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Optical detection of paramagnetic and cyclotron resonance in semiconductors Booth, Ian 1985

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Optical Detection of Paramagnetic and Cyclotron Resonance in Semiconductors By IAN J . M. BOOTH B.S c . j M . S c , Lakehead U n i v e r s i t y , 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Physics) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March 1985 (§) Ian Jeremy M. Booth, 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t 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 or her representatives. It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of P hys i c s The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e April 1. 1985 DE-6 (3/81) ABSTRACT O p t i c a l D e t e c t i o n of Magnetic Resonance (ODMR) has been used to observe both paramagnetic and diamagnetic resonance o f p h o t o - e x c i t e d e l e c t r o n s and h o l e s i n GaP, ZnTe and AgBr. P a r a m a g n e t i c r e s o n a n c e o f c o n d u c t i o n e l e c t r o n s i n GaP has be e n s t u d i e d and t h e m i c r o w a v e f r e q u e n c y and power dependence o f the e f f e c t a n a l y s e d . The maximum s i g n a l s t r e n g t h was observed to produce approximately 1% change i n l u m i n e s c e n c e a t 1.6 K. The g v a l u e d e d u c e d f r o m t h e resonance was 2.000 +_ 0.005. The resonance was homogeneously broadened g i v i n g the e l e c t r o n l i f e t i m e as a p p r o x i m a t e l y 4 nanoseconds. Paramagnetic resonance of e l e c t r o n s and holes has a l s o been d e t e c t e d i n AgBr. The background s i g n a l s present i n ODMR experiments have been i n v e s t i g a t e d and are shown to be caused by diamagnetic or c y c l o t r o n r e s o n a n c e h e a t i n g o f p h o t o e x c i t e d c a r r i e r s . Measurements a t microwave f r e q u e n c i e s o f 9.2 and 36.3 GHz have been made on GaP,ZnTe and AgBr, and c y c l o t r o n resonance of e l e c t r o n s and holes observed. The e f f e c t i v e masses of l i g h t and heavy h o l e s i n GaP were found t o be 0.154 +_ 0.01 and 0.626 +_ 0.06 r e s p e c t i v e l y w h i l e the e l e c t r o n e f f e c t i v e mass was 0.36 _+ 0.10. The e l e c t r o n s c a t t e r i n g t i m e was s h o r t e r t h a n t h a t f o r h o l e s by a f a c t o r o f a p p r o x i m a t e l y t h r e e , most l i k e l y due to s c a t t e r i n g by i s o e l e c t r o n i c n i t r o g e n i m p u r i t i e s . Resonances were o b s e r v e d i n ZnTe a t e f f e c t i v e mass v a l u e s o f 0.30 + 0.20 and 0.76 + 0.20 i i corresponding to e l e c t r o n s and heavy h o l e s . In both GaP and ZnTe r e s o n a n c e s due t o e l e c t r o n s and h o l e s a ppeared i n d i f f e r e n t luminescence bands i n d i c a t i n g the s e n s i t i v i t y of d i f f e r e n t r e c o m b i n a t i o n c e n t r e s to h e a t i n g of e i t h e r c a r r i e r t y p e . C y c l o t r o n r e s o n a n c e o f e l e c t r o n s and h o l e s was a l s o o b s e r v e d i n AgBr and showed the e f f e c t s o f c o n d u c t i o n and v a l e n c e band n o n - p a r a b o l i c i t y . A f e a t u r e i n the e l e c t r o n r e s o n a n c e i n d i c a t e d enhanced t r a p p i n g of e l e c t r o n s w i t h c e r t a i n e n e r g i e s by e m i s s i o n of one or more LO phonons. i i i TABLE OF CONTENTS A b s t r a c t . Chapter 1. I n t r o d u c t i o n . 1 1.1 H i s t o r i c a l . 1 1.2 Paramagnetic Resonances. 6 1.3 Advantages of ODMR. 13 1.4 C y c l o t r o n Resonance. 14 1.5 Overview of the t h e s i s . 16 Chapter 2. Apparatus and Experimental Techniques. 19 2.1 Apparatus. 19 2.2 Experimental Procedures. 25 2.3 Commentary. 29 Chapter 3. G a l l i u m Phosphide and Zinc T e l l u r i d e . 30 3.1 I n t r o d u c t i o n . 30 3.2 E x c i t o n formation and luminescence i n GaP. 32 1.3 Other work on GaP. 42 3.4 R e s u l t s . 43 3.5 D i s c u s s i o n . 53 3.6 C y c l o t r o n Resonance. 58 3.7 ODMR i n ZnTe. 71 3.8 Other M a t e r i a l s . 78 3.9 Summary. 79 Chapter 4. S i l v e r Bromide. 82 4.1 AgBr. 82 4.2 ODMR i n AgBr. 82 4.3 R e s u l t s . 86 4.4 D i s c u s s i o n . 93 4.5 Summary. 99 Chapter 5. Con c l u s i o n s and Suggestions f o r Further Work .102 5.1 G a l l i u m Phosphide. 102 5.2 Zinc T e l l u r i d e . 103 5.3 S i l v e r Bromide. 104 5.4 Curve f i t t i n g . 105 5.5 Comments and Suggestions f o r Further Work. 106 Appendix A. Curve F i t t i n g . 110 S t a t i s t i c a l A n a l y s i s . 118 B i b l i o g r a p h y . 122 iv LIST OF TABLES Table 3.1. Microwave induced luminescence changes. 41 Table 3.2. GaP C y c l o t r o n Resonance r e s u l t s . 68 Table A . l . Gaussian L.S. c o e f f i c i e n t s . 113 Table A.2. L o r e n t z i a n L.S. c o e f f i c i e n t s . 113 Table A.3. Revised Gaussian L.S. c o e f f i c i e n t s . 117 Table A.4. Revised L o r e n t z i a n L.S. c o e f f i c i e n t s . 117 Table A.5. C o r r e l a t i o n c o e f f i c i e n t s and c o n f i d e n c e 119 l i m i t s . v LIST OF FIGURES F i g . 1 .1 Bas i c ODMR experiment. 5 F i g . 1 .2 Luminescence p r o c e s s e s . 8 F i g . 2 .1 Apparatus. 20 F i g . 3 .1 GaP b a n d s t r u c t u r e . 31 F i g . 3 .2 GaP-N and GaP-Bi luminescence. 35 F i g . 3 .3 E x c i t o n s t a t e s i n GaP. 37 F i g . 3 .4 ODMR i n GaP-N. 44 F i g . 3 .5 ODMR i n GaP-S. 45 F i g . 3 .6 ODMR i n GaP-Bi. 46 F i g . 3 .7 ODMR microwave power dependence. 48 F i g . 3 .8 GaP-N Zeeman spectrum. 50 F i g . 3 .9 ODMR s i g n a l at 36.3 GHz. 52 F i g . 3 .10 GaP c y c l o t r o n resonance. 59 F i g . 3 .11 GaP-N c y c l o t r o n resonance. 61 F i g . 3 .12 GaP-S c y c l o t r o n resonance. 62 F i g . 3 .13 GaP-Bi c y c l o t r o n resonance. 64 F i g . 3 .14 C y c l o t r o n resonance at 36.3GHz. 65 F i g . 3 .15 ZnTe luminescence. 73 F i g . 3 .16 ZnTe ODMR at 5220 A.U. 75 F i g . 3 .17 ZnTe ODMR at 5290 A.U. 76 F i g . 4 .1 AgBr b a n d s t r u c t u r e . 83 F i g . 4 .2 AgBr luminescence. 85 F i g . 4 .3 ODMR i n AgBr. 87 F i g . 4 .4 ODMR i n AgBr. 88 F i g . 4 .5 C y c l o t r o n resonance i n AgBr. 89 F i g . 4 .6 Low power c y c l o t r o n resonance s i g n a l . 91 vi F i g . 4. 7 Power dependent c y c l o t r o n resonance s i g n a l . 92 F i g . A. 1 The Nelder-Mead m i n i m i z a t i o n procedure. 112 F i g . A. 2 The convergence p r o c e s s . 114 F i g . A. 3 Gaussian and L o r e n t z i a n f i t s to d a t a . 116 F i g . A. 4 F i t s from IA5. 121 v i i ACKNOWLEDGEMENTS I t g i v e s me much p l e a s u r e t o t h a n k my r e s e a r c h s u p e r v i s o r , D r . C . F . S c h w e r d t f e g e r , f o r h i s a d v i c e and i n s t r u c t i o n . The h e l p g i v e n by Dr. R. B a r r i e and Dr. J . E l d r i d g e i n c r i t i c i z i n g t h i s t h e s i s and i m p r o v i n g i t s p r e s e n t a t i o n i s g r a t e f u l l y acknowledged. Thanks a r e a l s o due to Dr.W.Czaja f o r h i s h e l p f u l c r i t i c i s m o f our p u b l i c a t i o n s . Our a p p r e c i a t i o n i s due t o Dr.J.Merz and Dr.W.Czaja f o r d o n a t i n g samples o f Z i n c T e l l u r i d e and S i l v e r Bromide. The a s s i s t a n c e o f my p a r e n t s i n t h e a n a l y s i s o f d a t a , which was i n v a l u a b l e , i s g r e a t l y a p p r e c i a t e d . F i n a l l y t h a n k s a r e due t o NSERC f o r the award o f a post-graduate S c h o l a r s h i p and to the U n i v e r s i t y of B r i t i s h Columbia f o r a Teaching A s s i s t a n t s h i p , and to NSERC Grant # 67/2228 f o r sup p o r t i n g p a r t of the work. v i i i Chapter 1. INTRODUCTION 1.1 Historical. P r e c e s s i o n o f t h e s p i n o f an e l e c t r o n was f i r s t observed by P.Zeeman i n 1896 a f t e r t h e o r e t i c a l p r e d i c t i o n s by S i r J o s e p h L a rmor. When a m a g n e t i c f i e l d i s a p p l i e d p a r a l l e l to the s p i n a x i s of the e l e c t r o n , p r e c e s s i o n occurs about the f i e l d d i r e c t i o n w i t h a frequency given by: (o = gueB/tt where B i s the magnetic f i e l d , ne the magnetic moment of the e l e c t r o n , g the Lande f a c t o r ( = 2.0023 f o r f r e e space), and Yi i s Planck's c o n s t a n t . Quantum m e c h a n i c a l l y t h i s means t h a t the energy l e v e l s o f t he e l e c t r o n i n a m a g n e t i c f i e l d w i l l be s e p a r a t e d by amounts M<y and, f o r the e l e c t r o n , t h e r e w i l l be two l e v e l s c o r r e s p o n d i n g t o s p i n s p a r a l l e l and a n t i - p a r a l l e l t o the magnetic f i e l d . T r a n s i t i o n s between the two s p i n s t a t e s can be induced by e l e c t r o m a g n e t i c f i e l d s o f f r e q u e n c y w, and t h e s e t r a n s i t i o n s correspond to a b s o r p t i o n or to induced e m i s s i o n 1 of a p h o t o n . T h i s i s known as p a r a m a g n e t i c r e s o n a n c e . The change i n the e l e c t r o n s p i n i n such a t r a n s i t i o n i s u n i t y s i n c e the s p i n changes from +1/2 t o -1/2 and a p h o t o n of s p i n 1 i s absorbed or e m i t t e d . Thus the t r a n s i t i o n conserves both energy and angular momentum. The t r a n s i t i o n i s c a u s e d by the i n t e r a c t i o n s o f the e l e c t r o n magnetic f i e l d w i t h the magnetic component of the e l e c t r o m a g n e t i c f i e l d which must be p e r p e n d i c u l a r t o the a p p l i e d magnetic f i e l d . E l e c t r o n s a t a f i n i t e t e m p e r a t u r e i n a m a g n e t i c f i e l d w i l l tend to r e d i s t r i b u t e t h e i r s p i n e n e r g i e s i n such a way as t o p r o d u c e a B o l t z m a n n d i s t r i b u t i o n o f e n e r g y d i f f e r e n c e s . Thus, when an e l e c t r o m a g n e t i c f i e l d i s a p p l i e d at r e s o n a n c e , a net a b s o r p t i o n of e n e r g y w i l l o c c u r as e l e c t r o n s move from the l o w e r t o the h i g h e r e nergy s t a t e , and t h i s a b s o r p t i o n can be measured i n a v a r i e t y o f ways. T h i s i s the b a s i s of e l e c t r o n p a r a m a g n e t i c r e s o n a n c e (EPR) s t u d i e s which have been used to determine magnetic resonance f r e q u e n c i e s of e l e c t r o n s i n semiconductors. In a t y p i c a l EPR e x p e r i m e n t t h e m a t e r i a l u n d e r i n v e s t i g a t i o n i s placed i n a magnetic f i e l d i n a microwave c a v i t y . The microwave f r e q u e n c y i s f i x e d a t the r e s o n a n t frequency of the c a v i t y , and the magnetic f i e l d i s swept. At resonance the i n c r e a s e d a b s o r p t i o n of the microwave power by the sample changes the Q f a c t o r o f the c a v i t y . T h i s c a u s e s 2 an observable change i n the microwave power r e f l e c t e d from the c a v i t y . I n 1952 B r o s s e l a n d B i t t e r (1) i n v e s t i g a t e d paramagnetic resonance of e l e c t r o n s i n mercury vapour w i t h the atoms i n an e x c i t e d s t a t e . The e x c i t a t i o n was p r o d u c e d by i r r a d i a t i o n w i t h i n t e n s e l i g h t of a p p r o p r i a t e wavelength. E l e c t r o n s i n the e x c i t e d s t a t e n o r m a l l y decay t o t h e i r ground s t a t e e m i t t i n g photons whose p o l a r i z a t i o n depends on t h e i r s p i n p r i o r to the decay pr o c e s s . The a p p l i c a t i o n of a p a r a m a g n e t i c r e s o n a n c e s i g n a l c h a n g e d t h e r e l a t i v e p o p u l a t i o n s of the s p i n s t a t e s of the e l e c t r o n s and thus the p o l a r i z a t i o n of the emitted l i g h t ; t h i s change was d e t e c t e d . The f i r s t o b s e r v a t i o n i n a s o l i d m a t e r i a l was t h a t of Geschwind et a l . (2) who measured luminescence changes from Cr i m p u r i t i e s i n A 1203. S i n c e then many o t h e r s u b s t a n c e s have been s t u d i e d and resonances have been observed (3-10). In a m a g n e t i c f i e l d c h a r g e d p a r t i c l e s p a r t i c i p a t e i n another type of phenomenon known as c y c l o t r o n resonance. A c h a r g e d p a r t i c l e , moving a t r i g h t a n g l e s to a m a g n e t i c f i e l d , e x p e r i e n c e s a f o r c e evxB where e i s the e l e c t r o n c h a r g e , and B t h e m a g n e t i c f i e l d . T h i s r e s u l t s i n c i r c u l a r m o t i o n about the m a g n e t i c f i e l d d i r e c t i o n a t a n g u l a r f r e q u e n c y eB/m, where m i s the e l e c t r o n mass. These o r b i t s a r e q u a n t i z e d so t h a t an i n f i n i t e s e r i e s of l e v e l s e x i s t 3 s e p a r a t e d by ene r g y M<a • T r a n s i t i o n s between t h e s e l e v e l s can be i n d u c e d by an e l e c t r o m a g n e t i c f i e l d b e cause o f the i n t e r a c t i o n of the e l e c t r i c component of t h i s f i e l d w i t h the e l e c t r o n . The a b s o r p t i o n o f energy f r o m the a p p l i e d f i e l d can be measured i n the same way as t h a t d e s c r i b e d f o r EPR. The e f f e c t was f i r s t observed i n gaseous plasmas by Lax et a l . i n 1950 (11). I t was l a t e r seen i n t h e s e m i c o n d u c t o r Ge by D r e s s e l h a u s e t a l . i n 1953 (12) and has s i n c e been observed i n other s o l i d m a t e r i a l s . D e t e c t i o n o f c y c l o t r o n r e s o n a n c e by i t s e f f e c t s on l u m i n e s c e n c e has o n l y r e c e n t l y been r e p o r t e d by R o m e s t a i n and Weisbuch (13) i n CdTe and by Baranov e t a l . i n Ge (14). I t i s to be noted t h a t t h e e f f e c t s o f c y c l o t r o n r e s o n a n c e h ave been o b s e r v e d i n ODMR e x p e r i m e n t s as background s i g n a l s u n d e r l y i n g the d e s i r e d p a r a m a g n e t i c resonance s i g n a l s (7,15-17). A Typical Experiment. The e s s e n t i a l elements of an ODMR experiment are shown i n Fig.1.1. The m a t e r i a l on which the measurements are to be t a k e n i s g e n e r a l l y c o o l e d t o t h e l i q u i d h e l i u m t e m p e r a t u r e r a n g e , s i n c e p a r a m a g n e t i c r e s o n a n c e s and the l u m i n e s c e n c e p r o c e s s e s used t o o b s e r v e them a r e s t r o n g l y a f f e c t e d by t e m p e r a t u r e . The sample may be doped w i t h 4 FIG. L i BASIC ODMR EXPERIMENT DATA COLLECTION CHOPPED MICROWAVES i m p u r i t i e s t o produce p a r t i c u l a r t y p e s of r e c o m b i n a t i o n c e n t r e s . F r e e c a r r i e r s a r e g e n e r a t e d by an e x c i t a t i o n source, u s u a l l y a l a s e r although arc lamps, e l e c t r o n beams or x-rays are sometimes used. The c a r r i e r s recombine i n v a r i o u s ways, the most common l u m i n e s c e n t p r o c e s s e s b e i n g the decay of e l e c t r o n s , e i t h e r f r e e or bound to an i m p u r i t y c e n t r e , and d o n o r - a c c e p t o r p a i r r e c o m b i n a t i o n . At h i g h enough e x c i t a t i o n l e v e l s , bound m u l t i - e x c i t o n complexes at i m p u r i t y c e n t r e s and e l e c t r o n - h o l e drops may be observed. A magnetic f i e l d i s generated e i t h e r by a co n v e n t i o n a l e l e c t r o m a g n e t o r by a s u p e r c o n d u c t i n g magnet. M a g n e t i c r e s o n a n c e s a r e e x c i t e d by a microwave f i e l d w h i c h i s g e n e r a l l y h e l d at a f i x e d frequency w h i l e the magnetic f i e l d sweeps through the resonances. Resonance h e a t i n g of the c a r r i e r s or t h e i r s p i n s a f f e c t s the recombination processes and r e s u l t s i n o b s e r v a b l e changes i n the l u m i n e s c e n c e e i t h e r i n t o t a l i n t e n s i t y , p o l a r i z a t i o n , or w a v e l e n g t h , w h i c h i s m o n i t o r e d a f t e r a p p r o p r i a t e f i l t e r i n g . The microwaves a r e chopped t o produce an a.c. s i g n a l w h i c h i s measured by a l o c k - i n d e t e c t o r or s i m i l a r d e v i c e . 1.2 Paramagnetic Resonances. The most common a p p l i c a t i o n of ODMR to date has been i n the d e t e c t i o n of paramagnetic resonances of c a r r i e r s , f r e e or bound. A number o f t e c h n i q u e s have been d e v e l o p e d t o enhance the s e n s i t i v i t y of the b a s i c ODMR experiment. The e f f e c t s of e l e c t r o n paramagnetic resonance may be i l l u s t r a t e d by t h e s i m p l e examples shown i n F i g . 1.2. F i g . 1.2(a) shows a t y p i c a l d o n o r - a c c e p t o r p a i r system w i t h a l l o w e d recombinations of a s p i n 1/2 e l e c t r o n and a s p i n 3/2 h o l e . A l l o w e d t r a n s i t i o n s a r e ones i n w h i c h the s p i n o f the e l e c t r o n s y s t e m changes by u n i t y or z e r o d u r i n g the d e c a y , compensating f o r the s p i n of the photon e m i t t e d . On average h a l f o f the d o n o r - a c c e p t o r p a i r s p o p u l a t e d w i l l have s p i n s t a t e s t h a t a l l o w o p t i c a l t r a n s i t i o n s , the other h a l f w i l l decay by n o n - r a d i a t i v e p r o c e s s e s . The EPR t r a n s i t i o n s shown between the the e l e c t r o n s p i n s t a t e s w i l l cause p a i r s w i t h o p t i c a l l y d i s a l l o w e d t r a n s i t i o n s to become allowed,and v i c e v e r s a . Since p a i r s with o p t i c a l l y a llowed t r a n s i t i o n s w i l l r e c o m b i n e f a s t e r t h a n t h o s e w i t h o u t , the net e f f e c t o f the r e s o n a n c e s i g n a l w i l l be t o i n c r e a s e l u m i n e s c e n c e a t the expense of n o n - r a d i a t i v e decays. The s p i n s t a t e s of the e l e c t r o n s and holes are s p l i t i n the m a g n e t i c f i e l d and an EPR t r a n s i t i o n between e l e c t r o n s p i n s t a t e s can cause a s p i n - f o r b i d d e n r e c o m b i n a t i o n t o become a l l o w e d . In the absence o f t h e EPR r e s o n a n c e o n l y e l e c t r o n - h o l e p a i r s w i t h t h e a p p r o p r i a t e s p i n s c a n recombine, thus the resonance i n c r e a s e s the luminescence. An e x c i t o n i s a bound system of an e l e c t r o n and a h o l e , 7 FIG. 1.2 LUMINESCENCE PROCESSES b) Exciton levels formed by spin 1/2 electrons and spin 3/2 holes. Transitions involving a change of 0 or +1 in Mj are allowed while those causing a change of +2 are forbidden as shown. 8 somewhat s i m i l a r to a hydrogen atom. F i g . 1.2(b) shows the e x c i t o n s t a t e s formed from s p i n 1/2 e l e c t r o n s and s p i n 3/2 h o l e s . An example of such a system i s GaP w h i c h w i l l be c o n s i d e r e d i n Chapter 3. The e x c i t o n s t a t e s formed depend on the p o p u l a t i o n s of the i n i t i a l e l e c t r o n and h o l e s p i n s t a t e s . In p a r t i c u l a r the |2,+2> e x c i t o n s t a t e s , w i t h d i p o l e f o r b i d d e n o p t i c a l decays, are more l i k e l y to form when the e l e c t r o n spins are heated thus red u c i n g the luminescence. In theory a change i n luminescence of 50% co u l d be observed at ab s o l u t e zero f o r a s a t u r a t i o n epr s i g n a l . These p o i n t s are d i s c u s s e d i n more d e t a i l i n Chapter 3. In p r a c t i c e c h a n g e s o f t h e o r d e r o f 1% a r e t o be e x p e c t e d . A s i m i l a r argument can be a p p l i e d i n the c a s e o f h o l e p a r a m a g n e t i c r e s o n a n c e . A number o f p r o c e s s e s a r e present i n a p r a c t i c a l experiment which reduce the s i z e of the observed s i g n a l . Obviously the sample i s not at absolute z e r o so t h a t the c a r r i e r s p i n s w i l l n o t be c o m p l e t e l y p o l a r i z e d . In a d d i t i o n the c a r r i e r s p i n temperature may be h i g h e r t h a n t h e sample t e m p e r a t u r e d e p e n d i n g on the s p i n l a t t i c e r e l a x a t i o n t i m e and f r e e c a r r i e r l i f e t i m e s . Once e x c i t o n s a r e formed t h e r m a l i z a t i o n may o c c u r w i t h i n the e x c i t o n l e v e l s 'washing out1 the e f f e c t s of the resonance i f i t o n l y a f f e c t e d the c a r r i e r s w h i l e f r e e . A maximum change i n l u m i n e s c e n c e s h o u l d be p r o d u c e d by s a t u r a t i n g the p a r a m a g n e t i c r e s o n a n c e , but i f t h i s i s i n h o m o g e n e o u s l y broadened, i.e. d i f f e r e n t p a r t s of the c r y s t a l have s l i g h t l y d i f f e r e n t resonant f r e q u e n c i e s , o nly a s m a l l packet of spins 9 can be s a t u r a t e d at one time. In some c a s e s t h e f a c t o r s j u s t m e n t i o n e d may be o v e r c o m e o r u s e d t o a d v a n t a g e t o e n h a n c e s i g n a l d e t e c t a b i l i t y . C o n d u c t i o n e l e c t r o n s p i n r e s o n a n c e (CESR) i s w i d e l y used t o measure the g v a l u e o f f r e e e l e c t r o n s (6,10,18). I n s t e a d o f r e l y i n g on t h e r m a l i z a t i o n or s p i n s e l e c t i v e r e c o m b i n a t i o n to produce a p o l a r i z a t i o n i n s p i n s , e l e c t r o n s are produced i n a p a r t i c u l a r s p i n s t a t e by u s i n g c i r c u l a r l y p o l a r i z e d l i g h t f o r e x c i t a t i o n . The r e c o m b i n a t i o n r a d i a t i o n e m i t t e d p a r a l l e l to the a p p l i e d m a g n e t i c f i e l d w i l l be c i r c u l a r l y p o l a r i z e d p r o v i d e d t h e e l e c t r o n s 'remember' t h e i r i n i t i a l s p i n s , and a m a g n e t i c r e s o n a n c e s i g n a l w i l l show up as a decrease i n t h i s p o l a r i z a t i o n . In order to generate s p i n p o l a r i z e d e l e c t r o n s , the e x c i t a t i o n l i g h t must be a p p l i e d p a r a l l e l to the magnetic f i e l d (since a t r a n s v e r s e magnetic f i e l d r a p i d l y d e p o l a r i z e s them), and s h o u l d be r e s o n a n t w i t h the band gap. The method works b e s t i n s y s t e m s w here t h e r e c o m b i n a t i o n t i m e o f t h e e l e c t r o n s i s l e s s than t h e i r s p i n t h e r m a l i z a t i o n t i m e . In a c o n v e n t i o n a l ODMR experiment where s p i n p o p u l a t i o n d i f f e r e n c e s a r e not p r o d u c e d by the e x c i t a t i o n l i g h t , c i r c u l a r p o l a r i z a t i o n i s s o m e t i m e s v i s i b l e i n t h e luminescence, and a c o n s i d e r a b l e enhancement can be seen i n 10 an ODMR s i g n a l by monitoring only one p o l a r i z a t i o n . In some c a s e s e g u a l and o p p o s i t e s i g n a l s a r e seen by l o o k i n g a t o p p o s i t e l y p o l a r i z e d components o f the l u m i n e s c e n c e , t h u s the p a r a m a g n e t i c r e s o n a n c e does not change t h e t o t a l i n t e n s i t y o f the l u m i n e s c e n c e s i g n i f i c a n t l y but o n l y i t s p o l a r i z a t i o n , and an e x p e r i m e n t t h a t m o n i t o r e d t o t a l i n t e n s i t y would not giv e a s i g n a l (17,19). Since d i f f e r e n t c i r c u l a r p o l a r i z a t i o n s w i t h i n an e m i s s i o n l i n e correspond to t h e r e c o m b i n a t i o n o f e x c i t o n s w i t h d i f f e r e n t s p i n components, t h i s w i l l e x h i b i t Zeeman s p l i t t i n g i n a magnetic f i e l d . Thus s i m i l a r enhancements i n ODMR s i g n a l s may be obtained by obse r v i n g s i n g l e Zeeman components. In general the Zeeman components w i l l o n l y be d i s t i n c t a t h i g h e r magnetic f i e l d s c orresponding to microwave f r e q u e n c i e s i n the r e g i o n of 30 GHz or above. An ODMR s i g n a l c o r r e s p o n d s t o t h e change i n r e l a t i v e s p i n p o p u l a t i o n s o f e l e c t r o n s o r h o l e s as the m a g n e t i c r e s o n a n c e e x c i t a t i o n i s t u r n e d on or o f f . A s a t u r a t i o n r e s o n a n c e s i g n a l would e q u a l i z e the s p i n s ( i . e . d e p o l a r i z e them c o m p l e t e l y ) and g i v e the g r e a t e s t s i g n a l . In many c a s e s t h e p a r a m a g n e t i c r e s o n a n c e i s i n h o m o g e n e o u s l y broadened so th a t the microwave e x c i t a t i o n can only a f f e c t a f r a c t i o n o f the t o t a l s p i n s a t any t i m e as i t sweeps t h r o u g h the r e s o n a n c e , and thus a s a t u r a t i o n s i g n a l c a n n o t be r e a l i z e d . A method sometimes used to overcome t h i s i s to modulat e t h e f i e l d , ( u s u a l l y t he a p p l i e d m a g n e t i c f i e l d although the microwave frequency c o u l d be modulated instead) 11 o v e r a s m a l l range a t a f r e q u e n c y h i g h e r than the s p i n r e l a x a t i o n t i m e , a l l o w i n g more p a r t i c l e s to p a r t i c i p a t e i n the r e s o n a n c e a t any t i m e , and t h e r e b y i n c r e a s i n g t h e ODMR s i g n a l (7,15,20,21). In l u m i n e s c e n c e s p e c t r a h a v i n g c o n t r i b u t i o n s from s e v e r a l r e c o m b i n a t i o n c e n t r e s or p r o c e s s e s i t i s o f t e n d e s i r a b l e to i d e n t i f y which components e x h i b i t a p a r t i c u l a r ODMR s i g n a l . T h i s c an be done by s e t t i n g t he m a g n e t i c f i e l d a t resonance and sweeping through the spectrum w i t h a monochromator, measuring the ODMR s i g n a l and comparing t h i s 'ODMR s p e c t r u m ' w i t h the a c t u a l o p t i c a l s p e c t r u m . T h i s method can be c o m p l i c a t e d by the f a c t t h a t l u m i n e s c e n c e bands n ot showing the ODMR s i g n a l may s t i l l have b r o a d background s i g n a l s c a u s e d by l u m i n e s c e n c e changes due t o microwave d i e l e c t r i c or c a r r i e r h e a t i n g . By doing a second scan w i t h the magnetic f i e l d o f f resonance and s u b t r a c t i n g , the t r u e s p e c t r a l dependence o f the ODMR s i g n a l may be o b t a i n e d , b u t i n s i t u a t i o n s where s e v e r a l r e s o n a n c e s a r e p r e s e n t , o r s i g n a l — t o — n o i s e r a t i o s a r e p o o r , i t i s o f t e n b e t t e r t o do a s e r i e s o f m a g n e t i c f i e l d s c a n s a t d i f f e r e n t wavelengths corresponding to s a l i e n t f e a t u r e s i n the o p t i c a l s p e c t r u m (such as s t r o n g e m i s s i o n peaks from d i f f e r e n t c entres) to deduce the s p e c t r a l dependence. 12 1•3 Advantages o f ODMR. ODMR l o o k s a t r e s o n a n c e s v i s i b l e , a t l e a s t i n p r i n c i p l e , w i t h c o n v e n t i o n a l microwave a b s o r p t i o n EPR techniques. Depending on the system being c o n s i d e r e d , ODMR may have s e v e r a l advantages. Observation of an EPR s i g n a l r e q u i r e s the a b s o r p t i o n of a measurable amount of microwave power by a weak m a g n e t i c d i p o l e t r a n s i t i o n and subsequent d i s s i p a t i o n o f t h i s power v i a s p i n r e l a x a t i o n . In p a r t i c u l a r , a t low t e m p e r a t u r e the EPR s i g n a l t e n d s t o sa t u r a t e and become unobservable unless very low microwave power l e v e l s are used, and t h i s g i v e s a poor s i g n a l to noise r a t i o . As ODMR c a r r i e r s are photo-generated, t h i s o b v i a t e s the n e c e s s i t y f o r doping (except f o r s u i t a b l e recombination c e n t r e s ) . The weak magnetic d i p o l e t r a n s i t i o n s e x c i t e d by the EPR s i g n a l c a use m a c r o s c o p i c changes i n the o p t i c a l t r a n s i t i o n p r o b a b i l i t y , and e f f e c t i v e l y a m p l i f y the EPR s i g n a l . F u r t h e r m o r e a s a t u r a t i o n o f t h e s p i n s by t h e microwave e x c i t a t i o n r e s u l t s i n a maximum ODMR s i g n a l (although i t may a l s o broaden i t ) and so i s not a problem as i n c o n v e n t i o n a l EPR. In a d d i t i o n to g i v i n g b e t t e r s i g n a l s i n a p p r o p r i a t e c i r c u m s t a n c e s , ODMR serves as a t o o l to study luminescence processes as w e l l as paramagnetic resonances. ODMR s i g n a l s ' from f r e e c a r r i e r s can i n d i c a t e how r e c o m b i n a t i o n a t a p a r t i c u l a r c e n t r e i s a f f e c t e d by the s p i n s o f the r e c o m b i n i n g p a r t i c l e s , and ODMR of p a r t i c l e s 13 trapped at luminescence c e n t r e s g i v e s i n f o r m a t i o n d i r e c t l y about the nature and symmetry of the c e n t r e s . 1.4 Cyclotron Resonance C o n v e n t i o n a l d e t e c t i o n o f c y c l o t r o n r e s o n a n c e i n s e m i c o n d u c t o r s i n v o l v e s m e a s u r i n g t h e a b s o r p t i o n o f microwaves by f r e e . c a r r i e r s i n a magnetic f i e l d (22). The c a r r i e r s may be t h e r m a l l y or o p t i c a l l y g e n e r a t e d , or may come f r o m d o n o r o r a c c e p t o r i m p u r i t i e s . C y c l o t r o n r e s o n a n c e measurements g i v e i n f o r m a t i o n on the e f f e c t i v e mass o f e l e c t r o n s and h o l e s , and t h e i r m o b i l i t y . Measurement of c y c l o t r o n resonance i s i n some ways analogous to t h a t o f p a r a m a g n e t i c r e s o n a n c e , however the c y c l o t r o n resonance i s e x c i t e d by the e l e c t r i c f i e l d component of the microwaves r a t h e r than by the magnetic component as i n EPR, and i t t e n d s t o be much s t r o n g e r and more r e a d i l y o b s e r v a b l e . S e v e r a l f a c t o r s l i m i t t h e u s e f u l n e s s o f the t e c h n i q u e , h o w e v e r . The s c a t t e r i n g t i m e o f t h e f r e e c a r r i e r s determines the width of the c y c l o t r o n s i g n a l i n most ca s e s , and i s g e n e r a l l y much s h o r t e r than the s p i n r e l a x a t i o n time w h i c h g o v e r n s the w i d t h o f EPR l i n e s . The c o n d i t i o n f o r o b t a i n i n g a d i s t i n c t r e s o n a n c e i s W ct S l , uc b e i n g the c y c l o t r o n f r e q u e n c y and T the s c a t t e r i n g t i m e o f the c a r r i e r s . In many cases t h i s p r e c l u d e s the o b s e r v a t i o n of c y c l o t r o n resonance at reasonable microwave f r e q u e n c i e s and 14 m a g n e t i c f i e l d s t r e n g t h s . Doping w i t h donor or a c c e p t o r i m p u r i t i e s a l s o t e n d s t o r e d u c e c a r r i e r m o b i l i t y , and c y c l o t r o n r e s o n a n c e measurements a r e g e n e r a l l y made on samples of high p u r i t y . S a t u r a t i o n of the resonance i s not a problem as i n EPR, but a p p l i c a t i o n of e x c e s s i v e microwave power may h e a t the c a r r i e r s and change t h e i r s c a t t e r i n g p r o b a b i l i t y c a u s i n g asymmetry i n the r e s o n a n c e . I f the conduction or valence band i n que s t i o n i s s i g n i f i c a n t l y non-p a r a b o l i c , t h i s w i l l a l s o r e s u l t i n a change i n the apparent e f f e c t i v e mass. O p t i c a l d e t e c t i o n of c y c l o t r o n r e s o n a n c e has been r e p o r t e d only r e c e n t l y i n GaAs and CdTe (13) and i n Ge (14). The resonances of e l e c t r o n s and holes i n GaAs and CdTe were observed by mo n i t o r i n g changes i n luminescent i n t e n s i t y and l i n e s h a p e i n d u c e d by c a r r i e r h e a t i n g . In Ge the r e s o n a n t h e a t i n g produces observable decreases i n e l e c t r o n - h o l e drop luminescence. The measurements are i n many ways analogous to ODMR e x p e r i m e n t s a l t h o u g h t h e y tend t o r e l y on o b s e r v i n g changes i n t o t a l i n t e n s i t y r a t h e r than l o o k i n g at changes i n p o l a r i z a t i o n as i s o f t e n done i n ODMR. O p t i c a l d e t e c t i o n o f c y c l o t r o n r e s o n a n c e o f f e r s few d i r e c t advantages over the more commonly used technique of measuring microwave c y c l o t r o n a b s o r p t i o n by photo-generated c a r r i e r s , s i n c e t h i s a b s o r p t i o n i s r e a d i l y observable being much stronger than i n EPR s i g n a l s . However, by usi n g o p t i c a l 15 d e t e c t i o n , i n f o r m a t i o n may be o b t a i n e d about t r a p p i n g and l u m i n e s c e n c e p r o c e s s e s and t h e i r s e n s i t i v i t y t o c a r r i e r temperature. 1.5 Overview of the thesis Chapter 2 d e s c r i b e s the experimental procedure and the a p p a r a t u s u s e d , and d i s c u s s e s t h e r e l a t i v e m e r i t s of the d i g i t a l p hoton c o u n t i n g t e c h n i q u e used i n p a r t of the work and those of l o c k - i n d e t e c t i o n . C h a p t e r 3 r e v i e w s p r e v i o u s work on p a r a m a g n e t i c and c y c l o t r o n r e s o n a n c e s i n GaP and ZnTe and p r e s e n t s the r e s u l t s of our i n v e s t i g a t i o n of these m a t e r i a l s . In GaP paramagnetic resonance of e l e c t r o n s was observed i n luminescence from B i and S i m p u r i t i e s ; t h i s had not been r e p o r t e d i n the l i t e r a t u r e p r e v i o u s l y and supports the work of Cavenett on ODMR from N c e n t r e luminescence. The expected c h a n g e i n l u m i n e s c e n c e c a u s e d by t h e r e s o n a n c e was c a l c u l a t e d and good a g r e e m e n t was f o u n d w i t h t h e e x p e r i m e n t a l l y o b s e r v e d s i g n a l . By u s i n g two microwave f r e q u e n c i e s i t was d e t e r m i n e d t h a t the r e s o n a n c e s were h o m o g e n e o u s l y b r o a d e n e d , and a c a r r i e r l i f e t i m e o f approximately 4 nanoseconds was deduced from the widths of the resonances, a r e s u l t not p r e v i o u s l y r e p o r t e d . C y c l o t r o n r e s o n a n c e o f e l e c t r o n s and l i g h t and heavy 16 holes was observed to cause a decrease i n luminescence from N, S and B i c e n t r e s . A l t h o u g h the e f f e c t i v e mass v a l u e s determined from these measurements were not s i g n i f i c a n t l y more a c c u r a t e than t h o s e a l r e a d y p u b l i s h e d , d i f f e r e n t c e n t r e s were shown to be s e n s i t i v e to c y c l o t r o n h e a t i n g of e l e c t r o n s o r h o l e s d e p e n d i n g on t h e t r a p p i n g p r o c e s s i n v o l v e d , a phenomenon not p r e v i o u s l y seen. A c a l c u l a t i o n o f the e f f e c t based on the t h e o r e t i c a l t r a p p i n g c r o s s - s e c t i o n o f the N i m p u r i t y showed good agreement with the experimental r e s u l t s . C y c l o t r o n r e s o n a n c e o f e l e c t r o n s and h o l e s was a l s o o b s e r v e d i n v a r i o u s l u m i n e s c e n c e bands from ZnTe, however i n t e r p r e t a t i o n o f the r e s u l t s was d i f f i c u l t b e cause o f u n c e r t a i n t y i n the i m p u r i t y content of the c r y s t a l . C h a p t e r 4 d e t a i l s o u r i n v e s t i g a t i o n o f A g B r . Paramagnetic resonances observed u s i n g ODMR were shown to resemble s u b s t a n t i a l l y those of other r e s e a r c h e r s . C y c l o t r o n r e s o n a n c e was a l s o o b s e r v e d i n the l u m i n e s c e n c e from i s o e l e c t r o n i c i o d i n e c e n t r e s and showed some i n t e r e s t i n g f e a t u r e s n ot seen i n c o n v e n t i o n a l c y c l o t r o n r e s o n a n c e experiments on t h i s m a t e r i a l . In p a r t i c u l a r an enhancement of luminescence shown i n p a r t of the e l e c t r o n resonance l i n e i n d i c a t e d an i n c r e a s e d t r a p p i n g p r o b a b i l i t y f o r e l e c t r o n s w i t h c e r t a i n e n e r g i e s due to i n t e r a c t i o n w i t h o p t i c a l phonons. The e f f e c t i v e masses o f hot e l e c t r o n s c a l c u l a t e d 17 from the r e s u l t s a g r e e d s u b s t a n t i a l l y w i t h t h e o r e t i c a l p r e d i c t i o n s . Chapter 5 c o n t a i n s our c o n c l u s i o n s and some suggestions f o r f u r t h e r work. An appendix d e s c r i b e s a new method f o r n o n - l i n e a r curve f i t t i n g which was d e v i s e d i n connection w i t h the e x t r a c t i o n o f d a t a from the r a t h e r n o i s y s i g n a l s p r o d u c e d i n our experiments. T h i s i s compared w i t h another method which has been p r o p o s e d r e c e n t l y and i s shown t o be l e s s s u s c e p t i b l e to convergence to f a l s e minima. 18 Chapter 2.Apparatus and Experimental Techniques. 2.1 Apparatus A b l o c k d i a g r a m of the equipment used i n the ODMR e x p e r i m e n t s i s shown i n Fig.2.1. The l i q u i d h e l i u m Dewar used i n the i n i t i a l work d i f f e r e d from the one shown i n being s m a l l e r and c o n t a i n i n g no superconducting magnet. The m a g n e t i c f i e l d was o r i g i n a l l y s u p p l i e d by a V a r i a n electromagnet. Due to the bulk of t h i s d e v i c e luminescence c o u l d be v i e w e d o n l y i n a d i r e c t i o n a t r i g h t a n g l e s t o the m a g n e t i c f i e l d ( o u t o f t h e same window u s e d f o r t h e e x c i t a t i o n beam i n f a c t ) r a t h e r t h a n p a r a l l e l t o t h e m a g n e t i c f i e l d as shown f o r t h e s u p e r c o n d u c t i n g magnet Dewar. Both Dewars had an outer j a c k e t to c o n t a i n the l i q u i d n i t r o g e n p r e - c o o l a n t . H e l i u m , once t r a n s f e r r e d , c o u l d be a l l o w e d t o b o i l o f f i n t o a r e t u r n l i n e , a t a p p r o x i m a t e l y a t m o s p h e r i c p r e s s u r e , or be pumped o u t , t h u s c o o l i n g the l i q u i d t o below i t s lambda p o i n t (2.2 d e g r e e s K.). The vapour pressure of the helium c o u l d be measured by means of a mercury manometer attached to the Dewar. Both i n n e r Dewars (c o n t a i n i n g the helium) were c o n s t r u c t e d from Pyrex g l a s s to a l l o w o p t i c a l measurements and to reduce heat conduction up the w a l l s . Quartz windows were provided i n the outer metal c a s i n g o f the Dewars. The Dewar vacuum was m a i n t a i n e d c o n t i n u o u s l y by a pumping system c o n s i s t i n g of a d i f f u s i o n pump and a r o u g h i n g pump. The vacuum was b e t t e r t h a n 10~4 t o r r . 19 FIG. 2,1 APPARATUS MICROWAVE SWITCH KLYSTRON SQUARE WAVE GENERATOR LOCK - IN DETECTOR TRAVELLING WAVE TUBE AMPLIFIER NOVA II COMPUTER A / D CONV. LASER SPECTROMETER ISOLATOR MAGNET POWER SUPPLY MICROWAVE GUIDE PHOTOMULTIPLIER MICROWAVE DETECTOR MODE SWEEP MONITOR PUMPED LIQUID H E SUPERCONDUCTING MAGNET LIQUID HE DEWAR Apparatus showing 9.2 GHz microwaves and superconducting magnet. Both Dewars, when f i l l e d , would r e t a i n l i q u i d h e l i u m f o r between two and t h r e e hours d e p e n d i n g on the power d i s s i p a t i o n of the microwaves and the l i g h t being used, and whether the helium was being pumped to a lower temperature. The e l e c t r o - m a g n e t used i n the i n i t i a l measurements produced f i e l d s o f up to 15 k i l o g a u s s , i t s power s u p p l y c o u l d be computer c o n t r o l l e d e i t h e r to s e t a p a r t i c u l a r f i e l d s t r e n g t h , or t o produce a f i e l d w h i c h was swept between preassigned l i m i t s . The f i e l d was c a l i b r a t e d u s i n g the EPR r e s o n a n c e o f d i p h e n y l p i c r y 1 h y d r a z y l (DPPH) a t g=2.0037 wh i c h was o b s e r v e d by c o n v e n t i o n a l microwave a b s o r p t i o n . The s u p e r c o n d u c t i n g magnet used i n l a t e r e x p e r i m e n t s p r o v i d e d f i e l d s up t o 50 k i l o g a u s s . A d e t a i l e d d e s c r i p t i o n of t h i s d e v i c e has been given by O . Z i e m i l i s (23). The power supply f o r t h i s magnet c o u l d be d r i v e n e i t h e r by the computer or by a sweep box. The magnet was a l s o provided w i t h a ' p e r s i s t e n t s w i t c h ' which allowed the power supply to be turned o f f once the d e s i r e d f i e l d was reached. T h i s could e l i m i n a t e h e a t i n g from the c u r r e n t leads i n the DewarJ however, s i n c e our e x p e r i m e n t s a l w a y s i n v o l v e d sweeping the magnetic f i e l d , t h i s f a c i l i t y was not used. O p t i c a l e x c i t a t i o n o f the sample was p roduced by a 21 Spectra Physics 185 argon i o n l a s e r which generated 1/2 Watt o f power a t 4880 A.U. and c o u l d be t u n e d t o o t h e r w a v e l e n g t h s i n the range 4580 A.U. t o 5145 A.U. The u l t r a -v i o l e t e x c i t a t i o n r e q u i r e d f o r the s t u d i e s o f AgBr was p r o v i d e d by a S p e c t r a P h y s i c s 285 helium-cadmium l a s e r o p e r a t i n g a t 3250 A.U. or by a PEK 500 Watt mercury a r c lamp. A narrow band of l u m i n e s c e n c e from the sample was s e l e c t e d by a Spex monochromator and d e t e c t e d by a Hamamatsu R928 p h o t o m u l t i p l i e r tube which had a good response i n the range o f i n t e r e s t . The o u t p u t o f the p h o t o m u l t i p l i e r f e d a pulse shaping e l e c t r o n i c c i r c u i t as a p r e l i m i n a r y to photon c o u n t i n g . Microwave e x c i t a t i o n was a v a i l a b l e at 9.2 and 36.3 GHz. At 9.2 GHz a p p r o x i m a t e l y 10 Watts of power was p r o v i d e d by a Hughes model 1177 t r a v e l l i n g wave tube a m p l i f i e r d r i v e n by a r e f l e x k l y s t r o n . The o u t p u t of t h e k l y s t r o n was f e d t o the a m p l i f i e r t h r o u g h a d i o d e s w i t c h w h i c h a l l o w e d t h e microwaves to be modulated (chopped) by a square wave from a pulse g e n e r a t o r , the on and o f f times being e q u a l . The sample was mounted on a n o n - c o n d u c t i n g ( t e f l o n or q u a r t z ) r o d i n t h e c e n t r e o f a TE102 c a v i t y c o u p l e d to the waveguide by a s m a l l h o l e and a moveable t e f l o n p l u g to a l l o w impedance matching. 22 The microwave power r e f l e c t e d from the c a v i t y was d e t e c t e d i n one arm o f a 'magic Tee' and t h i s s i g n a l was used t o tune the k l y s t r o n t o r e s o n a n c e w i t h the c a v i t y and to a d j u s t the impedance match. A u t o m a t i c t u n i n g o f the k l y s t r o n t o the c a v i t y was not used because the f r e q u e n c y d r i f t was not l a r g e enough to cause problems, e s p e c i a l l y i n v i e w o f the l a r g e w i d t h s of the r e s o n a n c e s o b s e r v e d . The c h o p p i n g would a l s o t e n d t o i n t e r f e r e w i t h the a u t o m a t i c t u n e r . O p t i c a l a c c e s s t o t h e c a v i t y was p r o v i d e d by c i r c u l a r holes i n the s i d e s and s l o t s i n the bottom p l a t e . These were so p l a c e d as t o i n t e r f e r e as l i t t l e as p o s s i b l e w i t h the c u r r e n t f l o w a s s o c i a t e d w i t h t h e TE102 mode. Q f a c t o r s o f around 2000 were o b t a i n e d , the exact value v a r y i n g w i t h the p a r t i c u l a r sample under i n v e s t i g a t i o n . At 36.3 GHz a V a r i a n r e f l e x k l y s t r o n p r o v i d e d up to 800 m i l l i w a t t s of power. Chopping was achieved by modulating the r e f l e c t o r v o l t a g e w i t h a s q u a r e wave which s w i t c h e d the k l y s t r o n on and o f f one of i t s modes. The sample was mounted i n t h e open end o f a waveguide w i t h no c a v i t y r e s o n a t o r . This provided good o p t i c a l access although i t reduced the a v a i l a b l e microwave f i e l d s t r e n g t h . A r e s o n a t o r , when p r o p e r l y tuned t o t h e s o u r c e , s h o u l d a m p l i f y t h e m i c r o w a v e p o w e r d e n s i t y by a f a c t o r 23 approximately equal to the resonant Q v a l u e . There were two r e a s o n s f o r n ot u s i n g a r e s o n a t o r : f i r s t , b ecause adequate o p t i c a l access would be d i f f i c u l t to p r o v i d e , e s p e c i a l l y f o r the c o l l e c t i o n of luminescence which r e q u i r e s holes i n the bottom o f t h e r e s o n a t o r ; and s e c o n d , because the s i z e o f some of the samples used would have made them d i f f i c u l t to accommodate i n the system. The net e f f e c t would have been to reduce the Q f a c t o r of a resonator to such an extent t h a t i t was not deemed worthwhile u s i n g one. I t s h o u l d be n o t e d t h a t p a r a m a g n e t i c r e s o n a n c e s a r e e x c i t e d by t h e m a g n e t i c component o f t h e microwave f i e l d , w h i l e c y c l o t r o n r e s o n a n c e s r e s p o n d t o the e l e c t r i c f i e l d component. The TE102 c a v i t y used a t 9.2 GHz has a node i n the e l e c t r i c f i e l d a t i t s c e n t r e , and a maximum m a g n e t i c f i e l d , t hus i t was n e c e s s a r y t o d i s p l a c e the samples f r o m t h e c e n t r e o f t h e c a v i t y i n c y c l o t r o n r e s o n a n c e measurements. At 36.3 GHz no such problems e x i s t e d s i n c e no c a v i t y was u s e d . We b e l i e v e t h a t t h i s s i m p l e method f o r producing a v a r i a b l e f i e l d has not been d e s c r i b e d b e f o r e . I t was c r i t i c a l i n det e r m i n i n g the e x i s t e n c e of the c y c l o t r o n resonances d i s c u s s e d i n chapters 3 and 4. Changes i n de t e c t e d luminescence, synchronous wi t h the microwave c h o p p i n g , were d e t e c t e d u s i n g e i t h e r a l o c k - i n d e t e c t o r or an up-down counter. The l a t t e r d e v i c e c o n s i s t e d of a d i g i t a l e l e c t r o n i c counter which co u l d be switched to 24 c o u n t p o s i t i v e l y o r n e g a t i v e l y a t the microwave c h o p p i n g frequency. Thus o p t i c a l counts generated w i t h the microwave source switched on were s u b t r a c t e d from those produced w i t h the m i crowaves o f f . S i n c e the o n / o f f t i m e s were e q u a l , any microwave-induced change i n the luminescence showed up as a net p o s i t i v e o r n e g a t i v e c o u n t . I t was found n e c e s s a r y t o s u p p r e s s i n c o m i n g p u l s e s f o r a few m i c r o s e c o n d s each t i m e the counter was switched to prevent t r a n s i e n t pulse e r r o r s . Data were c o l l e c t e d w i t h a N o v a l l m i n i c o m p u t e r w h i c h cou l d sweep e i t h e r the magnetic f i e l d or the spectrometer i n a s e r i e s o f s t e p s o v e r the d e s i r e d r a n g e , p a u s i n g a t each step to re c o r d the output of the l o c k - i n d e t e c t o r or the up-down c o u n t e r . I f t h e p h o t o l u m i n e s c e n c e s p e c t r u m was r e q u i r e d , t he computer c o u l d r e c o r d the o u t p u t o f t h e p h o t o m u l t i p l i e r system d i r e c t l y by u s i n g an a n a l o g t o d i g i t a l c o n v e r t e r . The number o f s t e p s i n a s c a n , and the t i m e s p e n t i n c o l l e c t i n g data at each s t e p , were set by the o p e r a t o r . 2.2 Experimental Procedures. In most ODMR e x p e r i m e n t s the change i n l u m i n e s c e n c e c a u s e d by the microwave r e s o n a n c e was l e s s t h a n 1% so t h a t o b t a i n i n g adequate s i g n a l to n o i s e r a t i o s was o f t e n a p r o b l e m . As an i l l u s t r a t i o n : f o r an ODMR s i g n a l c a u s i n g a 0 . 1 % change i n luminescence w i t h a photon count r a t e of one 25 m i l l i o n per second, and a data c o l l e c t i o n time of one second per s t e p , the ODMR s i g n a l would g i v e an o u t p u t o f 1000 counts. T h i s was equal to the s t a t i s t i c a l f l u c t u a t i o n i n the one m i l l i o n photon c o u n t so t h a t the s i g n a l t o n o i s e r a t i o was u n i t y . S i n c e the s t a t i s t i c a l f l u c t u a t i o n s i n c r e a s e as the square r o o t of the t o t a l count, and the s i g n a l i n c r e a s e s l i n e a r l y , i t would be n e c e s s a r y t o spend 100 seconds per step to o b t a i n a s i g n a l to n o i s e r a t i o of 10. A t y p i c a l scan c o n t a i n e d 50 s t e p s and took about 1.5 h o u r s . S i n c e low f r e q u e n c y e f f e c t s such as d r i f t i n the count r a t e and microwave frequency become s i g n i f i c a n t over such t i m e s , data were g e n e r a l l y a c q u i r e d w i t h a s t e p t i m e o f 5 seconds and the computer was programmed to repeat the scan as many times as d e s i r e d and t o a v e r a g e the r e s u l t s . Low f r e q u e n c y n o i s e was thus f i l t e r e d out. E f f o r t s were made to extend the a v a i l a b l e running time by r e d u c i n g the heat l o s s from the Dewars, s i n c e the s i g n a l t o n o i s e r a t i o o f weak s i g n a l s c o u l d be i m p r o v e d by l o n g e r data c o l l e c t i o n t i m e s . Because the l i q u i d helium was u s u a l l y pumped to below the lambda p o i n t to reduce b u b b l i n g , i t was not p o s s i b l e t o t r a n s f e r more h e l i u m w i t h o u t i n t e r r u p t i n g t h e e x p e r i m e n t . When more h e l i u m was t r a n s f e r r e d i n t o an a l r e a d y c o l d Dewar, t h e o p t i c a l windows o f t e n became contaminated w i t h a i r which g e n e r a l l y leaked i n and f r o z e on to the i n n e r s u r f a c e s o f the f l a s k . B a f f l e s and i n s u l a t i o n were used to reduce heat leaks caused by conduction through 26 the h e l i u m gas and by r a d i a t i o n from the t o p of the Dewar. The maximum running times obtained were l i m i t e d by heat conduction down the Dewar w a l l s , waveguide, and i n the case of the superconducting magnet Dewar, the magnet support rods and c u r r e n t l e a d s . T h i s heat conduction was c a l c u l a t e d to be a p p r o x i m a t e l y 5 Watts f o r t h e s u p e r c o n d u c t i n g magnet and would be s u f f i c i e n t t o b o i l o f f 10 l i t r e s o f l i q u i d h e l i u m (a t y p i c a l amount used i n a run) i n approximately two hours due to the low l a t e n t heat of v a p o u r i z a t i o n of helium. The h e a t g e n e r a t e d by the 9.2 GHz m icrowaves a t f u l l power was approximately 2.5 Watts a l l o w i n g f o r l o s s e s i n the waveguide system and the 50% duty c y c l e due to chopping. The maximum l a s e r power was l e s s t h a n one h a l f Watt. Thus the l e n g t h of runs was even more s e v e r e l y l i m i t e d i n some experiments. Since the up-down counter was used i n t e r c h a n g e a b l y w i t h the l o c k - i n d e t e c t o r , a c o m p a r i s o n o f t h e two d e v i c e s i s i n o r d e r . The up-down counter reduces s t a t i s t i c a l f l u c t u a t i o n s i n the photon c o u n t s by summing a l a r g e number o f them as the s i g n a l g a t h e r i n g time i s i n c r e a s e d . The l o c k - i n d e t e c t o r m o n i t o r s an a n a l o g s i g n a l w hich i s p r o p o r t i o n a l t o the o p t i c a l count r a t e , and t h i s w i l l have the same s t a t i s t i c a l f l u c t u a t i o n s . The l o c k - i n d e t e c t o r r e d u c e s t h e s e w i t h the low-pass f i l t e r a f t e r d e t e c t i o n has o c c u r r e d and, f o r longer data c o l l e c t i o n t i m e s , the time constant of t h i s f i l t e r can be i n c r e a s e d t h u s r e d u c i n g the n o i s e . In our a p p a r a t u s the computer was programmed t o r e a d the l o c k - i n o u t p u t t w e n t y times per step and to average the r e s u l t s . T h i s produced the same e f f e c t as a longer time constant without smearing the s i g n a l f r o m s t e p t o s t e p . T h u s , i n p r i n c i p l e , t h e s i g n a l / n o i s e p e r f o r m a n c e s of the two systems s h o u l d be approximately the same. The l o c k - i n d e t e c t o r has the advantage o f b e i n g phase s e n s i t i v e so t h a t i f t h e l u m i n e s c e n c e changes a r e d e l a y e d w i t h r e s p e c t to the microwave s i g n a l t h i s can be compensated f o r by a d j u s t i n g the phase a n g l e on the l o c k - i n . The same e f f e c t c o u l d be achieved w i t h an up-down counter by s h i f t i n g the up-down s w i t c h i n g pulses w i t h r e s p e c t to the microwave s w i t c h i n g s i g n a l , b u t t h i s w o u l d r e q u i r e a d d i t i o n a l e l e c t r o n i c s . L o c k - i n d e t e c t o r s c o u l d operate i n the 100 kHz range i f i t were d e s i r e d t o s t u d y ODMR s i g n a l s a t such f r e q u e n c i e s : f o r example i n the examination of s p i n l a t t i c e r e l a x a t i o n times; w h i l e d i g i t a l up-down counters c o u l d not r e a d i l y be switched as r a p i d l y without causing unacceptable c o u n t i n g e r r o r s . The up-down c o u n t e r c o u l d o p e r a t e a t v e r y low s w i t c h i n g s p e e d s , however. In our work s w i t c h i n g f r e q u e n c i e s from 20 to 5000 Hz were used, most experiments b e i n g done a t 500 Hz. The q u a l i t y o f d a t a o b t a i n e d from the l o c k - i n d e t e c t o r and from the up-down counter was found to be about the same. The main advantage of the up-down counter was t h a t i t gave a n u m e r i c a l v a l u e f o r the ODMR s i g n a l 28 which, by comparison w i t h the observed o p t i c a l count r a t e , i n d i c a t e d the magnitude of the s i g n a l as a percentage change i n luminescence. 2.3 Commentary. I t s h o u l d be n o t e d t h a t a d e l a y o f a p p r o x i m a t e l y 6 months was in t r o d u c e d i n t o the experiments by b u i l d i n g work r e q u i r e d to i n s t a l l the superconducting magnet. Operation of the s y s t e m was a l s o s l o w e d down by t h e n a t u r e o f the c o m p u t i n g s y s t e m . The i n p u t was v i a punched paper t a p e and an o l d f a s h i o n e d t e l e p r i n t e r . T h u s , t o i n p u t the o p e r a t i n g s y s t e m r e q u i r e d about 20 m i n u t e s i f a l l went s m o o t h l y . In many c a s e s , however, a system f a u l t i n t h e l a s t s t a g e s o f input made a re - r u n n e c e s s a r y . A t e l e p r i n t e r i s not a s a t i s f a c t o r y s u b s t i t u t e f o r the t e r m i n a l i n p u t used on even the l e a s t e x p e n s i v e o f modern home computers. 29 Chapter 3. Gallium Phosphide and Zinc Telluride. 3.1. Introduction G a l l i u m p h o s p h i d e i s a I I I - V s e m i - c o n d u c t o r w i t h a c u b i c l a t t i c e . The band s t r u c t u r e i s shown i n F i g . 3 . 1 . The v a l e n c e band i s t w o f o l d d e g e n e r a t e a t the r p o i n t k = 0 , the heavy hole band having approximately e i g h t times the d e n s i t y of s t a t e s o f the l i g h t h o l e band. The t h i r d h o l e band i s s p l i t o f f by the s p i n o r b i t i n t e r a c t i o n and has i t s maximum 0 . 1 2 7 eV below the other two ( 2 4 ) . The conduction band has three e q u i v a l e n t minima l y i n g a l o n g the [ 1 , 0 , 0 ] d i r e c t i o n s a t the X p o i n t s ( 2 5 ) . The conduction band minimum at the r p o i n t l i e s above the minima a t t h e X p o i n t s by 0 . 5 eV as shown, thus t h e minimum band gap o f i n t e r e s t i n most e l e c t r o n i c and l u m i n e s c e n c e measurements i s i n d i r e c t . The c o n d u c t i o n and v a l e n c e bands a r e a p p r o x i m a t e l y s p h e r i c a l at the r p o i n t w i t h e f f e c t i v e masses 0 . 1 3 (26 ) f o r the e l e c t r o n s and 0 . 6 7 and 0 . 1 7 f o r the heavy and l i g h t holes ( 27 ) r e s p e c t i v e l y , a l l values are i n u n i t s of mass of the f r e e e l e c t r o n . The X p o i n t minima a r e a n i s o t r o p i c w i t h l o n g i t u d i n a l and t r a n s v e r s e e f f e c t i v e mass parameters = 1.5 and mt = ° -1 8 ( 2 8 ) • The g v a l u e o f e l e c t r o n s bound t o n e u t r a l d o n o rs has been measured to be 1 . 9 9 7 6 + 0 . 0 0 0 8 by E P R experiments ( 2 9 ) , 30 FIG. 3.1 G A P BANDSTRUCTURE Direct band gap Indirect band gap 2.878 EV 2.339 EV 0.127 EV Valence bands r x 31 and a v a l u e o f 1.996 +_ 0.002 was d e t e r m i n e d f o r photo e x c i t e d e l e c t r o n s u s i n g ODMR (30 ). The g value of holes has been es t i m a t e d from Zeeman measurements of e x c i t o n s bound at n i t r o g e n i m p u r i t i e s t o be 0.99 +_ 0.06 (31). 3.2. Exciton formation and luminescence in GaP O p t i c a l r e c o m b i n a t i o n o f p h o t o - e x c i t e d e l e c t r o n s and h o l e s o c c u r s l a r g e l y a t d e f e c t s and i m p u r i t y s i t e s . An important c l a s s of recombination c e n t r e s are i s o e l e c t r o n i c i m p u r i t i e s w h i c h form l o c a l i z e d s t a t e s o f e x c i t o n s i n the band gap. N i t r o g e n and b i s m u t h form such c e n t r e s i n GaP being i s o e l e c t r o n i c w i t h phosphorous. N i t r o g e n i n p a r t i c u l a r i s g e n e r a l l y p r e s e n t as a r e s i d u a l i m p u r i t y i n GaP i n c o n c e n t r a t i o n s o f t h e o r d e r o f one p a r t i n a m i l l i o n . E x c i t o n recombination can a l s o occur at n e u t r a l donors such as s u l p h u r , s e l e n i u m and t e l l u r i u m w hich s u b s t i t u t e f o r phosphorous as donors i n GaP (29). The e f f i c i e n c y of o p t i c a l r e c o m b i n a t i o n a t n e u t r a l donors i s much l o w e r than a t i s o e l e c t r o n i c c e n t r e s due to the high p r o b a b i l i t y of Auger r e c o m b i n a t i o n/w i t h the donor e l e c t r o n t a k i n g the energy of the e x c i t o n and becoming i o n i z e d (32). D o n o r - a c c e p t o r p a i r (DAP) r e c o m b i n a t i o n i s a n o t h e r important process i n m a t e r i a l s w i t h a high d e n s i t y of donors and a c c e p t o r s , i n which e l e c t r o n s and ho l e s trapped at donor and a c c e p t o r i m p u r i t i e s r e c o m b i n e r a d i a t i v e l y , t h e r e c o m b i n a t i o n e n e r g y d e p e n d i n g on t h e d o n o r - a c c e p t o r 32 s e p a r a t i o n . A m o d i f i c a t i o n of t h i s process has been observed i n GaP i n which donor bound e l e c t r o n s recombine w i t h holes t r a p p e d a t i s o e l e c t r o n i c b i s m u t h c e n t r e s (33). In our measurements, however, donor-acceptor p a i r r ecombination was not s i g n i f i c a n t . E x c i t o n s may form a t i s o e l e c t r o n i c r e c o m b i n a t i o n c e n t r e s by two methods. An e l e c t r o n and h o l e may form an e x c i t o n w h i l e f r e e and the e x c i t o n become t r a p p e d a t an i m p u r i t y , or the i m p u r i t y may bind one p a r t i c l e f i r s t a f t e r which the second becomes trapped i n the Coulomb f i e l d of the f i r s t p a r t i c l e (30). In GaP the i s o e l e c t r o n i c i m p u r i t y b i s m u t h has been shown t o b i n d a h o l e w i t h an e nergy o f approximately 40 meV by DAP luminescence measurements (33) as w e l l as by the o b s e r v a t i o n of d o n o r - l i k e e l e c t r o n e x c i t e d s t a t e s at bismuth c e n t r e s (34) and by a n a l y s i s of the phonon a s s i s t e d recombination of bound e x c i t o n s (35). The n i t r o g e n c e n t r e i s t h o u g h t t o be an e l e c t r o n t r a p although the b i n d i n g energy of approximately 8 meV deduced from r a d i a t i v e decay t i m e measurements (36) has made t h i s more d i f f i c u l t t o p r o v e . A n a l y s i s of the phonon a s s i s t e d r e c o m b i n a t i o n of n i t r o g e n bound e x c i t o n s s u p p o r t s t h i s i n t e r p r e t a t i o n ( 3 7 ) a s d o e s a c o m p a r i s o n o f e l e c t r o n e g a t i v i t y d i f f e r e n c e s between n i t r o g e n , bismuth, and the phosphorous atoms which they r e p l a c e (38). 33 The f r e e e x c i t o n i n GaP has a b i n d i n g e n e r g y of 10 meV (39), and on the i s o e l e c t r o n i c i m p u r i t i e s n i t r o g e n and b i s m u t h the t o t a l b i n d i n g e n e r g i e s a r e 21 meV and 107 meV r e s p e c t i v e l y (36). Luminescence i s p r i m a r i l y observed from t r a p p e d e x c i t o n s . The l u m i n e s c e n c e s p e c t r u m o b s e r v e d from n i t r o g e n and b i s m u t h c e n t r e s d i f f e r s m a r k e d l y as shown i n Fig.3.2. The n i t r o g e n luminescence spectrum i s dominated by the so c a l l e d A and B l i n e no-phonon t r a n s i t i o n s . The A and B l i n e s are caused by e x c i t o n s w i t h t o t a l angular momenta J of 1 and 2 r e s p e c t i v e l y , formed by the a n t i p a r a l l e l o r p a r a l l e l a l i g n m e n t o f a s p i n 1/2 e l e c t r o n w i t h a s p i n 3/2 h o l e . The phonon a s s i s t e d t r a n s i t i o n of A and B e x c i t o n s are r e l a t i v e l y weak due t o t h e s m a l l b i n d i n g energy of the e l e c t r o n to the n i t r o g e n atom (40). At lower energy a t h i r d l i n e , g e n e r a l l y r e f e r r e d t o as the C l i n e r e s u l t s f r o m the r e c o m b i n a t i o n o f e x c i t o n s a t n e u t r a l s u l p h u r d o n o r i m p u r i t i e s . The bismuth c e n t e r luminescence i s dominated by phonon a s s i s t e d t r a n s i t i o n s . At low t e m p e r a t u r e the A l i n e i s not seen due t o t h e r m a l i z a t i o n w i t h the B l i n e w h i c h i n t h i s c ase l i e s 2.7 meV l o w e r i n e n e r g y . The B l i n e , no-phonon t r a n s i t i o n , i s seen o n l y w eakly s i n c e the decay o f the J=2 e x c i t o n i s f o r b i d d e n and can o n l y o c c u r by m i x i n g w i t h the A l i n e s t a t e s i n the p r e s e n c e o f a m a g n e t i c f i e l d , c r y s t a l s t r a i n s , or w i t h the a s s i s t a n c e of phonons. The f a c t t h a t a no-phonon t r a n s i t i o n can be seen a t a l l i n an i n d i r e c t gap semiconductor i s due to the f a c t t h a t , being l o c a l i z e d at an 34 LU U o 2.305 EV 2.315 EV i I c B IT J l U 5370 A 5340 A C O I 2,20 EV - The A and B lines due to N and the C li n e caused by S impurities are shown C L . , 2.PQ FV < CJ3 a i < C D CD 5000 A The B exciton no phonon l i n e and are seen 35 G A P - B I numerous phonon replicas 5500 A i m p u r i t y , the e l e c t r o n or hole wave-function i s spread out i n k space and a f i n i t e p r o b a b i l i t y o f a d i r e c t t r a n s i t i o n e x i s t s . The bulk of the luminescence from the bismuth c e n t r e i s contained i n the broad band of phonon a s s i s t e d t r a n s i t i o n s , the v a r i o u s peaks c o r r e s p o n d t o c o m b i n a t i o n s o f d i f f e r e n t t y p e s o f phonons and have been i d e n t i f i e d by Dean and h i s co-workers (33). The g r e a t e r s t r e n g t h of the phonon r e p l i c a s i n t h e B i s p e c t r u m as compared t o the N s p e c t r u m i s due to the s t r o n g e r b i n d i n g of the h o l e t o the B i atom, which r e s u l t s i n stronger c o u p l i n g to the phonon modes. The e x c i t o n s t a t e s formed at i s o e l e c t r o n i c i m p u r i t i e s i n GaP have been d e s c r i b e d by C a v e n e t t (30) i n e x p l a i n i n g t h e e f f e c t o f e l e c t r o n p a r a m a g n e t i c r e s o n a n c e on photoluminescence. The e x c i t o n s t a t e s formed from s p i n 1/2 e l e c t r o n s and s p i n 3/2 holes are shown i n F i g 3.3 w i t h t h e i r e x p e c t e d s p l i t t i n g i n a m a g n e t i c f i e l d . The z e r o f i e l d s p l i t t i n g shown f o r t h e B l i n e has b e e n o b s e r v e d i n l u m i n e s c e n c e f r o m b i s m u t h (41) and i n m u l t i - e x c i t o n complexes w i t h N c e n t r e s (42) but i s unobservable f o r s i n g l e e x c i t o n s bound t o n i t r o g e n atoms. The s p l i t t i n g has been a t t r i b u t e d to the c r y s t a l f i e l d which i s expected to be f e l t more s t r o n g l y at the bismuth i m p u r i t y which i s r e p u l s i v e to the e l e c t r o n i n an e x c i t o n (41). However Morgan (43) has shown t h a t such s p l i t t i n g can be c a u s e d by c o u p l i n g o f the 36 FIG, 3.3 EXCITON STATES IN G A P ELECTRONS 1/2 n: -1/1 n, HOLES J = l J = 2 Ol TT O l 1 . 1 = 1 . 0 = 1 „ - 1 = 2 . 2 = 2 . 1 = 2 , 0 = 2 , - 1 = 2 , -2 = -1/2 11/2,1$3/2,1/2) + 3/2 |l/2>-l/2)f3/2^/2) vJl\\jiry7)\i>riAii) - vrrJi/2,i/2)/3/2,-i/2) 1/2 11/2,-172) (3/2,-1/2) - /3>2 Jl/2,l/2>/3/2,-3/2) 172,172)13/^ ,3 )^ 1/2 11/2,-1/^ l3/2,3/2> + /J/2 |l/2,l/2)/3/2,l/?) 1//2 | l/2,l/2)|3/2,-1^> + l//?/l/2,-l/2>/3/2,l/?) 1/2 |l/2,l/2)|3/2,-3/2> +/3Z2 / l/2,-17?>/3/2,-l/2> l^ ,-l/2))3/2,-3^> I Highly forbidden 0 , 0 The exciton states formed by a spin 1/2 electron and a spin 3/2 hole are shown with their composition, s p l i t t i n g i n a magnetic f i e l d , and optical transitions e x c i t o n to phonon modes w i t h r3 and T$ symmetries. Coupling to the mode (corresponding to s t r a i n along the [1,0,0] a x i s ) t e n d s to r a i s e the t r i p l e t w h i l e c o u p l i n g t o the mode ([ 1 , 1 , 1 ] a x i s ) r a i s e s t h e d o u b l e t . As a l r e a d y m e n t i o n e d , the J=2 e x c i t o n s can o n l y decay by m i x i n g w i t h the J=l s t a t e s , thus the |2,2> and |2,-2> e x c i t o n s having no c o r r e s p o n d i n g A s t a t e s to mix w i t h have d i p o l e f o r b i d d e n t r a n s i t i o n s and do not c o n t r i b u t e l u m i n e s c e n c e t o t h e B l i n e . In a magnetic f i e l d the v a r i o u s Zeeman components are e x p e c t e d t o be c i r c u l a r l y p o l a r i z e d as s hown, a± r e p r e s e n t i n g r i g h t and l e f t c i r c u l a r p o l a r i z a t i o n f o r luminescence e m i t t e d p a r a l l e l to the magnetic f i e l d w h i l e ir r e p r e s e n t s l i n e a r p o l a r i z a t i o n i n l u m i n e s c e n c e e m i t t e d a t r i g h t angles to the f i e l d . To c a l c u l a t e the expected change i n luminescence from the A and B l i n e s w i t h the a p p l i c a t i o n o f an e l e c t r o n p a r a m a g n e t i c r e s o n a n c e s i g n a l , the r e l a t i v e r a t e s o f f o r m a t i o n of the v a r i o u s e x c i t o n s t a t e s a r e c a l c u l a t e d a s s u m i n g a t h e r m a l d i s t r i b u t i o n o f e l e c t r o n and h o l e s p i n s t a t e s (ni - ng ) b e f o r e e x c i t o n f o r m a t i o n , a l s o a s s u m i n g t h a t the p r o b a b i l i t y of a p a r t i c u l a r e x c i t o n f o r m i n g i s p r o p o r t i o n a l to the p o p u l a t i o n s of e l e c t r o n s and holes w i t h the a p p r o p r i a t e s p i n s t a t e s . The e x c i t o n s t a t e s p i n wave f u n c t i o n s shown i n Fig.3.3 must be m u l t i p l i e d by t h e i r complex conjugates to give the 38 p r o b a b i l i t i e s , thus the c o e f f i c i e n t s of the v a r i o u s e l e c t r o n and h o l e s p i n s t a t e s t h a t make up the e x c i t o n l e v e l s a r e squared. For example, the r e l a t i v e number of | l , l > e x c i t o n s formed would be: Pl l = nl « n 4 /4 + 3.n2-n3 /4 Taking the t o t a l number of e l e c t r o n s or holes to be: n = nl + n2 + n3 + n4 + ns + n6 the v a l u e s of n i - n6 m aY D e c a l c u l a t e d assuming a thermal d i s t r i b u t i o n : — ae — ae n i= n . e / ( 1 + e ) ~ae n2 = n/(1 + e ) ~3 ah , , , "ah "2ah - 3a h n 3 = n . e / ( 1 + e + e + e ) -2ah -oth ~2ah ~3ahv n 4 = n . e / ( 1 + e + e + e ) where: ae = ge$H/kT ah = gh&H/kT ge and gn b e i n g the e l e c t r o n and h o l e g v a l u e s , H the ma g n e t i c f i e l d , g t h e Bohr magnetron and kT the t h e r m a l energy. When an EPR s i g n a l i s a p p l i e d , the p o p u l a t i o n s o f the 39 e l e c t r o n s p i n s t a t e s a r e e q u a l i z e d a s s u m i n g a . s a t u r a t i o n s i g n a l . T h e r e f o r e : J"*! = n2 = n/2 The r e l a t i v e f o r m a t i o n r a t e s of the v a r i o u s e x c i t o n s t a t e s have been c a l c u l a t e d u s i n g t h i s procedure as shown i n Table 3.1. The e l e c t r o n and h o l e g v a l u e s a r e t a k e n t o be 2 and 1, r e s p e c t i v e l y f o r t e m p e r a t u r e s o f 1.6 and 4 d e g r e e s K and a ma g n e t i c f i e l d s t r e n g t h o f 3.4 k i l o G a u s s . The change i n i n t e n s i t y w i t h the a p p l i c a t i o n of microwaves i n d i c a t e d by Pu i s shown f o r e a c h s t a t e and the t o t a l change i n i n t e n s i t y f o r the A and B l i n e s i s a l s o c a l c u l a t e d . S e v e r a l p o i n t s are w o r t h n o t i n g . The A and B l i n e s a r e b o t h e x p e c t e d t o decrease i n i n t e n s i t y at the EPR resonance as more e x c i t o n s a r e f o rmed i n t h e n o n - r a d i a t i v e | 2,2> s t a t e r the change i n the A l i n e i s g r e a t e r t h a n t h a t i n t h e B l i n e , and the e f f e c t decreases r a p i d l y w i t h i n c r e a s i n g temperature. I t can a l s o be seen t h a t the changes i n i n d i v i d u a l e x c i t o n s t a t e s are l a r g e r than i n the t o t a l luminescence, and can be e i t h e r p o s i t i v e or n e g a t i v e so t h a t i f t he change i n one Zeeman c o m p o n e n t o f t h e A o r B l i n e i s m o n i t o r e d u s i n g h i g h r e s o l u t i o n s p e c t r o s c o p y o r a c i r c u l a r p o l a r i z a t i o n f i l t e r the ODMR s i g n a l observed can be e i t h e r p o s i t i v e or negative depending upon which component i s used, and should be l a r g e r than the ODMR s i g n a l shown by the e n t i r e (A or B) l i n e . 40 TABLE 3.1 MICROWAVE INDUCED LUMINESCENCE CHANGES P l l P U1 p10 p Y o P l - l p¥ - l 1.6 K 0.5212 0.4834 0.4087 0.4047 0.3170 0.3384 4 K 0.5077 0.4931 0.4599 0.4591 0.4158 0.4275 P22 p * 2 P2l ^ 1 ?20 P 2o P2-1 P 2 - l P2-2 P2-2 A l i n e change B l i n e change 0.4291 0.5000 0.4217 0.4501 0.4087 0.4047 0.3917 0.3633 0.3720 0.3258 1.636% 0.327% 0.4715 0.5000 0.4661 0.4792 0.4599 0.4591 0.4529 0.4399 0.4453 0.4213 0.267% 0.051% The numbers i n t h i s t a b l e r e p r e s e n t the r e l a t i v e p o p u l a t i o n s o f the v a r i o u s e x c i t o n s t a t e s w i t h and without a resonance s i g n a l . They are not n o r m a l i z e d . 41 A number o f p r o c e s s e s may r e d u c e the e x p e r i m e n t a l l y o b s e r v e d ODMR s i g n a l s below the l e v e l s p r e d i c t e d by the t h e o r y . N o n - s a t u r a t i o n o f t h e e l e c t r o n s p i n s by t h e microwave s i g n a l , e i t h e r due to inadequate microwave power or t o inhomogeneous b r o a d e n i n g o f the e l e c t r o n r e s o n a n c e , w o u l d r e d u c e t h e e f f e c t s e e n i n a l l e x c i t o n s t a t e s . T h e r m a l i z a t i o n between the d i f f e r e n t Zeeman components would d i m i n i s h t he l a r g e r ODMR s i g n a l s e x p e c t e d i n i n d i v i d u a l Zeeman l i n e s and the s i g n a l s from the e n t i r e A or B l i n e s would be reduced as w e l l . T h e r m a l i z a t i o n between the A and B l i n e s t a t e s would e q u a l i z e the s i z e of the ODMR s i g n a l seen i n e i t h e r l i n e , i n c r e a s i n g t h e B and d e c r e a s i n g t h e A s i g n a l . I n c o m p l e t e t h e r m a l i z a t i o n o f the e l e c t r o n s p i n s before e x c i t o n f o r m a t i o n would reduce the observed e f f e c t which depends on t h e r m a l l y induced s p i n p o l a r i z a t i o n of the e l e c t r o n p o p u l a t i o n . 3.3 Other work on GaP T i t l e and h i s c o - w o r k e r s have o b s e r v e d p a r a m a g n e t i c resonance of e l e c t r o n s at n e u t r a l donor i m p u r i t i e s S,Se and Te i n GaP (29,44). They o b t a i n e d a g v a l u e o f 1.9976 _+ 0.0008 which they p r e d i c t should be approximately the same as the g v a l u e o f an e l e c t r o n i n the c o n d u c t i o n band. C a v e n e t t (30) has measured th e c o n d u c t i o n e l e c t r o n g v a l u e d i r e c t l y u s i n g ODMR measurements of luminescence from the N c e n t r e , o b t a i n i n g t he v a l u e g=1.996 +_ 0.002. The s i g n a l 42 o b s e r v e d b y C a v e n e t t was s m a l l e r t h a n p r e d i c t e d t h e o r e t i c a l l y , r e p r e s e n t i n g o n l y a 0.1% c h a n g e i n l u m i n e s c e n c e , no d e p e n d e n c e o f t h e ODMR s i g n a l on p o l a r i z a t i o n was found, and the B l i n e appears to have given as s t r o n g a s i g n a l as t h e A l i n e i n c o n t r a s t t o t h e t h e o r e t i c a l p r e d i c t i o n s . ODMR s i g n a l s i n luminescence from Cu doped GaP have a l s o been observed (45) and are a t t r i b u t e d to microwave induced t r a n s i t i o n s between e x c i t o n s t a t e s at d e f e c t s which i n v o l v e p a i r s of Cu atoms. 3 . 4 R e s u l t s ODMR s i g n a l s i n luminescence from N,S and B i ce n t r e s i n GaP were measured and a r e shown i n F i g s . 3.4 t o 3.6 (46). The g v a l u e s d e r i v e d f o r the t h r e e l u m i n e s c e n c e c e n t r e s agree t o w i t h i n t he e x p e r i m e n t a l e r r o r g i v i n g a v a l u e g = 1.9993 +_ 0.005 which i s a l s o i s o t r o p i c . Attempts were made to o b s e r v e r e s o n a n c e s o f h o l e s o r t o t o o b s e r v e r e s o n a n c e s between e x c i t o n s t a t e s ; these were, however, u n s u c c e s s f u l . Some e f f o r t was made to analyse the observed resonances i n more d e t a i l . The N and S ce n t r e s were both present i n the same sample as r e s i d u a l i m p u r i t i e s . D i f f e r e n t samples were used to measure the B i center luminescence, and these had a f a i r l y heavy and somewhat inhomogeneous d o p i n g o f B i . The ODMR s i g n a l s from the B i samples were observed to be weaker than t h o s e from the p u r e r samples used f o r the N and S measurements. 43 The e l e c t r o n ODMR si g n a l seen as a 1% change i n the N luminescence FIG. 3.5 O D M R IN 6 A P -MAGNETIC FIELD KG ODMR signal from the S luminescence FIG. 3.6 O D M R IN G A P - B I 3.5 MAGNETIC FIELD KG The O D M R siqnal seen s<= a r , n i a seen as an 0.1% change in the Bi luminescence The microwave power dependence o f the ODMR s i g n a l s t r e n g t h from the N l u m i n e s c e n c e was measured and the r e s u l t s a r e shown i n Fig.3.7. The f i t shown by the s o l i d l i n e i s c a l c u l a t e d on the b a s i s o f a two l e v e l s y s t e m a t the sample t e m p e r a t u r e (1.6 de g r e e s K) b e i n g s a t u r a t e d by a r a d i o frequency f i e l d . The experimental p o i n t s were obtained by s c a n n i n g the r e s o n a n c e a t a s e r i e s o f microwave power s e t t i n g s , t h e s c a t t e r b e i n g p r i m a r i l y due t o d r i f t i n the o p t i c a l system and sample t e m p e r a t u r e between s c a n s . The r e s u l t s i n d i c a t e t h a t s a t u r a t i o n o f the r e s o n a n c e was a c h i e v e d a t the maximum microwave power l e v e l s , g i v i n g an ODMR s i g n a l t h a t r e p r e s e n t e d a p p r o x i m a t e l y a 1% change i n luminescence. S i m i l a r measurements on the B i luminescence ODMR s i g n a l , a l t h o u g h hampered by the poor s i g n a l t o n o i s e r a t i o , i n d i c a t e d t h a t t h i s resonance was a l s o s a t u r a t e d . The r e l a t i v e ODMR s i g n a l s t r e n g t h from the A and B l i n e s of the N l u m i n e s c e n c e was measured by s e l e c t i n g the A or B l i n e w i t h t h e s p e c t r o m e t e r and s c a n n i n g the r e s o n a n c e . Both l i n e s were found to giv e the same ODMR s i g n a l s t r e n g t h . The B i c e n t r e l u m i n e s c e n c e was a l s o o b s e r v e d t o show the ODMR s i g n a l e q u a l l y i n the z e r o phonon l i n e and the phonon r e p l i c a s . Attempts were made to observe the p r e d i c t e d enhancement of the ODMR s i g n a l by s e l e c t i n g p a r t i c u l a r Zeeman components u s i n g a c i r c u l a r p o l a r i z a t i o n a n a l y s e r , t a k i n g t h e 47 •3,7 O D M R MICROWAVE POWER DEPENDENCE SIGNAL PERCENT •0016 . 008 . 04 0,2 1,0 MICROWAVE POWER WATTS The N luminescence ODMR signal strength as a function o microwave power. The resonance i s seen to be saturated maximum power 48 l u m i n e s c e n c e p a r a l l e l t o the m a g n e t i c f i e l d . No change i n the ODMR s i g n a l c o u l d be seen f o r e i t h e r r i g h t o r l e f t c i r c u l a r p o l a r i z a t i o n . T h i s prompted an i n v e s t i g a t i o n of the Zeeman s p l i t t i n g of t h e A and B l i n e s ; a t y p i c a l s p e c t r u m i s shown i n F i g . 3 . 8 . w i t h t he e x c i t o n s t a t e s r e s p o n s i b l e f o r the v a r i o u s l i n e s shown. C i r c u l a r p o l a r i z a t i o n i s e x p e c t e d i n the <2,+_l| and <l,+_l| l i n e s and s h o u l d r e s u l t i n t h e i r e x t i n c t i o n when a c i r c u l a r a n a l y z e r o f the a p p r o p r i a t e p o l a r i z a t i o n i s p l a c e d i n t h e o p t i c a l s y s t e m . T h i s was done and no v a r i a t i o n i n the Zeeman s p e c t r u m was seen f o r e i t h e r p o l a r i z a t i o n . Thus a s i g n i f i c a n t c i r c u l a r p o l a r i z a t i o n of the Zeeman components was not being produced even a t the hi g h magnetic f i e l d s used. ( A p o l a r i z a t i o n of a few percent may have e x i s t e d but would have been too s m a l l to be seen by the method j u s t d e s c r i b e d ) . ODMR measurements of i n d i v i d u a l components cou l d not be made s i n c e t he s p l i t t i n g s c o u l d not be r e s o l v e d a t the magnetic f i e l d s t r e n g t h used i n the ODMR experiment. Temperature dependent measurements of the ODMR s i g n a l s were r a t h e r l i m i t e d s i n c e the samples were immersed i n l i q u i d h e l i u m , g e n e r a l l y pumped to below the lambda p o i n t to e l i m i n a t e b u b b l i n g . By f o c u s s i n g the l a s e r e x c i t a t i o n onto a s m a l l a r e a o f t h e s a m p l e and i n c r e a s i n g t h e power 49 FIG. 3.8 G A P - N ZEEMAN SPECTRUM 2,310 EV 2.315 EV 5355 A 5345 A The spectrum of the N f p n t ra i , ° f 2 5 k Gauss S t^S S « S : " S " 2=?J 3 " ' a 9 n e t l C f i e l d y uirrerent exciton components 50 s i g n i f i c a n t h e a t i n g c o u l d be p r o d u c e d . For the GaP- N sample the r a t i o o f the A and B l i n e l u m i n e s c e n c e p r o v i d e s a rough thermometer s i n c e at low temperatures t h e r m a l i z a t i o n favours the B l i n e . Comparing the ODMR r e s u l t s f o r low and high l e v e l l a s e r e x c i t a t i o n , the ODMR s i g n a l s t r e n g t h was observed to drop by a f a c t o r o f a p p r o x i m a t e l y 2 a t h i g h l a s e r power w h i c h a p p a r e n t l y h e a t e d the l u m i n e s c i n g r e g i o n o f the sample t o roughly 2 degrees K. In t h e B i doped sample h i g h l a s e r power d e n s i t i e s were o b s e r v e d t o b r i n g up a s e r i e s o f new l i n e s i n t h e luminescence spectrum i n c l u d i n g one at 5555A.U. j u s t above the B l i n e . O bviously these were the A l i n e and i t s phonon r e p l i c a s w h i c h a r e not seen a t a l l a t low t e m p e r a t u r e due t o the g r e a t e r s p l i t t i n g between t h e A and B l i n e s . No ODMR s i g n a l s c o u l d be d e t e c t e d i n the new l i n e s ; p r e s u m a b l y t h e in c r e a s e d temperature made the e f f e c t unmeasurable. The r e s u l t s m e n t i o n e d so f a r were o b t a i n e d f r o m measurements at 9.2 GHz microwave frequency. A measurement of t he ODMR s i g n a l was a l s o made a t 36.3 GHz f o r the N c e n t r e l u m i n e s c e n c e w i t h r e s u l t s shown i n F i g . 3.9 . The s i g n a l was c o n s i d e r a b l y weaker than a t 9.2 GHz d e s p i t e the f a c t t h a t a c c o r d i n g t o t h e o r y , t h e ODMR e f f e c t s h o u l d g e t stro n g e r at higher magnetic f i e l d s . T h i s was presumably due to the lower a v a i l a b l e microwave power l e v e l and absence of 51 FIG. 3.9 O D M R SIGNAL AT 36.3 GHZ a r e s o n a n t c a v i t y (the 9.2 GHz c a v i t y a m p l i f i e d the power l e v e l at the sample by a f a c t o r of the order of 1000). By c o m p a r i n g t h e w i d t h s of the r e s o n a n c e s a t 9.2 and 36.3 GHz i t c a n be s e e n t h a t t h e r e s o n a n c e r e t a i n e d approximately the same width i n f i e l d i.e. became r e l a t i v e l y narrower i n frequency i n d i c a t i n g t h a t the l i n e width i s due to homogeneous broadening. 3.5 Discussion Our o b s e r v a t i o n s of ODMR of e l e c t r o n s i n GaP suggest the f o l l o w i n g remarks. The f a c t t h a t the s i g n a l was observed f o r s e v e r a l l u m i n e s c e n c e s i n c l u d i n g N w h i c h a c t s as an e l e c t r o n t r a p and B i which i s a h o l e t r a p shows t h a t the e f f e c t i s due t o r e s o n a n c e o f e l e c t r o n s i n the c o n d u c t i o n band, a t l e a s t i n the c a s e o f B i . C a v e n e t t (30) has suggested t h a t f o r the N c e n t r e the e l e c t r o n trapped at the N c e n t r e b e f o r e c a p t u r i n g a h o l e i s a f f e c t e d by t h e r e s o n a n c e . I f t h i s i s s o , i t must have th e same g v a l u e and s p i n r e l a x a t i o n time as the f r e e e l e c t r o n s to w i t h i n the a c c u r a c y of t h e e x p e r i m e n t s . Measurements at 36.3GHz i n d i c a t e d t h a t t h e r e s o n a n c e was homogeneously b r o a d e n e d , g i v i n g t h e s p i n r e l a x a t i o n t i m e as a p p r o x i m a t e l y 4 nanoseconds from the l i n e w i d t h s . Whether t h i s r epresents the s p i n - l a t t i c e r e l a x a t i o n t i m e or the e l e c t r o n l i f e t i m e b e f o r e t r a p p i n g a h o l e , w h i c h i s known t o be s h o r t e r t h a n the e x c i t o n decay t i m e (36) i s not c l e a r . The l i n e w i d t h 53 observed by Cavenett (30) was comparable to our r e s u l t s . The l i n e w i d t h s observed by T i t l e (29) u s i n g c o n v e n t i o n a l EPR at 77 degrees K were a p p r e c i a b l y s m a l l e r than ours (by as much as a f a c t o r o f 4) a l t h o u g h t h e l i n e w i d t h s i n c r e a s e d w i t h i m p u r i t y c o n c e n t r a t i o n . Since the EPR r e s u l t s would not be s u b j e c t t o l i f e t i m e b r o a d e n i n g due t o r e c o m b i n a t i o n , and s i n c e our samples were o f h i g h e r p u r i t y t h a n T i t l e ' s doped m a t e r i a l , i t i s r e a s o n a b l e , t o c o n c l u d e t h a t t h e l i f e t i m e determined from our r e s u l t s r e p r e s e n t s the e l e c t r o n l i f e t i m e a g a i n s t hole c a p t u r e . An a t t e m p t was a l s o made t o d e t e r m i n e t h e l i n e broadening mechanism by a n a l y s i n g the resonance l i n e shapes. The r e s u l t s are given i n Appendix A f o r s e v e r a l sets of data from the N c e n t r e l u m i n e s c e n c e . However, i t c o u l d n o t be c o n c l u s i v e l y shown whether the data were b e t t e r f i t t e d by a Gaussian or by a L o r e n t z i a n l i n e p r o f i l e . The s t r e n g t h o f the ODMR s i g n a l seen from the N c e n t r e luminescence was observed to be equal f o r the A and B l i n e , r e p r e s e n t i n g a p p r o x i m a t e l y a 1% change i n l u m i n e s c e n c e a t resonance which i s l a r g e r than the p r e d i c t e d s i g n a l f o r the B l i n e but s m a l l e r than f o r the A l i n e . T h i s i s presumably due t o t h e r m a l i z a t i o n between A and B l i n e s t a t e s w h i c h i s known t o be r a p i d (36) , and would r e s u l t i n the ODMR induced changes i n the two l i n e s being averaged. Thus the observed s i g n a l i s the same as th a t which would be obtained 54 by monitoring the A and B l i n e s combined. Agreement w i t h theory i s then q u i t e good, and the e x p e r i m e n t a l l y observed s i g n a l approximates the maximum p r e d i c t e d t h e o r e t i c a l l y . The ODMR s i g n a l o b s e r v e d i n the B i l u m i n e s c e n c e was c o n s i d e r a b l y weaker than t h a t of the N centre s i g n a l . The Bi luminescence at 1.6 degrees K d e r i v e s e n t i r e l y from the B l i n e but the ODMR s i g n a l should s t i l l be the average of the A and B l i n e s i g n a l s s i n c e the A e x c i t o n s a r e s t i l l f ormed but t h e r m a l i z e i n t o B e x c i t o n s due to the l a r g e r s p l i t t i n g . The r e a s o n f o r the weaker s i g n a l i s p r o b a b l y the l o n g e r recombination time f o r e x c i t o n s at B i ce n t r e s ( r e p o r t e d l y a f a c t o r o f 30 g r e a t e r t h a n f o r N (36) ) wh i c h would a l l o w more t h e r m a l i z a t i o n w i t h i n the B e x c i t o n s t a t e s , t h u s weakening the s i g n a l . Our i n a b i l i t y t o o b s e r v e enhancement o f the ODMR s i g n a l s by d e t e c t i n g c i r c u l a r l y p o l a r i z e d components of the l u m i n e s c e n c e was e x p l a i n e d by the absence o f c i r c u l a r p o l a r i z a t i o n i n the Zeeman components of the A and B l i n e s even at high magnetic f i e l d s . Zeeman s t u d i e s of the N, S and B i c e n t r e s i n GaP r e p o r t e d i n the l i t e r a t u r e (31,41) have not d e s c r i b e d the o b s e r v a t i o n of p o l a r i z a t i o n i n the Zeeman components, although there i s no statement t h a t p o l a r i z a t i o n was l o o k e d f o r and not f o u n d . C a v e n e t t (30) r e p o r t s h a v i n g looked f o r p o l a r i z a t i o n dependence of the ODMR s i g n a l from the N centre w i t h negative r e s u l t s . Why p o l a r i z a t i o n has not been seen i s not c l e a r but may be due t o c r y s t a l s t r a i n s or 5 5 d e f e c t s . The B l i n e o p t i c a l decay occurs through mixing with the A l i n e s t a t e s by s t r a i n s o r an a p p l i e d m a g n e t i c f i e l d . In our e x p e r i m e n t s i t was o b s e r v e d t h a t the B l i n e i n t e n s i t y was not s i g n i f i c a n t l y a f f e c t e d by the magnetic f i e l d s used, i n d i c a t i n g t h a t c r y s t a l d e f e c t s were p r e d o m i n a n t l y r e s p o n s i b l e f o r the m i x i n g of the e x c i t o n l e v e l s . S i n c e o b s e r v a t i o n o f m a g n e t i c c i r c u l a r p o l a r i z a t i o n depends on a l i g n m e n t o f the e x c i t o n s w i t h the m a g n e t i c f i e l d , the p r e s e n c e o f random d e f e c t s i n t e r a c t i n g s t r o n g l y w i t h the e x c i t o n s w i l l d i s o r i e n t them and r e d u c e t h e c i r c u l a r p o l a r i z a t i o n of the e m i t t e d luminescence. Such e f f e c t s would a l s o b r o a d e n t h e Zeeman l i n e s and an i n v e s t i g a t i o n a l o n g these l i n e s might r e s o l v e the q u e s t i o n . A n o t h e r n e g a t i v e r e s u l t was the f a i l u r e t o o b s e r v e resonances e i t h e r of holes or between e x c i t o n s t a t e s . I n t e r -e x c i t o n resonances are expected at g=0.75 and g=1.25 f o r the A and B e x c i t o n s r e s p e c t i v e l y (8). C a v e n e t t (30) r e p o r t s seeing a very weak resonance at g = 1.35 corresponding to the B l i n e , but we were unable to d e t e c t t h i s s i g n a l , presumably due t o i n a d e q u a t e s e n s i t i v i t y . The A l i n e i s even more d i f f i c u l t to observe s i n c e i t causes a r e d i s t r i b u t i o n w i t h i n t h e A l i n e s t a t e s a l l o f w h i c h h a v e a l l o w e d o p t i c a l t r a n s i t i o n s , thus no net change i n luminescence o c c u r s . The r e s o n a n c e would m a n i f e s t i t s e l f as a change i n the A l i n e 56 l u m i n e s c e n c e p o l a r i z a t i o n b u t , as j u s t m e n t i o n e d , t h i s cannot be seen. Resonance of holes should manifest i t s e l f as a decrease i n luminescence as f o r the e l e c t r o n resonance, however the e f f e c t would be s m a l l e r because o f the l o w e r h o l e g v a l u e . A c a l c u l a t i o n of the A l i n e f o r a temperature of 1.6 degrees K p r e d i c t s a change i n l u m i n e s c e n c e o f 1.6 % . A l t h o u g h , i n p r i n c i p l e , a change of t h i s magnitude should be v i s i b l e , the s i g n a l would be weakened by inhomogeneous broadening of the hole resonance from c r y s t a l d e f e c t s . T h i s i s due to the much l a r g e r e f f e c t o f the c r y s t a l l a t t i c e on the h o l e g v a l u e than on the e l e c t r o n g v a l u e t h r o u g h s p i n - o r b i t c o u p l i n g (29) . The number of e f f e c t s observed or not observed t h a t can be a t t r i b u t e d to c r y s t a l d e f e c t s suggests th a t ODMR s t u d i e s on c a r e f u l l y prepared samples of higher q u a l i t y than those a v a i l a b l e t o us s h o u l d be i n t e r e s t i n g . A l t e r n a t i v e l y , the e f f e c t o f e x t e r n a l l y a p p l i e d s t r a i n s on ODMR and luminescence c o u l d be s t u d i e d . F i n a l l y t he t e m p e r a t u r e dependence o b s e r v e d f o r the ODMR s i g n a l i n GaP - N agreed approximately w i t h theory, a f a c t o r of 2 decrease i n the s i g n a l f o r h e a t i n g to 2 degrees K b e i n g somewhat g r e a t e r t h a n e x p e c t e d . However, the e s t i m a t i o n of temperature from the A to B l i n e r a t i o was of l i m i t e d accuracy because of the unequal h e a t i n g of d i f f e r e n t 57 p a r t s of the sample. 3 . 6 C y c l o t r o n Resonance ODMR e x p e r i m e n t s on GaP-N o f t e n showed n o n - r e s o n a n t background s i g n a l s , a p p a r e n t l y microwave h e a t i n g i n d u c e d changes i n l u m i n e s c e n c e . In some br o a d s c a n s , l o o k i n g f o r o t h e r r e s o n a n c e s , t h i s b a c k g r o u n d was o b s e r v e d t o be mag n e t i c f i e l d d e p e n d e n t . I t was t h e r e f o r e d e c i d e d t o i n v e s t i g a t e i t . F i g 3.10 shows the r e s u l t o f a bro a d ODMR sweep, the background f a l l s o f f to near zero at high f i e l d . The e l e c t r o n ODMR s i g n a l shows up on the h i g h s i d e o f t h i s l a r g e s i g n a l . The background s i g n a l r e p r e s e n t s a decrease i n l u m i n e s c e n c e o f s e v e r a l p e r c e n t w i t h the a p p l i c a t i o n o f mi c r o w a v e s . The ap p e a r a n c e o f the s i g n a l s u g g e s t s a v e r y b r o a d c y c l o t r o n r e s o n a n c e w h i c h i s e x p e c t e d i f microwave h e a t i n g o f p h o t o - e x c i t e d c a r r i e r s i s r e s p o n s i b l e . To t e s t t h i s h y p o t h e s i s a sample was moved i n t o a r e g i o n o f the microwave c a v i t y where the e l e c t r i c f i e l d was s t r o n g e r , the s i g n a l was o b s e r v e d t o i n c r e a s e as e x p e c t e d f o r c y c l o t r o n resonance. The microwave power dependence was measured and i t was observed th a t the s i g n a l i n c r e a s e d l i n e a r l y w i t h the microwave power. A l l p a r t s of the N luminescence were seen to be a f f e c t e d e q u a l l y by the resonance. L u m i n e s c e n c e f r o m S c e n t r e s was o b s e r v e d and a 58 3.10 G A P CYCLOTRON RESONANCE • «• • • • d i f f e r e n t s i g n a l was seen. F i g s . 3.11 and 3.12 show the s i g n a l s o b s e r v e d i n N and S l u m i n e s c e n c e w i t h f i t s f o r the c y c l o t r o n r e s o n a n c e e q u a t i o n : PA a 1 + O ) C T 2 + W 2 T 2 x Ne2x (1 + w2x2 - O J 2 T2)2 + 4 O I 2 T2 m* where PA is the power absorbed from the microwave f i e l d , u i s the microwave f r e q u e n c y ,t n e c y c l o t r o n f r e q u e n c y given by: uc = eH/m* e being the e l e c t r o n i c charge, H the magnetic f i e l d , m* the c a r r i e r e f f e c t i v e mass, and T the c a r r i e r s c a t t e r i n g t i m e . Inhomogeneous broadening w i l l r e s u l t i f u or m* are energy dependent as i s l i k e l y at higher c a r r i e r temperatures due to phonon s c a t t e r i n g . The c u r v e f i t t i n g p r o c e d u r e used i s d e s c r i b e d i n Appendix A. I t w i l l be seen t h a t the S luminescence g i v e s a s i g n a l suggesting a resonance at higher f i e l d than f o r the N l u m i n e s c e n c e . Assuming t h a t t h e s i g n a l s a r e cau s e d by c y c l o t r o n resonance, the e f f e c t i v e mass values i n d i c a t e d are 0.89 +_ 0.25 f o r the S and 0.36 + 0.1 f o r the N. The quot e d e r r o r bounds were obtained by v a r y i n g the f i t parameters and c o m p a r i n g the r e s i d u a l s t o see how much change i n the e f f e c t i v e mass parameter was needed a p p r e c i a b l y to worsen the f i t . S e v e r a l sets of data were obtained f o r each c e n t r e , and the v a r i a t i o n i n the r e s u l t s f o r these was a l s o used to 60 signal from the N luminescence showing electron cyclotron resonance FIG. 3.12 G A P - S CYCLOTRON RESONANCE ODMR signal from the S luminescence showing hole cyclotron resonance help a r r i v e at the value s given above. The values of &JT f o r the two c e n t r e s were o f the o r d e r o f 0.9 f o r the S and 0.3 f o r the N c e n t r e , the low O>T f o r the N resonance accounts f o r the l a r g e e r r o r i n the e f f e c t i v e mass. The e f f e c t i v e masses deduced from the two r e s o n a n c e s suggest e l e c t r o n s and heavy h o l e s . I t was hypothesized t h a t t r a p p i n g a t l u m i n e s c e n c e c e n t r e s was r e d u c e d by c y c l o t r o n h e a t i n g o f the f r e e c a r r i e r s , and t h a t h e a t i n g o f the c a r r i e r type trapped f i r s t would have the g r e a t e s t e f f e c t on the l u m i n e s c e n c e f r o m t h a t c e n t r e . N b i n d s an e l e c t r o n w eakly and a n e u t r a l S donor s h o u l d c a p t u r e a h o l e f i r s t b e f o r e a n o t h e r e l e c t r o n . A t t e m p t s were made to o b s e r v e c y c l o t r o n r e s o n a n c e i n GaP-Bi w i t h the r e s u l t s shown i n F i g 3.13. The r e s o n a n c e appears to be caused by heavy holes as suggested by the f a c t t h a t B i i s a hole t r a p , but the value of wx i s too low to be su r e due t o i n c r e a s e d i m p u r i t y s c a t t e r i n g i n the doped c r y s t a l s . Since the e l e c t r o n and l i g h t and heavy hole resonances should a l l be present to some extent i n the luminescence but c o u l d not be r e s o l v e d because o f the low v a l u e s o f & T , measurements were made at 36.3 GHz w i t h the r e s u l t s shown i n F i g . 3.14. The s i g n a l t o n o i s e r a t i o was p o o r e r because o f the low microwave power and absence of a c a v i t y , but i t can 63 FIG. 3.13 G A P - B i CYCLOTRON RESONANCE A l MAGNETIC FIELO ODMR signal from the Bi centre showing a very broad resonance attributed to holes FIG. 3.14 CYCLOTRON RESONANCE AT 36.3 GHZ ODMR signal from N luminescence showing l i g h t and heavy hole resonances be seen t h a t t h e r e s o n a n c e s a r e b e t t e r r e s o l v e d . I t was found th a t the N and S luminescence gave s i m i l a r resonances at the h i g h e r frequency, two resonances were seen which lead to e f f e c t i v e mass v a l u e s o f 0.154 +_ 0.015 and 0.626 _+ 0.03. T h e s e c o r r e s p o n d t o t h e l i g h t and h e a v y h o l e s . The d i f f e r e n c e i n i n t e n s i t i e s between the two resonances i s to be e x p e c t e d s i n c e the l i g h t h o l e band has a l o w e r d e n s i t y o f s t a t e s than the heavy hole band. The e l e c t r o n resonance was not r e s o l v e d but the f i t s c a l c u l a t e d f o r the l i g h t and heavy h o l e s i n d i c a t e d the p r e s e n c e o f the e l e c t r o n s i g n a l as an u n d e r l y i n g e f f e c t . A 'baseline s l o p e1 parameter was used i n f i t t i n g the l i g h t and heavy h o l e peaks w h i c h were each f i t t e d i n d i v i d u a l l y . The b a s e l i n e slopes were i n c l u d e d to take account of f i e l d dependent s i g n a l s present underneath the r e s o n a n c e b e i n g f i t t e d (such as the t a i l o f o t h e r r e s o n a n c e s ) , w h i c h w o u l d n o t be a c c o u n t e d f o r by t h e c y c l o t r o n r e s o n a n c e f o r m u l a . The b a s e l i n e s l o p e s c a l c u l a t e d f o r the l i g h t and heavy hole resonances d i f f e r e d markedly, i n d i c a t i n g another u n d e r l y i n g s i g n a l . The peak o f the e l e c t r o n r e s o n a n c e would have been a t the v a l l e y between the h o l e p e a k s , but because o f the e l e c t r o n ' s l o w e r W T v a l u e and s p l i t t i n g o f the e l e c t r o n resonance due to the a n i s o t r o p i c e f f e c t i v e mass, i t was not r e s o l v e d . C y c l o t r o n resonance measurements by Schwerdtfeger (27) u s i n g microwave a b s o r p t i o n o f p h o t o - e x c i t e d c a r r i e r s a t 66 35GHz gave s i g n a l s s i m i l a r t o t h o s e shown i n F i g . 3.14; the e l e c t r o n r e s o n a n c e was n o t s e e n e x c e p t as a p o s s i b l e ' f i l l i n g i n ' of the v a l l e y between the hole resonances. The GaP-Bi samples were a l s o r u n a t 36.3GHz but the resonance thought to be due to holes was s t i l l too broad to give a u s e f u l value of e f f e c t i v e mass. The r e s u l t s of our measurements of c y c l o t r o n resonance i n GaP a r e shown i n T a b l e 3.2 w h i c h g i v e s the e f f e c t i v e mass and ui values determined from 9.2GHz and 36.3GHz and the range o f v a l u e s g i v e n i n t h e l i t e r a t u r e . Our r e s u l t s show an apparent d i s c r e p a n c y between the 9.2GHz and 36.3GHz e f f e c t i v e mass valu e s of the heavy h o l e s . The 9.2GHz value d e t e r m i n e d f r o m the S l u m i n e s c e n c e s i g n a l i s p r o b a b l y t o o h i g h b e c a u s e o f u n r e s o l v e d l i g h t h o l e and e l e c t r o n c o n t r i b u t i o n s to the s i g n a l which would tend to d i s t o r t the f i t . We next c o n s i d e r the mechanism by w h i c h c y c l o t r o n h e a t i n g o f c a r r i e r s r e d u c e s t h e l u m i n e s c e n c e f r o m a r e c o m b i n a t i o n c e n t r e . S i n c e the e n t i r e l u m i n e s c e n c e was observed to be a f f e c t e d e q u a l l y , the e f f e c t must be due to a r e d u c t i o n i n the t r a p p i n g p r o b a b i l i t y of heated c a r r i e r s at the c e n t r e , or e l s e to impact i o n i z a t i o n of c a r r i e r s a l r e a d y trapped before they can recombine. 67 TABLE 3.2 GaP CYCLOTRON RESONANCE RESULTS 6JT mnh m Ih 9.2 GHz 0.36+0.1 3 6.3 GHz 0.3 0.89+0.25 0.626+0.03 0.8 0) T 2.6 0.154+_0.015 2.4 L i t e r a t u r e ITlj = 1.5 mt = 0.18 average = 0.35 0.52(A) 0.67+.04(B) 0.88(C) 0.16(A) 0.17+.01(B) 0.132(C) A. Bandstructure c a l c u l a t i o n s (78) B. C y c l o t r o n resonance (27) C. Bandstructure measurements (78) 68 The e x p e c t e d h e a t i n g o f e l e c t r o n s a t the maximum microwave power l e v e l s used was e s t i m a t e d t a k i n g the s c a t t e r i n g t i m e t o be g i v e n by the e l e c t r o n r e s o n a n c e UT v a l u e s a t 9.2 GHz. The maximum microwave e l e c t r i c f i e l d s t r e n g t h i n s i d e the sample was c a l c u l a t e d to be of the order o f 100 V/Cm g i v i n g an a v e r a g e e l e c t r o n h e a t i n g o f approximately 0.5 meV. Since the N ce n t r e binds an e l e c t r o n w i t h an energy o f 8 meV, and t h e b i n d i n g e n ergy a t S and B i cen t r e s i s even l a r g e r , the p o s s i b i l i t y of impact i o n i z a t i o n by microwave heated e l e c t r o n s can be r u l e d o u t . Experimental evidence f o r the energy dependence of the t r a p p i n g p r o b a b i l i t y of c a r r i e r s i n GaP has been obtained by Dean ( 4 7 ) i n e x c i t a t i o n s p e c t r u m measurements. H i s work showed i n c r e a s e d luminescence from the i s o e l e c t r o n i c c e n t r e s N and B i when the ph o t o - e x c i t e d c a r r i e r s were generated near to the band edges u s i n g r e s o n a n t e x c i t a t i o n , and when c a r r i e r s c o u l d t h e r m a l i z e r a p i d l y to the bottom of the band by phonon e m i s s i o n . A t h e o r e t i c a l a n a l y s i s o f t r a p p i n g c r o s s s e c t i o n s o f e l e c t r o n s at i o n i z e d i m p u r i t i e s i n semiconductors has been made by M.Lax (77). He shows t h a t the t r a p p i n g c r o s s s e c t i o n should i n c r e a s e w i t h d e c r e a s i n g temperature as e l e c t r o n s can be t r a p p e d i n t o i n c r e a s i n g l y l a r g e o r b i t s a b o u t t h e i m p u r i t i e s . Lax a l s o c a l c u l a t e s the t r a p p i n g c r o s s s e c t i o n f o r n e u t r a l i m p u r i t i e s and f i n d s a 1/T dependence. 6 9 T r a p p i n g of an e l e c t r o n a t a n e u t r a l i s o e l e c t r o n i c N i m p u r i t y i n GaP i s more c o m p l i c a t e d s i n c e the shall o w bound s t a t e f o r t h i s c e n t r e w i l l produce str o n g resonant t r a p p i n g and s c a t t e r i n g e f f e c t s ( 3 8 ) . A c a l c u l a t i o n o f t h e p s e u d o p o t e n t i a 1 f o r the N i m p u r i t y i n GaP by F a u l k n e r (790 shows a deep narrow p o t e n t i a l w e l l . Faulkner has c a l c u l a t e d t h e s c a t t e r i n g and t r a p p i n g c r o s s s e c t i o n s f o r t h i s p o t e n t i a l f o r e l e c t r o n s and f i n d s an e n e r g y dependence o f the form: l / ( E j + Ee) EI i s t h e b i n d i n g e n e r g y of the e l e c t r o n on the N atom, and E e the e l e c t r o n k i n e t i c e n e r g y p r i o r t o t r a p p i n g . In our m e a s u r e m e n t s t h e maximum h e a t i n g e x p e c t e d f r o m t h e microwaves was 0.5 meV and t h e t h e r m a l e nergy o f t h e e l e c t r o n s a t 1.6 d e g r e e s K o n l y 0.13 meV w h i l e E j fo r t h e N c e n t r e i s 8 meV, thus the t r a p p i n g c r o s s s e c t i o n s h o u l d d e c r e a s e a p p r o x i m a t e l y l i n e a r l y w i t h i n c r e a s i n g microwave power. T h i s was o b s e r v e d . The d e c r e a s e i n l u m i n e s c e n c e expected f o r the maximum microwave h e a t i n g i s es t i m a t e d to be 5.8 % , i n good agreement w i t h the observed s i g n a l s which r e p r e s e n t an approximately 5 % decrease i n i n t e n s i t y . I t may be q u e s t i o n e d whether t r a p p i n g c r o s s s e c t i o n s c a l c u l a t e d f o r p l a n e wave e l e c t r o n s a r e a p p l i c a b l e t o e l e c t r o n s i n c y c l o t r o n o r b i t s , f o r example, an e l e c t r o n i n a c y c l o t r o n o r b i t about an i m p u r i t y might have an i n c r e a s e d 70 t r a p p i n g p r o b a b i l i t y . The p s e u d o p o t e n t i a l s at i s o e l e c t r o n i c i m p u r i t i e s a r e s h o r t range e f f e c t s , , t h a t c a l c u l a t e d by F a u l k n e r f o r N i n GaP i s n e g l i g i b l e beyond two l a t t i c e s p a c i n g s or about 10 A.U. The c y c l o t r o n o r b i t r a d i u s of e l e c t r o n s i n the l o w e s t Landau l e v e l f o r the r e s o n a n c e m a g n e t i c f i e l d s t r e n g t h i s a p p r o x i m a t e l y 100 A.U., so the i s o e l e c t r o n i c t r a p s h o u l d n o t be a b l e t o 'see' t h e d i f f e r e n c e between t h e c y c l o t r o n o r b i t and a p l a n e wave e l e c t r o n . 3 .7 ODMR i n ZnTe Samples of z i n c t e l l u r i d e were obtained from J.Merz at B e l l L a b o r a t o r i e s . These were doped w i t h i s o e l e c t r o n i c o xygen, one sample c o n t a i n i n g the i s o t o p e O^g. R e s i d u a l i m p u r i t i e s such as p h o s p h o r o u s , w h i c h forms a s h a l l o w acceptor l e v e l when s u b s t i t u t i n g f o r Te, were a l s o p r e s e n t . Z i n c t e l l u r i d e has a d i r e c t band gap o f 2.38 eV (48), the v a l e n c e band maximum b e i n g d e g e n e r a t e . The e f f e c t i v e masses o f l i g h t and heavy h o l e s i n ZnTe have been measured by S t r a d l i n g (49) u s i n g c y c l o t r o n r e s o n a n c e a b s o r p t i o n measurements o f t h e r m a l l y e x c i t e d h o l e s a t a microwave frequency of 1556 Hz. The e f f e c t i v e masses were: 71 0.154 hh[100] 0.64 0.69 'hhtHO] 0.69 the heavy h o l e band b e i n g non s p h e r i c a l . The e l e c t r o n e f f e c t i v e mass has been e s t i m a t e d a t between 0.12 and 0.22 from magneto-optical s t u d i e s of luminescence from shallow acceptors and donors (50,51). ODMR measurements on ZnTe have been made by K i l l o r a n , Cavenett and Dean (14) who observed the e f f e c t s of e l e c t r o n p a r a m a g n e t i c r e s o n a n c e as a change i n the p o l a r i z a t i o n o f d o n o r - a c c e p t o r p a i r l u m i n e s c e n c e i n P doped ZnTe. The g value obtained was +0.401 and was a t t r i b u t e d to resonance of e l e c t r o n s on u n i d e n t i f i e d shallow donors, p o s s i b l y A l atoms s u b s t i t u t i n g f o r Zn. L a r g e background s i g n a l s were a l s o r e p o r t e d and were dependent on the m a g n e t i c f i e l d , the w a v e l e n g t h and the p o l a r i z a t i o n o f the l u m i n e s c e n c e b e i n g measured. The luminescence spectrum of our ZnTe sample i s shown i n F i g . 3.15 . The near band gap l u m i n e s c e n c e has a s h a r p peak a t 5220 A.U. T h i s i s commonly seen i n ZnTe and i s a t t r i b u t e d to e x c i t o n r ecombination at a number of shallow a c c e p t o r s i n c l u d i n g P s u b s t i t u t i n g f o r Te, and L i and Cu s u b s t i t u t i n g f o r Zn ( 1 4 ) . O t h e r l i n e s c o r r e s p o n d t o 72 ZnTe luminescence spectrum showing near band gap luminescence and the deeper 0 isoelectronic centre spectrum r e c o m b i n a t i o n a t a c c e p t o r s and d o n o r s . The l u m i n e s c e n c e spectrum of the oxygen c e n t r e s shows the expected s e r i e s of phonon r e p l i c a s a l r e a d y o b s e r v e d f o r t h i s i s o e l e c t r o n i c i m p u r i t y (52). Attempts were made to observe the e l e c t r o n resonance i n v a r i o u s p a r t s o f the l u m i n e s c e n c e , b o t h by m o n i t o r i n g the t o t a l i n t e n s i t y and by u s i n g a c i r c u l a r p o l a r i z a t i o n a n a l y s e r . No s i g n a l was seen anywhere i n the v i c i n i t y of the e x p e c t e d v a l u e o f g=0.401. M a g n e t i c f i e l d d e p e n d e n t b a c k g r o u n d s i g n a l s w ere s e e n i n a l l p a r t s o f t h e l u m i n e s c e n c e , however, and t h e s e were i n v e s t i g a t e d u s i n g 9.2GHz microwaves w i t h t h e r e s u l t s shown i n F i g s . 3.16 and 3.17. Two d i s t i n c t l i n e s h a p e s were observed depending upon which p a r t of the luminescence was monitored. The 5220 A.U. l i n e and the oxygen c e n t r e l u m i n e s c e n c e b o t h gave r e s o n a n c e s w h i c h s u g g e s t e d an e f f e c t i v e mass o f the o r d e r o f 0.3, w h i l e the 5290 A.U. peak gave a r e s o n a n c e w i t h an e f f e c t i v e mass v a l u e o f a p p r o x i m a t e l y 0.8. An unusual f e a t u r e of these resonances i s t h a t they r e p r e s e n t an i n c r e a s e i n t h e l u m i n e s c e n c e a t r e s o n a n c e r a t h e r than a d e c r e a s e o f t h e t y p e seen i n most o f t h e o t h e r c y c l o t r o n resonance r e s u l t s . Measurements were a l s o made a t 36.3GHz but no u s e f u l r e s u l t s were o b t a i n e d but t h e low power l e v e l made the 74 FIG. 3.16 ZNTE ODHR AT 5220 A ODMR signal showing an increase in luminescence caused by electron cyclotron resonance FIG. 3.17 ZNTE ODMR AT 5290 A i — 1 — 10 20 MAGNETIC FIELD KG Hole resonance in 5290 A.U. luminescence s i g n a l too weak to observe. The e f f e c t i v e mass v a l u e s deduced from the 9.2 GHz r e s o n a n c e s were: 0.8 +_ 0.2 and 0.3 +_ 0.2 h a v i n g DT v a l u e s o f the o r d e r of 0.9 and 0.2 r e s p e c t i v e l y . These v a l u e s s u g g e s t heavy holes and e l e c t r o n s , or p o s s i b l y l i g h t h o l e s . In view of the d i f f e r e n c e i n the cox v a l u e s f o r t h e two r e s o n a n c e s , the low e f f e c t i v e mass s i g n a l was p r o b a b l y c a u s e d by e l e c t r o n s r a t h e r than by the l i g h t holes which were observed by S t r a d l i n g to have approximately the same WT value as the heavy h o l e s . The f a c t t h a t the e f f e c t o f the r e s o n a n c e s was t o i n c r e a s e luminescence suggests t h a t there are n o n - r a d i a t i v e decay processes which compete f o r e l e c t r o n s and h o l e s , and which are i n h i b i t e d by microwave c a r r i e r h e a t i n g . However, d i f f e r e n t resonances are observed i n d i f f e r e n t luminescence bands w h i c h c o n t r a d i c t s t h i s h y p o t h e s i s s i n c e , i f non-r a d i a t i v e p r o c e s s e s a r e i n h i b i t e d , a l l the l u m i n e s c e n c e s h o u l d i n c r e a s e i n p r o p o r t i o n and t h e o b s e r v e d r e s o n a n c e should be the same i n a l l bands. Another p o s s i b i l i t y i s t h a t the observed luminescence bands c o r r e s p o n d t o e x c i t o n r e c o m b i n a t i o n a t i o n i z e d a c c e p t o r s and donors. Evidence has been obtained from Zeeman measurements t h a t the 5220 A.U. luminescence o r i g i n a t e s from i o n i z e d a c c e p t o r s (51). I o n i z e d i m p u r i t i e s w i l l t e n d to be 77 n e u t r a l i z e d by photo-generated e l e c t r o n s and holes (13) and c y c l o t r o n h e a t i n g i s e x p e c t e d t o r e d u c e the r a t e a t w h i c h i o n i z e d atoms ar e n e u t r a l i z e d e i t h e r by r e d u c i n g the t r a p p i n g p r o b a b i l i t y as was o b s e r v e d i n GaP, o r by i m p a c t i o n i z a t i o n of n e u t r a l i z e d atoms. Thus the number of i o n i z e d c e n t r e s a v a i l a b l e f o r l u m i n e s c e n c e would be i n c r e a s e d , a l t h o u g h t h e e x c i t o n t r a p p i n g r a t e might be r e d u c e d by the h e a t i n g . I t should be pointed out t h a t o p t i c a l recombination of e x c i t o n s at n e u t r a l donors and acceptors i s a l s o expected but w i l l be much l e s s e f f i c i e n t due t o the n o n - r a d i a t i v e Auger r e c o m b i n a t i o n p r o c e s s a l r e a d y d i s c u s s e d f o r GaP. I t f o l l o w s t h a t an i n c r e a s e i n t h e number o f i o n i z e d c e n t r e s should r e s u l t i n an i n c r e a s e i n luminescence. Our i n a b i l i t y t o o b s e r v e the e l e c t r o n p a r a m a g n e t i c r e s o n a n c e was p r o b a b l y due t o the absence of a p p r o p r i a t e donor i m p u r i t i e s needed to produce the donor-acceptor p a i r l u m i n e s c e n c e r e p o r t e d by K i l l o r a n e t a l (14) w hich was not v i s i b l e i n our sample. 3.8 Other Materials. ODMR measurements were made on samples of CdS and C d l n2 S 4 and m a g n e t i c f i e l d dependence background s i g n a l s were o b s e r v e d . The cox v a l u e s o f t h e s e r e s o n a n c e s were too low t o g i v e any measure o f c a r r i e r e f f e c t i v e mass, i t was not even p o s s i b l e to determine whether the resonances were due 78 to e l e c t r o n s or h o l e s . I t was evident t h a t , to o b t a i n u s e f u l r e s u l t s , c y c l o t r o n ODMR e x p e r i m e n t s need t o be done w i t h h i g h p u r i t y m a t e r i a l s and a t h i g h microwave f r e q u e n c i e s . This i s g e n e r a l l y true f o r c o n v e n t i o n a l c y c l o t r o n resonance work. 3 . 9 Summary ODMR measurements were used t o o b s e r v e the e f f e c t o f paramagnetic resonance of e l e c t r o n s on luminescence from N, S, and B i i m p u r i t i e s i n GaP. ODMR s i g n a l s had n o t been p r e v i o u s l y r e p o r t e d from S and B i luminescence and our r e s u l t s c o n f i r m the i n t e r p r e t a t i o n t h a t the s i g n a l seen f o r N i m p u r i t i e s i s due to resonance of pho t o - e x c i t e d conduction band e l e c t r o n s . A c a l c u l a t i o n was made of the e x p e c t e d l u m i n e s c e n c e change as a r e s u l t o f t h e r e s o n a n c e and was found to agree very w e l l w i t h the observed s i g n a l s t r e n g t h when the r a p i d t h e r m a l i z a t i o n between the A and B l i n e s was taken i n t o account. The temperature dependence of the e f f e c t was measured o v e r a l i m i t e d range by l a s e r h e a t i n g o f the sample and the d e c r e a s e i n s i g n a l p r e d i c t e d t h e o r e t i c a l l y was o b s e r v e d . The r e s o n a n c e was shown t o be homogeneously b r o a d e n e d g i v i n g a l i f e t i m e o f 4 nano s e c o n d s . By c o n s i d e r i n g t h e r e s u l t s o f c o n v e n t i o n a l EPR on GaP i t was i n f e r r e d t h a t t h i s l i f e t i m e was the e l e t r o n - h o l e c a p t u r e t i m e . C i r c u l a r p o l a r i z a t i o n e f f e c t s were a b s e n t from the luminescence, t h i s was a t t r i b u t e d to the e f f e c t s of c r y s t a l d e f e c t s on e x c i t o n s which were shown to be c o n s i d e r a b l e . Our 79 i n a b i l i t y t o see p a r a m a g n e t i c h o l e r e s o n a n c e e f f e c t s was a l s o t h o u g h t t o be due t o c r y s t a l d e f e c t s c a u s i n g homogeneous broadening of the hole s i g n a l . C y c l o t r o n resonance of e l e c t r o n s and holes was observed by ODMR, the f i r s t s u c h measurement i n t h i s m a t e r i a l . The s e n s i t i v i t y of d i f f e r e n t luminescence bands to e l e c t r o n or h o l e r e s o n a n c e was shown t o be d e t e r m i n e d by the t r a p p i n g processes f o r the corresponding i m p u r i t i e s , the c a r r i e r type trapped f i r s t by a n e u t r a l i m p u r i t y had the g r e a t e s t e f f e c t when heated. The magnitude and temperature dependence of the e f f e c t was m e a s u r e d and c o m p a r e d w i t h t h e o r e t i c a l p r e d i c t i o n s f o r the t r a p p i n g c r o s s s e c t i o n of the N i m p u r i t y and good agreement was f o u n d . A c c u r a t e v a l u e s o f l i g h t and heavy hole e f f e c t i v e masses were obtained by measurements at 36.3 GHz and a g r e e d w i t h t h e r e s u l t s o f c o n v e n t i o n a l c y c l o t r o n r e s o n a n c e e x p e r i m e n t s . The e l e c t r o n r e s o n a n c e c o u l d not be r e s o l v e d p r o p e r l y a t 36.3 GHz, p r e s u m a b l y due to t he a n i s o t r o p i c e l e c t r o n e f f e c t i v e mass and s h o r t e r s c a t t e r i n g t i m e , p r o b a b l y c a u s e d by r e s o n a n c e s c a t t e r i n g from N i m p u r i t i e s . ODMR s t u d i e s of ZnTe showed e l e c t r o n and hole c y c l o t r o n resonances and, as i n GaP, d i f f e r e n t luminescence bands gave s i g n a l s c orresponding to e l e c t r o n s or h o l e s . U n l i k e the GaP r e s u l t s , t h e Z.nTe l u m i n e s c e n c e was i n c r e a s e d by t h e c y c l o t r o n r e s o n a n c e s . I t was h y p o t h e s i z e d t h a t i o n i z e d 80 i m p u r i t y c e n t r e s were r e s p o n s i b l e f o r most of the near band gap l u m i n e s c e n c e , an a s s u m p t i o n s u p p o r t e d by Zeeman measurements r e p o r t e d i n the l i t e r a t u r e , and t h a t c y c l o t r o n h e a t i n g i n c r e a s e d t h e number o f i o n i z e d i m p u r i t i e s . R e c o m b i n a t i o n a t n e u t r a l c e n t r e s c o u l d be r e d u c e d c o r r e s p o n d i n g l y but such r e c o m b i n a t i o n s would be l e s s e f f i c i e n t o p t i c a l l y due t o n o n - r a d i a t i v e Auger p r o c e s s e s . The i n c r e a s e i n luminescence observed f o r the i s o e l e c t r o n i c oxygen c e n t r e l u m i n e s c e n c e p r e s u m a b l y r e p r e s e n t e d a n e t i n c r e a s e i n the f r e e c a r r i e r p o p u l a t i o n caused by r e d u c e d t r a p p i n g a t o t h e r c e n t r e s . I f our i n t e r p r e t a t i o n o f the r e s u l t s i s c o r r e c t , t h i s technique c o u l d provide a v a l u a b l e t o o l f o r i d e n t i f y i n g l u m i n e s c e n c e b a n d s i n ZnTe as o r i g i n a t i n g f r o m i o n i z e d or n e u t r a l a c c e p t o r s or d o n o r s , e s p e c i a l l y i n cases where other t e c h n i q u e s , such as Zeeman s p e c t r o s c o p y , do n o t work (e.g. due t o u n r e s o l v a b l e s p l i t t i n g s ) . Attempts to observe the e l e c t r o n paramagnetic resonance i n ZnTe by ODMR were u n s u c c e s s f u l due t o a l a c k o f a p p r o p r i a t e d o n o r s t o p r o d u c e t h e d o n o r - a c c e p t o r luminescence band i n which the e f f e c t manifests i t s e l f . 81 Chapter 4 . S i l v e r Bromide. 4.1 AgBr S i l v e r b r o m i d e i s a h i g h l y p o l a r m a t e r i a l w i t h an i n d i r e c t band gap o f 2.69 eV (53). The b a n d s t r u c t u r e i s shown i n F i g . 4.1 and i s , i n some r e s p e c t s , the i n v e r s e o f t h a t i n GaP. The c o n d u c t i o n band minimum i s c e n t r e d a t the r p o i n t and i s approximately s p h e r i c a l , w h i l e the fou r valence band maxima l i e a t the X p o i n t s and a r e e l l i p t i c a l , g i v i n g a hole an a n i s o t r o p i c e f f e c t i v e mass (54). Both conduction and v a l e n c e bands a r e a p p r e c i a b l y n o n - p a r a b o l i c due t o the strong electron-phonon c o u p l i n g to be d e s c r i b e d l a t e r . S e v e r a l pure c r y s t a l s o f AgBr were o b t a i n e d from W.Czaja, EPF, Lausanne, S w i t z e r l a n d . These i n c l u d e d one c r y s t a l w i t h i d e n t i f i e d c r y s t a l axes. The c r y s t a l s , though not i n t e n t i o n a l l y doped, contained some r e s i d u a l i m p u r i t i e s . The main i m p u r i t y was i o d i n e which, being c h e m i c a l l y s i m i l a r t o b r o m i n e , i s g e n e r a l l y p r e s e n t i n u n d o p e d AgBr i n c o n c e n t r a t i o n s of the order of one p a r t per m i l l i o n . 4.2 ODMR i n AgBr. The l u m i n e s c e n c e s p e c t r u m o f AgBr c o n t a i n s two p r i n c i p a l f e a t u r e s . A weak zero phonon l i n e and a s e r i e s of m u l t i - p h o n o n r e p l i c a s f r o m e x c i t o n r e c o m b i n a t i o n on i s o e l e c t r o n i c i o d i n e c e n t r e s forms a broad band which peaks 82 FIG. 4.1 AGBR BANDSTRUCTURE r k L € = O.I5eV 8 = 0.58eV 83 a t a p p r o x i m a t e l y 4900 A.U. as shown i n Fig.4.2. At lower e n e r g y a b r o a d f e a t u r e l e s s c o n t i n u u m peaks a t around 5700 A.U. This l a t t e r band i s thought to a r i s e from e l e c t r o n - h o l e r e c o m b i n a t i o n a t i n t e r s t i t i a l s i l v e r atoms or m u l t i - a t o m s i l v e r s p ecks (55,56), and i s enhanced e i t h e r by e x p o s i n g the c r y s t a l t o l i g h t or by s t r e s s e s i n d u c e d i n t h e r m a l c y c l i n g to l i q u i d helium temperatures. I t can be reduced by a n n e a l i n g the sample a t 200 d e g r e e s C f o r 24 hours and c o o l i n g to room temperature s l o w l y (53,57). ODMR m e a s u r e m e n t s on AgBr have b e e n r e p o r t e d p r e v i o u s l y , f i r s t by Hayes, Owen and Walker (58), and by M a r c h e t t i and h i s co-workers (56,59). Hayes e t a l observed a s i n g l e resonance at g=1.8 i n the 5700 A.U. luminescence band u s i n g a microwave f r e q u e n c y o f a p p r o x i m a t e l y 20 GHz. M a r c h e t t i (56), u s i n g 10 Watts of microwave power at 35 GHz, has observed a s e r i e s of resonances i n the same luminescence band a t g v a l u e s o f 1.49, 1.75, 1.81 and 2.08 a l l a p p a r e n t l y i s o t r o p i c . He a t t r i b u t e d the g=1.49 and g=2.08 v a l u e s t o f r e e e l e c t r o n , and t o h o l e p a r a m a g n e t i c r e s o n a n c e s r e s p e c t i v e l y . He assigned the two i n t e r m e d i a t e resonances to e l e c t r o n s t r a p p e d on the d e f e c t o r c e n t r e r e s p o n s i b l e f o r the 5700 A.U. luminescence. T h i s i n t e r p r e t a t i o n was v e r i f i e d by comparing the e f f e c t s on s i g n a l s from samples doped with v a r i o u s c a r r i e r t r a p p i n g i m p u r i t i e s . M a r c h e t t i and Burberry (59) have a l s o s t u d i e d ODMR s i g n a l s from i o d i n e c e n t r e luminescence u s i n g AgBr c r y s t a l s doped w i t h v a r i o u s l e v e l s of i o d i n e . At i n t e r m e d i a t e d o p i n g l e v e l s (of the o r d e r o f 84 FIG. 4.2 AGBR LUMINESCENCE 2.1 EV 2.4 EV 2.5 EV 2.6 EV 6000 5500 5100 4900 4700 WAVELENGTH A 100 ppm) a s i n g l e b r o a d r e s o n a n c e a t about g=5.65 was o b s e r v e d . They a t t r i b u t e d t h i s t o t r a n s i t i o n s w i t h i n the angular momentum s t a t e s of the i o d i n e bound e x c i t o n . 4.3 R e s u l t s . The r e s u l t s of our measurements (75) on the 5700 A.U. l u m i n e s c e n c e b a n d , a t 9.2 and 36.3 GHz a r e shown i n F i g s . 4.3. and 4.4. At 9.2 GHz two r e s o n a n c e s were seen a t g = 2.07 +_ 0.02 and g = 1.81 +_ 0.02 and were i s o t r o p i c to w i t h i n the e x p e r i m e n t a l e r r o r s . In some o f the d a t a a t h i r d peak was v i s i b l e merged w i t h the l a r g e s i g n a l a t g=1.81 and on the h i g h f i e l d , low g v a l u e , s i d e . A t 36.3 GHz o n l y one r e s o n a n c e was s e e n a t g = 1.708 +_ 0.01 w h i c h was a l s o i s o t r o p i c . The 4900 A.U. i o d i n e e m i s s i o n band y i e l d e d a v e r y d i f f e r e n t ODMR s p e c t r u m . No t r a c e o f any of the r e l a t i v e l y s h a r p EPR l i n e s seen from the 5700 A.U. band was d e t e c t e d u s i n g e i t h e r 9.2 or 36.3 GHz microwave s t i m u l a t i o n . Instead, two b r o a d e r r e s o n a n c e s were o b s e r v e d as shown i n F i g . 4.5. These we a t t r i b u t e to c y c l o t r o n resonance of e l e c t r o n s and h o l e s . This i s supported by the s t r i k i n g s i m i l a r i t y of these r e s u l t s to those obtained by d i r e c t d e t e c t i o n of c y c l o t r o n resonance r e p o r t e d by other workers (60-65). However, there are d i f f e r e n c e s which w i l l be d i s c u s s e d l a t e r . 86 FIG. 4.3 ODMR IN AGBR • • • g • 2.07 9.2 GHz g - 1.81 _L 1 2.9 3.5 MAGNETIC FIELD kG 4.1 ODMR of 5700 A.U. band showing electron and hole resonances FIG. 'l . ' l ODMR IN AGBR J L 12 14 16 18 20 MAGNETIC FIELD kG Electron resonance at high frequency 00 FIG. L\,5 CYCLOTRON RESONANCE IN A G B R T m* • 0.29 m*«l.l •• • 36.3 GHz 1 10 20 MAGNETIC FIELD kG Cyclotron resonance of electrons and holes in I luminescence U n l i k e the EPR r e s o n a n c e s , w h i c h caused i n c r e a s e d e m i s s i o n , the s i g n a l s r e p r e s e n t a decrease i n luminescence a t r e s o n a n c e . The lo w e r r e s o n a n c e , a t t r i b u t e d t o e l e c t r o n c y c l o t r o n resonance, was i s o t r o p i c . The higher resonance was b r o a d e n e d i n c e r t a i n d i r e c t i o n s b u t t h e w i d t h o f t h e r e s o n a n c e , and the poor s i g n a l t o n o i s e r a t i o , made i t i m p o s s i b l e t o d e t e r m i n e whether t h i s was caused by the u n r e s o l v e d s p l i t t i n g o f the l i n e w h i c h i s e x p e c t e d f o r a hole c y c l o t r o n resonance i n t h i s m a t e r i a l . At 9.2 GHz, where more microwave power was a v a i l a b l e , the power dependence of the c y c l o t r o n resonances was s t u d i e d w i t h t h e r e s u l t s shown i n F i g s . 4.6 and 4.7. A t low power l e v e l s t he e l e c t r o n and h o l e r e s o n a n c e s b o t h appear t o be homogeneously broadened l i n e s g i v i n g approximately the same e f f e c t i v e mass v a l u e s as the 36.3 GHz r e s u l t s . As the microwave power l e v e l was i n c r e a s e d the h o l e r e s o n a n c e s t r e n g t h e n e d and b r o a d e n e d , w h i l e t h e e l e c t r o n r e s o n a n c e changed s i g n ( i . e . luminescence i n c r e a s e d at resonance) and broadened. The s p e c t r a l dependence of the ODMR s i g n a l s was che c k e d by s c a n n i n g t h e i o d i n e s p e c t r u m w i t h t h e m a g n e t i c f i e l d s e t a t the peak o f the e l e c t r o n and h o l e r e s o n a n c e s . T h e ODMR ' s p e c t r a * s o o b t a i n e d r e s e m b l e d t h e photoluminescence spectrum. I t s h o u l d be no t e d t h a t the ODMR s i g n a l s from the e l e c t r o n and h o l e r e s o n a n c e s s i t on a l a r g e n o n - r e s o n a n t background s i g n a l presumably caused by d i e l e c t r i c h e a t i n g . 90 FIG, 4.6 LOW POKER CYCLOTRON RESONANCE SIGNAL Electron cyclotron resonance at low frequency showing homogeneous line shape FIG. 4.7 POWER DEPENDENT CYCLOTRON RESONANCE SIGNAL •••• • • • ••• * ' • V . • 10 M A G N E T I C F I E L D kG Electron and hole resonance I FULL POWER II - 10 DB s as a function of microwave power I U _20 nB IV - 30 DB A l s o no t r a c e o f t h e c y c l o t r o n r e s o n a n c e s o r background i s seen i n the 5700 A.U. luminescence band. 4.4 D i s c u s s i o n . Our ODMR r e s u l t s f r o m t h e 5700 A.U. band a g r e e s u b s t a n t i a l l y w i t h t h o s e o f Hayes e t a l and M a r c h e t t i , the 9.2 GHz d a t a showing the h o l e r e s o n a n c e a t g = 2.07 and the two t r a p p e d e l e c t r o n r e s o n a n c e s merged w i t h the g=1.81 r e s o n a n c e s t r o n g e r . At 36.3 GHz o n l y the g=1.7 r e s o n a n c e i s seen, i n d i c a t i n g t h a t the g=1.81 s i g n a l becomes r e l a t i v e l y w e a k e r a t h i g h e r f i e l d . T h i s a g r e e s w i t h M a r c h e t t i ' s o b s e r v a t i o n t h a t t h i s r e s o n a n c e d e c r e a s e s i n i n t e n s i t y a t lo w e r t e m p e r a t u r e (4.2 d e g r e e s K t o 1.7 d e g r e e s K) s i n c e i n both c a s e s t h e s p l i t t i n g o f s p i n s t a t e s i n the m a g n e t i c f i e l d i n c r e a s e s w i t h r e s p e c t t o the t h e r m a l e n e r g y . Our f a i l u r e to observe the other l i n e s at high frequency may be a t t r i b u t e d t o t h e low microwave power a v a i l a b l e . The f a c t t h a t t h e g=1.81 and g=1.7 r e s o n a n c e s a r e a l m o s t c o m p l e t e l y merged a t l o w e r f r e q u e n c y i n d i c a t e s t h a t the l i n e s a r e a t l e a s t i n p a r t homogeneously br o a d e n e d . F a i l u r e t o o b s e r v e EPR l i n e s i n the i o d i n e c e n t r e luminescence i s probably due to the f a c t t h a t , being an i s o e l e c t r o n i c c e n t r e , the e x c i t o n decay times are longer which a l l o w s g r e a t e r t h e r m a l i z a t i o n of s p i n s before r e c o m b i n a t i o n . C y c l o t r o n r e s o n a n c e o f e l e c t r o n s i n AgBr has been observed by s e v e r a l r e s e a r c h e r s u s i n g c o n v e n t i o n a l microwave 93 a b s o r p t i o n t e c h n i q u e s and photo g e n e r a t e d c a r r i e r s . The f i r s t measurement was made by A s c a r e l l i and Brown (60) who observed an asymmetric and s t r o n g l y temperature dependent s i g n a l which i n d i c a t e d an e f f e c t i v e mass of 0.27. B a x t e r and A s c a r e l l i (61), and Tamura and Masumi (62,63,64) have s t u d i e d the t e m p e r a t u r e dependence o f t h i s resonance i n more d e t a i l by changing the l a t t i c e temperature and i n c r e a s i n g the c a r r i e r temperature u s i n g high microwave f i e l d s . Tamura and Masumi observed an i n c r e a s e i n e f f e c t i v e mass of up to 15% w i t h high l e v e l s of microwave e x c i t a t i o n , which they compared w i t h the t h e o r e t i c a l p r e d i c t i o n s of Lee, Low and P i n e s (LLP) (66) and L a r s e n (67). Hodby and co-workers (65) have observed an i n c r e a s e i n apparent e l e c t r o n e f f e c t i v e mass o f a p p r o x i m a t e l y 5% a t v e r y h i g h microwave f r e q u e n c i e s and magnetic f i e l d s t r e n g t h s at which the f i r s t e x c i t e d c y c l o t r o n l e v e l i s a p p r o x i m a t e l y 20% of the LO phonon e n e r g y . They m o n i t o r e d the c y c l o t r o n r e s o n a n c e by measuring changes i n sample p h o t o c o n d u c t i v i t y . C y c l o t r o n r e s o n a n c e of h o l e s has been seen o n l y by Tamara and Masumi (54) who used microwave a b s o r p t i o n at 34 GHz. They o b s e r v e d a r e s o n a n c e a t m*=0.99 f o r a m a g n e t i c f i e l d p a r a l l e l t o the [1,0,0] d i r e c t i o n . T h i s r e s o n a n c e s p l i t i n t o two l i n e s when the f i e l d was a p p l i e d along other axes. 94 Both e l e c t r o n and h o l e e f f e c t i v e masses i n AgBr a r e s t r o n g l y e n ergy dependent due to n o n - p a r a b o l i c i t y of the e l e c t r o n and v a l e n c e bands. T h i s i s due to the s t r o n g c o u p l i n g between c a r r i e r s and LO phonons ( ae= i . 6 , ah = 2.8) (54). a i s the c o n s t a n t f o r c o u p l i n g o f e l e c t r o n s and h o l e s to the l o n g i t u d i n a l o p t i c a l phonon mode and i s d e f i n e d as: a = <e2/jl)(i/e < B - l /e s) ( m b/2ncoL O)l/2 where es and em a r e the low and h i g h f r e q u e n c y l a t t i c e d i e l e c t r i c c o n s t a n t s , MwL0 the e n e r g y o f a l o n g i t u d i n a l o p t i c a l phonon, and mD t n e b a n d mass o f t h e e l e c t r o n w h i c h i s the e f f e c t i v e mass i n the absence of the electron-phonon i n t e r a c t i o n . The l a t t i c e r e l a x a t i o n e n e r g y i n the p r e s e n c e o f an e l e c t r o n i s approximately equal to awL0)A, and f o r value s of a l p h a g r e a t e r t h a n 6 the e l e c t r o n becomes t r a p p e d i n the p o t e n t i a l w e l l so produced (65). A t h e o r e t i c a l a n a l y s i s o f t h e p o 1 a r o n - e 1 e c t r o n e f f e c t i v e mass i n s t r o n g l y p o l a r m a t e r i a l s by Lee, Low and P i n e s (66). i s c a r r i e d o n l y t o t h e f i r s t o r d e r ; i t p r e d i c t s the i n c r e a s e i n e f f e c t i v e mass caused by e l e c t r o n - p h o n o n i n t e r a c t i o n without c a l c u l a t i n g the energy dependence. The work o f L a r s e n (67), however, i n d i c a t e s a s t r o n g l y energy dependent mass. In p a r t i c u l a r , when the e l e c t r o n approaches the LO phonon energy o f 17.2 mev the e l e c t r o n mass s h o u l d 95 i n c r e a s e r a p i d l y to reach a value approximately 40% g r e a t e r than t h a t f o r a c o l d e l e c t r o n f o r a c o u p l i n g of a =1.6. Our r e s u l t s w i t h o p t i c a l l y detected resonance agree i n some r e s p e c t s with those obtained by c o n v e n t i o n a l methods. The s p l i t t i n g o f the h o l e r e s o n a n c e seen by Tamura and Masumi (54) was not r e s o l v e d i n our work, due to homogeneous l i n e b r o a d e n i n g and, a t 36.3 GHz, by poor s i g n a l t o n o i s e r a t i o . S p l i t t i n g s h o u l d be a p p a r e n t w i t h t h e a p p l i e d m a g n e t i c f i e l d a l o n g the [1,1,1] d i r e c t i o n w h i c h was the o r i e n t a t i o n used i n many o f our e x p e r i m e n t s . The s h i f t i n h o l e r e s o n a n c e t o h i g h e r e f f e c t i v e mass a t h i g h microwave power l e v e l s was t o be e x p e c t e d from the non p a r a b o l i c nature of the valence band. The asymmetry of the e l e c t r o n c y c l o t r o n r e s o n a n c e showed unusual f e a t u r e s . In c o n v e n t i o n a l e l e c t r o n resonance experiments the e l e c t r o n s i g n a l u s u a l l y d i s p l a y s a t a i l on the high l e v e l f i e l d s i d e due to hot e l e c t r o n s with g r e a t e r e f f e c t i v e mass. Our r e s u l t s a t 36.3 GHz showed an i n v e r t e d t a i l : t h e main peak a p p e a r e d as a d e c r e a s e i n l u m i n e s c e n c e w h i l e the t a i l showed an i n c r e a s e . Thus microwave h e a t i n g of c o l d e l e c t r o n s r e d u c e d t h e i r r e c o m b i n a t i o n r a t e a t i o d i n e c e n t r e s , presumably by reducing t h e i r t r a p p i n g p r o b a b i l i t y , w h i l e h e a t i n g of hot e l e c t r o n s i n c r e a s e d t h e i r r ecombination r a t e . For the low microwave powers u s e d , the h e a t i n g i s s m a l l compared to the c a r r i e r temperature so t h a t the e f f e c t can not be a s c r i b e d to an i n c r e a s e i n the hot e l e c t r o n 96 p o p u l a t i o n at the expense of c o l d e l e c t r o n s due to microwave h e a t i n g . A p o s s i b l e e x p l a n a t i o n i s t h a t h ot e l e c t r o n s can drop q u i c k l y onto t r a p s w i t h the e m i s s i o n o f one or more LO phonons. Such e f f e c t s have been observed i n other m a t e r i a l s , Malm and H a e r i n g (68) m e a s u r e d t h e d e p e n d e n c e o f photoluminescent i n t e n s i t y from recombinatio n c e n t r e s i n CdS as a f u n c t i o n o f e x c i t a t i o n w a v e l e n g t h and showed t h a t recombination i s enhanced when e l e c t r o n s can drop to a bound s t a t e w i t h the e m i s s i o n of an i n t e g r a l number of LO phonons. Dean (47) has o b s e r v e d the same p r o c e s s i n e x c i t a t i o n s p e c t r a o f GaP f o r b o t h N and B i l u m i n e s c e n c e c e n t r e s . A s i m i l a r e f f e c t has r e c e n t l y been o b s e r v e d i n e x c i t a t i o n s p e c t r a o f AgBr doped w i t h v a r i o u s i m p u r i t i e s (76). In the p r e s e n t c a s e , r e s o n a n t h e a t i n g o f an e l e c t r o n near the LO phonon e n e r g y would i n c r e a s e i t s p r o b a b i l i t y of making a r a p i d t r a n s i t i o n to a bound s t a t e a t an i o d i n e i m p u r i t y . I t should be noted t h a t the i s o e l e c t r o n i c i o d i n e c e n t r e t r a p s a h o l e f i r s t , t h e n an e l e c t r o n i s a t t r a c t e d t o the c h a r g e d c e n t r e and e n t e r s one of a set of hydr o g e n - l i k e o r b i t s (69). Thus t h e r e w i l l be a band of e n e r g i e s j u s t below the LO phonon e n e r g y from w h i c h e l e c t r o n s can make a phonon a s s i s t e d t r a n s i t i o n to a bound s t a t e . The theory of polaron mass presented by Larsen (67) p r e d i c t s a r a p i d i n c r e a s e i n e f f e c t i v e mass as the e l e c t r o n reaches the LO phonon energy, due t o t h e s t r o n g e 1 e c t r o n - p h o n o n i n t e r a c t i o n . F o r a 97 c o u p l i n g of a=1.6 the theory p r e d i c t s an i n c r e a s e of about 40% i n e f f e c t i v e mass o v e r t h a t f o r a c o l d e l e c t r o n , although the accuracy of the theory i s q u e s t i o n a b l e i n t h i s r a n g e . The n e g a t i v e t a i l o f t h e e l e c t r o n r e s o n a n c e i n our data shows general agreement w i t h t h i s t h e o r y , the peak of t h i s f e a t u r e a p p e a r e d i n f i e l d s between 20% and 50% h i g h e r than the main e l e c t r o n s i g n a l . The t a i l was inhomogeneously broadened due to r a p i d v a r i a t i o n i n e l e c t r o n e f f e c t i v e mass near the LO phonon energy. At 9.2 GHz the e l e c t r o n resonance showed no a p p r e c i a b l e asymmetry, homogeneous broadening having become dominant. At s u f f i c i e n t l y h i g h l e v e l s o f microwave power the s i g n a l i n v e r t e d and b r o a d e n e d . T h i s i n d i c a t e s t h a t the e l e c t r o n s had been h e a t e d t o near the LO phonon energy so t h a t t h e n e g a t i v e t a i l o f the r e s o n a n c e was s t r o n g e r t h a n the low ene r g y e l e c t r o n peak. The b r o a d e n i n g of the s i g n a l was caus e d by i n c r e a s e d s c a t t e r i n g o f t h e hot e l e c t r o n s by a c o u s t i c and o p t i c a l phonons (64). An a t t e m p t was made to e s t i m a t e t h e h e a t i n g e x p e c t e d from the microwaves. The rms e l e c t r i c f i e l d s t r e n g t h i n the microwave c a v i t y i n t h e v i c i n i t y o f t h e sample a t maximum e x c i t a t i o n was c a l c u l a t e d to be 180 V/Cm. Approximating the sample by an e l l i p s o i d gave the f i e l d s t r e n g t h i n s i d e the sample as 90 V/Cm (70). The e l e c t r o n s c a t t e r i n g t i m e was c a l c u l a t e d from the CUT v a l u e o f the low power e l e c t r o n resonance at 9.2 GHz, g i v i n g the average energy acquired by 98 an e l e c t r o n between s c a t t e r i n g s as a p p r o x i m a t e l y 28 meV. T h i s f i g u r e i s o b v i o u s l y an o v e r e s t i m a t e s i n c e s c a t t e r i n g i n c r e a s e s due to e m i s s i o n of a c o u s t i c and o p t i c a l phonons as t h e e l e c t r o n s a r e h e a t e d , but i t i n d i c a t e s t h a t h e a t i n g o f the f r e e e l e c t r o n s of the order of one LO phonon energy does occur at the h i g h e s t l e v e l s of microwave e x c i t a t i o n . 4.5 Summary C y c l o t r o n resonance of e l e c t r o n s and holes i n AgBr has b e en s t u d i e d u s i n g ODMR. Our work has shown t h a t r e c o m b i n a t i on at i o d i n e i s o e l e c t r o n i c i m p u r i t i e s i s a f f e c t e d by c y c l o t r o n h e a t i n g o f e l e c t r o n s and h o l e s as w e l l as by microwave d i e l e c t r i c h e a t i n g . A l l p a r t s of the i o d i n e bound e x c i t o n l u m i n e s c e n c e were shown t o be e q u a l l y a f f e c t e d i n d i c a t i n g t h a t t h e e f f e c t s were c a u s e d by changes i n the t r a p p i n g r a t e o f e l e c t r o n s and h o l e s a t t h e c e n t r e s r a t h e r t han by changes i n the e x c i t o n decay p r o c e s s e s . C y c l o t r o n h e a t i n g o f h o l e s and c o l d e l e c t r o n s r e d u c e d t h e i r r e c o m b i n a t i o n at i o d i n e c e n t r e s , w h i l e h e a t i n g of e l e c t r o n s near th e LO phonon energy i n c r e a s e d t h e i r t r a p p i n g r a t e . This i s e x p l a i n e d by the enhanced t r a p p i n g of a hot e l e c t r o n by the e m i s s i o n o f an LO phonon. Measurements a t l o w e r microwave frequency w i t h s u f f i c i e n t power to heat the bulk of t h e e l e c t r o n s 'to a p p r o x i m a t e l y the LO phonon e n e r g y showed c o n s i d e r a b l e enhancement o f the l u m i n e s c e n c e a t resonance, s u b s t a n t i a t i n g t h i s e x p l a n a t i o n . 99 T h i s t e c h n i q u e p r o v i d e d a means o f m e a s u r i n g the e f f e c t i v e mass o f hot e l e c t r o n s near t h e LO phonon energy d i r e c t l y . A c o m p a r i s o n o f the e f f e c t i v e mass o f the hot e l e c t r o n s determined by t h e i r c y c l o t r o n resonance w i t h t h a t p r e d i c t e d by theory g i v e s reasonable agreement. C y c l o t r o n resonance of holes was a l s o observed but the expected s p l i t t i n g c o u l d not be r e s o l v e d due to the width of the r e s o n a n c e and i n s u f f i c i e n t microwave power a t h i g h frequency. The ODMR r e s u l t s o b t a i n e d f r o m t h e 5700 A.U. luminescence band c o n f i r m those of Hayes et a l and M a r c h e t t i (58,56). The absence of c y c l o t r o n resonance e f f e c t s i n t h i s l u m i n e s c e n c e i n d i c a t e s t h a t t r a p p i n g a t t h e c e n t r e s r e s p o n s i b l e i s much l e s s s e n s i t i v e to c y c l o t r o n h e a t i n g of c a r r i e r s . The n a t u r e of t h e s e c e n t r e s i s not c o m p l e t e l y u n d e r s t o o d , a l t h o u g h t h e y appear t o i n v o l v e some t y p e o f d e f e c t . The p a r a m a g n e t i c r e s o n a n c e s of e l e c t r o n s bound t o t h e t r a p p i n g c e n t r e were shown t o be h o m o g e n e o u s l y broadened. I t i s w o r t h n o t i n g t h a t a l t h o u g h o p t i c a l d e t e c t i o n o f c y c l o t r o n resonance has been r e p o r t e d i n very few m a t e r i a l s , such r e s o n a n c e s may have been o b s e r v e d but not r e c o g n i z e d . The resonance r e p o r t e d by M a r c h e t t i and Burberry (59) i n the luminescence of i o d i n e doped AgBr at g=5.65, and a t t r i b u t e d 100 to a t r a n s i t i o n between s t a t e s of the i o d i n e bound e x c i t o n , was a l m o s t c e r t a i n l y the e l e c t r o n c y c l o t r o n r e s o n a n c e s i g n a l . The g r e a t e r w i d t h o f t h e i r r e s o n a n c e compared t o t h o s e r e p o r t e d h e r e , and i t s l a c k o f s t r o n g asymmetry, i s p r e s u m a b l y due t o t h e h i g h e r l e v e l o f i o d i n e d o p i n g and consequent i n c r e a s e i n i m p u r i t y s c a t t e r i n g . 1 0 1 Chapter 5. Conclusions and Suggestions for further work. 5.0 Introduction. S e c t i o n s 5.1 t o 5.4 c o n t a i n b r i e f s t a t e m e n t s which d e f i n e t he new r e s u l t s w h i c h a r e r e p o r t e d i n the body o f t h i s t h e s i s . S e c t i o n 5.5 c o n t a i n s some s u g g e s t i o n s f o r f u r t h e r work. 5.1 Gallium Phosphide. 1) ODMR s i g n a l s from B i and S i m p u r i t i e s have been observed, they c o n f i r m t h a t the N s i g n a l corresponds to conduction e l e c t r o n resonance. The s i g n a l s were shown to be s a t u r a t e d and homogeneously broadened i n d i c a t i n g a l i f e t i m e of approximately 4 nano seconds. 2) The maximum s i g n a l expected was c a l c u l a t e d and found to give good agreement wi t h the experimental r e s u l t s . T h e c o m p a r i s o n s h o w e d t h a t t h e r e i s r a p i d t h e r m a l i z a t i o n b e t w e e n t h e A and B l i n e s . The temperature dependence of the s i g n a l was measured over a l i m i t e d r a n g e and was f o u n d t o d e c r e a s e w i t h temperature as p r e d i c t e d . 3) P o l a r i z a t i o n e f f e c t s e x p e c t e d i n the ODMR s i g n a l were not o b s e r v e d . T h i s was shown t o be due t o a l a c k of c i r c u l a r p o l a r i z a t i o n and c o n f i r m e d by Zeeman 102 measurements. The h o l e p a r a m a g n e t i c r e s o n a n c e s i g n a l was a l s o a b s e n t . Both e f f e c t s were a t t r i b u t e d t o c r y s t a l s t r a i n s and d e f e c t s . 4) C y c l o t r o n r e s o n a n c e o f e l e c t r o n s and h o l e s was observed by ODMR. Luminescence c e n t r e s were shown to be most s e n s i t i v e to c y c l o t r o n h e a t i n g of the c a r r i e r type f i r s t t r a p p e d by the n e u t r a l c e n t r e . The microwave power dependence of the e f f e c t was measured and showed good a g r e e m e n t w i t h t h e o r y f o r t h e N c e n t r e . Q u a l i t a t i v e agreement was a l s o o b t a i n e d f o r the S c e n t r e . Measurements a t 36.3 GHz gave a c c u r a t e v a l u e s f o r l i g h t and heavy hole e f f e c t i v e masses, these agreed w i t h c y c l o t r o n r e s o n a n c e r e s u l t s o b t a i n e d by o t h e r workers. 5.2 Zinc Telluride. 1) ODMR m e a s u r e m e n t s on ZnTe r e v e a l e d c y c l o t r o n resonances of e l e c t r o n s and h o l e s . As i n GaP d i f f e r e n t r e s o n a n c e s were o b s e r v e d i n d i f f e r e n t l u m i n e s c e n c e bands. U n l i k e GaP, the resonances caused an i n c r e a s e i n luminescence. T h i s was a t t r i b u t e d to an i n c r e a s e i n the number o f i o n i z e d i m p u r i t i e s as a r e s u l t o f c a r r i e r h e a t i n g which r e s u l t e d i n more e f f i c i e n t luminescence. The s i g n a l t o n o i s e r a t i o a t 36.3 GHz was t o o low to all o w u s e f u l r e s u l t s to be obtained f o r t h i s frequency. 103 2) The e l e c t r o n paramagnetic resonance s i g n a l was not s e e n . T h i s was e x p l a i n e d by the absence o f donor-acceptor p a i r luminescence bands from our samples due t o a l a c k of a p p r o p r i a t e i m p u r i t i e s . No p a r a m a g n e t i c r e s o n a n c e s i g n a l c o u l d be seen i n any o f the bound e x c i t o n luminescence. 5.3 S i l v e r Bromide. 1) P a r a m a g n e t i c r e s o n a n c e s o f h o l e s and t r a p p e d e l e c t r o n s were observed and the e l e c t r o n resonance was shown to be homogeneously b r o a d e n e d . Other r e s u l t s agreed with those a l r e a d y r e p o r t e d i n the l i t e r a t u r e . 2) C y c l o t r o n r e s o n a n c e o f e l e c t r o n s and h o l e s was o b s e r v e d by ODMR i n t h e i o d i n e bound e x c i t o n l u m i n e s c e n c e . The r e s o n a n c e s c a u s e d a d e c r e a s e i n l u m i n e s c e n c e , but a t a i l on the e l e c t r o n r e s o n a n c e c o r r e s p o n d i n g t o h o t e l e c t r o n s showed i n c r e a s e d l u m i n e s c e n c e . E x p e r i m e n t s a t 9.2 GHz w i t h adequate microwave power to heat the e l e c t r o n p o p u l a t i o n showed t h a t h o t e l e c t r o n s d i d , i n f a c t , e n h a n c e t h e l u m i n e s c e n c e from t h e i o d i n e c e n t r e . The h e a t i n g e f f e c t s were c a l c u l a t e d t o be of the o r d e r of the LO phonon energy and the e f f e c t was e x p l a i n e d by the i n c r e a s e d t r a p p i n g r a t e f o r t h o s e e l e c t r o n s a b l e t o drop t o a bound s t a t e w i t h the e m i s s i o n o f an LO 104 p h o n o n . The e f f e c t i v e mass o f h o t e l e c t r o n s was e s t i m a t e d from the c y c l o t r o n r e s o n a n c e r e s u l t s and found t o agr e e w i t h the t h e o r e t i c a l p r e d i c t i o n s t o w i t h i n the experimental e r r o r . 3) The poor s i g n a l to noise r a t i o at 36.3 GHz prevented a more a c c u r a t e c o m p a r i s o n w i t h t h e o r y . The h o l e r e s o n a n c e was o b s e r v e d t o broaden and s h i f t t o h i g h e r e f f e c t i v e mass as e x p e c t e d a t h i g h microwave power l e v e l s , b u t the h o l e r e s o n a n c e s c o u l d not be r e s o l v e d p r o p e r l y to permit a more d e t a i l e d a n a l y s i s . 5.4 Curve f i t t i n g . 1) An o r i g i n a l method o f n o n - l i n e a r c u r v e f i t t i n g was d e v e l o p e d t o a l l o w t h e b e s t f i t s o f t h e o r e t i c a l p r o f i l e s t o n o i s y d a t a t o be made. T h i s was compared t o the o t h e r a v a i l a b l e methods and was found t o c o n v e r g e r a p i d l y and to be r e l a t i v e l y i n s e n s i t i v e t o f a l s e minima. 2) The method was a p p l i e d to our data i n an attempt to use s t a t i s t i c a l c r i t e r i a i n d i s c r i m i n a t i n g between v a r i o u s mechanisms. 105 5 . 5 Comments and Suggestions f o r F u r t h e r Work. 1) I t has been shown t h a t the background s i g n a l s o f t e n p r e s e n t i n ODMR e x p e r i m e n t s a r e caused by microwave h e a t i n g and, i n p a r t i c u l a r , c y c l o t r o n h e a t i n g o f f r e e c a r r i e r s . In some c a s e s c y c l o t r o n r e s o n a n c e s may have been observed i n ODMR experiments and mistaken f o r EPR s i g n a l s , as was ment i o n e d i n the c a s e o f AgBr. S i n c e c y c l o t r o n h e a t i n g i s caused by the microwave e l e c t r i c f i e l d and EPR by t h e m a g n e t i c c o m p o n e n t t h e two processes can be d i s t i n g u i s h e d by p l a c i n g the sample at the nodes o f a microwave r e s o n a t o r . Some c o n v e n i e n t means o f moving the sample i n the r e s o n a t o r d u r i n g an e x p e r i m e n t , and w i t h o u t d i s t u r b i n g the f i e l d i n the r e s o n a t o r , i s d e s i r a b l e and should be developed. 2) The use o f ODMR t o o b s e r v e c y c l o t r o n r e s o n a n c e i s s u b j e c t t o t h e same l i m i t a t i o n s as c o n v e n t i o n a l c y c l o t r o n resonance measurements due to sh o r t c a r r i e r s c a t t e r i n g t i m e s i n many m a t e r i a l s and c o n s e q u e n t l y broad resonances. The e f f e c t i v e mass values r e p o r t e d i n t h i s t h e s i s were c o m p a r a b l e w i t h t h o s e d e t e r m i n e d by co n v e n t i o n a l c y c l o t r o n experiments. The main advantage i n u s i n g ODMR i s t h a t i n f o r m a t i o n may be g a i n e d about t r a p p i n g and luminescence processes which are a f f e c t e d by the r e s o n a n c e s . The r e s u l t s r e p o r t e d h e r e showed both r e d u c t i o n s and i n c r e a s e s i n t r a p p i n g a t i m p u r i t i e s as a r e s u l t o f c y c l o t r o n h e a t i n g , i n some c a s e s 106 a l l o w i n g t h e o r e t i c a l p r e d i c t i o n s to be t e s t e d . 3) One o f the f a c t o r s l i m i t i n g the u s e f u l n e s s o f ODMR i s t h e q u a l i t y o f the s i g n a l s t h a t can be o b t a i n e d . In cases where the resonance produces o n l y a s m a l l change i n l u m i n e s c e n c e , o r where the l u m i n e s c e n c e i t s e l f i s weak, the s t a t i s t i c a l n o i s e i n the l u m i n e s c e n c e may obscure the d e s i r e d s i g n a l s . In some cases t h i s may be re m e d i e d by u s i n g h i g h microwave power l e v e l s o r s t r o n g e r e x c i t a t i o n s o u r c e s , but t h i s i s not a l w a y s p o s s i b l e t e c h n i c a l l y . S i g n a l averaging as d e s c r i b e d i n t h i s t h e s i s can be used to improve the s i g n a l to no i s e r a t i o as much as i s d e s i r e d i f s u f f i c i e n t t i m e i s s p e n t i n c o l l e c t i n g d a t a . In our e x p e r i m e n t s , the r u n n i n g t i m e o f the Dewars imposed a l i m i t on the t i m e t h a t c o u l d be sp e n t on such d a t a c o l l e c t i o n b e c a u s e , as e x p l a i n e d i n C h a p t e r 2, r e f i l l i n g t he Dewar d u r i n g a run posed g e n e r a l l y insurmountable d i f f i c u l t i e s . Some e f f i c i e n t means of f i l l i n g a Dewar w i t h l i q u i d helium e v e n w h i l e b e i n g pumped on seems d e s i r a b l e . The a l t e r n a t i v e , of c o n s t r u c t i n g a Dewar which has a longer running t i m e , might produce some improvement but h a r d l y the f a c t o r of 10 or so which i s needed. 4) The r e s u l t s o f ODMR s t u d i e s on GaP showed s e v e r a l n e g a t i v e r e s u l t s w hich were a t t r i b u t e d t o c r y s t a l d e f e c t s . Measurements on h i g h q u a l i t y , s t r a i n f r e e , 107 c r y s t a l s would t h e r e f o r e be of i n t e r e s t . A l t e r n a t i v e l y , the e f f e c t s of s t r a i n s on o b s e r v e d e f f e c t s c o u l d be s t u d i e d by a r t i f i c i a l l y s t r e s s i n g t he c r y s t a l s . The a b s e n c e o f p o l a r i z a t i o n r e p o r t e d h e r e was o n l y approximate, c i r c u l a r p o l a r i z a t i o n of a few percent may have e x i s t e d and been u n d e t e c t a b l e . A more s e n s i t i v e measurement o f the m a g n e t i c c i r c u l a r p o l a r i z a t i o n o f the Zeeman components of e x c i t o n s i n GaP could a l l o w a more d e f i n i t e a n a l y s i s of the d e p o l a r i z i n g e f f e c t s i n GaP. The p r e d i c t e d p o l a r i z a t i o n dependent ODMR s i g n a l s i n GaP-N l u m i n e s c e n c e s h o u l d be o b s e r v a b l e i n the Zeeman components o f the e x c i t o n l i n e s . To s e p a r a t e t h e s e s p e c t r o s c o p i c a 1 l y i n an ODMR e x p e r i m e n t would r e q u i r e microwave f r e q u e n c i e s o f the o r d e r o f 70 GHz. An i n t e r e s t i n g f e a t u r e of the ODMR c y c l o t r o n r e s o n a n c e r e s u l t s was t h e d i f f e r e n c e i n t h e s i g n a l s observed at 9.2 and 36.3 GHz from the N luminescence, a br o a d e l e c t r o n s i g n a l b e i n g dominant a t 9.2 GHz w h i l e the h o l e r e s o n a n c e s were more a p p a r e n t a t 36.3 GHz. Measurements at an i n t e r m e d i a t e frequency such as 20GHz s h o u l d h e l p t o show w h e t h e r t h e e l e c t r o n s i g n a l d i s a p p e a r s due to unresolved s p l i t t i n g as we suggest. . 5) The ZnTe r e s u l t s i n d i c a t e a means of d i s t i n g u i s h i n g i o n i z e d or n e u t r a l donor or a c c e p t o r r e c o m b i n a t i o n c e n t r e s by the resonances shown i n t h e i r luminescence. A t e s t of our i n t e r p r e t a t i o n of these resonances could 108 be made by u s i n g a ZnTe sample doped w i t h an a c c e p t o r or donor w i t h known l u m i n e s c e n c e p r o p e r t i e s . B e t t e r r e s o l u t i o n of the observed c y c l o t r o n resonances c o u l d be obtained i f s u f f i c i e n t microwave power was a v a i l a b l e a t higher f r e q u e n c i e s such as 36.3 GHz. 6) The e l e c t r o n c y c l o t r o n r e s o n a n c e i n AgBr showed an i n t e r e s t i n g enhancement of t r a p p i n g f o r hot e l e c t r o n s . A h i g h e r microwave power l e v e l a t 36.3 GHz where the asymmetry of t h i s resonance i s v i s i b l e would a l l o w the e f f e c t s of s i g n i f i c a n t microwave h e a t i n g to be s t u d i e d as was done a t 9.2 GHz. B e t t e r s i g n a l t o n o i s e r a t i o s c o u l d a l s o be o b t a i n e d which would a l l o w a b e t t e r c o m p a r i s o n t o be made w i t h the t h e o r y . R e s o l v i n g the s p l i t t i n g of the hole resonances should be p o s s i b l e and s i m i l a r e f f e c t s might be v i s i b l e i n them. A s t u d y o f o t h e r p o l a r m a t e r i a l s such as AgCl and KBr u s i n g t h i s technique i s a l s o i n d i c a t e d . 109 APPENDIX 1. Curve F i t t i n g . To d e t e r m i n e which of the two h y p o t h e s e s r e g a r d i n g s i g n a l output p r o f i l e was c o r r e c t , i t was necessary to f i n d l e a s t - s q u a r e s f i t s f o r the e x p r e s s i o n s : y ( i ) = A + E . i + B.exp(-D(C-i)2) A . l y ( i ) = A + E . i + (l+C2D2+i2D2)(1+C2D2)(B-A) A.2 (l-CzD*+izDz) + 4CZDZ I t i s t o be n o t e d t h a t t h e terms A + E . i a r e i n c l u d e d b ecause the base s i g n a l o u t p u t i s known t o have a p o s i t i v e s lope f o r i n c r e a s i n g frequency. The a u t h o r has p r e v i o u s l y d e s c r i b e d a method f o r f i t t i n g the p l a i n L o r e n t z i a n c u r v e t o e x p e r i m e n t a l d a t a (71). However, r e c e n t l y (72) i t has been s u g g e s t e d t h a t the method of Nelder and Meade (73), i n somewhat m o d i f i e d form, i s s u p e r i o r to other methods. The Nelder and Meade procedure had been t e s t e d a l r e a d y i n c o n n e c t i o n w i t h our p r e v i o u s work and had been found t o c o n v e r g e s l o w l y and to be d i f f i c u l t t o s t a r t . I t was thus thought worth t e s t i n g the proposed new v a r i a n t . U n f o r t u n a t e l y the p r i n t e d v e r s i o n of the new procedure was w r i t t e n i n a non-standard v e r s i o n of the PASCAL language and was i n c o m p r e h e n s i b l e . A new v e r s i o n was t h e r e f o r e w r i t t e n i n BASIC t o r u n on t h e computer a v a i l a b l e w i t h the 110 e x p e r i m e n t a l equipment d e s c r i b e d above, and l a t e r i n FORTRAN77 t o r u n on a much f a s t e r computer which was then a v a i l a b l e . In e s s e n c e , f o r two v a r i a b l e s , the p r o c e d u r e i s as f o l l o w s : suppose t h a t the c o n t o u r s R=.l, R=.05 e t c . i n F i g u r e A . l r e p r e s e n t e q u a l v a l u e s o f the r e s i d u a l s o f the t r i a l f u n c t i o n and the experimental data f o r : R = (y(xl,x2). - yo b s (xl,x2) ) 2 Any t h r e e n o n - c o l 1 i n e a r i n i t i a l p o i n t s a r e t a k e n i n the (xl,x2) space, al,a2 and a3 say. N a t u r a l l y , the c l o s e r these are to the a c t u a l minimum the more r a p i d l y w i l l the process converge. The a l g o r i t h m then proceeds as f o l l o w s : 1) Evaluate the r e s i d u a l s at al,a2,a3. 2) Suppose t h a t a i has the l a r g e s t r e s i d u a l . Then ( i n N d i m e n s i o n s ) e v a l u a t e the r e s i d u a l a t a new p o i n t a i ' w h i c h i s a n t i - s y m m e t r i c w i t h r e s p e c t t o a i t h r o u g h the p o i n t which i s the c e n t r o i d of the remaining p o i n t s . 3) I f the r e s i d u a l at a i ' i s s m a l l e r than t h a t at a i but n o t s m a l l e r than the l e a s t r e s i d u a l a t one o f the r e m a i n i n g p o i n t s , a i ' r e p l a c e s a i and the process i s repeated. 4) I f the r e s i d u a l at a i1 i s l e s s than any other r e s i d u a l , a n o t h e r new p o i n t a i " i s d e f i n e d a t d o u b l e the d i s t a n c e from the c e n t r o i d . I f the r e s i d u a l at t h i s p o i n t i s again the lowest, a i " i s a c c e p t e d , o t h e r w i s e a i1 i s a c c e p t e d . The process then r e p e a t s . 5) I f a i ' has a higher r e s i d u a l than a i , a new p o i n t a i ' " i s t e s t e d , where a i ' " i s h a l f way between a i1 and the c e n t r o i d . I f the r e s i d u a l i s now l e s s t h a n t h a t a t a i t h e new p o i n t i s a c c e p t e d . I f n o t , a l l p o i n t s e x c e p t the one w i t h the lowest r e s i d u a l are moved h a l f way towards the c e n t r o i d and the process r e p e a t s . F i g . A . l . I l l FIG. A l THE NELDER - MEAD MINIMIZATION 4 PROCEDURE i » . The three starting points a^ to a^ are shown on a conour map with the three new t r i a l points marked by * 112 A gra p h i c i l l u s t r a t i o n of the way i n which the process works i s gi v e n i n F i g u r e A.2 The new method was a p p l i e d t o the d a t a s e t s d e r i v e d from our e x p e r i m e n t s . Convergence from a p l a u s i b l e t r i a l i n p u t ( d e r i v e d by i n s p e c t i n g t h e d a t a and r o u g h l y e v a l u a t i n g base-slope and h e i g h t , peak p o s i t i o n height and width) was f a i r l y s l o w ( c a . 20 minutes) i n BASIC. The FORTRAN v e r s i o n was f a s t e r ( c a . 2 m i n u t e s ) . R e s u l t s f o r 5 data s e t s are shown i n Tables A . l and A.2. Data Set # IA5 IA6 IA7 IA8 A 5489.36 4638.04 1015.07 1874.05 B 11082.3 11991.2 5075.37 10622.52 C 19.0711 20.2828 18.2713 23.8522 D .222158 .239845 .249994 .108304 E .348464 -.099438 .195465 .021466 Res i d u a l 6.039E6 1.279E7 5.339E6 3.893E7 Table A . l . Gaussian L.S. c o e f f i c i e n t s . Data Set # IA5 IA6 IA7 IA8 A 251.655 254.673 -319.256 223.065 B 3012.29 3031.71 179.129 2175.93 C 18.7898 20.1411 18.0421 23.6111 D .159806 .148402 .264559 .143477 E -56.8243 -6.47207 -27.6918 -21.7666 Re s i d u a l 5.294E7 7.583E7 8.980E6 4.511E7 Table A.2. L o r e n t z i a n L.S. c o e f f i c i e n t s . In t e r m s o f the r e s i d u a l s i t i s c l e a r t h a t the G a u s s i a n curve p r o v i d e s the best f i t to the data. However, i n s p e c t i o n 113 FIG, A2 THE MINIMIZATION PROCESS 114 o f t h e p l o t s o f c a l c u l a t e d and o b s e r v e d d a t a p o i n t s suggested t h a t the L o r e n t z i a n f i t might have converged to a f a l s e minimum. A t y p i c a l example i s shown i n F i g u r e A.3. where i t i s seen t h a t the L o r e n t z i a n a p p e a r s t o under-estimate the data at the lower end. A number o f f u r t h e r runs were made w i t h d i f f e r e n t s t a r t i n g c o n d i t i o n s i n the hope t h a t a l t e r n a t i v e , and b e t t e r , parameters would be o b t a i n e d . These were u n a v a i l i n g . I t was n e x t d e c i d e d to t r y our own method (71). In essence t h i s takes each of the t r i a l parameters i n t u r n and seeks the v a l u e of t h a t p a r a m e t e r w h i c h g i v e s the l e a s t r e s i d u a l . A f t e r c y c l i n g through the v a r i a b l e s the process i s repeated from the s t a r t u n t i l no f u r t h e r change o c c u r s . The d e t e r m i n a t i o n o f the b e s t v a r i a b l e v a l u e s i s a c h i e v e d by q u a d r a t i c i n t e r p o l a t i o n u s i n g : x ( i + l ) = x ( i ) + dx(fm - fp)/(2fm-4f0+2fp) where: fm = f ( x i - d x ) fO = f ( x i ) f p = f(xi+dx) S i n c e i t i s assumed t h a t the r e s i d u a l s a r e q u a d r a t i c f u n c t i o n s o f p o s i t i o n t h i s may lead to divergence when the c o n d i t i o n i s not s a t i s f i e d . To avoid t h i s , the programme i s 115 FIG. A3 GAUSSIAN AND LORENTZIAN FITS TO DATA A comparison of two possible line shapes f i t t e d to the ODMR signal from GaP-N showing the deviation of the Lorentzian f i t at low f i e l d so a r r a n g e d as t o t a k e as the ne x t v a l u e o f x i t h a t member o f x ( i + l ) , x i - d x , x i , o r x i + d x w h i c h g i v e s t h e l e a s t r e s i d u a l . The r e s u l t s d e r i v e d f r o m t h e o p e r a t i o n o f t h i s programme, u s i n g as s t a r t i n g v a l u e s t h o s e g i v e n i n T a b l e s A . l . and A.2. are shown i n t a b l e s A.3. and A.4. Data Set # IA5 IA6 IA7 IA8 A B C D E R e s i d u a l 5630.67 11229.3 19.0879 .222943 -8.78307 5.668E6 4379.02 11960.6 20.2518 .241384 15.0888 1.195E7 1019.99 5054.56 18.2207 .258487 4.72859 5.123E6 1662.56 10428.8 23.6277 .111812 19.1017 3.558E7 Table A.3. Revised Gaussian L.S. c o e f f i c i e n t s Data Set # IA5 IA6 IA7 IA8 A 4295.33 3015.40 497.539 -1562.43 B 5181.97 3796.65 804.270 1298.64 C 19.0892 20.0000 18.1076 23.4852 D .279086 .290409 .334848 .121133 E 3.40091 -19.4032 -8.86383 -44.7434 Res i d u a l 4.856E6 1.650E7 5.801E7 3.826E7 Table A.4. Revised L o r e n t z i a n L.S. c o e f f i c i e n t s . I t i s e v i d e n t t h a t t h e IA5 and IA6 L o r e n t z i a n c o e f f i c i e n t s have changed c o m p l e t e l y . A l s o i t w i l l be seen t h a t w h i l s t the r e s i d u a l s f o r IA6 t o IA8 s t i l l show t h a t the Gaussian v e r s i o n i s s u p e r i o r , the d i f f e r e n c e i s not so great as b e f o r e . In a d d i t i o n , f o r IA5, the L o r e n t z i a n now g i v e s a 117 lower r e s i d u a l although by a very s m a l l amount. S T A T I S T I C A L A N A L Y S I S The standard Chi-square t e s t f o r goodness of f i t i s not a p p l i c a b l e t o d a t a o f the t y p e i n v o l v e d i n our e x p e r i m e n t s s i n c e t h e y do not i n v o l v e f r e q u e n c i e s . I t was t h e r e f o r e decided to compute the c o r r e l a t i o n c o e f f i c i e n t s , d e f i n e d by: r = - x ) ( y i - y)//z(xi - x ) 2 . l (y i - y)2 A. 3 . where the x^ a r e c a l c u l a t e d v a l u e s and the y^ a r e the observed v a l u e s . In p r a c t i c e A.3. i s used i n the form: r = £xi . y i - (Exj.) ( l y i ) /N J(txi - ( £ x i )z/ N ) ( % i - (^YOZ/N) T h i s r e d u c t i o n i s s a t i s f a c t o r y so long as r i s not so s m a l l t h a t c a n c e l l a t i o n r e s u l t s i n l o s s of a c c u r a c y . The 95% c o n f i d e n c e l i m i t s on r can be d e r i v e d u s i n g F i s h e r ' s t r a n s f o r m a t i o n (74) to normal form: z = l o g ( ( 1 + r ) / ( 1 - r ) ) / 2 The r e s u l t s are shown i n Table A.5. 118 Gaussian IA5 IA6 IA7 IA8 Upper 9 5% .996 .992 .981 .980 r .994 .989 .973 .973 Lower 95% .992 .984 .961 .964 L o r e n t z i a n IA5 IA6 IA7 IA8 Upper 95% .997 .992 .984 .984 r .995 .985 .969 .971 Lower 9 5% .993 .970 .939 .949 Table A.5. C o r r e l a t i o n c o e f f i c i e n t s and c o n f . l i m i t s . I t i s c l e a r t h a t i n the c a s e s o f IA5-IA8 the G a u s s i a n curve g i v e s s u p e r i o r c o r r e l a t i o n , although the d i f f e r e n c e i s s m a l l . The d i f f e r e n c e f o r IA5 i s i n the r e v e r s e s e n s e , however the d i f f e r e n c e i s so s m a l l t h a t the r e s u l t i s not s i g n i f i c a n t . T h i s c o n c l u s i o n i s supported by the values of the hypo t h e s i s t e s t s t a t i s t i c (74): H0 = ( z i - zn)/ az _ z i • where az _ = / l / (N-3) +1/ (N-3) t o "* The valu e s are: IA5 -.316 IA6 .661 IA7 .256 IA8 .175 w h i c h s u p p o r t s t h e a s s e r t i o n t h a t t h e G a u s s i a n and L o r e n t z i a n f i t s are not s i g n i f i c a n t l y d i f f e r e n t at the 95% 119 l e v e l w h i c h i s a c c e p t e d as t h e l e a s t f o r w h i c h t h i s s t a t i s t i c i s v a l i d . In a d d i t i o n i t may be remarked t h a t the b a s e - l i n e slope f o r IA5 i s n e g a t i v e f o r b o t h G a u s s i a n and L o r e n t z i a n f i t s . 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S l i w c z u k , U., Nakamura, K., and von der O s t e n , W., S o l i d State Comm. 4 5 , 1013 (1983) 77. Lax, M., Phys. Rev. 1 1 9 , 1502 (1960) 78. C z a j a , W., Phys. d. kondensierten M a t e r i e . 1 2 , 226 (1971) 79. F a u l k e n e r , R.A., Phys. Rev. 1 7 5 , 991 (1968) 125 PUBLICATIONS I. Booth, M. Hawton, and W. Keeler "Pressure Dependent Compensation in InSb" Phys. Rev. B. Vol. 25, pg. 7713 (1982) I. Booth, C. Schwerdtfeger, and W. Czaja "ODMR of Bismuth and Sulpher in GaP" Solid State Comm. Vol. 45, pg. 677 (1983) I. Booth and A.D. Booth "Fisher's Exact Probability Test: the calculation", Math. Gaz. Vol. 67, pg. 131 (1983) I. Booth and A.D. Booth "On a class of least squares curve fitting problems." J . Comp. Phys. Vol. 53, pg. 72 (1984) I. Booth and A.D. Booth "PET revisited, a 40 year overview" Physics in Canada Vol. 40, pg. 57 (1984) I. Booth and A.D. Booth "An interesting determinant", Math. Gaz. Vol. 68, pg. 281 (1984) I. Booth "Non-equilibrium effect in electromagnetic resonators". Speculation in Science and Technology (Accepted 1984) I. Booth and A.D. Booth "A practical problem in Coordinate Transformation" J . Oceanography (accepted 1984) I. Booth and C. Schwerdtfeger "Optically detected cyclotron resonance in AgBr", Phys. Stat. Sol. (submitted) S. Fong, W. Keeler, and I. Booth "Pressure dependent Hall effect measurements in InSb", 1979 Congress of the CAP I. Booth and A.D. Booth "Computer development and construction in Saskatoon" CIPS Conference proceedings (1984) 

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