Physica status solidi / A.: Volume 48, Number 1 July 16 [Reprint 2021 ed.] 9783112494820, 9783112494813

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plxysica status solidi (a)

> *

ISSN 0031-8965

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VOL. 48 • NO. 1 • JULY 1978

Classification Scheme 1. Structure of Crystalline Solids 1.1 Perfectly Periodic Structure 1.2 Solid-State Phase Transformations 1.3 Alloys. Metallurgy 1.4 Microstructure (Magnetic Domains See 18; Ferroelectric Domains See 14.4.1) 1.5 Films 1.6 Surfaces 2. Non-Crystalline State 3. Crystal Growth 4. Bonding Properties 5. MössBauer Spectroscopy 6. Lattice Dynamics. Phonons 7. Acoustic Properties 8. Thermal Properties 9. Diffusion 10. Defect Properties (Irradiation Defects See 11) 10.1 Metals 10.2 Non-Metals 11. Irradiation Effects (X-Ray Diffraction Investigations See 1 and 10) 12. Mechanical Properties (Plastic Deformations See 10) 12.1 Metals 12.2 Non-Metals 13. Electron States 13.1 Band Structure 13.2 Fermi Surfaces 13.3 Surface and Interface States 13.4 Impurity and Defect States 13.5 Elementary Excitations (Phonons See 6) 13.5.1 Excitons 13.5.2 Plasmons 13.5.3 Polarons 13.5.4 Magnons 14. Electrical Properties. Transport Phenomena 14.1 Metals. Semi-Metals 14.2 Superconductivity. Superconducting Materials and Devices 14.3 Semiconductors 14.3.1 Films 14.3.2 Surfaces and Interfaces 14.3.3 Device. Junctions (Contact Problems See 14.3.4) 14.3.4 High-Field Phenomena, Space-Charge Effects, Inhomogeneities, Injected Carriers (Electroluminescense See 20.3; Junctions See 14.3.3) 14.4 Dielectrics 14.4.1 Ferroelectrics 15. Thermoelectric and Thermomagnetic Properties 16. Photoconductivity. Photovoltaic Effects 17. Emission of Electrons and Ions 17.1 Field Emission Microscope Investigations 18. Magnetic Properties 18.1 Paramagnetic Properties 18.2 Ferromagnetic Properties 18.2.1 Ferromagnetic Films 18.3 Ferrimagnetic Properties 18.4 Antiferromagnetic Properties (Continued

on cover three)

phys. s tat* sol. (a) 48 (1978)

Author Index V . N . ABRAMOV B . S . ACHABYA A . F . AKKERMAN S . P . ALEKSANDROVA 0 . K . ALEKSEEVA W . H . M. ALSEM S . AMELINCKX V . N . ANDREEV V . E . ANTONOV K . I . ARAI H . AREND M . A . ARIANDIAGA K . ARLAUSKAS M . ASCHE R . ASSENOV V . L . AVER YANOV M . BABOUT C. BALASTJBRAMANIAN L . BALDI C. BANSAL H . J . VON BARDELEBEN K . BARTKOWSKI J.BARTON H . BÄSSLER C. L . BAUER 1. T . BELASH A . G . BELOUS S. BESSE A . BHALLA A . BITTAR A . V . BOBYL B . BOCHU Y U . V . BOGATYREV D . BOICE L . P . BOLSHAKOV B . BONIFACE O. Y U . BORKOVSKAYA J . BORKOWICZ H . BOSSAC . . A . BOSTANJOGLO A . G. BRAGINSKAYA D . BRÄUNIG W . BRODKORB P . M . BRONSVELD E . BUHRIG A . BUROFF V . N . BYKOV J . G. B Y R N E G . F . CEROFOLINI M . CHABIN E . I . CHAIKINA P . CHANTIKUL G . CHASSAGNE

287 235 K47 609 K97, K169 497 383, 39, K 5 K153 K185 175 53 53 K149 323 K193 K93 459 K71 523 K119 K145 215 K51 K15 555 K185 183 99 431 K123 249 581 K127 551 281, K 1 1 5 417 K55 225 369 481 K L 15 533 K157 497 K63 K109 K97 551, K 8 3 523 67 281 79 425

H . S . CHEN J . CHENAVAS K . L . CHOPRA S . Y . CHUANG F . A . CHUDNOVSKII A . COLLOMB J . W . CORBETT A . CORET T . CORNELISSENS F . COSANDEY C. S . G . COUSINS L . E . CROSS S . M. DAVIDSON T . H . O'DELL R . DILLER N . L . DMITRUK J . DOERSCHEL M . DORIKENS L . DORIKENS-VANPRAET P . DOUBRAVA V . DUTTA W . ECKE J . T . EDMOND M. EGÉE P . EVEN H . - G . FABIAN H . FABIG E . FABRE N . V . FADEEVA W . R . FAHRNER G. FERLA J . FERNANDEZ R . FERRETTI A . S . FILIPCHENKO P . FLEISCHMANN G. F L E U R Y R . FLORIAN M. H . EL-FOULY J . DE FOUQUET G. FRIGERIO K . FUKAMICHI K.FUNKE V . V . GAGULIN A . V . GAISANYUK R . K . GARTIA R . GAUTHIER H . P . GEMÜND S . S . GEORGIEV E . V . GEROVA L . GERWARD

K181 581 257 K181 K153 581 K31 465 K5 555 113 431 KL 59 513 K55 KLL 133 133 K93 257 K161 395 89 137 369 407 137 183 533 523 53 533 2 8 1 , K L 15 439 417 K35 395 99 523 175 KL 79 183 K131 235 459 481 609 609 113

616

Author Index

F . GILLETTA K . D . GLINCHUK A . J . GLOVER A . GOLTZENE I . S . GORBAN E . GRATZ G . A . GRISHCHENKO V . A . GRITSENKO Y . GROS C . GUITTARD

67 593 155 K145 329 473 329 31 581 459

C . HANSCH J . R . HANSCOMB A . HAYDAR A . HEIDEMANN H . HEMSCHIK C H . HERZIG G . HILSCHER T . HIRATA L . W . HOBBS P . HOLUJ P . HÖSCHL M . E . HOUGHTON K . HÜBNER J . P . HUVENNE

KLL 79 465 K179 377 A . T . MACRANDER K79 K . MAEDA 473 4 5 1 . J . MAEGE M . MAKI 425 R . S H . MALKOVICH 191 A . M . MANCINI K43 C . MANFREDOTTI 71 M . MANZEL 147 M . MABEZIO 417 S . A . MABSHALL 603 T . MARSHALL K1 A . MABTINAITIS 287 T . MASUMOTO M . MATSUDA 175 P H . MAZOT K181 E . E . MEERSON K101 G . H . MELKUMYAN 191 D . MELVILLE 551 H . MENNIGER 581 I . A . MERILOO K149 B . MEYER C. MEYER K179 V . I . MIKHAILOV 137 N . F . MIRON K141 V . V . MITIN K203 K . P . MITROFANOV K31 M . MOLDOVANOVA 209 P . M . MOONEY 175 P . MORAVEC . 447 E . A . MOVCHAN 609 J . MUCHA KLL B . MÜLLER K59 M . MÜLLER 263 T . MURA 555 R . MURRI K55 M . I . MUSATOV 225

V . M . IEVLEV D . E . IOANNOU B . G . IVANOV T . JAGIELINSKI G. J . JAN M . JEDLICKA A . JESMANOWICZ M . L . JOHNSON J . C . JOUBERT G . JTJSKA J . KALUS G . KAMARINOS T . KANADANI A . M . KAPITONOV J . KARINS W . I . KHAN M . KIKTJCHI N . KINOSHITA K . I . KIROV F . - G . KIBSCHT J . KOCKA T . I . KOLCHENKO Y . KOMEM R . V . KONAKOVA J . KOREC A . P . KORENKO F . P . KORSHUNOV U . KÖSTER K . I . KUGEL G . KÜHNEL

K203 K127 313 K131 K63

T. E. L. V. A.

B . KURENKEEV KURODA F . KURTENOK A . KUZMINIKH I . KUZNETSOV

J . VAN LANDUYT G . LAUTZ Y.H.LEE M . LEFELD-SOSNOWSKA P . LEGRAND D . LESUEUR V . A . LEVDIK H . LÖFFLER V . M . LOMAKO

K. K. P. A.

NAKAGAWA NARAYANDA.S NATH KAURIZBAEV

281 105 323 K175 287 39, 383,

K5 121 K31 565 417 K123 K97 369, K 6 7 263 571 587 407 105 241 293 293 K161 581 165 165 K43 175 105 99 31 23 209 407 287 K145 581 K169 K97 323 183 KL93 K31 K43 323 221 533 K51 447 293 287 587 K71 257, 345 K115

Author I n d e x E . NEBAUER H . T . G. NILSSON E . NOSSABZEWSKA-ORLOWSKA

K109 345 225

M. OHTA H . OPPERMANN

K141 377

S . PANCHANADEES WARAN C. J . DE PATER G. S . PEKAR H . E . PELTNER J . PELZL A. V . PETROV V . A.PETROV S . V . PLOTNIKOV M. V . PLOTNTKOVA V . A . POKOEVA ß . K . PONOMABEV E . G. PONYATOVSKII A.N.POPKOV A . V . PROKHOROVICH

K83 503 249 K79 K35 K153 K131 K175 183 241 K185 K185 K115 593

M. QUINTARD

99

M. RACHWALSKA W . RACZYÄSKI M. RADHAKRISHNAN J . RAFALOWICZ H . RAIDT V . V . RATNAM B . RAVEAU W . REICHELT M. B . O'REILLY W.RICHTER R . DE RIDDER C. RIDOU A. RIZZO W . H . ROBINSON V . E . RODIONOV J . ROOS M. ROSENBERG P . L . ROSSITER D . ROUBY E . W . VAN ROYEN E . I . ROZUM J . RUZYLJ-O

297 K27 K71 215, 221 407 235 301 377 489 513 383 67 293 155 593 53 K35 71 439 497 KL 75 199

K.SACHSE A. SAKAKIBARA A. SAKALAS A. P . SAKALAS M. VAN SANDE S. SAPRU O. G. SARBEY S . B . S . SASTRY S . SATERLIE V . A . SAVASTENKO

' .

121 K141 K43 329 383 K189 323 ; . K189 551 K135

K SCHINDLER P . SCHLOTTER CH. SCHNITTLER C. SCHWAB G. H . SCHWUTTKE D . SEGERS R . A SERWAY YA. L . SHAIOVICH V . P . SHANTAROVICH M. K . SHEINKMAN A . V . SHEKOYAN A . U . SHELEG E . V . SHVEDOV W.SIEGEL O SIMMICH S . P . SINITSA J . SKÄCHA T . SKOSKIEWICZ E . M. SMOKOTIN A . S . SODEIKA V . V . SOKOLOV S . P . SOLOVIEV B . SPRUSIL T . STANEK J . STAUN OLSEN G. STAUPENDAHL G. N. STEPANOV V . A. STRELTSOV F . STUDER C. S . SUNANDANA J . - E . SUNDGREN P . SÜPTITZ S . TAKEUCHI M. J . TELLO G. VAN TENDELOO E . I . TERUKOV P . THEVENARD V. G. TEIESSEN A. V . TITOV V . V. TITOV A . K . TKACHENKO Y U . A. TKHORIK M. TREILLEUX 0 . A. TROITSKII P . K . TSENG N . TSUYA 1. I . TYCHINA W . K . UNGER R . W . URE, J R V . YALVODA H . VARGAS L . VASANELLI Y U . N . VENEVTSEV S. VENGRIS

617 K199 K15 357 K145 335 133 165 543 K97, K169 249 23 K135 603 K63 K67 31 K93 KL65 K203 329 K131 183 K113 297 113 K199 K203 K23 301 K19 345 K109 587 53 3 9 , 383, K 5 377, K 1 5 3 425 K185 183 13 329 K55 425 229 K181 175 329 K89 K83 K101 K35 293 183 K149

618

Author Index

G . VERGÜTEN

417

G . C . VEZZOLI

K75

M. WOLF

137

R . WOLF

P . VLKTOROVITCH E . VLACHÂ

K113

G . VOIGT

407

S . A . VOROBIEV P. VOSTRÎ V . I . VOVNENKO

D . WLOSEWICZ

A . WOLFENDEN A . WOLKENBERG

K175 K39,

K113 593

M . YAMADA K . H . YANG R . T . YOUNG

G. WEIDNER

K105

R . WERNHARDT

K35

E . ZIEGLER

E . WIESER

K51

R . A . ZVINCHUK

physica status solidi (a) applied research Board of Editors S. A M E L I N C K X , Mol-Donk, J . A U T H , Berlin, H. B E T H G E , Halle, K. W. B Ö E R , Newark, P. G Ö R L I C H , Jena, G. M. H A T O Y A M A , Tokyo, C. HILSUM, Malvern, B. T. K O L O M I E T S , Leningrad, W. J . M E R Z , Zürich, A. S E E G E R , Stuttgart, G. S Z I G E T I , Budapest, K. M. VAN V L I E T , Montréal Editor-in-Chief P. G Ö R L I C H Advisory Board L. N. A L E K S A N D R O V , Novosibirsk, W. A N D R Ä , Jena, E. B A U E R , Clausthal-Zellerfeld, G. C H I A R O T T I , Rom, H. C U R I E N , Paris, R. G R I G O R O V I C I , Bucharest, F. B. H U M P H R E Y , Pasadena, E. K L I E R , Praha, Z. M Ä L E K , Praha, G. O. M Ü L L E R , Berlin, Y. N A K A M U R A , Kyoto, T. N. R H O D I N , Ithaca, New York, R. SIZMANN, München, J . S T U K E , Marburg, J . T. W A L L M A R K , Göteborg, E. P. W O H L F A R T H , London

Volume 48 • Number 1 • Pages 1 to 270, K l to K100, and AI to A8 July 16, 1978 PSSA 48(1) 1 - 2 7 0 , Kl—KlOO, A l — A 8 (1978) ISSN 0031-8965

AKADEMIE-VERLAG-

BERLIN

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S c h r i f t l e i t e r u n d v e r a n t w o r t l i c h f ü r d e n I n h a l t : P r o f e s s o r D r . D r . h . c. P . G ö r l i c h , D D R 1 0 2 - B e r l i n , N e u e S c h ö n h a u s e r S t r . 20 b z w . D D R - 6 9 J e n a , S c h i l l b a c h s t r . 2 4 . V e r l a g : Akademie-Verlag, D D R - 1 0 8 Berlin, Leipziger Straße 3 - 4 : F e r n r u f : 2 2 3 6 2 2 1 u n d 2 2 3 6 2 2 9 ; T e l e x - N r . : 1 1 4 4 2 0 ; B a n k : S t a a t s b a n k der D D R , Berlin, K t o . - N r . : 6836-26-20712. C h e f r e d a k t e u r : D r . H . - J . H ä n s c h . R e d a k t i o n s k o l l e g i u m : P r o f . D r . E . G u t s c h e , D r . H . - J . H ä n s c h , D r . H . L a n g e , D r . S. O b e r l ä n d e r . Anschrift der R e d a k t i o n : D D R 102-Berlin, Neue Schönhauser Str. 20; F e r n r u f : 2 8 2 3 3 8 0 . Veröffentlicht u n t e r der L i z e n z n u m m e r 1620 d e s P r e s s e a m t e s b e i m V o r s i t z e n d e n d e s M i n i s t e r r a t e s d e r D e u t s c h e n D e m o k r a t i s c h e n R e p u b l i k . G e s a m t h e r s t e l l u n g : V E B D r u c k e r e i „ T h o m a s M ü n t z e r " , D D R - 5 8 2 B a d L a n g e n s a l z a . E r s c h e i n u n g s w e i s e : D i e Z e i t s c h r i f t „ p h y s i c a s t a t u s solidi ( a ) " e r s c h e i n t j e w e i l s a m 16. e i n e s j e d e n M o n a t s . J ä h r l i c h e r s c h e i n e n 6 B ä n d e zu j e 2 H e f t e n . B e z u g s p r e i s e i n e s B a n d e s 160,— M z u z ü g l i c h V e r s a n d s p e s e n ( P r e i s f ü r d i e D D R 120,— M). B e s t e l l n u m m e r dieses B a n d e s : 1085/48. (c) 1978 b y A k a d e m i e - V e r l a g B e r l i n • P r i n t e d i n t h e G e r m a n D e m o c r a t i c R e p u b l i c . A N ( E D V ) 20735

P R O F E S S O R Dr. rer. nat. habil. EGON G U T S C H E I N H O N O U R OF H I S 50th B I R T H D A Y

On the 15th of July 1978 Professor

E G O N GTJTSCHE,

member of the Editorial Staff

of physica status solidi (a) and physica status solidi (b) and member of the Board of Editors of physica status solidi (b), celebrates his 50th birthday. From the first year of appearance of physica status solidi (1961) he has essentially contributed to the development of the journal as well as to the preparation and foundation of physica status solidi (a) (1970). He has also deserved well of the further prosperity of the two series existing since then by giving valuable scientific advice based on his profound knowledge and experience as solid-state physicist, as well as constructive organisational recommendations. His 50th birthday is an occasion of appreciating his merits and of thanking him for his unresting activity for this journal. Health and creativity may be granted to him in future.

i

Contents Page

Review Article V. V. TITOV

Ion Implantation — Problems and Perspectives

13

Original Papers G . H . MELKUMYAN a n d A . V . SHEKOYAN

On the Theory of Self-Action of Ultrasonic and Hypersonic Waves . . . .

23

V . A . GRITSENKO, E . E . MEERSON, a n d S. P . SINITSA

Unsteady Silicon Nitride Conductivity in High Electric Fields

31

R . W O L F , G . VAN T E N D E L O O , J . VAN L A N D U Y T , a n d S . A M E L I N C K X

Electron Diffraction and High Resolution Electron Microscopic S t u d y of Ordering in t h e Gold-Manganese System (II)

39

M . A . ARRIANDIAGA, M . J . TELLO, J . FERNANDEZ, H . A R E N D , a n d J . R o o s

T. H .

O'DELL

Calorimetric Study of Order-Disorder Phase Transitions in Long-Chain (C J! H2n+iNH 3 ) 2 CuCI 4 Compounds

53

Static Wall Structure in Bubble Films under Large In-Plane Fields . . .

59

M . CHABIN, F . GILLETTA, a n d C. RIDOU

Thermal Properties of TlCdF 3 and R b C a F 3 near Their Phase Transitions .

67

M . E . HOUGHTON a n d P . L . ROSSITER

Induced Anisotropy in an Fe-27.5 Cr-17.5 Co-0.5 Al Alloy

71

J . R . HANSCOMB a n d P . CHANTIKUL

M. EGÉE

The Effect of Strontium Chloride as I m p u r i t y on the Thermoelectric Power of Potassium Chloride

79

Effect of a Direct Electric Field on t h e Photoluminescence Processes a n d Model of t h e Luminogen Centre in ZnS : Cu

89

S . B E S S E , M . Q U I N T A R D , P H . MAZOT e t J . D E F O U Q U E T

Influence de l'hydrogène sur le f r o t t e m e n t intérieur du titane

99

E . KURODA, M . MATSUDA, a n d M . MAKI

Growth and Characterization of Silicon Ribbon Crystals Grown with Wetting and Non-Wetting Dies

105

6

Contents Page

C . S . G . COUSINS, L . G E R W A R D , a n d J . STAUN O L S E N

Multiple Diffraction in Crystals Studied by an X - R a y Energy-Dispersive Method

G . LAUTZ a n d K .

SACHSE

Noise Spectra of Hot Carriers in n-Germanium

D . SEGERS, M . DORIKENS, a n d L .

121

DORTKENS-VANPRAET

Temperature Dependence of Positron Annihilation Parameters in Bismuth

P . VIKTOROVITCH, G . KAMARINOS, P . E Y E I T , a n d B .

K.

HUBNER

113

133

FABRE

Correlation between Interface States and MIS Silicon Solar Cell Performances

137

Chemical Bond and Related Properties of Si0 2 (V)

147

W . H . ROBINSON, A . J . GLOVER, a n d A .

WOLFENDEN

Electrical-Mechanical Coupling of Dislocations in KC1, NaCI, LiP, and CaF2

155

S . A . MARSHALL, T . MARSHALL, a n d R . A . S E R W A Y

Electron Spin Resonance Absorption Spectrum of Trivalent Gadolinium in the Oxide YA1G

M . KIKTTCHI, K . FITKAMICHI, T . MASUMOTO, T . J A G I E L I N S K I , K . I . A R A I , a n d N .

165

TSUYA

Giant AE Effect and Elinvar Characteristics in Amorphous F e - B Binary Alloys

175

V . V . GAGTJLIN, N . V . F A D E E V A , A . G . B E L O U S , A . V . T I T O V , K . P . M I T R O F A N O V , M . V . P L O T N I K O V A , S . P . SOLOVIEV, a n d Y u . N . V E N E V T S E V

New Seignette-Magnets with Hexagonal Barium Titanate Structure . . .

F . H O L U J a n d A . JESMANOWICZ

J . RUZYLLO

A. WOLKENBERG

183

E P R of Fe 3 + in Andalusite and Kyanite at V-Band and the Pair Spectra .

191

Model of Structural Transformations on the Chemically Etched Silicon Surface during Thermal Oxidation

199

Capacitance Measurements of the Silicon-Silicon Dioxide-Potassium Chloride Water Solution Interface as a Method to Determine the Fixed Charge Value and Its Centroid

203

W . I . KHAN a n d D . MELVILLE

Magnetic Anisotropy Associated with Iron Substitution in Y 2 (Coj;Fei_z) 17 . 209

Contents

7 Page

K . BARTKOWSKI, D . WLOSEWICZ, a n d J . RAFALOWICZ

Electrical Resistivity Anisotropy of Tin Monocrystals of Different Concentration of Chemical Impurities in the Temperature Range 5 to 70 K . . .

215

J . MUCHA a n d J . RAFALOWICZ

Thermal Conductivity Minimum of Aluminium

221

J . BORKOWICZ, J . K O R E C , a n d E . N O S S A R Z E W S K A - O R L O W S K A

O.

A.

TROITSKII

Optimum Growth Conditions in Silicon Vapour Epitaxy

225

Fractionation of Stable Isotopes of Metals by Combined Electric Migration and Zone Melting

229

R . K . GARTIA, B . S . ACHARYA, a n d V . V . RATNAM

Effect of Re-Irradiation on Zx Centres

235

R . S H . MALKOVICH a n d V . A . POKOEVA

Diffusion of an Ionized Impurity in a Semi-Infinite Semiconductor . . . .

241

A . V . BOBYL, G . S. PEKAR, a n d M . K . SHEINKMAN

Dark Conductivity and Photoconductivity of Nickel-Doped CdS Single Crystals

249

V . D U T T A , P . N A T H , a n d K . L . CHOPRA

Structural and Electrical Properties of Polycrystalline Ge Films

257

T . I . K O L C H E N K O a n d V . M . LOMAKO

Removal and Scattering of Charge Carriers by Defect Clusters in Semiconductors

263

Short Notes D . E . IOANNOTJ a n d S . M . D A V I D S O N

SEM Observation of Dislocations in Boron Implanted Silicon Using Schottky Barrier EBIC Technique

K1

T . C O R N E L I S S E N S , G . VAN T E N D E L O O , J . VAN L A N D U Y T , a n d S . A M E L I N C K X

Peierls Distortion, Chain Polytypism, and Dislocation Coupling in NbS 3 .

.

K5

Dislocation Reactions in Plastically Deformed Silicon Observed b y X - R a y Topography

Kll

F . - G . KIRSCHT, C. HANSCH, a n d J . DOERSCHEL

8

Contents Page

P . SCHLOTTER a n d H . B Ä S S L E E

Sensitized Injection into Anthracene Crystals from Surface Oxidation Products

K15

E S R Saturation of S 0 7 in X-Irradiated K H S 0 4

K19

Shear Stresses Induced b y Hydrostatic Pressure near the Surface of an I n clusion

K23

Permeability, Diffusivity, and Solubility of Hydrogen and Deuterium in Pure Iron a t 10 to 60 °C

K27

C . S . S U N AND AN A

V . A . STRELTSOV

W.

RACZYNSKI

P . M . M O O N E Y , R . T . Y O U N G , J . K A R I N S , Y . H . L E E , a n d J . W . CORBETT

Defects in Laser Damaged Silicon Observed b y DLTS

K31

R . F L O R I A N , J . P E L Z L , M . R O S E N B E R G , H . VARGAS, a n d R . W E R N H A R D T

P. VOSTR Y

Photoacoustic Detection of Phase Transitions

K35

On the Influence of Silver on the Recovery Spectrum of Quenched Cadmium Foils

K39

P . H Ö S C H L , P . MORAVEC, A . M A R T I N A I T I S , a n d A . S A K A L A S

Study of Photo-Hall Effect on Single Crystals of Cadmium Telluride Doped with Chlorine

K43

A . F . AKKERMAN

Reflection of Slow Hydrogen and Helium Ions from Solid Surfaces . . . .

K47

J . BARTON, E . W I E S E R , a n d M . MÜLLER

Investigation of t h e a - y Phase Transformation by Annealing of a ColdWorked F e - M n Base Alloy

K5I

0 . Y u . BORKOVSKAYA, N . L . D M I T R U K , R . Y . K O N A K O V A , a n d Y u . A . T K H O R I K

J . KOÖKA

Investigation of Radiation Defects in GaAs b y Means of Schottky Diode Characteristics

K55

Influence of Contacts on t h e AC Conductivity of Glasses

K59

E . ZIEGLER, W . SIEGEL, G . K Ü H N E L , a n d E . BUHRIG

Incorporation of Gallium in ZnSiP 2

K63

0 . SIMMICH a n d H . L Ö F F L E R

A Simple Model to Describe Isothermic Phase Transformations in Binary Alloys

K67

Contents

9 Page

K . K A R A YAXDAS, M . R A D H A K R I S H N A N , a n d C . B A L A S U B B A M A N I A N

Annealing Study of Electrical Resistivity and Defect Density in Silver Films K71 G. C.

VEZZOLI

Peaked Electrical Conductivity in Liquid Bismuth and Associated Optical Scattering

K75

H . E . PELTNER a n d CHR. HERZIG

New Application of the Knudsen Method for a Direct Determination of Thermodynamic Activities

K79

S. PANCHANADEESWARAN, R . W . U R E , J R . , a n d J . G . B Y R N E

W. K . UNGER

Positron Trapping at Precipitates in Aluminum-4 w t % Copper Single Crystals

K83

Search for Light-Induced Magnetization in Magnetic Semiconductors . .

K89

P . DOTJBRAVA, V . L . A V E R Y A N O V , a n d J . S K A C H A

Spectral Characteristics of Photodarkening of a-As60Se40 Films

K93

0 . K . A L E K S E E V A , V . N . B Y K O V , V . A . L E V D I K , N . F . MTRON, a n d V . P . SHANTAROVICH

Positron Study of Electron-Irradiated Vanadium

K97

Pre-printed Titles of papers to be published in the next issues of physica status solidi (a) and physica status solidi (b)

A1

Contents

11

Systematic List Subject classification: 1.1

Corresponding papers begin on the following pages (pages given in italics refer to the principle subject classification) : 113

1.2

39, 53, 67,.K35, K51, K67,

1.3

39, K83

1.4

39, 71, K5, K23

1.5

257

1.6

199

2

31, 147, K59,

3

13, 105, 225, 229, K79

4

147, 199

5

K51

7

23, K35

8

67, 133, 221

9

229, 241, K27

10.1 10.2

K75

K93

99, K39, K63, K68, K71, K83 . . . .

79, 155, 235, Kl, K5,

Kll

11

13, 263, K19, K31, K47, K55, K97

12.1

99, K23

13

121

13.1

147

13.3

137

13.4

89, 191, 249, 263, K15, K31, K43,

14.1

215, K39, K71, K75

14.3 14.3.1

89, 105, 263, K59, . . . .

31, 257

14.3.2

. . . .

203

14.3.3

. . . . . .

137, 203, K55

14.3.4

. . . .

31, 121, K59

14.4 14.4.1

K63

147 . . . .

183

15

79

16

137, 249, K15, K43, K93

18.2

59, 71, 175, 209

18.3

183

18.4

183, K89

19

165, 191, K19

20.1

K75, K93

20.3

89, 235

K63

12

Contents

21

221, 229, K23, K 3 9 , K 4 7 , K 6 7 , K 7 5 , K 8 3

21.1

39, 99, 209, K 9 7

21.1.1

71, 175, K 2 7 , K 4 7 , K 5 1

21.6

39, K 7 1 , K 7 9

21.7

133, 215

22

31, 241, K 5 , K 5 9 , K 9 3

22.1.1

121, 257

22.1.2

13, 105, 113, 137, 199, 203, 225, K l , K l l , K31

22.2.1

263, K 5 5

22.4.1

89, 249

22.4. 3

K43

22.5.2

79, 155, 235

22.5. 3

155

22.6

147

22.8

53, 191, K35, K 6 3 , K 7 5

22.8.1

67, 183, K 1 9

22.8.2

165, K 8 9

22.9

K15

Contents of Volume 48 Continued on Page 278

Review

Article

phys. stat. sol. (a) 48, 13 (1978) Subject classification: 3 and 11; 22.1.2 I. V. Kurchatov

Institute of Atomic Energy,

Moscow

Ion Implantation—Problems and Perspectives By V . V . TITOV

Contents 1.

Introduction

2. Advantages

of ion-implantation

doping

— statements

3. Limitations

of ion-implantation

doping

and methods

and

reality

of their

overcoming

3.1 Radiation-enhanced annealing of defects 3.2 Pulsed annealing 3.3 Pulsed radiation-enhanced annealing 4.

Conclusion

References

1. Introduction Some time ago the ion implantation was a qualitative jump in semiconductor physics and technology. After promising qualitative results have been obtained the main efforts were focussed on the expansion of the research area (in addition to silicon other more or less promising semiconductor compounds were tried to dope using the ion implantation method) and on the introduction of new techniques to semiconductor industry. Now this tendency approaches saturation and new ideas for further progress in theory and practice of ion implantation are needed. The present paper is concerned with an analysis of two fruitful ideas, these (judging by the first experiments) can help to achieve new progress in ion implantation. The radiation-enhanced annealing and pulsed annealing of structural defects of ion-implanted layers are the ideas of interest. The modern technology makes it possible to realize these ideas by different ways. Experimental check and comparison of these advantages and limitations is an extensive area of investigation. 2. Advantages of Ion-Implantation Doping — Statements and Reality In the sixties, when the laboratory ion implantation techniques began to be applied in semiconductor industry, the new method was widely discussed with respect to the numerous benefits of implantation doping of a monocrystalline target. These advantages are as follows: 1) any impurity can be introduced into the given semiconductor; 2) any semiconductor can be subjected to the implantation doping; 3) the impurity can be implanted in any concentration, independent of its solubility in the target material;

14

V . V . TITOV

4) the distribution profile of the implanted impurity can be varied by means of altering the electric parameters of the ion beam; 5) the location of the doped layer and configuration can be easily provided due to mechanical masking (by placing a mask on the target surface or by means of photolitography); 6) the target temperature during implantation may be varied from liquid helium temperature to the melting point. In particular, ion implantation can be carried out at room temperature; 7) the annealing temperature after implantation is substantially lower than the diffusion temperature since the parameters of the semiconductor target do not get worse after annealing; 8) the implantation is carried out under high vacuum conditions so that the purity of the process is higher than that of the high-temperature diffusion technique; 9) The dopant may represent an inexpensive material of technological purity (or, more often, the salt of this substance is used); 10) ion implantation processing can be, in principle, easily made automatic since the basic parameters of doping (depth, concentration, profile) may be controlled by electric values (ion beam current, accelerating voltage). The experience gained from the implantation doping of semiconductors has, however, shown that the above advantages are not so easily realized and not to an extent that would be desirable. Returning to the above statements, let us consider in more detail how far and under what conditions the above advantages may be realized. 1) Any impurity can be introduced into the given semiconductor. This is always true, however, it is important for the semiconductor technology that the impurity atoms be not only introduced into the target specimen, but they should be made electrically active, i.e. as a rule, they should occupy substitutional sites in the lattice (or in the corresponding sublattice). In some cases the latter problem turns out to be more complicated than the implantation of impurities itself (especially in semiconductor compounds). This problem has not yet been solved for certain systems. 2) Any semiconductor can be subjected to the implatation doping. In a number of cases this "apparent" condition may be realized only by applying special operations. First of all this applies to the decomposition of binary (and ternary) semiconductor compounds, when a considerable number of atoms of one kind (as a rule, of the more volatile elements of the V and V I groups) escape from the surface during the implantation and subsequent annealing. In this case the desired doping effect may be obtained with a thin protecting film being "transparent" for fast doping ions, and "nontransparent" for the volatile component. Another difficulty is faced when the implantation is made in polymorphous semiconductors. It is sometimes not clear if the layer amorphized during the implantation can be brought into the crystalline form that we need. In particular, after the implantation and subsequent annealing diamond changes into graphite, and this imposes certain limitations on the implantation regimes: the diamond cannot be amorphized, i.e. the doping temperature should be sufficiently high. 3) The impurity can be implanted in any concentration, independent of its solubility in the target material. In fact, the process of impurity implantation is in no way connected with the solubility, this is a highly nonequilibrium process. However, on annealing the defects after the implantation at elevated temperatures, we restore the thermodynamic equilibrium in the semiconductor with the introduced impurity. In this case the amount of impurities being introduced above the solubility limit is found to be not only electrically inactive, but also very often to form precipitates of

Ion Implantation — Problems and Perspectives

15

other phases, giving rise to dislocations or defect clusters. This can be seen, for example, in "negative" annealing. 4) The distribution profile of the impurity being implanted can be varied in a wide range by altering the electric parameters of the ion beam. Indeed, the possibilities of the implantation method are substantially more comprehensive than those of the diffusion method. It is possible to realize profiles which are an arbitrary superposition of the Gaussian curves exp (—(R — x)2/2(AR)2). However, the values R and AR are connected one with another, and this fact appreciably narrows the class of profiles accessible for implantation doping. For example, the implantation doping can yield a buried inversion layer, in this case, however, the relationship between the implanted layer depth, its width, and the impurity concentration cannot be arbitrary (the higher the concentration in the layer and the deeper the layer the broader it should be). Additional difficulties appear in subsequent annealing when the diffusion redistribution appreciably changes the shape of the initial profile. And, finally, there always exist a low-concentration area difficult for control, which is caused by channelling and is located in the "tail" of the distribution curve. Experience has shown that the channelling cannot be completely eliminated by any crystal-beam disorientation and this fact should be always taken into account. 5) The doped layer location can be easily provided due to mechanical masking. In fact, the technique to localize the implantation layer up to submicron sizes is simpler (or it is not more complicated) than in the diffusion technology. However, it is difficult to obtain p-n junctions with high breakdown voltages due to "extremely" strong localization of the doped layer by a vertical edge mask. A small radius of curvature at the p-n junction boundary limits the breakdown voltages to rather modest values. To increase the working voltages it is necessary to deepen the junction by diffusion, and in this case many advantages of the implantation doping are naturally lost. 6) The range of target temperatures during doping may be very broad from liquid helium temperatures to the melting point. This rather substantial advantage of the implantation method (especially if one does not need to take care to temperature at all) becomes not so bright if we take into account that after doping the semiconductor should be heated to anneal the radiation defects. Furthermore, it turned out that in many cases there was a quite definite range of optimum implantation temperatures. 7) The annealing temperature after implantation is substantially lower than the diffusion temperatures so that the parameters of the semiconductor target do not get worse after annealing. In many cases this advantages are completely realized, and semiconductor devices with good parameters can be made after annealing at low temperatures. Nevertheless any annealing (even at very high temperature) is not able to eliminate completely the defects caused by implantation. Therefore, the leakage currents of implanted p-n junctions (especially in large-gap semiconductors) are considerably higher than those in diffusion p-n junctions. Besides, even minimum annealing temperatures were found to be too high for certain semiconductor materials (for example, Au-doped silicon fails at temperatures higher than 400 °C, while the usual silicon annealing temperature after implantation is 600 to 700 °C). 8) The implantation is carried out under high-vacuum conditions so that the process is purer than the high-temperature diffusion technique. When single samples are doped with small doses in laboratory there were no doubt about the high purity of the implantation method. In industry, however, at higher ranges and doses the importance of a certain process became apparent. In mass separation of an ion beam all foreign ions fall on the vacuum chamber walls of the implantation installation as the ion energy is sufficiently high to sputter the wall material, while the total intensity of foreign beams is sometimes substantially higher than the intensity of the work-

16

V . V . TITOV

ing ion beam. If the installation is in operation for a long time then due to multifold resputtering all the inner surfaces of the vacuum chamber and of the ion collector are found to be covered with a film containing all elements of the construction material, the diffusion oil cracking products, and all elements of the ion source crucible accumulated since the last cleaning of the installation. The same elements are found at the surfaces of the samples. Moreover, a part of the sputtered atoms is found inside the semiconductor (due to "drive-in" doping by the ion beam). Thus, the purity problem needs to be treated carefully when dealing with the implantation doping. The problem of purity is solved to considerable extent if the doping surface is covered with a thin protecting film. Before annealing it is etched (together with a wall material layer sputtered on it), and by placing supplementary diaphragms and shields into the working volume of the implantation chamber. 9) The dopant may be an inexpensive material of technological purity (or more often, the salt of this substance is used). This is the only benefit of the method which works always and to full extent. 10) The possibility to make the implantation process completely automatic has not yet been realized to yield a real automatic line. The necessity of multifold photolitography with many different operations almost excludes the possibility of complete automation in microelectronics ("almost" is used because the locality of operations can be in principle provided by using focused electron and ion beams). The idea of the automatic lines is very promising and can be realized in the production of such devices as power diodes or solar cells. Both insufficient production scope and insufficient attention to this line of research seem to be responsible for such a situation. 3. Limitations of Ion-Implantation Doping and Methods oi Their Overcoming This brief consideration of the features of implantation doping shows that all its advantages are unambiguous although each of them either has been already realized or may be realized in a sufficiently wide range of applications [1]. It is clearly seen that most of the "obstacles" preventing the realization of the technological advantages of the implantation doping are related to two physical processes: 1) many radiation defects are caused by the implantation in the doped layer; 2) after the implantation the semiconductor has to be heated, for annealing the radiation defects, to sufficiently high temperatures (although it is lower than the diffusion temperatures). Therefere, one of the most important directions of the implantation doping physics is the search for ways to decrease the production of defects due to implantation and to find means to increase the efficiency of radiation defect annealing with simultaneously reduced temperatures of this process. In recent years two promising ideas supported by experiments have appeared. Both ideas are concerned with the improvements of the annealing process. Let us consider them in more detail. 3.1 Radiation-enhanced

annealing

of

defects

It is known that ionizing radiation either intensifies certain processes or slows down some of them. There are processes which can proceed only under the action of radiation. The general validity of this law follows from the fact t h a t under the action of high-energy radiation as a rule some energy can be locally released in a solid, this energy being higher than the energy barrier of any physical process (except for nuclear processes) [2], In semiconductors, the radiation effect (of photons with any wavelengths, electrons, atomic particles) leads to the following: a) defects are produced in the layer being irradiated (if the energy and mass of the radiation " q u a n t u m " are sufficient ;b) ionization occurs, i.e. the energy transferred by the radiation " q u a n t u m "

Ion Implantation — Problems and Perspectives

17

in a single interaction is larger than the energy gap) and the exciton concentration increases (i.e. of "not quite free" electron-hole pairs); c) "heating" of free carriers takes place. Finally, all these kinds of excited state change to ordinary heating of the solid (with the exception of defects, however, the radiation types causing damage are naturally not used for radiation-stimulated annealing of the defects). During some time, however, the high-energy quanta (as compared with thermal energy) move in the semiconductor. Indeed the energy of a pair of carriers is of the order of 1 eV (corresponding to the width of the energy gap), the exciton energy slightly differs from this value, and both are more than an order of magnitude larger than the mean thermal energy ( « 0.025 eV at room temperature, and « 0.1 eV at 1000 °C). Both the charge carriers and excitons propagate freely in a defectless semiconductor crystal, but any inhomogeneity, and in particular, radiation defects become a centre of attachment or a recombination centre. Since in the process of recombination the energy of a pair or an exciton is released just in the recombination centre it becomes clear that such processes are very useful for the annealing of the defects [3]. Another factor which may intensify the annealing in an irradiated semiconductor is associated with the fact that the annealing activation energy depends on the charge state of the defect. Under irradiation a high concentration of excess current carriers of both signs occurs in the semiconductor. This means that the annealing rate can be increased since all more or less stable charge states of the defects will be present in appreciable concentration in the implanted layer. What kind of radiation is to be used for the best annealing stimulation ? I t is apparent that heavy atomic particles are not suitable for this purpose (they themselves damage the crystal), electrons and photons remain to be used. The energy of the radiation quantum cannot be chosen arbitrarily. The upper energy limit is given by the threshold of direct defect formation ( ~ 150 keV for electrons in silicon). The lowenergy limit is defined by the width of the energy gap. 1 ) There are some more recommendations concerning the choice of the energy range and kind of stimulating radiation. I t is desirable that "nonthermal" energy should not be released in the whole of the semiconductor volume, but it should be released mainly within the implantation layer. This indicates that the ion implanted layer should be irradiated by photons or electrons. The energies of the electrons or light quanta should be chosen such that their mean range was a close to that of the implanted ions as possible. Since the latter usually amounts to hundreds of Angstroms this fact limits the choice of the upper energy of the stimulating electrons to « 1 to 3 keV while the lowest energy of the stimulating light quanty is confined to a value for which the absorption coefficient is not lower than 3 X 10 3 to 104 c m - 1 . The second limit of the stimulating radiation energy interval determining the minimum range is insufficient in most cases, since ambipolar diffusion of the excess carriers causes broadening of their concentration profile up to depths, which may be a few times larger (and in some cases, even tens or hundreds times) than the depth of the implanted layer. 3.2 Pulsed

annealing

If the rate of defect annealing is compared to that of diffusion migration of an impurity it is not difficult to make the trivial conclusion provided that all other conditions being equal (the same activation energy, the same temperature), that it takes the same time for the annealing of a single defect as that being needed for the migra1 ) However, when the radiation intensities are very high, multi-photon excitation and pair generation are possible even at quantum energies lower than the energy gap. The efficiency of multi-photon processes is, however, substantially less than that of single-photon excitation.

2

physica (a) 48/1

18

V . V . TITOV

tion of the impurity atom from one lattice site to another neighbour site. It means that the annealing of single defects should be finished long before it is possible to detect the diffusion of the impurity by any method. This conclusion is also supported by the fact that the diffusion activation energy is in most cases considerably larger than the defect annealing activation energy. Experiments have given conclusive evidence of this fact [4, 5]: thermal annealing is usually completed in the first few minutes while it takes usually a few hours to vary the profile due to diffusion. Since this effect has been observed in a wide range of temperature it is quite natural to extrapolate towards reducing the annealing time and simultaneously increasing the temperatures to extreme values [5]. In this case the limit is determined by the heating and cooling rates. However, if ordinary semiconductor wafers being 200 to 300 jim thick are considered and conventional annealing with warming up the wafer throughout the entire thickness is carried out in a furnace the annealing time obviously cannot be made substantially less than 3 s, i.e. we cannot expect any qualitative effect here as compared with 30 min annealing. 3.3 Pulsed

radiation-enhanced

annealing

B y combining the ideas being considered it is not difficult to suggest a few ways for the realization of pulsed annealing with radiation stimulation in practice [6 to 8], So far, the following powerful pulsed sources of stimulating radiation (and simultaneously the sources of thermal energy) have been considered as being well known: an electron beam, white light of pulsed lamps, and laser monochromatic radiation. I t should be pointed out that the pulsed character of annealing can be provided with a constant radiation source [9] if a stimulating beam is focused at a sufficiently small area (to have necessary power) and this focused beam should scan the implanted layer surface (or the semiconductor sample should be moved under the beam). The first experiments [6 to 13] on the annealing of the implantation layers by irradiating them with a light pulse from a solid-state laser (ruby and neodymium glass laser) not only justified the expectations but also offered some additional positive effects. In this connection it is reasonable to consider in more detail processes occurring in a semiconductor under irradiation by a powerful short light pulse [14, 15], The state of the bombarded layer varies due to the following factors: 1) Thermal heating. In contrast to conventional prolonged thermal annealing, only a thin surface layer is heated in this case, and not the bulk semiconductor material. 2) Mechanical effect. In the ns regime the light pressure reaches ~ 10 s N/m 2 for the power of ss 100 MW/cm 2 . This pressure is not very large, however, due to the great rates of pressure increase and drops a powerful shock wave is produced in the irradiated material. The mechanical stresses caused by the temperature gradient are, however, more dangerous for the irradiated material. If the implanted layer is heated by AT and the extension of the layer is not possible (because of the thick cold substrate) the compression pressure of the heated layer along the surface is p = Ecu. AT, where E is the elastic modulus, and a the thermal expansion coefficient. For example, at A T = 600 °C a pressure as high as 109 N/m 2 is observed for silicon. I t is interesting to note that although this value is considerably larger than the material strength, silicon is not destroyed under such laser irradiation. 3) Ionization and excitation of the semiconductor atoms. The radiation intensity is so great in this case (especially in the ns regime) that in addition to the above mechanisms of radiation stimulation, multiphoton excitation should be taken into account. Moreover, when the concentration of nonthermal energy is high, a process opposite to annealing is possible to occur, when the system of atoms can be transferred to a state thermodynamically less in equilibrium than before the irradiation.

Ion Implantation — Problems and Perspectives

19

4) The probability for the system to be transferred into a non-equilibrium state under powerful pulsed irradiation is rather high due to another reason. After complete ing the light pulse the cooling rate of the layer being irradiated is substantially higher t h a n in other methods used for thermal processing (even in the most hard quenching techniques), i.e. the semiconductor may be "frozen" in a state similar to thermodynamic equilibrium at the maximum temperature, even if the radiation stimulation is not taken into account. To determine the relative role of the above four factors in various pulsed annealing methods with radiation stimulation Table 1 lists the basic annealing characteristics attainable at the modern technological level. All values are relevant to annealing of silicon doped by implantation up to 0.5 [i.m with a dose exceeding the amorphization dose. The basic energy parameters of the methods presented -in the table (energy, pulse duration, power) are realized in the following way. White light is obtained by focusing the radiation of pulsed xenon lamps, a broad electron beam is produced by a powerful magnetron or plasma source, a scanning point electron beam is generated by an electron gun with a point cathode. The monochromatic laser beam is generated by a pulsed Q-switched (ns) or free-generating (ms) laser and due to the scanning of a focused beam of a cw laser. The greatest heating is naturally observed in those points where the absorbed energy is distributed in a layer with smallest thickness. One can see from the comparison of the table data t h a t for equal annealing energies the annealing temperature rises with pulse duration (the deposited energy grows more rapidly than the thickness of the heated layer). Mechanical effect. A shock wave is essential only in the ns regime, i.e. if a Q-switched laser is used for irradiation. Longitudinal compression is proportional to the heating temperature and is the greatest at large pulse durations. I t should be pointed out when the layer being heated is large the substrate also exhibits a mechanical effect of opposite sign, i.e. an extension. Ionization and excitation. If single-quantum processes are considered, the maximum effect appears to be produced in layers with the highest generation intensity. I n this case radiation stimulation may appreciably vary, depending on the kind of recombination, (direct or indirect recombination). When direct recombination takes place the photons carry the energy into the crystal depth. Therefore, an increase in the irradiation power, i.e. the generation rate in indirect gap semiconductors may lead to a decreased efficiency of single-quantum processes. On the other hand, the probability of multi-photon absorption grows in the ns regime. Quenching. The cooling rate is proportional to the temperature gradient in an irradiated semiconductor, thus it should be maximum at ns laser annealing. Since multi-photon processes occur under the same conditions it is just in this range that the structures with maximum deviation from thermodynamic equilibrium should be obtained. The sources of radiation listed in the table may be divided into two groups according to the dominating mechanism of energy transfer. For intrinsic optical absorption (ruby and Ar lasers, and a neodymium glass laser, to a less extent) the energy release processes occurring in the semiconductor are almost independent of the dopant concentration and state of crystalline structure (the same is applied to electron irradiation). If the intrinsic absorption is small (neodymium glass and C0 2 lasers), the efficiency of laser annealing depends sufficiently on the carrier concentration present before the annealing and on the defect level of the irradiated layer. Additional selectivity of long-wavelength radiation absorption seems very attractive, in this case, 2*

20

V .

»

T i t o v

60 tí

2

i 2

is

y .

ira x

o

m

"3D

X

X

IN

M

•

•tí o S

» 2 ö ft

°

o

X

m

X

o

X

P5

2

x

3 •tí

ò

io XI tí

X

X

0 is the speed of US or HS waves in the absence of disturbances and T is the temperature increment. Substituting (3) into (1) we obtain the equation entirely coinciding with the appropriate equation in optics. As we deal with a narrow beam, the cross-sectional dimensions of which are much smaller than the length, we can take advantage of the method of slowly varying amplitude as in the nonlinear optics, and, hence, we may use the nonlinear optics results [5 to 15]. Equation (1) should be solved simultaneously with the thermal conductivity equation of the form [5 to 15] ecv8-T-=xAT +

^\A\*,

(4)

On the Theory of Self-Action of Ultrasonic and Hypersonic Waves

25

where o is the medium density, cp the specific heat capacity at constant pressure of the medium, A, a are amplitude and absorption coefficients, respectively, of US or HS waves, and x is the thermal conductivity. 3. Results and Estimates Until the characteristic relaxation time x = ocpa2jix has elapsed (a is the beam radius, x the thermal conductivity), the process is unsteady in the volume occupied by the wave and the results of non-stationary theory should be used. After the time t p the process is stationary and we have the following equation for the dimensionless width of the beam / allowing for diffraction [5 to 7, 15]: d2/ _ dz2

aexp(-az) Rmf

+

1_ -Kg/3 '

1

'

where r t /=— a >

t> -"»J =

2jlxa2

8(1 /«») 8T

flVTT~2\

W

0

is the parameter having the dimension of a length and characterizing the force of thermal refraction due to the medium heating, P 0 is the initial power of US or HS wave in the point z — 0, Rg = a2k/2 is the diffraction length of the beam or the range of the first Fresnel zone. The formula of critical power is (7)

P V°

dl^

Re*

Let us estimate the critical power for substances with dvjdT 0. Such are metals as aluminium, beryllium, tungsten, copper, iron etc. [18], dielectrics as magnesium oxide etc. [17], and the majority of alloys. We shall make estimates for magnesium oxide and aluminium. We shall need for these estimates the value of the coefficient of high-frequency sound wave absorption which is known to be a function of many factors: medium properties and temperature, frequency and direction of sound wave propagation, in the nonlinear case — intensity and amplitude of the wave, external electric and magnetic fields etc. There are many mechanisms of sound wave absorption. We shall use only those values of the sound absorption coefficient which are obtained by means of mechanisms giving rise to the increase of medium temperature, e.g. thermoelasticity and phonon-phonon interaction. The absence of electric and magnetic fields is assumed. The amplitude dependence of the absorption coefficient is also neglected. The influence of point defects and dislocations on the absorption of high-frequency sound waves is neglected due to its smallness [23]. For the majority of substances 8T V AT [1 to 3, 17, 18]. The estimate of the critical power by formula (7) for aluminium gives x = = 200 W/mK- 1 (at approximately 180 °C) [18]. a « 1 m" 1 at v = 108 Hz and a «s » 102 m _ 1 at v — 109 Hz [16]. Then we have following values for critical powers and 0

26

G . H . M e l k u m y a n and A. V. S h e k o y a x

intensities : = 0.1 cm

1.

v = IO8 Hz = 1 cm

2.

v = IO8 Hz a = 0.1 cm v = 109 Hz

3.

3 W,

I = 1

W cm2 '

7 = 1

W cm2 '

10~2 cm v = 10« Hz

s

IO"2 W ,

X

» 3

' [ v = 1109 Hz

5.

I = 104

;3

/a == 11 cm

4.

3

X

cm'

IO"4 W ,

I = 10" 4

IO"4 W ,

/ = 108

X

a = 10~3 cm

6.

w

3 x 10 2 W,

I = 108

W cm:2'

W cm 2' w

As is seen from these estimates of critical intensities, the self-focusing is impossible for beams with cross-sectional dimensions nearly equal to the wavelength, because the intensities are higher than is necessary for the destruction of the medium. For wider beams the intensities are low and hence self-focusing is experimentally observable. The estimate of the critical power by formula (7) for magnesium oxide gives ¡X » 30 W / m K - 1

at

T = 300 K

[18] .

The absorption coefficients are a as 2 m - 1

v = 108 Hz

at

and

a » 2 x 102 m" 1

v = 1010 Hz [20].

at

Then the critical values of power and intensity are 1. 2.

(a = r

U

0.1 cm

= = 66 X x

10 - 8

cm

a = 1 cm = 6 x

10" 8

cm

3.

a = 0.1 cm X = 6 x 1 0 ' 9 cm

4.

( a = 11 cm '{X = 6 x 10~9 cm

5.

= 10~3 cm = 6 x 10- 8 cm

• e

6. 7.

a = 10" 4 cm A = 6 x 10" 9 cm a = 10~2 cm

X = 6 x IO"9 cm

: 3 x 10- 1 W ,

I = 10

w cm-1 w

-3

X

10" 3 W ,

10"

:3

X

10- 5 W ,

10-3

: 3 x 10- 4 W ,

I = 10-4

cm2 W cm 2' W cm2

103 w ,

I = 109

W . cm 2 '

30 W ,

I = 109

W cm 2'

3 x 10" 3 W ,

I = 10

W cm2

On the Theory of Self-Aotion of Ultrasonic and Hypersonic Waves

27

J u s t as in the case of aluminium, here also for very narrow beams the cross-sectional dimensions are near the sound wavelength and the intensities are higher t h a n the medium destruction values. However, when the width of the beam is large as compared with the wavelength, critical intensities are low and self-focusing is possible. 4. Equation of Thermal Self-Focusing with due Regard' for the Elastic Nonlinearity As is seen from the estimates of critical intensties for aluminium they sometimes t a k e rather large values, so t h a t one must take account of the elastic nonlinearity. To obtain the starting nonlinear equation, we restrict the expansion of the elastic energy in terms of the deformation tensor to cubic terms and have the following onedimensional equation [21]: 1 82U d2U d2U W (8) 2 7 2 8i 8z dz2 8z where y is a dimensionless constant. Generalizing equation (8) to the three-dimensional case and taking into account {3) we obtain / I + W U ^ 8 T eu 1 + y

T

,

1

d2U

= AU

(9)

8z~

which can be transformed to the following form: 8(1jv 2

y eu\ vl 8z

8T

82U

= Af7 .

(10)

T o obtain the equation for the amplitude of US or HS waves, it is necessary to subs t i t u t e into (10) the expression U(x, y, z) = A(x, y, z) exp \i((at — kz)] and taking into account the inequalities 8M

8A

8z2

8z

•

:

f1 .'

•

i

\ •

:

( • i

w

'

200

i I

I

I ,

204

{

•

000

004

Fig. 11. Diffraction p a t t e r n from an area containing as well monoclinic I I as orthorhombic structures. 9 f-c.c. spots; O two variants of monoclinic I I phase; +, O three variants of orthorhombic phase

Fig. 12. Atom movements transforming the monoclinic I into the monoclinic I I s t r u c t u r e

Electron Diffraction Study of Ordering in the Gold-Manganese System ( I I )

51

fraction pattern; in this stage it is a superposition of different patterns as analysed in Fig. l i b . The corresponding image is reproduced in Fig. 13, i.e. with orthorhombicmonoclinic I and monoclinic I I structure present simultaneously. The orientation of the A P B ' s in the monoclinic I I phase is apparently not strictly confined to (102) planes, since continuous streaks having the shape of "accolades" associated with the 101 and 103 reflections are produced; they exhibit re-inf or cements at the locations where diffraction spots due to the orthorhombic structure and due to several variants of the monoclinic I I structure would come (Fig. 11). In a first stage spots with a + -j- shift appear along the [100] streaks through 101 and 103, indicating that in an intermediate stage the monoclinic I structure becomes more prominent. The transition presumably proceeds as follows: orthorhombic —>- monoclinic I -»• monoclinic I I . I t is reasonable to assume that at any given moment the amount of monoclinic I will be small since the latter will be transformed progressively into monoclinic I I as it forms. The mechanism for incorporating the excess manganese into the D0 22 structure is clearly similar to that for accomodating the oxygen deficiency in Ti0 2 by changes in the orientation and spacing of the shear planes [5]. I t is interesting to note that the structures of Au5Mn2 and of Au 4 Mn can both be considered as being derived from the Au 3 Mn (D0 22 ) structure by a crystallographic shear operation (Fig. 14). In the D0 22 structure the (101) planes are composed of

Pig. 13. Area containing simultaneously orthorhombic and monoclinic I and I I structures 4*

52

R.

WOLF

et al.: Ordering in the Gold-Manganese System (II) Tig. 14. The Au 5 Mn 2 and the Au4Mn structure can be derived from the Au 3 Mn(D0 22 ) structure by crystallographic shear. The Au3Mn structure has three pure (101) Au layers in between pure Mn layers. The Au 5 Mn 2 structure is formed by removing one Au layer and shifting the bottom crystal part over -J- [201] every other Au3Mn slab. Au 4 Mn results from introducing in every Au3Mn slab an extra Au layer and widening the slab by shifting over -i- [201]

jpro •

•

o

(DO,,

AusMn2

either gold or manganese in the succession Mn-Au-Au-Au-Mn-Au-Au-Au-Mn. Extracting every sixth gold plane and closing the gap b y means of a displacement with a vector R = = -1- [201] produces the Au B Mn 2 structure. On the other hand, opening a one-layer gap in the succession of (101) planes by means of a displacement over a vector i t = -j- [201] after each triplet of gold layers and inserting a fourth gold layer, one obtains the composition Au,Mn as well as the associated tetragonal structure. 5. Conclusions The observations reported here suggest a great similarity between the mechanisms b y which small deviations from an exact simple composition can be incorporated into a n alloy and into a shear structure. I n both cases nonconservative interfaces are introduced, of which the spacing and orientation are such as to realize t h e correct composition. K n o w n structures of gold-manganese alloys can consistently be interpreted on the same basis. The formation mechanism is in both cases based on t h e propagation of hairpin-shaped configurations of interfaces. Acknowledgements

One of us (R. W.) is much indebted to the Antwerp "Hoge R a a d voor D i a m a n t " for financial support. Thanks are due to Dr. J . Colard of the y-spectrometry at S.C.K./C.E.N, for the activation analysis. References [ 1 ] G . VAN TENDELOO, R . W O L F , J . VAN L A N D U Y T , a n d S . AMELINCKX, p h y s . s t a t . s o l . ( a ) 4 7 , 5 3 9 (1978). [ 2 ] J . VAN L A N D U Y T ,

R . DE R I D D E E ,

R . GEVEES,

and

S . AMELINCKX, M a t e r .

Res.

Bull.

5,

353

(1970). [ 3 ] G . VAN TENDELOO, R . W O L F , a n d S . AMELINCKX, p h y s . s t a t . s o l . ( a ) 4 0 , 5 3 1

(1977).

[ 4 ] R . W O L F , G . VAN TENDELOO,' J . VAN L A N D U Y T , a n d S . AMELINCKX, p h y s . s t a t . s o l . ( a ) 4 7 , 2 4 1 (1978). [ 5 ] J . VAN L A N D U Y T

and S.

AMELINCKX, J . (Received

Solid State Chem. March

9,

1978)

6, 222 (1973).

53

M. A. ARRIANDIAGA et al. : Study of Order-Disorder Phase Transitions phys. stat. sol. (a) 48, 53 (1978) Subject classification: 1.2; 22.8 Laboratory

Department of Physics, Faculty of Science, University of Bilbao (a) and of Solid State Physics, Swiss Federal Institute of Technology, ETH Zürich

(b)

Calorimetric Study of Order-Disorder Phase Transitions in Long-Chain (C„H2„+iNH3)2CuCl4 Compounds By M . A . ARRIANDIAGA ( a ) , M . J . TELLO ( a ) , J . FERNANDEZ ( a ) , H. A E E N D (b), and J . Roos (b)

Differential scanning calorimetry (DSC) reveales two transition steps in (CnH2n + lNH3)2CuCl4 compounds with n 5. They consist both of one or several peaks and differ in their thermal hysteresis behaviour. They can be interpreted by the theory of melting of flexible molecules. Differential-Kalorimetrie in einem dynamischen Temperaturregime zeigt zwei Umwandlungsstufen in (CreH2M + iNH3)2CuCl4-Verbindungen mit n Ja 5. Beide weisen einen oder mehrere Peaks auf und unterscheiden sich durch ihr thermisches Hystereseverhalten. Sie können aufgrund der Theorie des Schmelzens flexibler Moleküle verstanden werden.

1. Introduction

The melting of crystals containing flexible or semiflexible long-chain molecules is of great interest especially with respect to order-disorder phenomena involved [1], In addition to positional and orientational disorder there exists configurational disorder. Whereas the positional and orientational terms are constant the configurational contribution in a homologous series is a function of the number of units per molecule. Recently an interesting phenomenon of partial melting [2 to 4] was observed in layer-structure compounds of the formula (CMH2n+iNH3)2 MC14 where M stands for a divalent cation. According to [3] compounds with M = Mn, Cu, Fe, Hg should correspond also in the case of long alkyl-chains to a "two-dimensional" perovskite structure consisting of corner-sharing octahedra of the macro-anions MC1|~ sandwiched by two alkyl-ammonium layers with no intercalation between neighbouring layers. Structural phase transitions in short-chain compounds (n 3) of these layer-perovskites are now fairly well understood [5, 6]. Calorimetric measurements [7] confirmed their behaviour differing from long-chain compounds. This paper is an attempt of a calorimetric study of compounds of the (CmH2n+iNH3) • • CuCl4 family with 5 rg w rgj 18 aimed at a closer analysis of the influence of the chain length and at a better understanding of the complicated nature of DSC patterns within the framework of the theory of melting of flexible molecules. 2. Experimental Part 2.1

Procedure

Experimental techniques, calibration, evaluation of data and accuracy of experimental results were already described in [7, 8]. Some of the measurements were carried out in a Perkin-Elmer DSC-2B and a Mettler TA-2000 calorimeter, with no relevant differences between both instruments. Heating rate and sensitivity are shown on each figure.

53

M. A. ARRIANDIAGA et al. : Study of Order-Disorder Phase Transitions phys. stat. sol. (a) 48, 53 (1978) Subject classification: 1.2; 22.8 Laboratory

Department of Physics, Faculty of Science, University of Bilbao (a) and of Solid State Physics, Swiss Federal Institute of Technology, ETH Zürich

(b)

Calorimetric Study of Order-Disorder Phase Transitions in Long-Chain (C„H2„+iNH3)2CuCl4 Compounds By M . A . ARRIANDIAGA ( a ) , M . J . TELLO ( a ) , J . FERNANDEZ ( a ) , H. A E E N D (b), and J . Roos (b)

Differential scanning calorimetry (DSC) reveales two transition steps in (CnH2n + lNH3)2CuCl4 compounds with n 5. They consist both of one or several peaks and differ in their thermal hysteresis behaviour. They can be interpreted by the theory of melting of flexible molecules. Differential-Kalorimetrie in einem dynamischen Temperaturregime zeigt zwei Umwandlungsstufen in (CreH2M + iNH3)2CuCl4-Verbindungen mit n Ja 5. Beide weisen einen oder mehrere Peaks auf und unterscheiden sich durch ihr thermisches Hystereseverhalten. Sie können aufgrund der Theorie des Schmelzens flexibler Moleküle verstanden werden.

1. Introduction

The melting of crystals containing flexible or semiflexible long-chain molecules is of great interest especially with respect to order-disorder phenomena involved [1], In addition to positional and orientational disorder there exists configurational disorder. Whereas the positional and orientational terms are constant the configurational contribution in a homologous series is a function of the number of units per molecule. Recently an interesting phenomenon of partial melting [2 to 4] was observed in layer-structure compounds of the formula (CMH2n+iNH3)2 MC14 where M stands for a divalent cation. According to [3] compounds with M = Mn, Cu, Fe, Hg should correspond also in the case of long alkyl-chains to a "two-dimensional" perovskite structure consisting of corner-sharing octahedra of the macro-anions MC1|~ sandwiched by two alkyl-ammonium layers with no intercalation between neighbouring layers. Structural phase transitions in short-chain compounds (n 3) of these layer-perovskites are now fairly well understood [5, 6]. Calorimetric measurements [7] confirmed their behaviour differing from long-chain compounds. This paper is an attempt of a calorimetric study of compounds of the (CmH2n+iNH3) • • CuCl4 family with 5 rg w rgj 18 aimed at a closer analysis of the influence of the chain length and at a better understanding of the complicated nature of DSC patterns within the framework of the theory of melting of flexible molecules. 2. Experimental Part 2.1

Procedure

Experimental techniques, calibration, evaluation of data and accuracy of experimental results were already described in [7, 8]. Some of the measurements were carried out in a Perkin-Elmer DSC-2B and a Mettler TA-2000 calorimeter, with no relevant differences between both instruments. Heating rate and sensitivity are shown on each figure.

54

M . A . ARRIANDIAGA, M . J . T E L L O , J . FERNANDEZ, H . A R E N D ,

2.2 Influence

of heating

and

J.

Roos

rate

Working with long-chain compounds it is difficult to resolve all peaks (see e.g. [9]). Since a closer study makes it necessary to resolve as many thermal effects as possible experimental runs with different heating rates were performed. Examples of these are shown in Fig. 1 and 2 for compounds with n = 10 and 14, respectively. Fig. 1 shows two runs with different heating rates. A single effect appears for vc = 5 K/min whereas for vc = 2 K/min two peaks are resolved and a peak temperature shift is observed. Similar results are obtained for the compound with n = 14 both as to resolution and as to temperature shifts of the peaks. This can be seen from the two curves run with vc = 1.25 K/min and vc = 0.3125 K/min shown in Fig. 2. I t must be pointed out that the temperature shift decreases as the heating rate is lowered. The heating rate has moreover an influence on enthalpy changes in each peak. An adequate heating rate for each compound can be found. Influence of repeated heating and cooling cycles: Successive cycles influence peak number, form, enthalpy change, and temperature related to order-disorder phase transitions in these compounds. Fig. 3 shows an example of five successive cycles with increasing and decreasing temperatures under the same experimental conditions for the compound with n = 16. As will be shown later the manifold effects observed can be attributed to two steps showing both a different thermal hysteresis. The first one extends from 335 to 358 K and the second one from 358 to 365 K . In the heating cycles some changes in the peak shapes and enthalpy changes involved in individual peaks are observed, the changes being more pronounced between the first and the second cycle. On cooling a much better reproducibility in the shape of the curves is experienced in subsequent cycles. The first step shows in contrast to the second one a pronounced thermal hysteresis of about 4 K . In spite of changes of magnitude and form of individual effects, the total enthalpy associated with each step remains constant with successive cycles. Thus these have no influence on the total energy required for the order-disorder phase transition.

360

Fig. 1

Fig. 2

370

T(K)—

Fig. 3

Fig. 1. Influence of the heating rate in the n = 10 compound. (1) vc — 5, (2) 2 K/min Fig. 2. Influence of the heating rate in the n = 14 compound. (1) v(. = 1.25, (2) 0.3125 K/min Fig. 3. Influence of the heating cycles on the calorimetrie curves of the n = 16 compound. (1) First scanning with increasing temperature, (2) second scanning with decreasing temperature, etc. (vc = 0.3125 K/min)

Study of Order-Disorder Phase Transitions in Long-Chain Compounds

310 330

350

55

370 ÏÏK)•

Fig. 4

Fig. 5

Fig. 6

Fig. 4. Influence of the heating cycles on the order-disorder phase transitions of the n = 18 compound (vc = 2 K/min) Fig. 5. First scanning for n = 12 (vK = 0.5 K/min) and n = 13 compounds (vc = 0.3125 K/min) Fig. 6. Linear dependence of AH and A„

xO

Fig. 1 shows that we expect Bv to cause M to tilt away from the easy axis within the domains and our first task is to find