Physica status solidi: Volume 29, Number 2 October 1 [Reprint 2021 ed.] 9783112494349, 9783112494332

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V O L U M E 29 • N U M B E R 2 • 1 9 6 8

physica status solidi B o a r d of E d i t o r s P. A 1 G R A I N , Paris, S. A M E L I N C K X , Mol-Donk, V. L. B O N C H - B R U E V I C H , Moskva, W . D E K E Y S E R , Gent, W. F R A N Z , Münster, P. G Ö H L I C H , Jena, E. G R I L L O T , Paris, R. K A I S C H E W , Sofia, P. T. L A N D S B E R G , Cardiff L. N É E L , Grenoble, A. P I E K A R A , Warszawa, A. S E E G E R , Stuttgart, F. S E I T Z , Urbana, O. S T A S I W , Berlin, M. S T E E N B E C K , Jena, F. S T Ö C K M A N N , Karlsruhe, G. S Z I G E T I , Budapest, J. T A U C , Praha Editor-in-Chief P. G Ö R L I C H Advisory Board M. B A L K A N S K I , Paris, P. C. B A N B U R Y , Reading, M. B E R N A R D , Paris, W. B R A U E R , Berlin, W. C O C H R A N , Edinburgh, R. C O E L H O , Fontenay-aux-Roses, H.-D. D I E T Z E , Saarbrücken, J . D . E S H E L B Y , Cambridge, P.P. F E O F I L O V , L e n i n g r a d , J . HOPFIELD, Princeton, G. J A C O B S , Gent, J. J A U M A N N , Köln, E. K L I E R , Praha, E. K R O E N E R , Clausthal-Zellerfeld, R. KUBO, Tokyo, M. M A T Y À S , Praha, H. D. M E G A W , Cambridge T. S. MOSS, Camberley, E. N A G Y , Budapest, E. A. N I E K I S C H , Jülich, L. P A L , Budapest, M. R O D O T , Bellevue/Seine, B. V. R O L L I N , Oxford, H. M. R O S E N B E R G , Oxford, R. V A U T I E R , Bellevue/Seine

Volume 29 • Number 2 • Pages 447 to 892, K85 to K186, and A5 to A8 October 1, 1968

AKADEMIE-VERLAG•

BERLIN

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Contents Page

Review Article A . SEEGER a n d K . P . CHIK

Diffusion Mechanisms and Point Defects in Silicon and Germanium

455

Stability of the Dislocation Dipole in Half-Space

543

An Infrared Spectrophotometric S t u d y of Vitreous Selenium Doped with Selenium Dioxide

551

Anisotropy of High-Field Helicon Propagation in P b T e

559

Original Papers D. J .

BACON

R . A. Bun,LEY W.

SCHILZ

F . F . L A V R E N T E V , O . P . S A L I T A , a n d V . L . VLADIMIROVA

Dislocation Mobility in t h e {1122} Slip System of Zinc Single Crystals R . KERSTEN

569

Hyperfine and Quadrupole Interactions of the F-Centre in KCl as Measured b y E N D O R

575

One-Phonon Relaxation of Hydroxyl Ions in Alkali Halide Crystals

587

H . PFLEIDERER

P E M Effect with Short-Circuited Dember Voltage

597

A.

The Valence Bond Approximation in Crystals —Application to an Analysis of t h e Ultraviolet Spectrum in Quartz

605

B. G.

DICK

R . R U F FA

D . I . BOWER, E . CLARIDGE, a n d I . S . T . TSONG

Low-Temperature Elastic Constants and Specific H e a t s of F.C.C. Nickel-Iron Alloys

617

K . KLEINHENZ a n d P . RUNOW

Herstellung dünner Bor-Folien und elektronenmikroskopische Beobachtung ihrer Baufehler

627

D . BÄUERLE a n d B . FRITZ

Vibrational Spectra of Uj-Centres in K I J.

639

KOLODZIEJCZAK

Nonlinear Magnetooptical Phenomena in Semiconductors (I) . . .

645

E . S. MEIERAN a n d I. A. BLECH

Contrast Asymmetries in Lang Topographs of Crystals Strained b y Thin Films

653

V . S . CHINCHOLKAB a n d H . - G . U N R U H

D. VESELi D. VESEL*

Surface Layers of Triglycine Sulfate Single Crystals

669

The Study of Deformation of Thin Foils of Mo under t h e Electron Microscope

675

The Study of Slip Bands on t h e Surface of Mo Single Crystals . . .

685

R . G. HOWELL a n d D . J . NEWMAN

High Resolution S t u d y of Crystal Field Lines in t h e F a r I n f r a - R e d J .DILLINGER,

Ö. KONAK,

V . PROSSER,

J . S A K , a n d M . ZVARA

Phonon-Assisted Exciton Transitions in A n B V I Semiconductors 30«

697 707

450

Contents Page

O . V . BOGDANKEVICH,

M. SAUVAGE

N . A . BORISOV,

I . V . R R U K O V A , a n d B . M . LAVRUSHIN

Temperature Dependence of Laser Threshold Current Density and Emission Spectra in Electron-Beam Pumped Gallium Arsenide Lasers

715

Observations de sources et de réactions entre dislocations partielles de macle sur des topographies aux rayons X

725

K . N . SHRIVASTAVA

Phonon-Induced Hyperfine Coupling of V 2 + Ion in Cubic Crystalline Fields

J . E . LEWIS,

H . RODOT, a n d P . H A E N

R . VON JAN C . SIMOI,

The Low-Temperature Thermoelectric Power and Thermal Conductivity of GeTe and of Some GeTe-MnTe Alloys

743

Scattering Effects with Channeled Ions

755

I . HRIANCA, a n d P . CRACIUN

W. F R A N K V . BECKMANN,

Exoemission of Electrons without Photostimulation

761

Die kritische Schubspannung mit zweiwertigen Kationen dotierter Alkalihalogenide (II)

767

W . BRUCKNER,

B. TUCK

W . FUCHS,

G. RITTER, a n d H . WEGENER

The Measurement of the Anisotropy Constant of Antiferromagnetic F e P 0 4 by Means of the Mössbauer Effect

781

Effect of Heat Treatments on GaAs Luminescence

793

J . P . GUIGAY a n d R . H . W A D E

Mainly on the Fresnel Mode in Lorentz Microscopy

M . AVEROUS,

737

799

G . BOUGNOT, a n d J . CALAS

E . Z. DZIUBA,

Conduction Bands of GaSb-InSb Mixed Crystals with a Low Concentration of InSb

D . N I C U L E S C U , a n d N . NICULESCU

J . DELAPLACE,

Energy Band Structure of Z ^ H g i - ^ T e Solid Solutions

J . C . NICOUD,

813

D . SCHUMACHER, a n d G . VOGL

Low-Temperature Neutron Radiation Damage and Recovery in Beryllium

K . H . J . BUSCHOW,

807

819

J . F . F A S T , a n d A . S . VAN DER GOOT

Magnetic Properties of Some Co-Rich Erbium Cobalt Intermetallic Compounds

G . E . ARKHANGELSKII,

Z . L . MORGENSHTERN, a n d V . B . N E U S T R U E V

On the Nature of the Colour Centres of Ruby

825 831

R . C . T H I E L a n d C . B . VAN DEN B E R G

A. MEHRA P . P . SALHOTRA,

Temperature Dependence of Hyperfine Interactions in Near-Stoichiometric FeS (I)

837

Optical Absorption of MN 2+ -Doped Alkali Halides

847

E . C . SUBBARAO, a n d P . V E N K A T E S W A R L U

Polymorphism of Rubidium Nitrate

859

R . R A M J I R A O a n d R . SRINIVASAN

Calculation of the Generalized Griineisen Parameters for Acoustic Waves in Uniaxial Crystals from the Third Order Elastic Constants

865

Contents

45 I Page

A . JOSTSONS a n d P . G . MCDOUGALL

Fault Structures in Ti 2 0

873

Erratum

891

E . FELDTKELLER

Short Notes J.

Induced Impurity Breakdown Oscillations and Observation of Traps Lying Higher t h a n the Indirect Band Edge in GaP . . . . K85

GYULAI

P . FLÖGEL,

E . NEBAUER,

H . - J . ULLRICH,

S. DÄBRITZ, a n d E . ZIMMER

Electron Microprobe and Scanning Electron Microscope Investigations on Plate-Shaped CdS Single Crystals K89 E . E . GALLONI a n d R . ZIMMERMAN

Double Diffraction in Epitaxially Grown Nickel Polycrystalline Films K91 S . E . BRONISZ a n d D . L . D O U G L A S S

Grain Growth in Thin Films of Th0 2 , Np0 2 , and P u 0 2 J . PIEKOSZEWSKI,

K95

J . SUWALSKI, a n d S. LIGENZA

Mössbauer Effect Study in Chalcopyrite Y U . A . GOLDBERG,

K99

M . E . LEVINSHTEIN, a n d D . N . NASLEDOV

Magnetic Field Influence on the Low-Frequency Oscillations of Gunn Diodes K103 E . V . R . S A S T R Y a n d T . M . SRINIVASAN

Growth and Bleach of F-Centers in KCl with Interstitial Cobalt . . K107 D. K. ROY

On the Determination of Impurity Concentration in the Alloyed Region of a Tunnel Diode Kill

B . F . ROTHENSTEIN a n d I . ARTZNER

On the Internal Barkhausen Effect

K117

L. N. CoJOCARtr Effects of Fission Fragments on Electric Properties of the U 0 2 - S i 0 2 System K119 G. ROTH u n d Y . NAUNDORF

Messung der Aktivierungsenergien der Versetzungsverankerung in Kupfer nach Elektronenbestrahlungen bei 78 °K K123 J.

C.

B.

PEGEL

JOUSSET

Défauts d'irradiation dans l'Uranium a et règle de Matthiessen Self-Vibrations of Parallel Edge Dislocations

H . R . VYDYANATH,

.

. K127

K133

D . H . SASTRY, a n d K . I . VASU

On the Kinetics of Clustering in a Magnesium-3%-Zinc Alloy . . . K137 W . W . WALKER a n d L . J . DEMER

Indentation Creep in Crystals E . P . BERDNIKOV,

K141

V . A . DROZDOV, a n d L . A . MOZGOVAYA

On the Relation between Microhardness and Point Defects of Crystals K145

452

Contents Page

G . CHANUSSOT a n d H . A B E N D

Thermocurrents in Paraelectrie BaTiO a E . POETIN

K149

Photocurrent Amplification b y a Magnetic Field

K153

I . S. MCLINTOCK a n d J . C. ORR

Determination of Integrated Absorption in ESR Measurements. . . K157 S. HAUSSÜHL

Piezoelektrisches und elektrisches Verhalten von Lithiumjodat .

.

. K159

I . GAAL a n d L . U R A Y

Investigation of Non-Conductive Second Phases by Means of the Shape Factor of Electrical Resistance K163 H.-P. HENNIG

On the Conduction Mechanism in the Instable Range of a Double Injection Diode K167

S . J . SIVONEN a n d E . J . SUONINEN

Temperature Dependence of the Magnetic Ordering in Gd-GdFe 2 Phase Mixtures K171 H . BACHERT a n d S . RAAB

The Influence of External Optical Coupling on the Threshold Current Density of GaAs Injection Lasers K175 J . L . L E V E Q U E , T . ANAGNOSTOPOULOS, H . B I L G E R , a n d P . M O S E R

Point Defects in Iron-Carbon Solid Solution Studies b y Magnetic After-Effect Measurements K179 E . KIERZEK-PECOLD, J . KOIODZIEJCZAK, a n d I . PRACKA

Optical Constants of Crystalline CaB 6

K183

Pre-printed Titles of papers to be published in the next issue

A5

Contents

453

Systematic List Subject classification: 1.2 1.4

Corresponding papers begin on the following pages (pages given in italics refer to the principal subject classification): 837, 859 627, K91, K95

2

551

3 3.1 3.2

859 K89, K95 605

4

653, 799, 873, K89, K137, K163

6 6.1 7

587, 617, 639, 707, 737, 743, 847, 865, K133 781, 837, K99 865

8

617, 743, 859, 865

9

455

10 10.1 10.2

455, 543, 551, 627, 653, 725, 767, 847, 873, K107, K141, K149 569, 675, 685, 819, K123, K133, K137, K179 575, 587, 639, 831, K107

11 12 12.1 13 13.1 13.2 13.4

455, 755, 819, K119, K123, K127, K179 K145, K159 617, K123 559, 743, 761 605, 807, 813, K183 707 455, 715, 793, 831, 847, K85, Kill

. . . . . . .

14.1 14.3 14.3.2 14.4. 1 14.4.2 15 16 17 18 18.2 18.3 18.4

819, K127, K137, K163, K171 559, 807, 813, K119, K159 K103, Kill K85, K103, K167 669, K149 743, K119, K145 597, K85, K153 761 645 617, 799, K117, K171, K179 825 781, 837

19 20 20.1 20.2 20.3

455, 559, 551, 715, 793,

575, 737, K157 645 605, 639, 697, 707, 813, 847, K183 K175 831

K145,

454 21 21.1 21.1.1 21.3 21.4 21.5 22 22.1 22.1.1 22.1.2 22.1.3 22.2.1 22.2. 2 22.2.3 22.4.1 22.4.2 22.4.3 22.5.2 22.5. 3 22.6 22.8

Contents 675, 685, 761, K163 617, 825, K91, K117, K123, K137 617, K117, K171, K179 569, 819, K137 825, K171 K127 559, 645, 743, 837, K183 627 455, K i l l , K167 455, 653, K145 551 653, 715, 793, K103, K153, K175 K85 597, 807 707, K89 707 707, 813 575, 587, 639, 767, 847, K107, K141 K141 605, 737, 831, 873, K95, K119, K141 697, 725, 743, 781, 859, K99, K119, K159

The Author Index of Volume 29 Begins on Page S93 (It will be delivered together with Volume 30, Number 1.)

Review Article phys. stat. sol. 29, 455 (1968) Subject classification: 9 and 10; 11; 13.4; 19; 22.1.1; 22.1.2 Institut für Physik am Max-Planck- Institut für Metallforschung, Stuttgart, and Institut für theoretische und angewandte Physik der Universität Stuttgart

Diffusion Mechanisms and Point Defects in Silicon and Germanium By A . SEEGER a n d K . P . C H I K

1.

Introduction

1.1 Introductory remarks 1.2 Outline and scope of the review 2.

Diffusion

2.1 Self-diffusion 2.2 Impurity diffusion 2.3 Discussion 3. Point defects in thermal

equilibrium

3.1 General discussion 3.2 The experiments of Smith and Holland 4. Precipitation

from

solid

solutions

4.1 4.2 4.3 4.4

Survey of experimental results Theory of precipitation Comparison between theory and experiments Nucleation and complex-formation during precipitation from supersaturated solutions 4.5 Direct observations of precipitation 5 . Quenching

experiments

5.1 General discussion 5.2 Quenching of germanium 5.3 Quenching of silicon 6. Irradiation

studies

6.1 Irradiation of silicon 6.2 Irradiation of germanium

456 7.

A. S e e g e r and K. P. C h i k

Theory

of point

defects

in silicon

and

germanium

7.1 Introductory remarks 7.2 Energy levels 7.3 Energies of formation and migration and atomic configurations of the defects 8.

Conclusions

1. Introduction 1.1 Introductory

remarks

Diffusion processes play an important role in various aspects of modern semiconductor technology. The most important of these applications appears to he the generation of p - n junctions by diffusion of impurity atoms at elevated temperatures, without melting of the crystal or formation of a liquid alloy. The diffusing impurities are either offered to the semiconductor surface in the gaseous state or are applied to the surface as a solid or liquid compound. By suitable choices of the impurity concentration at the surface and of the heating treatment, depth and sharpness of the junctions can be controlled quite accurately. These techniques have given rise to important technologies in rectifier and transistor production. (For a general background in transistor physics and technology see, e.g., [1]). The diffusion technique described in the preceding paragraph permits the controlled formation of thin layers with high impurity concentration, i.e. low resistivity, in a matrix of higher resistivity. For high frequency transistors it is desirable to have the reversed situation, namely, a thin layer of high resistivity adjacent to a heavily doped matrix of low resistivity. This cannot be achieved by diffusion of impurities into the crystal. Instead, a thin layer of relatively pure Si or Ge is grown epitaxially on a heavily doped single crystal of Si and Ge at elevated temperatures by thermal decomposition of gaseous compounds such as SiCl4 or Gel 4 , which dissociate easily at sufficiently high temperatures (for details see, e.g., [2]). If the temperature is too high, however, the impurities may diffuse from the substrate into the epitaxial layer and reduce the desired difference in resistivity. Thus in the epitaxial technique diffusion is an undesirable feature and must be suppressed by working at the lowest possible temperature. As a third example for semiconductor phenomena in which impurity diffusion plays a definite role, we mention the so-called thermal conversion of Ge. I t was observed that n-type Ge which was quenched rapidly from high temperatures (e.g. 800 °C) tended to become converted into p-type material [3]. This "thermal conversion" is structure sensitive (i.e., it depends on the degree of perfection of the crystal) and may be reversed by prolonged heating at 500 °C. Fuller et al. [4] found that the process of conversion is accompanied by the diffusion of a p - n boundary from the surface of the germanium specimen into its interior. The corresponding diffusion coefficient of the "thermal acceptors" was found to be large (0.95 X 10~4 cm 2 /s at 850 °C). Considerable effort has gone into the identification of these "thermal acceptors". (For a review of this work up to 1956 see Letaw [5].) Van der Maesen et al. [6] found t h a t after heat treatment at 800 °C copper impurities in Ge act as acceptors. This acceptor action suggested that the copper impurities are located on substitutional sites and t h a t

Diffusion Mechanisms and Point Defects in Silicon and Germanium

457

t h e y are t h u s relatively immobile. The original conductivity can be restored b y prolonged heating a t 500 °C. This is explained as due t o t h e precipitation of t h e electrical active substitutional copper atoms a t internal sources for v a c a n t sites. However, the diffusion of Cu in Ge is found t o be a f a s t process which cannot be reconciled with t h e small mobility of t h e substitutional Cu atoms. This difficulty was resolved b y v a n der Maesen a n d B r e n k m a n [7], who proposed t h a t Cu atoms m a y be dissolved both on substitutional a n d on interstitial sites. The diffusion current is t h e n carried b y t h e f a s t diffusing interstitials. This model was later supplanted b y t h e 'Frank a n d Turnbull dissociative mechanism', which takes also into account t h e role of vacancies [8]. These diffusion and precipitation processes, which are not confined t o Cu in Ge, will be discussed in detail in Section 4. Thermal conversion of Si has also been reported, b u t it seems t o be due t o different kinds of impurities (see Section 5.3). I n view of t h e importance of diffusion processes, numerous experimental determinations of diffusion coefficients in semiconductors have been carried out [9], I t has become customary t o classify i m p u r i t y diffusors into slow a n d fast diffusors. Diffusion coefficients of slow diffusors are of the order of m a g n i t u d e of or u p t o about 102 times higher t h a n self-diffusion coefficients. Fast diffusors usually diffuse several orders of magnitudes faster t h a n slow diffusors. Typical representatives of slow diffusors are Group I I I a n d Group V elements of t h e periodic table, i.e. those usually employed as acceptors or donors in p - n junctions. Group I and Group V I I I elements constitute t h e most i m p o r t a n t fast diffusors (vz. t h e above example of " t h e r m a l conversion" in Ge). The diffusion mechanisms of some fast diffusors h a v e received considerable attention in the literature (see Section 2.2.3). I t has been concluded t h a t these mechanisms involve interstitial diffusion in one form or another. W e shall r e t u r n t o some of these mechanisms later. The mechanisms for slow i m p u r i t y diffusion m a y be expected t o be related t o those for self-diffusion in Si a n d Ge. I n most of t h e literature it has been assumed without m u c h scrutiny t h a t t h e self-diffusion mechanism in Si a n d Ge is similar t o t h a t in metallic elements, i.e., t h a t self-diffusion proceeds via a vacancy mechanism. I n t h e face centred cubic metals, which is t h e class of mono-atomic crystals so f a r most extensively investigated with regard t o diffusion mechanisms, there is ample evidence t h a t self-diffusion occurs via a defect mechanism a n d not t h r o u g h a " d i r e c t " exchange of two neighbouring atoms or t h r o u g h a " r i n g " exchange [10] involving t h r e e or more atoms. F u r t h e r more, for those f.c.c. metals t h a t have been studied in detail it has indeed been shown t h a t the main contribution t o self-diffusion is t h e migration of monovacancies present in t h e r m a l equilibrium. A recent analysis of t h e available experimental d a t a on Si a n d Ge, however, has led to t h e conclusion [11] t h a t t h e situation in these crystals m u s t be different f r o m and more complicated t h a n in t h e above-mentioned metals. For f u r t h e r elucidation of the self-diffusion mechanisms in Si and Ge information on point defects in these crystals is required. As we shall outline in Section 1.2, t h e possibilities for experimental studies of point defects in Si a n d Ge are q u i t e different from t h e approaches applicable t o metals. Quite a few of t h e techniques t h a t have been found informative in metals cannot be applied t o Si a n d Ge. On t h e other hand, semiconductors offer possibilities t h a t h a v e no analogues in metals. The electron spin resonance technique, infra-red absorption spectroscopy, induced photoconductivity measurements, a n d Hall coefficient mea-

458

A . Seegeb and K . P. Chik

surements are employed extensively to study defects in semiconductors. These methods are related to the specific electronic structures of these defects or are associated with the possibility of different charge states. The studies of diffusion of Cu and other fast diffusors provide further informations on vacancies. W e shall see that by combining the various techniques it is possible to arrive at a consistent picture for the diffusion mechanisms and the properties of the elementary point defects in Si and Ge. This picture will indeed turn out to be rather different from that familiar for metals. Diffusion coefficients D may either be defined macroscopically or microscopically. 1 ) Macroscopically I) connects the gradient of the concentration C of the diffusing species with the flux J of that species in an otherwise homogeneous crystal at constant temperature, according to

J=-D

gradC.

(1.1)

( W e see that the diffusion coefficient D is in general a symmetric second-rank tensor. In cubic crystals, which are the only ones we shall consider in this review, it reduces to a single scalar quantity D.) The microscopic definition of the diffusion coefficient goes back to Einstein and Smoluchowski. I t relates the «-component Dx of the diffusion coefficient to the mean square displacement Ax 2 of the diffusing species in «-direction (assumed to be parallel to one of the principal axes of the _D-tensor) and the time interval t during which diffusion takes place, according to the equation

The equivalence of (1.1) and (1.2) can easily be verified by calculating the mean square displacement of particles diffusing away from a point source by means of the macroscopic diffusion equation, to be obtained by substituting (1.1) into the continuity equation 8G — + divJ=0.

(1.3)

The macroscopic definition (1.1) constitutes the theoretical basis of most experimental methods for determining diffusion coefficients, e.g., the chemical and tracer techniques and the p-n-junction method (which is a technique specific for semiconductors, see Section 2.2.1). The microscopic definition (1.2) forms the starting point for the theoretical interpretation of diffusion coefficients in terms of such quantities as jumpfrequencies of atoms, defect concentrations, and lattice parameters. I t is also the basis for the experimental determination of diffusion coefficients by nuclear magnetic resonance measurements [12 to 15a], This technique, however, has not yet been applied to Si or Ge. Often the temperature dependence of the diffusion coefficient is found to obey an Arrhenius equation (k = Boltzmann's constant, T = absolute tem*) For background information on diffusion in crystals (mainly metals and alloys) in the same spirit as the present paper, but with more details, the reader is referred to Shewmon [12].

Diffusion Mechanisms a n d P o i n t Defects in Silicon and Germanium

459

D(T) = D 0 e x p ( - A j .

(1.4)

perature)

I n such cases, the diffusion is characterized b y just two quantities, t h e preexponential factor D0 and the activation energy of diffusion Q. However, it is not uncommon, especially among t h e fast diffusors, t h a t the experimental results cannot be described by (1.4) with temperature-independent quantities D 0 and Q. E.g., for the above-mentioned diffusion of Cu in Ge it has been found t h a t D cannot be characterized by a unique function of temperature T, b u t is strongly dependent on the degree of perfection of the material, in particular its dislocation density (see Section 4.1). 1.2 Outline and scope of the

review

The present review has been written with the interests of the solid s t a t e physicist in mind, who is more concerned with general principles and techniques on one hand, and the similarities and differences between different classes of solids on the other hand t h a n with collections of experimental d a t a on specific systems. Since we shall consider only the elemental semiconductors Si and Ge, leaving out semiconducting compounds such as t h e III-V-compounds, it is natural to use for comparison the metals with cubic crystal structures. We shall find particularly illuminating the comparison with f.c.c. metals such as Cu, Ag, Au, Ni, and P t , which have melting points and cohesive energies similar t o those of the valence crystals Si and Ge. The experimental methods for the study of point defects in crystals can be classified into two broad groups: (i) Experiments in which the defect concentrations and distributions are essentially those corresponding to thermal equilibrium a t the measuring temperature T. (ii) Experiments in which the point defects are not in thermal equilibrium, i.e., the crystal is a t least locally either supersaturated or undersaturated with point defects. (i) The two most important techniques of the first group are diffusion studies and measurements t h a t detect the presence of point defects in thermal equilibrium. Other techniques belong also to this group, e.g., the measurement of the transport of m a t t e r in a thermal gradient or in an electrical field (including, in t h e case of ionic crystals, the ionic conductivity and t h e ionic Hall effect) [16]. We shall see (Section 3.1) t h a t the concentrations of point defects in Si and Ge are by several orders of magnitude lower t h a n those in metals with comparable melting points. As a consequence, it has not yet been possible to detect directly the presence of point defects in Si and Ge in thermal equilibrium at high temperatures. I n principle, such investigations would give t h e free energy of formation (i.e., energy of formation Ev and entropy of formation 8s) of those defects t h a t dominate in thermal equilibrium, i.e., t h a t have the lowest free energy of formation G¥ = E¥ - T Sv (1.5) of all the different types of intrinsic point defects (e.g., vacancies, divacancies» self-interstitials). I n the absence of such direct information, diffusion measurements are all the more important for the study of point defects with low GFvalues in Si and Ge. Diffusion d a t a will take a prominent position in our discussion (Section 2).

460

A . SEEGEB a n d K . P . CHIK

Due to the low concentration of point defects in thermal equilibrium, selfdiffusion in Si and Ge is much slower than in metals (cf. Table 1). The range of useful tracer measurements of self-diffusion in Si and Ge is therefore restricted to a comparatively small temperature interval at high temperatures. By fitting such measurements to (1.4) D0- and Q-values for self-diffusion can be deduced. From the fact t h a t the experimental results can be fitted by temperature independent choices of D0 and Q over small temperature intervals it should not be concluded t h a t the activation energies of self-diffusion are independent of temperature in wide temperature ranges. In fact, arguments have been given by Seeger and Swanson [11] t h a t this is not so (see Section 2.3). Fortunately, in semiconductors supplementary informations on the mechanism of self-diffusion can be obtained in various ways, which we shall now briefly outline. a) As mentioned in Section 1.1, the diffusion mechanism of the slowly diffusing impurities, such as the Group I I I and Group V elements, may be expected to be related to the mechanism of self-diffusion. A correlation between the magnitude of the diffusion coefficient and the acceptor or donor properties of the diffusing impurities has been found (Section 2.2.2). This allows conclusions on the nature of the self-diffusion mechanism to be drawn (Section 2.3.3). b) The addition of impurities will in general change the self-diffusion rate of the matrix. I n semiconductors, this effect may be much larger and more specific than in metals for the following reason: The electrical effects from the addition of an atom of different valency to a metal is screened out by a redistribution of the conduction electrons over a distance comparable with t h a t between nearest neighbour atoms. A substituted foreign atom of a size not too different from t h a t of the atoms of the metallic matrix will therefore interact with intrinsic point defects present in thermal equilibrium only over a short distance, and the effect of a small impurity concentration on the self-diffusion coefficient will thus be small. In semiconductors, the effect of adding acceptor or donor impurities can be very large. Such additions will in general change the position of the Fermi level and thus influence the bulk of the crystal. Consider, for the sake of the argument, a p-type material which contains the equilibrium concentration of monovacancies possessing an acceptor level near the middle of the forbidden gap. If donors with levels close to the conduction band are added, the vacancy acceptor levels will be filled and the charge state (and other properties) of the vacancies will be altered. From this example we see t h a t a small addition of suitable impurities may change considerably both the free energy of formation (thus the equilibrium concentration) and the mobility of intrinsic point defects in semiconductors. If these defects are responsible for self-diffusion, the effects just described will result in changes of the self-diffusion coefficient. From the observed signs and magnitudes of such changes conclusions as to the nature and properties of the self-diffusion mechanism can be drawn (Section 2.3.4). c) As we shall outline presently, for one particular self-diffusion mechanism, namely t h a t via monovacancies, the diffusion coefficient may be determined in an indirect way at rather low temperatures [17], By investigating whether the tracer measurements of self-diffusion at high temperatures and the indirect determinations at low temperatures are compatible with each other it can be decided whether the high temperature mechanism is a vacancy mechanism or not, and, if not, whether a change in the mechanism of self-diffusion as a func-

Diffusion Mechanisms and Point Defects in Silicon and Germanium

461

tion of temperature is to be expected. This possibility is peculiar to semiconducting valence crystals and has no analogue in metals. I t is based on the following facts: a) The diffusion coefficients of the fast diffusing impurities, such as Cu, Ni, Au, are so high that the diffusion of these impurities can be followed in reasonable time scales at temperatures as low as half the absolute temperature of melting. p) The impurities mentioned under a) may be dissolved in Si and Ge both substitutionally and interstitially, the interstitial configuration being much more mobile (van der Maesen and Brenkman [7]). The transition from one configuration to the other involves vacant lattice sites according to the "chemical" reaction (Frank and Turnbull [8]) interstitial impurity + vacancy

substitutional impurity.

(1-6)

y) I t is possible to distinguish between the substitutional and the interstitial configurations of a given impurity by means of electrical measurements, e.g., by determining energy levels through the Hall effect. The theory and the application of this technique will be covered in Section 4. I t will become evident that the method has considerable potential and that further measurements promise to give interesting results not only on self-diffusion, but also on vacancy properties. (ii) Turning now to the second growp of point defect investigations, we consider first the three classical methods for generating supersaturations of point defects, namely, a) quenching from high temperatures, b) plastic deformation, and c) irradiation by fast particles or y-rays. a) The basic idea of the quenching experiments is to cool a specimen down from high temperatures at a rate which is fast enough to prevent the defects present in thermal equilibrium at high temperatures from annealing out. I f the final temperature is low enough, these defects (or any "reaction products" formed by them during the quench) are "frozen in". They may then be studied by raising the specimen to suitable temperatures. B y increasing the temperature in a subsequent annealing treatment gradually, it is in general possible to deal with one mobile type of defects at a time and to determine, e.g., the activation energies of motion of the defects introduced by the quenching and annealing treatment. In metals this technique has proven to be rather powerful for investigating vacancy type defects (for a review up to 1964 see [18]). For a number of reasons, which will be discussed in Section 5.1, the quenching technique is not nearly as useful for Si and Ge. In interpretating quenching results one has to be careful in view of possible interferences from impurities. From the present experimental evidence it appears that most of the quenching results have to be reinterpretated. A fairly detailed discussion of the present situation will be given in Section 5. b) Plastic deformation of semiconductors has been reviewed by Haasen and Seeger [19], Haasen [20], and recently in particular detail by Alexander and Haasen [21], In addition to dislocations, plastic deformation creates both vacancyand interstitial-type point defects. With regard to the study of point defects plastic deformation appears thus at first sight as a more complicated technique than either quenching or irradiations. Nevertheless, due to the ease with which deformation experiments may be carried out on most metals, even at temperatures low enough to suppress the point defect mobilities completely, such experi-

462

A . SEEGER a n d K . P . CHIK

ments have contributed substantially to the experimental investigation of point defects in metals. By contrast, Si and Ge can be deformed plastically only at temperatures at about or above two thirds of the melting temperature. At such temperatures extensive precautions to avoid contamination by fast diffusors are required. If single vacancies or interstitials were generated during the plastic deformation, they would anneal out instantaneously on account of their low energies of migration (see Section 6). However, as pointed out by Haasen and Seeger [19], Seeger [22], and also by Penning et al. [23], as a consequence of the fact t h a t the diamond structure contains two atoms in the elementary cell, a jog formed in a dislocation line by the intersection with another dislocation extends from one {111}-glide plane to the next nearest parallel { l l l } - p l a n e rather than the nearest one. Non-conservative motion of such jogs will thus create divacancies rather than monovacancies (or di-interstitials rather t h a n single interstitials). Tweet [24] has found t h a t plastic deformation ofGe introduces an acceptor level 0.1 eV above the valence band which anneals out during moderate annealing before the dislocations introduced by plastic deformation become affected. Since there are good theoretical reasons t h a t the energy of migration of a divacancy is substantially higher than t h a t of a single vacancy (Section 2.3.1) and divacancies might thus be retained at the deformation temperature, the 0.1 eV acceptor level has been attributed to the divacancy [19, 22, 23]. On the other hand, Bliek and Schröter [25] and Schröter [26] are of the opinion that the 0.1 eV level might have to be attributed to dislocations, mainly on the grounds t h a t in their experiments the position of the acceptor level appears to vary with its degree of occupation. I n Si the divacancy has been identified by electron spin resonance and infrared absorption measurements (see Section 6.1). I t appears therefore of considerable interest to carry out deformation experiments on Si analogous to those of Tweet [24] and to see whether divacancies can indeed be found after plastic deformation. c) Partly due to the inherent limitations of the quenching and deformation experiments, irradiation studies have become the most widely used tool for the investigation of point defects in semiconductors. One of the advantages is t h a t it is possible to carry out the irradiation in the range of liquid-helium temperatures. Energetic radiation causes individual atoms to be displaced from their lattice sites. I n this way, both interstitial and vacancy type defects t.re generated. The higher the energy transferred from the incident radiation to the Si or Ge atoms, the more complex defects are created during irradiation. Electron- and y-irradiations can be arranged such as to create only rather simple defects; they are therefore of particular importance for the study of point defects. Since by means of electrical and optical measurements small concentrations of point defects can be detected, irradiation experiments on semiconductors may be performed already at small dose levels, thus reducing the cooling problems at the very low-temperatures required for freezing-in the most mobile point defects. E.g., it is possible to employ y-irradiation [27] or to perform neutron irradiation experiments in a neutron beam outside the reactor [28], whereas these procedures are applicable to metals only for special experiments, e.g. measurements of internal friction and elastic modulus of very pure specimens [29]. A disadvantage of low-temperature irradiation experiments is t h a t the ionizing action of most of the irradiations employed and the extremely small electrical conductivity of pure semiconductors at low temperatures may prevent electronic equilibrium to be reached during the experiment. Some of these dis-

Diffusion Mechanisms and Point Defects in Silicon and Germanium

463

advantages may be overcome by using photoconductivity as a tool for studying the defects [28]. A competent survey of the irradiation of semiconductors by electrons and related problems from the viewpoint of investigating point defects has recently been published by Corbett [30]. Our discussion of the irradiation experiments (Section 6) can therefore be rather brief and will be restricted essentially to those aspects t h a t are required to establish the connection with the main topics of this review. d) Some of the disadvantages of the quenching experiments can be reduced or avoided by "up-quenching", i.e., raising the temperature rapidly from a low to a high value, thus creating an "undersaturation" of point defects, and observing the establishment of equilibrium by generation and migration of the defects dominating the thermal equilibrium. This technique avoids possible associations of these defects with each other or with impurities beyond those corresponding to thermal equilibrium. Instead of employing a large temperature jump it may be experimentally simpler to cycle the specimen temperature over a relatively small range and to observe the time lag in the establishment of equilibrium. Smith and Holland [31] and Holland [32] have performed such measurements on Ge. I n this technique the deviations of the defect concentrations from thermal equilibrium are kept small throughout the experiments. Although not all aspects of their experiment are well understood, the results of Smith and Holland appear to fall into the pattern of the other investigations. These experiments will be discussed in Section 3.2. e) A technique for introducing an extraordinarily high concentration of defects into a metal is the "quenching condensation" of a metal from its vapour on to a cold substrate, which has been extensively employed by Hilsch and his associates [33, 34]. The analogous technique for Si and Ge is the evaporation in a vacuum and deposition of an amorphous thin film on a substrate (which may be kept at room temperature). The X-ray investigations of Richter and Breitling [35] indicate that, comparing the atomic arrangement of the amorphous solid with t h a t of the crystal, the basic tetrahedra remain intact (apart from the possibility of small distortions). Whereas in the crystal these tetrahedra form regular chains, in the amorphous solid neighbouring tetrahedra are presumably irregularly rotated along the directions joining two neighbouring atoms [36]. Amorphous Si and Ge constitute thus examples of solids t h a t possess essentially the same short-range order as the corresponding crystal, but no long-range order. Since the irregularly rotated tetrahedra cannot fill the space completely, amorphous Si and Ge must contain a high density of vacancies. An order-of-magnitude idea of this "vacancy concentration" can be obtained from the fact that, according to the X-ray data [35], the mass densities of amorphous Si and Ge are about 10% lower than those of the crystals. Extensive electrical and optical investigations (see [36, 37]) have shown t h a t amorphous germanium exhibits at low temperatures p-type "impurity" conduction with an activation energy of 0.18 eV, whereas at higher temperatures it shows intrinsic conduction corresponding to an energy gap of 0.55 eV. If an amorphous layer deposited below 350 °K is annealed between 350 and 630 °K, the conductivity in the "impurity" range may be reduced irreversibly by as much as a factor of 25, and the onset of intrinsic conduction is shifted correspondingly to lower temperatures [36b]. This suggests a lowering of the acceptor density and thus a connection between the acceptors in amorphous Ge and vacancy-type 31 physica 29/2

464

A. SEEGEE and K . P.

CHIK

imperfections in the crystals. Detailed experiments on amorphous Ge and Si may well be capable of giving further information on the properties of vacancies and vacancy clusters in the crystals. A possible relation to high-temperature diffusion will be discussed in Section 2.3.2. f) Another potential technique for introducing a high concentration of intrinsic defects, which does not yet appear to have been applied for quantitative studies, is the application of very high pressures. Both Si (at 200 kbar) and Ge (at 120 to 125 kbar) undergo a transformation to a high-pressure metallic phase [38a, b, c]. After removing the pressure silicon is found to have a density of 2.55 g/cm 3 , which is about 10% higher than that of normal Si [38b], This denser phase is a body-centered cubic structure built up from distorted tetrahedra (lattice constant (6.64 + 0.01) A, suggesting 16 Si atoms per unit cell). This dense phase, which is more metallic than the diamond structure, changes upon heating to temperatures of 200 to 600 °C to a mixture of a hexagonal structure (wurtzite type) with the "ordinary" diamond structure. It appears feasible that the metastable high-density phase might serve as a model for a high concentration of interstitial atoms. In the interests of easy reading and concise presentation we shall discuss the theoretical interpretation of the various types of experiments as we go along in presenting the experimental data. Theoretical results that do not easily fit into this scheme of presentation will be briefly summarized in Section 7. In a final Section 8 we shall attempt to interrelate the conclusions drawn in the other sections and summarize the picture emerging from the present review. Although we have endeavoured not to leave out any observations and ideas that are likely to be of importance for our subject, completeness in listing the literature was not our primary aim. In fact, in several areas the literature is so large that we had to confine ourselves to a discussion of those papers that have an immediate bearing on the interrelation of point defect properties and diffusion mechanisms. E.g., we shall leave out or mention only briefly those diffusion data that do not yet lend themselves to atomistic interpretations (for a collection of diffusion data up to 1960 see Boltaks [9]) as well as many of the irradiation data. Since the effects of energetic irradiation on semiconductor are of considerable importance for a number of applications, the field of radiation studies of semiconductors has been very active in recent years. Those readers who are interested in the irradiation effects in semiconductors per se are referred to a series of conference reports [39 to 45] in addition to the already mentioned book by Corbett [30] and review articles by Crawford [27], Vavilov [46], and Bauerlein [46a], 2. Diffusion 2.1

Self-diffusion

The standard approach to measuring self-diffusion in solids is the use of radioactive tracers. The diffusion coefficient _DSD is obtained by comparing the distribution of tracer atoms resulting from a diffusion treatment with a theoretical distribution profiles. The theoretical distribution profiles are obtained by solving the diffusion equations under certain boundary conditions describing the experimental conditions (see, e.g., [47]). The distribution of tracer atoms can be determined by different methods, e.g., the removal of successive layers [48] or absorption methods [49, 50], The accuracy of the

Diffusion Mechanisms and Point Defects in Silicon and Germanium

^ CO

%

P?

S1

O

00

T? © ? oi—i 1o—1 o or-4 X X X 00 X X 1—( f—l 1—1 (Tm)) for M and Pt the divacancy contributions have been eliminated, so that in Table 1 the preexponential factors and activation energies for metals are typical for a monovacancy mechanism of self-diffusion. Comparison of the data presented in Table 1 shows the following differences between the valence crystals and the metals: a) Self-diffusion is much slower in the valence crystals than in the metals. This is true at the melting point, where the ratio of the self-diffusion coefficients of the metals to those of Si and Ge is of the order 103 to 10 4 , but even more so at lower temperatures. b) The preexponential factors Z)®D are significantly larger in the valence crystals, particularly in Si, than in the metals. The ratio of the preexponential factor of Si to that of Ge is of the same order of magnitude as the corresponding ratio of Ge to metals.

T{°C)

800

900

600

700

1300

0.80

035

0.90

0.95

T(°C)

1200

1100

WO

Fig. 1. Temperature dependence of self-diffusion coefficients in Ge. O Widmer and Gunther-Mohr [52], • Valenta und I l a m a s a s t r y [53], A Letaw et al. [51]

Fig. 2. Temperature dependence of self-diffusion coefficients in Si. O Peart [57], x Fairfield and Masters [55, 56], • Ghoshtagore [54]

Diffusion Mechanisms and Point Defects in Silicon and Germanium

467

c) The fact that in Si and Ge D®D is much higher although Z)SD itself is several orders of magnitudes smaller than in metals has the consequence that the activation energies of self-diffusion are considerably larger for the valence crystals than for the metals. These striking differences between valence crystals and metals cast considerable doubt on the common belief that the self-diffusion mechanism in Si and Ge is also predominantly a monovacancy mechanism. The problem has been discussed in detail by Seeger and Swanson [11] and will be considered in Section 2.3. In a number of metallic systems, the effect of a concentration Ct of foreign atoms on the self-diffusion coefficient of the matrix atoms has been studied. For small impurity concentrations the results can be represented in the form D SD (O f ) = D S D (0) ( 1 + 6 Ct) ,

(2.2)

where |6| is typically less than one hundred. Choosing metallic solutes in Ag at 1000 ° K as an example (data taken from [69]), b is found to vary for nine different solutes between —8.2 (Pd) and + 8 7 (Pb), |6| being generally larger the larger the valency difference between solute and solvent. In semiconductors the effects of impurities on the self-diffusion coefficient may be much larger if the impurities act as donors or acceptors. This is exemplified in Table 2. Ge tracer atoms are found to diffuse faster in heavily doped n-type Ge and slower in heavily doped p-type Ge than in intrinsic Ge. The size of the effect suggests that it is primarily due to the change in Fermi level caused by the doping and that self-diffusion must proceed via a defect mechanism, the energy of formation of the defect responsible for self-diffusion (and possibly also its migration energy) being dependent on the position of the Fermi level. Specifically, Valenta and Ramasastry [53] showed that they could account fairly well for the observed changes of the self-diffusion coefficient in n-doped samples in terms of the shift in Fermi-level, assuming a vacancy mechanism of diffusion. The effects in p-type materials were somewhat higher than the authors expected from theory. This discrepancy was reinvestigated by Widmer [70] using p-type Ge (doped with 2 X 1020 Ga atoms/cm 3 ). His experimental results agreed within experimental error with those of Valenta. However, Widmer points out that the discrepancy between experiment and theory is removed if a weight factor 2 due to spin degeneracy is correctly allowed for in calculating the neutral vacancy concentration (see Section 2.3.4). The effect of heavy doping on self-diffusion in Si was studied by Ghoshtagore [54] and in more details by Fairfield and Masters [56]. Ghoshtagore measured the selfTable 2 Doping effects on self-diffusion in Ge after Valenta and Ramasastry [53] Type intrinsic n P P

Doping level (atoms/cm 3 ) ,

6 x 1018 5 x 1019 1020

Do ( was reported to be increased for P-doped samples and slightly decreased for B-doped samples. Fairfield and Masters [56], however, found an increase of D S D in both n- and p-type samples. These results will be discussed in Section 2.3.4. 2.2 Impurity

2.2.1 General

diffusion

considerations

Impurity diffusion may be studied by the standard radio-tracer techniques, analogous to those mentioned in Section 2.1. In addition, for impurities acting as donors or acceptors, the more convenient p-n junction method is also available and has been extensively used. In this method, the base material to be studied is doped such that the type of the electrical conduction is opposite to that generated when the impurity has diffused in. The diffusion profile is obtained by locating the p-n junction developed after diffusion as a function of diffusion time. To evaluate D, further information on the total concentration of diffusing material and the initial concentration of uniformly distributed current carriers in the specimen are required [71]. The p-n junction method differs from the standard radio-tracer technique in that it provides information on the diffusion of electrically active impurity atoms in a uniformly doped sample, whereas by means of the tracer methods diffusion in intrinsic materials may also be investigated. I f the impurities exist both in charged and uncharged states during diffusion, both methods can be applied simultaneously to differentiate between the diffusion of these two species [72], 2.2.2 Group III

and Group V impurities

Impurities of the Group I I I and Group V elements in Ge and Si behave as acceptors and donors, respectively, with a single energy level close to the edges of the energy bands. They are therefore easily ionized and can be studied conveniently by the p-n junction method. A very large number of papers has been published on the diffusion of Group I I I and Group Y elements in Ge and Si. In most of them p-n junction methods have been used. The impurity diffusion coefficients are of the order of 1 to 100 times greater than the self-diffusion coefficients; according to the distinction made in Section 1.1 these impurities have to be considered as slow diffusors. A glance at the diffusion parameters D0 and Q reported by different authors may be confusing (Tables 3 and 4). The discrepancies in the results reported arise presumably from different experimental conditions employed by different workers. I t is found that the diffusion may be influenced by the magnitude of the doping and by the surface concentration of the impurities. One explanation is that due to the large difference in diffusion constants of ionized impurities and of the associated electrons or holes, an internal electric field is created in the semiconductor and affects the distribution of the impurity atoms [82, 85, 99]. The effect of doping on Dsh'Ge, DAs'Ge, and DIn'Ge 2) seems to be small for a doping concentration < 1018 cm - 3 [74] and lies within the accuracy of the mea2 ) The first element in the superscript denotes the diffusion impurity and the second the host crystal.

Diffusion Mechanisms and Point Defects in Silicon and Germanium

469

Table 3 Group I I I and Group V impurity diffusion in Ge*) Solute B Al Ga

In

Z)0 (cm2/sec)

P

As

Sb

Bi

Reference

16 x 109

4.6

PN

[71

40

3.14

PN

[71]

2.16 2.41 3.0 2.83 a) 2.2 b) 1.72 c)

FPN PN VPN, PN T

[73] [71] [74] [75]

3.02

T

[76]

0.03 20 16.37 0.031 2.9 x 10"4

33 T1

Method

Q (eV)

1700

3.4

Remarks

only 2 measurements only 2 measurements influence of sample purity on diffusion a) Q = 40 Q cm, b) g = 2.8 Q cm, c) g = 0.007 Q cm. Q = resistivity of sample before impurity diffusion

[77]

2.5

2.48

PN

[71]

0.71 10 2.1

2.2 2.5 2.4

FPN PN VPN, P N

[73] [71] [74]

5

2.5

PN

[78]

3

2.43

effect of doping within accuracy of measurement corrected for internal electric field effect

[79]

0.71 10 1.2

2.2 2.5 2.3

FPN PN, T VPN, PN

[73] [71] [74]

1.4 1.3 3.5

2.3 2.26 2.45

ODT PN

[80] [81] [78]

1.2

2.3

PN

[82]

3.2

2.41

T

[76]

3

2.5

effect of doping within accuracy of measurements effect of surface concentration on D studied effect of internal electric field corrected internal electric field effect corrected

[83]

*) P N : p - n junction method; F P N : Fuller's p - n junction method [73]; T : radioactive tracer method; VPN: volume p - n junction method [74]; ODT: out-diffusion of tracers.

470

A. Seeger and K. P. Chik

surements. Niedermayer [78] found that Z)As/Ge and Z)sb/Ge increase slightly if the surface (impurity) concentration Cs is greater than 1018 cm - 3 (to about a factor of 3 at Cs = 1020 cm -3 ). However, no systematic deviations among results from different authors for Dsh'Ge, DAs'Ge, D In / Ge , Z)Ga/Si, and D As / Si are found for the temperature range investigated. A summary of the present available diffusion data is given in Tables 3 and 4. The diffusion of B and P in Si shows pronounced effects of degree of doping and of surface concentration. Maekawa and Oshida [88] showed that _DB/Si Table 4 Group III and Group V impurity diffusion in Si Solute

Method

Reference

A> ( c m »

0(eV)

10.5 3.2 17.1 15.8 10.7

3.66 3.5 3.66 3.7 3.64

PN PN PN PN PN

[84] [85] [86] [87] [88]

8 4.8 2800

3.45 3.34 3.77

FPN PN

[84] [89] [90]

3.6 270 2.1

3.49 4.15 3.5

FPN PN PN

[84] [91] [92]

In

16.5 19.4

3.89 3.86

PPN T

[84] [98]

T1

16.5

3.88

PPN

[84]

10.5

3.66 2.4 to 2.6

PN PN

[84] [93]

B

,{ Ga

|

P

As Sb Bi

|

29

3.88

PN, T

[72]

0.32 68.6 2.56

3.54 4.2 3.9

PPN PN

[84] [94] [95]

5.6 12.9

3.92 3.95

PPN T

[84] [96]

4.6 4.1

FPN PN

[84] [97]

1030 896

Remarks

effect of doping and surface concentration studied, enhanced diffusion after heavy doping

D affected by surface concentration and doping very fast diffusion at high doping level

471

Diffusion Mechanisms and Point Defects in Silicon and Germanium

increases by a factor of 100 if the doping concentration is raised from 9 x 1014 cm - 3 to 1.4 x 1019 cm - 3 and Ca exceeds 2 x 1019 cm -3 . They suggested that the enhancement of diffusion may be due to formation of dislocation loops from boron clusters. Similar enhancement of diffusion is also found in _Dp/Si [72], B y using radioactive tracers and the p-n junction method simultaneously, Maekawa [72] showed that a fast-diffusing component is probably associated with interstitial diffusion of neutral P. Parker [100] tried to explain this enhancement of diffusion as due to formation of excess vacancies from moving dislocation jogs. A general survey of the diffusion data is given in Tables 5 and 6, where the most representative data are listed. The results may be summarized as follows. In Ge, Group I I I elements diffuse about 100 times slower than Group V elements and have about the same diffusion rate as self-diffusion. The faster diffusing Group Y elements are further characterized by smaller activation energies and smaller preexponential factors than those for self-diffusion. In Si, on the contrary, Group V elements diffuse about 10 times slower than Group I I I elements. The diffusion coefficients of Group V elements are of the same order as the self-diffusion coefficient. Furthermore, the preexponential factors are for all impurities in Si smaller than that for self-diffusion. Table 5 Representative impurity diffusion data of Group I I I and Group V elements in Ge Group I I I Element B Al Ga In T1

Group V

D„ (cm2/s) G(eV)

-Do.94 Tm (cm2/s)

Element

Do (cm2/s)

1.6 x 109

2.5x10-"

N P As Sb Bi

2.5 3 1.2 3

40 24 1700

QSD = 3 e y , Z)SD

4.6 3.14 3.0 « 3.4

« 10" 12 1.5x10" 1 2 «a lO" 11

10.8 cm2/s, Df>

=

0(eV)

A).94 Tm (cm2/s)

i=S 10" 10 2.48 2.4 « 1.5 X i o - 1 0 2.3 «a 2 x 10- 10 2.5 « 10- 10

& 10" 12 cm2/s [52].

Table 6 Representative impurity diffusion data of Group I I I and Group V elements in Si Group I I I

Group V -Do.94 Tm (cm2/s)

Element D0 (cm2/s) G(eV) B Al Ga In T1

3 to 10 m 5 40 «¿16.5

3.5to3.6 «3.3 3.9 «3.9 3.9

16

«

10"11

« «

10-11 10-11

3 X10" 1 0 2.5X10- 1 1

m ^ ® o ft ro O ® Sí S o f t Bo ¡3

O

a

.. c3 SC O tí "'S ft > .2 «3¡ O -2 TS •P CÔ (D t»

ft-rt

cS «O

® 2ft s

O CO O

,,

r—i r—i i—i C