Physica status solidi: Volume 16, Number 2 August 1, 1966 [Reprint 2021 ed.] 9783112498224, 9783112498217

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plxysica status solidi

VOLUME 16 NUMBKK 2 1

Contents Review Artlclo J . R . L).V_LE

Page Alloyed Semiconductor l l c t e r o j u n e t i o n s

351

Original l'apers M. TOMAHEK

Some R e m a r k s a b o u t Electronic Correlation in Crystal Surfaces : The Ideal (100) Surface of a Semi-Infinite Diamond-Like Crystal 389

I I . DUJÎE.JKO a n d S . O L S Z E W S K I

Quantum-Statistical Calculations on the W o r k Function of Metals

399

Z. SROLBEK

On the Thory of the Supercxchange I n t e r a c t i o n in Ionic Crystals : K N i F s . . . 405

II. LEMKE

Zur Zeitabhängigkeit raumladungsbegrenztcr I n j e k t i o n s s t r ö m e in I-Ialbleitern 413

H. LEMKE

Zeitabhängigkeit p-Silizium

raumladungsbegrenztcr

Injektionsströme in

Fc-dotiertem

427

S . CEKESAKA, T . F E D E R I G H I , a n d F . PIEKAGOSTIXI

Determination of Diffusion Coefficients in Metals by Resistometric Method — Application to t h e Diffusion of Zn in AI 439

>1. A T T A K D O a n d J . M . G A I X I O A X

A Field Ion Microscope Study of Neutron I r r a d i a t e d Tungsten

449

A . G . SAMOILOVIOH, M . V . N I T S O V I C H , a n d V . M . N I T S O V I C H

On t h e Theory of Anisotropic Thermoelectric Power in Semiconductors . . . .

IC. H . J . U L S C H O W a n d J . F . F A S T

Magnetic and S t r u c t u r a l Characteristics of Some E q u i a t o m i c Germanides

Rare-Earth

11. A . W R I E D T a n d S . A K A J S

Ferromagnetic Curie T e m p e r a t u r e of Some I r o n - Z i n c Solid Solutions

459 467 475

M . J . STOWELL a n d T . J . L A W

I n t e r r u p t e d Vapour Deposition of Epitaxial Gold Films Grown Inside a n Elect r o n Microscope 479

J . T i t i X ' s c i i a n d R . SANDKOCK

Energy Band S t r u c t u r e s of Selenium and Tellurium (Kohn-Rostoker Method) 487 li. STEINBEISS

Untersuchungen über Ummagnetisierungsprozessc in R c c h t c c k f e r r i t c n . . . .

C H R . L E H M A N N ' a n d On 1 ' . tShIeG M UND Mechanism

of S p u t t e r i n g

M . M . SHUKLA a n d B . DAYAL

Lattice Vibrations of Aluminium on t h e Basis of Krebs's Model

499 507 513

M . BAXCIE-GRILLOT e t P . BOURTAYHE

Émission photoluminescente visible du gadolinium inclus dans le l'öseau cristallin du sulfure de zinc 517

1 ' . CI U v o x e t J . L A J Z E B O W I C Z

D. J . BARBER V. V. RATXAM V. V. RATXAM

Mesures du t e m p s de r e t o u r n e m e n t ferroélectrique de K l l 2 P O j Electron Microscopy of Irradiation-Induced Defect Clusters i n Magnesium Fluoride On the Electrical a n d Magnetic Properties of Coloured a n d Uncolourcd Calcium Fluoride Crystals On t h e Colour Centres and X - R a y Luminescence of Calcium Fluoride Crystals

F . HIUAGXKT, J . D E V E X Y I , G . CLERC, O . M A S S E N E T , I I . MONTMORY, a n d A . Y E L O N

Interactions between Domain Walls in Coupled Films

W . BRODKORB u n d W .

525 531 549 559 569

HAUBENREISSER

Zur Theorie des Ferromagnetismus magnetisch anisotroper Schichten m i t kubischer K r i s t a l l s t r u k t u r (II) 577 J . VAX LANDUYT Determination of the Displacement Vector a t t h e Anti-Phase Boundaries in Rutile b y Contrast E x p e r i m e n t s i n t h e Electron Microscope 585 M . L . MUKHERJEE a n d H . N . BOSE

Nonradiative Destruction of F-Ccntres in X - I r r a d i a t e d KCl Dped w i t h Anionic I m p u r i t i e s 591 (Continued

on cover three)

physica status solidi B o a r d of E d i t o r s P. A I G R A I N , Paris, S. A M E L I N C K X , Mol-Donk, W. D E K E Y S E R , Gent, W. F R A N Z , Münster, P. GÖRLICH, 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 f i E L , Grenoble, A. P I E K A R A , Poznan, A. S E E G E R , Stuttgart, 0. S T A S I W , Berlin, M. S T E E N B E C K , Jena, F. STÖCKMANN, Karlsruhe, G. SZIGETI, Budapest, J . TAUC, Praha Editor-in-Chief P. GÖRLICH 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. COCHRAN, Edinburgh, R. COELHO, Fontenay-aux-Roses, H.-D. DIETZE, Aachen, J . D. E S H E L B Y , Cambridge, 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, M. M A T Y Ä S , Praha, H. D. MEG A W , Cambridge, T. S. MOSS, Camberley, E. NAGY, Budapest, E. A. N I E K I S C H , Jülich, L. P A L , Budapest, M. RODOT, Bellevue/Seine, B. V. R O L L IN, Oxford, H. M. R O S E N B E R G , Oxford, R. V A U T I E R , Bellevue/Seine

Volume 16 • Number 2 • Pages 349 to 802 and K 105 to K 220 August 1, 1966

A K A D E M I E - V E R L A G . B E R L I N

Subscriptions and Orders for single copies should be addressed to AKADEMIE-VERLAG GmbH, 108 Berlin, Leipziger Straße 3—4 or to Buchhandlung KUNST UND WISSEN, Erich Bieber, 7 Stuttgart l,Wilhelmstr. 4 — 6 or to Deutsche Buch-Export uDd -Import GmbH, 701 Leipzig, Postschließfach 160

Editorial Note: "physica status solidi" undertakes that an original paper accepted for publication before the 8 l h of any month will be published within 50 days of this date unless the author requests a postponement. In special cases there may be some delay between receipt and acceptance of a paper due to the review and, if necessary, revision of the paper.

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Review Article phys. stat. sol. 16, 351 (1966) Solid State Physics

Division,

Mullard

Research Laboratories,

Saljords,

Redhill

(Surrey)

Alloyed Semiconductor Heterojunctions By J . R . DALE

Contents 1.

Introduction

2. Heterojunction

structures

2.1 Metallurgical considerations 2.2 Theoretical considerations 2.2.1 Energy band diagram 2.2.2 Photocurrent response 3. Fabrication

3.1 3.2 3.3 3.4

and metallurgical

variables

The interface alloyed hetero junction The solution grown hetero junction The vapour transport-interface alloyed hetero junction Summary

4. Interface

characteristics

4.1 Electrical properties 4.2 Electro-optical properties 5.

Conclusions

References

1. Introduction Heterojunctions are defined as junctions between two semiconductors with different energy band structures. In principal, they may be either gradual junctions in which two bulk crystals are joined by an alloy series of continuously varying composition, or abrupt junctions in which there is a sharply defined interface between two homogeneous semiconductors. Interest in hetero junction devices was stimulated in the late 1950's by the work of Kroemer. The concept of quasielectric and magnetic fields for variable energy gap semiconductors was initiated [1, 2] and a theory presented [3] for a wide band gap emitter transistor. Later a number of articles by other investigators were published [4, 5, 6] which dealt with similar considerations. The interest in heterojunctions has also spread to the field of solar energy convertors [7, 8]. Theoretical considerations by Emtage [9] have shown that it might be 23»

352

J . R . DALE

possible to incorporate a heterojunction type structure into a photovoltaic converter which could give an efficiency as high as 40%. With recent observation of highly efficient light emission from forward biased p-n junctions in GaAs [10, 11] a number of opto-electronic transistor devices have been proposed [12 to 16] using heterojunction structures. With the advent of epitaxial vapour growth techniques [17] considerable interest was stimulated in heterojunctions where one crystal was vapour deposited on another. Anderson [18 to 20] and Marinace [21] first reported the properties and theoretical problems associated with this type of junction. A number of workers [22 to 32] carried out a more intensive investigation into the Ge-GaAs system originally studied by Anderson and extended the work to other systems, such as Ge-Si, InP-GaAs, GaP-GaAs, Ge-GaP, InAs-GaAs, GaAsj _ ^P^-GaAs and Ga^Ini -^-GaAs. In this series of papers the general conclusion reached appears to be that there are a large number of discrepancies which make uncertain the complete validity of the dicontinuous energy gap model, which shows energy discontinuities in the conduction and valence band edges at the junction interface. An attractive and alternative approach to the fabrication of heterojunctions by vapour transport technique is that of alloying. Three different systems have been used, these are: a) Interface alloying where the low melting point material is placed in a temperature gradient, with the high temperature side in contact with the high melting point material. b) A solution growth process where one of the materials is put into solution with a suitable solvent at an elevated temperature. This solution is then put in contact with the substrate and allowed to cool slowly growing a semiconductor layer which may contain some of the solvent and substrate. c) A combination of both interface alloying and vapour deposition. Here the substrate is held at a temperature higher than the melting point of the vapour deposited material so that on deposition alloying takes place at the interface. Interface alloying techniques have been used to make heterojunctions betweeen GaAs-Ge, GaAs-GaSb [33, 35], InSb-GaSb [34], Ge-Si [36], and InAs-GaSb [37], Solution growth techniques have been used to grow heterojunctions between GaAs-GaSb^As! _ x , GaAs-Ga x Ini -^As, GaAs-Mn 2 As [38], GaAs-GaP [28], and Ge-Ge^Sii _ x [88]. The vapour transport-interface alloying technique has at present only been successfully used to make Ge-Si alloyed heterojunctions [39]. However at the present time, since little attention has so far been given to the metallurgical variables of the processes which are of considerable importance in the interpretation of junction phenomena, any interpretation of the measurements obtained from alloyed heterojunctions, in terms of simple heterojunction theory, must be viewed with considerable scepticism. 2. Heterojunction Structures 2.1 Metallurgical

considerations

I n a semiconductor heterojunction it is implied t h a t there is an intimate contact or bond between the different semiconductor materials. The degree of perfection of fit can vary to a great extent and is dependent on the lattice match of

353

Alloyed Semiconductor Heterojunctions

IN

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£ * «4-1 cO ° '3 ® -p fi ® C ^ Ml

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ij ® CL TO tD ^

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£ fi

PM fi

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354

J. R . DALE

the two materials, their orientation, contamination by impurities, and the continuity of any polar bonds which are involved in the system, for example such as exist in the Group I I I to V semiconductors. Lattice constants for some diamond and zinc blende structures are listed in Table 1. From this table it can be seen that very few semiconductor pairs with close la' tice constants can be found if systems such as GaAs-Ga^Ini _ xAs are neglected. For many applications the most desirable heterojunctions would be between two semiconductors of a three component system, here lattice mismatch of 3 to 4 % or greater would be expected, except in the case of Ge-GaAs where a lattice mismatch of only 0 . 0 7 % is observed. As a result of this, in most heterojunctions, defects mainly in the form of edge type dislocations must be present near the interface. These will give a number of dangling bonds or bond deficiencies which will tend to produce an interface charge. Fig. l a shows dislocations at the boundary of two diamond type semiconductors joined at the (111) plane and Fig. l b shows in three dimensions, a grid consisting of three equiangularly spaced sets of edge type dislocations on the (111) plane. The minimum number of dislocations of any type which must be present has been calculated by Oldham and Milnes [40] directly from the difference in surface bond energy on the semiconductors. For semiconductors having lattice constants and X2 where X1 is less than A2 the difference in surface bond energy AN s is given by AN a = JVs1 — NBi where Nal and Ns2 are the surface bond energies on either semiconductor which depend only on and and the particular interface plane. ANa is the minimum dangling bond density in the interface plane and is therefore equal to the total length of dislocations per unit area times the number of dangling bonds per unit length. When there are i sets of dislocations with each set consisting of parallel dislocations with a spacing h between the dislocations in the set, then AN a = i/hc Here c is the mean spacing between dangling bonds on the dislocation and i is determined by the symmetry of the interface plane. Read [41] has developed a formula for c as a function of the magnitude of the Burgers vector b and the Fig. 1. a) A view of a possible single array of partial edge dislocations for a (111) heterojunction. The dislocation lines lie in the , , and C = A,B;

j , h = 1.....4;

|0 = 0

and where W is the energy. B y using new variables =

1

= e « w =

iW

rjfc

-

°

x

«2 — 4 y 2 x 1 — 1) y " e = p z= l

3 bs ) = N '

n

z

na — l

1

d

L n S m > m ) a w , . C - «3 &.),

¿J e^Mt-m^) y

p

(

r

_

%

(12)

bt - n2 b2 - n3 b3) .

Fig. 1. An ideal (100) surface plane of a diamond-like crystal. The shaded plane represents the crystal surface. Surface orbitals projecting towards vacuum may be seen

The Ideal (100) Surface of a Semi-Infinite Diamond-Like Crystal

395

nv n2, ns are integers defining crystal lattice points with position vectors rn = n x + m2 b 2 + n3 b3 . The (100) surface plane is characterized by the relation n3 = 1. It cuts two bonds, connecting a surface B atom with its two neighbouring A atoms (see Fig. 1). The two B atom surface orbitals projecting towards vacuum will be denoted by indices p = 7,8. According to the general theory [3], the coefficients flj v p n , and the surface state energy of 4- s p i n electrons are determined by the following system of equations [7, 15]: where

pn,=

—y Lpn,; io dj\ 8 1 — y

. 20 e i d j [ n ,

(13)

in

P n3

3

2 71

n

J 0

A>>

^ '

Ap'p is the determinant A ' with the p'-th row and the p-th column omitted. We respect the boundary conditions on the crystal surface by taking dj. io = 0 ,

dj.20 = 0.

(15)

Putting n3 = 0, p = 1,2 in (13), we therefore have two equations:

— y ¿10; 10 ^ i s i — y ¿10; 20

dj\ 71 = 0 ,

— y ¿20; 10 ^ 8 1 — y ¿20; 2 0 d j \

(16)

= 0

n

with the following solubility condition: ¿10; 10 ¿20;20 — ¿10;20 ¿20;10 = 0 > (1^) which determines the energies of surface states. Equation (17) has been treated in [7], B y lengthy transformations, it has been rearranged and finally split in two equations (see [7] equations (20), (21); compare also equations (18), (19) of [15]): = 0 ,

where

{vl — 4) 1»! V

1

¡h = x

1

(19) (20)

A = 1 n v;q} > The last possible configuration is :

W

= {itf K h YT YV v Q •

Z == {y>' + ip'~ yj'+

(5)

ip'.z) .

(6)

3. The Energy Separation between Parallel and Antiparallel Spin Configurations The wavefunctions M' and N' are, of course, not the eigenfunctions of total spin. If we denote the eigenfunction of S 2 = 0 by A and the eigenfunction of S2 = 1 ( 1 + l ) = 2 b y the two appropriate linear combinations of M' and N' are given by

0A = 2-V2 A {M' - N') ,

0V = 2-!/2 B (M' + N') .

(7)

A and B are the normalization constants equal to (1 — and (1 + Sm'n1) _ 1 / 2 respectively and SM>= (M'\N"). The problem resembles now closely that one of triplet-singlet separation in hydrogéné molecules. To find the energies of parallel and antiparallel spin configurations, we have to solve the secular equation (M'\3e\M'y

- E

(M'\X\N'y

- SM.N. E