1988, p. 1. Canham, L.T.: Diffusion and Solubility of Alkali Metals, in: Properties of Silicon. London and New York: INSPEC, The Institution of Electrical Engineers, 1988. Gösele, U, Tan, T.Y.: Point Defects and Diffusion in Silicon and Gallium Arsenide. Defect Diffus. Forum 59 (1988) 1. Singh, R.: Rapid thermal processing. J. Appl. Phys. 63 (1988) R59. Stolwijk, N.A., Perret, M., Mehrer, H.: Interstitial-substitutional Diffusion in Group III-V and Group IV Semiconductors: The Role of Dislocations. Defect Diffus. Forum 59 (1988) 79. Weber, E.R.: Diffusion and Solubility of Transition Metals, in: Properties of Silicon. London and New York: INSPEC, The Institution of Electrical Engineers, 1988. Fahey, P.M., Griffin, P.B., Plummer, J.D.: Point Defects and Dopant Diffusion in Silicon. Rev. Mod. Phys. 61 (1989) 289. Frank, W.: The Interplay of Solute- and Self-diffusion - a Key for Revealing Diffusion Mechanism in Silicon and Germanium. Defect Diffus. Forum 75 (1991) 121. Schröter, W., Seibt, M., Gilles, D.: High-temperature Properties of 3d Transition Elements in Si: Mater. Sciene and Technology, Cahn, R.W., Haasen, P., Kramer, E.J. (eds.), Electronic Structure and Properties of Semiconductors, Schröter, W. (ed.), Weinheim: VCH Vol. 4 (1991) p. 539. Frank, W.: Diffusion in Crystalline Silicon and Germanium - The State-of-the-art in Brief, in: Crucial Issues in Semiconductor Materials and Processing Technologies, Coffa, S., Priolo, F., Rimini, E., Poate, J.M. (eds). NATO ASI Ser., Vol. E 222 (1992) 383. Gösele, U., Tan, T.Y.: Diffusion in Semiconductors - Unsolved Problems. Defect Diffus. Forum 83 (1992) 189. Stolwijk, N.A.: Atomic Transport in Semiconductors: Diffusion Mechanisms and Chemical Trends. Defect Diffus. Forum 95-98 (1993) 895. Davies, G., Newman, R.C.: Carbon in Monocrystalline silicon: Handbook on Semicond. ed. by T.S. Moss, Vol. 3 ed. by S. Mahajan (1994) 1557. Hu, S.M.: Non-equilibrium Point Defects and Diffusion in Silicon. Mater. Sci. Eng. R13 (1994) 105. Newman, R.C., Jones, R.: Diffusion of Oxygen in Silicon. Semicond. Semimet. 42 (1994) 289. Stolwijk, N.A., Bracht, H., Hettwer, H.-G., Lerch, W., Mehrer, H., Rucki, A., Jäger, W.: Defect Injection and Diffusion in Semiconductors. Mater. Sci. Forum 155-156 (1994) 475. McQuaid, S.A., Binns, M.J., Londos, C.A., Tucker, J.H., Brown, A.R., Newman, R.C.: Oxygen Loss During Thermal Donor Formation in Czochralski Silicon: New Insights into Oxygen Diffusion Mechanisms. J. Appl. Phys. 77 (1995) 1427.
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Fuller, C.S., Ditzenberger, J.A.: Phys. Rev. 91 (1953) 193. Dunlap jr., W.C., Bohm, H.V., Mahon jr., H.P.: Phys. Rev. 87 (1954) 822. Fuller, C.S., Severins, J.C.: Phys. Rev. 96 (1954) 21. Fuller, C.S., Ditzenberger, J.A.: Phys. Rev. 96 (1954) 1439. Morin, F.J., Maita, J.P.: Phys. Rev. 94 (1954) 1525. Morin, F.J., Maita, J.P.: Phys. Rev. 96 (1954) 28. Compaan, K., Haven, Y.: Trans. Faraday Soc. 52 (1956) 786. Fuller, C.S., Ditzenberger, J.A.: J. Appl. Phys. 27 (1956) 544. Goldstein, B.: Bull. Am.Phys. Soc. Ser. II 1 (1956) 145. Miller, R.C., Savage, A.: J. Appl. Phys. 27 (1956) 1430. Van Wieringen, A., Warmoltz, N.: Physica 22 (1956) 849. Fuller, C.S., Morin, F.J.: Phys. Rev. 105 (1957) 379. Gallagher, C.J.: J. Phys. Chem. Solids 3 (1957) 82. Petrov, D.A., Shaskov, Yu.M., Akimchenko, I.P.: Vopr. Metall. Fiz. Poluprovodn. Tr. Soveshch. 2nd 1956, 1957, 130; Chem. Abstr. 54 (1960) 17190c. 57Sou1 Southgate, P.D.: Proc. Phys. Soc. London Sect. B 70 (1957) 804. 57Str1 Struthers, J.D.: J. Appl. Phys. 27 (1956) 1560; Erratum: J. Appl. Phys. 28 (1957) 516. 58Bol1 Boltaks, B.I., Sozinov, I.I.: Sov. Phys. Tech. Phys. 3 (1958) 636. 58Com1 Compaan, K., Haven, Y.: Trans. Faraday Soc. 54 (1958) 1498. 58Kur1 Kurtz, A.D., Gravel, C.L.: J. Appl. Phys. 29 (1958) 1456. 58Mai1 Maita, J.P.: J. Phys. Chem. Solids 4 (1958) 68. 58Pet1 Petrov, D., et al.: IMET Report on "Impurity Diffusion Processes in Semiconductors" 1958. 59Car1 Carlson, R.O., Hall, R.N., Pell, E.M.: J. Phys. Chem. Solids 8 (1959) 81. 59Har1 Hartke, J.L.: J. Appl. Phys. 30 (1959) 1469. 59Log1 Logan, R.A., Peters, A.J.: J. Appl. Phys. 30 (1959) 1627. 59Pel1 Pell, E.M.: Bull. Am. Phys. Soc. 4 (1959) 320. 59Roh1 Rohan, J.J., Pickering, N.E., Kennedy, J.: J. Electrochem. Soc. 106 (1959) 705. 59Sah1 Sah, C.T. et al.: J. Phys. Chem. Solids 11 (1959) 288. 59Sha1 Shashkov, M., Akimchenko, I.P.: Sov. Phys. Dokl. (English Transl.) 4 (1959) 1115. 60Bol1 Boltaks, B.I., Kulikov, G.S., Malkovich, R.Sh.: Sov. Phys. Solid State (English Transl.) 2 (1960) 2134. 60Bol2 Boltaks, B.I., Kulikov, G.S., Malkovich, R.Sh.: Sov. Phys. Solid State (English Transl.) 2 (1960) 167. 60Bus1 Busch, G., Vogt, O.: Helv. Phys. Acta 33 (1960) 769. 60Das1 Dash, W.C.: J. Appl. Phys. 31 (1960) 2275. 60DAs2 D'Asaro, L.A.: Solid State Electron. 1 (1960) 31. 60Dri1 Drimer, D., Taranu, P., Hafner, A., Vescan, L., Nemoda, L.: Acad. Rep. Pop. Rom. Fil. Iasi Stud. Cercet. Stiint. Fiz. Stiinte Teh. 13 (1960) 39. 60Haa1 Haas, C.: J. Phys. Chem. Solids 15 (1960) 108. 60Kur1 Kurtz, A.D., Yee, R.: J. Appl. Phys. 31 (1960) 303. 60Lud1 Ludwig, G.W., Woodbury, H.H.: Proc. Int. Conf. Semicond. Phys., Prague 1960, p. 596. 60Pel1 Pell, E.M.: Phys. Rev. 119 (1960) 1014. 60Pel2 Pell, E.M.: Phys. Rev. 119 (1960) 1222. 60Sou1 Southgate, P.D.: Proc. Phys. Soc. London 76 (1960) 385; 398. 61Bol1 Boltaks, B.I., Shih-yin, H.: Sov. Phys. Solid State (English Transl.) 2 (1961) 2383. 61New1 Newman, R.C., Wakefield, J.: J. Phys. Chem. Solids 19 (1961) 230. 61Que1 Queisser, H.J.: J. Appl. Phys. 32 (1961) 1776. 61Sub1 Subashiev, V.K., Landsman, A.P., Kukharskii, A.A.: Sov. Phys. Solid State (English Transl.) 2 (1961) 2406.
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2-200 61Tan1 61Wil1 62Arm1 62Mac1 62Mae1 62Sch1 62She1 62Thu1 62Wil1 62Yan1 63Cal1 63Mal1 63Moc1 64Bol1 64Bol2 64Gro1 64Hal1 64Kat1 64Kre1 64Lut1 64Mae1 64Raj1 64Sch1 64Svo1 64Was1 64Wat1 64Wil1 65Cal1 65Cal2 65Cal3 65Jos1 65Oke1 65Pom1 65Spr1 66Bec1 66Gho1 66Iiz1 66Law1 66Law2 66Mar1 66Mas1 66Maz1 66Mil1 66Nic1 66Pea1 66Pra1 66Rup1 66Rut1 66Sch1 67Bon1
2 Diffusion in silicon, germanium and their alloys Tannenbaum, E.: Solid State Electron. 2 (1961) 123. Williams, E.L.: J. Electrochem. Soc. 108 (1961) 795. Armstrong, W.J.: J. Electrochem. Soc. 109 (1962) 1065. Mackintosh, I.M.: J. Electrochem. Soc. 109 (1962) 392. Maekawa, S.: J. Phys. Soc. Jpn. 17 (1962) 1592. Schwuttke, G.H., Queisser, H.J.: J. Appl. Phys. 33 (1962) 1540. Shepherd, W.H., Turner, J.A.: J. Phys. Chem. Solids 23 (1962) 1697. Thurston, M.O., Tsai, J.C.C.: Ohio State University Research Foundation, Rept. No. 1233-4Q, 1962. Williams, R.L., Webb, P.P.: IRE Trans. Nucl. Sci. 9 (1962) 160. Yanasigawa, S. et al.: Nippon Kinzoku Gakkaishi 26 (1962) 324. McCaldin, J.O., Widmer, A.E.: J. Phys. Chem. Solids 24 (1963) 1073. Malkovich, R.Sh., Alimbarashvili, N.A.: Sov. Phys. Solid State (English Transl.) 4 (1963) 1725. Mochov, Yu.N.: Izv. Vyssh. Uchebn. Zaved. SSSR 6 (1963) 41. Boltaks, B.I., Kulikov, G.S.: Sov. Phys. Solid State (English Transl.) 6 (1964) 1519. Boltaks, B.I., Dzhafarov, T.D.: Sov. Phys. Solid State (English Transl.) 5 (1964) 2649. Grove, A.S., Leistiko jr., O., Sah, C.T.: J. Phys. Chem. Solids 25 (1964) 985. Hall, R.N., Racette, J.H.: J. Appl. Phys. 35 (1964) 379. Kato, T., Nishi, Y.: Jpn. J. Appl. Phys. 3 (1964) 377. Kren, J.G., Masters, B.J., Wajda, E.S.: Appl. Phys. Lett. 5 (1964) 49. Luther, L.C., Moore, W.J.: J. Chem. Phys. 41 (1964) 1018. Maekawa, S., Oshida, T.: J. Phys. Soc. Jpn. 19 (1964) 253. Raju, P.S., Rao, N.R.K., Rao, E.V.K.: Indian J. Pure Appl. Phys. 2 (1964) 353. Schmidt, P.F., Stickler, R.: J. Electrochem. Soc. 111 (1964) 1188. Svob, L.: Phys. Status Solidi 7 (1964) K1. Washburn, J., Thomas, G., Queisser, H.J.: J. Appl. Phys. 35 (1964) 1909. Corbett, J.W, McDonald, R.S., Watkins, G.D.: J. Phys. Chem. Solids 25 (1964) 873. Wilcox, W.R., LaChapelle, T. J.: J. Appl. Phys. 35 (1964) 240. McCaldin, J.O., Little, M.J., Widmer, A.E.: J. Phys. Chem. Solids 26 (1965) 1119. McCaldin, J.O.: Nucl. Instrum. Methods 38 (1965) 153. McCaldin, J.O.: Prog. Solid State Chem. 2 (1965) 9. Joshi, M.L., Wilhelm, F.: J. Electrochem. Soc. 112 (1965) 185. O'Keeffe, T.W., Schmidt, P.F., Stickler, R.: J. Electrochem. Soc. 112 (1965) 879. Pommering, D.: Acta Phys. Austriaca 20 (1965) 338. Sprokel, G.J., Fairfield, J.M.: J. Electrochem. Soc. 112 (1965) 200. Beck, C.G., Stickler, R.: J. Appl. Phys. 37 (1966) 4683. Ghoshtagore, R.N.: Phys. Rev. Lett. 16 (1966) 890. Iizuka, T.: Jpn. J. Appl. Phys. 4 (1966) 1018. Lawrence, J.E.: J. Appl. Phys. 37 (1966) 4106. Lawrence, J.E.: J. Electrochem. Soc. 113 (1966) 819. Martin, J., Haas, E., Raithel, K.: Solid State Electron. 9 (1966) 83. Masters, B.J., Fairfield, J.M.: Appl. Phys. Lett. 8 (1966) 280. Mazur, R.G., Dichey, D.H.: J. Electrochem. Soc. 113 (1966) 255. Millea, M.F.: J. Phys. Chem. Solids 27 (1966) 315. Nicholas, K.H.: Solid State Electron. 9 (1966) 35. Peart, R.F.: Phys. Status Solidi 15 (1966) K119. Pratt, B., Friedman, F.: J. Appl. Phys. 37 (1966) 1893. Rupprecht, H., Schwuttke, G.H.: J. Appl. Phys. 37 (1966) 2862. Ruth, R.P.: Proc. II. Int. Conf. Electron and Ion Beam Sci. Technol. 2 (1966) 1117. Schwuttke, G.H., Fairfield, J.M.: J. Appl. Phys. 37 (1966) 4394. Bonzel, H.P.: Phys. Status Solidi 20 (1967) 493.
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Dudko, G.V., Kolegaev, M.A., Cherednichenko, D.I.: Elektron. Obrab. Mater. Akad. Nauk Moldavia SSR 6 (1967) 58. Fairfield, J.M., Masters, B.J.: J. Appl. Phys. 38 (1967) 3148. Ghoshtagore, R.N.: Phys. Status Solidi 20 (1967) K89. Gittler, F.L.: J. Electrochem. Soc. 114 (1967) 63C. Kao, Y.C.: Electrochem. Soc. Technol. 5 (1967) 90. Pavlov, P.V., Uskov, V.A., Zorin, E.I., Tetel'baum, D.I., Baranova, A.S.: Sov. Phys. Solid State (English Transl.) 8 (1967) 2221. Smith, A.M.: Fundamentals of Silicon Integrated Device Technology Vol.1, Englewood Cliffs, New Jersey: Prentice Hall, 1967, p. 204. Sterkhov, V.A., Panteleev, V.A., Pavlov, P.V.: Sov. Phys. Solid State (English Transl.) 9 (1967) 533. Svob, L.: Solid State Electron. 10 (1967) 991. Yoshida, M., Saito, K.: Jpn. J. Appl. Phys. 6 (1967) 573. Babikova, J.F., Gruzin, P.L., Kazakevich, V.I.: Metall. Metalloved. Chist. Met. 7 (1968) 141. Clark, A.H., Macdougall, J.D., Manchester, K.E., Roughan, P.E., Anderson, F.W.: Bull. Am. Phys. Soc. 13 (1968) 376. Dobson, P.S., Filby, J.D.: J. Cryst. Growth 3 (1968) 209. Duffy, M.C., Barson, F., Fairfield, J.M., Schwuttke, G.H.: J. Electrochem. Soc. 115 (1968) 84. Duffy, M.C., Barson, F., Fairfield, J.M., Schwuttke, G.H.: J. Electrochem. Soc. 115 (1968) 1290. Fairfield, J.M., Schwuttke, G.H.: J. Electrochem. Soc. 115 (1968) 415. Fisher, A.W., Amick, J.A.: RCA Rev. 29 (1968) 549. Hackler, W.A., Kikuchi, C.: Nucl. Sci. Eng. 31 (1968) 175. Hsueh, Y.W.: Electrochem. Technol. 6 (1968) 361. Ichimiya, T., Furuichi, A.: Int. J. Appl. Radiat. Isot. 19 (1968) 573. Itoh, T., Inada, T., Kanekawa, K.: Appl. Phys. Lett. 12 (1968) 244. Jungbluth, E.D., Chiao, H.C.: J. Electrochem. Soc. 115 (1968) 429. Nagano, K., Iwauchi, S., Tanaka, T.: Jpn. J. Appl. Phys. 7 (1968) 1361. Nakanuma, S., Yamagishi, S.: J. Electrochem. Soc. Jpn. 36 (1968) 3. Okamura, M.: Jpn. J. Appl. Phys. 7 (1968) 1067. Robertsen, J.B., Franks, R.K.: Solid State Commun. 6 (1968) 825. Yeh, T.H., Hu, S.M., Kastl, R.H.: J. Appl. Phys. 39 (1968) 4266. Alvarez, J.L.: An. Fis. 65 (1969) 299. Bailey, R.F., Mills, T.G.: 1st Int. Symp. Semicond. Silicon, 1969, p. 481. Barry, M.L., Olofsen, P.: J. Electrochem. Soc. 116 (1969) 854. Denisova, L.A., Sakharov, B.A., Sokolov, E.B., Khorvat, A.M.: Izv. Akad. Nauk SSSR Neorg. Mater. 5 (1969) 995. Masters, B.J., Fairfield, J.M.: J. Appl. Phys. 40 (1969) 2390. Okamura, M.: Jpn. J. Appl. Phys. 8 (1969) 1440. Parry, E.P., Porter, M.S., McCaldin, J.O.: Solid State Electron. 12 (1969) 500. Tsai, J.C.C.: Proc. IEEE 57 (1969) 1499. Vick, G.L., Whittle, K.M.: J. Electrochem. Soc. 116 (1969) 1143. Wills, G.N.: Solid State Electron. 12 (1969) 133. Arai, E., Terunuma, Y.: Jpn. J. Appl. Phys. 9 (1970) 410. Bakhadyrkhanov, M.K., Boltaks, B.I., Kulikov, G.S., Pedyash, E.M.: Sov. Phys. Semicond. (English Transl.) 4 (1970) 739. Bakhadyrkhanov, M.K., Boltaks, B.I., Kulikov: Sov. Phys. Solid State (English Transl.) 12 (1970) 144. Barry, M.L.: J. Electrochem. Soc. 117 (1970) 1405. Bendik, N.T., Garnyk, V.S., Milevskii, L.S.: Sov. Phys. Solid State (English Transl.) 12 (1970) 150.
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2 Diffusion in silicon, germanium and their alloys Chan, T.C., Mai, C.C.: Proc. IEEE 58 (1970) 588. Chik, K.P.: Radiat. Eff. 4 (1970) 33. Convers, D., Dupraz, J., Mascotto, R., Venezia, A.: Helv. Phys. Acta 43 (1970) 765. Dash, S., Joshi, M.L.: IBM J. Res. Dev. 14 (1970) 453. Ferrin, I., Bemski, G., Parker, W.: Phys. Lett. A 32 (1970) 65. Gamo, K., Doi, A., Masuda, K., Namba, S., Ishihara, S., Kimura, I.: Jpn. J. Appl. Phys. 9 (1970) 333. Gamo, K., Masuda, K., Namba, S., Ishihara, S., Kimura, I.: Appl. Phys. Lett. 17 (1970) 391. Ghoshtagore, R.N.: Phys. Rev. Lett. 25 (1970) 856. Ghoshtagore, R.N.: Appl. Phys. Lett. 17 (1970) 137. Gittler, F.L., Porter, R.A.: J. Electrochem. Soc. 117 (1970) 1551. Hsueh, Y.W.: J. Electrochem. Soc. 117 (1970) 807. Huang, J.S.T., Welliver, L.C.: J. Electrochem. Soc. 117 (1970) 1577. Itoh, T., Ohdomari, I.: J. Appl. Phys. 41 (1970) 434. Katsuta, M., Ouchiyama, T.: Shin Nippon Denki Giho 5 (1970) 9. Kesperis, J.S.: J. Electrochem. Soc. 117 (1970) 554. Klimkova, O.A., Nigazova, O.R.: Phys. Status Solidi (a) 3 (1970) K93. Kovalev, R.A., Bernikov, V.B., Pashintsev, Yu.I., Marasanov, V.A.: Sov. Phys. Solid State (English Transl.) 11 (1970) 1571. Lyutovich, A.S., Prutkin, V.P., Pashkudenko, V.P., Sevastyanov, K.N., Shasaidov, S.S.: Krist. Tonkikh Plenok 1970, 91. Matzke, HJ.: Radiat. Eff. 3 (1970) 93. Meyer, O., Mayer, J.W.: J. Appl. Phys. 41 (1970) 4166. Meyer, O., Mayer, J.W.: Solid State Electron. 13 (1970) 1357. Mokhov, J.N., Skachkov, N.N., Kaverznev, V.P.: Zh. Fiz. E. Abstract 5E843 (1970) Namba, S., Masuda, K., Gamo, K., Doi, A., Ishihara, S., Kimura, I.: Radiat. Eff. 6 (1970) 115. Prutkin, V.P., Lyntovich, A.S., Kardzhaubaev, M.J.: Krist. Tonkikh Plenok (1970) 139. Ridgway, J.W.T., Haneman, D.: Phys. Status Solidi 38 (1970) K31. Sladkov, I.B., Tuchkevich, V.V., Schmidt, N.M.: Fiz. Tekh. Poluprovodn. (Leningrad) 4 (1970) 793. Taft, E.A., Carlson, R.O.: J. Electrochem. Soc. 117 (1970) 711. Thai, N.D.: Solid State Electron. 13 (1970) 165. Thai, N.D.: J. Appl. Phys. 41 (1970) 2859. Titov, V.V.: Phys. Status Solidi (a) 2 (1970) 203. Uskov, V.A., Pavlov, P.V., Kuril'chik, E.V., Pashkov, V.I.: Sov. Phys. Solid State (English Transl.) 12 (1970) 1181. Yoshida, M., Saito, K.: Jpn. J. Appl. Phys. 9 (1970) 1217. Yoshida, M., Kanamori, S.: Jpn. J. Appl. Phys. 9 (1970) 338. Zalar, S.M.: J. Appl. Phys. 41 (1970) 3458. Zyuz, L.N., Kiv, A.E., Niyazova, O.R., Umarova, F.T.: Sov. Phys. JETP Lett. (English Transl.) 12 (1970) 147. Allen, W.G., Anand, K.V.: Solid State Electron. 14 (1971) 397. Brown, D.M., Kennicott, P.R.: J. Electrochem. Soc. 118 (1971) 293. Brümmer. O., Hofmann, M.: Phys. Status Solidi (a) 5 (1971) 199. Chiu, T.L., Ghosh, H.N.: IBM J. Res. Dev. 15 (1971) 472. Fränz, I., Langheinrich, W.: Solid State Electron. 14 (1971) 835. Ghoshtagore, R.N.: Phys. Rev. B 3 (1971) 2507. Ghoshtagore, R.N.: Phys. Rev. B 3 (1971) 397. Ghoshtagore, R.N.: Phys. Rev. B 3 (1971) 389. Kennedy, D.P., Murley, P.C.: Proc. IEEE 59 (1971) 335. Klimkova, O.A., Niyazova, O.R.: Sov. Phys. Solid State (English Transl.) 12 (1971) 1760. Larue, J.C.: Phys. Status Solidi (a) 6 (1971) 143.
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2 Diffusion in silicon, germanium and their alloys 93Aga1 93Bag1 93Bor1 93Bra1 93Bra2 93Che1 93Cof1 93Cow1
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Lando lt -Bö rnst ein New Series III/33A
2-220
2 Diffusion in silicon, germanium and their alloys
93Rot1 93Sca1
Roth, D.J., Huang, R.Y.S., Plummer, J.D., Dutton, R.W.: Appl. Phys. Lett. 62 (1993) 2498. Scandurra, A., Galvagno, G., Raineri, V., Frisina, F., Torrisi, A.: J. Electrochem. Soc. 140 (1993) 2057. 93Sob1 Sobolev, N.A., Alexandrov, O.V., Gresserov, B.N., Gusinskii, G.M., Naidenov, V.O., Sheck, E.I., Stepanov, V.I., Vyzhigin, Yu.V., Chepik, L.F., Troshina, E.P.: Solid State Phenom. 32-33 (1993) 83. 93Sol1 Solmi, S., Maccagnani, P., Canteri, R.: J. Appl. Phys. 74 (1993) 5005. 93Sul1 Sultan, A., Lobo, M., Bhattacharya, S., Banerjee, S., Batra, S., Manning, M., Dennison, C.: J. Electron. Mater. 22 (1993) 1129. 93Vic1 Vicente, J., Enriquez, L., Rubio, E., Bailon, L., Barbolla, J.: J. Electrochem. Soc. 140 (1993) 868. 93Vys1 Vysotskaya, V.V., Gorin, S.N.: Defect Diffus. Forum 103-105 (1993) 221. 93Wij1 Wijaranakula, W.: Appl. Phys. Lett. 62 (1993) 2974. 93Wij2 Wijaranakula, W.: J. Appl. Phys. 73 (1993) 1004. 93Wij3 Wijaranakula, W.: Jpn. J. Appl. Phys. 32 (1993) 3872. 93Wil1 Willems, G.J., Maes, H.E.: J. Appl. Phys. 73 (1993) 3256. 93Zho1 Zhong, L., Shimura, F.: Jpn. J. Appl. Phys. 32 (1993) 1113. 93Zho2 Zhong, L., Shimura, F.: J. Appl. Phys. 73 (1993) 707. 94Abd1 Abdurakhmanov, K.P., Vitman, R.F., Kulikov, G.S., Lebedev, A.A., Utamuradova, Sh.B., Yusupova, Sh.A.: Semiconductors (English Transl.) 28 (1994) 52. 94Aok1 Aoki, N., Kanemura, T., Mizushima, I.: Appl. Phys. Lett. 64 (1994) 3133. 94Bak1 Bakhadirkhanov, M.K., Askarov, Sh.I., Norkulov, N.: Phys. Status Solidi (a) 142 (1994) 339. 94Bra1 Bracht, H., Stolwijk, N.A., Mehrer, H.: Mater. Sci. Forum 143-147 (1994) 785. 94Bra2 Bracht, H., Stolwijk, N.A., Mehrer, H.: Proc. Electrochem. Soc. 94-10 (1994) 593. 94Cow1 Cowern, N.E.B.: Appl. Phys. Lett. 64 (1994) 2646. 94Cow2 Cowern, N.E.B., van de Walle, G.F.A., Zalm, P.C., Vandenhoudt, D.W.E.: Appl. Phys. Lett. 65 (1994) 2981. 94Gos1 Gossmann, H.-J., Rafferty, C.S., Vredenberg, A.M., Luftman, H.S., Unterwald, F.C., Eaglesham, D.J., Jacobson, D.C., Boone, T., Poate, J.M.: Appl. Phys. Lett. 64 (1994) 312. 94Hab1 Habu, R., Iwasaki, T., Harada, H., Tomiura, A.: Jpn. J. Appl. Phys. 33 (1994) 1234. 94Häß1 Häßler, C., Pensl, G.: Mater. Sci. Forum 143-147 (1994) 123. 94Jun1 Jung, P.: Nuclear Instrum. Methods Phys. Res. Sect. B 91 (1994) 362. 94Kri1 Kringhoj, P., Elliman, R.G.: Appl. Phys. Lett. 65 (1994) 324. 94Lat1 Latukhina, N.V., Rozhkov, V.A., Romanenko, N.N.: Russian Microelectronics 23 (1994) 28 94Lem1 Lemke, H.: Proc. Electrochem. Soc. 94-10 (1994) 695. 94Ler1 Lerch, W., Stolwijk, N.A., Mehrer, H.: Meas. Sci. Technol. 5 (1994) 835. 94Ler2 Lerch, W.: Doctoral Thesis, University of Münster, 1994. 94Lou1 Lourdudoss, S., Zhang, S.-L.: Appl. Phys. Lett. 64 (1994) 3461. 94Mes1 Mesli, A., Heiser, T., Mulheim, E.: Mater. Sci. Eng. B 25 (1994) 141. 94Mit1 Mitlehner, H., Schulze, H.-J.: EPE Journal 4 (1994) 36. 94Nak1 Nakashima, H., Sadoh, T., Kitagawa, H., Hashimoto, K.: Mater. Sci. Forum 143-147 (1994) 761. 94Nob1 Nobili, D., Solmi, S., Parisini, A., Derdour, M., Armigliato, A., Moro, L.: Phys. Rev. B 49 (1994) 2477. 94Oki1 Okino, T., Onishi, M.: Jpn. J. Appl. Phys. 33 (1994) 3362. 94Pea1 Pearton, S.J., Abernathy, C.R., Ren, F.: Defect Diffus. Forum 111-112 (1994) 1. 94Pic1 Pichaud, B., Mariani, G., Taylor, W.J., Yang, W.-S.: Solid State Phenom. 35-36 (1994) 491. 94Rak1 Rakhimbaev, D., Avezmuradov, A., Rakhimbaeva, M.D.: Inorg. Mater. (English Transl.) 30 (1994) 418. 94Sze1 Szeles, Cs., Nielsen, B., Asoka-Kumar, P., Lynn, K.G., Anderle, M., Ma, T.P., Rubloff, G.W.: J. Appl. Phys. 76 (1994) 3403. 94Tak1 Takahashi, M., Morooka, M., Ueda, F., Hashimoto, F.: Jpn. J. Appl. Phys. 33 (1994) 1713.
Landolt -Börnst ein New Series III/33A
2 Diffusion in silicon, germanium and their alloys 94Thi1 94Yam1 94Zim1 95Ale1 95Ant1 95Bra1 95Dat1
2-221
Thilderkvist, A., Kleverman, M., Grimmeiss, H.G.: Phys. Rev. B 49 (1994) 16338. Yamanaka, H., Aoki, Y.: Jpn. J. Appl. Phys. 33 (1994) L559. Zimmermann, H.: Mater. Sci. Forum 143-147 (1994) 1647. Alexandrov, O.V., Sobolev, N.A., Shek, E.I.: Semicond. Sci. Technol. 10 (1995) 948. Antonova, I.V., Shaimeev, S.S.: Semiconductors (English Transl.) 29 (1995) 1. Bracht, H., Stolwijk, N.A., Mehrer, H.: Phys. Rev. B 52 (1995) 16542. Datar, S.A., Gove, H.E., Teng, R.T.D., Lavine, J.P.: Nucl. Instrum. Methods Phys. Res. Sect. B 99 (1995) 549. 95Gal1 Galvagno, G., La Via, F., Saggio, M.G., La Mantia, A., Rimini, E.: J. Electrochem. Soc. 142 (1995) 1585. 95Gha1 Ghaderi, K., Hobler, G., Budil, M., Mader, L., Schulze, H.J.: J. Appl. Phys. 77 (1995) 1320. 95Gha2 Ghaderi, K., Hobler, G.: J. Electrochem. Soc. 142 (1995) 1654. 95Gos1 Gossmann, H.-J., Stolk, P.A., Eaglesham, D.J., Rafferty, C.S., Poate, J.M.: Appl. Phys. Lett. 67 (1995) 3135. 95Hol1 Holm, B., Bonde Nielsen, K.: J. Appl. Phys. 78 (1995) 5970. 95Kov1 Koveshnikov, S.V., Rozgonyi, G.A.: Appl. Phys. Lett. 66 (1995) 860. 95Kul1 Kulikov, G.S., Chichikalyuk, Yu.A., Yusupova, Sh.A.: Semiconductors (English Transl.) 29 (1995) 242. 95Ler1 Lerch, W., Stolwijk, N.A., Mehrer, H., Poisson, Ch.: Semicond. Sci. Technol. 10 (1995) 1257. 95Mon1 Monson, T.K., Van Vechten, J.A., Zhang, Q.S.: Appl. Phys. Lett. 66 (1995) 854. 95Mon2 Monson, T.K., Van Vechten, J.A., Zhang, Q.S.: J. Electro. Chem. Soc. 142 (1995) 2077. 95Nag1 Nagel, D., Frohne, C., Sittig, R.: Appl. Phys. A 60 (1995) 61. 95Nag2 Nagel, D., Kuhlmann, U., Sittig, R.: Proc. 3rd Int. Rapid Thermal Processing Conf. RTP'95, Fair, R.B., Lojek, B. (eds.), publ. by RTP'95, 16 Scenic Terrace, Round Rock, TX78664, 1995, p. 109. 95Nai1 Naidenov, V.O., Sobolev, N.A., Alexandrov, O.B., Bresler, M.S., Gusev, O.V., Gusinskii, G.M., Shek, E.I., Makaviichuk, M.I., Parshin, E.O.: Nucl. Instrum. Methods Phys. Res. Sect. B 99 (1995) 587. 95Rob1 Roberts, S., Parker, G.: Mater. Lett. 24 (1995) 307. 95Sob1 Sobolev, N.A.: Semiconductors (English Transl.) 29 (1995) 595. 95Sto1 Stolk, P.A., Gossmann, H.-J., Eaglesham, D.J., Jacobson, D.C., Poate, J.M., Luftman, H.S.: Appl. Phys. Lett. 66 (1995) 568. 95Sze1 Szeles, Cs., Nielsen, B., Asoka-Kumar, P., Lynn, K.G., Anderle, M., Ma, T.P., Rubloff, G.W.: Mater. Sci. Forum 175-178 (1995) 545. 95Wit1 Wittel, F., Dunham, S.: Appl. Phys. Lett. 66 (1995) 1415. 95Yak1 Yakimov, E., Mariani, G., Pichaud, B.: J. Appl. Phys. 78 (1995) 1495. 95Yos1 Yoshida, M., Arai, E.: Jpn. J. Appl. Phys. 34 (1995) 5891. 95Yos2 Yoshida, M.: Mater. Sci. Forum 196-201 (1995) 1595. 96Hei1 Heiser, T., Mesli, A.: Appl. Phys. Lett. 68 (1996) 1868. 96Kov1 Koveshnikov, S.V., Rozgonyi, G.A.: Appl. Phys. Lett. 68 (1996) 1870. 96Yos1 Yoshida, M., Arai, E.: Jpn. J. Appl. Phys. 35 (1996) 44.
Lando lt -Bö rnst ein New Series III/33A
2 Diffusion in silicon, germanium and their alloys
2-222
[Ref. p. 2-237
2.3 Diffusion in germanium 2.3.1 Tables for 2.3 (See Figs. 211-230, p. 231) 2.3.1.1 Solute elements of group IA to group VIII (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
0.38
800-910 780-930
permeation measurements, mass spectrometry D > 5·10−5 cm2s−1, permeation measurements, mass spectrometry
211
56W 60F
300
D = 3.5·10−9 cm2s−1, hydrogen passivation of deep levels, DLTS
0.46
350-800
pn-junction
212
53F
0.51
150-600
ion drift mobility, pn-junction
211 212
54F1
0.57
300-400
incremental sheet resistance, 4-point probe
212
66P
0.42
24-61
ion drift mobility, capacitance measurements
212
69S
0.50
23-550
D0 and Q given for 327 °C (curved Arrhenius plot), pn-junction and ion pairing, pressure dependence
212
72V
0.43
50-150
implanted 6Li+, nuclear reaction, polycrystalline Ge
212
75K
(−93)-(−3)
mobility relaxation due to ion-pairing, Hall effect, curved Arrhenius plot
212
76H
Group IA
H in Ge 2.72·10−3
84P
Li in Ge 1.3·10−3 2.5·10
−3
9.1·10−3 1.1·10
−4
1.78·10
−3
1·10−6
Na in Ge 0.07
2.08
700-850
pn-junction, C0 = 1017-l018 cm−3 from neutron activation analysis
0.029 0.185 0.395
1.55 1.51 2.0
660-830 520-640 700-820
radiotracer, n-type Ge: 40 Ωcm radiotracer, n-type Ge: 10 Ωcm radiotracer, p-type Ge: 28 Ωcm
211
77S
2.5
720-920
pn-junction, thermal probe
211
61B
74G
Group IIA
Be in Ge 0.5
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-223
T-range [°C]
Remarks
Fig.
Ref.
900
D = 8·10−9 cm2s−1, C0 = 1·1015 cm−3, incremental sheet resistance
79H
800
D = 6.5·10−13 cm2s−1, radiotracer
60M
775-930
radiotracer, interstitial diffusion
Mg in Ge
Group VB
Ta in Ge
Group VIII
Fe in Ge 0.13
1.1
−7
213
2 −1
57B1
800
D = 2.3·10 cm s radiotracer, exponential profiles due to deep traps
1.12 0.87
750-850 750-850
radiotracer, low dislocation density radiotracer, high dislocation density
213
61W1
0.91
700-875
pn-junction, C0 = 2.4·1014- 3.7·l015 cm−3
213
54M
800
D ≈ (3-8)·10–5 cm2s–1, resistivity measurements, D varies with depth, Nii-Nis exchange suggested
61W1
Co in Ge 0.16 4.4·10−3
Ni in Ge 0.8
55M
2.3.1.2 Solute elements of group IB and group IIB (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
0.18
700-900
resistivity and radiotracer, C0 = 2.l·1015 - 4.7·1016 cm−3
214
54F2
800
D ≈ (3-8)·10–5 cm2s–1, resistivity measurements, D varies with depth, first account of Cui-Cus exchange
Group IB
Cu in Ge 1.9·10−4
Lando lt -Bö rnst ein New Series III/33A
55M
2 Diffusion in silicon, germanium and their alloys
2-224
D0 [cm2s−1]
Q [eV]
[Ref. p. 2-237
T-range [°C]
Remarks
700-900
evaluation of literature data: [54F2, 56T], first account of the dissociative mechanism: see also [59S, 80E, 90S2]
56F
710
D ≈ 2·10–8 cm2s–1: most perfect crystals available D > 4·10–5 cm2s–1: crystals with small-angle grain boundaries radiotracer and resistivity, Cu penetration increases with increasing dislocation density: 104-106 cm–2, departures from Fick’s law observed
56T
760-875
effects of dislocations, resistivity, pn-junction and autoradiography, dissociative model
57F
Fig.
Ref.
Cu in Ge (cont.)
4·10−2
1.0
600-700
radiotracer, interstitial-substitutional exchange
63b
4·10−3
0.33
348-750
radiotracer, autoradiography, highly Ga-doped crystals, diffusivity of interstitial Cui
64H
660-745
incremental sheet resistance and pn-junction, dissociative mechanism, see also [72H]
70S2
577-927
average D0 and Q of curved Arrhenius plot, spreading resistance, dissociative mechanism
800-1200
comparison of Cu in Ge (dissociative mechanism) with Au in Si (kick-out mechanism)
5.5
7.8·10−5
1.55
214 215
85S1 85S2
0.084 800-905
D = ca. 4·10−5cm2s−1, spreading resistance, Cuilimited dissociative diffusivity including [54F2], comparison with vacancy-limited diffusivity, see also [85S1]
1.0
730-900
radiotracer, "fast" diffusion
57B2
710
2·10−6 cm2s−1 (interstitial) D = 3.6·10−8 cm2s−1 (substitutional) radiotracer, exponential profiles
61W1
62K2
214 216
90S1 91B
Ag in Ge 4.4·10−2
4·10−2
2.23
770-920
radiotracer, "slow" diffusion
1.62·10−4
0.45
776-915
low and high dislocation density, spreading resistance, Agi-limited diffusivity via dissociative mechanism
214 217
91B
2.2
600-900
pn-junction, thermal probe, parameters recalculated from Arrhenius plot
219
55D
Au in Ge 12
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [°C]
Remarks
800
D = 7.4·10−10 cm2s−1 radiotracer, doping dependence, directly interstitial or Aui-V pair migration
2-225
Fig.
Ref.
Au in Ge (cont.) 66M
2.5·102 3.5·10−6
2.3 0.63
600-750 800-900
neutral Au atoms positively charged Au atoms Sb-doped single crystals, pn-junction method
219
68G
1.93·10−2
1.53
702-898
radiotracer, low dislocation density, comparison with [91B], generalized dissociative mechanism
218 219
91A
1.05·10−2
1.52
596-916
low and high dislocation density, spreading resistance, Aui-limited diffusivity via dissociative mechanism
214 219
91B
5.3
2.7
650-900
pn-junction, parameters recalculated from given Arrhenius plot
221
54D
0.65
2.55
825-918
radiotracer, C0 = 1.3·1017- 4.4·1017cm−3
221
56K
Group IIB
Zn in Ge
102
−8
2 −1
800
D = 2·10 cm s , radiotracer, "fast" diffusion
2.99
708-902
single crystal, spreading resistance
220 221
95G
4.42
760-915
radiotracer, substitutional diffusion by vacancies
220
60K
Fig.
Ref.
62K1
Cd in Ge 1.75·109
2.3.1.3 Solute elements of group IIIA (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
6.0·108
4.5
700···900
pn-junction, parameters recalculated from given Arrhenius plot
9.5·106
4.5
760-850
incremental sheet resistance, D0 and Q recalculated from Arrhenius plot without data points, C0 < 5·1018 cm−3
B in Ge
Lando lt -Bö rnst ein New Series III/33A
54D 220
67M
2-226
2 Diffusion in silicon, germanium and their alloys
D0 [cm2s−1]
[Ref. p. 2-237
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
1.0·102
3.2
750-850
incremental sheet resistance, D0 and Q recalculated from Arrhenius plot without data points, C0 ≤ 5·1020 cm−3
1.0·103
3.45
554-905
SIMS
9.8·10−4
2.2
525-775
nuclear reaction, (p, γ) resonance broadening
82R
10
3.0
650-900
pn-junction, parameters recalculated from Arrhenius plot
54D
1.4·102
3.31
554-916
SIMS, also isotope effect
150-300
epitaxial growth of Ge on GaAs, out-diffusion from substrate, SIMS
92D
650-900
concentration profiles from impedance measurements
55B
800
D = 6.9·10−8 cm2s–1 radiotracer, "fast" diffusion
62K1
750-920
radiotracer, dependence on the purity of Ge observed
62S
410-900
anomalously high ion-drift mobility probably due to dislocations, autoradiography
64B2
Al in Ge 67M
220
82D1
Ga in Ge
220
86S
In in Ge 20
3.0
16.4
2.84
10
2.78
510-880
radiotracer
65P
33
3.04
700-855
radiotracer, C0 = 2·1019- 8·1019 cm−3
67P
3
2.47
650-850
radiotracer, enhanced diffusion due to dislocations
70D
1.8·104
3.63
554-919
SIMS
5.8·10
220
82D2
Tl in Ge 0.06
2.7
1.7·103
3.4
estimated values 800-930
radiotracer, C0 = 2·1017-9.5·1018 cm−3
59r 220
62T
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
2 Diffusion in silicon, germanium and their alloys
2-227
2.3.1.4 Solute elements of group IVA (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
2.9
650-900
nuclear reaction,weak dependence on conductivity type and pre-annealing
226
81R
7.8
2.97
766-928
radiotracer
37
3.12
750-883
radiotracer, chemical sectioning, parameters recalculated from Arrhenius plot, doping dependence
44 10.8
3.14 3.01
731-916 731-916
radiotracer, Steigman technique radiotracer, Gruzin technique
222A 61W2
3.14
900-924 413-697
two different radiotracers: isotope effect within dissociative model from the precipitation [57T] and solubility [57W] of Cu following [58P]
222A 75C
44.5 24.8
3.14
549-890
radiotracer, sectioning by ion-beam sputtering, doping dependence
222A 83V
21.3
3.11
577-927
deduced from the dissociative diffusivity and solubility of Cu
222A 85S1
13.6
3.09
535-904
radiotracer, sectioning by ion-beam sputtering, dependence on hydrostatic pressure and doping
222A 85W 223 224 226
12
3.0
543-690
70
Ge/74Ge isotope heterostructure grown by molecular-beam epitaxy, SIMS, isotope interdiffusion
222B 95F2
3.05
798-846
radiotracer, D0 and Q recalculated from the data also given by [75s]
226
58V
no further specifications
226
63b
Si in Ge 0.24
Ge in Ge 222A 56L 57V
Sn in Ge 70 1.7·10−2
1.9
2
3.05
710-900
Gaussian-type broadening of implanted layer, RTA and furnace annealing, SIMS and RBS, vacancy mechanism
226
94K
8.4·102
3.26
555-930
diffusion from surface layer or gas phase, SIMS, vacancy mechanism
225 226
95F1
1.5·10
Lando lt -Bö rnst ein New Series III/33A
2-228
2 Diffusion in silicon, germanium and their alloys
D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
3.6
800
D0 calculated from given values of Q and D (800°C) = 2.0·10−14 cm2s–1
[Ref. p. 2-237
Fig.
Ref.
Pb in Ge 1.6·103
63b
2.3.1.5 Solute elements of group VA (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
1.2
2.4
650-900
pn-junction, parameters recalculated from Arrhenius plot
3.3·102 1.0·10−2
3.1 2.1
600-780 600-750
C0 ≈ (3-7)·1018 cm−3 : nearly intrinsic C0 ≈ (5-8)·1019 cm−3 : extrinsic 4-point probe + electrochemical sectioning
0.71
2.2
710-900
pn-junction, C0 = 3·1017- 1·1020 cm−3
52F
2.2
2.3
700-900
pn-junction, parameters recalculated from Arrhenius plot
54D
2.4
670-900
pn-junction and impedance measurements
2.9
800-900
pn-junction, parameters recalculated from Arrhenius plot, also grain boundary diffusion
59K
2.43
750-900
pn-junction, C0 (800°C) = 2·1017 cm−3
61A1
P in Ge 54D 227
78M
As in Ge
2.1 1.5·10
2
3
15
16
227
−3
55B
1.5
2.39
580-870
C0 = 5·10 -5·10 cm , capacitance measurements, pn-junction data of [60V] included
62W
5.0
2.5
750-850
pn-junction, correction for internal electric field, C0 ≤ 1017 cm−3
64N
10.3
2.49
700-790
pn-junction, GaAs layer as As source, C0 = 1·1019 cm−3
68I
0.71
2.2
710-905
pn-junction, C0 = 7.2·1017- 2·l020 cm−3
228
52F
4.2
2.4
600-900
pn-junction and radiotracer data, parameters recalculated from Arrhenius plot
228
54D
Sb in Ge
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [°C]
Remarks
700-900
pn-junction and impedance measurements
2-229
Fig.
Ref.
228
55B
228
56K
228
57M
Sb in Ge (cont.) 1.2
2.3
18
19
−3
1.4
2.3
750-925
radiotracer, C0 = 4·l0 - 4·10 cm , C0 increases with decreasing temperature
1.3
2.26
800-900
radiotracer, out-diffusion, Cbulk ≤ 2·1017cm−3 15
18
−3
646-928
dependence on Sb doping: 1.2·l0 -l.5·l0 cm , radiotracer technique, see also [63B]
58B
4.6·102
2.9
800-900
pn-junction, parameters recalculated from Arrhenius plot, also grain-boundary diffusion
59K
0.05
2.0
750-850
pn-junction, low surface concentration
60V
700-900
dependence on Al doping: 2.4·1014-3·1018 cm−3, various pn-junction techniques
61A2
146
2.86
700-880
pn-junction, parameter recalculated from Arrhenius plot, C0 ≈ 1·1019 cm−3
228
61F
6.3
2.5
750-900
radiotracer, effect of internal electric field studied, C0 < 1·1020 cm−3
228
64B1
450-900
anomalously high ion-drift mobility probably due to dislocations, autoradiography
64B2 228
64N
3.5
2.45
750-850
pn-junction, correction for internal electric field, C0 ≤ 1017 cm−3
2.2·10−1
2.18
720-900
radiotracer and electrical methods, doping dependence, electric field effect: [61L], C0 ≥ ni
65B
600-740
no effect of plastic deformation during diffusion, pn-junction
65C
3.2
2.43
700-855
radiotracer, C0 = 7.5·1018-2.6·1019 cm−3
228
67P
507
2.8
560-840
incremental sheet resistance, 4-point probe, C0 = 1·1016- 5·1018 cm−3
227 228
67W
21
2.08
650-850
radiotracer, enhanced diffusion due to dislocations
6.5
2.57
700-800
no further indications
70D 228
70S
Bi in Ge 3.3
2.5
Lando lt -Bö rnst ein New Series III/33A
estimated values
59r
2-230
2 Diffusion in silicon, germanium and their alloys
[Ref. p. 2-237
2.3.1.6 Solute elements of group VIA to group VIIIA (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
Group V1A
O in Ge 0.17
2.02
0.40
2.08
calculation on the basis of internal friction data [58S]
60H
285-760
stress-induced dichroism, infrared absorption, internal friction data from [58S] included
227
64C
920
D ≈ 10−9 cm2s−1
59T
920
D ≈ 1010 cm2s−1
59T
770-880 770-900
radiotracer, "skin" diffusion radiotracer, "slow" diffusion
800
D = 5·10−7 cm2s−1, radiotracer, "fast" diffusion
795-872
permeation measurements, mass spectrometry
S in Ge
Se in Ge
Te in Ge 2.0 5.6
2.82 2.43
227 229
62I 62K1
Group VIIIA
He in Ge 6.1·10−3 1.8·10
−3
0.69
0.608 527-857
heavy B doping, He produced by neutron activation of 10B or exposure to plasma, He release kinetics, mass spectrometry
1.2
gas release after implantation of radiotracer
230
56W 64L
Xe in Ge 5·10−6
250-980
210 230
70M
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
2 Diffusion in silicon, germanium and their alloys
2-231
2.3.2 Figures for 2.3
–4
10
Temperature T [°C] 500 400 300
900 700
–5
10
H [60F]
200
10
–6
Ge :X
10
–6
10
–7
10
–9
10
2 –1
Li [54F1]
–8
10
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
Ge :Li
a b
–8
10
–9
10
–10
10
Na [77S]
–10
10
–11
–12
10
–12
–13
10
–13
10
10 Be [61B]
–14
10
–14
1 2 3 4 5
–15
0.8
1.6 2.0 2.4 –3 –1 Inv. temp. 1/T [10 K ] Fig. 211. Ge:H, Li, Na, Be. Diffusion coefficient D of group IA (H, Li, Na) and group IIA (Be) elements in germanium vs. inverse temperature 1/T. The straight lines are data from the literature.
–4
–11
10
10
10
–100
–7
10
10
Temperature T [°C] 200 100 0 –50
500
–5
1.2
Temperature T [°C] 800
900
10
1
2
3 4 5 6 –3 –1 Inv. temp. 1/T [10 K ] Fig. 212. Ge:Li. Diffusion coefficient D of lithium vs. inverse temperature 1/T. Solid lines: a [53F], b [54F1]; 1: [66P], 2: [69S], 3: [72V], 4: [75K], 5: [76H]; dashed line: extrapolation of b.
700
8 6 4
Ge :X
2
Ni [54M]
2 –1
Diff.coeff. D [cm s ]
–5
10
8 6 4
Co [61W1]
2 –6
10
8 6
Fe [57B1]
4 2 –7
10
0.83
Lando lt -Bö rnst ein New Series III/33A
0.87
0.91 0.95 –3 –1 Inv.temp. 1/T [10 K ]
0.99
1.03
Fig. 213. Ge:Fe, Co, Ni. Diffusion coefficient D of group VIIIB elements in germanium vs. inverse temperature 1/T. The solid (Fe, Ni) and dashed (Co) lines are data from the literature.
2 Diffusion in silicon, germanium and their alloys
10
800
Temperature T [°C] 700
600
19
10
Cu (b)
–5
Ge :Cu
10
10
–3
–7
–5
10
–6
10
17
10
eq
10
Cu (a)
–8
10
–7
10
16
10
–9
10
–8
[54F2] [91B] [91B] [85S1] [91B]
–10
10
–11
10
600
Tm
Cu solubility Cs [cm ]
2 –1
18
Ge :X
Ag
–6
10 Diff.coeff. D [cm s ]
Temperature T [°C] 800 700
900
0.8
10
15
10
2 –1
900
–4
[Ref. p. 2-237
Eff.diff.coeff. Deff [cm s ]
2-232
eq
Cs Deff
Au 14
0.9
1.0 1.1 1.2 –3 –1 Inv. temp. 1/T [10 K ] Fig. 214. Ge:Cu, Ag, Au. Diffusion coefficient D of copper, silver and gold in germanium vs. inverse temperature 1/T as indicated. Data marked as Cu(a) and Cu(b) originate from virtually dislocation-free and dislocation-rich Ge single crystals, respectively, and are interpreted within the theory of the dissociative mechanism as the vacancy-limited and interstitialcopper-limited diffusivity of substitutional Cu [91B].
10
–9
10
0.8
0.9 1.0 1.1 1.2 –3 –1 Inv. temp. 1/T [10 K ] Fig. 215. Ge:Cu. Effective diffusion coefficient Deff and solubility Cseq of substitutional copper in dislocationfree germanium vs. inverse temperature 1/T. The slope of the dashed line corresponds to an activation energy of 1.55 eV. The product ½Deff Cseq yields values for the vacancy contribution to the tracer self-diffusion coefficient (see number 6 in Fig. 222A) [85S2].
16
4⋅10
Ge :Cu 2
T = 851 °C, t = 780 s –3
Cu conc. Cs [cm ]
16
10
8 6 4
T = 853 °C, t = 900 s 2
15
10
0
1
2 Depth x [mm]
3
4
Fig. 216. Ge:Cu. Concentration Cs of substitutional copper in germanium vs. depth x. Data result from spreading-resistance profiling of Ge single crystals with virtually low (triangles) or high (circles) dislocation density. Diffusion temperature T and time t are as indicated. The solid lines represent erfc-type fits based on a constant diffusivity [91B, 90S1].
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
2 Diffusion in silicon, germanium and their alloys
15
17
10
10 8
Ge :Ag
8 6
6 4
T = 870 °C, t = 990 s
2
–3
Au conc. Cs [cm ]
–3
Ag conc. Cs [cm ]
2
14
10
15
10 8 6 4 2
T = 869 °C, t = 1620 s
6
0
0.9 1.2 1.5 1.8 Depth x [mm] Fig. 217. Ge:Ag. Concentration Cs of substitutional silver in germanium vs. depth x. Data result from spreading-resistance profiling of Ge single crystals with an Ag diffusion source of the front surface and either a plain (circles) or a Au-deposited (triangles) back surface. Diffusion temperature and time are as indicated. Solid lines are erfc-type fits based on a constant diffusivity [91B].
–8 8 6 4
10
0.3
900
14 10 8 6 4
0.6
800
Temperature T [°C] 700 600
2
10
120 160 200 240 280 Depth x [µm] Fig. 218. Ge:Au. Concentration Cs of substitutional gold in germanium vs. depth x. Data originate from spreading-resistance measurements on low-dislocated Ge samples after diffusion treatments for temperature T and time t as indicated. The solid lines are best fits based on the complementary error function [91A, 91B].
500
–9
Ge :X Cd [60K]
–12
10
2 –1
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
600
Tl [62T] Zn [95G]
–13
10
–14
10
[55D]
2 –11
[91B]
–15
10
In [82D2]
B [67M] Ga [86S]
–16
10
8 6 4
Al [82D1]
–17
10
2 –12
1.0 1.1 1.2 1.3 –3 –1 Inv. temp. 1/T [10 K ] Fig. 219. Ge:Au. Diffusion coefficient D of gold in germanium vs. inverse temperature from various references as indicated. Data points result from spreading-resistance measurements on single crystals with low (triangles) or high (closed circles) dislocation density [91A, 91B].
Lando lt -Bö rnst ein New Series III/33A
Temperature T [°C] 700
–10
[91A]
8 6 4
0.8
800
10
–10
10
900
80
–11
2
10
40
10
10
10
0
10
[68G]
–9 8 6 4
T = 596 °C, t = 16.8 d
13
Ge :Au
2
T = 727 °C, t = 2 d
2
8
13
Ge :Au
16 10 8 6 4
4
4⋅10
2-233
0.9
–18
10
0.82
0.90
0.98 1.06 1.14 1.22 –3 –1 Inv. temp. 1/T [10 K ] Fig. 220. Ge:Zn, Cd, B, Al, Ga, In, Tl. Diffusion coefficient D of group IIB (Zn, Cd) and group IIIA (B, Al, Ga, In, Tl) elements in germanium vs. inverse temperature 1/T. The straight lines are data from the literature.
2-234
–10
10
2 Diffusion in silicon, germanium and their alloys
900
Temperature T [°C] 800
700
–11
10
Ge :Zn
–13
2 –1
[56K]
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
10
[54D] –13
10
–16
–17
–18
10 –15
0.85
0.90 0.95 1.00 1.05 1.10 –3 –1 Inv. temp. 1/T [10 K ] Fig. 221. Ge:Zn. Diffusion coefficient D of zinc in germanium vs. inverse temperature 1/T. Data originating from various authors as indicated were obtained from pn-junction depth [54D], radiotracer [56K] and spreading-resistance measurements [95G].
0.8
0.9
Ge :Ge
74
70
Ge
Ge
annealed
as grown
0.2
intrinsic
1.00 Norm. diff. coeff. D(n)/D(ni)
74
Ge( Ge) conc. C70(C74) [atomic fraction]
70
deduced
1.25
0.6
0
tracer
1.0 1.1 1.2 1.3 –3 –1 Inv. temp. 1/T [10 K ] Fig. 222A. Ge:Ge. Self-diffusion coefficient measured by radioactive and stable tracers or deduced from the solubility and diffusion/precipitation of copper vs. inverse temperature 1/T. 1: [56L]; 2: [61W2]; 3: [75C]; 4: [83V]; 5: [85W]; 6: [95F2] tracer; 7: [85S1]; 8: [58P] recalculated by [85S1].
Ge :Ge
0.4
1 2 3 4 5 6 7 8
–19
10
1.0 0.8
Tm
–15
10
–14
0.80
Ge :Ge
–14
10
10
500
10
10
[95G]
10
Temperature T [°C] 700 600
–12
10
–12
800
10
–11
10
900
[Ref. p. 2-237
0.75 0.50
0.25
100
200
300 400 500 600 Depth x [nm] Fig. 222B. Ge:Ge. Concentrations C70 (solid curve and closed circles) and C74 (dashed curve and open circles) of 70Ge and 74Ge, respectively in a germanium isotope heterostructure vs. depth x, as measured by SIMS. The curves (solid and dashed) represent the as-grown (not annealed) sample, whereas the symbols (open and closed) are the data taken from a diffusion-annealed (636 °C, 19.5 h) part of the same sample [95F2].
0.50 0.75 1.00 1.25 1.50 Norm. e conc. n/ni Fig. 223. Ge:Ge. Doping dependence of the selfdiffusion at T = 700C. The ratio of the tracer selfdiffusion coefficient in highly doped to that in intrinsic germanium D(n)/D(ni) vs. the ratio of the corresponding free-electron density n/ni. The dashed lines indicate the intrinsic case [85W].
0
0.25
Landolt -Börnst ein New Series III/33A
Ref. p. 2-237]
2 Diffusion in silicon, germanium and their alloys
–15
6
4⋅10
10
Ge :Ge
Ge :Sn
76
Ge
5
–15
10
10
T = 900 °C, t = 3600 s erfc
8
2 –1
Diff.coeff. D [cm s ]
2-235
4
10
Rel.intensity Irel
6
4
1 2 3 4
2
3
10
2
10
120 –16
10
0
1
3 4 5 6 7 Pressure p [kbar] Fig. 224. Ge:Ge. Pressure dependence of germanium self-diffusion for various types and degrees of doping at T = 700C. Tracer self-diffusion coefficient D vs. hydrostatic pressure p;. 1: Sb:3.1018 cm–3; 2: intrinsic; 3: Ga:3.1018 cm–3; 4: Ga:2.1019 cm–3 [85W].
2
900
–9
10
800
Temperature T [°C] 700 600
–10
1
6 8 10 12 Depth x [µm] Fig. 225. Ge:Sn. Relative intensity of detected tin atoms with mass number 120 in germanium vs. depth x. Data result from in-depth SIMS analysis of a Ge single crystal which was Sn-diffused via the gas phase for temperature T and time t as indicated. The SIMS signal of 76Ge was also recorded (upper line) [95F1].
500
–9
10
–15
10
2 –1
2 –1
Ge [85W] Sn [94K]
–14
Si [81R] Sn [95F1]
–16
10
–17
10
300
Ge :X
gas phase thin film
–18
O [64C]
–13
10
–14
10
–15
10
P [78M]
Sb [67W]
–16
10 10
–18
10 Ge [85W]
–19
1.3 1.0 1.1 1.2 –3 –1 Inv. temp. 1/T [10 K ] Fig. 226. Ge:Sn, Ge, Si. Diffusion coefficient D of tin, germanium and silicon in germanium vs. inverse temperature 1/T as indicated. Symbols represent data obtained by SIMS after Sn diffusion either from a thin surface layer or from the gas phase as indicated [95F1]. Lando lt -Bö rnst ein New Series III/33A
As [55B]
–17
10
0.8
–12
10
Sn [63B]
Diff.coeff. D [cm s ]
Sn [58V]
–12
Diff.coeff. D [cm s ]
Te [62I]
–11
10
10
Temperature T [°C] 700 600 500 400
900
–10
4
10
10
10
2
10
–11
–13
0
10
Ge :X
10
Sn
10
0.9
–19
10
–20
10
1.8 1.2 1.4 1.6 –3 –1 Inv. temp. 1/T [10 K ] Fig. 227. Ge:P, As, Sb, O, Te. Diffusion coefficient D of group VA (P, As, Sb) and group VIA (O, Te) elements in germanium vs. inverse temperature 1/T. The straight lines are data from the literature. 0.8
1.0
2-236
2 Diffusion in silicon, germanium and their alloys
3
7
19
10
5
–3
Tm = 937 °C 4
–11
10
8 6 4
1
2 8 6 4
2
–13
10
0.80
0.90 0.95 1.00 1.05 1.10 –3 –1 Inv. temp. 1/T [10 K ] Fig. 228. Ge:Sb. Diffusion coefficient D of antimony in germanium vs. inverse temperature 1/T. 1 [52F, 57M]; 2 [54D]; 3 [55B, 56K]; 4 [61F]; 5 [64B1, 64N]; 6 [67P]; 7 [67W]; 8 [70S].
–5
10
900
0.85
700
Temperature T [°C] 500 400
300
He [64L]
Ge :He Ge :Xe
–6
10
–7
10
He [56W]
–8
I
17
10
II III
10
8
2
18
10
16
6
–12
10
Ge :Te
20
10
Te conc. C [cm ]
2 –1
Diff.coeff. D [cm s ]
2
21
10
Ge :Sb
2 –10 10 8 6 4
Temperature T [°C] 800 700
900
–9 10 8 6 4
[Ref. p. 2-237
15
10
–5
–4
–3
–2
–1
1 10 10 10 Depth x [µm] Fig. 229. Ge:Te. Diffusion profile of tellurium in germanium for T = 800C and an annealing time of 52 h 15 min. Concentration C vs. penetration depth x. The roman figures indicate different regimes designated by "skin" (I), "slow" (II), and "fast" (III) diffusion [62I]. 10
10
10
10
–9
2 –1
Diff.coeff. D [cm s ]
10
–10
10
–11
10
–12
10
–13
10
–14
10
Xe [70M]
–15
10
–16
10
–17
10
–18
10
0.8
1.0
1.2 1.4 1.6 1.8 2.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 230. Ge:He, Xe. Diffusion coefficient D of group VIIIA elements in germanium vs. inverse temperature 1/T. The straight lines are data from the literature.
Landolt -Börnst ein New Series III/33A
2 Diffusion in silicon, germanium and their alloys
2-237
2.3.3 References for 2.3 2.3.3.1 Textbooks 63b 74t
Boltaks, B.I.: Diffusion in Semiconductors. London: Infosearch Ltd., 1963. Tuck, B.: Introduction to Diffusion in Semiconductors. Stevenage: Peter Peregrinus, 1974.
2.3.3.2 Data collections 70s 84l
89s
90s
Sharma, B.L.: Diffusion in Semiconductors, Clausthal-Zellerfeld: Trans. Tech. Publications, 1970. Langheinrich, W., Haberle, K.: Technology of Si, Ge, and SiC, in: Landolt-Börnstein, New Series, Vol. III/17c, Schulz, M., Weiss, H. (eds.), Berlin, Heidelberg, New York: Springer Verlag, 1984, p. 118. Stolwijk, N.A.: Diffusion of Impurities in Germanium: Impurities and Defects in Group IV Elements and III-V Compounds, in: Landolt-Börnstein, New Series, Vol. III/22b, Schulz, M. (ed.), Berlin: Springer Verlag, 1989, 207. Sharma, B.L.:Diffusion in Silicon and Germanium. Defect Diffus. Forum 70 (1990) 1.
2.3.3.3 Review papers 59r 68s 70g 73h 75s 78w 84f
87f
91f
92f
92g
Reiss, H., Fuller, C.S.: Diffusion Processes in Germanium and Silicon, in: Semiconductors, Chap. 6, Hannay, N.B. (ed.), New York: Reinhold, 1959, p. 222. Seeger, A., Chik, K.P.: Diffusion Mechanisms and Point Defects in Silicon and Germanium. Phys. Status Solidi 29 (1968) 455. Glasow, W.M., Sanshow, W.S.: Die Germanium- und Silizium-Zweistofflegierungen. Berlin: VEB Deutscher Verlag der Wissenschaften, 1970. Hu, S.M.: Diffusion in Silicon and Germanium, in: Atomic Diffusion in Semiconductors, Shaw, D. (ed.), London, New York: Plenum Press, 1973, p. 217. Shaw, D.: Self- and Impurity Diffusion in Ge and Si. Phys. Status Solidi (b) 72 (1975) 11. Willoughby, A.F.W.: Atomic Diffusion in Semiconductors. Rep. Prog. Phys. 41 (1978) 1665. Frank, W., Gösele, U., Mehrer, H., Seeger, A.: Diffusion in Silicon and Germanium, in: Diffusion in Crystalline Solids, Murch, G. (ed.), New York, London: Academic Press ,1984, p. 63. Frank, W., Stolwijk, N.A.: Diffusion Mechanisms and Thermal-equilibrium Defects in Silicon and Germanium. Mater. Sci. Forum 15-18 (1987) 369. Frank, W.: The Interplay of Solute- and Self-diffusion - a Key for Revealing Diffusion Mechanism in Silicon and Germanium. Defect Diffus. Forum 75 (1991) 121. Frank, W.: Diffusion in Crystalline Silicon and Germanium - The State-of-the-art in Brief, in: Crucial Issues in Semiconductor Materials and Processing Technologies, Coffa, S., Priolo, F., Rimini, E., Poate, J.M. (eds). NATO ASI Ser., Ser. E 222 (1992) 383. Gösele, U., Tan, T.Y.: Diffusion in Semiconductors - Unsolved Problems. Defect Diffus. Forum 83 (1992) 189.
Lando lt -Bö rnst ein New Series III/33A
2-238 93s
2 Diffusion in silicon, germanium and their alloys Stolwijk, N.A.: Atomic Transport in Semiconductors: Diffusion Mechanisms and Chemical Trends. Defect Diffus. Forum 95-98 (1993) 895.
2.3.3.4 Articles 52F 53F 54D 54F1 54F2 54M 55B 55D 55M 56F 56K 56L 56T 56W 57B1 57B2 57F 57M 57T 57V 57W 58B 58P 58S 58V 59K 59S 59T 60F 60H 60K 60M 60V 61A1 61A2 61B 61F 61L 61W1 61W2
Fuller, C.S: Phys. Rev. 86 (1952) 136. Fuller, C.S., Ditzenberger, J.A.: Phys. Rev. 91 (1953) 193. Dunlop jr., W.C.: Phys. Rev. 94 (1954) 1531. Fuller, C.S., Severiens, J.C.: Phys. Rev. 96 (1954) 225. Fuller, C.S., Struthers, J.D., Ditzenberger, J.A., Wolfstirn, K.B.: Phys. Rev. 93 (1954) 1182. van der Maesen, F., Brenkman, J.A.: Philips Res. Rep. 9 (1954) 225. Bösenberg, W.: Z. Naturforsch. (a) 10 (1955) 285. Dunlop jr., W.C.: Phys. Rev. 97 (1955) 614. van der Maesen, F., Brenkman, J.A.: J. Electrochem. Soc. 102 (1955) 229. Frank, F.C., Turnbull, D.: Phys. Rev. 104 (1956) 617. Kosenko, V.E.: Proc. Acad. Sci. USSR, Phys. Ser. (English Transl.) 20 (1956) 1399. Letaw jr., H., Portnoy, W.M., Slifkin, L.: Phys. Rev. 102 (1956) 636. Tweet, A.G., Gallagher, C.J.: Phys. Rev. 103 (1956) 828. van Wieringen, A., Warmoltz, N.: Physica 22 (1956) 849. Bugai, A.A., Kosenko, V.E., Miselyuk, E.G.: Sov. Phys. Tech. Phys. (English Transl.) 2 (1957) 183. Bugai, A.A., Kosenko, V.E., Miselyuk, E.G.: Sov. Phys. Tech. Phys. (English Transl.) 2 (1957) 1553. Fuller, C.S., Ditzenberger, J.A.: J. Appl. Phys. 28 (1957) 40. Miller, R.C., Smits, F.M.: Phys Rev. 107 (1957) 65. Tweet, A.G.: Phys. Rev. 106 (1957) 221. Valenta, M.W., Ramasastry, C.: Phys. Rev. 106 (1957) 73. Woodbury, H.H., Tyler, W.W.: Phys. Rev. 105 (1957) 84. Boltaks, B.I., Prokhorov, V.M., Novozhilova, L.I.: Sov. Phys. Tech. Phys. (English Transl.) 3 (1958) 921. Penning, P.: Phys. Rev. 110 (1958) 586. Southgate, P.D.: Phys. Rev. 110 (1958) 855. Valenta, M.W.: Ph. D. Thesis, Univ. Illinois 1958 (Univ. Microfilm 58-5509); Bull. Am.Phys. Soc. 2 (1958) 102. Karstensen, F.: Z. Naturforsch. (a) 14 (1959) 1031. Sturge, M.D.: Proc. Phys. Soc. 73 (1959) 297. Tyler, W.W.: J. Phys. Chem. Solids 8 (1959) 59. Frank, R.C., Thomas jr., J.E.: J. Phys. Chem. Solids 16 (1960) 144. Haas, C.: J. Phys. Chem. Solids 15 (1960) 108. Kosenko, V.E.: Sov. Phys. Solid State (English Transl.) 1 (1960) 1481. Miselyuk, E.G., Kosenko, V.E., Khomenko, L.A., Ignatkov, V.D.: Int. J. Appl. Radiat. Isot. 9 (1960) 192. Veloric, H.S., Greig, W.J.: RCA Rev. 21 (1960) 437. Albers, W.: Solid State Electron. 2 (1961) 85. Akimchenko, I.P., Milevskii, L.S.: Sov. Phys. Solid State (English Transl.) 2 (1961) 1891. Belyaev, Yu.I., Zhidkov, V.A.: Sov. Phys. Solid State (English Transl.) 3 (1961) 133. Fa, C., Zuleeg, R.: Solid State Electron. 3 (1961) 18. Lehovec, K., Slobodskoy, A.: Solid State Electron. 3 (1961) 45. Wei, L.Y.: J. Phys. Chem. Solids 18 (1961) 162. Widmer, H., Gunther-Mohr, G.R.: Helv. Phys. Acta 34 (1961) 635.
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2 Diffusion in silicon, germanium and their alloys 62I 62K1 62K2 62S 62T 62W 64B1 64B2 64C 64H 64N 64L 65B 65C 65P 66M 66P 67M 67P 67W 68G 68I 69S 70D 70M 70S 72H 72V 74G 75C 75K 76H 77S 78M 79H 80E 81R 82D1 82D2 82R 83V 84P 85S1 85S2 85W
2-239
Ignatkov, V.D., Kosenko, V.E.: Sov: Phys. Solid State (English Transl.) 4 (1962) 1193. Kosenko, V.E.: Sov. Phys. Solid State (English Transl.) 3 (1962) 1526. Kosenko, V.E.: Sov. Phys. Solid State (English Transl.) 4 (1962) 42. Sandulova, A.V., Dronyuk, M.I., Rybak, V.M.: Sov. Phys. Solid State (English Transl.) 3 (1962) 2128. Tagirov, V.I., Kuliev, A.A.: Sov. Phys. Solid State (English Transl.) 4 (1962) 196. Wölfle, R., Dorendorf, H.: Solid State Electron. 5 (1962) 98. Boltaks, B.E, Dzhafarov, T.D.: Sov. Phys. Solid State (English Transl.) 5 (1964) 2061. Badenko, L.A.: Sov. Phys. Solid State (English Transl.) 6 (1964) 762. Corbett, J.W., McDonald, R.S., Watkins, G.D.: J. Phys. Chem. Solids 25 (1964) 873. Hall, R.N., Racette, J.H.: J. Appl. Phys. 35 (1964) 379. Niedermayer, A.R.H.: Phys. Status Solidi 6 (1964) 741. Luther, L.C., Moore, W.J.: J. Chem. Phys. 41 (1964) 1018. Boltaks, B.I., Grabchak, V.P., Dzhafarov, T.D.: Sov. Phys. Solid State (English Transl.) 6 (1965) 2542. Calhoun, C.D., Heldt, L.A.: Acta Metall. 13 (1965) 932. Pantaleev, V.A.: Sov. Phys. Solid State (English Transl.) 7 (1965) 734. Millea, M.F.: J. Phys. Chem. Solids 27 (1966) 309. Pratt, B., Friedman, F.: J. Appl. Phys. 37 (1966) 1893. Meer, W., Pommerrenig, D.: Z. Angew. Phys. 23 (1967) 369. Pavlov, P.V.. Uskov, V.A.: Sov. Phys. Solid State (English Transl.) 8 (1967) 2377. Wills. G.N.: Solid State Electron. 10 (1967) 1. Gromova, O.N., Khodunova, K.M.: Fiz. Khirn. Obrab. Mater. 5 (1968) 150; Diffus. Defect. Data 3 (1969) 142. Isawa, N.: Jpn. J. Appl. Phys. 7 (1968) 81. Sher, A.H.: J. Appl. Phys. 40 (1969) 2600. Dudko, G.V., Marunina, N.I., Sukhov, G.V., Cherednichenko, D.I.: Sov. Phys. Solid State (English Transl.) 12 (1970) 1016. Matzke, Hj.: Radiat. Eff. 3 (1970) 93. Spiric, V.V., Damianovic, A.: Fizika (Alma-Ata) 2 (1970) 155. Huntley, F.A.: Philos. Mag. 26 (1972) 1047. Vanfleet, H.B., Decker, D.L., Curtin, H.R.: Phys. Rev. B 5 (1972) 4849. Goncharov, L.A., Chevleishvili, N.G.: Inorg. Mater. (English Transl.) 10 (1974) 540. Campbell, D.R.: Phys. Rev. B 12 (1975) 2318. Kastal'sku, A.A., Tashpulatov, B.M.: Sov. Phys. Solid State (English Transl.) 16 (1975) 1803. Hufschmidt, M., Moller, W., Pfeiffer, T.: Vak.-Tech. 25 (1976) 206. Stojic, M., Spiric, V., Kostoski, D.: Inst. Phys. Conf. Ser. 31 (1977) 304. Matsumoto, S., Niimi, T.: J. Electrochem. Soc. 125 (1978) 1307. Ho, L.T.: Appl. Phys. Lett. 35 (1979) 409. Edelin, G.: Phys. Status Solidi (b) 98 (1980) 699. Räisänen, J., Hirvonen, J., Anttila, A.: Solid State Electron. 24 (1981) 333. Dorner, P., Gust, W., Lodding, A., Odelius, H., Predel, B.: Acta Metall. 30 (1982) 941. Dorner, P., Gust, W., Lodding, A., Odelius, H., Predel, B., Roll, U.: Z. Metallkd. 73 (1982) 325. Räisänen, J.: Solid State Electron. 25 (1982) 49. Vogel, G., Hettich, G., Mehrer, H.: J. Phys. C 16 (1983) 6197. Pearton, S.J., Kahn, J.M., Hansen, W.L., Haller, E.E.: J. Appl. Phys. 55 (1984) 1464. Stolwijk, N.A., Frank, W., Hölzl, J., Pearton, S.J., Haller, E.E.: J. Appl. Phys. 57 (1985) 5211. Stolwijk, N.A., Frank, W.: Proc. 13th Int. Conf. Defects in Semiconductors, Kimerling, L.C., Parsey jr., J.M. (eds.), Warrendale, PA: The Metallurgical Soc. AIME, 1985, p. 285. Werner, M., Mehrer, H., Hochheimer, H.D.: Phys. Rev. B 32 (1985) 3930.
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2-240 86S 90S1 90S2 91A 91B 92D 94K 95F1 95F2 95G
2 Diffusion in silicon, germanium and their alloys Södervall, U., Odelius, H., Lodding, A., Roll, U., Predel, B., Gust, W., Dorner, P.: Philos. Mag. A 54 (1986) 539. Stolwijk, N.A., Wenwer, F., Bracht, H., Mehrer, H.: Diffusion in Materials, Laskar, A.L., et al. (eds.), The Netherlands: Kluwer Academic Publishers, 1990, p. 297. Stolwijk, N.A.: Phys. Status Solidi (b) 157 (1990) 107. Almazouzi, A., Bernardini, J., Moya, E.G, Bracht, H., Stolwijk, N.A., Mehrer, H.: J. Appl. Phys. 70 (1991) 1345. Bracht, H., Stolwijk, N.A., Mehrer, H.: Phys. Rev. B 43 (1991) 14465. Demirel, A.L., Strite, S., Agarwal, A., Ünlü, M.S., Morkoc, H., Rockett, A.: J. Vac. Sci. Technol. B 10 (1992) 664. Kringhøj, P., Elliman, R.G.: Appl. Phys. Lett. 65 (1994) 324. Friesel, M., Södervall, U., Gust, W.: J .Appl. Phys. 78 (1995) 1. Fuchs, H.D., Walukiewicz, W., Haller, E.E., Dondl, W., Schorer, R., Abstreiter, G., Rudnev, A.I., Tikhomirov, A.V., Ozhogin, V.I.: Phys. Rev. B 51 (1995) 16817. Giese, A.: Diploma Thesis, University of Münster, 1995.
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
2 Diffusion in silicon, germanium and their alloys
2-241
2.4 Diffusion in silicon-germanium alloys 2.4.1 Tables for 2.4 ((See Figs. 231-249, p. 249) (1 eV = 96.485 kJ/mol) D0 [cm2s−1]
Q [eV]
T-range [°C]
Remarks
Fig.
Ref.
Self-diffusion in SiGe bulk crystals Ge in SiGe 1.54·103 4.0·102 1.1·102 0.43 1.0 33 11
4.65 4.25 3.8 3.1 2.9 3.0 3.0
1200-1381 1155-1302 1077-1252 968-1151 856-1040 820-1024 731-916
intrinsic diffusivity in Si intrinsic diffusivity in Si0.898Ge0.102 intrinsic diffusivity in Si0.776Ge0.224 intrinsic diffusivity in Si0.692Ge0.308 intrinsic diffusivity in Si0.446Ge0.554 intrinsic diffusivity in Si0.223Ge0.777 intrinsic diffusivity in Ge, see [61Wid1] CZ-Si single crystals and Si1-xGex polycrystals (10 grains/cm2), radiotracer 71Ge, mechanical sectioning, vacancy mechanism up to about 70 at% Si and interstitialcy mechanism above 70 at% Si proposed
231 232
74Vay1 75Vay1
34 2.2·103 2.0·103
3.8 4.2 4.3
1077-1252 1142-1252 1077-1252
intrinsic diffusivity in Si0.80Ge0.20 DGe in B-doped (2·1019 cm−3 ) Si0.80Ge0.20 DGe in P-doped (2·1019 cm−3 ) Si0.80Ge0.20 intrinsic and doped polycrystalline Si0.80Ge0.20 , radiotracer 71Ge, mechanical sectioning, DGe enhanced for B- and P-doping at T ≥ 1175 oC, interstitialcy mechanism
231 232
75Vay1
233
85Bea1
Interdiffusion in Si/Ge or SiGe/Si superlattices (SL) 3·104
5.0
Lando lt -Bö rnst ein New Series III/33A
800-1050
1.6 nm Ge layer on Si capped with 10 nm Si, 1.6-50 nm thick strained Si1-xGex (0.2 ≤ x ≤ 1) or multiple SiGe/Si layers grown by MBE on Si, Si cap, furnace annealing and RTA, RBS, interdiffusion increases with increasing Ge content, strain reduces Q by about 0.6x eV, Q for the 1.6 nm Ge layer in Si equals value for Ge diffusion in Si
800
DSi ≈ 2·10−18 cm2s−1 in Ge DGe ≈ 10−19 cm2s−1 in Si 0.2 µm thick short-period strained Si (12 ML) / Ge (8 ML) SL grown by MBE at 350 oC on 20 nm Si0.4Ge0.6 , Raman spectroscopy, diffusion of Si into Ge for T > 600 oC
88Bru1
2-242
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [°C]
Remarks
[Ref. p. 2-256
Fig.
Ref.
Interdiffusion in Si/Ge or SiGe/Si superlattices (SL) (cont.) 6.4·10−4
7.43·102 6.75·102
3.1
4.4 4.4
640-782
symmetrically strained Ge/Si SL grown by MBE on Ge0.4Si0.6 , SL periodicity 3.3 nm, effective Ge fraction of the SL 40 at.%, X-ray diffraction, vacancy mechanism proposed
89Cha1
825-975
10 nm thick strained Si0.8Ge0.2 grown by MBE at 500 oC on 20 nm Si, 10 nm Si cap, RBS, interdiffusion equals and exceeds DGe in Si given by [73Vay1] for T > 925 oC and T < 925 oC, respectively, interdiffusion enhanced by elastic strain
89Hol1
900
two periods of Si0.88Ge0.12 (50 nm) / Si (50 nm) or six periods of Si0.88Ge0.12 (190 nm) / Si (100 nm) grown by MBE at 550 oC on 50 nm Si, RBS, TEM, strain relaxation by enhanced interdiffusion or mainly by dislocation multiplication
89Iye1
700-880 700-880
strain-dependent interdiffusion coefficient bulk interdiffusion coefficient strained SL with 60 periods of Si0.65Ge0.35 (4 nm) / Si (12 nm) grown by MBE at 530 oC on 150 nm Si, X-ray diffraction, initial interdiffusion enhancement attributed to nonequilibrium defects, composition gradients and coherency strain effects considered
233
90Pro1
short-period (< 1.5 nm) strained Si/Ge SL short-period (3.7 nm) strained Si/Ge SL Si/Ge SL grown by MBE on various Si1-xGex (0 ≤ x ≤ 1) buffers at 350 oC and 400 oC, 5 nm Si cap, X-ray diffraction, initially enhanced interdiffusion possibly caused by strain and compositions gradients, high Q due to Si diffusion into Ge, vacancy mechanism proposed
234
90Bar1
640-985
symmetrically strained Ge/Si SL grown by MBE on Ge0.4Si0.6 , SL periodicity 3.3 nm, effective Ge fraction of the SL 40 at.%, furnace annealing and RTA, X-ray diffraction, vacancy mechanism proposed
233
90Cha1
850-1010
50 nm strained Si1-xGex layers (x = 0.07, 0.17, 0.33) grown by MBE on 100 nm Si at 560 oC, 50 nm Si cap, in situ RBS during resistance heating, interdiffusion in the tail of Ge profiles comparable with DGe in Si given by [74Vay1], higher interdiffusion inside the SiGe layer, strain relaxation due to interdiffusion
235
90Wal1 90IJz1 89Wal1
0.5-1.5 550-700 2.5 600 & 700
1.4·10−3
3.1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [°C]
Remarks
2-243
Fig.
Ref.
Interdiffusion in Si/Ge or SiGe/Si superlattices (SL) (cont.) < 657
short-period strained Si/Ge SL grown by MBE at about 300 oC, Raman spectroscopy, interdiffusion decreases with increasing Si concentration, no influence of strain observed, SL with less abrupt interfaces more stable against heat treatment
91Fri1
4.5·103 14
4.6 3.9
900 900
asymmetrically strained SL (ASL) symmetrically strained SL (SSL) 20 periods of Si0.7Ge0.4 (7 nm) / Si (14 nm) grown by MBE on 200 nm Si (ASL structure) or on 400 nm Si0.8Ge0.2 (SSL structure) at 490 oC, X-ray diffraction, Raman spectroscopy, external stress experiments confirm enhanced interdiffusion in SSL compared to ASL, enhanced Ge diffusion into Si layers under tensile stress, no temperature range indicated
236
92Pro1
3.4 20.4 0.4 1.3 4.2 3.5·102 2.8·102 16 4
4.0 4.1 3.6 3.7 3.8 4.5 4.4 4.0 3.7
960-1125 950-1125 930-1075 930-1075 900-1075 1000-1125 975-1100 930-1075 930-1050
asymmetrically strained SL (ASL), x = 0.20 ASL, x = 0.27 ASL, x = 0.45 ASL, x = 0.63 ASL, x = 0.70 symmetrically strained SL (SSL), x = 0.20, y = 0.18 SSL, x = 0.28, y = 0.23, D0 recalculated SSL, x = 0.46, y = 0.24 SSL, x = 0.68, y = 0.37 5 periods of Si (10 nm)/ Si1-xGex (10 nm) grown by MBE on 100 nm Si (ASL structure) or on 600 nm Si1-yGey (SSL structure) at 550 oC, RTA, RBS, interdiffusion increases with increasing Ge concentration both in ASL and SSL, no significant influence of strain or dislocations on Q and D0 observed, interstitialcy mechanism suggested for SSL
237 238
92Hol1 91Hol1
700
15 periods of strained Si (205.2 nm) / Si55Ge45 (4.65 nm) grown by MBE at 450-500 oC and 50 periods of Si (12 ML) / Ge (2 ML) grown at 350 oC, RTA, X-ray reflectometry, initially strain-enhanced and composition-dependent interdiffusion, interdiffusion smaller than DGe deduced from [74Vay1], sharp interfaces increase SL thermal stability
93Bar1
600
Si (12 ML) / Ge (12 ML) and Si (19 ML) / Ge (9 ML) SL amorphized by As implantation, Raman spectroscopy, damage-induced interdiffusion more pronounced in Si (12 ML) / Ge (12 ML)
93Det1
Lando lt -Bö rnst ein New Series III/33A
233
2-244
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
T-range [°C]
Remarks
[Ref. p. 2-256
Fig.
Ref.
Interdiffusion in Si/Ge or SiGe/Si superlattices (SL) (cont.) 1.0·10−6
2.47
800-900
strained Si0.84Ge0.16 / Si quantum wells of width 7.3 nm grown by MBE at 700 oC on Si, photoluminescence spectroscopy, no strain relaxation by formation of misfit dislocations, Q representative for the initial stage of interdiffusion, D0 recalculated
233
93Sun1
900-1050
20-120 nm compressively strained Si1-xGex (x = 0.1- 0.3) grown by CVD or MBE on a Si buffer, Si cap, furnace annealing or RTA, X-ray diffraction, SIMS, interdiffusion increases exponentially with Ge content, Q decreases linear with x, strain effects due to elastic relaxation of the lattice around native point defects, vacancy mechanism
240
94Cow1
86.7 0.31
4.58 5.36
993 & 1006 interdiffusion via neutral vacancies 993 & 1006 interdiffusion via doubly negatively charged vacancies 62 nm thick strained Si0.75Ge0.25 grown by MBE on 100 nm Si, 100 nm Si cap, X-ray diffraction, SIMS, nonlinear dependence of interdiffusion on Ge content deduced
0.7 2·10−10
3.94 1.78
800-900 760-880
symmetrically strained Si (19 ML) / Ge (9 ML) symmetrically strained Si (12 ML) / Ge (12 ML) 33 periods of Si/Ge grown by MBE at 350 oC on a buffer layer, capping layers, Raman spectroscopy, proposes diffusion jumps to be released by electronic transitions
650-800
5 periods of strained Si (30 nm) / Si1-xGex (5.8 nm) (x = 0.41, 0.56) grown by MBE on Si at 450 oC, heat treatment after pre-annealing at 665 oC, photocurrent spectroscopy, interdiffusion increases with increasing Ge content, D0 calculated by taking into account data for Q given by [74Vay1]
95Gai1
1050
interdiffusion coefficient D ≈ 1.1·10−14 cm2s−1 16 nm and 32 nm thick strained Si0.85Ge0.15 layers grown by CVD on Si at 800 oC, Si cap, RTA, photoluminescence spectroscopy, blue shift of SiGe no-phonon recombination line correlates with the degree of interdiffusion
95Sou1
0.2
94Zau1
233
95Det1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
T-range [°C]
Remarks
2-245
Fig.
Ref.
239
96Cow1
Interdiffusion in Si/Ge or SiGe/Si superlattices (SL) (cont.) 875
compressively strained Si1-xGex (x ≤ 0.3) grown by CVD or MBE on Si, Si cap, Si/SiGe/Si/SiGe structures with unstrained Si1-xGex grown on a graded SiGe buffer, annealing in N2 or O2, SIMS, interdiffusion in strained SiGe higher than in unstrained SiGe and retarded under oxidizing conditions, evaluates the contribution of strain to interdiffusion mediated by the vacancy and interstitialcy mechanism, strain effects due to elastic relaxation proposed
Foreign-atom diffusion in Si1-xGex alloys, Si/Ge, or SiGe/Si superlattices (SL) Co in SiGe 850
5 nm strained Si between two Si0.8Ge0.2 (40 nm, 80 nm) layers grown by MBE on 1200 nm Si, 5 nm Si cap, also SiGe synthesized by annealing of Ge-implanted Si, Co implantation, SIMS, X-ray diffraction, RBS, Co diffusion out of the SiGe layer, Co precipitation at SiGe/Si and Si/Si substrate interfaces
91Dek1
600 & 750
layers of 300 nm Si, 300 nm Ge and 10-34 nm Ni deposited on oxidized Si substrates by electron gun evaporation, RBS, X-ray diffraction, interdiffusion of polycrystalline Ge and Si films induced by Ni diffusion, interdiffusion more pronounced for Ni/Ge/Si than for Ni/Si/Ge structures
86Pai1
800-1050
intrinsic diffusivity of B in relaxed Si0.7Ge0.3 10 µm thick B-doped (1015 cm−3) Si0.7Ge0.3 grown by CVD on Si, B implantation, SIMS, vacancy and interstitialcy mechanism suggested
Ni in SiGe
B in SiGe 3.6·10−7
1.79
Lando lt -Bö rnst ein New Series III/33A
241
92Mat1
2-246
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-256
T-range [°C]
Remarks
Fig.
Ref.
860
D0 = 3.3·10−17 cm2s−1, diffusion via neutral defects D+ = 3.3·10−18 cm2s−1, diffusion via singly positively charged defects 0.6 nm thick strained Si0.83Ge0.17 with a 0.2 nm B-doped mid-layer grown by CVD on Si at 625 oC, 0.6 nm Si cap, SIMS, RBS, DB smaller in strained SiGe than in Si layers, applies standard B-diffusion model taken from Si
242
93Kuo1
B in SiGe (cont.)
1.44·103
4.4
850-1000
intrinsic diffusivity of B in strained Si0.7Ge0.3 15 nm thick Si0.7Ge0.3 with a 5 nm B-doped midlayer grown by CVD at 630 oC on 400 nm B-doped Si, B-doped Si cap, 5 nm B-doped regions in the centre of Si1-xGex (x = 0.1, 0.2, 0.3, 0.4, 0.5) layers separated by 50 nm intrinsic Si grown by MBE at 500 oC, SIMS, DB smaller in strained SiGe compared to unstrained Si and retarded with increasing Ge content, reduced DB attributed to changes in point defect concentrations caused by band-gap narrowing
241 243
93Mor1
2.31·10−5 1.16·10−5
2.27 2.27
900-1025 900-1025
intrinsic diffusivity of B in strained Si0.95Ge0.05 intrinsic diffusivity of B in strained Si0.90Ge0.10 0.8 nm thick Si0.95Ge0.05 or 0.45 nm Si0.90Ge0.10 with an initial 0.1 nm B-doped layer grown by CVD on Si, 100 nm Si cap, RTA, SIMS, DB retarded in SiGe compared to Si, applies diffusion model for heterostructures given by [92Hu1]
241
93Loe1
0.58
3.55
evaluation of DB data given by [93Mor1], retardation of DB linearly dependent on compressive strain, Q increases by 17 eV per unit of relative strain, diffusion mainly via interstitialcy mechanism
94Cow1
850
about 40 nm thick strained B-doped Si1-xGex (x = 0.20, 0.25) grown by CVD at 625 oC between 5-15 nm thick intrinsic Si1-xGex layers on Si, Si cap, As implantation, RTA, implant-damage enhanced DB, enhancement reduced by short laser annealing or O concentrations of about 1020 cm−3
95Gha1
900-1000
intrinsic diffusivity of B in strained Si0.7Ge0.3 350 nm thick B-implanted Si0.7Ge0.3 grown by CVD on Si at 650 oC, SIMS, DB in SiGe faster than in Si
241
95Gri1
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
D0 [cm2s−1]
Q [eV]
2 Diffusion in silicon, germanium and their alloys
2-247
T-range [°C]
Remarks
Fig.
Ref.
800
20 nm thick B-doped Si1-xGex grown by CVD between 20 nm intrinsic Si1-xGex layers (x = 0 or 0.10, 0.20) on relaxed Si1-yGey (y = 0 or 0.10, 0.15, 0.20) with a linearly graded Si1-y'Gey' (y' = 0 to y) buffer beneath, Si1-yGey cap, strain adjustment by choice of y, SIMS, RBS, DB in SiGe decreases with increasing Ge content, weak influence of strain on DB
244
95Kuo1
800
DB = 1.7·10−17cm2s−1 , intrinsic diffusivity of B in strained Si0.903Ge0.097 DB = 1.2·10−17cm2s−1 , intrinsic diffusivity of B in strained Si0.82Ge0.18 20 nm thick B-doped Si1-xGex grown by CVD between 20 nm undoped Si1-xGex layers, Si cap, annealing in Ar or O2, SIMS, oxidation-enhanced DB, predominance of interstitialcy mechanism
245
95Kuo2
800-1050
intrinsic diffusivity of P in relaxed Si0.7Ge0.3 10 µm thick B-doped (1015 cm−3) Si0.7Ge0.3 grown by CVD on Si, P implantation, SIMS, vacancy and interstitialcy mechanism proposed
241
91Mat1 92Mat1
900
DSb ≈ 3.5·10−15 cm2s−1 in strained Si0.91Ge0.09, 20 nm thick Sb-doped Si1-xGex between 45 nm undoped Si1-xGex layers grown by MBE on 100 nm Si, Si cap, SIMS, DSb higher in SiGe than in Si, higher vacancy mobility and/or vacancy concentration in SiGe proposed
900-1030
1µm thick relaxed Si0.91Ge0.09 with a thin Sb-doped layer below the surface grown by MBE on compositionally graded SiGe, 200 nm thick strained Si0.91Ge0.09 with a Sb-doped layer in the centre grown on Si, 100 nm Si cap, SIMS, DSb in relaxed SiGe enhanced compared to bulk Si, DSb in compressively strained SiGe enhanced compared to relaxed SiGe, Q decreases by 13 eV per unit of relative strain, vacancy mechanism
B in SiGe (cont.)
P in SiGe 3.7·10−7
1.62
Sb in SiGe
Lando lt -Bö rnst ein New Series III/33A
95Pai1
246 247
96Kri1
2-248
D0 [cm2s−1]
2 Diffusion in silicon, germanium and their alloys
Q [eV]
[Ref. p. 2-256
T-range [°C]
Remarks
Fig.
Ref.
850-1028 850-1028 850-1028 850-1028 729-880
intrinsic diffusivity of Sb in relaxed Si intrinsic diffusivity of Sb in relaxed Si0.9Ge0.1 intrinsic diffusivity of Sb in relaxed Si0.8Ge0.2 intrinsic diffusivity of Sb in relaxed Si0.7Ge0.3 intrinsic diffusivity of Sb in relaxed Si0.5Ge0.5 Si1-xGex with a 11-50 nm thick Sb layer below the surface grown by MBE on compositionally graded SiGe, SIMS, DSb increases with increasing Ge content, x2 dependence of Q observed, vacancy mechanism
248 249
96Nyl1
Sb in SiGe (cont.) 2.0·101 4·101 1.3·102 8·101 4.2·101
4.08 4.07 4.07 3.89 3.63
Special effects related to SiGe layers 900
50 nm B-doped Si covered with 100 nm Si and 5 nm Si0.5Ge0.5 by CVD, annealing under oxidizing conditions, SIMS, thin SiGe layer suppresses oxidation-enhanced DB in Si
89Gou1
950
70 nm thick strained Si0.9Ge0.1 grown by CVD on Si at 550 oC followed by 50 nm Si, atop 200 nm thick polycrystalline B-, P-, or As implanted Si, SiO2 cap, SIMS, P and As concentration decrease and B concentration increases within SiGe compared to the Si layer
91Hu1
850
variously thick strained Si1-xGex layers grown on intrinsic/B-doped/intrinsic Si structures, Si cap, annealing in Ar or O2, SIMS, oxidation-enhanced DB in Si not affected by Si1-xGex layer
95Kuo2
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
2 Diffusion in silicon, germanium and their alloys
2-249
2.4.2 Figures for 2.4
–10 10 8 6 4
Temperature T [°C] 1000
1200
800
5.0
Si1–xGex :Ge Activity energy Q [eV]
2 –12 8 6 4 2 –13
10
b a
8 6 4
g
d c e
2.6
0.7
0.4 0.6 0.8 1.0 Ge molar fraction x Fig. 232. SiGe:Ge. Activation energy Q of germanium diffusion in polycrystalline Si1-xGex vs. molar Ge fraction x of the alloy [74Vay1, 75Vay1].
Fig. 233. SiGe:Interdiffusion. Interdiffusion coefficient D for asymmetrically (ASL) and symmetrically (SSL) strained Ge/Si or Si1-xGex/Si superlattices vs. inverse temperature 1/T. Data from [85Bea1], [90Pro1] and [93Sun1] show diffusivities for ASL of Ge/Si, Si0.65Ge0.35/Si and Si0.84Ge0.16/Si, respectively. Data from [90Cha1] and [95Det1] represent diffusivities for SSL of Ge/Si and Si(19 ML))/Ge(9 ML) (a) or Si(12 ML)/Ge(12 ML) (b), respectively. Data from [92Hol1] represent diffusivities for Si0.54Ge0.46/Si SSL.
0
–14
10
–15
10
0.2
1000
900
Temperature T [°C] 800
700
Si1–xGex /Si
[92Hol1]
–16
2 –1
0.8 0.9 1.0 –3 –1 Inv. temp. 1/T [10 K ] Fig. 231. SiGe:Ge. Diffusion coefficient D of germanium in polycrystalline Si1-xGex for x = 0 (a), 0.102 (b), 0.20 (c), 0.224 (d), 0.308 (e), 0.554 (f), 0.777 (g) and 1.0 (h) vs. inverse temperature 1/T. Solid lines show intrinsic Ge diffusivities. Data marked with a to g are from [74Vay1, 75Vay1] and show enhanced Ge diffusivities with increasing Ge concentration. Data marked with h represent DGe in pure Ge given by [61Wid1]. Dashed and dotted lines, respectively, show diffusivities of Ge in B- and P-doped Si0.80Ge0.20 given by [75Vay1].
Lando lt -Bö rnst ein New Series III/33A
3.4 3.0
–14
0.6
3.8
f
h
2
10
4.2
10
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
2 –11 10 8 6 4
10
Si1–xGex :Ge
4.6
[93Sun1]
[85Bea1]
–17
10
a [95Det1]
b
–18
10
[90Cha1] –19
10
[90Pro1]
–20
10
0.75
0.80
0.85 0.90 0.95 1.00 –3 –1 Inv. temp. 1/T [10 K ]
1.05
1.10
10
800
Temperature T [°C] 700 650 600
750
1 –18
2 –1
Diff.coeff. D [cm s ]
10
550
4
0.90
–16
10
–17
10
–21
x = 0.07 x = 0.17 x = 0.33
–18
10
–22
0.95
1.00 1.05 1.10 1.15 1.20 1.25 –3 –1 Inv. temp. 1/T [10 K ] Fig. 234. SiGe:Interdiffusion. Interdiffusion coefficient D given by [90Bar1] for short-period (≤ 1.5 nm) strained Si/Ge superlattices vs. inverse temperature 1/T. The solid lines represent diffusivities for superlattices of Si (7.9 ML)/Ge(2.3 ML) (4) and Si (6.6 ML)/Ge(2.0 ML) (3) grown on a Si buffer. Coarsely dashed lines represent diffusivities for superlattices of Si(5.3 ML)/Ge(3 ML) (6) and Si(6.1 ML)/Ge(4.7 ML) (5) grown on a Si0.4Ge0.6 buffer. Finely dashed lines represent diffusivities for superlattices of Si(2.1 ML)/Ge(7.1 ML) (2) and Si(2.6 ML)/Ge(6.3 ML) (1) grown on a Ge buffer.
800
Interdiffusion
–15
10
6
10
10
Temperature T [°C] 900 850
Si/Si1-xGex/Si
5
–20
10
1000
Si/Ge
3
–19
10
Interdiffusion
2
10
–14
[Ref. p. 2-256
2 –1
–17
2 Diffusion in silicon, germanium and their alloys
Diff.coeff. D [cm s ]
2-250
0.76
0.78
0.80 0.82 0.84 0.86 0.88 0.90 –3 –1 Inv. temp. 1/T [10 K ] Fig. 235. SiGe:Interdiffusion. Interdiffusion coefficient D for strained Si/Si1-xGex/Si superlattices (for various Ge concentrations) vs. inverse temperature 1/T. Full and open symbols represent diffusivities derived from the tail and the full width at half-maximum, respectively, of Ge profiles obtained by RBS. The data show a faster interdiffusion inside the SiGe layer [90Wal1].
0
Si1–xGex /Si Interdiffusion
Norm.intensity ln (I/I0)
– 0.2 – 0.4
Fig. 236. SiGe:Interdiffusion. Normalized x-ray intensity I of the first superlattice peak of an externally tensibly stressed and unstressed asymmetrically strained superlattice vs. time t of heat treatment at 900C. The intensity decay shows enhanced interdiffusion due to external stress [92Pro1].
– 0.6 – 0.8 – 1.0
tensibly stressed unstressed 0
40
80 120 Time t [min]
160
200
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
70
Energy E [MeV] 0.8 1.0
0.6
10
8 6
Interdiffusion
30
f
2
g
i
h
[92Hol1,91Hol1]
–14
2 –1
40
900
Si/Si1-xGex
4
before annealing after (T = 1025 °C t = 100 s)
50
2-251
Temperature T [°C] 1000
1100
–13
Si/Si0.73Ge0.27
60
Norm. yield
1.2
10
Diff.coeff. D [cm s ]
80
2 Diffusion in silicon, germanium and their alloys
8 6 4 2
–15
10
8 6
20
d
4
10 Si 0 300
400
2
Ge
500
600 700 800 900 Channel Fig. 237. SiGe:Interdiffusion. RBS spectrum of an asymmetrically strained 5 period Si/Si0.73Ge0.27 superlattice before (solid line) and after (dashed line) rapid thermal annealing at 1025C for 100 s. The decrease of the amplitude of the Si- and Ge-related oscillations show substantial interdiffusion [92Hol1].
a
b
c
e
–16
10
0.70
0.74
0.78 0.82 0.86 –3 –1 Inv. temp. 1/T [10 K ] Fig. 238. SiGe:Interdiffusion. Interdiffusion coefficient D for asymmetrically strained Si/Si1-xGex superlattices (ASL) with x = 0.20 (a), 0.27 (b), 0.45 (c), 0.63 (d), and 0.70 (e) (solid lines) and symmetrically strained superlattices (SSL) with x = 0.20 (f), 0.28 (g), 0.46 (h), and 0.68 (i) (dashed lines) vs. inverse temperature 1/T. Solid and dashed lines from [92Hol1, 91Hol1] show enhanced interdiffusion both in ASL and SSL with increasing Ge concentration, respectively. 22
2⋅10
22
10
Si/Si0.7Ge0.3/Si
8 6
Fig. 239. SiGe:Interdiffusion. Concentration C of germanium vs. depth x for an as-grown sample (dotted line) Si/Si0.7Ge0.3/Si layer and after subsequent annealing for 2 hours at 875 C in N2 (solid line) or oxidizing ambient (dashed line: 1% O2; long dashed line 100% O2). Profiles obtained by SIMS show retarded interdiffusion under oxidizing conditions [96Cow1].
Lando lt -Bö rnst ein New Series III/33A
N2
100 % O2
–3
Ge conc. C [cm ]
4 2
as grown
21
10
1 % O2
8 6 4 2
20
10
170
180
190
200 210 Depth x [nm]
220
230
2-252
2 Diffusion in silicon, germanium and their alloys
3
10
Si/Si1-xGex/Si 2
1
2 –1
Diff.coeff. D [cm s ]
Norm. diff. conc. D/D (s = 0)
Inter diff.
10
B
B [93Loe1]
P [91Mat1,92Mat1]
2 –14 8 6 4
10
a
2 –15 10 8 6 4
b
10
–2
10
10
B [93Mor1]
2 –17
– 0.04
– 0.08 – 0.12 – 0.16 – 0.20 Compressive strain s/kT Fig. 240. SiGe:Interdiffusion, B. Interdiffusion coefficients (upper data) and diffusion coefficients of boron (lower data), respectively, for Si/Si1-xGex/Si (x = 0.1-0.3) and Si0.7Ge0.3 superlattices vs. compressive strain s in units of kT. Both diffusivities D are normalized to the corresponding values in unstrained material. Data from [94Cow1] obtained after annealing of the Si/SiGe/Si structure at 900C (open circles), 950C (inverted triangles) and 1030C (triangles) show enhanced interdiffusion by compressive strain whereas the diffusivity of boron at 972C (full circles) given by [93Mor1] is retarded. The slopes of the solid lines reflect a decrease and an increase in the activation energy of interdiffusion and B diffusion under compressive strain, respectively [94Cow1].
0.82 0.86 0.90 0.94 –3 –1 Inv. temp. 1/T [10 K ] Fig. 241. SiGe:B,P. Diffusion coefficient D of boron and phosphorous in Si1-xGex vs. inverse temperature 1/T. The straight lines show data from the literature for intrinsic conditions. Data from [92Mat1] and [93Mor1, 95Gri1] show diffusivities of B in relaxed and strained Si0.7Ge0.3 , respectively. Data from [93Loe1] represent diffusivities of B in strained Si0.95Ge0.05 (a) and Si0.90Ge0.10 (b). Data from [91Mat1, 92Mat1] give diffusivities of P in relaxed Si0.7Ge0.3.
0.74
0.78
–15
2⋅10
–15
10
8 6 4
2 –1
Diff.coeff. D [cm s ]
0
Si :B
2 –16
10
Fig. 242. SiGe:B. Diffusion coefficient D of boron in epitaxially grown layers of Si and strained Si0.83Ge0.17 vs. B concentration. Data show a lower diffusivity of B in SiGe compared to Si as well as less enhancement of D with increasing B concentration [93Kuo1].
B [92Mat1] B [95Gri1]
2 –16 8 6 4
–1
10
800
Si1-xGex :B,P
2 –13 10 8 6 4
10
Temperature T [°C] 900
1000
–12 8 6 4
10
[Ref. p. 2-256
8 6
Si0.83Ge0.17 :B
4 2 –17
10
16
10
17
10
18
10 –3 B conc. C [cm ]
19
10
20
10
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
2 Diffusion in silicon, germanium and their alloys
2.5
15.0
Si1-yGey : B
12.5
–3 19
1.5 y = 0.5
0.4
0.3
0.2
0.1
1.0 0.5
Norm. diff. coeff. D/D (y = 0.5)
2.0 B conc. C [10 cm ]
2-253
10.0 7.5 5.0 2.5
0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0 Depth x [µm] Ge molar fraction y a b Fig. 243a, b. SiGe:B. (a): Concentration C of boron vs. depth x of a strained multilayer structure with different Ge concentration in each layer measured by SIMS before (dashed line) and after (solid line) annealing at 975C for 70 s. (b): Intrinsic diffusion coefficient D of boron in Si1–yGey normalized to its value for y = 0.5 vs. Ge content y. Data show a decrease of DB with increasing Ge content [93Mor1]. –16
2⋅10
(Si1-yGey/Si1-xGex) :B
(x = 0,y = 0)
–16
10 2 –1
Diff.coeff. D [cm s ]
8
Fig. 244. SiGe:B. Intrinsic diffusion coefficient D of boron in Si1-xGex grown on Si1-yGey substrates vs. strain s which is adjusted by the choice of the Ge content in the diffusion layer and the substrate indicated by (x, y). Data from [95Kuo1] show a decrease of D with increasing Ge content as well as weak influence of strain (s < 0: compression; s > 0: tension) on D in SiGe.
Lando lt -Bö rnst ein New Series III/33A
6
(0.11,0.10)
4
(0.115,0.195)
(0.10,0)
2
(0.21,0)
(0.225,0.105)
(0.21,0.185) (0.22,0.152)
–17
10
-1.0
-0.8
-0.6
-0.4 -0.2 Strain s [%]
0
0.2
0.4
2-254
2 Diffusion in silicon, germanium and their alloys
19
10
19
10
8 6
Si
4
Si0.82Ge0.18 : B
4
Si
Si0.82Ge0.18 : B
Si
2
–3
B conc. C [ cm ]
2
8 6
Si
–3
B conc. C [ cm ]
[Ref. p. 2-256
18
10
8 6
8 6
4
4
2
2
17
10
18
10
17
10 0.08 0.10 0.12 0.04 0.06 0.08 0.10 0.12 Depth x [µm] Depth x [µm] a b Fig. 245a, b. SiGe:B. Concentration C of boron vs. depth x in Si0.82Ge0.18 measured by SIMS before (closed circles) and after (open circles) annealing at 800 C for 540 min and 60 min under inert (a) and oxidizing (b) ambient, respectively. Solid line in (b) shows the profile calculated by applying a multiplicative enhancement factor of 10 to the intrinsic diffusivity that was obtained from fitting of the experimental profile (open circles) in (a) [95Kuo2]. 0.04
0.06
19
19
4⋅10
Si
2
Si0.91Ge0.09 : Sb
4⋅10
Si
2
19
Si
8
6
6
4
4
–3
2 18
10
8 6
2 18
10
8 6
4
4
17
17
10
10
2
2
16
2 ⋅10
Si0.91Ge0.09 : Sb
19
10
8
Sb conc. C [ cm ]
–3
Sb conc. C [ cm ]
10
Si
16
2 ⋅10 200 300 400 0 100 200 300 400 Depth x [nm] Depth x [nm] a b Fig. 246a, b. SiGe:Sb. Concentration C of antimony vs. depth x in relaxed (a) and compressively strained (b) Si0.91Ge0.09 measured by SIMS before (closed circles) and after (open circles) annealing at 1028C for 30 min. Solid lines represent the result of fitting of experimental profiles. Data show enhanced DSb in strained SiGe compared to relaxed SiGe [96Kri1]. 0
100
Landolt -Börnst ein New Series III/33A
Ref. p. 2-256]
2 Diffusion in silicon, germanium and their alloys
1000
–14
4⋅10
Temperature T [°C]
–13
10
Temperature T [°C] 900 800
1000
Si/Si1-xGex :Sb
Si0.91Ge0.09 : Sb
2 –14
10
900
–14
10
8 6
e 2 –1
2 –15 8 6 4 2 –16
Diff.coeff. D [cm s ]
2 –1
Diff.coeff. D [cm s ]
4
10
relaxed compress.strained
–15
10
d –16
10
c
10
b
8 6 –16
4 ⋅10
0.76
2-255
–17
0.80 0.82 0.84 0.86 0.88 –3 –1 Inv. temp. 1/T [10 K ] Fig. 247. SiGe:Sb. Diffusion coefficient D of antimony in relaxed and compressively strained Si0.91Ge0.09 vs. inverse temeprature 1/T. Data show enhanced DSb in strained SiGe compared to relaxed SiGe [96Kri1].
a
10
0.78
–18
10
0.76
0.80
0.84 0.88 0.92 0.96 1.00 –3 –1 Inv. temp. 1/T [10 K ] Fig. 248. SiGe:Sb. Diffusion coefficient D of antimony in relaxed Si1-xGex for x = 0 (a), 0.1 (b), 0.2 (c), 0.3 (d), and 0.5 (e) vs. inverse temperature 1/T. Data show enhancement of Sb diffusivity under intrinsic conditions with increasing Ge concentration [96Nyl1].
4.5
Si/Si1-xGex :Sb
Fig. 249. SiGe:Sb. Activation energy Q of antimony diffusion in relaxed Si1-xGex vs. the Ge concentration x of the Si-Ge alloy. Data from [96Nyl1] are well described by a quadratic composition dependence (dashed line) rather than by a linear interpolation (solid line) between the values for pure Si [96Nyl1] and Ge [90Sha1].
Lando lt -Bö rnst ein New Series III/33A
Activation energy Q [eV]
4.0 3.5
3.0 2.5 2.0
0
0.2
0.4 0.6 Ge molar fraction x
0.8
1.0
2-256
2 Diffusion in silicon, germanium and their alloys
2.4.3 References for 2.4 61Wid1 73Vay1 74Vay1 75Vay1 85Bea1
Widmer, H., Gunther-Mohr, G.R.: Helv. Phys. Acta 34 (1961) 635. McVay, G.L., DuCharme, A.R.: J. Appl. Phys. 44 (1973) 1409. McVay, G.L., DuCharme, A.R.: Phys. Rev. B 9 (1974) 627. McVay, G.L., DuCharme, A.R.: Inst. Phys. Conf. Ser. 23 (1975) 91. Bean, J.C., Fiory, A.T., Hull, R., Lynch, R.T.: Proc. 1st Int. Symp. on Si MBE, Bean, J.C. (ed.), Pennington NJ: The Electrochem. Soc., 1985, p. 385. 86Pai1 Pai, C.S., Marshall, E.D., Lau, S.S.: Thin Solid Films 136 (1986) 37. 88Bru1 Brugger, H., Friess, E., Abstreiter, G., Kasper, E., Kibbel, H.: Semicond. Sci. Technol. 3 (1988) 1166. 89Cha1 Chang, S.J., Wang, K.L., Bowman jr., R.C., Adams, P.M.: Appl. Phys. Lett. 54 (1989) 1253. 89Hol1 Holländer, B., Mantl, S., Stritzker, B., Jorke, H., Kasper, E.: J. Mater. Res. 4 (1989) 163. 89Iye1 Iyer, S.S., LeGoues, F.K.: J. Appl. Phys. 65 (1989) 4693. 89Gou1 LeGoues, F.K., Rosenberg, R., Meyerson, B.S.: Appl. Phys. Lett. 54 (1989) 751. 89Wal1 van de Walle, G.F.A., van Ijzendoorn, L.J., van Gorkum, A.A., van den Heuvel, R.A., Theunissen, A.M.L., Gravesteijn, D.J.: Thin Solid Films 183 (1989) 183. 90Bar1 Baribeau, J.-M., Pascual, R., Saimoto, S.: Appl. Phys. Lett. 57 (1990) 1502. 90Cha1 Chang, S.J., Arbet, V., Wang, K.L., Bowman jr., R.C., Adams, P.M., Nayak, D., Woo, J.C.S.: J. Electron. Mater. 19 (1990) 125. 90Ijz1 van Ijzendoorn, L.J., van de Walle, G.F.A., van Gorkum, A.A., Theunissen, A.M.L., van den Heuvel, R.A., Barrett, J.H.: Nucl. Instrum. Methods Phys. Res. Sect. B 50 (1990) 127. 90Pro1 Prokes, S.M., Wang, K.L.: Appl. Phys. Lett. 56 (1990) 2628. 90Wal1 van de Walle, G.F.A., van Ijzendoorn, L.J., van Gorkum, A.A., van den Heuvel, R.A., Theunissen, A.M.L.: Semicond. Sci. Technol. 5 (1990) 345. 91Dek1 Dekempeneer, E.H.A., Zalm, P.C., Vriezema, C.J., van den Heuvel, R.A.: J. Appl. Phys. 70 (1991) 4263. 91Fri1 Friess, E., Schorer, R., Eberl, K., Abstreiter, G.: J. Vac. Sci. Technol. B 9 (1991) 2045. 91Hol1 Holländer, B., Mantl, S., Stritzker, B., Butz, R.: Nucl. Instrum. Methods Phys. Res. Sect. B 59/60 (1991) 994. 91Hu1 Hu, S.M., Ahlgren, D.C., Ronsheim, P.A., Chu, J.O.: Phys. Rev. Lett. 67 (1991) 1450. 91Mat1 Mathiot, D., Dupuy, J.C.: Appl. Phys. Lett. 59 (1991) 93. 92Hol1 Holländer, B., Butz, R., Mantl, S.: Phys. Rev. B 46 (1992) 6975. 92Hu1 Hu, S.M.: Phys. Rev. B 45 (1992) 4498. 92Mat1 Mathiot, D., Dupuy, J.C.: Mater. Sci. Forum 83-87 (1992) 1303. 92Pro1 Prokes, S.M., Glembocki, O.J., Godbey, D.J.: Appl. Phys. Lett. 60 (1992) 1087. 93Bar1 Baribeau, J.-M.: J. Appl. Phys. 74 (1993) 3805. 93Det1 Dettmer K., Kessler, F.R., Freiman, W., Beserman, R., Khait, Yu.L.: Appl. Surf. Sci. 65/66 (1993) 501. 93Kuo1 Kuo, P., Hoyt, J.L., Gibbons, J.F., Turner, J.E., Jacowitz, R.D., Kamins, T.I.: Appl. Phys. Lett. 62 (1993) 612. 93Loe1 Loechelt, G.H., Tam, G., Steele, J.W., Knoch, L.K., Klein, K.M., Watanabe, J.K., Christiansen, J.W.: J. Appl. Phys. 74 (1993) 5520. 93Mor1 Moriya, N., Feldman, L.C., Luftman, H.S., King, C.A., Bevk, J., Freer, B.: Phys. Rev. Lett. 71 (1993) 883. 93Sun1 Sunamura, H., Fukatsu, S., Usami, N., Shiraki, Y.: Appl. Phys. Lett. 63 (1993) 1651. 94Cow1 Cowern, N.E.B., Zalm, P.C., van der Sluis, P., Gravesteijn, D.J., de Boer, W.B.: Phys. Rev. Lett. 72 (1994) 2585. 94Zau1 Zaumseil, P., Jagdhold, U., Krüger, D.: J. Appl. Phys. 76 (1994) 2191. 95Det1 Dettmer, K., Freiman, W., Levy, M., Khait, Yu.L., Beserman, R.: Appl. Phys. Lett. 66 (1995) 2376. Landolt -Bö rnst ein New Series III/33A
2 Diffusion in silicon, germanium and their alloys 95Gai1
2-257
Gail, M., Brunner, J., Nützel, J., Abstreiter, G., Engvali, J., Olajos, J., Grimmeiss, H.: Semicond. Sci. Technol. 10 (1995) 319. 95Gha1 Ghani, T., Hoyt, J.L., Mc Carthy, A.M., Gibbons, J.F.: J. Electron. Mater. 24 (1995) 999. 95Gri1 Grider, D.T., Öztürk, M.C., Ashburn, S.P., Wortman, J.J., Harris, G., Maher, D.: J. Electron. Mater. 24 (1995) 1369. 95Kuo1 Kuo, P., Hoyt, J.L., Gibbons, J.F., Turner, J.E., Lefforge, D.: Appl. Phys. Lett. 66 (1995) 580. 95Kuo2 Kuo, P., Hoyt, J.L., Gibbons, J.F., Turner, J.E., Lefforge, D.: Appl. Phys. Lett. 67 (1995) 706. 95Pai1 Paine, A.D.N., Morooka, M., Willoughby, A.F.W., Bonar, J.M., Phillips, P., Dowsett, M.G., Cooke, G.: Mater. Sci. Forum 196-201 (1995) 345. 95Sou1 Souifi, A., Benyattou, T., Guillot, G., Bremond, G., Dutartre, D., Warren, P.: J. Appl. Phys. 78 (1995) 4039. 96Cow1 Cowern, N.E.B., Kersten, W.J., de Kruif, R.C.M., van Berkum, J.G.M., de Boer, W.B., Gravesteijn, D.J., Bulle-Liewma, C.W.T.: Proc. 4th Int. Symp. on Process Phys. and Modeling in Semicond. Technol., Srinivasan, G.R., Murthy, C.S., Dunham, S.T. (eds.): Proc. Electrochem. Soc. 96-4 (1996) 195. 96Kri1 Kringhøj, P., Nylandsted-Larsen, A., Shirayev, S.Yu.: Phys. Rev. Lett. 76 (1996) 3372. 96Nyl1 Nylandsted-Larsen, A., Kringhøj, P.: Appl. Phys. Lett. 68 (1996) 2684.
Lando lt -Bö rnst ein New Series III/33A