UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Excitonic luminescence in doped silicon Thewalt, Michael Ludwig Wolfgang 1977

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1977_A1 T43.pdf [ 5.12MB ]
Metadata
JSON: 831-1.0085753.json
JSON-LD: 831-1.0085753-ld.json
RDF/XML (Pretty): 831-1.0085753-rdf.xml
RDF/JSON: 831-1.0085753-rdf.json
Turtle: 831-1.0085753-turtle.txt
N-Triples: 831-1.0085753-rdf-ntriples.txt
Original Record: 831-1.0085753-source.json
Full Text
831-1.0085753-fulltext.txt
Citation
831-1.0085753.ris

Full Text

EXCITONIC LUMINESCENCE IN DOPED SILICON by MICHAEL LUDWIG WOLFGANG THEWALT B.'Sc, McMaster University, 1972 M.Sc, Un i v e r s i t y of B r i t i s h Columbia, 1975 A THESIS SUBMITTED IN THE REQUIREMENTS DOCTOR OF PARTIAL FULFILMENT OF FOR THE DEGREE OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Physics) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1977 © Michael Ludwig Wolfgang Thewalt, 1977 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. \ Department of Physios The University of Brit ish Columbia 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 Date September 30, 1977 i ABSTRACT The photoluminescence spectrum of s i l i c o n doped with phosphorus, boron, aluminum and gallium impurities i s studied i n the 1.6 to 27 K temperature range. New structure i s observed i n the spectra of s i l i c o n doped with each of these impurities. These studies strongly support the bound multiexciton complex explanation of the l i n e series observed i n l i g h t l y doped s i l i c o n , an explanation which has recently been questioned. Many of the recent predictions of the structure of these complexes are v e r i f i e d . In p a r t i c u l a r , a bound excited state of the phosphorus bound exciton i s reported f o r the f i r s t time. S i m i l a r l y , i t i s shown that many of the bound multiexciton complexes also have such excited states, and the importance of these excited states i n the determination of the binding energies of the complexes i s demonstrated. The broadenings of the phonon-assisted bound exciton l i n e s i n s i l i c o n are studied f o r the f i r s t time and the f i r s t d i r e c t observation of the e f f e c t s of the free exciton ground state s p l i t t i n g i n s i l i c o n are reported. i i TABLE OF CONTENTS Page Abstract i Table of Contents i i L i s t of Tables i v L i s t of Figures v L i s t of Abbreviations i x Acknowledgements x Chapter J INTRODUCTION 1 1.1 s General Introduction 1 1.2 The Purpose'of t h i s Thesis . ............... 5 1.3 The Outline of t h i s Thesis .... 6 Chapter 2 EXPERIMENTAL DETAILS , 8 2.1 The Computer-Controlled Signal Averaging System ... 8 2.2 Experimental De t a i l s 10 2.3 The Photomultiplier Tube Detector .... 14 Chapter 3 RESULTS AND ANALYSES . . 1 7 3.1 S h e l l Model of the Bound Multiexciton Complexes ... u 3_. 2 Phosphorus Bound Excitons' (One-Electron Transitions) 31 3.3 Phosphorus Bound Excitons (Two-Electron Transitions) 40 3.4 Phosphorus Bound Multiexciton Complexes 45 3.5 Acceptor Bound Excitons (One-Hole Transitions) .... 57 3.6 Acceptor Bound Excitons (Two-Hole Transitions) .... 68 3.7 Acceptor Bound Multiexciton Complexes 74 i i i Page Chapter 4 SUMMARY AND CONCLUSIONS .. ... 80 Appendix A Broadening of Phonon-Assisted Bound Exciton 84 Luminescence i n S i l i c o n Appendix B Ground State S p l i t t i n g of the Free Exciton in. 92 S i l i c o n Bibliography 101 i v LIST OF TABLES Table Page ; 3.1 Energies and i n t e n s i t y r a t i o s of the phosphorus one-electron t r a n s i t i o n s . ......................... 35 3.2 Energies of the momentum-conserving phonons ............. 45 3.3 Energies of the phosphorus BE two-electron t r a n s i t i o n s .. 45 3.4 Energies and i n t e n s i t y r a t i o s of the acceptor BE one-hole t r a n s i t i o n s .• 67 3.5 Energies of the acceptor BE two-hole t r a n s i t i o n s and binding energies of the even-parity acceptor excited states 73 A . l F u l l widths at half-maximum (FWHM) of the BE phonon broadenings 88 A.2 Ratios of the phonon broadening widths 88 V LIST OF FIGURES Figure Page 2.1 Block diagram of the computer-controlled spectrometer system 9 2.2 Block diagram of the photon counting c i r c u i t 11 2.3 Diagram of the r e f l u x i n g dewar system 13 2.4 Response of the photomultiplier tube detector versus photon energy 16 3.1 Level scheme f o r the Zeeman s p l i t t i n g i n the " s i m p l i f i e d " SD BE model 23 3.2 SM t r a n s i t i o n scheme f o r the SD BE and BMEC 27 3.3 The photoluminescence spectrum of phosphorus-doped s i l i c o n at 19 K. The l i n e s labeled 2S(T 1) and 2 S ( r 3 j 5 ) are the NP r e p l i c a s of two-electron t r a n s i t i o n s . The i n t e n s i t i e s of the NP one-electron and two-electron t r a n s i t i o n s have been mu l t i p l i e d by factors of 1.8 and 30 as compared to the TO r e p l i c a l i n e s , r e s p e c t i v e l y . The low energy edge of the FE TO l i n e from an i n t r i n s i c sample i s shown as a dashed l i n e f o r comparison 33 3.4 The logarithms of some of the i n t e n s i t y r a t i o s of the phosphorus BE l i n e s p l o t t e d versus the inverse of the temperature. The s t r a i g h t l i n e s have the predicted slope f o r an excited state energy of 4.31 meV. The deviations of the low temperature points from these s t r a i g h t l i n e s are discussed i n the text 37 3.5 The NP r e p l i c a of some of the phosphorus BE two-electron t r a n s i t i o n s at 4.2 K 41 3.6 The TO r e p l i c a of the phosphorus BE 2S two-electron t r a n s i t i o n s at 20.4 K. The predicted l o c a t i o n of the 2S(Ti) l i n e o r i g i n a t i n g from the excited BE i s indicated by an arrow 44 3.7 The NP r e p l i c a of the phosphorus BE two-electron t r a n s i t i o n s which leave the donor i n the l S f l ^ ) and lS(r 5) states 47 v i Figure .Page 3.8 The e x c i t a t i o n dependence of the i n t e n s i t y r a t i o s of adjacent KAPS l i n e s p l o t t e d f o r the d i f f e r e n t impurities. The i n t e n s i t y r a t i o of the m=n+l l i n e r e l a t i v e to the m=n l i n e i s given f o r a l l values of n f o r which data are a v a i l a b l e . For AT and Ga the m=l i n t e n s i t y i s that of the X^ 0 1 line,, while the m=2 i n t e n s i t y i s the sum of the 2,g and 2,y lumin-escence l i n e s . For boron the t o t a l a+B+Y i n t e n s i t y i s used f o r m=l, and f o r m=2 the l i n e s could not even be resolved. A l l measurements were taken i n the NP r e p l i c a 49 3.9 The photoluminescence l i n e s due to the TO and NP r e p l i c a s of the phosphorus BE and BMEC one-electron t r a n s i t i o n s at 4.2 K. The B 1 and B 2 l i n e s occur at the expected energies f o r boron contamination, but as explained i n the text the B 1 l i n e probably consists p a r t i a l l y of phosphorus B 1 luminescence. The two l i n e s marked with a s t e r i s k s seem to be associated with the l i n e 51 3.10 The proposed energy l e v e l scheme of the phosphorus BE and BMEC f o r m<4. The energies are derived from the measured energies of the luminescence l i n e s and i t i s assumed that i n F i g . 3.9 the B 1 and B 1 l i n e s are super-imposed. Only.in the i s o l a t e d donor i s the s p l i t t i n g between the l S ( r 3 ) and l S ( r 5 ) l e v e l s taken into account. The threshold energies for the d i s s o c i a t i o n of an m=n BMEC int o a FE plus an m=n-l complex are shown on the ri g h t • .... ............ 54 3.11 Photoluminescence spectra of the phosphorus NP KAPS l i n e s f o r m<5. Only the width of the a^p l i n e i s seen to be li m i t e d by the spectrometer r e s o l u t i o n . D e f i n i t e i n d i c a t i o n s of structure i n the e x p a n d a^ p l i n e s i s seen 56 3.12 The NP and TO r e p l i c a s of the gallium BE luminescence at 14.5 K. The G a ^ 6 and Ga^'^ cannot be resolved due to phonon broadening. Note the revers a l of the inten^ s i t i e s of the l i n e s i n the two r e p l i c a s : The a^p l i n e i s due to phosphorus contamination 59 3.13 The NP and TO r e p l i c a s of the photoluminescence of aluminum-doped s i l i c o n at 14.5 K. The m=2 and m=3 aluminum KAPS l i n e s are also observed. The NP i n t e n s i t y has been increased by a fa c t o r of 2.4 r e l a t i v e to the TO r e p l i c a i n t e n s i t y ............ 61 v i i Figure Page 3.14 The boron BE NP spectrum at 4.2 and 1.8 K. A t r i p l e t structure due to states which are i n thermal e q u i l i -brium seems indicated 62 3.15 The NP energies of a l l the acceptor l i n e s i s compared. Only the OC'1*01 energy i s seen to be strongly impurity-dependent 65 3.16 The TO r e p l i c a of the boron BE two-hole t r a n s i t i o n s i s shown. For c l a r i t y , the 4r 8 + and 5r 8 + l i n e s have t h e i r i n t e n s i t i e s m u l t i p l i e d by a f a c t o r of 10. The TO PBE l i n e i s approximately 70 times as intense as the 2 T 8 + l i n e .... 70 3.17 The NP r e p l i c a of the gallium BE two-hole t r a n s i t i o n s i s shown. For c l a r i t y the i n t e n s i t i e s of the lower energy l i n e s have been m u l t i p l i e d by a f a c t o r of 12 . r e l a t i v e to the 2r 8 + l i n e . The NP PBE l i n e i s approxi-mately 60 times as intense as the 2r 8 + l i n e . The 2T 8 + l i n e i s on the low energy t a i l of the much more intense TO PBE l i n e 72 3.18 The NP r e p l i c a of the luminescence of gallium-doped s i l i c o n at 4.2 K i s shown. The a^p l i n e i s due to phosphorus contamination. The r e l a t i v e i n t e n s i t i e s of the 2,3 and 2,y l i n e s are given i n the t r a n s i t i o n diagram. The a s t e r i s k indicates the predicted p o s i t i o n of the 2,a l i n e . The i n t e n s i t i e s of the m>l l i n e s have been increased by a factor of 10 r e l a t i v e to the PBE l i n e ... . 75 3.19 The NP r e p l i c a of the luminescence of aluminum-doped s i l i c o n at 4.2 K i s shown. The a^p l i n e i s due to phosphorus contamination. The i n t e n s i t i e s of the m>l l i n e s have been m u l t i p l i e d by a f a c t o r of 13 r e l a t i v e to the PBE l i n e s 78 A . l The TO, L0 and TA r e p l i c a s of the phosphorus PBE l i n e at 4.2 K. The s o l i d l i n e i s the f i t to the experi-mental lineshapes obtained by convoluting the NP r e p l i c a s i with Gaussiariabroadenings, and s h i f t i n g by the phonon energies V 87 A.2 The TA r e p l i c a of the gallium PBE l i n e showing the very pronounced low energy t a i l .............. 91 v i i i Figure B.l B.2 B.3 Page • The LO and TO r e p l i c a s of the d e r i v a t i v e absorption spectrum of the FE at 1.4 K. The LO i n t e n s i t y has been m u l t i p l i e d by a factor of 5.7 f o r c l a r i t y . The dotted extensions of the low energy edges of the two r e p l i c a s show the contribution of the A 6 l e v e l to the TO lineshape .... ... .... 94 The LO and TO r e p l i c a s of the FE luminescence at 1.6 K. The LO i n t e n s i t y has been m u l t i p l i e d by a fa c t o r o f 2 ... 96 The LO and TO r e p l i c a s of the FE luminescence at 2.1 K. The structure of the TO l i n e i s c l e a r e r than i n F i g . B.2 due to the greater population of the A 7 l e v e l at 2.2 K 98 i x LIST OF ABBREVIATIONS bound exciton(s) bound multiexciton complex(es) B r i l l o u i n Zone electron-hole droplet free exciton an acronym f o r the l i n e series f i r s t reported by Kaminskii, Alkeev, Pokrovskii and S v i s t u n o v a 1 0 l o n g i t u d i n a l a c o u s t i c a l (phonon) l o n g i t u d i n a l o p t i c a l (phonon) momentum-conserving process m i l l i e l e c t r o n V o l t p r i n c i p a l bound exciton (line) no phonon the s h e l l model proposed by K i r c z e n o w 1 6 ' 1 7 transverse acoustical (phonon) transverse o p t i c a l (phonon) X ACKNOWLEDGEMENTS I would l i k e to thank my supervisor Dr. R.R. Parsons f o r h i s fri e n d s h i p , encouragement and guidance throughout t h i s p r o j e c t ; and also Dr. R. Barrie f o r h i s assistance during Dr. Parsons* absence. I also thank Dr. G. Kirczenow, Dr. J . Rostworowski and Dr. J.W. Bichard f o r t h e i r many h e l p f u l and stimulating discussions. This research p r o j e c t was supported by the National Research Council of Canada (grant number 67-6714), and I thank the Council f o r a postgraduate sc h o l a r s h i p . 1 CHAPTER 1  INTRODUCTION 1.1 General Introduction C r y s t a l l i n e s i l i c o n i s an i n d i r e c t band gap semiconductor with a f o u r - f o l d degenerate valence band maximum at the center of the B r i l l o u i n zone (BZ) and s i x two-fold degenerate conduction band minima located at (0.85,0,0) and the f i v e equivalent locations i n the BZ. In the ground state the valence band i s completely f u l l and the conduction band i s completely empty. I f s u f f i c i e n t energy i s supplied, an electron can be excited across the energy gap into the conduction band, leaving behind a hole i n the valence band. ( A very convenient way of generating such electron-hole p a i r s i s to illuminate the c r y s t a l with photons having energies greater than that of the i n d i r e c t band gap. If the energy of the absorbed photons i s less than that of the d i r e c t band gap a momentum conserving process (MCP) must accompany the generation of electron-hole p a i r s since the valence band maximum and the conduction band minima do not occur at the same lo c a t i o n i n the BZ. In general, the MCP i n pure s i l i c o n could be eit h e r the absorption or emission of phonons having the required c r y s t a l momentum. At cryogenic temperatures the phonon population i s such that only phonon emission need be considered as a MCP. Conversely, an electron-hole p a i r may recombine accompanied by the emission of a photon and a momentum-conserving phonon. Since the photon energy w i l l be equal to the i n i t i a l energy of the electron-hole 2 p a i r minus the energy of the emitted phonon, the luminescence spectrum of s i l i c o n consists of several phonon r e p l i c a s which are s h i f t e d from the true t r a n s i t i o n energy by the energies of the emitted phonons. In s i l i c o n there are four types of phonons with wave vectors along the [100] d i r e c t i o n : TO, LO, TA and LA. A l l of these phonon r e p l i c a s except the LA are observed i n the s i l i c o n luminescence spectrum. Of the three observed phonon r e p l i c a s the TO i s by f a r the strongest. At low temperatures the e l e c t r o s t a t i c a t t r a c t i o n between an electron and a hole i n a semiconductor can cause them to form a stable complex known as a free exciton (FE). 1 In s i l i c o n the binding energy of a FE i s 14.7 ± 0.4.meV2 which i s much larger than kT i n the usual range of cryogenic temperatures employed i n the study of luminescence from s i l i c o n . Thus i n t h i s temperature range the concentration of FE f a r outweighs the concentration of free electrons and free holes. The main features of the luminescence spectrum of i n t r i n s i c s i l i c o n at cryogenic temperatures and moderate e x c i t a t i o n l e v e l s are therefore the phonon r e p l i c a s of the FE. At high e x c i t a t i o n l e v e l s the "gas" of FE condenses into a " l i q u i d " phase, a degenerate plasma of electrons and holes known as the electron hole droplet (EHD). 3 S i l i c o n i s often doped with elements from Group III or Group V of the pe r i o d i c table. These impurities are known as acceptors or donors, re s p e c t i v e l y . In the ground state a hole i s bound to each acceptor impurity and an electron i s bound to each donor. In t h i s configuration the impurities are known as neutral donors and acceptors. 3 In 1958 Lampert 4 suggested that complexes c o n s i s t i n g of an electron-hole p a i r bound to a neutral donor or acceptor impurity i n a semiconductor should be stable with respect to d i s s o c i a t i o n into a neutral impurity and a FE. The existence of these complexes was f i r s t demonstrated by Haynes 5, who studied the photoluminescence spectrum of s i l i c o n doped with donors and acceptors. These complexes were named bound excitons (BE) since unlike the FE they could not move through the c r y s t a l . Since the BE can have no k i n e t i c energy, t h e i r luminescence l i n e s are very sharp, unlike the FE luminescence which has a Maxwell-Boltzmann shape, the width of which increases with increasing temperature. In addition to the normal phonon r e p l i c a s a no-phonon (NP) l i n e was observed f o r the BE. In the NP process the c r y s t a l momentum i s coupled to the ent i r e c r y s t a l by the impurity, with e f f e c t i v e l y no expenditure of energy. The strength of the NP BE l i n e r e l a t i v e to the phonon r e p l i c a s increases with increasing impurity i o n i z a t i o n energy. Haynes 5 found that the binding energy of the BE r e l a t i v e to the low energy edge of the FE band was approximately one-tenth of the i o n i z a t i o n energy of the impurity to which the BE was bound. This i s true only f o r shallow impurities. The photoluminescence spectra of BE i n s i l i c o n was further studied by Dean et a l . 6 In a study of the absorption due to BE i n s i l i c o n , Dean et a l . 7 reported a doublet s p l i t t i n g of the BE ground state f o r the acceptors B, A l , Ga and In. It was l a t e r r e a l i z e d that the value given f o r the B BE s p l i t t i n g was i n error due to the presence of the then-unrecognized LO phonon r e p l i c a . 8 The cathodoluminescence spectrum of BE i n acceptor doped s i l i c o n has been studied i n d e t a i l by Vouk and Lightowlers 9 who reported observing no s p l i t t i n g f o r B, a 4 doublet s p l i t t i n g f o r A l , Ga and In and a t r i p l e t s p l i t t i n g f o r the very deep acceptor T l . In studying the photoluminescence spectra of s i l i c o n doped with B and P, Kaminskii, Pokrovskii and eOTWorkers 1 0 -observed several sharp luminescence l i n e s l y i n g at energies below that of the BE l i n e s . They a t t r i b u t e d these l i n e s , which w i l l hereafter be r e f e r r e d to as KAPS lin e s following Kirczenow 1 6, to the r a d i a t i v e recombination of an electron-hole p a i r i n a complex containing more than one such p a i r bound to ei t h e r a neutral donor or a neutral acceptor. These e n t i t i e s were named bound multiexciton complexes (BMEC). In t h i s simple BMEC model recombination of electron-hole p a i r s i n complexes containing progressively greater numbers of p a i r s would r e s u l t i n progressively lower energy luminescence l i n e s since the binding energy increases with increasing numbers of p a i r s due to c o r r e l a t i o n e f f e c t s . The KAPS l i n e s were further studied by Sau e r 1 1 and by Kosai and Gershewzoni,11'2 and i n both cases the BMEC model was strongly supported by the new r e s u l t s . Follow-ing S auer 1 1 we labe l the BE and BMEC with an integer m which equals the number of electron-hole p a i r s bound to the neutral impurity. Thus fo r the BE m equals one. Transitions are l a b e l l e d with the same value of m as t h e i r i n i t i a l states. S i m i l a r l i n e s were also seen i n germanium by M a r t i n . 1 3 However, i n 1976 Sauer and Weber 1 4 reported that the re s u l t s of t h e i r stress and Zeeman s p l i t t i n g studies of the BE and some of the KAPS l i n e s i n P, L i and B doped s i l i c o n r uled out any BMEC explanation f o r the KAPS l i n e s . In addition they stated that the large 5 energy s h i f t of some of the KAPS lin e s r e l a t i v e to the FE threshold would be d i f f i c u l t to rec o n c i l e with a model based on BMEC. They considered a number of other possible models but a l l were found to have severe d i f f i c u l t i e s , and none could explain the previously r e p o r t e d 1 0 - 1 2 KAPS l i n e behaviour as well as the BMEC model had. Morgan 1 5 proposed a new model f o r the KAPS l i n e s based on polyexciton' complexes bound to BE by van der Waals i n t e r a c t i o n s , but no attempt was made to show that t h i s new model could q u a l i t a t i v e l y explain the known properties of the KAPS l i n e s . 1.2 The Purpose of t h i s Thesis In the preceding section the research into the nature of the KAPS l i n e s which had taken place up to the time t h i s t hesis project was begun has been outlined. The l a s t study of the KAPS l i n e s at that time, that of Sauer and Weber 1 4, l e f t the question of the o r i g i n of these l i n e s completely open. The primary purpose of t h i s thesis was to demon-strate that contrary to the assertions of Sauer and Weber 1 4, the KAPS li n e s were indeed due to the r a d i a t i v e recombination of electron-hole p a i r s i n BMEC. Concurrent to the research described i n t h i s t h e s i s , another member of the S o l i d State Physics group, Dr. G. Kirczenow, developed a model giving d e t a i l s of the structure of the BMEC. 1 6' 1 7 This new model was named the S h e l l Model (SM) owing to i t s s i m i l a r i t y to the S h e l l Models of atomic and nuclear physics. It was shown that the SM of the BMEC could explain a l l of the experimental data including the stress and Zeeman s p l i t t i n g studies. The SM predicted that a number 6 of a dditional l i n e s should e x i s t i n the luminescence spectrum of BE and BMEC associated with s u b s t i t u t i o n a l donors. Many of these new l i n e s were subsequently observed and are reported f o r the f i r s t time i n t h i s thesis and the preliminary reports which preceded i t . While t h i s research was underway two a d d i t i o n a l papers dealing with the KAPS l i n e s were published. Dean et a l . 8 reported the observation of donor KAPS l i n e s i n 6-SiC and also showed that with a few reasonable assumptions the BMEC could indeed explain, at least q u a l i t a -t i v e l y , the stress and Zeeman s p l i t t i n g data given by Sauer and Weber 1 4, as well as giving a possible explanation of the seemingly large binding energies of some of the BMEC. In these papers Dean et a l . 8 f i r s t mentioned the p o s s i b i l i t y that the p a r t i c l e s would f i l l s h e l l s formed by the degenerate sin g l e p a r t i c l e l e v e l s , although they did not describe the nature of these s h e l l s as d e t a i l e d by Kirczenow. 1 6> 1 7 In addition to these studies, r e l a t e d work'concerning the behaviour of BE and FE i n s i l i c o n was performed and the r e s u l t s are described i n the Appendices. 1.3 The Outline of t h i s Thesis In Chapter 2 the s a l i e n t features of the experimental apparatus and methods used i n these studies are described. Only a b r i e f d e s c r i p t i o n of the computer c o n t r o l l e d signal averaging system i s included since i t has already been described i n great d e t a i l . 1 8 In Chapter 3 the main r e s u l t s of photoluminescence studies of the structure of BE and BMEC i n s i l i c o n are presented i n 7 d e t a i l . These r e s u l t s are interpreted i n terms of Kirczenow's l b> 1 7 SM. A b r i e f conclusion i s presented i n Chapter 4. In Appendix 1 the r e s u l t s of a study of the broadening of BE phonon r e p l i c a luminescence i n s i l i c o n i s given. In Appendix 2 high r e s o l u t i o n photoluminescence and derivative-absorption studies of the FE i n s i l i c o n are described, and the determination of the ground state s p l i t t i n g of the FE i s presented. The main r e s u l t s of t h i s i n v e s t i g a t i o n have already been p u b l i s h e d . 1 9 - 2 3 8 CHAPTER 2 EXPERIMENTAL DETAILS : 2.1 The Computer-Controlled Signal-Averaging System Since the minicomputer-controlled i n f r a r e d spectrometer system used i n these studies has already been described i n considerable d e t a i l , 1 8 only a b r i e f d e s c r i p t i o n w i l l be presented here i n order to describe the modifications of the apparatus which have not been previously reported. In F i g . 2.1 the basic o u t l i n e of the system i s shown. The minicomputer i s a Data General Nova 2-4. In addition to the functions shown i n the diagram the computer can also control the power of the e x c i t a t i o n source, a Spectra Physics model 165 A r + l a s e r with a maximum output of 1.5 watts ( a l l l i n e s ) . The l a s e r control feature was, however, r a r e l y required. For t h i s project the spectrometer described i n reference 18 was replaced by a Perkin-Elmer model E l spectrometer i n the double-pass configuration. This spectrometer has a f o c a l length of 58 cm and an f/8 aperture. In a l l cases a 576 lines/mm grating was used and the maximum obtainable r e s o l u t i o n was Q..Q7 meV ( f u l l width at half-maximum [FWHM]). It was p a r t i c u l a r l y simple to connect the Perkin-Elmer spec-trometer to the signal averaging system since the wavelength drive i n t h i s spectrometer uses the same type of stepping motor which had been used i n the previous spectrometer. The experiments described i n Appendices 1 and 2 were performed with the same l i q u i d nitrogen cooled germanium detector-9 Teletype Minicomputer x - y P l o t t e r Scope Control Un i t Paper Tape Reader Paper Tape Punch Interface In tegrator Lock-In A m p l i f i e r Spectrometer Figure 2 . 1 Block diagram o f the computer-controlled spectrometer system 10 preamplifier combination (RCA model 67-07-B) reported p r e v i o u s l y . 1 8 As before, the e x c i t a t i o n l i g h t was chopped and phase s e n s i t i v e detection was employed. For the other studies reported here a much more s e n s i t i v e detector was used, namely a photomultiplier tube. This tube w i l l be described i n more d e t a i l below. The sig n a l from the photomultiplier was processed i n the photon-counting mode using a c i r c u i t which was designed as part of t h i s project. The photon counting c i r c u i t was under the d i r e c t control of the minicomputer and automatically transferred data to i t . A block diagram of t h i s c i r c u i t i s given i n F i g . 2.2. Although a phase s e n s i t i v e detection option was a v a i l a b l e a l l work was done using continuous i l l u m i n a t i o n . 2.2 Experimental Details A l l spectra were obtained with samples d i r e c t l y immersed i n a cryogenic f l u i d . For the temperature range 1.6 K to 4.2 K a helium dewar constructed e s p e c i a l l y f o r photoluminescence work was employed. The bath temperature was determined by measuring the helium vapour pressure. Sample heating proved not to be a problem as long as the e x c i t a t i o n l i g h t was not focussed into a very small spot. This dewar had a l i q u i d nitrogen cooled r a d i a t i o n s h i e l d and a metal l i q u i d helium can with a volume of j u s t over three l i t r e s . The metal helium can was connected to a glass tube by a glass-to-metal seal and the glass tube was connected to a S p e c t r o s i l (high p u r i t y fused s i l i c a ) cuvette by a graded glass-to-quartz t r a n s i t i o n . The S p e c t r o s i l cuvette was of very good o p t i c a l q u a l i t y and square cross-section, and i t s near-infrared lumines-cence when excited by A r + l a s e r l i g h t was very much less than that of the Pyrex tube which had been used previously. 11 enable load Gating Input Comparator Lock-In Input 1 Comparator Gated Mode Normal Mode Q Lock-In Mode Normal Mode clock up/down 20 B i t Binary Counter clear S h i f t Register s h i f t Computer Interface output 2_ Figure 2.2 Block diagram o f the photon counting c i r c u i t 12 For luminescence studies at temperatures greater than 4.2 K a r e f l u x i n g dewar designed and constructed by Dr. R.R. Parsons was used. In t h i s dewar the samples were also immersed d i r e c t l y i n a cryogenic l i q u i d held i n a S p e c t r o s i l cuvette. Usually hydrogen was used as the coolant, which provided temperatures i n the 14.5 to 20 K range. In addition, l i q u i d neon was employed f o r temperatures i n the 25 to 27.2 K range. Since the samples were immersed i n the cryogenic f l u i d s sample heating was not a problem. The coolant temperature was determined by measuring i t s . vapour pressure. A diagram of the r e f l u x i n g dewar system i s shown i n F i g . 2.3. A Corning Glass 1-69 F i l t e r was placed at the e x i t aperture of the A r + l a s e r to block any near-infrared l i g h t from escaping. In most cases the l a s e r beam was directed at the sample without the use of any focusing o p t i c s , which resulted i n a 3 to 4 mm beam diameter. The l a s e r was operated i n the m u l t i l i n e mode. The samples were not usually polished since i t was found that the r a d i a t i v e e f f i c i e n c y of polished samples was no higher than that of cut or cleaved samples which had been etched i n a 20:1 mixture of HNO3 and HF u n t i l they were smooth. The samples were always given a quick etch i n t h i s mixture and rinsed i n d i s t i l l e d water before being inserted into the dewar. It was found that the maximum signal i n t e n s i t y could be obtained from t h i n s l a b - l i k e samples which were illuminated on t h e i r f l a t faces, had t h e i r edges p a r a l l e l to the spectrometer s l i t s and were d i r e c t l y f a c i n g the c o l l e c t i o n o p t i c s . A Perkin-Elmer 1.0 to 1.75 y bandpass f i l t e r located d i r e c t l y i n front of the spectrometer entrance s l i t s prevented the e x c i t a t i o n l i g h t from entering the spectrometer and producing spurious r e s u l t s . 13 Temperature Sensor Manometer Reservoir Temperature Co n t r o l l e r Needle Valve Solenoid Valve Vacuum Pump S p e c t r o s i l Cuvette L i q u i d Nitrogen Cooled Shield Dewar Vacuum Can Figure 2.3 DiagTam o f the r e f l u x i n g dewar system 14 Since phase s e n s i t i v e detection was not used i t was necessary to eliminate any spurious near-infrared signals i n the laboratory. It was found that the major background r a d i a t i o n was due to the l i n e spectrum of mercury which i s copiously emitted by fluorescent lamps. Another problem which was encountered was the absorption caused by atmospheric water vapour. These very narrow absorption l i n e s produced sharp i n t e n s i t y drops of up to twenty percent i n the luminescence spectrum and were p a r t i c u l a r l y noticeable i n the TO phonon r e p l i c a region. The boron PBE TO r e p l i c a was most affected by these absorption l i n e s since two very strong l i n e s occur i n t h i s region. When low r e s o l u t i o n scans are taken the problem i s not so pronounced since the sharp dips are e f f e c t i v e l y smoothed out. The problem was eliminated by purging the spectrometer with dry nitrogen gas. 2.3 The Photomultiplier Tube Detector The most s i g n i f i c a n t improvement of the apparatus under-taken as part of t h i s project was the replacement of the germanium detector described i n section 2.1 with a photomultiplier tube. Previously, photomultiplier tubes having the well known SI spectral response had been tested and found to be less suitable than the germanium detector since they were only marginally more s e n s i t i v e i n the NP region and became r a p i d l y worse for longer wavelength photons. In the TO r e p l i c a region the SI response drops so r a p i d l y that the r e l a t i v e i n t e n s i t i e s of the TO KAPS series are s i g n i f i c a n t l y modified. The tube used f o r the experiments reported here was a VPM-159 manufactured by Varian Associates. This tube has an InGaAsP 15 photocathode, numerical aperture of f/4 and twelve dynode stages. It must always be kept at a temperature below -20°C and i n the present apparatus i t i s kept at a temperature of -78°C i n a dewar cooled by dry i c e . The standard VPM-159 has a very sharp c u t o f f at a wavelength of 1.1 u but the one used for these experiments had a custom t a i l o r e d photocathode with usable response to 1.2 u, which i s adequate f o r studying FE, BE and KAPS luminescence i n s i l i c o n . In F i g . 2.4 the measured near-infrared response of the tube i s shown. The locations of some of the major luminescence l i n e s of phosphorus doped s i l i c o n , which are described i n Chapter 3, are shown f o r comparison. The dark count rate of t h i s tube was found to be on the order of ten per second, and at 1.07 u (PBE NP region) the quantum e f f i c i e n c y quoted by Varian i s about 1.6%. Thus the e f f e c t i v e noise input power of t h i s tube at 1.07 u i s close to 1 x 10~ 1 5 watts, which represents about two orders of magnitude improvement over the germanium detector. 16 1030 1160 P H O T O N E N E R G Y ( m e V ) Figure 2.4 Response of the photomultiplier tube detector versus photon energy. 17 CHAPTER 3 RESULTS AND ANALYSIS 3.1 Shell Model of the Bound Multiexciton Complexes Some of the d e t a i l s of Kirczenow's 1 6> 1 7 SM of the BMEC are discussed i n t h i s section i n order that the nomenclature used i n describing the experimental r e s u l t s i n the following sections w i l l be cle a r . Dean et a l . 8 were the f i r s t to suggest that as electron-hole p a i r s are added to a BE, forming BMEC of increasing complexity, the electrons and holes w i l l f i l l the degenerate s i n g l e - p a r t i c l e l e v e l s i n s h e l l s . Dean et a l . 8 did not consider the nature or e f f e c t s of these s h e l l s on the t r a n s i t i o n s , but only considered the t o t a l angular momentum of each complex. By applying t o t a l angular momentum s e l e c t i o n r u l e s , they showed that the Zeeman s p l i t t i n g data of Sauer and Weber 1 4 could be q u a l i t a t i v e l y explained by the o r i g i n a l BMEC model although the thermal-i z a t i o n of the Zeeman l i n e s could only p a r t i a l l y be understood. Since Dean et a l . 8 retained the o r i g i n a l model of the BMEC i n which the i n i t i a l and f i n a l states of each KAPS t r a n s i t i o n are assumed to be complexes which are i n t h e i r ground states, they concluded that the binding energies of the BMEC were given by the energy differences between the FE threshold and the KAPS l i n e s . The increasing binding energies of complexes containing greater numbers of electron-hole p a i r s was ascribed to the e f f e c t s of i n t e r p a r t i c l e c o r r e l a t i o n s . In rep l y to the objections of Sauer and Weber 1 4 and Morgan 1 5 that the BMEC model could not explain such large binding energies, Dean et a l . 8 stated that the r e s u l t s of c a l c u l a t i o n s of the binding energies of BE showed that 18 t h i s energy should be about 0.44 times the impurity i o n i z a t i o n energy. The observed BE binding energy i s only about one-quarter of t h i s value and Dean et a l . suggested that the reduction was due to quenching by quantum fl u c t u a t i o n s i n the highly degenerate BE ground state. Thus as more electron-hole p a i r s are added to the complex the fl u c t u a t i o n s would be reduced and the binding energy should approach the predicted value of 0.4!4, times the impurity i o n i z a t i o n energy. It should be noted that Sauer and Weber 1 4 have considered a model f or the KAPS l i n e s i n which the i n i t i a l and f i n a l states of a l l the KAPS t r a n s i t i o n s were excited states of the BE and the neutral impurity, r e s p e c t i v e l y . It i s very u n l i k e l y that such a model could account f o r the energies of the KAPS l i n e s , since even the lowest l y i n g donor excited state i s s p l i t from the donor ground state by an energy which i s considerably larger than the energy difference between the m=2-KAPS l i n e and the FE threshold. Thus, i n the model suggested by Sauer and Weber,14 the i n i t i a l state of the m=2' KAPS t r a n s i t i o n (and by implication a l l the other KAPS t r a n s i t i o n s as well) i s an unbound excited state of the BE. It seems u n l i k e l y that the thermal d i s s o c i a t i o n l i f e -times of such unbound excited states of the BE could be as long as the 300 nsec decay times which Kosai and Gershenzon 1 2 have reported f o r the m=2 and m=3 phosphorus KAPS l i n e s . In developing the SM K i r c z e n o w 1 6 * 1 7 sought to explain the stress and. Zeeman 'S,pllutings '.of, the'SKAPS -lines reported by Sauer and Weber 1 4 while r e t a i n i n g the BMEC model. In addition, the SM explained the large energy s h i f t s of some of the KAPS l i n e s by showing that they are p a r t i a l l y due to the fa c t that some of the t r a n s i t i o n s r e s u l t i n excited f i n a l states. 19 In the SM the wave function of a BE or BMEC i s represented by a properly antisymmetrized product of single p a r t i c l e wave functions. These single p a r t i c l e wave functions are c l a s s i f i e d according to t h e i r transformation properties under the tetrahedral point group T^ since i n a s i l i c o n l a t t i c e the shallow s u b s t i t u t i o n a l donor and acceptor impurities occupy s i t e s having tetrahedral symmetry. The representations are l a b e l l e d according to Koster et a l . 2 4 Where t h i s i s h e l p f u l , the T d representation labels of the s i n g l e p a r t i c l e wave functions are augmented by spectroscopic labels describing the nature of the envelope of the wave function. For the moment the p o s s i b i l i t y of s p l i t t i n g s a r i s i n g from the i n t e r a c t i o n s of the p a r t i c l e s i n the t e t r a h e d r a l l y symmetric environment of the complexes w i l l be ignored. Let us begin by applying the SM to the s u b s t i t u t i o n a l donor (SD) BE and BMEC. Kohn 2 5 has shown that the s i x - f o l d (excluding spin) degeneracy of electrons i n the i n d i r e c t conduction band of s i l i c o n i s l i f t e d by v a l l e y - o r b i t s p l i t t i n g f o r electrons i n the t e t r a -hedral l y symmetric environment of the donor ion. The I S - l i k e ground state of the donor i s s p l i t into a nondegenerate, a two-fold and a t h r e e - f o l d degenerate l e v e l which transform as r"i, r 3 and T5. In addition Kohn 2 5 demonstrated that only the state has a large p r o b a b i l i t y amplitude near the donor core and therefore i t i s most strongly bound and becomes the ground state of the SD. It was f i r s t suggested by Thomas et a l . 2 6 that f o r BE associated with donor impurities having large a t t r a c t i v e v a l l e y - o r b i t s p l i t t i n g s (such as the s u b s t i t u t i o n a l donors i n s i l i c o n ) the v a l l e y -o r b i t s p l i t t i n g , which favours p l a c i n g both electrons i n the r, l e v e l , 20 should outweigh by a considerable margin the o r i e n t a t i o n a l e f f e c t s a r i s i n g from the v a l l e y anistropy which would favour p l a c i n g the addi t i o n a l electron i n the T 3 or T 5 ( r 3 5) states. Thus the SD BE ground state contains two T1 electrons and one TQ hole. We w i l l label t h i s configuration | 2 I , 1 ; i r 8 | . This model f o r the SD BE ground state was s u c c e s s f u l l y used to explain q u a l i t a t i v e l y the SD BE Zeeman spectra i n gallium phosphide 2 6 and i n s i l i c o n * : 2 7 The SM of the SD BMEC i s based upon an extension of t h i s model. When an extra exciton i s added to the SD BE, thus forming an m=2 BMEC, the a d d i t i o n a l hole can,>be placed i n the same TQ s h e l l as the o r i g i n a l hole since a l S - l i k e r 8 s h e l l can contain up to four holes. However, the added electron cannot be placed into the l S - l i k e Ti electron s h e l l , ^ f o r . t h i s s h e l l can hold only two electrons. Therefore the addi t i o n a l electron must be placed i n the I S - l i k e T 3 j 5 s h e l l . (In the BMEC we do not d i s t i n g u i s h between the r 3 and the T 5 shell's isinoe the r 3 - T 5 s p l i t t i n g of the SD i s much less than the r ] _ - r 5 s p l i t t i n g . ) It i s assumed that i n the BMEC the IS T 3 j 5 s h e l l i s more t i g h t l y bound than any s h e l l other than IS since t h i s i s the case for the neutral donor. Thus the ground state of the SD m=2 BMEC i s denoted J 2 r 1 , i r 3 5 ; 2 r 8 j , and s i m i l a r l y the m= 3 BMEC i s j 2T j., 2 T 3 ? 5 ; 3 T 8 [, etc. For m>4 there must be an a d d i t i o n a l hole s h e l l but the l S - l i k e F 3 j 5 s h e l l w i l l only become f i l l e d at m=ll. In the SM a l l of the SD KAPS l i n e s are due to processes i n which a r ; electron recombines with a T 8 hole, and no other p a r t i c l e s i n the complex change state during these t r a n s i t i o n s (which i s to say that the KAPS t r a n s i t i o n s are one-electron one-hole t r a n s i t i o n s ) . 21 Kirczenow 1 7 has shown that t h i s model can q u a l i t a t i v e l y explain the s t r e s s - s p l i t t i n g s of the phosphorus BE and KAPS l i n e s reported by Sauer and Weber. 1 4 The s i m i l a r i t y between t h e i r phosphorus BE Zeeman spectra and that of the f i r s t three KAPS l i n e s i s also explained since i n a l l cases the i n i t i a l state s p l i t t i n g s are those of the j= 3/2 r8 h°l e which recombines and the f i n a l state s p l i t t i n g i s due to the unpaired electron. The reason f o r decreasing thermalization f o r complexes of increasing m i s c l e a r l y that, since holes are fermions, when more holes are added to the r 8 s h e l l i t becomes more f i l l e d and therefore the thermalization e f f e c t s are reduced. For m=4 the T 8 s h e l l i s completely f u l l and the i n i t i a l state should show no thermalization (assuming that the next hole s h e l l i s s u f f i c i e n t l y removed). At t h i s point we note that the i n t e n s i t i e s of the Zeeman l i n e s predicted f o r t h i s model of the SD BE by Thomas et a l . 2 6 are inco r r e c t i n that while the i n t e n s i t i e s given i n F i g . 2 of that paper are the correct t o t a l i n t e n s i t i e s f o r the t r a n s i t i o n s , the p o l a r i z a t i o n s of the l i n e s are l a b e l l e d e i t h e r p a r a l l e l or perpendicular which would indic a t e that the i n t e n s i t i e s are being measured f o r l i g h t emitted transverse to the magnetic f i e l d . However, the i n t e n s i t i e s of Zeeman t r a n s i t i o n s measured f o r emission transverse to the magnetic f i e l d are not the same as the t o t a l i n t e n s i t i e s since f or" Am^.=0light i s emitted only transverse to the magnetic f i e l d while f o r Anu=±l l i n e a r l y p o l a r i z e d l i g h t "is emitted transverse to the f i e l d and, i n addition, c i r c u l a r l y p o l a r i z e d l i g h t i s emitted along the axis of the f i e l d . Cherlow et a l . 2 7 have reproduced the incor r e c t diagram of Thomas et a l . 2 6 i n t h e i r paper. The proper transverse t r a n s i t i o n p r o b a b i l i t i e s are given 22 by Sauer and Weber 1 4 (who did not comment on the difference between t h e i r values and those of Thomas et a l . 2 6 ) and by Kirczenow. 1 7 The t r a n s i t i o n scheme given by Thomas et a l . 2 6 i s shown i n F i g . 3.1 along with the corrected i n t e n s i t i e s . The t h e o r e t i c a l transverse i n t e n s i t i e s of the Zeeman li n e s f o r the l4m^4 SD complexes have been calculated by Kirczenow 1 7 using the corrected t r a n s i t i o n p r o b a b i l i t i e s , and i n i t i a l state populations given by the fermi s t a t i s t i c s of m holes i n the four non-degenerate l e v e l s . These i n t e n s i t i e s were cal c u l a t e d for the p a r t i c u l a r experimental conditions used by Sauer and Weber. 1 4 I n t e r e s t i n g l y enough the agreement i s quite good except that f o r a l l four values of m Kirczenow's c a l c u l a t i o n s over-estimate the i n t e n s i t i e s of the t r a n s i t i o n s l a b e l l e d 3a and 4 i n F i g . 3.1 by a f a c t o r of about two, and i t was these t r a n s i t i o n p r o b a b i l i t i e s which were corrected by Sauer and Weber 1 4 and Kirczenow 1 7 by the same fac t o r of two. Thus i f Kirczenow 1 7 had used the i n c o r r e c t t r a n s i t i o n p r o b a b i l i t i e s given by Thomas et a l . 2 6 , h i s p r e d i c t i o n s would have agreed exactly with the observations of Sauer and Weber. 1 4 A possible explanation of t h i s rather unsatisfactory r e s u l t i s provided by a consideration of the e f f e c t of t o t a l i n t e r n a l r e f l e c t i o n s upon the luminescence spectrum. Since s i l i c o n has a r e f r a c t i v e index of about 3.44, the r e f l e c t i v i t y f o r photons incident normal to the s i l i c o n surface i s 0.3, while f o r angles of incidence greater than the c r i t i c a l angle of 16.9 degrees the photons undergo t o t a l i n t e r n a l r e f l e c t i o n . Thus the p r o b a b i l i t y f o r transmission i s much less than that f o r r e f l e c t i o n when averaging over a l l angles of incidence, and since l i g h t l y doped s i l i c o n i s e f f e c t i v e l y transparent 23 m j +3/2 +1/2 -1/2 -3/2 f f ± II II 1/6 1/6 1/3 1/3 1/6 1/6 2/3 2/3 +1/2 -1/2 ± 1/2 1/2 SUBSTITUTIONAL DONOR BOUND EXCITON _L P o l a r i z a t i o n 1/2 1/2 Intensity Ratios Given i n Ref. 26 Corrected Intensity Ratios L. SUBSTITUTIONAL DONOR Figure 3.1 Level scheme for the Zeeman s p l i t t i n g i n the " s i m p l i f i e d " SD BE model. 24 to the luminescence photons one concludes that most of the photons emitted by the c r y s t a l have undergone i n t e r n a l r e f l e c t i o n s p r i o r to emission. Neither Sauer and Weber 1 4 nor Cherlow et a l . 2 7 mention any attempts to reduce t h i s e f f e c t i n t h e i r Zeeman studies of s i l i c o n . This e f f e c t may be accentuated by the f a c t that s i l i c o n samples used for photoluminescence studies often have rather nonplanar surfaces due to repeated etching. In addition, the sample o r i e n t a t i o n i s usually adjusted so as to maximize the very weak luminescence signal and t h i s procedure no doubt r e s u l t s i n the spectrometer entrance s l i t s being imaged onto a section of the sample which has a high p r o b a b i l i t y of transmitting not only the d i r e c t l y incident photons but also the ones which have undergone i n t e r n a l r e f l e c t i o n s . Given that many of the photons which are detected have undergone several i n t e r n a l r e f l e c t i o n s one can no longer be c e r t a i n of which d i r e c t i o n the photons were o r i g i n a l l y emitted. The l i m i t of t h i s behaviour would be the case i n which photons emitted i n any d i r e c t i o n had an equal p r o b a b i l i t y of leaving the c r y s t a l i n a given d i r e c t i o n . In t h i s case, when studying the i n t e n s i t i e s of the Zeeman components i n the transverse d i r e c t i o n one should use the t o t a l t r a n s i t i o n p r o b a b i l i t i e s given by Thomas et a l . 2 6 and not the transverse t r a n s i t i o n p r o b a b i l i t i e s used by Kirczenow. 1 7 So i n the l i m i t of completely random i n i t i a l emission d i r e c t i o n s , Kirczenow's 1 7 c a l c u l a t i o n s would agree very well with the observations of Sauer and Weber. 1 4 Of course t h i s model would have pronounced e f f e c t s on the p o l a r i z a t i o n of the luminescence since the l i g h t emitted along the magnetic f i e l d i s not l i n e a r l y p o l a r i z e d , and therefore the l i n e s for which A m ^ i l w i l l have a reduced p o l a r i z a t i o n 25 ratio due to the addition of the circularly polarized light to the linearly polarized component. In addition, the linearly polarized light from a l l of the transitions will be partially depolarized by the internal reflections. Cherlow et al., 2 7 in studying the Zeeman spectra of the SD BE in silicon, found exactly these results; namely the components having Am..=0 were partially polarized and those with Am_.=±l were essentially unpolarized. However, Sauer and Weber14 claim that a l l the components are polarized, unfortunately without giving any information as to the polarization ratios. Due to these conflicting results i t is not clear i f the discrepancy in Kirczenow's intensities can be explained by the effect described above. Clearly i t would be very desirable to have more extensive data on the Zeeman splittings of the BE and KAPS lines. Let us now return to a consideration of the SM of the SD BE and BMEC. As was stated previously, the PBE and all the KAPS lines are assumed to result from the recombination of a hole with a Tj electron. Thus the PBE can be written: J 2 r 1 ; r 8 j -»- { i r ^ + photon (+ phonon) (3.1) where l l ^ is the ground state of the SD and (+ phonon) indicates that the transition may either be phonon assisted or occur via the NP process. Similarly the m'th KAPS transition is: | 2 r l 3 (m-l)r 3 j 5;mr 8l + j i r ^ O n - l ) ^ 5;(m-l)r 8| + photon (3.2) (+ phonon) The final state of this transition is an excited state of the m-1 complex in which one of the electrons is promoted to the r 3 j 5 shell. This 26 excited state need not nec e s s a r i l y be bound, i t can also be i n resonance with the FE continuum so long as i t s d i s s o c i a t i o n time i s greater than about 10 1 1 seconds (in order to explain the sharpness of the l i n e s ) . Thus the SM of the SD BMEC shows that the energy difference between the m'th SD KAPS l i n e and the FE threshold i s equal to the binding energy of the m'th BMEC /.plus the excited state s p l i t t i n g of the (m-1) 'th complex. C l e a r l y the model predicts more t r a n s i t i o n s than just the PBE and KAPS l i n e s . I f ^ i r 1 , i r 3 5 ; i r 8 j . , the excited state of the BE, i s bound then one should be able to observe two new t r a n s i t i o n s : j l r l > l r 3 , 5; i r8 } U'tl} + Photon + phonon (3.3) { l T ^ i r g ^ i r g l { i r 3 j 5 [ + photon (+ phonon) (3.4) In process (3.3) the SD i s l e f t i n the ground state whereas i n (3.4) i t i s l e f t i n e i t h e r the 1ST 3 or l S r 5 excited state (note that i n the SD the l S r 3 and l S r 5 states are s p l i t by a measurable amount and therefore (3.4) w i l l produce two d i s t i n c t l i n e s ) . In process (3.4) a phonon need not be emitted since the Ti electron which recombines i n t e r a c t s strongly with the impurity central c e l l and therefore the p r o b a b i l i t y of NP recombination can be quite high. On the other hand i n process (3.3) i t i s a T 3 J 5 electron which recombines and since the T 3 J 5 electrons do not i n t e r a c t strongly with the impurity central c e l l and the hole i s r e p e l l e d by the p o s i t i v e donor ion the recombination should be predominantly phonon-assisted. In the SM t r a n s i t i o n (3.1) i s l a b e l l e d a 1 , (3.2) i s a"1, (3.3) i s <5 and (3.4) i s y 1-The SM t r a n s i t i o n s f o r l<m<4 are shown i n F i g . 3.2. 27 BMEC 4 c4 BMEC3 £ 3 cr3 BMEC2 /3 2 G 2 r- v r 4 r 3 iS i BE y 2 a l neutral donor s •{r !4 r 3 , 5 ;4 r 8 } •{2r!.3r3,5;4r j } {2rl2r 3 , 5;3r 8} . f T% I /•"« T t *>) tr;2.r^,5;2r8} r i ^ ^ p i I JL p <L 9 X J {r 3 s 5 } Figure 3.2 SM t r a n s i t i o n scheme f o r the SD BE and BMEC 28 Just as y 1 connects an excited i n i t i a l state of the BE with an excited f i n a l state of the SD, the m'th BMEC i n i t s excited state may decay into the (m-l)'th complex i n i t s excited state v i a the ym t r a n s i t i o n : j l r 1 , m r 3 ) 5 ; m r 8 } j l T j , ( m - l ) r 3 j 5 ; (m-l)r 8| + photon + phonon. ( 3 . 5 ) As with y 1* Y " 1 should be predominantly phonon a s s i s t e d since i t i s a r 3 5 electron which recombines. F i n a l l y , the m'th BMEC i n i t s ground state may undergo the t r a n s i t i o n l a b e l l e d 8 m ^ which r e s u l t s i n an (m-l)'th complex i n i t s ground state: \2Tl,(m-l)r3j5;mr8j j 2 r x , ( m - 2 ) T 3 } 5 ; ( m - l ) T 8 } + photon + phonon ( 3 . 6 ) In the above t r a n s i t i o n m must be greater than one, i n other words a BE cannot be the i n i t i a l state of a 6 t r a n s i t i o n . The 8 t r a n s i t i o n s must be predominantly phonon as s i s t e d because the recombining electron comes from the r 3 ) 5 s h e l l . Since the 8 t r a n s i t i o n s connect ground states, the binding energy of the m'th BMEC i s given by the energy difference of the 8 m * l i n e and the FE threshold. In the above discussion of the SM of the SD BE and BMEC the p o s s i b i l i t y of excited states with no electrons has been ignored since these states are expected to be unbound. Also, the p o s s i b i l i t y of a s p l i t t i n g i n the m.=2 BMEC due to hole-hole coupling i s neglected, since as we s h a l l see f o r the acceptor BE t h i s s p l i t t i n g seems to depend very strongly on the i n t e r a c t i o n of the two holes with the central c e l l which w i l l of course be very small f o r a p o s i t i v e l y charged impurity core. 29 For m>4 there w i l l be more than one hole s h e l l which w i l l lead to the p o s s i b i l i t y of excited states due to the promotion of a hole from the inner s h e l l to the outer, and thus one would expect more than two tr a n s i t i o n s o r i g i n a t i n g from the ground state of SD BMEC f o r m>4. The second hole s h e l l of the acceptor BMEC may well be the l S - l i k e r 7 state associated with the s p l i t - o f f valence band, since t h i s state i s the lowest l y i n g excited state of the acceptor i m p u r i t i e s . 2 8 Now l e t us consider the SM of the acceptor BE and BMEC. The inner hole s h e l l i s l a b e l l e d TQ and i s f o u r - f o l d degenerate (except when occupied by two holes when i t may be s p l i t due to hole-hole i n t e r -actions) . Since electrons are r e p e l l e d by the negatively charged impurity ion, the v a l l e y - o r b i t s p l i t t i n g i s expected to be very small and the inner electron s h e l l should be highly degenerate. Therefore the s t r u c t u r a l diagrams f o r the L<m-s4 acceptor complexes given by Dean et a l . 8 agree completely with the SM. For m^3 the KAPS l i n e s connect the ground states of the i n i t i a l and f i n a l complexes. However, i n the SM excited states of the acceptor complexes which are analogous to the previously described SD donor complex excited states must be considered. These excited states would be due to the promotion of a hole from the inner TQ s h e l l to an outer s h e l l . Excited states due to the electron populations are not considered at t h i s time. It i s evident that f o r m>3 an acceptor BMEC can undergo t r a n s i t i o n s analogous to both the SD a 4 and 8 3 trans-i t i o n s . Since the inner hole s h e l l of the m=4 acceptor BMEC contains four holes while the outer hole s h e l l contains only one i t seems very probable that the t r a n s i t i o n i n v o l v i n g recombination of an inner s h e l l hole would be stronger than that i n v o l v i n g the outer hole. It i s therefore reasonable to p r e d i c t that the m>3 boron KAPS t r a n s i t i o n s 30 leave complexes i n excited states and that t h i s i n part explains the low energies of these l i n e s . F i n a l l y one must consider the implications of the SM f o r the case of the i n t e r s t i t i a l donor lithi u m , f o r which a large number of KAPS l i n e s have been observed. 1 2 In the lit h i u m donor ground state the electron i s i n the highly (10-fold) degenerate ISITS^.5 l e v e l and there-fore the structure of the lit h i u m BE and BMEC bears more s i m i l a r i t y to that of the acceptors than to the donors. Only f o r the m>4 BMEC w i l l the p o s s i b i l i t y of S-like t r a n s i t i o n s r e s u l t i n g i n excited f i n a l states a r i s e . Again, these excited states w i l l be due to the promotion of a hole from the inner s h e l l . Thus the SM pre d i c t s that f o r m>4 the lit h i u m KAPS l i n e s are produced by t r a n s i t i o n s which r e s u l t i n excited f i n a l states. For m$10 the electron s h e l l structure may give r i s e to other 3-like t r a n s i t i o n s i f the IS F^ s h e l l i s s i g n i f i c a n t l y s p l i t from the IS T 3 J5 s h e l l . In any case these t r a n s i t i o n s are c e r t a i n l y expected f o r m>llp since i n these complexes some electrons would e x i s t i n s h e l l s outside the IS s h e l l . The l i t h i u m BMEC spectrum i s c l e a r l y i n need of further experimental study. The following sections contain the main r e s u l t s of the studies undertaken during t h i s project. Additional aspects of the SM and of other relevant theories are given where necessary. Some of the implications of the SM w i l l be discussed i n Chapter 4. 31 3.2 Phosphorus Bound Excitons (One-Electron Transitions) Due to a lack of s u f f i c i e n t l y pure samples containing other SD impurities, the only SD studied as a part of t h i s project was phosphorus. Fortunately the previously r e p o r t e d 1 0 ' 1 1 ' 1 2 studies of the KAPS l i n e s also used phosphorus-doped s i l i c o n and thus d i r e c t comparison i s possible. It should be noted that u n t i l the r e s u l t s of the studies reported here were published i t was generally assumed that the SD BE i n s i l i c o n had no bound excited states. Once the SM had been proposed i t was necessary to search f o r any evidence of such SD BE bound excited states. Nishino and Hamakawa29 had previously published derivative-absorption spectra of doped s i l i c o n which showed a new absorption process "nearly" at the FE threshold i n a l l the SD-doped samples. Even though t h e i r experimental r e s o l u t i o n was i n s u f f i c i e n t to determine whether the new t r a n s i t i o n s were j u s t above or below the FE threshold Nishino and Hamakawa29 stated that the new t r a n s i t i o n s were FE t r a n s i t i o n s . No explanation was given for the narrowness of the new l i n e s , which would be d i f f i c u l t to r e c o n c i l e with an FE process. Since the new structure was observed only i n SD doped s i l i c o n Nishino and Hamakawa29 concluded that the new t r a n s i t i o n s were "FE two-electron t r a n s i t i o n s involving the v a l l e y - o r b i t states of a donor". Why thervpro.posedd t r a n s i t i o n s were named two-electron t r a n s i t i o n s i s not c l e a r since they do not involve a change i n state of the second (donor) electron. I t w i l l be shown i n t h i s section that the photolumines-cence spectrum of phosphorus-doped s i l i c o n c l e a r l y reveals t r a n s i t i o n s 32 o r i g i n a t i n g from a bound excited state of the BE. It seems very l i k e l y that the new absorptions seen by Nishino and Hamakawa29 are also due to t h i s excited state of the SD BE, and are thus the reverse of the 6 process shown i n F i g . 3.2. Although Nishino and Hamakawa29 have not analysed t h e i r lineshapes or i n t e n s i t i e s , t h e r e l a t i v e strength of the new absorption process r e l a t i v e to the PBE l i n e agrees reasonably well with the r a t i o of the t r a n s i t i o n i n t e n s i t i e s obtained from the photo-luminescence r e s u l t s presented here. Recently Nishino et a l . 3 0 have presented new data on the temperature behaviour of the new absorption process which they claim rules out any BE bound excited state explana-t i o n . The v a l i d i t y of t h e i r arguments w i l l be discussed at the end of t h i s section. A l l of the spectra described i n t h i s section were obtained from high-purity float-zone r e f i n e d phosphorus-doped samples. The impurity concentrations quoted are those provided by the supplier. Since the conclusions drawn from these experiments do not depend upon an accurate knowledge of the impurity concentrations, no attempt was made to v e r i f y these values. This i s true of a l l concentrations quoted i n t h i s t h e s i s . In Fig.3i3 the photoluminescence spectrum of a sample containing 1.2 x 1 0 1 6 phosphorus impurities per cm3 and at a temperature of 19 K i s shown. The l i n e s are l a b e l l e d according to the SM trans-i t i o n s shown i n F i g . 3.2. The a 1 l i n e i s the well known PBE l i n e of phosphorus. 6 The 6 l i n e i s seen only i n the phonon r e p l i c a s , as was predicted by the SM. No sign of i t could be detected in the NP region down to a l e v e l of about one five-hundredth of the a* I D i n t e n s i t y , which 33 >-•z. LULU O r -LU~ O in i UJ V/-FETO* tr. TO" 'TO' : | V 1 TO /"yT0 TO \ -xi 16—3 ) Si (P I.2xl0 , vcm 19 K -X30 NP" TV . I o o / r V* x / i i i l i r 1 l& T A r N P y ' 2s(r3 5 > ; 8 T A V ^ X « I I //-I I I WA I 1 1—I—I 1 1 1 " 1 1083 1095 1116 1132 PHOTON ENERGY (meV) Figure 3.3 The photoluminescence spectrum o f phosphorus-doped s i l i c o n at 19 K. The l i n e s l a b e l e d 2 S ( T j ) and 2 S ( T 3 > 5 ) are the NP r e p l i c a s of two-electron t r a n s i t i o n s . The i n t e n s i t i e s of the NP one-electron and two-electron t r a n s i t i o n s have been m u l t i p l i e d by f a c t o r s o f 1.8 and 30 as compared to the TO r e p l i c a l i n e s , r e s p e c t i v e l y . The low energy edge o f the FE TO l i n e from an i n t r i n s i c sample i s shown as a dashed l i n e f o r comparison 34 indicates that the i n t e r a c t i o n of the r 3 j 5 electron with the impurity cen t r a l c e l l i s indeed very small. The two l i n e s l a b e l l e d y 1 and y 1 * a r e seen i n both the phonon and NP r e p l i c a s as predicted by the SM. The reason two y 1 l i n e s are observed while F i g . 3.2 only indicates one i s that the r 3 and T 5 states of the phosphorus IS l e v e l are s p l i t by an observable amount. Dean et a l . 6 had e a r l i e r observed the y doublet f o r several SD including phosphorus,but had not resolved the two components. As a r e s u l t they thought the l i n e exhibited Maxwell-Boltzmann behaviour and therefore ascribed i t to a FE two-electron t r a n s i t i o n i n which a donor impurity was l e f t i n a v a l l e y - o r b i t excited state. The l i n e s l a b e l l e d 2S(T 1) and 2S(T 3 5) are two-electron t r a n s i t i o n s and w i l l be discussed i n the next section. The energies of the NP l i n e s are given i n Table 3.1. The energy differences between the 6 l i n e and the y 1 and Y 1* l i n e s are 11.8 ± 0.1 and 12.97 ± 0.1 meV, i n agreement with the s p l i t t i n g s of the phosphorus IS to IS r 5 and IS r 3 l e v e l s which are known 3 1 to be 11.62 ± 0.1 and 13.0 ± 0.1, r e s p e c t i v e l y . Thus the s p l i t t i n g of the r 3 and r 5 l e v e l s of the BE must be too small to observe i n these experiments. The energy differences between the 5'- l i n e and the y 1 and y 1 * l i n e s do not match the v a l l e y - o r b i t s p l i t t i n g energies of phosphorus. The o r i g i n of the 6' l i n e i s not known at t h i s time. Spectra were also obtained using a sample containing 6 x 1 0 1 6 phosphorus impurities per cm3 and the only differences were that i n the more heavily doped sample the BE l i n e s were s l i g h t l y broader and the FE to BE i n t e n s i t y r a t i o was reduced. Both of these e f f e c t s are to 35 Table 3.1 Energies and Intensity Ratios of the Phosphorus One-Electron Transitions Luminescent Line NP Energy (meV) Intensity Ratios a 1 1150.01 a 2 1146.47 a 3 1143.71 a 4 1141.72 a 5 1140.46 a 6 1139.31 B 2 1147.90 6 2 / a 3 3 3 1145.60 B 3 /ak  PT0 X TO <5 1154.32 L 6TA / aTA ] 6' 1153.73 Y 1 1142.52 • [ y l / a 1 ] Y 1* 1141.35 LY 1*/^ 1] 0.95 ± 0.1 1.8 ± 0.2 9.2 ± 0.8 3.1 ± 0.2 1.2 ± 0.3 Note: Line cenergies are^accurateito 0.05 meV. A l l energies are f o r the NP r e p l i c a . Where no NP r e p l i c a could be observed the phonon r e p l i c a energy was converted to the NP energy by adding the energy of the phonon. For the i n t e n s i t y r a t i o s the l i n e s are NP r e p l i c a s unless otherwise noted. Ratios enclosed i n square brackets are the infinite-temperature r a t i o s of the l i n e s i n thermal equilibrium. The NP FE threshold i s 1154.59 (+0.05 - 0.1) meV. 36 be expected. This observation coupled with the fact that there was no v a r i a t i o n i n the i n t e n s i t y r a t i o s of the l i n e s (excluding the FE) as the e x c i t a t i o n power was changed rules out a FE explanation f o r the o r i g i n of the new l i n e s . Also, as can be seen from Table 3.1, the & l i n e i s 0.27 (+0.1 -0.15) meV below the FE threshold and t h i s also shows that the excited state of the phosphorus BE i s a bound state with respect to formation of a FE and a phosphorus impurity i n i t s ground state. In F i g . 3.4 the logarithm (base 10) of the i n t e n s i t y r a t i o s of some of the new l i n e s with respect to the a* l i n e are p l o t t e d R NP R as a function of the inverse temperature. I f a l l of the l i n e s originate from the same excited state of the phosphorus bound exciton then t h e i r curves i n F i g . 3.4 should a l l be s t r a i g h t l i n e s of i d e n t i c a l slope. Since the energy difference between the ground state of the BE and i t s excited state i s 4.31 ± 0.1 meV as determined by the a 1 to & s p l i t t i n g , the slope of the l i n e should be -21.7 K. From F i g . 3.4 i t i s c l e a r that the i n t e n s i t y r a t i o s of a l l the l i n e s have the same temperature dependence but at the lowest temperature values a l l the l i n e s deviate from the predicted slope. This i s most l i k e l y due to a deficiency i n the experi-mental technique since the sample temperature was determined by measuring the vapour pressure of the gas i n the r e f l u x i n g dewar, which was shown i n Fi g . 2.3. The vapour pressure w i l l be determined by the temperature of the heat exchanger, but c l e a r l y i f heat i s being supplied to the sample a temperature difference w i l l e x i s t between the l i q u i d cryogen and the heat exchanger i n order to drive the r e f l u x i n g action. This temperature difference i s expected to be greatest at low temperatures where the vapour pressure changes most r a p i d l y with temperature. I f t h i s e f f e c t 37 10 T (K ) Figure 3.4 The logarithms o f some o f the i n t e n s i t y r a t i o s o f the phosphorus BE l i n e s p l o t t e d versus the inverse o f the temperature. The s t r a i g h t l i n e s have the p r e d i c t e d slope f o r an e x c i t e d s t a t e energy of 4.31 meV. The d e v i a t i o n s of the low temperature points from these s t r a i g h t l i n e s are discussed i n the text 38 i s to explain the deviations of the low temperature points from the stra i g h t l i n e s of slope -21.7 K i t i s necessary to assume that f o r the lowest temperature (14.5 K) points the sample was two degrees higher i n temperature than the heat exchanger, which does not seem unreasonable. In any case i t i s c e r t a i n that the changing slope at low temperatures which i s suggested by F i g . 3.4 cannot be r e a l since at l i q u i d helium temperatures no sign of any of these new li n e s could be observed. At 4.2 K an upper l i m i t of 0.001 times the i n t e n s i t y of the a ^ p l i n e can be placed on the sum of the y 1 and y 1 * i n t e n s i t i e s . Now l e t us return to the l a t e s t paper of Nishino et a l . 3 0 i n which they claim to prove the FE o r i g i n of t h e i r new absorption l i n e s . (At the time t h e i r r e s u l t s were submitted there was no evidence i n the l i t e r a t u r e f o r SD BE excited states. However, the preliminary r e p o r t 2 1 of the SD BE studies described here was published j u s t p r i o r to t h e i r l a t e s t paper. 3 0) Their arguments were based upon two points: the temperature dependence of the absorption i n t e n s i t y of the new structure versus that of the PBE l i n e , and the temperature dependence of the trans-i t i o n energy of the new process as compared to that of the FE threshold. Let us consider t h e i r i n t e n s i t y argument f i r s t . They stated that i t "seems" that the new process i s s t i l l observable at temperatures as high at 77 K i n s p i t e of the "nearly" complete disappear-ance of the PBE l i n e . No quantitative r e s u l t s are given, and i t i s not s u r p r i s i n g that the new t r a n s i t i o n can be seen at higher temperatures than the PBE l i n e , f o r at low temperatures i t i s at least twice as strong as the PBE l i n e . Since the new process overlaps the sharp low energy edge of the FE absorption i t i s d i f f i c u l t to obtain accurate i n t e n s i t i e s 39 from t h e i r F i g . 1. However, t h e i r F i g . 1 seems to be consistent with a constant i n t e n s i t y r a t i o up to at least 38 K, contrary to t h e i r state-ment. Furthermore, they argued that i f the new process had been due to a BE t r a n s i t i o n i t s i n t e n s i t y should have decreased more ra p i d l y than that of the PBE l i n e as the temperature was increased. The reason given f o r t h i s was that since the suggested excited state would be less t i g h t l y bound than a BE i n i t s ground state i t would have a shorter l i f e t i m e due to thermal d i s s o c i a t i o n and therefore be weaker. This argument i s misleading, since to f i r s t order the t o t a l absorption c o e f f i c i e n t s f o r the formation of excited BE (or ground state BE) do not depend upon t h e i r l i f e t i m e s once they are created. I f the l i f e t i m e i s s u f f i c i e n t l y short the t r a n s i t i o n s w i l l be broadened due to the uncertain-ty p r i n c i p l e . F i g . 1 of reference 30 shows no evidence of such a broadening. Thus i t i s probable that the decrease i n the.integrated i n t e n s i t y of the PBE absorption which occurs as the temperature i s rai s e d i s due not to BE l i f e t i m e e f f e c t s but to the reduction of the number of donors which are i n t h e i r ground states, since at temperatures of 38 K and above a s i g n i f i c a n t number of the donors w i l l be i n the v a l l e y -o r b i t excited states. The second argument presented by Nishino et a l . 3 0 was that since the temperature dependence of the t r a n s i t i o n energy of the new structure was i d e n t i c a l to that of the FE threshold, the new structure must be due to an FE process. This i s not a v a l i d conclusion since the primary source of the temperature dependence of the FE thresh-o l d i s the change of the s i l i c o n band gap with temperature, and not any 40 change of the FE binding energy. 3 2 S i m i l a r l y one would not expect the BE binding energy to show any strong temperature dependence,and there-fore the energy of the PBE t r a n s i t i o n should have the same temperature dependence as the FE threshold. A cursory examination of F i g . 1 i n the paper of Nishino et a l . 3 0 reveals that t h i s i s indeed the case. Since there i s no reason to suspect that the excited state of the BE w i l l behave d i f f e r e n t l y i t i s c l e a r that the second argument presented by Nishino et a l . 3 0 does not discriminate between FE and BE processes. 3.3 Phosphorus Bound Excitons (Two-Electron Transitions) Transitions of the donor BE which involve a change of state of the electron which i s not recombining are r e f e r r e d to as two-electron t r a n s i t i o n s . Such t r a n s i t i o n s were f i r s t observed i n S i C 3 3 and GaP. 3 4 A si n g l e t r a n s i t i o n of t h i s type was observed i n the photo-luminescence spectra of s i l i c o n doped with ei t h e r As, P or Sb by Dean et a l . 6 who concluded that the donor electron was l e f t i n an S - l i k e even p a r i t y excited state by these t r a n s i t i o n s . Thus the s e l e c t i o n rules f or BE two-electron t r a n s i t i o n s and i n f r a r e d absorption are seen to be complementary f o r the SD. In F i g . 3.5 the two-electron BE t r a n s i t i o n s of a zone-r e f i n e d sample containing 1 x 1 0 1 5 phosphorus impurities per cm3 and at a temperature of 4.2 K are shown. A very s i m i l a r spectrum has been published by S a u e r 3 5 who demonstrated that the energy s h i f t s i o f the S - l i k e l i n e s from the PBE agreed reasonably well with the predictions of the e f f e c t i v e mass theory, p a r t i c u l a r l y i n the case of the 2S(Ti) f o r which the t h e o r e t i c a l value has been corrected to take into account the 41 1106 |||7 PHOTON ENERGY (meV) Figure 3.5 The NP replica of some of the phosphorus BO two-electron transitions at 4.2 K 42 e f f e c t s of c e n t r a l - c e l l c o r r e c t i o n s . 3 6 The f a c t that no 2S(T3 5) l i n e i s observed v e r i f i e s that both electrons i n the ground state BE are i n the l S ( T i ) state as was assumed previously. The spectrum shown i n F i g . 3.5 reveals two l i n e s which have not been previously observed. The energy of the weak l i n e labeled,.. 2P Q coincides exactly with the energy one would p r e d i c t using the known 3 7 energy of the phosphorus 2P 0 excited state. Since t h i s excited state has odd p a r i t y i t should be forbidden for two-electron t r a n s i t i o n s . It may r e s u l t from perturbations caused by impurity-impurity i n t e r a c t i o n s but t h i s could not be v e r i f i e d since for more heavily doped samples the 2S(Ti) l i n e broadened and obscured the region of i n t e r e s t . The other new l i n e i s l a b e l l e d 3DQ since that l e v e l has even p a r i t y and i t s calculated binding energy of 3.75 meV agrees very well with the energy of the luminescence l i n e . 6 8 The energies of a l l of the l i n e s discussed i n t h i s section are given i n Table 3.3, as well as the energy differences between these l i n e s and the PBE l i n e . These energy differences equal the energies of the correspond-ing phosphorus excited states, measured from the ground state. The considerable discrepancy between the energy s h i f t of the 2S(T 1) l i n e of the phosphorus BE given by S a u e r 3 5 (34.97 ± 0.05 meV) as compared to that given by Dean et a l . 6 (33.6 ± 0 . 3 meV) was at f i r s t a puzzle, but the SM and the new r e s u l t s reported here provide a s o l u t i o n . Since the spectra presented by S a u e r 3 5 were taken at 2 K the BE were i n the ground state and therefore there i s only one 2S two-electron t r a n s i t i o n , namely the 2S(Ti). Dean et a l . 6 worked at temperatures of 15 K and above and thus the e f f e c t s of the excited state of the SD BE must be considered. In the NP r e p l i c a , according to the SM the electron 43 which recombines i s i n the Ti s h e l l and the remaining electron i s i n the r 3 ) 5 s h e l l . Therefore the excited BE w i l l have a NP two-electron t r a n s i t i o n leaving the donor i n the 2S(T3 5) rather than the 2S(r1) state. This t r a n s i t i o n i s shown i n F i g . 3.3, and i t s temperature behaviour which i s given i n F i g . 3.4 shows that i t s i n i t i a l state i s indeed the excited BE. The energy difference between the S l i n e and the 2SCr 3 )s) l i n e i s 36.51 ± 0.1 meV which i s i n good agreement with the value of 36.24 ± 1.1 meV predicted by e f f e c t i v e mass t h e o r y . 3 6 Due to i n s u f f i c i e n t r e s o l u t i o n Dean et a l . 6 did not resolve the 2 S ( r 3 j 5 ) and the 2S(T 1) l i n e s and therefore the energy diffe r e n c e between t h e i r 2S l i n e and the PBE l i n e given i n t h e i r paper i s a c t u a l l y an average value of the energy differences between the PBE and the two 2S l i n e s observed i n the studies reported here. The excited state of the SD BE may undergo a second two-electron t r a n s i t i o n i f the process i s phonon a s s i s t e d . In t h i s trans-i t i o n the r 3 5 electron would recombine and the donorrelectron would be l e f t i n the 2S(Pi) state. This t r a n s i t i o n has not been observed, as i s indicated i n F i g . 3.6. Unfortunately the detector s e n s i t i v i t y has dropped by a f a c t o r of three at t h i s wavelength and therefore the spectrum i s somewhat noisy. As a possible explanation f o r the low i n t e n s i t y of t h i s t r a n s i t i o n we note that the two-electron t r a n s i t i o n strength i s proportional to the admixture of the f i n a l donor states i n t o the i n i t i a l BE state. Now the ground state SD BE has two electrons i n the s h e l l , and due to e l e c t r o s t a t i c repulsion they cannot both have as high a p r o b a b i l i t y density near the impurity core as can a s i n g l e electron i n the Ti l e v e l of a SD. Therefore i t i s reasonable to expect that the IS 44 r l 1 I — » J - i 055 PHOTON ENERGY (meV) Figure 3.6 The TO r e p l i c a of the phosphorus BE 2S two-electron t r a n s i t i o n s at 20.4 K. The predicted l o c a t i o n of the 2S(Ti) l i n e o r i g i n a t i n g from the excited BE i s indicated by an arrow 45 Table 3.2 Energies of the' Momentum-Conserving Phonons TO - 58.05 meV LO - 56.15 meV TA - 18.7 meV Table 3.3 Energies of the Phosphorus BE Two-Electron Transitions Luminescence NP Energy Binding Energy* Intensity Ratio** Line (meV) ( m eV) 2S(r 1)/a 1 = 0.048 ± 0.005 [2S(r3 5 ) / a l ] = 0.55 ± 0.05 25(1!) 1115 .04 + 0. 05 10.6 2S(r 3 j 5) 1117 .81 + 0. 05 9.06 2P o 1115, .9 + 0. 05 11.46 3D 0 1108 .21 + 0. 08 3.7-7 3S 1109 .7 + 0. 05 5.26 4S 1107, .62 + 0. 05" 3.18 5S 1106 .91 + 0. 08 2.47 6S 1106, .37; + 0. 07 1.93 ;The binding energies were determined using the value 45.57 meV f o r the l S C F ^ binding energy (references 37 and 68). The i n t e n s i t y r a t i o s r e f e r to NP r e p l i c a s and the r a t i o enclosed i n square brackets i s the i n f i n i t e temperature l i m i t for.the two l i n e s i n thermal equilibrium. 46 Ti wave functions of the SD BE ground state w i l l contain a considerable admixture of higher S - l i k e Ti states. On the other hand the sing l e electron i n the s h e l l of the excited SD BE w i l l have a wave function more s i m i l a r to that of the IS Ti SD l e v e l and therefore w i l l contain less admixture of higher states r e s u l t i n g i n a lower two-electron t r a n s i t i o n i n t e n s i t y . The o r i g i n of the small bump at the high energy edge of F i g . 3.6 i s not known. I t could perhaps be the 2S(Ti) two-electron t r a n s i t i o n of a SD BE excited state which i s i n resonance with the FE continuum. Such states have been observed i n germanium. 3 8 F i n a l l y , spectra of the "forbidden" two-electron t r a n s i t i o n s from the phosphorus BE ground state to the IS r 3 and IS T5 l e v e l s of the phosphorus donor are shown i n F i g . 3.7. The i n t e n s i t y of the lS(r 5) l i n e increased from 0.001 times the i n t e n s i t y of the PBE l i n e i n the sample containing 1.2 x 1 0 1 6 phosphorus impurities per cm3 to about 0.006 of the PBE i n t e n s i t y i n a sample doped f i v e times as heavily, i n d i c a t i n g that t h i s forbidden t r a n s i t i o n occurs due to impurity-impurity i n t e r a c t i o n s . The behaviour of the lS(r 3) l i n e was i d e n t i c a l to that of the l S ( r 5 ) . The energy s h i f t s of the two l i n e s r e l a t i v e to the PBE l i n e agree with the known 3 1 energies of the phosphorus 1S(T 3) and lS(r 5) excited states. 3.4 Phosphorus Bound Multiexciton Complexes In the previous sections i t was shown that the phosphorus BE has a bound excited state which behaves as predicted by the SM. As mentioned i n section 3.1 K i r c z e n o w 1 6 ' 1 7 has already shown that previous r e b u t t a l s 1 4 of the BMEC o r i g i n of the KAPS l i n e s do not apply i f the 47 1135 PHOTON 1140 ENERGY (meV) Figure 3.7 The NP r e p l i c a o f the phosphorus BE two-electron t r a n s i t i o n s which leave the donor i n the lS(r3) and lS(r5) s t a t e s 48 s t r u c t u r e of the BMEC i s as described i n the SM. In t h i s s e c t i o n new evidence of the v a l i d i t y o f the SM of the BMEC w i l l be presented. F i r s t , l e t us consider the e x c i t a t i o n power dependence of the KAPS l i n e i n t e n s i t i e s . I t i s w e l l k n o w n 1 1 ' 1 2 that w i t h i n a s e r i e s c o n s i s t i n g o f the BE and KAPS l i n e s a s s o c i a t e d w i t h a given i m p u r i t y , the i n t e n s i t y o f the lower energy (greater m) l i n e s increases more r a p i d l y w i t h i n c r e a s i n g e x c i t a t i o n power. This i s to be expected s i n c e the higher m complexes contain more e x c i t o n s . Rather than p l o t t i n g the absolute i n t e n s i t i e s of the l i n e s versus e x c i t a t i o n l e v e l as was done p r e v i o u s l y 1 1 , 1 2 i t i s more r e v e a l i n g to p l o t the i n t e n s i t y r a t i o s of adjacent l i n e s versus e x c i t a t i o n l e v e l . In F i g . 3.8 the i n t e n s i t y r a t i o s o f the m=n+l versus m=n l i n e s are p l o t t e d f o r the a v a i l a b l e values of n i n a l l the i m p u r i t i e s s t u d i e d as par t of t h i s p r o j e c t . Here we w i l l deal only with the phosphorus curves. F i g . 3.8 shows that the slopes of a l l the curves are always p o s i t i v e , as would be expected i n any BMEC model, since FE concentration increases w i t h i n c r e a s i n g e x c i t a t i o n . The s a t u r a t i o n e f f e c t s apparent f o r a l l the curves are thought to be due to the upper l i m i t placed upon the FE d e n s i t y by the formation of e l e c t r o n - h o l e d r o p l e t s . The m=2 t o m=l i n t e n s i t y r a t i o i s seen t o be much lower than any o f the other r a t i o s , and t h i s can be explained by the SM. The BE has a f i l l e d e l e c t r o n s h e l l (the IS Fj) and because of t h i s f i l l e d s h e l l i t i s expected to be more " i n e r t " , i n analogy with the e f f e c t s o f f i l l e d s h e l l s i n atomic p h y s i c s . This " i n e r t n e s s " r e s u l t s i n a low cross-s e c t i o n f o r FE capture, thus e x p l a i n i n g the low pop u l a t i o n o f m=2 BMEC. Since the m=2 and m=3 SD BMEC do not have f i l l e d s h e l l s t h e i r FE capture cross s e c t i o n s w i l l be l a r g e r , e x p l a i n i n g the much greater values of the 49 EXCITATION INTENSITY (W) Figure 3.8 The e x c i t a t i o n dependence of the i n t e n s i t y r a t i o s of adjacent KAPS l i n e s p l o t t e d f o r the d i f f e r e n t i m p u r i t i e s . The i n t e n s i t y r a t i o of the m=n+l l i n e r e l a t i v e to the m=n l i n e i s given f o r a l l values of n f o r which data are a v a i l a b l e . For Al and Ga the m=l i n t e n s i t y i s that of the l i n e , while the m=2 i n t e n s i t y i s the sum o f the 2,(3 and 2,y lumin-escence l i n e s . For boron the t o t a l a+B+y i n t e n s i t y i s used f o r ra=l, and f o r m=2 the l i n e s could not even be resolved. A l l measurements were taken i n the NP r e p l i c a 50 m=3 to m=2 and m=4 to m=3 i n t e n s i t y r a t i o s . The m=4 SD BMEC has a f i l l e d hole s h e l l , and as expected the m=5 to m=4, i n t e n s i t y r a t i o i s lower than the previous two r a t i o s . . . Si m i l a r arguments may be applied to the e x c i t a t i o n power dependence of the l i t h i u m KAPS l i n e s reported by Kosai and Gershenzon. 1 2 From t h e i r data i t i s obvious that the m=2 to m=l, m=3 to m=2 and m=4 to m=3 i n t e n s i t y r a t i o s are a l l quite high. This i s a r e s u l t of the inverted ordering of the v a l l e y - o r b i t states of the i n t e r s t i t i a l l i t h i u m donor, which r e s u l t s i n an inner electron s h e l l capable of holding ten electrons as compared to two f o r the SD. The i n t e n s i t y r a t i o s drop o f f markedly at the m=5 to m=4 r a t i o as a r e s u l t of the f i l l i n g of the inner hole s h e l l i n the m=4 l i t h i u m BMEC. A more rigorous t e s t of the v a l i d i t y of the SM would be the presence of the new t r a n s i t i o n s of the SD BMEC predicted by the SM, as described i n section 3.1. The ym l i n e s would be very d i f f i c u l t to observe since temperatures of at least 15 K would be necessary to popu-l a t e the excited states, and at these temperatures the KAPS luminescence l i n e s become very weak. The 8m l i n e s , on the other hand, should be observed even at very low temperatures. In F i g . 3.9 the NP and "TO iphonon r e p l i c a s :„of t h e . luminescence spectrum of a sample at 4.2 K and containing 1 x 1 0 1 5 phosphorus impurities per cm3 i s shown. The NP r e p l i c a i s almost i d e n t i c a l to that presented by Sauer, 1 1 but i n the TO phonon r e p l i c a several new l i n e s are observed. Two of these are d e f i n i t e l y assigned to the B 2 and 8 3 t r a n s i t i o n s f o r the following:three reasons. . 51 Z UJ UJ o ;z i . i o CO UJ 3 -J 1081 1093 1140 PHOTON ENERGY (meV) Figure 3.9 The photoluminescence l i n e s due to the TO and NP r e p l i c a s o f the phosphorus BE and BMEC one-electron t r a n s i t i o n s at 4.2 K. The B 1 and B 2 l i n e s occur at the expected energies f o r boron contamination, but as explained i n the text the B 1 l i n e probably c o n s i s t s p a r t i a l l y of phosphorus 8 1 luminescence. The two l i n e s marked with a s t e r i s k s seem to be associated with the l i n e 52 The 8 2 to a 3 and 8 3 to a 4 i n t e n s i t y r a t i o s are independent of e x c i t a t i o n power over a wide e x c i t a t i o n range, even though the i n t e n s i t i e s of the a™ l i n e s with respect to each other change markedly over t h i s range of e x c i t a t i o n powers. The g 2 and B 3 l i n e s were also observed i n a sample containing 5 x 1 0 1 3 phosphorus impurities per cm3 and the 8 2 to a 3 and 3 3 to a 4 i n t e n s i t y r a t i o s were the same f o r both samples. F i n a l l y , these two i n t e n s i t y r a t i o s d i d not depend upon temperature i n the 4.2 K to 1.8 K range. Thus i t i s evident that the B 2 and a 3 t r a n s i t i o n s have the same i n i t i a l state, namely the m=3 BMEC. S i m i l a r l y the i n i t i a l state ofbboth the 8 3 and a 4 t r a n s i t i o n s i s the m=4 BMEC. The energies and i n t e n s i t y r a t i o s of these l i n e s are given i n Table 3.1. In order to complete an energy-level diagram f o r the BE and BMEC up to m=3 i t i s s t i l l necessary to locate the g 1 t r a n s i t i o n . The energy diffe r e n c e between the a 2 and 8 1 l i n e s should be equal to the difference i n energy between the a 1 and 6 l i n e s , as can be seen i n Fig. 3.2. This would place the g 1 at the same energy as the l i n e which has been l a b e l l e d B^Q, the energy of which i s i d e n t i c a l to that of the boron PBE l i n e . The sample c l e a r l y contains some boron contamination because the m=2 boron KAPS l i n e l a b e l l e d B 2^ i s also present. However, there i s reason to believe that the B ^ l i n e consists p a r t i a l l y of B 1 luminescence. The B 1^ to B 2^ i n t e n s i t y r a t i o i s very large compared to the r a t i o i n samples which contain predominantly boron impurities. Also, the B 1 to a 2 i n t e n s i t y r a t i o remained constant over a wide range of ex c i t a t i o n power, which i s predicted f o r the 31 l i n e but u n l i k e l y f o r the boron BE l i n e . In samples doped with approximately equal concentrations of boron and phosphorus the B 1 to a 2 i n t e n s i t y r a t i o decreased markedly 53 with increasing l a s e r power. Therefore i t seems reasonably c e r t a i n that the l i n e l a b e l l e d B 1^ i n Fi g . 3.9 consists p a r t i a l l y of B1,^  luminescence. This conclusion i s drawn from the r e s u l t s of the 1 x 1 0 1 5 cm3 sample since i n the other samples the boron contamination was much more of a problem. In F i g . 3.10 the energy l e v e l s of the phosphorus BE and BMEC up to m=3 are presented subject to the previous conclusion that the 8 1 and B 1 l i n e s are superimposed. Some of the features of t h i s l e v e l diagram can be q u a l i t a t i v e l y explained by the SM. The binding energy of an electron-hole p a i r i n the ground state of the m=2 BMEC i s seen to be less than that of the electron-hole p a i r i n the BE, while the binding energies of electron hole pairs i n the higher BMEC are a l l greater than that of the p a i r i n the BE and increase with increasing m as would be expected due to c o r r e l a t i o n e f f e c t s . The anomalously low binding energy of the m=2 BMEC i s due to the fact that i t s one T 3 5 electron does not in t e r a c t with the two electrons i n the f i l l e d Ti s h e l l . In F i g . 3.10 we see that the excited state of the m=2 phosphorus BMEC i s not bound with respect to the formation of a FE and a ground state BE. This probably r e s u l t s from the increased s t a b i l i t y of the ground state SD BE due t o i i t s f i l l e d electron s h e l l . Even though the m=2 excited state i s not bound, the a 3 l i n e w i l l s t i l l be sharp provided the d i s s o c i a t i o n time of the m=2 BMEC excited state i s not too short. This seems probable since the l e v e l l i e s only about 0'.4. meV above the FE threshold. This idea i s supported by the photoconductivity spectra of donor^'doped germanium reported by Sokolov and Novikov 3 8 who observed absorptions due to resonant BE excited states well above the 54 m = 4 4594.30 a4:1141.72 m = 3 FE + m=2 3452.58 J 3455.39 /?: 1145.60 J, 3448.70 a°:\ 143.71 m - c 2304.99 j F E , B E /3 :1147.90 4, 2300.80 2304.60 BE (m = l) a :l 146.47 1154.32 fFE + ND 154.59 /3':| 150.78 a':ll50.0l neutral donor /•| 142.52^ 1150.01 -r ,*:||4l.35 I 12.97 r, 1 -2 11.8 8:1154.324 p ; 5 1 I Figure.3,10 The proposed energy l e v e l scheme of the phosphorus BE and BMEC f o r m<4. The energies are derived from the measured energies of the luminescence lines and i t i s assumed that i n Fig. 3.9 the B 1 and B 1 l i n e s are.super-imposed. Only i n the i s o l a t e d donor i s the s p l i t t i n g between the l S ( r 3 ) and lSfl's) l e v e l s taken into account. The threshold energies for the d i s s o c i a t i o n of an m=n BMEC into a FE plus an m=n-l complex are shown on the r i g h t 55 FE threshold. Several a d d i t i o n a l features of the phosphorus photo-luminescence spectrum shown i n F i g . 3.9 also merit discussion. The two l i n e s marked with asterisks appear to be associated with the a 5 ^ l i n e , although due to t h e i r very low i n t e n s i t y t h i s could not be v e r i f i e d over a wide range of e x c i t a t i o n power. I f they are associated with the recombination of the m=5 BMEC then t h i s would v e r i f y that t h i s complex has holes i n two d i s t i n c t s h e l l s , as predicted by the SM. Another feature seen i n Fi g . 3.9 i s the low energy t a i l on the a 2p l i n e . This t a i l has a maximum amplitude of 0.04 times the a 2 i n t e n s i t y and NP i s quite broad, tapering o f f slowly i n i n t e n s i t y to about 1.5 meV below the a^p l i n e . This l i n e has been observed i n a l l samples and i s found to show no temperature dependence. The probable o r i g i n of t h i s l i n e i s an a 2 t r a n s i t i o n which r e s u l t s e i t h e r i n a higher BE excited state than the one we have considered i n the SM, or i n a FE plus an i s o l a t e d phosphorus impurity. The f i r s t evidence of f i n e structure i n the phosphorus KAPS l i n e s has also been observed and i s shown i n F i g . 3.11. Of a l l the l i n e s only the a^p l i n e width i s seen to be l i m i t e d by the spectro-meter r e s o l u t i o n . There are d e f i n i t e signs of an unresolved doublet structure f o r a^p and a t r i p l e t structure for « 2p. This structure has been resolved by Parsons 3 9 with the aid of a high r e s o l u t i o n Fabry-Perot spectrometer. Parsons 3 9 found that the s p l i t t i n g s could be explained within the framework of the SM. 56 »3 PHOTON ENERGY (meV) Figure 3.11 Photoluminescence spectra of the phosphorus NP KAPS lines for m<5. Only the width of the cx^p line is seen to be limited by the spectrometer resolution. Definite indications of structure in the expand a^ p lines is seen 57 3.5 Acceptor Bound Excitons (One-Hole Transitions) The PBE photoluminescence l i n e i n acceptor-doped s i l i c o n was f i r s t observed by Haynes 5 who found that, as f o r the donor case, the acceptor BE had a binding energy which was approximately one-tenth of the impurity i o n i z a t i o n energy. The photoluminescence spectrum of acceptor-doped s i l i c o n was further studied by Dean et a l . 6 who observed a d d i t i o n a l l i n e s a t t r i b u t e d to two-hole and two-phonon t r a n s i t i o n s . The ground state of the BE associated with the acceptors A l , Ga and In was found to be s p l i t into a doublet by Dean et al.,/ using absorption spectroscopy. As Dean et a l . 8 have recently pointed out, the r e p l i c a of the then-unrecognized LO phonon was mistaken f o r a s p l i t ground state of the boron BE i n reference 7. The doublet s p l i t t i n g of the acceptor BE ground state was explained i n terms of the j - j coupling of the two j = 3 / 2 holes to give J=0 and J=2. A doublet was also observed i n the derivative-absorption spectrum of aluminum-doped s i l i c o n by Nishino and Hamakawa,29^1 who could not observe any s p l i t t i n g of the boron BE l i n e . The cathodoluminescence spectrum of acceptor-doped s i l i c o n was studied i n great d e t a i l by Vouk and Lig h t o w l e r s . 9 ' 1 + 0 They observed thermalizing doublet structures f o r the luminescence of BE associated with A l , Ga and In impurities and a thermalizing t r i p l e t structure f o r the much deeper T l impurity. Also observed were several two-phonon and two-hole processes. The photoluminescence l i n e s of the BE associated with the acceptors B, A l and Ga which were studied as a part of t h i s p r o j e c t were a l l found to have a t r i p l e t structure. In the case of B a l l three l i n e s 58 are very close together and are not well resolved, while f o r A l and Ga the upper l i n e of the previously reported doublet 7* 9> 2 9 ° , 4 0 i s found to consist of two unresolved l i n e s . A preliminary report of the t r i p l e t s p l i t t i n g of the gallium BE was published s h o r t l y before Lightowlers and Henry 4 1 presented very s i m i l a r r e s u l t s f o r Al-doped s i l i c o n . Both of these publications dealt mainly with the acceptor BMEC which are discussed i n section 3.7, and both reports drew almost i d e n t i c a l conclu-sions . The 15 K NP and TOphonon photoluminescence spectrum of the gallium BE i s shown i n F i g . 3.12. In the figu r e and a l l the follow-ing discussions, acceptor BE and BMEC one-hole t r a n s i t i o n s w i l l be labeled X^£p, where X i s replaced by the chemical symbol of the impurity, m i s equal to the number of excitons bound i n the i n i t i a l state of the complex (as discussed p r e v i o u s l y ) , MCP (momentum conserving process) i s replaced by the symbol of the p a r t i c u l a r MCP of the luminescence l i n e i n question and y i s a s t r i c t l y phenomenological label used to d i s t i n g u i s h s p l i t l i n e s f o r which a l l the other labels are i d e n t i c a l . The lowest energy t r a n s i t i o n of a mu l t i p l e t i s assigned y=a, the next 8 etc. The t r i p l e t structure of the gallium BE luminescence i s c l e a r l y evident i n F i g . 3.12, as i s the a^p l i n e due to phosphorus contamination. A l l the aluminum and gallium doped samples used i n these studies were Czochralski-grown c r y s t a l s and had s i g n i f i c a n t l y higher concentrations of impurities than did the float-zone r e f i n e d phosphorus and boron samples. The energies and i n t e n s i t i e s of the unresolved B+y doublet were obtained under the assumption that both components had 59 PHOTON E N E R G Y (meV) Figure 3.12 The NP and TO r e p l i c a s o f the g a l l i u m BE luminescence a t 14.5 K. The Ga^B and G a j ' Y cannot be resolved due t o phonon broadening. Note the r e v e r s a l o f the i n t e n -s i t i e s o f the l i n e s i n the two r e p l i c a s . The ri* l i n e i s due to phosphorus contamination 60 i d e n t i c a l widths. The i n t e n s i t i e s of the three l i n e s were found to thermalize i n the 14.5 to 20 K temperature range and i n addition the two upper l i n e s were found to be almost unobservably weak at 4.2 K and below. Vouk and Lightowlers 9» 4 0 have done a caref u l study of the thermalization of the X1'^ + X 1'^ doublet (which was unresolved i n t h e i r studies) with respect to the X 1' 0 1 l i n e f o r X=B, Al and Ga, and also f o r the three l i n e s they observed i n the case of T l impurities. The spectrum of aluminum-doped s i l i c o n shown i n F i g . 3.13 i s very s i m i l a r to that of gallium. Note the lower energy l i n e s which are labeled with m=2 and 3. These are'the KAPS l i n e s due to aluminum BMEC and w i l l be discussed i n greater d e t a i l i n section 3.7. The magnitude of the s p l i t t i n g s are seen to be smaller f o r aluminum than f o r gallium, which i s not s u r p r i s i n g since gallium has a greater i o n i z a t i o n energy. Note also that the phonon-assisted l i n e s are always broader than the NP l i n e s . This i s always true of BE luminescence i n s i l i c o n and i s discussed i n Appendix A. The s p l i t t i n g of the ground state of the boron BE was observed for the f i r s t time as a part of these studies. A t y p i c a l NP spectrum i s shown i n Fig. 3.14 and the thermalization behaviour at the two temperatures of 4.2 and 1.8 K i s obvious. This structure i s much too narrow to be seen i n the broadened phonon r e p l i c a l i n e s . The l i n e s are again assigned the labels a, 8 and y i n order of increasing energy but t h i s i s not meant to imply that the ordering of the BE states i s the same f o r B as i t i s f o r A l and Ga. The energies and the i n f i n i t e -temperature i n t e n s i t y r a t i o s of the acceptor BE one-hole t r a n s i t i o n s are given i n Table 3.4. It was necessary to assume that the 8 and y 61 PHOTON ENERGY (meV ) Figure 3.13 The NP and TO r e p l i c a s o f the photoluminescence of aluminum-doped s i l i c o n at 14.5 K. The m=2 and m=3 aluminum KAPS l i n e s are also observed. The NP intensity-has been increased by a f a c t o r o f 2.4 r e l a t i v e to the TO r e p l i c a i n t e n s i t y 62 Figure 3.14 The boron BE NP spectrum a t 4.2 and 1 . 8 K. A t r i p l e t structure due to states which are i n thermal e q u i l i -brium seems indicated 63 components of A l and Ga had equal width, and s i m i l a r l y that a l l three components of the boron BE l i n e had equal widths (which were equal to the spectrometer r e s o l u t i o n l i m i t ) . Let us now consider the nature of the three l e v e l s of the acceptor BE ground state. When speaking of the a, B and y l e v e l s we are r e f e r r i n g only to A l and Ga since the ordering for B may be d i f f e r e n t . Vouk and L i g h t o w l e r s 9 * 4 0 have considered three possible models f o r the s p l i t t i n g s which they observed (namely none f o r B, doublet f o r A l , Ga and In and a t r i p l e t f o r Tl) . A l l three models are-;based on the concept of the j - j coupling of the two j = 3 / 2 holes i n the acceptor BE producing two s p l i t states having J=0 and J=2. Before proceeding we note, as did Vouk and Lightowlers, 9 that the J notation i s not accurate since i t ignores the c r y s t a l symmetry, e.g. the ground state of the acceptor i s TQ and not J = 3 / 2 . Nevertheless the J notation may s t i l l give useful r e s u l t s . In analogy to atomic systems one would expect the J=2 l e v e l to l i e below the J=0 l e v e l as a r e s u l t of the e l e c t r o s t a t i c i n t e r a c t i o n s of the two h o l e s . 4 2 It has been suggested that the J=0 state of the acceptor BE may l i e below the J=2 due to the l o c a l s t r a i n and Stark f i e l d s of the i m p u r i t y 4 3 or to i n t e r a c t i o n s with the c e n t r a l c e l l p o t e n t i a l . 4 4 This inverted ordering appears to have been confirmed f o r BE associated with deep-acceptors i n GaAs. 4 5 It may be that the very small s p l i t t i n g s of the boron BE are due to the proximity of boron to the changeover point between "regular" ordering and the " i r r e g u l a r " (J=2 lowest) ordering, since boron i s the only acceptor with a smaller tetrahedral radius than s i l i c o n . In addition the J = 1 /\ electron may 64 i n t e r a c t with the J=2 l e v e l to produce s p l i t J=5/2 and 3 / 2 l e v e l s , i n which case the lowest l e v e l would be J = 1 / 2 a n d the highest J = 3 / 2 . 4 5 This ordering of the three l i n e s i n the acceptor BE luminescence was t e n t a t i v e l y suggested by Vouk and L i g h t o w l e r s 9 > 4 0 , Lightowlers and Henry 4 1 and Thewalt. 2 3 In t h i s scheme the a, 6 and y l e v e l s would correspond to J=1/2> V2 a n a " 3/2 (excluding the boron BE as noted p r e v i o u s l y ) . Vouk and L i g h t o w l e r s 9 ' 4 0 and Lightowlers and Henry 4 1 went on to state that the observed t r a n s i t i o n i n t e n s i t i e s of the various components did not agree with the predicted i n t e n s i t i e s f o r J = 1 / 2 ' 5/z o r 3/2 t 0 J = 3 /2 t r a n s i t i o n s of 1:1:4, as calculated by White 4 6 and Morgan. 4 7 However, these t h e o r e t i c a l predictions should not be applied d i r e c t l y to the case of the acceptor BE i n s i l i c o n f o r two reasons. F i r s t , the c a l c u l a t i o n s do not take into account the many-valley nature of the conduction band in s i l i c o n and second, they r e f e r to a d i r e c t band-gap semiconductor. Since s i l i c o n has an i n d i r e c t band-gap and requires a MCP during recombination, the t r a n s i t i o n p r o b a b i l i t i e s c a l c u l a t e d by White 4 6 and Morgan 4 7 cannot be applied d i r e c t l y , as was done by Vouk and L i g h t o w l e r s 9 ' 4 0 and Lightowlers and Henry. 4 1 These authors compared the i n t e n s i t i e s of the NP luminescence l i n e s with the theory, ignoring the fa c t that the NP process depends upon the overlap of the hole wavefunctions with the impurity central c e l l . This e f f e c t w i l l change the NP i n t e n s i t y r a t i o s of the l i n e s , since from the energies of the luminescence l i n e s one finds that the X 1' 0 1 i n i t i a l state i n t e r a c t s more strongly with the impurity central c e l l than do the other BE l e v e l s , as can be seen i n F i g . 3.15. 65 m=4 B —> Al —> Ga —> 1 _ / J L m=3 i / • • m=2 A CO 0 0 © 1 : ; y(3 cr / rrv i T J L I L 1143 1151 PHOTON ENERGY (meV) Figure 3.15 The N P energies of a l l the acceptor lines i s compared. Only the X 1 > a energy i s seen to be strongly impurity-dependent 66 This e f f e c t i s also d i r e c t l y apparent i n F i g . 3.12 and 3.13 when one compares the r a t i o of X^p01 to ^ p ^ + Y luminescence to the same r a t i o i n the TO r e p l i c a (note that phonon broadening makes i t impossible to resolve and X ^ ) . In both cases the a to 3+y i n t e n s i t y r a t i o i s greater i n the NP r e p l i c a than i n the TO r e p l i c a , which i s consistent with the previous observation that only the energy of the a l e v e l shows a strong i n t e r a c t i o n with the impurity central c e l l . The NP r e p l i c a to TO phonon r e p l i c a i n t e n s i t y r a t i o f o r Ga 1' 0 1 i s about 0.55 while for G a l 5 ^ + Y i t i s only 0.28; f o r A l 1 ' 0 1 the r a t i o i s approxi-mately 0.44 while f o r A l 1 > ^ + Y i t i s 0.3. This increased coupling of the a t r a n s i t i o n to the NP process f o r deeper impurities explains the increasing a to 6+y i n t e n s i t y r a t i o observed by Vouk and L i g h t o w l e r s 9 ' 1 + 0 i n going from A l to Ga to In. I t i s not c l e a r whether the nature of the three l e v e l s they observed f o r the thallium BE i s the same as the t r i p l e t s observed f o r Al and Ga, since f o r the very t i g h t l y bound thallium BE i t w i l l be necessary to consider the e f f e c t s of the s p l i t - o f f valence band. Kirczenow 1 7 has suggested that the t r i p l e t s p l i t t i n g of the acceptor BE ground state may be s o l e l y due to the i n t e r a c t i o n of the two r 8 holes i n the tetra-hed'raT.Ly symmetric f i e l d of the impurity, since r 8 x T 8 contains the three antisymmetric representations r l 5 r 3 and r 5 . This gives the t r i p l e t s p l i t t i n g without invoking any electron-hole coupling. It was shown 1 7 that the r e l a t i v e i n t e n s i t i e s of t r a n s i t i o n s from r l 5 r 3 and r 5 BE l e v e l s to the acceptor ground state should be 1:2:3, both f o r phonon a s s i s t e d and no-phonon processes. However, as has already been discussed, the i n t e n s i t y of the lowest-energy t r a n s i t i o n w i l l be enhanced i n the NP process. S i m i l a r l y , the t r a n s i t i o n s from the 67 Table 3.4 Energies and Intensity Ratios of the Acceptor BE One-Hole Transitions Luminescence Energy* Line (meV) Intensity Ratios** Ga (l,cO 1149 03 NP/TO = 0. 55 + 0. 1 (1,6) 1150 48 [1,6/1,a] = 1. 45 + 0. (1,Y) 1150 80 [l , Y / l , a ] = 1. 30 + 0. 15 (2,6) 1148 35 (2,Y) 1148 03 2,y/2,6 = 0. 80 + 0. 1 (3) 1146 17 NP/TO = 0.28 ± 0.05 Al -i (l,a) 1149.56 NP/TO = 0 .44 + 0 1 (1,6) 1150.72 [1,6/1,a] = 1 .60 ± 0 15 ( i , r ) 1150.87 [l , Y / l , a ] = 1 .20 ± 0 15 (2,6) 1148.37 (2,Y) 1148.21 2,y/2,B = 0 .65 ± 0 15 (3) 1146.119 (4) 1144.31 (l,a) 1150.625 (1,6) 1150.72 [1,6/1,a] = 2 .0 ± 0 4 (1, Y) 1150.795 [l,Y / l , c x ] = 1 .1 ± 0 3 _ (2) 1148.53 NP/TO ^ 0 .010 (3) 1146.34 NP/TO ^ 0 .010 (4) 1144.56 NP/TO = 0.30 ± 0.08 NP/TO = 0.015 A l l energies are those of the NP l i n e s . The energies are accurate to ±0.1 meV. Unless otherwise s p e c i f i e d , the i n t e n s i t y r a t i o s are those of the NP r e p l i c a s . Intensity r a t i o s enclosed i n brackets are the i n f i n i t e -temperature l i m i t s of the l i n e s i n thermal equilibrium. 68 m=2 BMEC to the r l s r 3 and T5 BE l e v e l s should have i n t e n s i t i e s of 1:2:3. I f the T l 3 T5 and T 3 states are taken to be the i n i t i a l states of the Xl'a, X 1*^ and X 1'^ BE t r a n s i t i o n s , r e s p e c t i v e l y , then t h i s model gives much better agreement with the experimental r e s u l t s than does the j - j coupling model. 1 7 3.6 Acceptor Bound Excitons (Two-Hole Transitions) Dean et a l . 6 observed a si n g l e BE two-hole t r a n s i t i o n f o r the acceptor B and concluded that as i n the case of the SD BE two-electron t r a n s i t i o n s (which are described i n section 3.3), the f i n a l state of the acceptor BE two-hole t r a n s i t i o n was an S - l i k e even-parity excited state of the acceptor impurity. Vouk and Lightowlers 9 have also t e n t a t i v e l y i d e n t i f i e d a l i n e they observed i n the cathodolumines-cence spectrum of boron-doped s i l i c o n as being due to a second BE two-hole t r a n s i t i o n . The work described here has already been p u b l i s h e d 4 8 and i s the f i r s t d e t a i l e d i n v e s t i g a t i o n of the acceptor BE two-hole t r a n s i t i o n s . These t r a n s i t i o n s are the only method of obtaining the energies of the even-parity S - l i k e acceptor excited states. These values w i l l be of i n t e r e s t i n t e s t i n g the predictions of t h e o r e t i c a l models 4 9 of the acceptors which have only very recently been brought into agree-ment with the experimentally d e t e r m i n e d 3 7 ' 5 0 binding energies of the odd-parity acceptor excited states. The spectra reported here were obtained from a f l o a t -zone r e f i n e d sample containing 2.2 x 1 0 1 5 B cm 3 and a Czochralski grown sample containing 2.6 x 1 0 1 6 Ga cm 3. The samples were immersed i n l i q u i d He and spectra were taken at both 4.2 K and 2KK. Neither the B 69 nor the Ga spectra showed any observable differences between these two temperatures. In F i g . 3.16 a portion of the photoluminescence spectrum of the B-doped sample i s shown. A l l of the l i n e s are due to BE recom-bination and i n a l l cases the momentum conserving process i s TO phonon emission. The energy s h i f t s of the l i n e s r e l a t i v e to the boron PBE to phonon l i n e are given i n Table 3.5. The l i n e labeled A i s considerably broader than the others and i s thought to be due to the emission of a Aj (LA) i n t e r v a l l e y s c a t t e r i n g phonon i n addition to the TO momentum conserving phonon. In a study of such two-phonon t r a n s i t i o n s of the free exciton i n S i Vouk and L i g h t o w l e r s 5 1 found the energy of t h i s phonon to be 25.7 ± 0.6 meV which agrees with the 25.31 ± 0.15 meV s h i f t of the A l i n e . At high e x c i t a t i o n i n t e n s i t y two unresolved bumps appear at approximately 2.2 and 4 meV below the A l i n e . Their energy s h i f t s and i n t e n s i t y dependence indi c a t e that they are the TO + A^LA) r e p l i c a s of the m=2 and m=3 bound multiexciton complexes associated with boron. - The o r i g i n of the l i n e labeled B i s notkknown. The remaining l i n e s are a l l due to boron BE two-hole t r a n s i t i o n s . The labels r e f e r to the r e s u l t i n g acceptor excited states and are taken from Baldereschi and L i p a r i . 4 9 The energy s h i f t s of two of the l i n e s correspond to the known energy le v e l s of the IFQ." arid 2r8~ odd-parity excited states of B and are labeled accordingly. The remaining l i n e s form a sing l e s e r i e s , Nr 8 +, with 2 < N < 5. The 2T 8 + l i n e was previously observed by Dean et a l . 6 and the 3r 8 + l i n e was observed by Vouk and Lightowlers 9 who t e n t a t i v e l y i d e n t i f i e d i t as a two-hole t r a n s i t i o n . A p l o t of the energy s h i f t s of these l i n e s versus N"2 can be 70 F i g u r e 3.16 The TO r e p l i c a of the boron BE two-hole t r a n s i t i o n s i s shown. For c l a r i t y , the 4 r 8 + and 5 r 8 + l i n e s have t h e i r i n t e n s i t i e s m u l t i p l i e d by a f a c t o r o f 10. The TO PBE l i n e i s approximately 70 times as intense as the 2 r 0 + l i n e 71 f i t t e d to a single s t r a i g h t line, i n d i c a t i n g that t h i s s e r i e s of acceptor excited states obeys the hydrogenic approximation quite well. Of course the point N=l, AE=0 does not l i e on t h i s l i n e since the central c e l l corrections f o r the impurity ground state are much larger than f o r the excited states. When extrapolated to N=°° t h i s l i n e gives the value 45.25 ± 0.25 meV f o r the i o n i z a t i o n energy of the B impurity i n S i , which agrees with the t h e o r e t i c a l value of 45.7 ± 0.3 meV.49 No t r a n s i t i o n r e s u l t i n g i n the s p l i t - o f f band T7+ excited state with an energy of 23.4 meV 4 9 could be observed. The experimental s i t u a t i o n with Ga i s not as good as with B since the TO r e p l i c a s of the Ga BE two-hole t r a n s i t i o n s occur at an energy below the detector cutoff. Thus the NP r e p l i c a had to be used when studying the Ga doped sample, but t h i s resulted i n considerable interference since the very strong TO PBE l i n e l i e s near some of the two-hole NP li n e s as can be seen i n F i g . 3.17. Nevertheless, the energy s h i f t s due to the excited states N r 8 + , 2 < N < 5, may s t i l l be obtained f o r Ga although the two odd-parity l e v e l s observed f o r B can not be observed. The o r i g i n of the l i n e labeled C i s not known, although from i t s l o c a t i o n i t may be s i m i l a r to the l i n e labeled B i n F i g . 3.16. As with boron a single s t r a i g h t l i n e can be f i t t e d to a p l o t of energy s h i f t vs N~ 2 f o r the Ga data and when extrapolated to N=°° a value of 73.4 ± 0.3 meV i s obtained f o r the i o n i z a t i o n energy of Ga, i n agreement with the th e o r e t i c a l value of 73.9 ± 0.3.49 From Table 3.5 we see that the binding energies of the even-parity excited states are quite s i m i l a r f o r B and Ga. Baldereschi and L i p a r i 5 2 have reported that the t h e o r e t i c a l binding energy of the 2r3+ state is. 8.65 meV which i s not i n agreement with the experimental values reported here. 72 > - I—| 1 1 i i r =3 L _ J 1 ! I L_ J 1 1 _j 1.076 1.090 PHOTON ENERGY ( e V ) Figure 3.17 The NP replica of the gallium BE two-hole transitions i s shown. For c l a r i t y the intensities of the lower energy lines have been multiplied by a factor of 12 r e l a t i v e to the 2TQ+ l i n e . The NP PBE line i s approxi-mately 60 times as intense as the 2Tg + l i n e . The 2 1 V ' line i s on the low energy t a i l of the much more intense TO PBE line 73 Table 3.5 Energies of the Acceptor BE Two-Hole T r a n s i t i o n s and Binding Energies of  the Even-Parity Acceptor E x c i t e d States Luminescence Energy S h i f t * Binding Energy** Line (meV) (meV) A 25.31 + 0.15 -B 37.50 + 0.25 -i r 3 30.42 + 0.1 (30. 38 ± 0. 02) + 14.83 2r 3~ 34.54 + 0.1 (34. 53 ± 0. 02) + 10.71 2r + 3 32.39 + 0.1 12.86 3r + 39.45 + 0.1 5.8 4r + 3 41.98 + 0.15 3.27 sr; 3 + 43.13 + 0.2 2.12 2r E + 1 60.80 + 0.25 12.6 3r( + 67.58 + 0.15 5.82 4r ? 70.14 + 0.15 3.26 s r 5 + 71.38 + 0.2 2.02 c 66.2 + 0.2 _ This i s the d i f f e r e n c e i n energy between the observed l i n e s and the PBE l i n e having the same MCP. In determining these b i n d i n g energies the ext r a p o l a t e d values of the ground s t a t e b i n d i n g energies were used: 45.25 ± 0.25 meV f o r B and 73.9 ± 0.3 meV f o r Ga. The maximum e r r o r f o r the B data i s ±0.35 meV, while f o r the Ga data i t i s ±0.45 meV. f Values obtained from f a r - i n f r a r e d a b s o r p t i o n . 3 7 ' 5 0 74 In conclusion, the energies of the f i r s t four even-parity excited states having T 8 + symmetry have been determined f o r B and Ga impurities i n S i by studying the BE two-hole photoluminescence l i n e s . In addition i t was found that the s i n g l e - p a r t i c l e wave functions of the holes i n the BE ground state have predominantly T 8 + symmetry and no observable admixture of the s p l i t - o f f Y7+ valence band states. 3.7 Acceptor Bound Multiexciton Complexes In the o r i g i n a l s t u d i e s 1 0 " 1 2 of the KAPS l i n e s the only acceptor impurity used was B. Photoluminescence spectra of s i l i c o n doped with A l and Ga were obtained as part of t h i s project i n order to see i f these impurities could also form BMEC and i f so, whether the large ground state s p l i t t i n g s of the BE associated with these acceptors had any e f f e c t upon the m=2 KAPS l i n e . As has been noted by Dean et a l . 8 , i f the BMEC model of the o r i g i n of the KAPS l i n e s i s correct then, since the BE i s the f i n a l state i n the m=2 t r a n s i t i o n , the m=2 KAPS l i n e associated with Al and Ga should show structure due to the f i n a l state s p l i t t i n g . While these studies were i n progress Vouk and L i g h t o w l e r s 4 0 published spectra showing the m=2 and 3 KAPS l i n e s of aluminum-doped s i l i c o n but t h e i r r e s o l u t i o n was poor and no structure was observed. The structure of the m=2 aluminum KAPS l i n e was l a t e r resolved by Lightowlers and Henry 4 1, but by that time the preliminary report of the completely analogous gallium KAPS l i n e s studied here had already been r e p o r t e d . 2 3 The 4.2 K NP luminescence spectrum of the sample containing 1 x 1 0 1 5 cm - 3 Ga i s shown i n Fi g . 3.18 with the l i n e s 75 Figure 3.18 The NP r e p l i c a of the luminescence o f gallium-doped s i l i c o n at 4.2 K i s shown. The ct^p l i n e i s due to phosphorus contamination. The r e l a t i v e i n t e n s i t i e s of the 2,3 and 2,y l i n e s are given i n the t r a n s i t i o n diagram. The a s t e r i s k i n d i c a t e s the p r e d i c t e d p o s i t i o n o f the 2,a l i n e . Hie i n t e n s i t i e s o f the m>] l i n e s have been increased by a f a c t o r of 10 r e l a t i v e to the PBE l i n e 76 labeled according to the scheme previously described. At t h i s temperature the Ga 1'^ a n ( ^ ^ l i n e s are very weak, but luminescence l i n e s at energies below that of Ga 1' 0 1 have appeared. We i d e n t i f y these new l i n e s as the m=2 and m=3 KAPS l i n e s associated with Ga impurities f o r several reasons. F i r s t , no other impurities have luminescence l i n e s at exactly these energies and we therefore conclude that the new l i n e s are associated with the presence of Ga (the small high energy t a i l on G a 3 p i s probably the phosphorus a 2 p l i n e ) . Secondly, the i n t e n s i t y r a t i o s of the l i n e s having d i f f e r e n t values of m are not strongly temperature dependent between 1.8 and 4.2 K as i s also the case f o r the well known B and P KAPS l i n e s . F i n a l l y , the i n t e n s i t y r a t i o s of the l i n e s having d i f f e r e n t values of m behave i n the expected way as a function of e x c i t a t i o n i n t e n s i t y . Thus the i n t e n s i t y of the m=n+l l i n e r e l a t i v e to the m=n l i n e always increases with increasing e x c i t a t i o n i n t e n s i t y , which i s of course j u s t what one would expect from the BMEC model. In Fi g . 3.8 the i n t e n s i t y r a t i o s of the m=n+l l i n e s r e l a t i v e to the m=n l i n e s f o r a l l the impurities studied are p l o t t e d as a function of the e x c i t a t i o n power. It was found that the m=2 Ga luminescence consists of a doublet s p l i t by 0.32 ± 0.03 meV and that the i n t e n s i t y r a t i o between these l i n e s which are labeled Ga 2*^ and Ga2>^ depends neither upon e x c i t a t i o n i n t e n s i t y nor upon temperature, thus i n d i c a t i n g that both t r a n s i t i o n s have the same i n i t i a l state. This s p l i t t i n g i s explained by the BMEC model i n which the f i n a l state of the m=2 KAPS t r a n s i t i o n i s a BE. This i s why the s p l i t t i n g energy between Ga2>^ and Ga 2> Y i s exactly equal to the s p l i t t i n g between Ga 1'^ a n c j G a l j Y , since i n the Ga 2> 8 t r a n s i t i o n the f i n a l state i s a BE i n the g state and s i m i l a r l y the f i n a l 77 state of the Ga 2'^ t r a n s i t i o n i s a BE i n the y state. One would also expect an m=2 t r a n s i t i o n i n which the f i n a l state i s an a BE, but none was observed. Unfortunately the s e n s i t i v i t y at that p a r t i c u l a r energy (marked by * i n Fig.3.18)is reduced by the presence of the phosphorus a^p luminescence and we can only place an upper l i m i t on the i n t e n s i t y of the Ga 2' a l i n e of less than 0.3 times the G a 2 ' i n t e n s i t y . Very recently Lyon et a l . 5 3 have reported the observation of the Ga 2' a l i n e at approximately t h i s i n t e n s i t y . In F i g . 3.19 the A l 4.2 K luminescence spectrum i s seen to be very s i m i l a r to that of Ga except that f o r Al an m=4 KAPS l i n e i s observed. These two l i n e s are i d e n t i f i e d as A l KAPS l i n e s f o r the same reasons as j u s t described f o r the Ga case. Again we f i n d that the m=2 KAPS luminescence consists of two l i n e s showing no thermalization or power dependence of t h e i r r e l a t i v e i n t e n s i t i e s and separated by an amount equal to the A l 1 ' ^ to A l 1 ' ^ BE s p l i t t i n g . This again confirms the p r e d i c t i o n of the BMEC model that the f i n a l state of the m=2 t r a n s i t i o n i s a BE. No s p l i t t i n g s were seen i n the m=3 and m=4 l i n e s i n d i c a t i n g that i f such s p l i t t i n g s e x i s t they are either too small to be observed or too large to be thermally populated at 4.2 K. One would likewise expect a s p l i t t i n g i n the m=2 KAPS luminescence of the B doped sample since, as we have shown previously, the B BE also has a s p l i t ground state. However, t h i s s p l i t t i n g would be most d i f f i c u l t to resolve due to i t s small s i z e and also because of the very low i n t e n s i t y of the boron BE l i n e s i n the NP r e p l i c a . 78 f A I N P >-H CO LU Ld O z: UJ c > CO IJJ =) Si (Al l . lxlO l 5 cm" 3 ) T = 4.2 K Al 2,y Al IMP xl r x!3 A I NP / N P A l ' ' ' / [ A I N P /" NP J i I L 1144 1152 PHOTON ENERGY (meV) Figure 3.19 The NP r e p l i c a o f the luminescence of aluminum-doped s i l i c o n at 4.2 K i s shown. The a^p l i n e i s due t o phosphorus contamination. The i n t e n s i t i e s o f the in>l l i n e s have been m u l t i p l i e d by a f a c t o r of 13 r e l a t i v e to the PBE l i n e s 79 The energies of the B, A l and Ga NP l i n e s are p l o t t e d i n F i g . 3.15. As has already been noted, of a l l the acceptor KAPS and BE l i n e s only the energy of the BE a l i n e i s s i g n i f i c a n t l y dependent upon the impurity species. Vouk and Lightowlers (1976) have seen that f o r the acceptors In and T l a l l the BE l i n e s are s h i f t e d down i n energy. This change i n behaviour could be due to the increasing r o l e of the s p l i t - o f f valence band f o r BE associated with acceptors having large i o n i z a t i o n energies. The dependence of the r e l a t i v e i n t e n s i t i e s of the KAPS lin e s upon the e x c i t a t i o n power can also be used to v e r i f y the BMEC model and show the v a l i d i t y of a SM approach. In F i g . 3.8 we see that f o r B the i n t e n s i t y of the m=n+l l i n e r e l a t i v e to the m=n l i n e i s quite high f o r n=l and 2 but drops sharply at n=3 and then r i s e s again f o r n=4. The same behaviour can also be seen i n the B data presented by Sauer. 1 1 This precipitous drop i n r e l a t i v e i n t e n s i t y i n going from m=3 to m=4 can be explained by the SM since the m=3 acceptor BMEC contains four holes and hence has a f u l l hole s h e l l , and so i n analogy to the nuclear and atomic SM one would expect the m=3 acceptor BMEC to be "stable" or " i n e r t " . Thus i t would have a reduced cross-section f o r FE capture, r e s u l t i n g i n a low population of m=4 BMEC. In the A l and Ga spectra the e f f e c t s of f i l l i n g the hole s h e l l are even more pronounced and cause the m=3 to m=2 i n t e n s i t y r a t i o to be much larger than the m=2 to m=l r a t i o . F i n a l l y , although the m=4 KAPS l i n e of A l could be observed only at the highest e x c i t a t i o n power i t i s c l e a r from F i g . 3.8 that the m=4 to m=3 i n t e n s i t y r a t i o i n the Al-doped sample i s much less than the m=3 to m=2 r a t i o , as expected. 80 CHAPTER 4 SUMMARY AND CONCLUSIONS The experimental r e s u l t s described i n the previous chapter have v e r i f i e d that the o r i g i n a l concept of BMEC i s the proper explanation of the o r i g i n of the KAPS l i n e s e r i e s . In addition, the v a l i d i t y of K i r c z e n o w ' s 1 5 ' 1 7 SM desc r i p t i o n of the BMEC structure has been demonstrated. The o r i g i n a l r e s u l t s obtained as a part of t h i s p roject are b r i e f l y outlined below. The phosphorus BE and BMEC were found to have bound excited states which r e s u l t i n at least s i x new luminescence t r a n s i t i o n s . The behaviour of these new l i n e s was shown to be consistent with the pred i c t i o n s of the SM. Trends i n the luminescence i n t e n s i t y r a t i o s of the KAPS l i n e s f o r a l l the impurities studied (as well as the lithium data presented p r e v i o u s l y 1 2 ) were explained i n terms of the SM. The t r i p l e t structure of the ground state of the shallow acceptors, including boron, was resolved f o r the f i r s t time, as was the structure i n the m=2 KAPS l i n e of gallium-doped s i l i c o n , proving that the f i n a l state of the m=2 KAPS t r a n s i t i o n i s the BE and thus again v e r i f y i n g the BMEC model. Four new li n e s were seen i n the two-electron spectrum of phosphorus BE and the energies of some of the acceptor even-parity excited states were obtained f o r the f i r s t time by examining the acceptor BE two-hole t r a n s i t i o n s . Let us now consider one f i n a l aspect of the BMEC, namely the binding energies of BMEC of d i f f e r e n t values of m and associated with d i f f e r e n t impurities. The binding energy of an m=n BMEC w i l l be defined 81 as the energy required to d i s s o c i a t e i t into a zero k i n e t i c energy FE and an m=n-l complex i n i t s ground state. Therefore the binding energy i s equal to the difference i n energy between the FE threshold and the luminescence l i n e which r e s u l t s when an electron-hole p a i r i n the ground state m=n complex recombines leaving behind the m=n-l complex i n i t s ground state. It was shown i n section 3.2 that the phosphorus a m (m>l) l i n e s are not due to t r a n s i t i o n s of t h i s type. The binding energy of the phosphorus m=n BMEC i s given by the energy diff e r e n c e between the g n - 1 l i n e and the FE threshold. For the acceptor case the KAPS l i n e s f o r m<4 leave behind complexes i n t h e i r ground states and therefore can be used to obtain the binding energies of the m<4 acceptor BMEC. I t i s assumed that the m>3 acceptor KAPS l i n e s r e s u l t from recombination of in n e r - s h e l l holes and therefore leave behind excited f i n a l states. The recombination of ou t e r - s h e l l holes i n the m>3 acceptor BMEC r e s u l t s i n luminescence l i n e s which cannot be observed since they overlap the much more intense KAPS l i n e s of the m<4 BMEC. This i s because the binding energy of the m=3 acceptor BMEC i s expected to be greater than that of the m=4 complex since the m=3 complex contains a closed s h e l l , i n analogy with the high i o n i z a t i o n energies of closed outer s h e l l ( i n e r t gas) atoms. Si m i l a r l y , f o r the l i t h i u m BMEC 1 2 the SM shows that f o r m<5 the KAPS l i n e s give the correct binding energies since they r e s u l t i n ground state complexes. As for the acceptors we w i l l assume that the li t h i u m KAPS l i n e s having energies below that of the m=4 l i n e are due to t r a n s i t i o n s which have excited f i n a l s t a t e s , and that t r a n s i t i o n s of m>4 li t h i u m BMEC which r e s u l t i n ground state complexes are not observed because 82 they overlap the much stronger m<5 KAPS l i n e s . With the help of the SM and the add i t i o n a l assumptions stated above, the previous c o m p l a i n t s 1 4 ' 1 5 that the binding energies of the BMEC were too high can be answered. The crux of these complaints was that i n the simple BMEC model the binding energies of the BMEC seemed to increase monotonically with complexity to a l i m i t i n g value which was much larger than that of an electron-hole p a i r i n an electron-hole-droplet (EHD), which i s given by the energy difference between the upper edge of the EHD l i n e (at zero temperature) and the FE threshold. This problem was most apparent f o r the lithium s p e c t r a . 1 2 Since the l i m i t of BMEC of increasing complexity i_s the EHD, t h i s did not seem reasonable. Also, a BMEC of intermediate complex-i t y may be thought of as a very small droplet, which would have i t s binding energy decreased r e l a t i v e to that of large EHD by the e f f e c t s of "surface tension". The impurity i n the BMEC w i l l act so as to increase the binding energy but t h i s e f f e c t should c l e a r l y decrease f o r BMEC containing large numbers of electron-hole p a i r s . Rather than disagreeing with the above statements, we show that they are consistent with the SM of the BMEC. In general, one would expect l o c a l maxima i n the BMEC binding energy vs m r e l a t i o n f o r values of m which r e s u l t i n closed s h e l l s , and these v a r i a t i o n s of the binding energy should become "smoothed out" for large values of m as the binding energy approaches that of the EHD. Thus the binding energies of the most t i g h t l y bound BMEC f o r P, L i , B, A l and Ga which have been  experimentally observed are given by the energy differences between the 83 FE threshold and the phosphorus 6 , L i m=4, B , A l 3 and Ga 3 luminescence l i n e s , r e s p e c t i v e l y . These binding energies are, re s p e c t i v e l y , 8.99, 9.88 1 2, 8.25, 8.4 and 8.42 meV, to within ±0.2 meV, and are not greatly d i f f e r e n t from the more recently determined values of the EHD binding energy, which are 8.7 meV5lf:.and 8.3 meV. 5 5 I f one wishes to compare the lowest energy KAPS l i n e s to the EHD l i n e , the comparison should not be made to the high energy edge of the EHD l i n e as was done by Morgan 1 5, since the lowest energy KAPS l i n e s are due to recombination of an electron and a hole from the innermost s h e l l s and thus leave behind a highly excited f i n a l state, while the highest energy t r a n s i t i o n s of the EHD leave the EHD i n i t s ground state. It i s more meaningful to compare these l i n e s to the low energy edge of the EHD, which i s due to the recombination of the lowest energy electron-hole p a i r i n the droplet and thus leaves the droplet i n a highly excited state. The lowest energy KAPS l i n e yet observed i s at 1078.4 meV 1 2 (TO-replica) which i s s t i l l 11.0 meV 5 5 above the low energy edge of the EHD TO-replica. Thus we see that the energies of the KAPS li n e s presents no problems f o r the SM of the BMEC. 8 4 APPENDIX A BROADENING OF PHONON-ASSISTED BOUND EXCITON LUMINESCENCE IN SILICON This Appendix contains the r e s u l t s of the f i r s t d e t a i l e d study of the e f f e c t s of phonon broadening upon the phonon-assisted BE luminescence i n s i l i c o n . The complete r e s u l t s have already been p u b l i s h e d , 1 9 and since the t h e o r e t i c a l calcula'tions';:contained i n that^paper were s o l e l y the work of Dr. G. Kirczenow they w i l l not be described here. Rather, the experimental method and r e s u l t s , as well as an i n t u i t i v e explanation of them w i l l be given. In reference 19 i t was claimed that the postulated broadening mechanism was a new one but i t has since been brought to our at t e n t i o n that the same process was b r i e f l y described by Dean et a l . 5 6 i n a study of BE luminescence i n GaP. Also, a much more d e t a i l e d a ccount 5 7 of t h i s e f f e c t i n GaP was i n press at the time reference 19 was submitted. The work described here i s nevertheless important as i t contains the only published data regarding the phonon-assisted BE linewidths f o r a number of impurities i n s i l i c o n . I t i s d i r e c t l y r e l a t e d to the study of the BMEC as w e l l , since the phonon-assisted BMEC luminescence i s broadened by the same process. The f i r s t published recognition of the non-zero l i n e -widths of some of the BE l i n e s was given by S a u e r 1 1 who noted that while the f u l l width at half-maximum (FWHM) was less than 0.05 meV f o r the phosphorus PBE NP l i n e , the FWHM of the boron PBE TO-phonon r e p l i c a was approximately 0.4 meV. Sauer did not make cl e a r whether he ascribed t h i s difference to the diffe r e n c e i n impurities or the diffe r e n c e i n MCP. Kosai and Gershenzon 1 2 stated that the FWHM of the phosphorus PBE NP 85 l i n e was less than 0.14 meV while that of the TO phonon r e p l i c a was approximately 0.4 meV, and were thus the f i r s t to conclude that the phonon-replica BE luminescence i n s i l i c o n was broad as compared to the NP l i n e . The experimental apparatus was the same as that described i n Chapter 2 except that f o r these experiments the photomultiplier detector was not yet ava i l a b l e and hence the RCA model 67-07-B germanium detector was used. The ultimate r e s o l u t i o n l i m i t of the spectrometer was such that the widths of some of the PBE NP l i n e s could not be resolved, but t h i s was i n any case unnecessary since what was of i n t e r e s t was the difference i n width between the NP l i n e and the phonon r e p l i c a s . This broadening was measured by recording the phonon and NP luminescence of each sample at exactly the same spectrometer s l i t width and sample or i e n t a t i o n . Thus the instrumental broadening was exactly the same for a l l the l i n e s of a given sample and the phonon broadening could be determined by matching the phonon r e p l i c a lineshape to the lineshape obtained by convoluting the NP l i n e with a Gaussian function of adjustable width. The Gaussian function was used to give the broadening because i t gave a good f i t , and not for any t h e o r e t i c a l reasons. It should be noted that even the NP PBE l i n e i s expected to have a f i n i t e width due to the e f f e c t s of concentration broadening, phonon broadening (thermal phonons - not the MCP phonons discussed here), ionized impurity broadening and s t r a i n broadening due to d i s l o c a t i o n s , as has been mentioned by Parsons. 3 9 A sample-dependent width f o r the phosphorus PBE NP l i n e was observed i n that paper, the two observed widths being 0.046 ± 0.004 and 0.068 ± 0.007 meV i n d i f f e r e n t samples. 86 The observed l i n e shapes of the phosphorus PBE LO, TO and TA phonon r e p l i c a s are shown i n Fi g . A . l along with the best f i t s obtained by convoluting the NP l i n e with a Gaussian Lineshape. The low-energy t a i l s which can be seen on the TO and the TA phonon r e p l i c a s w i l l be discussed l a t e r . The FWHM of the Gaussian broadenings which gave the best f i t s to the various l i n e s (ignoring the low-energy t a i l s ) are l i s t e d i n Table A . l , while i n Table A.2 the r a t i o s of the TA to TO and LO to TO broadenings are l i s t e d f o r each of the impurities studied. The LO r e p l i c a could not be resolved i n the bismuth-doped sample due to the superposition of the PBE l i n e s of contaminants i n t h i s luminescence region. The data i n Tables A . l and A.2 can be summarized as follows: 1) i f the donors and acceptors are considered separately, the magnitude of the phonon broadening increases with increasing BE binding energy, 2) the r a t i o of the broadenings f o r d i f f e r e n t phonon r e p l i c a s i s independent of impurity species, to within experimental error. These r e s u l t s cannot be wholly due to phonon l i f e t i m e broadening, which has often been invoked i n studies of the FE lineshape i n s i l i c o n , since i n that case the broadenings should not be impurity dependent. A more s a t i s f a c t o r y explanation takes into account the eff e c t s of the l o c a l i z a t i o n of the BE as well as the nature of the phonon dispersion curves i n the v i c i n i t y of (0.85,0,0) (and equivalent locations i n the BZ) which i s the value of the phonon c r y s t a l momentum involved i n electron-hole recombination i n s i l i c o n . The model i s e s s e n t i a l l y very simple. The l o c a l i z a t i o n of the electron-hole p a i r i n the BE r e s u l t s i n a spread i n the net c r y s t a l momentum of the p a i r due to the uncertainty p r i n c i p l e . This uncertainty 87 i 1 1 . I 1.0925 1.0965 PHOTON ENERGY (eV) Figure A . l The TO, LO and TA r e p l i c a s o f the phosphorus PBE l i n e at 4.2 K. The s o l i d l i n e i s the f i t to the experi-mental lineshapes obtained by convoluting the NP r e p l i c a s with Gaussian broadenings, and s h i f t i n g by the phonon energies Table A . l F u l l Widths of Half-Maximum (FWHM) of the BE Phonon Broadenings Impurity Binding Energy (meV) TO FWHM (meV) TA LO B 3. ,87 + 0. 15 0. 275 + 0. 035 0. 193 + 0. 045 1 .25 ± 0.12 P 4. .6 + 0. 15 0. 214 + 0. 01 0. 163 + 0. 015 1 .36 ± 0.06 As 5. .2 + 0. 2 0. 263 + 0. 015 0. 23 + 0. 02 1 .45 ± 0.1 Ga 5. .56 + 0. 15 0. 317 + 0. 03 0. 263 + 0. 06 1 .7 ± 0.3 Bi 7. .5 + 0. 2 0. 34 + 0. 03 0. 238 + 0. 06 No data Table A.2 Ratios of the Phonon Broadening Widths Impurity Concentration (cm"3) Phonon Broadening Ratios TA/TO LO/TO B P As Ga Bi 2 x 1 0 1 5 1 x 1 0 1 5 4 x 1 0 1 5 4.5 x 1 0 1 5 2 x 1 0 1 5 0.7 ± 0.3 0.76 ± 0 . 1 0.87 ± 0.13 0.83 ± 0.3 0.7 ± 0.25 4.5 ± 1.5 6.4 ± 0.6 5.5 ± 0.8 5.4 ± 1.5 No data 89 of the c r y s t a l momentum w i l l be larger f o r more t i g h t l y bound BE, and w i l l r e s u l t i n a spread i n the wavevectors of the momentum-conserving phonons emitted during recombination. i f the phonon energies are wavevector-dependent near (0..85,0,0) t h i s w i l l r e s u l t - i n - a spread i n the-energies of the luminescencecphotons^ --• The a p p l i c a t i o n of t h i s model to the experimental r e s u l t s was greatly s i m p l i f i e d by Kirczenow's ca l c u l a t i o n s (contained i n reference 19) showing that the LO, TO and TA phonons with wavevector nearly along [100] and equivalent d i r e c t i o n s i n s i l i c o n show no f i r s t -order energy dependence upon small displacements perpendicular to the [100] d i r e c t i o n . In other words, i f the spread i n net c r y s t a l momentum r e s u l t s i n a spread i n wavevector of the momentum-conserving phonons of (0.85 ± AK l 5 ± AK2, ±AAK 3) then to f i r s t - o r d e r we need only consider the e f f e c t s of ± AKj, and thus only the phonon dispersion curve along [100] i s needed to evaluate the r e s u l t s . In t h i s approximation i t was shown 1 9 that the shapes of a l l the phonon r e p l i c a s should be i d e n t i c a l except that t h e i r widths should scale as the f i r s t d e r i vatives of the energies of the associated phonons along [100] at the point (0.85,0,0). The best p u b l i s h e d 5 8 phonon dispersion curves f o r s i l i c o n i n the [100] d i r e c t i o n are not adequate f o r a quantitative comparison, but they d e f i n i t e l y show that the slope of the TA phonon dispersion curve at (0,85,0,0) i s s l i g h t l y less than that of the TO phonon, while that of the LO phonon i s much larger. This i s i n q u a l i t a t i v e agreement with the broadening r a t i o s given i n Table A.2. The low energy t a i l s of the TO and TA phonon r e p l i c a s which were mentioned previously must now be explained. This t a i l i s 90 most pronounced on the TA r e p l i c a of the gallium PBE l i n e , which i s shown i n F i g . A.2. The model which has j u s t been described can be modified to provide a very p l a u s i b l e explanation of t h i s low-energy t a i l by considering higher-order e f f e c t s , since although i t was shown 1 9 that to f i r s t - o r d e r the phonon energy was not changed f o r small displacements perpendicular to the [100] d i r e c t i o n , the phonon dispersion may have a large curvature i n perpendicular d i r e c t i o n s . There i s no published data regarding the phonon energies along d i r e c t i o n s perpendicular to [100] and passing through the point (0.85,0,0) but i t seems reasonable to suppose that the behaviour there w i l l not be too different-from that at (1,0,0), on the face of the BZ. Some data regarding the phonon energies on the zone face i s a v a i l a b l e 5 8 , and i t reveals that along s p e c i f i c d i r e c t i o n s the phonon dispersion i s strongly curved with a minimum at (1,0,0). Thus the spread i n phonon wavevector transverse to the [100] d i r e c t i o n w i l l r e s u l t i n low energy t a i l due to the non-zero curvature of the phonon dispersion perpendicular to [100]. This curvature i s seen to be considerably larger f o r the TA phonon than the TO 5 8, i n agreement with the observation that the TA r e p l i c a always has the most pronounced low-energy t a i l . The magnitude of the phonon l i f e t i m e broadening i n s i l i c o n i s not c l e a r , since a t y p i c a l width used i n the study of FE i s 0.34 meV f o r the TO phonon 5 9, which i s s i g n i f i c a n t l y larger than the TO phonon broadening of the phosphorus PBE l i n e given i n Table A . l . Thus i t seems that the FE broadening must be i n part due to processes other than phonon l i f e t i m e broadening. Figure A.2 The TA replica of the gallium PBE line showing the very pronounced low energy t a i l 92 APPENDIX B GROUND STATE SPLITTING OF THE FREE EXCITON IN SILICON In 1960 McLean and London showed that i n both Ge and S i the i n t e r a c t i o n of holes i n the degenerate valence band with the anis-t r o p i c e f f e c t i v e mass of electrons i n the conduction band would lead to a s p l i t t i n g of the ground state of the free exciton (FE) into two doubly-degenerate bands. 6 0 The t h e o r e t i c a l study of t h i s s p l i t t i n g has been extended to both the IS and 2S FE l e v e l s i n Ge, S i , GaP and A l S b . 6 1 Although the e f f e c t of t h i s s p l i t t i n g upon the o p t i c a l absorption of Ge had already been observed i n 1 9 5 9 6 2 ' 6 3 i t was not u n t i l very recently that evidence of t h i s s p l i t t i n g was obtained i n S i by Hammond et a l . 5 9 They showed that the temperature dependence of the i n t e n s i t y r a t i o of LO to TO phonon r e p l i c a luminescence of the FE i n S i could be explained by s p l i t FE ground states which have d i f f e r e n t r e l a t i v e rates f o r TO and LO phonon emission i n recombination. The experiments described i n t h i s section were intended to obtain an accurate value of the FE ground state s p l i t t i n g energy i n s i l i c o n by d i r e c t l y observing the e f f e c t s of the s p l i t t i n g i n absorption and photoluminescence spectra. The r e s u l t s have already been p u b l i s h e d . 2 0 The experimental apparatus used i n the luminescence studies was as described i n Chapter 2 except that the RCA model 67-07-B detector was used. The wavelength-derivative technique was used to study the FE absorption since t h i s method r e s u l t s i n a better signal-to-noise r a t i o . The d e r i v a t i v e of the FE absorption (which should t h e o r e t i c a l l y have a square-root shape i f the exciton dispersion i s parabolic) i s a sharp peak with a high energy t a i l . Wavelength-modulation of the spectrometer was 93 obtained by mounting a 2 mm thick quartz plate i n s i d e the spectrometer d i r e c t l y before the e x i t s l i t . This p l a t e was vibrated through a small angle about an axis p a r a l l e l to the ex i t s l i t , and thus deviated the l i g h t passing through i t i n a sinusoidal manner, r e s u l t i n g i n wavelength-modulated l i g h t passing through the exit s l i t . The derivative-absorption signal was demodulated with the use of a l o c k - i n a m p l i f i e r synchronized to the v i b r a t i n g plate. The magnitude of the transmitted l i g h t was also recorded so that the de r i v a t i v e s i g n a l could be compensated f o r increasing absorption i n the s i l i c o n c r y s t a l at shorter wavelengths. The d e r i v a t i v e absorption spectrum of the TO and LO re p l i c a s of the FE i n a 7 mm thick sample of i n t r i n s i c s i l i c o n i s shown i n F i g . B . l . Although not well resolved, the e f f e c t s of the FE ground state s p l i t t i n g can be seen i n both phonon r e p l i c a s . The structure of the two phonon r e p l i c a s i s not i d e n t i c a l since f o r the LO r e p l i c a the lower (A 6 ) state couples more strongly than the upper (A 7 ) state while the coupling strengths are reversed f o r the TO r e p l i c a , as has been shown by Hammond et a l . 5 9 In the EO r e p l i c a the A7 absorption causes a d i s t i n c t "bump" on top of the stronger Ag ^ absorption. A sophisticated analysis of t h i s lineshape i s impossible without a d d i t i o n a l assumptions, but c l e a r l y the s p l i t t i n g l i e s i n the range of 0.1 to 0.25 meV. The e f f e c t of the s p l i t t i n g on the TO r e p l i c a i s not as obvious but can nevertheless be c l e a r l y observed. In F i g . B . l . the low energy edges of both r e p l i c a s can be seen to be s t r a i g h t l i n e s , with the addition of " t a i l s " . The st r a i g h t l i n e sections are extrapolated as dotted l i n e s which makes i t c l e a r that although the LO r e p l i c a only has a very small t a i l , which can be ascribed to spectrometer r e s o l u t i o n and 94 I I I I 1211.0 1214.0 PHOTON ENERGY ( meV ) Figure B . l The LO and TO r e p l i c a s of the d e r i v a t i v e absorption spectrum of the FE at 1.4 K. The LO i n t e n s i t y has been m u l t i p l i e d by a f a c t o r of 5.7 f o r c l a r i t y . The dotted extensions of the low energy edges of the two r e p l i c a s show the c o n t r i b u t i o n of the A 6 l e v e l to the TO lineshape 95 line-broadening e f f e c t s , the t a i l of the TO r e p l i c a i s much more pronounced. A s t r a i g h t l i n e of d i f f e r e n t slope can be f i t t e d to the low-energy t a i l of the TO r e p l i c a , and the low-energy t a i l which extends beyond t h i s l i n e i s comparable i n s i z e to that of the LO r e p l i c a . The component which causes t h i s structure on the low-energy side of the TO r e p l i c a i s the FE A 6 absorption, the remainder of the l i n e being due to A 7 absorption. The energy difference between the two s t r a i g h t l i n e segments which were f i t t e d to the TO. r e p l i c a i s 0.2 ± 0.05 meV when the l i n e s are extrapolated to zero i n t e n s i t y . One could argue that the larger t a i l on the low-energy edge of the TO replica.was due to a greater phonon broadening f o r that p a r t i c u l a r r e p l i c a . The shape of the t a i l argues against t h i s i n t e r p r e t a t i o n , as does the f a c t that the required phonon-broadening would have to be several times larger than the l i m i t (FWHM <0.22 meV) set i n Appendix A. The FE luminescence of i n t r i n s i c s i l i c o n at a temperature of about 1.6 K i s shown i n F i g . B.2. In the o r i g i n a l p u b l i c a t i o n 2 0 the temperature was i n c o r r e c t l y given as 1.1 K, the d i f f e r e n c e being due to the helium pressure difference across a short length of narrow tubing i n s i d e the dewar. This problem, which i s only serious at low temperatures, was only discovered at a much l a t e r date. It has no e f f e c t upon the v a l i d i t y of the conclusions reached i n reference 20 since the sample temperature was not an important parameter. The LO r e p l i c a shown i n Fig. B.2 i s freer of any observable structure since the small A 7 contribution observed i n the LO absorption i s f urther reduced by the small thermal population of the A 7 FE state at these low temperatures. However, since the TO process couples much more 96 1 L_ I 1 I I 1096.0 1100.0 PHOTON ENERGY (meV) Figure B.2 The LO and TO r e p l i c a s of the F E luminescence at 1.6 K. The LO i n t e n s i t y has been m u l t i p l i e d by a f a c t o r o f 2 97 strongly to the A7 state than to the Ag, the differ e n c e i n populations of the two l e v e l s i s somewhat compensated f o r i n the TO r e p l i c a , and although no resolved structure i s observed, the TO r e p l i c a i s seen to be broad compared to the LO. The unresolved TO structure i s more apparent at higher temperature as can be*seen i n F i g . B.3. The s i z e of the FE ground state s p l i t t i n g can be obtained by s h i f t i n g the LO lineshape down i n energy by an amount equal to the differ e n c e i n energy between the LO and TO momentum-conserving phonons (thus superimposing the t r a n s i t i o n s ) and s c a l i n g the amplitude of the LO lineshape so as to match the low energy edge of the TO l i n e . By doing so the i n t e n s i t i e s of the Ag t r a n s i t i o n s are equalized. It was found that the LO i n t e n s i t y had to be increased by a fa c t o r of approxi-mately 1.4 i n order to achieve t h i s match. When the two scaled l i n e s are subtracted the A 6 components cancel out but the A 7 components do not, since the LO to TO i n t e n s i t y r a t i o i s d i f f e r e n t from that of the Ag component. The s p l i t t i n g i s then determined by taking the differ e n c e i n energy between the low energy edges of the TO r e p l i c a and of the lineshape which res u l t e d from the subtraction of the scaled and s h i f t e d LO r e p l i c a from the TO r e p l i c a . In both cases the p o s i t i o n of the low energy edge was taken to be the zero i n t e n s i t y intercept of a s t r a i g h t l i n e which was f i t t e d to the low energy edge of the luminescence l i n e -shape. Once again the s p l i t t i n g energy was found to be 0.2 ± 0.05 meV. This value was not s e n s i t i v e to the exact siz e of the s c a l i n g parameter although the shape of the l i n e obtained from the subtraction was. 98 Figure B. 3 The LO and TO replicas of the FE luminescence at 2.1 K. The structure of the TO line is clearer than in Fig. B.2 due to the greater population of the level at 2.2 K. 99 At the time that these r e s u l t s were published the only previous experimental work was that of Hammond et a l . 5 9 who determined the value of the s p l i t t i n g energy i n a more i n d i r e c t way. F i r s t they derived a five-parameter t h e o r e t i c a l expression which gave the r a t i o of the FE TO r e p l i c a to LO r e p l i c a i n t e n s i t y as a function of temperature, and then reduced t h i s to a three parameter equation using group-theory. The values of these three parameters, one of which was the ground state s p l i t t i n g energy, were obtained by performing a least-squares f i t of t h e i r expression to experimental data. They stated that the s p l i t t i n g energy was 0.6 (+00:1- 0.3) meV. The scatter i n t h e i r experimental data points was rather large and t h e i r t h e o r e t i c a l expression contained a number of assumptions, i n p a r t i c u l a r that both of the bands were parabolic and that the e f f e c t i v e masses were the same for A 6 and A 7 excitons. This i s c e r t a i n l y not the case i n germanium, although i t may be a more v a l i d approximation f o r s i l i c o n . 6 4 This estimate of the ground state s p l i t t i n g energy has recently been r e f i n e d by incl u d i n g lower-temperature data into the least-squares f i t and the new value of the s p l i t t i n g was estimated to be 0.4 ± 0.1 meV.65 The most recent c a l c u l a t i o n s 6 4 of the s p l i t t i n g energy are i n excellent agreement with experiment 6 6 f o r germanium, whereas for s i l i c o n the t h e o r e t i c a l value i s 0.46 meV.64 However, the authors of reference 64 suggested that the agreement should not be expected to be as good for s i l i c o n as i t was f o r germanium since the electron-hole exchange was ignored i n the c a l c u l a t i o n s . Also, i t i s less v a l i d to ignore the s p l i t - o f f valence band i n s i l i c o n since the spi n - o r b i t s p l i t t i n g i s considerably less than i n germanium. 100 In conclusion, i t i s most u n l i k e l y that the s p l i t t i n g of the FE ground state i n s i l i c o n could be as large as 0.46 meV 6 4 or even 0.4 meV since i f t h i s were the case the s p l i t t i n g would have been observed i n p r e v i o u s 6 7 high-resolution studies. (Note that the 1 meV s p l i t t i n g of the germanium FE ground state was observed i n 1 9 5 9 6 2 » 6 3 , even though the germanium experiment i s inherently more d i f f i c u l t due to the diffe r e n c e i n detector s e n s i t i v i t y between the two wavelength regions.) 101 BIBLIOGRAPHY Wannier, G., Phys. Rev. 52, 191 (1937); Dresselhaus, C , Phys. Chem. Solids 1_, 14 (1956); MacFarlane, G.G., McLean, T.P., Quarrington, J.E. and Roberts, V., Phys. Rev. I l l , 1245 (1958). Shaklee, K.L. and Nahory, R.E., Phys. Rev. Lett. 24, 942 (1970). See for example: J e f f r e y s , CD., Science 189, 955 (1975) f o r a general review. Lampert, M.A. , Phys. Rev. Lett. 1_, 450 (1958). Haynes, J.R., Phys. Rev. Lett. 4_, 361 (1960). Dean,.P.J., Haynes, J.R. and Flood, W.F., Phys. Rev. 161, 711 (1967). Dean, P.J., Flood, W.F. and Kaminsky, G., Phys. Rev. 163, 721 (1967). Dean, P.J., Herbert, D.C, Bimberg, D. and Choyke, W.J., "Proc. XIII Int. Conf. Phys. Sem.", Rome (Tipografia Marves, Rome, 1976), p.1298; Dean, P.J., Herbert, D.C, Bimberg, D. and Choyke, W.J. , Phys. Rev. Lett. 37, 1635 (1976). Vouk, M.A. and Lightowlers, E .C, J. Lumin. to be published. Kaminskii, A.S. and Pokrovskii, Ya.E., Zh. Eksp. Teor. F i z . Pis'ma Red. U, 381 (1970) [JETP Lett, U, 255 (1970)]; Kaminskii, A.S., Pokrovskii, Ya.E. and Alkeev, N.V., Zh. Eksp. Teor. F i z . 59, 1937 (1970) [Sov. Phys. - JETP 32, 1048 (1971)]; Pokrovskii, Ya.E., Kaminskii, A.S. and Svistunova, K., "Proc. X Int. Conf. Phys. Sem.", Cambridge, Mass. (U.S. AEC, S p r i n g f i e l d , Va., 1970), p.202; Pokrovskii, Ya.E., Phys. Status S o l i d i A 11_, 385 (1972). Sauer, R., Phys. Rev. Lett. 31_, 376 (1973). Kosai, K. and Gershenzon, M., Phys. Rev. B 9, 723 (1974). Martin, R.W., S o l i d State Comm. 1£, 369 (1974). Sauer, R. and Weber, J . , Phys. Rev. Lett. 36, 48 (1976). Morgan, T.N., "Proc. XIII Int. Conf. Phys. Sem.", Rome (Tipografia Marves, Rome, 1976), p.825. Kirczenow, G., S o l i d State Comm., 2_1, 713 (1977). Kirczenow, G., Can. J . Phys., to be published. 102 18. Thewalt, M.L.W., M.Sc. Thesis (unpublished), The University of B r i t i s h Columbia (1975). 19. Thewalt, M.L.W., Kirczenow, G., Parsons, R.R. and Barrie, R., Can. J. Phys. 54, 1728 (1976). 20. Thewalt, M.L.W. and Parsons, R.R., S o l i d State Comm. 20, 97 (1976). 21. Thewalt, M.L.W., S o l i d State Comm. 21, 937 (1977). 22. Thewalt, M.L.W., Can. J . Phys. to be published. 23. Thewalt, M.L.W., Phys. Rev. Lett. 3_8, 521 (1977). 24. Koster, G.F., Dimmock, J.O., Wheeler, R.G. and Statz, H., "Properties of the Thirty-Two Point Groups", M.I.T. Press (1963). 25. Kohn, W., i n " S o l i d State Physics", v o l . 5, edited by F. S e i t z and D. Turnbull, Academic Press (1957). 26. Thomas, D.G., Gershenzon, M. and H o f i e l d , J . J . , Phys. Rev. 131, 2397 (1963). 27. Cherlow, J.M., Aggarwal, R.L. and Lax, B., Phys. Rev. B 7, 4547 (1973). 28. Wright, G.B. and Mooradian, A., Phys. Rev. Lett. 1_8, 608 (1967). 29a. Nishino, T. and Hamakawa, Y., S o l i d State Comm. 1_6, 1105 (1975). 29b. Nishino, T. and Hamakawa, Y., Phys. Rev. B 12_, 5771 (1975). 30. Nishino, T., Nakayama, H. and Hamakawa, Y., S o l i d State Comm. 2_1_, 327 (1977). 31. Aggarwal, R.L. and Ramdas, A . K . P h y s . Rev. 140, A1246 (1965). 32. Bludau, W., Onton, A. and Heinke, W., J . Appl. Phys. 45, 1846 (1974). 33. Patrick, L., Hamilton, D.R. and Choyke, W.J., Phys. Rev. 143, 526 (1966) . 34. Dean, P.J., Cuthbert, J.D., Thomas, D.G. and Lynch, T.R., Phys. Rev. Lett. T8, 122 (1967). 35. Sauer, R., J . Lumin. 12/13, 495 (1976). 36. Kohn, W. and Luttinger, J.M., Phys. Rev. £8, 915 (1955). 37. Skolnick, M.S., Eaves, L., S t r a d l i n g , R.A., P o r t a l , J.C. and Askenazy, S., S o l i d State Comm. 1_5, 1403 (1974). 103 38. Sokolov, N.V. and Novikov, B.V., Sov. Phys. S o l i d State 17_, 2192 (1976). 39. Parsons, R.R., S o l i d State Comm.'22/ 671 (1977). 40. Vouk, M.A. and Lightowlers, E.C., "Proc. XIII Int. Conf. Phys. Sem.", Rome (Tipografia Marves, Rome, 1976), p.1098. 41. Lightowlers, E.C. and Henry, M.O., J . Phys. C 10, L247 (1977). 42. Condon, E.V. and Shortly, G.H., "The Theory of Atomic Spectra", Cambridge Uni v e r s i t y Press, 1935. 43. Morgan, T.N., "Proc. XII Int. Conf. Phys. Sem.", Stuttgart, (Teubner, Stuttgart, 1974), p.391. 44. A l l e n , J.W., Dean, P.J. and White, A.M., J . Phys. C 9, L113 (1976). 45. White^-A.M., Hi-nchldffe,M I ..rdDganjiiE. J., and Green, pP.D., S o l i d State Comm; f o , 497 (1972). 46. White, A.M., J . Phys. C 6, 1971 (1973). 47. Morgan, T.N., J . Phys. C I O, L131 (1977). 48. Thewalt, M.L.W., S o l i d State Comm. (to be published). 49. Baldereschi, A. and L i p a r i , N.O., "Proc. XIII lint. Conf. Phys. Sem.", Rome (Tipografia Marves, Rome, 1976), p.426. 50. Onton, A., Fisher, P. and Ramdas, A.K., Phys. Rev. 163, 686 (1967). 51. Vouk, M.A. and Lightowlers, E .C, J . Phys. C, (to be published). 52. Baldereschi, A. and L i p a r i , N.O., Phys. Rev. B 9, 1525 (1974). 53. Lyon, S.A., Smith, D.L. and M c G i l l , T.C., Report given at the March 1977 APS meeting, San Diego. 54. Vouk, M.A. and Lightowlers, E . C , J . Phys. C 8_, 3695 (1975). 55. Hammond, R.B., M c G i l l , T.C and Mayer, J.W., Phys. Rev. B 13, 3566 (1976). 56. Dean, P.J., Faulkner, R.A., Kimura, S. and Ilegems, M., Phys. Rev. B 4, 1926 (1971). 57. Dean, P.J. and Herbert, D.C, J . Lumin. 14, 55 (1976). 58. Tubino, R., P i s e r i , L. and Zerbi, C , J . Chem. Phys. 56, 1022 (1971). 104 59. Hammond, R.B., Smith, D.L. and M c G i l l , T.C., Phys. Rev. Lett. 35_, 1535 (1975). 60. McLean, T.P. and Loudon, R., J . Phys. Chem. Solids 15_, 1 (1960). 61. L i p a r i , N.O. and Baldereschi, A., Phys. Rev. B 8, 2697 (1973). 62. MacFarlane, G.G., McLean, T.P., Quarrington, J.E. and Roberts, V., J. Phys. Chem. Solids 8, 388 (1959). 63. Zwerdling, S., Roth, L.M. and Lax, B., J . Phys. Chem. Solids 8_, 397 (1959). 64. A l t e r e l l i , M. and L i p a r i , N.O., "Proc. XIII Int. Conf. Phys. Sem.", Rome, (Tipografia Marves, Rome 1976), p. 811. 65. Smith, D.L., Hammond, R.B., Chen, M., Lyon, S.A. and M c G i l l , T.C., "Proc. XIII Int. Conf. Phys. Sem.", Rome, (Tipografia Marves, Rome, 1976), p.1037. 66. Frova, A., Thomas, G.A., M i l l e r , R.E. and Kane, E.O., Phys. Rev. Lett. 34, 1572 (1975). 67. Nishino, T., Takeda, M. and Hamakawa, Y. S o l i d State Comm. 1_2, 1137 (1973). 68. Faulkner, R.A., Phys. Rev. 184, 713 (1969). Rostworowski, J.A., Thewalt, M. L. W. and Parsons, R.R., "Photoluminescent Detection of the Impurity Band i n S i l i c o n ( P ) " , S o l i c State Communications 18, 93(1975) . Cornish, W. D., Young, L. and Thewalt, M. L. W., "Space Charge F i e l d s : a Fringe Technique for Observing Such F i e l d s During Hologram Writing i n LiNb0 3", Applied Optics L5, 1258(1976). Thewalt, M. L. W. and Parsons R. R., "Direct Observation of the S p l i t t i n g of the Ground State of the Indirect Free Exciton i n S i l i c o n " , S o l i d State Communications 20, 97(1976). Thewalt, M.L.W., Kirczenow, G., Parsons, R.R. and Barrie, R.," Phonon Broadening of the Bound Exciton Luminescence i n S i l i c o n " , Canadian Journal of Physics 54, 1728(1976) . Thewalt, M.L.W.,: Fine Structure of the Luminescence from Excitons and Multiexciton Complexes Bound to Acceptors i n S i l i c o n " , Physical Review Letters 38, 521(1977). Thewalt, M.L.W.," Excited States of Donor Bound Excitons and Bound Multiexciton Complexes i n S i l i c o n " , S o l i d State Communications 21, 937(1977) . Parsons, R.R. and Thewalt, M.L.W.," Evidence for High Temperatue Electron-Hole Droplets i n Heavily Doped S i l i c o n " , S o l i d State Communications 21, 1087(1977). Thewalt, M.L.W.," Even-Parity Acceptor Excited States i n Si from Bound Exciton Two-Hole Transitions", S o l i d State Communicatios 23, 733(1977) . Thewalt, M.L.W.," Detai l s of the Structure of Bound Excitons and Bound Multiexciton Complexes i n S i " , Canadian Journal of Physics, (to be published). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085753/manifest

Comment

Related Items