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EPR study of CdIn₂S₄ Kerr, Richard Kelso 1971

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EPR STUDY OF CdliigS by RICHARD KELSO KERR A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of Physics We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1971 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia Vancouver 8, Canada Date N cnr. - i i -ABSTRACT Properties of Cdln^S^ have been studied using EPR. The temperature 2+ dependence of the hyperfine interaction for Mn impurities has been measured over the range 1 °K - 4 5 0 °K. The results have been interpreted using both the localized vibration model and the interaction with the 2+ phonon continuum. The g-tensor for Co dopants has been determined, yielding gj_= 4 . 0 7 ± . 1 5 , g„ = 6 . 0 0 ± . 0 5 with the distortion axes along 2+ 2+ the four < 1 l O directions. Both Mn and Co have a preference to substitute at a "B" site in the crystal. A 'conduction electron' signal that i s dependent on the sulphur vacancy concentration has been observed with an isotropic g = 1 . 6 8 ± . 0 0 5 . The g-value for a resonance ascribed to surface states was found to be 1 . 7 0 . Strain experiments indicate that the band gap is most probably a direct one. Preliminary studies of production of sulphur vacancies by heat treatment and light excitation of electrons have been performed. — i i i — TABLE OF CONTENTS Page Abstract i i Table of Contents i i i List of Figures v i List of Tables v i i Acknowledgements v i i i CHAPTER 1 - INTRODUCTION 1.1 General Introduction 1 1.2 Motivations 1 1.3 Thesis Outline 3 CHAPTER 2 - LITERATURE SURVEY: SAMPLES 2.1 Samples 4 2.2 Crystal Structure 5 2.3 Phase Transition 6 2.4 Optical Experiments 7 2.5 EPR Experiments 8 2.6 Band Calculations 9 2.7 The CdS - C d l n ^ - I n ^ System 11 2.8 Point Form Summary of Essential Features 12 CHAPTER 3 - APPARATUS AND OPERATION 3.1 Apparatus 14 3.2 Sensitivity 14 3.3 Resonant Cavities 16 CHAPTER 4 - TRANSITION IONS 4.1 Introduction to EPR Theory . 19 - i v -Page 4.2 Introduction to Crystal Field Theory 20 4.3 CdlxigS^tMn (a) Introduction 23 (b) Mn - Crystal Field Interaction 23 2+ (c) The Theory of the Hyperfine Interaction for Mn 24 (d) The Temperature Dependence of A 25 (e) Room Temperature Properties of the Spectra 27 (f) The Temperature Dependence of the Spectra 29 (g) Comments and Discussions of the Data 32 4.4 CdIn„S,:Co 2 4 (a) Introduction 35 (b) The Theory of Co in Octahedral Coordination 36 (c) Experimental Results 38 (d) Analysis and Discussion of the Data 41 4.5 Conclusions and Comments 45 CHAPTER 5 - 'CONDUCTION ELECTRONS' 5.1 Introduction 47 5.2 The Theory of the'g-Value for Banded Electrons 48 5.3 Properties of the Spectra 50 5.4 Sulphur Vacancies and Heat Treatment Techniques 53 5.5 Strain Effects 57 5.6 Light Excitation 58 5.7 Discussion and Comments 58 CHAPTER 6 - CONCLUSIONS 6.1 General Conclusions 61 6.2 Possible Additional Experiments 63 BIBLIOGRAPHY 65 APPENDIX 1 - Samples 68 APPENDIX 2 - The Measurement of "X" 69 - V -APPENDIX 3 - Maximum Sensitivity of a Microwave Bridge 71 and Detector APPENDIX 4 - Measurement of g and A in the Presence of an 73 Hyperfine Interaction APPENDIX 5 - Properties of Powder Spectra 75 APPENDIX 6 - Second Order g-Value Corrections for Co 2 + 77 - v i -LIST OF FIGURES Pass FIGURE 2.1 The normal cubic spinel structure for C d l n ^ 5 a FIGURE 2.2 Theoretical band structures of C d l n ^ 10 FIGURE 3.1 Experimental arrangement 15 FIGURE 3.2 T E 1 Q 2 cavity with provision for rotating the 18 sample holder FIGURE 4.1 The EPR signal for a Kramer's doublet 19 FIGURE 4.2 Experimental traces for Cdln^rMn 28 FIGURE 4.3 Experimental results for A(T) fitted to the 30 model of 5imanek and Orbach FIGURE 4.4 Experimental results for A(T) fitted to the 31 localized phonon model of Sdansky 2+ FIGURE 4.5 Orbital energy level diagram for Co in an 36 octahedral f i e l d FIGURE 4.6 Experimental traces for C d l n ^ t C o 2 * at 1.1 °K 40 2+ FIGURE 4.7 Plot of g vs. g n for Co in an octahedral fi e l d 43 2+ FIGURE 4 .8 Plot of gt| vs. x for Co in an octahedral field 44 FIGURE 5«1 'Conduction electron' resonance experimental traces 52 FIGURE 5.2 Surface state resonances 54 FIGURE 5*3 Qualitative effects of sulphur vapor pressure 56 on the 'conduction electron' EPR signal FIGURE A2.1 EPR spectrometer equivalent circuit 69 FIGURE A3.1 Schematic diagram of a magic tee reflection 71 spectrometer FIGURE A4.1 Representation of an 1=5/2 hyperfine spectrum 73 to second order FIGURE A5.1 Single line powder spectrum for anisotropic g-values 75 FIGURE A5.2 Three line powder spectrum for anisotropic g-values 76 - v i i -LIST OF TABLES TABLE 2.1 Experimental band gap values 8 2+ TABLE 4.1 Experimental values for C d l n ^ i M n 27 2+ TABLE 4.2 Experimental values for C d l n ^ t C o 41 TABLE 5.1 Comparison of donor electrons i n CdS and Cdl^S^ 59 TABLE A1.1 Available samples 68 - v i i i -ACKNOWLEDGEMENTS I wish to thank Dr. C.F. Schwerdtfeger for his supervision and assistance both in the preparation of the thesis and in the performance of the experiments. I would also like to express my gratitude to other members of my committee (Dr. R. Barrie, Dr. J. Eldridge and Dr. D. Balzarini) for their discussions and their indulgence in the time period leading up to the completion of the thesis, A scholarship from the National Research Council of Canada and a H.R. MacMillan Family Fellowship are gratefully acknowledged. Support for this work was also provided by the Department of Veteran's Affairs and was greatly appreciated. Research for the thesis was financed by the National Research Council through grants to Dr. Schwerdtfeger. Lastly, I would like to thank my wife Shirley for her constant encouragement and patience. -1-CHAPTER 1 - INTRODUCTION 1.1 GENERAL INTRODUCTION Cdln^S^ is a semiconductor that crystallizes in a cubic spinel form. Unlike most spinels i t i s neither ferri-y ferro-or antiferro-magnetic. It has a band gap of approximately 2 eV at room temperature. Optical properties such as photoluminescence and photoconductivity have been extensively studied but few EPR (electron paramagnetic resonance) experiments have been performed until the past year. Thus the substance is well suited for a general EPR study of i t s properties. The unusual features of the material include a Landau-type second o order phase transition at 403 K and an inability of X-rays to determine * the true crystal structure . Other properties such as band structure and crystal f i e l d parameters are intrinsically interesting. 1.2 MOTIVATIONS Owing to the nature of the study i t i s clarifying to present the purpose of the experiments in tabular form. The aims of the work are: (i) to investigate the prediction of Czaja and Krausbauer (1969) that there exist discrete energy levels within the band gap inherent to the intrinsic crystal structure. It is possible that these levels could exhibit an EPR signal i f they were occupied by electrons. ( i i ) to elucidate the nature of the luminescent centers by the study of deep donors (transition ions) and shallow donors (in this case, sulphur vacancies). ' * 2 + 3 + This is because Cd and In have the same number of electrons around the positive nuclear core. -2-( i i i ) to undertake a general EPR study of the material with the ultimate * aim of discussing the site assignment of impurities within the crystal . (iv) to study the reported second order phase transition at 403 °K (Czaja, 1969) both by observing the Mn 2 + resonance as the crystal is heated through the transition temperature and by heat treating the samples prior to a low temperature EPR experiment. (v) to observe the Mn spectrum, relate the temperature dependence to local or bulk properties of the crystal and establish a site assignment for the impurity. (vi) to try to resolve the problem of the crystal structure which may be one of; a normal spinel, a partially inverted spinel, or a fully inverted spinel . (vii) to observe an EPR signal from 'conduction electrons' so that the g-value may be related to band parameters and compared to other related materials. ( v i i i ) to investigate the physical production of sulphur vacancies and the associated EPR signal. (ix) to elucidate the nature of the band gap (direct or indirect) by applying uniaxial stress to a sample doped with sulphur vacancies. (x) to make a preliminary study of the effect of illuminating the samples with white light. For example the cationshave two possible sites having tetrahedral and octahedral symmetries respectively. The difference between these is a rearrangement of Cd and In on the cation sites. *** In practice i t i s impossible to determine whether the electrons are in a donor band or in the conduction band^ using EPR alone. -3-1.3 THESIS OUTLINE Chapter 2 contains a description of the samples used i n the experiments and a l i t e r a t u r e survey of Cdln^S^. Emphasis i s also placed on the CdS -CdLx^ - In 2S^ system. Chapter 3 contains a b r i e f description of the apparatus and a discussion of s e n s i t i v i t y . Chapter 4 contains both experimental results and immediate conclusions 2+ 2+ f o r the t r a n s i t i o n ions Mn and Co . An introduction to EPR, i n general, and to c r y s t a l f i e l d theory, i n particular, i s presented. Chapter 5 centers about the observed 'conduction electron' resonance along with additional studies of applied s t r a i n , l i g h t illumination, and the production of sulphur vacancies. A b r i e f introduction to g-value theory f o r banded electrons i s given. Chapter 6 contains general conclusions and a l i s t of additional experiments that could be performed. -4-CHAPTER 2 - LITERATURE SURVEY; SAMPLES 2.1 SAMPLES CdlrigS^ i s a semiconductor that may range in color and opacity from an almost-transparent deep red to an opaque black depending on the dopant and i t s concentration. A l l the crystals investigated were very brittle and chipped easily. Cdln^S^ has a melting point of 1105 °C and is conveniently synthesized by two main techniques; (i) directly from the melt in closed quartz ampoules under excess sulphur vapor pressure (Czaja and Krausbauer, 1969; Henning et al,,1969; Shand, 1969). ( i i ) from the elemental vapors using chemical transport with iodine as the transporter (Beun and Nitsche, 1960; Boorman, 1970; Abdulaev et al., 1969). The crystals for this thesis were obtained from sources utilizing both of these techniques (Appendix 1 ). Dr. W. Czaja generously supplied us with a large complement of samples grown using the f i r s t technique. Several other samples grown using the second method were obtained commercially from the New Brunswick Research and Productivity Council (NBRPC). These crystals were close to perfect octahedra with a l l faces being (111) planes. This facilitated the orientation of the samples and X-ray analysis proved unnecessary. 4 5 - 2 Dr. Czaja's samples had dislocation counts as low as 10 - 10 cm. 16 17 —3 for pure samples and the impurities had concentrations of 10 - 10 cm. Sometimes called the Stockbarger Technique (Shand, 1969). -5-16 17 —3 The crystals supplied by NBRPC also had impurity counts of 10 - 10 cmT . No data is available on their dislocation counts but normally crystals grown from the vapor phase are relatively free of dislocations(Boorman, 1970) 2.2 CRYSTAL STRUCTURE Cdln^S^ crystallizes in the spinel form having the same space group, 0^ (Fd3m), as the diamond structure. The primitive rhombohedral unit c e l l contains two formula units. The face centered, cubic, compound cel l contains eight formula units of Cdln^S^' and has a lattice constant of 10.797 X. Because of the complexity of the compound c e l l the problem is normally reduced to a consideration of the two cation sites in the substance (Figure 2.1). These sites are generally referred to as "A" and "B" sites in the literature for a l l spinels. The notation is derived from antiferromagnetic spinels which have spins aligned on "A" and "B" superlattices. If Cdln^S^ were a normal spinel the "A" site would be occupied by a Cd atom and the "B" site by an In atom. However, i t is very d i f f i c u l t -2+ 3+ i f not impossible- to distinguish between Cd and In ions by conventional X-ray techniques, since they are isoelectronic. It is only by indirect methods that one can determine the actual structure for this spinel (Suchow and Stemple, 1964). In the absence of any direct determination three possible structures have been suggested; (i) normal spinel {cd][ln„] S ( i i ) partially inverted spinel j c d^l^y^ l j^l^ 1 1^/^?] S ( i i i ) fully inverted spinel Icd^^In^^l^Cd^^In^^l S^ where j | = tetrahedral, "A',' site and "j ^ octahedral, "B", site. FIGURE 2.1 The normal cubic spinel structure for Cdln S . -6-The essential difference between ( i i ) and ( i i i ) is that in ( i i ) the Cd atoms are equally distributed on the "A" and "B" sites while in ( i i i ) the Cd atoms are randomly distributed on the two sites. 2.3 PHASE TRANSITION Czaja (1970) measured ^ ( T ) , the specific heat, and discovered an o anomaly in C^ at 403 K that he attributed to a second order phase transition of the Landau type (order - disorder). This anomaly was approximately a 1C$ change in C^ over a temperature range of ~5 °K. Very long times (^20 hours) were required for the establishment of internal equilibrium in the best crystals. However, when the samples were heat treated at 500 °C, sublimating sulphur from the samples to create sulphur vacancies, the relaxation times to establish internal equilibrium were lowered to a few hours. A Landau type second order phase transition can only occur in this crystal i f the structure is of type ( i i ) , the partially inverted spinel, due to group theoretical arguments (Haas, 1965). The order - disorder transition is then due to a reordering of the Cd and In ions on the "A" sites. Above 403 °K they are distributed randomly on the sites, while below 403 °K they are arranged in a diamond type superlattice at these sites. -7-2.4 OPTICAL EXPERIMENTS After the original synthesis and X-ray studies on Cdln^S^ powders by Hahn and Klinger (1950), most of the work reported in the literature has been optical in nature owing to the high photosensitivity of the compound. The f i r s t experiments (performed at room temperature) measured the photoconductivity of Cdln^S^ ( Bube and McCarroll, 1959; Beun and Nitsche, 1960; Koelmans and Grimmeiss, 1959)• A peak in conductivity with optical excitation less than the band gap was observed. A dependence of intrinsic dark conductivity on sulphur vapor pressure above the crystal-forming melt was noted by Koelmans and Grimmeiss. Hall measurements of Beun and Nitsche indicated that a l l of their samples were n - type. Later experiments extended the photoconductivity measurements to 77 °K ( Boltivets et al.,1969; Abdullaev et al.,1969). Abdullaev et al.demonstrated the significance of sulphur deficiency on the photoconductivity spectrum. The next set of experiments were photoluminescence studies ( Springford, 1963; Suchow and Stemple, 1964; Czaja and Krausbauer, 1969) performed from , o o 6 K up to 300 K. Springford and Czaja both saw two maxima in the emission spectrum. Springford attributed the luminescent centers to "anion complexes in the region of cation vacancies". Czaja refined this model by using the partially inverted spinel structure to label the two sites as Cd ions at "B" sites and In ions at "A" sites, each in conjunction with a nearby sulphur vacancy. Heat treatment changed the spectra but no clear relationship could be established between the length of time the sample was treated and the intensity of the observed luminescence. -8-Electroluminescence was studied by Suchow and Stemple but no quantitative results were reported. Thermoluminescence experiments were carried out by Springford (1963). Band gap energies were measured by several authors and may best be presented i n tabular form: E s Experimenter Temperature Method 2.18 eV Bube et al . , 1 9 5 9 2.2 eV Koelmans et al,,1959 2.35 eV Springford., 1963 2.3 eV Beun et al.,1960 2.3 eV Abdullaev et al.,1969 2.37 eV Czaja et al.,.969 2.22 eV Czaja et al.,1969 300 °K Photoconductivity 300 °K Optical absorption 90 °K Diffuse reflectivity 300 °K Optical absorption 77 °K Optical absorption 77 *K Optical absorption 300 °K Optical absorption TABLE 2.1 Experimental band gap values 2.5 EPR EXPERIMENTS EPR i n CdlngS^ has a short history, the f i r s t report appearing two years ago. This work was that of Czaja and Krausbauer (1969) who did EPR on a Mn doped sample. They observed the characteristic six line hyperfine 2+ spectrum ( i = 5/2) for the Mn ion and from the hyperfine splitting * constant, A, deduced the amount of covalent bonding present in the host. Next, Henning et al (1969) published EPR data for Cr doped samples. 3+ They concluded from the properties of the spectra that they observed Cr at "B" sites. A distortion axis in the <111> directions was established and values of g„ = 1.995 ± .005, g t = 2.000 t .005 and D = -(0.187 ± .002) cm. ^ were measured. for a discussion of the theory of this effect see Chapter 4. -9-Then, Brovm et al. ( 1970a, 1970b) published papers on Er and Yb doped samples. Both were found to substitute as triply positive charged ions 3+ at "B" sites having distortion axes in the <111> directions. For Yb 3+ they found g ( | = 3 . 4 5 t . 0 5 and g^ = 2 . 0 0 t . 0 5 while for Er the results were g(| = 1 . 9 0 t . 0 5 and gx = 9 . 0 ± . 2 . Optical data supported the site assignments. By analysing the crystal field splitting in terms of a point charge model they found that Czaja 1s model of a partially inverted spinel gave better agreement with experiment than either a normal, or a fully inverted spinel. However their results were far from conclusive. It i s interesting to note that in a l l work published where an impurity site i s investigated the cation always sits at a "B" site regardless of i t s charge state. 2 . 6 BAND CALCULATIONS Since the primitive c e l l of CdL^S^ contains two formula units and thus 64 valence electrons i t i s very d i f f i c u l t to carry out any worthwhile band structure calculations. The f i r s t person to attempt the problem was Rehwald (1967) who used the nearly free electron model. The main result was the identification of. symmetry properties of the bands. Then he applied the model pseudopotential of Heine, Abarenkov and Animalu as a perturbation to the nearly free electron model ( Figure 2 . 2 ) , thus obtaining representative energy levels for high symmetry points in the Brillouin Zone. He also did a rough tight binding calculation ( Figure 2 . 2 ) . From this work no prediction as to whether the band gap is direct or indirect could be made. The next attempt was by Meloni and Mula (1970) who used an empirical pseudopotential and a simplified model of the actual crystal structure in -10-MODEL POTENTIAL PERTURBATION E(k) IN eV <111>-k-<100> TIGHT-BINDING MODEL i E(k) 1. VALENCE BAND L r x -e<111>-k-<100>-^  PSEUDOPOTENTIAL • k E(k) IN eV 5- MODEL 4-3- L. ^ — ^ . c " r ^ C " " . - ^ - J ^ - . * 2- ""'.I-- A, A V " X 1 -0--1-- 9 -U, / ' A , / 5 — — \ <111>^ -k-><100> FIGURE 2.2 Theoretical band structures of CdIn„S -11-order to circumvent the problem of the large number of valence electrons in the unit c e l l ( Figure 2.2 ). They chose a fictitious unit c e l l containing 1/4 of a formula unit. Their predictions include a valence band maxima essentially the same as Rehwalds, but they predict an indirect band gap of ~2.1 eV with the minima in the <1lO directions. Czaja (1969) also predicted an indirect gap based on a simple argument. He reasoned that since I * ^ ^ w a s known to have an indirect gap ( Rehwald and Harbeke, 1965) and a continuous mixture between Cdln^S^ and Ii^S^ e x l s * e < l a s single crystals, then Cdl^S^ was likely to have an indirect gap. As yet this prediction has not been verified directly by experiment. 2.7 THE CdS - CdIn 2S 4 - I n ^ SYSTEM CdS is an extensively studied binary compound because of i t s photo-sensitivity and piezoelectric properties. It crystallizes in the Wurtzite structure which i s non-cubic. The effect of heat treatment on both optical and EPR spectra has been thoroughly studied (Brailsford and Woods, 1968; Boer and Kennedy, 1967). Optical absorptions and EPR signals have been attributed to both Cd and S vacancies. The S vacancy was found to contribute an EPR line characteristic of a shallow donor and was also found to be sensitive to light illumination of the sample (Morigaki, 1964)• Until recently no single crystal intermediate mixtures of the CdS -Cdln^S^ system have been reported, however Boorman has privately communicated that he has succeeded in synthesizing single crystals of stoichiometric composition within the mixture by using vapor transport techniques for growth. The other side of the system, CdIn„S. - In.-S , i s perhaps more -12-interesting because of the existence of continuous mixtures of the form Cd^ ^ I n ^ + ^ ^ S ^ . The mixed crystals, as well as the two end products, have a spinel structure. They have been studied optically by Czaja and Krausbauer (1969) and Suchow and Stemple (1964). Czaja found that the optical energy gaps of the crystals varied linearly with x in the mixture formula to an accuracy of 1 $ at 77 °K. Luminescence spectra were also observed as a function of x. Pure Ii^jS^ crystallizes in two phases, c< and ^ . There is an irreversible transition from C< to f i at 330 °C (Hahn and Klinger, 1950), and thus from normal crystal growing techniques the resultant product is the Q phase, which has a spinel structure with an ordered arrangement of sulphur vacancies. Microcrystals of the phase are created as a precipitate of a chemical reaction (Bube and McCarroll, 1959). The most comprehensive study of (3 -In^S^ is that of Rehwald and Harbeke (1965) * who did an extensive study of conduction mechanisms. They also heat treated their samples to show that the concentration and sign of the charge carriers could be attributed to sulphur deficiencies. They deduced an indirect energy gap of 1.1 eV and a direct gap of 2.03 eV. 2.8 POINT FORM SUMMARY OF ESSENTIAL FEATURES (i) There are two ways to grow Cdln^S^ crystals; directly from the melt and by chemical transport techniques. The crystals used in the experiments were grown using both methods. * Hall coefficient, resistivity, optical absorption -13-( i i ) The true crystal structure of CdlrigS^ is not directly established, except that i t is a spinel which is normal or partially inverted or totally inverted. ( i i i ) Observation of a second order phase transition in C led P Czaja to propose that the true structure was a partially inverted spinel since second order transitions of the Landau type are possible only for this structure. (iv) CdTj^S^ has been studied extensively by optical methods. Sulphur vacancies have been shown to play an important role in photo-conductivity, luminescence and absorption spectra. (v) EPR work has been confined to rare earths and transition elements. The results indicate that the cation impurity always substitutes at a "B" site regardless of i t s charge state. No shallow donor resonance has been reported. (vi) There have been two attempts at band structure calculations, the latest predicting an indirect band gap. (vii) The CdS - CdIn0S. - In_S_ system is of interest because CdlnJS. c. 4 c. 3 £ 4 may be thought of as composed of CdS + I^S^. Also since both Cdl^S^ and l n 2 ^ crystallize in spinel form there i s a continuous single crystal mixture between the two. The single crystals on the other side of the system (CdS - CdIn0S.) crystallize in hexagonal and t r i c l i n i c forms. - 1 4 -CHAPTER 3 - APPARATUS AND OPERATION 3.1 APPARATUS For most of the experiments a standard EPR detection arrangement with a 'magic tee 1 and r e f l e c t i o n cavity was used (Poole, 1 9 6 7 ) . However, fo r the l a t e r experiments a three port c i r c u l a t o r was u t i l i z e d (Figure 3 . 1 ) • This configuration has the advantage of allowing the entire signal from ' the cavity to f a l l upon the c r y s t a l detector and thus the signal/noise r a t i o i s improved by a factor of two over the standard 'magic tee 1 spectrometer. The s t a t i c magnetic f i e l d , H 0, i s monitored by an NMR (nuclear magnetic resonance) marginal o s c i l l a t o r spectrometer (Robinson, 1 9 5 9 ) , which i s essentially the MHz equivalent of a GHz r e f l e c t i o n cavity EPR spectrometer. 3 . 2 SENSITIVITY Since many of the experiments were concerned with searching f o r EPR signals (which may have been weak) f o r various dopants i n CdlngS^, i t was important to maintain the spectrometer at a high s e n s i t i v i t y . The change i n reflected power at resonance, &P, i s proportional to the imaginary part of the s u s c e p t i b i l i t y , X » to f i r s t order i n 1/Q (Appendix 2), Thus the requirements of optimum operation are two: ( i ) maximum s e n s i t i v i t y to SP ( i i ) detection of only the absorptive component I f a magic tee i s used the signal from the cavity s p l i t s equally between the detector arm and the klystron arm where i t i s dissipated i n the f e r r i t e i s o l a t o r . -15-HELIUM DEWAR FIGURE 3«1 Experimental Arrangement -16-In order to ensure these, a bias voltage must be applied to the c r y s t a l detector (Appendix 3). I f the bias i s applied v i a a balance arm f o r the 'magic tee 1 spectrometer, the maximum s e n s i t i v i t y of the spectrometer occurs at c r i t i c a l coupling, independent of the bias power reflected to the cr y s t a l (Appendix 3)« However, this i s not feasible f o r two reasons (Wilmshurst, 1967): ( i ) Near c r i t i c a l coupling, a phase change of 180° i n the signal may occur when passing through resonance. ( i i ) The phase of the bias voltage i s c r i t i c a l i n order to detect only the absorptive component. Thus, i n practice, the c r y s t a l detector was biased by undercoupling the cavity. Diode bias currents of 100 - 300^ JLamps were used. F l i c k e r noise (or 1/f noise; f = modulation frequency) i s generated i n the diode. This cannot be made minimal by using high frequencies because the modulation must penetrate the walls of the resonant cavity. 3.3 RESONANT CAVITIES For most low temperature experiments a standard TE^ QJ m 0 (i e» brass cavity was used. For elevated temperature measurements a Varian (model E-453 ) cavity was used. Elevated temperatures were produced by the Varian a i r flow and heater system and were measured by a thermistor placed close to the sample. 2+ For the low temperature measurements on Cdl^S^Mn a T E . ^ cavity with 0.005" thick stainless steel walls, electro-plated with copper on the inside was u t i l i z e d . Modulation c o i l s were constructed -17-and attached to the outs ide of the c a v i t y f o r immersion d i r e c t l y i n the He h a t h . This enabled the use of 100 KHz. modulation f i e l d and hence reduced the e f f e c t s of f l i c k e r noise i n the diode d e t e c t o r . However, w h i l e h igher frequency modulation should t h e o r e t i c a l l y increase the s i g n a l / n o i s e r a t i o by a s i g n i f i c a n t f a c t o r the arrangement had s e v e r a l drawbacks. Eddy c u r r e n t s , induced i n the c a v i t y w a l l s by the «— modulat ion were coupled to the s t rong s t a t i c f i e l d , H 0 , and mechanical v i b r a t i o n s of the c a v i t y were c rea ted . I n the EPR spectrum t h i s r e s u l t s i n a no ise component that increases as the s t a t i c f i e l d i s i n c r e a s e d . Another much more ser ious problem i s the product ion of the He bubbles a r i s i n g from the heat d i s s i p a t e d both by the c o i l s and the eddy currents i n the c a v i t y w a l l s . This bubbl ing causes l a r g e f l u c t u a t i o n s i n the c a v i t y c o u p l i n g and thus the c r y s t a l c u r r e n t . To minimize these e f f e c t s i t i s necessary to operate at low modulation power l e v e l s f o r very short per iods of t ime. 2+ For the C d L ^ S ^ r C o experiments a brass T E ^ ^ c a v i t y was designed that enabled the sample to be r o t a t e d w h i l e i n the He bath (F igure 3«2). The gear system was arranged so that one t u r n of the worm gear turned the sample h o l d e r through ~8°. There was s l a c k of one t u r n of the worm gear w i t h i n the gear t r a i n . This r o t a t i o n coupled w i t h the r o t a t i o n of the magnetic f i e l d produced the necessary degrees of freedom to o r i e n t the c r y s t a l a long i t s magnetic a x i s . I t i s worth mentioning that the sample ho lder was made of l u c i t e and the screws of t e f l o n . D i f f e r e n t i a l c o n t r a c t i o n between the l u c i t e and the brass spur gear necess i ta ted that the t e f l o n set screw be i n s e t i n t o the brass gear to stop s l i p p i n g at low temperatures. - 1 8 -STAINLESS STEEL TUBE BRASS FLANGE BRASS HOLDER FOR 6EAR SYSTEM -SOFT SOLDERED TO CAVITY BRASS WAVE GUIDE SECTION BRASS BOTTOM PLATE FIGURE 3.2 T E 1 Q 2 cavity with provision for rotating the sample holder BRASS WORM GEAR BRASS SPUR GEARS 5/16 LUCITE SAMPLE HOLDER - FIXED TO SPUR GEAR WITH AN OFF-SET TEFLON SCREW -19-CHAPTER 4 - TRANSITION IONS 4.1 INTRODUCTION TO EPR THEORY EPR is the resonant absorption of energy via magnetic dipole transitions between electronic energy levels. The energy level separation i s directly dependent on the applied magnetic f i e l d , "S ,^ and for a simple Kramer's doublet i s given by $E = g ^ ^ , where the Bohr magneton, ^> = ( l e l t f / ^ c ) , and g i s the spectroscopic splitting factor or 'g-value'. The absorption also depends upon the excess number of electrons in the lower energy state compared to the higher one. This i s determined by a Boltzmann factor exp(g ^ H0/kgT) and thus i t i s convenient to work at low temperatures and high magnetic fields. These properties are summarized in Figure 4.1. Figure 4.1 EPR signal for a Kramer's doublet -20-The finite line width of the absorption may be due to several causes in solids; (i) spin - lattice interaction, interaction of the dipole moment with phonons. ( i i ) spin - spin interaction, interaction between magnetic dipoles ( i i i ) unresolved fine or hyperfine structure, due to random strains or electric fields in the crystal. A necessary condition for observation of EPR in solids is that t h e crystal exhibit a paramagnetic moment. This moment may be produced in four ways; i » * ( i ; free electrons or holes, as in metals or doped semiconductors ( i i ) atoms with an unfilled electron shell ( i i i ) free radicals, with an unpaired electron (iv) an electron or hole trapped in a defect center. 4.2 INTRODUCTION TO CRYSTAL FIELD THEORY Transition ion impurities exhibit magnetic dipole moments due to the f i l l i n g of their electron shells in accordance with Hund's rules. In a solid an extra term must be added to the Hamiltonian for these electrons owing to the electrostatic interaction of the paramagnetic ion with i t s surrounding atoms. % = Zpf/2m - Eze%+ l/2^e 2/r• + X.L.S + J.A.I - Z e 6 ( r . J The f i r s t three terms are the 'free ion* Hamiltonian and the last three are, in order; the spin - orbit coupling, the hyperfine interaction, and the crystal field interaction. They are applied as perturbations to t h e free ion ground state. The hyperfine interaction J.A.I i 3 the * Loosely bound electrons or holes in shallow states are also placed in this category. -21-weakest and hence enters last in the perturbation formalism. If a point charge model for the neighboring atoms is assumed, the formalism may be categorized into three groups: (i) Weak Crystal Field - the crystal field interaction, e4*(r-)» i s weaker than the spin - orbit coupling, XL.S. The crystal f i e l d l i f t s the 2J + 1 degeneracy of the ionic ground state and since the energy differences are usually ~10 - 100 cm. \ EPR is only observed in the lowest state i f the selection rules for EPR (A.J =11) can be applied successfully. This case applies to the rare earth and actinide groups where the electrons in the shell contributing to the magnetic moment are shielded from the crystal f i e l d by outer electrons. ( i i ) Intermediate Crystal Field - the crystal field interaction i s stronger than the spin - orbit coupling. The 2L + 1 orbital degeneracy i s l i f t e d by the Stark splitting due to the crystal f i e l d and since the 4 - 1 splittings are —10 cm. , EPR is observed only from the lowest orbital levels. If the lowest level is an orbital singlet, L i s •quenched' (Slichter, 1963) and the magnetic properties are due to spin transitions. Spin - orbit interaction and small distortions of the cubic f i e l d further split the ground state and cause anisotropic g-values. This case occurs for the 3d shell in the iron group. ( i i i ) Strong Crystal Field - the crystal field is strong enough to 'remove' electrons from the ion - i.e. high covalency in bonding. The same formalism as before may be used i f one takes into account the fact that the coupling between electrons is broken down by the electric * f i e l d of the ligands. Ions of the platinum and palladium groups are of this type. * Hund's rules and Russell - Saunders coupling are invalid. - 22 -Since the ciystal f i e l d ultimately l i f t s the ground state degeneracy and separates the levels so that only the lower ones are populated, the magnetic properties may be described by a Hamiltonian containing an effective spin operator that acts only on the manifold formed by the lowest states. This general feature of a l l three cases is summarized by the so-called 'spin Hamiltonian'. The theory stated so far, based upon a point charge model, assumes that the electric f i e l d produced by a neighboring nucleus, screened by a spherical cloud of electrons is the same as a charge centered at i t s nucleus. This is only true i f the surrounding neighbor electron orbitals do not overlap with the impurity orbitals. Thus the theory does not apply quantitatively to crystals with appreciable covalent bonding. A better analysis of the problem using molecular orbital theory leads to several corrections for increasing covalency (Orton, 1968): (i) The magnitude of the effective spin - orbit coupling parameter, X, is lowered. This also means that jg-shiftsj are smaller. ( i i ) The orbital contribution to the magnetic properties is reduced. In ions where L isn't 'quenched' i t becomes more so for increasing covalency. ( i i i ) The hyperfine interaction parameter, A, is reduced. In fact the size of A for a fixed impurity may be used as a quantitative measure of covalent bonding (Kimmel, 1963). (iv) Superhyperfine interaction occurs. Since the impurity electrons have a finite probability of being at the neighboring nuclei a super-hyperfine contact interaction with the ligands may occur, exhibiting the EPR spectra characteristic of the nuclear spin of the ligands. - 2 3 -4 . 3 CdIn2S4:Mn 4 . 3 a Introduction In Cdln^S^ the two cations have charges of 2+ and 3+ respectively so that, assuming the impurities enter the lattice substitutional^, 2+ the EPR spectrum is expected to exhibit the properties of either Mn 3+ 3 + 4 or Mn . However Mn is a 3 d configuration that i s strongly affected by a cubic crystal f i e l d to yield a spin Hamiltonian with S = 2 (Abragam and Bleaney,1970) with a resultant zero f i e l d splitting and anisotropic 3+ spectrum. Because of relaxation effects the EPR of Mn is never observed at room temperature. The single isotropic spectrum, seen at room temperature and above, does not conform to this model and is therefore ascribed to Mn^+ with fine structure unresolved due to weak coupling to the lattice. The spectrum has a large hyperfine interaction reflecting the nuclear spin of the Mn'''' nucleus ( i = 5 / 2 ) . 2+ 4 . 3 b Mn - Crystal Field Interaction 2+ Mn is a member of the iron group that has the electronic con-5 # figuration 3d and, according to Hund's rules, the ionic ground state 6 * i s • It I s analysed using the intermediate crystal f i e l d approach. S - state ions are unusual because neither the cubic f i e l d nor the spin -orbit interaction, taken separately, to any order in perturbation theory give any splitting of the ground state. It is only when both are applied together that the degeneracy is l i f t e d . This is expected to be small since the f i r s t contribution occurs in f i f t h order (Low, 1 9 5 7 ) . * . . . ( 2 S + 1 ) _ Notation: L j A good discussion of Hund's rules is found in Pake (1962, p. 11) -24-Because of the weak coupling to the l a t t i c e , the spin - lattice 2+ relaxation time, , for Mn is f a i r l y long and shows l i t t l e temp-erature dependence, so that the resonance may be observed even at room temperature and above. Deviations from cubic symmetry cause the six -fold spin degenerate ground state to be split slightly. An effective spin Hamiltonian, for an axial distortion, may be written (Orton, 1968): % s = g(*H0.S + D(S2 - 1 / J ( S ) ( S + 1)) +(F/180)(35S^ - 30S(S + 1 )S 2 + 25S^ - 6S(S + 1) + 3S 2(S + 1) 2) +(a/6)(s£ + + S* -(l/5)S (S+1)(3S2+3S -1)) where the D and F terms are due to the axial distortion and the a term i s caused by the cubic component of the crystal f i e l d . The z-axis i s determined by the axial distortion in the crystal, not by the fi e l d , H0. In practice for many crystals the ligand f i e l d may be near - cubic and the fine structure may not be resolved, but may be the dominant factor in line width determination (Almeleh and Goldstein, 1962). 2+ 4.3c The Theory of the Hyperfine Interaction for Mn The Hamiltonian for the magnetic interaction of an electron with i t s nucleus may be written as (Abragam and Bleaney, 1970): % = 2f \« I . ( ( V r 3 ) - ( t / r 5 ) + 3 r(s.*)/r 5 + ( 8/3)TTs S(t)) where *o^ = the nuclear gyromagnetic ratio and I = nuclear spin. The f i r s t three terms are the classical interaction between magnetic dipoles while the last term i s the contact term, which i s usually dominant. For a general distribution of electrons about the nucleus the interaction i s ~* v •* 5 tensorial, I.A.S, however for the spherical distribution of 3d in a - 2 5 -cubic f i e l d i t becomes isotropic and may be written; A H F . = AI.S where A is a constant. If there is an axial distortion from cubic symmetry must exhibit axial symmetry (Orton, 1968): % = A I S + A (I S + I S ) ' w z z x x yy' It seems surprising that there should be a large hyperfine inter-2+ action for Mn since the 3d electrons have no probability of being at the nucleus and the magnetic dipole interaction is far too weak to explain the observed A-values. The magnitude of the interaction has been explained by introducing core polarization (Watson and Freeman, 1957) which also accounts for the negative sign of A (Simanek and Orbach, 1 9 6 6 ) . In addition, there is a 'configuration interaction' (Abragam and Bleaney, 1970) whereby the crystal field mixes in small amounts of excited state configurations with unpaired s-electrons which do have a significant probability of being at the nucleus and thus give rise to a contact hyperfine interaction. This mechanism results in a positive contribution to A and subtracts from the dominant mechanism of core polarization. Both mechanisms are responsible for the hyperfine interaction i n the transition group. 4 . 3 d The Temperature Dependence of A A large temperature dependence of A, over and above that explained 2+ by simple thermal expansion effects, was f i r s t observed for Mn and in the cubic f i e l d of MgO by Walsh et al» ( l 9 6 5 ) « The mechanism proposed was that the excited r.-like configurations which give the contribution to A are mixed into the ground state by a phonon - induced dynamic crystal f i e l d (Simanek and Orbach, 1 9 6 6 ) . By assuming a Debye spectrum for the phonons and a point charge model for the ligands, a -26-temperature dependence of the hyperfine coupling constant was determined: A (T ) = A(0)( 1 - CT4 \(x 3dx)/(e x- 1)) x = h v>/kT 0 where = the Debye temperature for the solid and C is a constant that, i n principle, can be calculated. Simanek and Huang (1966) improved on this model and showed that covalency effects tend to increase the value of C, previously calculated using the point charge approximation, although the form of the equation remained the same. Zdansky (1968) pointed out that i f the impurity has a mass or ionic radius differing appreciably from the host atom, local vibrational modes wi l l be set up at the impurity site. The mechanism (mixing of excited states by a dynamic non - cubic crystal field) remains identical, except that the dynamic non - cubic fi e l d i s induced by a localized phonon and not the continuum. The form of the dependence was derived as: A(T) = A(0)(1 - ]Tci(exp(fi<<u/kT) - 1 ) - 1 ) th where oo. is the resonant frequency of the i localized mode and i s a constant. Zdansky and Kubec (1969) observed the temperature 2+ dependence of A for CdStMn and found that the data could be explained with two local modes of vibration. It should be noted that even for one local mode, the mechanism of Zclansky and Kubec has two adjustable parameters, while the mechanism of Simanek and Orbach has only one. for Cdln S Q = 230 °K (Czaja and Krausbauer, 1969). -27-4«3e Room Temperature Properties of the Spectra The samples available were grown from both the melt and vapor phase techniques. The crystals with similar dopant concentrations exhibited a six line hyperfine spectrum with a rather large line width (Figure 4.2a), while samples with a larger concentration of dopants exhibited two super-imposed six line spectra (Figure 4.2b), one with a line width the same as the weak dopant spectrum and the other having a much narrower line width. Analysis of the EPR spectra yielded: TABLE 4.1 Experimental values for CdlngS^Mn2"1" Broad Lines Narrow Lines g-values 2.003 t .002 2.004 - .001 IAI 70.0 t .5 G 69.5 i .1 G & H l / 2 73 t 2 G 6.5 ± .5 G Where ^H^ 2 i s ^ e 'half width' between inflection points on the absorption spectrum. In the presence of second order effects there are corrections to g-value measurements and there is a correct technique for measuring A (Appendix 4). For the broad line spectrum the measurements of A and / 2 were obtained by computer f i t t i n g a sum of overlapping Lorentzians to the experimental traces (Figure 4.2a). The line shape was best approximated by a Lorentzian curve although this was by no means perfect. Both spectra were found to be isotropic with respect to crystal orientation. FIGURE 4.2 Experimental traces for Cdln S :Mn - 2 9 -4.3f The Temperature Dependence of the Spectra The hyperfine coupling constant, A, was found to be temperature dependent for both the narrow and the broad line spectra (Kerr and Schwerdtfeger, 1971). The errors for the narrow line spectrum were much smaller, owing to the relatively small line width and thus this spectrum was extensively studied. The results are plotted in Figures 4.3 and 4.4 for a temperature range 1.1 °K - 450 °K. Temperatures above 300 °K were measured with a calibrated thermistor while the dry ice - acetone temperature of 197 °K was measured with a thermometer. At 1.1 °K and 4.2 °K both spectra were saturated at moderate micro-wave power levels and the power had to be decreased in order to observe EPR transitions . Both ^H^y^ S were independent of temperature, within experimental error. *for no saturation 1»)( 2H 2T 1T 2 (Pake, 1962), where ? and T ? are longitudinal and transverse relaxation times and tf= gyromagnetic ratio. -32-4.3g Comments and Discussion of Data 2+ Because of the weak coupling of the 3d electrons of Mn to the lattice, their spectrum is insensitive to orientation and thus i t i s very d i f f i c u l t to ascribe the position of the impurity to either an "A" or a "B" site. However there are two indirect methods of labelling the spectra. Since the linewidth is independent of temperature and saturation occurs at 4 °K i t is likely that the linewidth source is inhomogeneous. One such source is unresolved fine structure 'smeared out' by random strains in the crystal. An observation that would conform to this picture i s that the line shape is neither Lorentzian or Gaussian as i t would be for a single line or a simple inhomogeneous broadening mechanism. If a postulate of cubic symmetry about each site i s made , then i t can be shown that to f i r s t order, the line width AH^/g * s proportional to the square of the cubic f i e l d strength (Stahl-Brada and Low, 1959). In tetrahedral symmetry the crystal f i e l d strength is 4/9 of the crystal f i e l d strength in octahedral symmetry so that one would expect LHl/2(tetrahedral, "A", site) v 1/5^ H 1/ 2(octahedral, "B", site). Thus the narrow line spectrum is ascribed to the "A" sites and the broad line spectrum to "B" sites. This discussion is at best qualitative since there is no way of ascertaining how much the cubic f i e l d i s distorted at each site. In a l l cases of paramagnetic impurities studied by EPR in which no D term in the spin Hamiltonian. - 3 5 -the site symmetry was determined i t was found that the anion preferred the "B" site regardless of i t s charge state. Thus at low dopant concentrations Mn would populate "B" sites and for higher concentrations would start to occupy "A" sites. The Debye theory of Simanek and Orbach for the temperature dependence of A has been used to interpret the data in Figure 4.3* The curve is normalized at 411 °K and 1.1 °K. This yields a value for the constant C = (1.6±0.3)X10" 1 1( O K ) - 4 . From Simanek and Orbach (1966) i t is seen that a theoretical value 2 3 5 for C, using the point charge model, is proportional to ( V ) / ( R Q C ) where V C is the crystal f i e l d strength, R is the anion - cation distance, ^ i s the density and c is the isotropic velocity of sound. Using an isotropic sound velocity for Cdln^S^ calculated from the Debye model one finds C * 10~^4 (°K)~ 4. Thus the theoretical value i s three orders of magnitude too low. Better agreement may be attained i f covalency effects are taken into account (s'imanek and Huang, 1966). In Figure 4.4 the local vibration model has been used to interpret the data. The resulting f i t i s better than the previous theory due to the additional parameter in the formula. The vibration frequency was 1 3 - 1 ' found to be 3«1 x 10 sec. and the 'coupling' C was 0.0167. The results should be comparable to CdS in a qualitative way since the nearest neighbor configuration is nearly the same . Zdansky and Kubec, using the Debye model, found for CdS:Mn2+that C = 2.58 x 10~13(°K)""f Even better agreement with theory was obtained by assuming two local R(CdS) = 2.52 I, R(CdIn2S4) = 2.56 1 -34-14 12 modes of frequencies G), = 4.25 x 10 and 1^= 1.11 x 10 with different 'couplings' C1 = 1.6 x 10 v and = 7.4 x 10 . If |A| i s used as a measure of covalency then, a l l other things being equal, C should be larger for Cdln^S^ than for CdS since the * former has more covalent bonding . This effect may be the dominant one. The Debye temperatures are comparable; the crystal field is tetrahedral in both cases; the densities are of the same order and the dependence on R is opposite to that observed. The concept of a local vibration model for explaining the temperature dependence of A is highly doubtful. The lower vibration frequency CJ, 2+ for CdS:Mn f a l l s in the acoustic phonon band where no localized phonons should be present and the upper frequency W t is well above the predicted localized frequencies for CdS;Mn of 284 cmT^  and 289 cmT^  (Nusimovici et a l . , 1970). In Cdln^S^rMn2-4" the mode frequency of 1 3 - 1 - 1 3.1 x 10 sec. = 990 cm. is too far away from the predicted values for CdS to be meaningful. Thus the localized vibration model is / \ 2+ 2+ discarded as a tenable theory for A(T] in both CdS:Mn and CdIn2S4:Mn . Also from the data, assuming the site assignments are valid, Mn 2 + has a strong preference to substitute into the "B" site. For a normal spinel this would require a charge compensation mechanism and thus an expenditure of energy by the crystal. For a partially (or fully) inverted spinel this i s not necessary. |A| at 300 °K for CdS:Mn i s 65 x 10"4cmT (Zciansky and Kubec, 1969) -35-A search for effects due to the phase transition at 130 °C (Czaja, 1970) was carried out but no quantitative results were obtained. A slight trend of increasing strength of the narrow line spectrum was seen but the expected line width increase due to fluctuations was not observed. In some ways this is not sur-prising since the effects of the transition were so small (10 % change in C ) and the order - disorder takes place on "A" sites which for P Mn would imply a third - nearest neighbor effect. 4.4 CdIn2S4:Co 4.4a Introduction Assuming Co enters the crystal in a substitutional site there are four possible ways i t can do so, without necessitating charge compensation. It can substitute at either an "A" or a "B" site as a triply or doubly "5+ charged anion. However, the Co ion is non-paramagnetic since, due to i t s larger charge, i t always substitutes in a strong field configuration which is diamagnetic (Orton, 1968) and hence would exhibit no EPR 2+ signal. Co at an "A" site should have a spin Hamiltonian with g ~> 2 and S = 3/2 (Orton, 1968; Ham et al.,1960) because of the tetrahedral f i e l d . Co 2 + at a "B" site should have a spin Hamiltonian with an an-isotropic g ~- 3 -*-7 and S = 1/2 (Orton, 1968; Abragam and Bleaney, 1970) because of the octahedral f i e l d . The features of the observed spectra conform to the latter as-2+ signment so that the resonance i s attributed to Co at a "B" site. There is also an underlying background spectrum which is thought to " 2+ be caused by Co at a "B" site surrounded by one or more sulphur -36-vacancies. The large number of possible sites for the vacancy around each impurity (6) plus the four inequivalent impurity sites in the crystal would lead to a random spectrum that exhibits properties very close to that of a powder (Appendix 5). 2+ 4.4b The Theory of Co in Octahedral Coordination The cubic f ie ld spl i ts the seven - fold degenerate ground state, 4 7 F, of the 3d configuration into two tr iplets and a singlet with a tr iplet lying lowest (Figure 4.5). P ~ T / — — TT.jTT j / C 4 > T r Tr; ' / ' / l*\ u . —• 14000 cm. / • WJfc_ \ \ \ \ \ . 1 $x. ~t ' free ion' + cubic field + 'I.'9.0^31 + XL.S 2+ FIGURE 4.5 Orbital energy level diagram for Co in an octahedral f ie ld Following the notation of Abragam and Pryce (1951), the energy levels in the diagram are labelled by their wave functions. Since an orbital tr iplet l ies lowest in energy, 'quenching' does not occur in this case and the magnetic properties of the ground state reflect both the orbital and spin magnetic moments. The ultimate ground state is a Kramers doublet independent of the sign of S (the trigonal spl i t t ing factor) and may be written as: -37-|l/2> = a|-1 ,3/2> + b|0,l/2> + c |1 ,-l/2> |-l/2> = a |1 ,-3/2> + b|0,-l/2> + cl-1 ,l/2> 2 2 2 where a + b + c = 1 . The s ta tes on the r i g h t l a b e l the o r b i t a l angular momentum and the s p i n , r e s p e c t i v e l y , of the lowest l y i n g t r i p l e t , (j) , created by the c r y s t a l f i e l d . Por a t r i g o n a l d i s t o r t i o n t h i s t r i p l e t may be w r i t t e n a s : An e f f e c t i v e o r b i t a l angular momentum 1 operat ing on the m a n i f o l d , (J>' , y i e l d s e f f e c t i v e Lande f a c t o r s , - oc and - , a long the symmetry a x i s and perpendicu lar to it(Abragam and Bleaney, 1970). S ince £ has a value near 1, f o r a 'weak' f i e l d ^ 1.5 and no e x c i t e d s ta tes are mixed i n t o the ground s t a t e by the c r y s t a l f i e l d . For a s t rong f i e l d oC * 1 (Abragam and P r y c e , 1951) G r i f f i t h (1961) has presented a s i m p l i f i e d v e r s i o n of the theory which i n c l u d e s the assumption ot^te. . A r e l a t i o n between g t and g ( i i n terms of a s i n g l e parameter x can now be w r i t t e n ; g „ = 2 + 4 ( « + 2 ) ( 3 / X 2 - 4 / ( X + 2 ) 2 ) / ( 1 + 6 / X 2 + 8 / ( X + 2 ) 2 ) g j L = 4(lW(x+2)+12/(x(x+2)2))/(l+6/x2+8/(x+2)2) where v a r i e s between 1 and 1 .5 . The t r i g o n a l s p l i t t i n g parameter, % , may a l s o be d e r i v e d as ; & = o(\((x+3)/2-3/x-4/(x+2)). This may be taken as a d e f i n i t i o n of the parameter x . The s p i n - o r b i t c o u p l i n g parameter, X , f o r the f r e e C o 2 + i o n has a value -180 cm. ^(Abragam and P r y c e , 1951). For a pure cubic f i e l d , $ = 0 (x = 2 ) , the expressions -38-reduce to g = g ( l = g^ = 2/3(ot+5), which leads to g-values of 4 -*-4.3 for the expected range of oC . In a distorted f i e l d the g-values may range as high as 9 or 10. Second order effects are caused by the admixing of upper orbital levels through spin - orbit coupling (Appendix 6), and may be significant. Covalency effects have been studied by Thornley et al,(1965). The effective spin - orbit coupling parameter and g-values are both reduced i n magnitude as the covalency is increased. 4»4c Experimental Results EPR signals were observed only at 4.2 °K and 1.1 °K owing to relaxation effects. There was no significant difference for the two temperatures and, thus, a l l data presented are for the lower temperature where the spectrometer has a higher sensitivity. Por an arbitrary orientation of the crystal the spectrum was too complicated to decipher since, assuming axial symmetry in"<311"> directions, the "B" sites have four inequivalent -<J1f> directions and thus four spectra each containing 8 hyperfine lines. The procedure adopted was to orient the sample so that one of the simple crystallographic directions was parallel to H 0 , where the spectra from different sites would coincide and simplify the EPR analysis. With a small rhombic distortion present the spectra from different sites would not coincide for any orientation. A broad background line, relatively independent of orientation, was present in a l l of the spectra (Figure 4.6). The similarity of this line to a powder spectrum is evident. For this reason i t was -39-ascribed to Co at "B" sites where one or more of the neighbors was a sulphur vacancy. The large number of possibilities for the relative position of the vacancy plus the four inequivalent sites would produce a. spectrum that closely resembled a powder spectrum. As a check of this postulate, a sample was heat treated at 400 °C for 12 hrs. in order to produce more sulphur vacancies. The strength of the background line increased noticeably with respect to the 'normal' spectrum. An experimental trace for H 0in a <100"> direction i s shown in Figure 4.6. A l l <111> directions are at the same angle, 54.74°, to a 1^00"> direction. If the distortion axis i s <111"> the spectra should collapse into a simple eight - line pattern characteristic of the nuclear spin ( i = 7/2) of the Co"^ nucleus. This collapse does occur partially; however, the inability to resolve the spectrum into eight lines suggests that there i s a rhombic distortion in the crystal f i e l d . Further evidence for a small rhombic distortion i s provided by the unresolved spectra at large angles to Olf?. An experimental trace for H a in a <111^ direction i s shown in Figure 4.6. The lower eight lines retained their internal structure and intensity when the crystal was rotated. For this reason this part of the spectrum was attributed to the one <111> direction parallel to H6. The measurement of g u directly from this spectrum i s the most accurate experiment, since no summing from different sites occurs. The upper pattern was very sensitive in both internal structure and intensity to crystal orientation and is therefore attributed to the o three <111> directions at 70.53 from Hft. Quantitative measurements on these lines were not possible. -40--41-An experimental trace f or T20 i n a {110^ direction i s also shown i n Figure 4.6. Both the lower and upper portions of the spectrum were sensitive to c r y s t a l orientation. This i s expected since there are two ^111^ directions at 90° and two at 35.26° to H 0. Using the conclusions of the previous experiments the lowest l i n e s were attributed to the < U O directions at 35.26 to H e. As before, no quantitative measurements were possible f o r the upper l i n e pattern. Using the experiments with *3 i n these three simple directions the results are presented i n tabular form: J _ g(&) A(S) 0° 6.00 t.05 85.0 ±.05 G 35.26° 5.461 .1 87.0 i 1.0 G 54.740 4.58 or 4.92 t.1 96.0 i1.0 G 2+ TABLE 4.2 Experimental values f o r Cdln^.'Co % i s the angle between H e and the <1"M> axis i n question. The two values are quoted f or g(54.74°) because the spectrum i s not un-ambiguously resolved. For a rhombic f i e l d the angles would also be s l i g h t l y d i f f e r e n t but are s t i l l representative f o r the cases of non-zero As ©• increases the rhombic f i e l d should cause the expected collapse of spectra to be less re a l i z a b l e . This behaviour i s noted f o r © = 70.53° and especially f o r 90°. 4.4d Analysis and Discussion of the Data The background l i n e described i n the previous section has the general features of a powder spectrum (Appendix 5), although exhibiting a s l i g h t anisotropy. I t has a correlation with sulphur vacancy 2+ .concentration. For these two reasons i t i s ascribed to Co at a -42-"B" site surrounded by one or more sulphur vacancies. 2+ The remaining spectra are attributed to Co ions at regular 2-"B" sites, surrounded by an octahedral array of S ions that i s distorted to form a rhombic crystal field at the impurity site. The data obtained from the three simplest crystallographic directions are not sufficient to determine the parameters in a spin Hamiltonian that * reflects rhombic symmetry . Despite this shortcoming some useful information may s t i l l be derived. Assuming that the rhombic distortion causes the two possible g(54.74°) values, the f i r s t and last line in the (nine - line) spectrum should be half as intense as the rest. From Figure 4.6 i t i s seen that this i s approximately true. Thus ge$(54.74°) i s taken as an arithmetic mean of the two possible values so that analysis can be carried out for an axial spin Hamiltonian, 9(s= e , »^H z s z + g ^ H s + H XSx). This procedure i s equivalent to defining gv= l/2(g x + g y). Thus geW(54.74°) = 4.75 £.1. For the other angle, 35.26°, i t i s assumed that the rhombic fie l d i s not strong enough to resolve the spectra. Using this data a value g = 4.07 ±.15 i s calculated while glv i s measured directly as 6.00 t.05. A graph of g± vs. g„ for the f i r s t order theory of Gri f f i t h i s presented in Figure 4.7. It i s seen that the experimental point for 2+ • ' ** Cdln^S^tCo i s well on the weak field side of the curve . Other data points are taken from Orton (1968,p. 202). Second order corrections *<%= g HS + g H S + g HS °z z z Bx x x y y y ** the extreme weak field case i s C<,= 1.5 -43--45-give a better agreement the theoretical range of points (g„ jgj.) and the experimental point (Appendix 6). Using the extremal value for cC and the experimentally determined g„ a value for the parameter x can be read from Figure 4.8 and 8 , the trigonal splitting parameter, can be evaluated as a f i r s t order calculation. If the value of X for a free ion (-180 cm."^ ) is used i t i s found that S = 446 cm. *. Covalency would tend to reduce S . The hyperfine interaction tensor, A, should also exhibit the symmetry of the g-tensor, but for a small rhombic term may also be approximated by the axial case. The hyperfine interaction Hamiltonian takes the form: A = A„I S + A,(l S + I S ) n z z J-v x x y y ' The formula, g 2(9)A 2(©) = g 2A 2sin 29-+ g2A2cos29-(Abragam and Bleaney, 1970), is useful in interpreting the data. A„ is measured as 85.0 i.5 G while calculations yield A x = 101 £ 4 G. 4.5 CONCLUSIONS AND COMMENTS The search for the effects of the second order phase transition at 403 K was in vain, both for Mn and Co doped samples. A Co-doped sample was heated to "300 °C for 5 hrs., quenched, and then placed in a microwave cavity at 1 °K and 4 °K. It was thought that the slow approach to internal equilibrium observed by Czaja (1970) would have allowed some changes to be 'frozen' in the crystal, however the effect * c the reduction of 0 occurs mainly because the effective spin - orbit coupling parameter is reduced with increasing covalency -46-was not observed. Other transition elements that were studied were V, Cr, Fe and Cu. A resonance from Cr was observed that had features in common with the C r ^ spectrum in Cdl^S^ reported in the literature (Henning et al.,1969). No other useful EPR signals were seen. Samples doped with Ag, a member of the palladium (4d) group, were also examined in the spectrometer. The platinum (5d) group members Au and Hg were studied. The X-band spectrum of Eu, a rare earth (4f) group member, also yielded no signal. The null results from these experiments could be due to several reasons. The ion may exist in a non-paramagnetic configuration in the crystal. The line width due to random strains in the crystal or a relaxation effect may be excessively wide. Or, the solubility of the impurity in Cdln^S^ may be low enough so that there is not a sufficient concentration of impurities to create a measurable EPR signal. 2 + 2 + One connecting feature between the EPR spectra of Mn and Co in CdLrigS^ i s that both exhibited a preference for the "B" site, even though their charge state would require compensation by the crystal i f the structure were a normal spinel. This indicates that a partially or fully inverted spinel i s more probable than the normal structure. -47-CHAPTER 5 'CONDUCTION ELECTRONS' 5.1 INTRODUCTION 2+ 2+ In the previous chapter Mn and Co systems were discussed where the magnetic moment was produced by unpaired electrons localized about their parent nucleus. In this chapter a resonance i s reported that i s due to unlocalized electrons existing as a shallow donor impurity * band or conduction electrons. Evidence for this explanation of the resonance i s presented in sections 5.3 and 5.4. The g-value i s the measurable quantity of the most interest. Just as in the case of the crystal field interaction i t i s the spin - orbit coupling that ultimately causes the g-shift for conduction electrons. Under the assumption of interaction with only the nearest contributing band, relations between the g-shift, the effective mass tensor, the spin - orbit splitting of the nearest band and the energy separation to the band may be derived. The linewidth of the EPR signal exhibited the properties of i n -complete motional narrowing. This i s the only mechanism that leads to an increase of line width with a temperature decrease. •Since this thesis does not distinguish the observed resonance as either of these two cases the electrons w i l l be referred to as 'conduction electrons' for convenience. -48-5.2 THE THEORY OF THE g^VALUE FOR BANDED ELECTRONS If shallow donors are present in Cdln^S^, using the hydrogen -like approximation, their ground state energy will l i e at a value, * / 2 oE = 13.6 m /mK eV below a conduction band minimum. The dielectric constant, VC , has been measured as 12.7 t.4 at 4.2 °K (Slagsvold, 1971). * * The effective mass m is unknown at present. However, assuming m « m, we find ^E-85 meV. Since the band gap is ~2.2 eV this means that the wave function of the donor ground state i s almost entirely made up of conduction band wave functions and should thus exhibit properties of the conduction band. Since the predicted band structure of CdlngS^ has four minima at the Brillouin Zone edges in the <111> directions (Meloni and Mula, 1970) i t i s of interest to study the g-value theory for Ge. This was developed by Roth (i960) under the assumption of validity of the effective mass approximation and using Tc.p perturbation theory for the nearest contributing level. The ultimate result i s an isotropic g-value of the form; g = 2 - S(m/(3mt) + 2m/(3m1) - 1)/|E| where $ is the spin - orbit splitting of the nearest contributing level,|E | i s the energy separation between the conduction band and this level, and m^  and m are the longitudinal and transverse effective masses, respectively, in each of the four valleys. In each valley the g-value exhibits an axial anisotropy given by: g(|- 2 - - S(m/mt - 1)/|E| and g j u- 2 ~ - SU/n^  - 1)/|E( . most certainly an upper limit. -49-The observed g-value is isotropic since, for a cubic crystal, the singlet ground state is an isotropic average over the four valleys. Another property of interest for Ge is that the inhomogeneous line broadening mechanism due to residual strains exhibits anisotropy, with the minimum line width occuring with H e aligned in a <IOO/> direction (Feher et al.,1959). This has been explained by Roth who uses the broadening mechanism of mixing of excited states into the ground state by the random strains. The effect due to shear strains vanishes for H0 parallel to <100>. If, however, the band gap should be a direct one, for a cubic crystal the Roth relations reduce to g = 2 - ^-(m/m - 1), where m i s the isotropic effective mass. The line shape and width of a conduction electron resonance is not an easy subject to discuss quantitatively. The quasi-continuous series of levels that participate in the EPR experiment need not a l l have the same magnetic field splittings since the levels observed have a range of k-values (i.e., they have slightly different g-values) When coupled with the density of states curve this effect may result in wide asymmetric resonances. There also may be an asymmetric i n -homogeneous broadening mechanism. Another factor that may cause asymmetry in CdIn0S. i s that i t is suspected to be slightly non-cubic the isotropic average is given by g = l/3g(, + 2/3gj. -50-(Boorman, 1971) so that the cubic averaging process for an isotropic g-value i s no longer valid. 5.3 PROPERTIES OP THE SPECTRA Resonances that are tentatively attributed to conduction electrons have been observed in several samples and also have been created in the laboratory by heat treatment. The evidence for labelling the resonance as produced by conduction electrons (or banded electrons) is four-fold: (i) The samples that showed a resonance also affected the quality factor of the microwave cavity. This indicates that 'free' carriers have been produced to increase the sample conductivity and make i t •lossy'. Intrinsic samples had no noticeable effect on the cavity Q. ( i i ) The fact that the line width is a decreasing function of temperature means that the resonance is incompletely motionally narrowed. This i s the only mechanism that satisfactorily explains the behaviour. The increasing 'freedom' of electrons at higher temperatures suggests that they are present either in an impurity band or in the conduction band. ( i i i ) In a solid, a single isotropic line having a g-value radically different from and less than a free electron value can only arise from a conduction electron state. Hole states are not 'visible' to EPR because of random strains interacting with the degeneracy at the valence band maximum. (iv) The signals have been produced in the lab by heat treating the samples. This is known to create sulphur vacancies (Koelmans and Grimeiss, 1959) which for CdS produce a shallow donor and thus a -51-characteristic shallow donor EPR signal (Brailsford and Woods, 1968). The appearence of a typical spectrum is shown in Figure 5.1. The line i s isotropic but varies slightly in width (a few Gauss) and g-value (* .002) for different samples. The variation in g with temperature may or may not be significant because i t is not clear where to measure g-values for such an asymmetric line. The choice made for these experiments was to measure g at the cross over point of the baseline. -52-9= 1.686 1.001 FIGURE 5.1 'Conduction electron' resonance experimental traces -53-The spectra appear to have Dysonian line shapes (Dyson, 1955) but a room temperature resistivity measurement yielded a resistivity, ^ 250 iL-cm., which is much too high to account for a skin depth effect (Slagsvold, 1966).* Another resonance that should exhibit some properties of the conduction band i s that due to the surface states. They arise from the f i n i t e boundary conditions imposed by a surface and are most noticeable in powders. The spectrum of a sample before and after i t was ground into a powder is shown in Figure 5«2. Another powder sample that was provided by Dr. I. Shepherd also exhibited a resonance with g ^1.76 and a large line width of ^ 70 G. This resonance was only observed at 77 °K. The sample did not exhibit a resonance characteristic of sulphur vacancies. 5.4 SULPHUR VACANCIES AND HEAT TREATMENT TECHNIQUES The conduction electron resonance was originally observed in one of Dr. Czaja's samples that had been heated until the vapor pressure of the sublimated sulphur was one atmosphere. This resonance has also been reproduced by heat treatment of intrinsic samples in evacuated closed quartz ampoules. A simple, open, cylindrical, two - element oven capable of attaining temperatures of " 650 C was used for a l l the experiments. This measurement was d i f f i c u l t to perform because of the problem of attaching leads to the sample. A four point probe could not be used and even a silver print contact method yielded slightly non-ohmic results. The value of 0 quoted was the slope of the I - V curve at low currents. The resistivity of intrinsic samples was too high to measure using available techniques in our laboratory. -54-9=1.68 SINGLE CRYSTAL 77 K POWDER POWDER POWDER FIGURE 5*2 Surface state resonances -55-It is obvious that sulphur vacancies are created, even for modest oven temperatures, since after quenching a deposit of sulphur on the side of the quartz tube is noted. However, the mechanism of producing the vacancy responsible for the observed resonance is not a simple one. Samples heated under a continuous vacuum had no EPR signals even though they strongly affected the cavity Q. On the other hand, equivalent samples heated under identical conditions in closed quartz ampoules had widely different signal strengths. One parameter in the technique that, despite the irreproducibility, affects the signal to a sufficient degree to enable one to make at least a qualitative comparison is the sulphur vapor pressure over the heated sample. Four identical intrinsic samples were placed in evacuated quartz ampoules having sealed volume ratios of 1:2:3:4. The unit of 3 volume was ^1.3 cm. and each sample weighed ^ .08 gm. Each sample was heated for 2 hrs. at 500 °C, quenched in water and then immediately placed in the EPR X-band spectrometer. The results for the f i r s t three samples are shown in Figure 5»3» The fourth sample had no resolvable signal. As far as possible a l l the parameters of the spectrometer were kept constant, however the most unreliable experiments are those at 1 °K since the helium pump introduces noise that is d i f f i c u l t to maintain at a constant level from one experiment to the next. The fact that the signal is enhanced for the smaller volumes (higher sulphur vapor pressure) does not imply that these volumes lead to the production of more sulphur vacancies, since the production of -56-HEAT TREATMENT VOLUME RATIO 9 = 1 - 6 8 106 v. FIGURE 5*3 Qualitative effects of sulphur vapor pressure on the •conduction electron' EPR signal -57-more charge carriers also degrades the Q of the microwave cavity and reduces the resulting signal/noise ratio. A study of the effect of the time of heat treatment, with other things constant, was inconclusive. However there was some evidence that the vacancies 'relaxed' out of the specimen as a function of time. 5.5 STRAIN EFFECTS* The application of uniaxial stress on a sample may resolve the question of whether or not the band gap is direct or indirect. For an indirect band gap the resulting strain produces two effects (Wilson and Feher, 1961). First, the valleys are shifted to different energy levels, depending on their orientation with respect to the strain axis, and thus are not equally populated. The resulting g-value i s no longer isotropic. Secondly, the g-values within each valley are changed since the applied strain changes the symmetry of the crystal and may admix bands that in the absence of strain would not contribute in the g-shift calculation. Normally i f g x and g„ in each valley are significantly different the application of strain w i l l cause a relatively large g-shift, which is predominantly due to valley repopulation (Feher and Wilson, 1960). If, however, the band gap is direct, strain causes a relatively small g-shift since the second mechanism is the only active one (Slagsvold, 1966). The apparatus used for this experiment was borrowed from Pieter Cullis who w i l l describe i t s operation in detail in his future thesis. -58-A rectangular sample was cut for the experiments. Uniaxial compressional stress was applied in two random directions at right angles to each other, of sufficient force to ultimately crush the sample. The resulting change in g-value was found to be less than t.001. 5.6 LIGHT EXCITATION An attempt was made to observe an effect on the EPR signal due to photo-created electrons. The relaxation time of the photo-created electrons i s expected to be much larger for an indirect band gap than for a direct gap. This is because the relaxation from an indirect band gap necessitates the emission of a phonon while the other case has a direct process. However, even i f the number of photo-created electrons i s large; for the equipment used, relaxation times in the _2 order of 10 sec. would be needed in order to see an effect. No effect was observed. 5.7 DISCUSSION AND COMMENTS Because of the samples increased conductivity, the incomplete motional narrowing of the EPR line and the g-shift from the free electron value the observed resonance in CdlnJS. is attributed to 2 4 either conduction electrons or to electrons in a donor band. Further-more, since sulphur vacancies are easily created by heat treatment and are known to produce a shallow donor level in CdS i t is most probable that the resonance is due to sulphur vacancy defect states in CdIn_S.. A 250 W. projector bulb was the light source; a flexible fiber optics light guide directed light to the cavity, and a quartz light pipe was used as a sample holder. -59-It i s impossible to derive any quantitative results from the g-value measurements because both the spin - orbit splitting, % , and the effect-«-».* ive mass tensor, m, are unknown. However i t i s noteworthy to compare the results to those of CdS (Slagsvold, 1966). g AHw^ Temperature CdS:I 1.77-1.79 12 G 1.7 °K Cdln-S, 1.68 19 G 1.1 °K 2 4 CdIn 2S 4 1.68 13 G 4.2 °K Table 5.1 Comparison of donor electrons in CdS and Cdl^S^ The g-tensor i s not isotropic for CdS because the crystal structure i s non-cubic. The line widths are measured as the fie l d between inflect-ion points of the absorption. The larger g-shift for CdL^S^ cannot be explained simply by the change in band gap energy. The g-value for conduction electrons has not been measured in any other spinels. The incomplete motional narrowing of the resonance i s not unusual for conduction electrons. For example i t has also been observed in Ge:P (Feher et al.,1959) and may be present in Si:P (Quirt, 1971). The laboratory preparation of samples exhibiting a conduction resonance appears to be very complex, and i s only studied qualitatively in this thesis. Sulphur vapor pressure was shown to be a contributing factor while other suspected parameters in the treatment process are; furnace temperature, time of heat treatment, shape of sample^ quenching i f EjCdS) = 2.58 eV while E ^ C d l n ^ ) = 2.3 eV ## If surface effects were important the sample shape would be a parameter. -60-technique and time lapse between heating and the EPR experiment. A study of time of heat treatment was inconclusive. Prom the surface state resonance i t i s also d i f f i c u l t to derive any quantitative results. One interesting feature, however, is that the intrinsic powder sample did not exhibit surface EPR lines at low temperatures. This indicates that electrons produced by the sulphur vacancies occupy the surface states of the powder or indeed, that the surface states themselves are sulphur vacancies whose states are modified by the nature of the surface. The surface EPR line i s not likely to be caused by an adsorbed gas radical on the surface since the g-value is relatively close to the value for conduction electrons. -61-CHAPTER 6 CONCLUSIONS 6.1 GENERAL CONCLUSIONS The significant results of this thesis are; (i) the observation of the temperature dependence of the hyperfine 2+ mteraction parameter, A, for CdL^S^cMn and the indirect correlation 2+ of the Mn with particular sites in the crystal. 2+ ( i i ) the observation of the g-tensor for CdIn2S^:Co and the direct correlation of the Co 2 + with "B" sites. ( i i i ) the observation of an EPR signal whose g-value is attributed to conduction electrons, the correlation of the signal to sulphur vacancy concentration, and the interpretation of the uniaxial strain experiments. These three results may be applied to the original motivations of the thesis (Section 1.2) in order to derive several general conclusions. The fact that there were no EPR signals in the intrinsic samples implies that the discrete luminescent levels within the band gap ( Czaja and Krausbauer, 1969) either were not occupied with enough unpaired electrons or they had an EPR resonance that was very broad. These levels were not conducting since the material behaved like a good insulator. The luminescent centers were attributed to sulphur vacancy com-plexes in the literature. Czaja and Krausbauer, as part of their model for the centers, required that the crystal structure be a partially inverted spinel. Experiments have shown that sulphur vacancies are * 13 / The sensitivity of the spectrometer is <->10 spins/Gauss line width. -62-present, even in crystals that are good insulators (CdlngS^tCo broad background line). The vacancies are also easily created by heat treatment. Since a l l ions studied by EPR that can be assigned to specific sites have a strong preference for the "B" site in the crystal, regardless of their charge state, i t is more probable that the crystal structure i s partially or fully inverted because a mechanism of charge compensation need not be invoked. It i s not surprising that the effects of the second order phase transition at 403 °K were not noted on either the EPR spectrum of 2+ CdL^S^iMn (observed continuously through the transition) or the EPR 2+ spectrum of Cdl^S^tCo (observed at 1.1 °K after the sample had been heated above 403 K and quickly quenched) since the effect i s , at best, a rearrangement of second - nearest neighbours. 2+ The temperature dependence of A for Cdl^S^rMn is best interpreted using the Debye model of ^ imanek and Orbach. The localized phonon model is not tenable since the predicted frequency of the local mode is too far away from the values for CdS:Mn which has essentially the same nearest neighbour configuration. The sulphur vacancy resonance is attributed to a donor level that may or may not be merged with the conduction band. Quantitative con-clusions from the g-value measurement may only be made when; the nature of the band gap is established, a measurement of the spin - orbit splitting of the valence band i s made, or the effective mass tensor in the conduction band is measured. Qualitatively, the g-value is useful in order to predict the g-value of conduction electrons in In 0S, within -63-the CdS - Cdl^S^ - Ii^S^ system. Assigning the same linear relation between CdS - Cdl^S^ as is between Cdl^S^ - In,^, the conduction electrons in I^S^ should have g ~1.6. The nature of the band gap is illuminated by the effects of strain on the conduction electron resonance. The null results indicate that either the band gap is direct or that g t - g u in each valley is small. The former is the more probable of the two. 6.2 POSSIBLE ADDITIONAL EXPERIMENTS An almost inevitable consequence of research leading to a thesis i s that some experiments are only partially completed or never attempted. This study has suggested several possibilities that may best be enumerated. (i) Cyclotron resonance - this may be a d i f f i c u l t experiment to perform since the electrons must remain in their cyclotron orbits for a relatively long time before they are scattered. Attempts on the available intrinsic samples grown from the melt were unsuccessful. Intrinsic samples grown from the vapor phase using a transport gas would probably offer a better chance of success. ( i i ) Optical absorption - a close look at the band gap absorption t a i l may resolve the question of whether or not the band gap is direct. If possible, i t would also be of interest to determine the spin - orbit splitting at the valence band maximum. ( i i i ) Hall measurements - i t would be interesting to determine whether any of the samples are predominantly p-type so that devices such as diodes and electroluminescent crystals may be developed. -64-(iv) Faraday rotation - one of the easiest methods, in principle, to get a value for m . The experiment could be performed at room tem-perature in the ordinary geometry and the Voigt geometry with the ratio of the two angular rotations vof the plane of polarization giving m directly (Lax, 1962). (v) Infrared studies - a study of the 'shallow donor' excited 2+ states may be feasible. Also the excited states of the Mn ion could be observed and the site symmetry deduced. (vi) Transport properties - may shed some light on the nature of the charge carriers and the band structure, however the difficulties with good electrical contacts make the experiments hard to do. (vii) Additional studies of heat treatment techniques - because of irreproducibility these experiments may be d i f f i c u l t , however they would s t i l l be interesting. ( v i i i ) Studies of the CdS - C d l n ^ - I n ^ system - CdS has been extensively studied, but l i t t l e i s known about II^J or the intermediate compounds on either side of Cdl^S^. For example, i t would be interesting to study the shallow donor sulphur vacancy resonance throughout the system. (ix) Additional optical excitation experiments - the experiment performed was only a preliminary one with a weak light source. It would seem that In^S^ might be a good starting place since pre-liminary experiments indicated that sulphur vacancies are easily produced. ## Experiments in this laboratory are presently being contemplated that w i l l monitor EPR transitions by looking at the polarization of emitted light. BIBLIOGRAPHY Abdullaev, G.B., Antonov, V.B., Guseinov, D.T., Nanu, R.Kh.t Salaev, E ' . Y U . , Sov. 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Czaja, W., and Krausbauer, L., phys. stat. solidi 3_3_, 191 (1969). Czaja, W., Phys. kondens Materie 10, 299 (1970). Dyson, F.J., Phys. Rev. 28, 349 (1955). Feher, G., Wilson, D.K., and Gere, E.A., Phys. Rev. Lett. 3_, 25 (1959). Feher, G., and Wilson, D.K., Bull. Am. Phys. Soc. 5_, 60 (i960). Gersmann, H.R., and Swalen, J.D., J. Chem. Phys. 3_6, 3221 (1962). Goldsborough, J.P., and Mandel, M., Rev. Sci. Inst. 3J., 1044 (i960). Griffith, J.S., 'The Theory of Transition - Metal Ions', Cambridge (1961). -66-Haas, C, J. Phys. Chem. Sol. 26, 1225 (1965). Hahn,H., and Klinger, W., Z. Anorg. Chemie 263., 177 (1950). Henning, J.C.M., Bongers, P.F., Van den Boom, H., and Voermans, A.B., Phys. Lett. 30A, 307 (1969). Kerr, R.K., and Schwerdtfeger, C.F., J. Phys. Chem. Sol. 3J2, 2007 (1971). Kimmel, H., Z. Naturforschung 18a, 650 (1963). Kneubuhl, F.K., J. Chem. Phys. 3J5, 1074 (i960). Koelmans, H., and Grimmeiss, H.G., Physica 25., 1287 (1959). Lax, B., Int. Sem. Conf. (Exeter), 265 (1962). Low, ¥., Phys. Rev. 105., 793 (1957). Meloni, F., and Mula, G., Phys. Rev. (B) 2, 392 (1970). Morigaki, K., J. Phys. Soc. Jap. 1_9., 1253 (1964). Nusimovici, M.A., Balkanski, M., and Birman, J.L., Phys. Rev. (B) 1_, 603 (1970) Orton, J.W., 'Electron Paramagnetic Resonance', I l i f f e Books Ltd. (1968). Pake, G.E., 'Paramagnetic Resonance', Benjamin (1962). Poole, CP. Jr., 'Electron Spin Resonance', Interscience (1967). Quirt, D., private communication, University of British Columbia (1971). Rehwald, V/., and Harbeke, G., J. Phys. Chem. Sol. 26, 1309 (1965). Rehwald, W., Phys, Rev. 1.5J5, 861 (1967). Robinson, F.N.H., J. Sci. Inst. 3j>, 481 (1959). Roth, L., Phys. Rev. U8, 1534 (i960). Shand, W.A., J. Crys. Growth 5., 203 (1969). Simanek, E., and Orbach, R., Phys. Rev. 145., 191 (1966). Simanek, E., and Huang, N., Phys. Rev. Lett. 17, 699 (1966). Slagsvold, B., PhD. Thesis, University of British Columbia (1966). Slagsvold, B., private communication (1971). Slichter, CP., 'Principles of Magnetic Resonance', Harper and Row (1963). Springford, M., Proc. Phys. Soc. 82, 1029 (1963). -67-Stahl-Brada, R.f and Low, W., Phys. Rev. 116, 561 (1959) . Suchow, L., and Stemple, N., J. Electrochem. Soc. 111, 191 (1964). Thornley, J.H.M., Windsor, C.G., and Owen, J., Proc. Roy. Soc. A284, 252 (1965) . Walsh, W.M., Jeener, J., and Bloembergen, N., Phys. Rev. 122, A1338 (1965). Watson, R.E., and Freeman, A.J., Phys. Rev. 123., 2027 0 957). Wieringen, Disc. Far. Soc. 19_, 148 ( 1 9 5 5 ) . Wilmshurst, T.H., 'Electron Spin Resonance Spectrometers', Adam Hilger (1967). Wilson, D.K., and Feher, G., Phys. Rev. 124, 1068 (1961). z'd'ansky, K., phys. stat. sol. 28, 181 (1968). Zdansky, K., and Kubec, F., J. Phys. Chem. Sol. 22, 2327 (1969). -68-APPENDIX 1 SAMPLES Table A1.1 Available samples Sample * Source Doping EPR Signal? Comments 672 C Intrinsic No red, transparent 755 C Intrinsic No red, transparent 764 C Intrinsic No red, transparent 806 C Intrinsic No red, transparent 850 C Intrinsic No red, transparent A237285B S Intrinsic Yes powder sample 657 C I No grey, opaque 640 C I No red, semi-trans. 689 C Cr(.5 Mole^) Yes grey, near opaque 695 C Cr(.27 MolejS) Yes red, semi-trans. 699 C Cr(.27 Mole$) Yes red, semi-trans. 754-7 C Cr(.05 Mole$) Yes grey, opaque 804 C Cr(.04 Mole#) Yes red, transparent V109 B Cr Yes red, opaque 694 C Ce No orange, trans. 748 C Ag(.1 Mole#) No red,' semi-trans. 765 C Ag(.5 Mole^) No red, opaque 757 C Mn(.1 Mole^) Yes red, transparent 775 C Mn(.01 Mole$) Yes red, transparent 775 C Mn(.05 Mole$) Yes red, semi-trans. 1911 NBRPC Mn(l50 ppm.) Yes red, semi-trans. 758 C Sn(5 Mole$) No grey, opaque 759 c Sn(.5 Mole$) No red, semitrans. 765 c Na(.5 Mole#) No red, transparent 767 c Au(.01 Mole^) No grey, opaque 771 c Cu(.1 Mole$) ? grey, opaque 772 c Cu(.5 Mole#) ? black, opaque 785 c Co(.05 Mole$) • Yes red, near opaque 1910 NBRPC CO(150 ppm.) Yes red, near opaque 1961 NBRPC Co(660 ppm.) Yes red, near opaque 785 C Fe(.1 Mole^) No red, near opaque 1974 NBRPC Fe(660 ppm.) No grey, opaque 796 C S - vacancy Yes grey, opaque 812 C Hg(.1 Mole^) Yes grey, opaque 815 c Eu(.1 Mole^) No grey, opaque 821 c P(.01 Mole$) No red, transparent 855 c Cl(5000 ppm.) No red, near opaque 1962 NBRPC V(100 ppm.) No grey, opaque 1965 NBRPC V(100 ppm.) No grey, opaque 2065 NBRPC , Ge(l00 ppm.) No red, transparent 2066 NBRPC Ge(l00 ppm.) No red, transparent 795 C Mn(.05 Mole$) Yes IngS^ 805 C Mn(.025 Mole$) Yes In 2S 5 *C = Dr. Czaja, R.C.A. Labs, Zurich, Switzerland NBRPC = New Brunswick Research and Productivity Council B = Bongers et at,- Phillips Research Lab, Holland S = Dr. I. Shepherd -69-APPENDIX 2 THE MEASUREMENT Q F A The EPR signal that i s observed in a normal experiment i s the change in power reflected to the crystal detector due to the power absorption of the sample at resonance. It can be shown that this signal i s proportional to /\ , the imaginary part of the susceptibility. An equivalent circuit for a cavity of an EPR spectrometer i s shown FIGURE A2.1 EPR spectrometer equivalent circuit It i s tacitly assumed that the characteristic wave guide impedance i s real. This i s strictly not true, but does not alter the calculations (Goldsborough and Mandel, 1960). The effect of a sample at resonance i s described by a small change in inductance L = L Q(1 + 4/tf',\X), where L Q = cavity inductance away from resonance, ^ = f i l l i n g factor «*. volume of sample/volume of cavity, and "y^ = complex susceptibility of sample = X,- i X where 7( and x" are real functions of CO . in Figure A2.1 Microwave Ideal Transformer = Coupling Iris -70-s h i f t of the frequency at resonance given by -l/2 ( W / L q ) S L . Now, away from resonance Q Q = UL^/R = 2lC(energy stored)/(energy dissipated) per cycle. The quantity measured by the spectrometer i s the change i n power reflected by the cavity at resonance which i s proportional to £ Q, the change i n the cavity quality factor due to a resonating sample. S Q = 6D 0 SL/R + S » W L O / R - U J J L S R / R 2 = 2Tr^Q oX' - 4TT^Q2X" The f i r s t term i s the dispersive part due to the change i n resonant frequency of the cavity. For \ ~ t h i s i s a factor 1 / Q q less than the second term and i s therefore usually neglected. o 2 n Thus bQ - - 4T\*^QQX and the quantity measured i s proportional II to y:. * 1 / Q ~ 1/8000 f o r a t y p i c a l X-band cavity. - 7 1 -APPENDIX 5 MAXIMUM SENSITIVITY OF A MICROWAVE BRIDGE AND. DETECTOR The s e n s i t i v i t y of an EPR spectrometer depends on the coupling of the cavity, the operation point of the diode detector on i t s I-V curve, and how bias i s applied to att a i n this operation point. Interrelations between these three conditions y i e l d an optimum condition f o r the micro-wave bridge. A schematic diagram of a magic tee r e f l e c t i o n spectrometer i s shown i n Figure A 5 . 1 . ^ & T u n e r Klyst ron Magic tee ^ f?y^ ^Crystal diode f?r detector I [ ^ - C a v i t y FIGURE A3.1 Schematic diagram of a magic tee r e f l e c t i o n spectrometer The r e f l e c t i o n c o e f f i c i e n t T"1 = complex r a t i o of reflected/incident E at any s p e c i f i c point. T^ = r e f l e c t i o n c o e f f i c i e n t at the cavity coupler i r i s away from resonance; = r e f l e c t i o n c o e f f i c i e n t at the cavity i r i s at resonance; and T£ = r e f l e c t i o n c o e f f i c i e n t at the tuner i n the balance arm of the bridge. Using the equivalent c i r c u i t of Figure A2 .1 i t i s calculated that = (R - R f i)/(R +.R6) and (R + S R - R 6)/(R + S R + R 6) where *bR i s a small quantity. One defines dps T^ -T^  = 2R6$R/(R+R6) =(S R/(2R ) ) (1 - "Q )• The power incident on the detector i s P c=l/ 4 | w h e r e i s the power incident on the tee. At resonance the cr y s t a l power becomes P c r = 1/4(1^ ,-^ 1 Pj^ * The change in crystal power may be defined as, SP = P c r - P c = l/4(2Re^(ro-T t)} + \%V\)?± , Now, (T^-^t) can be made real by adjusting the phase on the balance arm tuner so that for small SP, $P * 1/2?±%T{V0-\). It i s desirable, for two reasons, to be in the linear portion of the I-V curve of the diode detector; (i) for a given change in voltage, Sv, the detector has a maximum response, S i , in the linear region. ( i i ) in order to have the signal, S i , proportional to X , Si = must be proportional to§P. This i s true only for IV>$I, c or in the linear region. Thus, the EPR signal is a small change in current, S i , on a large background current, I. Por the linear region of crystal bias or, more simply,Si°t (1 - T£ ). r This has a maximum for = 0 independent of T£, Thus for maximum sensitivity the cavity should be c r i t i c a l l y coupled. The bias current for the detector can be attained by introducing reflections in the balance arm, not affecting the sensitivity. -73-APPENDIX 4 MEASUREMENT OF g AND A IN THE PRESENCE OF AN HYPERFINE INTERACTION cw -J> ->- + The Hamiltonian for a simple spin system i s g^H.S + AI.S where S is the spin of the electrons and I is the nuclear spin. Considering the second term as a perturbation, f i r s t order theory yields the energy levels E^  = g(*>HM + AMm where M and m are the electronic and magnetic quantum numbers respectively. The EPR selection rules, AM =11 and Lra = 0, are used to derive an expression for the resonant frequency; hV> = g ^ H + Am. For I = 5/2 (Mn ) this gives a spectrum of six equally spaced lines when sweeping H at constant h\> . To second order the energy levels are given by (Van Wieringen, 1955); A 2 E 2 = g £>HM + AMm - ~ (2mS(S + 1) - 2Ml(l + 1) - 2Mm(M - m)) . Applying the EPR selection rules yields the resonant condition; hW» = 1/2 (g^H + Am + ((g(*H + Am)2+ 2 A 2 ( l ( l + l) - m 2 ) ) 1 ^ 2 ) # For the case of I = 5/2 this leads to a pattern of lines slightly shifted from the f i r s t order case. This is represented schematically in Figure A4.1. Absorption x , ^ 1 5 _ x 4 x 1 y First bo rder •ri FIGURE A4.1 Representation of an 1=5/2 hyperfine spectrum to second order Thus, the entire spectrum i s shifted to a lower H D value, so that an experimental measurement of g would be in error by an amount %g; The calculation will be carried out for C d l n ^ where S=l/2 and 1=5/2. -74-%S = j g & l = 5/4 ^jy*. For A ~100 G and H c~3 x 10 5 G one finds Sg ~ 1 C f ' which is experimentally measurable. To second order, the hyperfine pattern is shifted toward the low field value, independent of the sign of A but the width of the entire pattern i s s t i l l 5A, and therefore the best method of determining A is to measure the fi e l d difference between the two extreme lines. APPENDIX 5 PROPERTIES OP POWDER SPECTRA Consider a spin system described by a Hamiltonian for a single crystal, *X = g H (* H Z S Z + S>.Q ^ Hx Sx + Hy Sy^' F ° r a f i x e d k l y s t r o n frequency, \> , the resonant fi e l d for a single spin is given by; H = i ! ^ _ - h\> g(e )Q> Cj>(g*cosV + g ^ s i n ^ )'"- * In a powder the spins are randomly oriented, with the fraction of spins having an angle in the range *B to + dfr being l / 2 s i n 8 d 9 . If dN is the fraction of spins in any d9^ having resonant fields in the interval dH, then dN = A(H)dH = l / 2 s i n © d & = l/2sin&-^.dH where the shape function A(H) = (gf4 - g 2 ) " 1 ^ 2 ^ ^ _ g 2)"" 1/ 2. A(H) 0 l ine width Finite line width dX" dH Experimental Trace FIGURE A5.1 Single line powder spectrum for anisotropic g-values -76-If there i s an hyperfine interaction present, also exhibiting axial symmetry, the resonant fi e l d for one spin i s , to f i r s t order; The resultant shape function A(H) is a superposition of shape functions for each hyperfine line (Gersmann and Swalen, 1962) FIGURE A5.2 Three line powder spectrum for anisotropic g-values It can be seen that for a large line width the spectrum reduces to a case similar to the finite line width case previously described. For a rhombic g and A even more 'smearing out' of the hyperfine structure in the powder spectra occurs (Kneubuhl, 1960). The experimental trace 2+ of a Co doped Cdl^S^ powder closely approaches the spectrum of a single spin randomly distributed. nuclear magnetic quantum number. ACH) 1 0 Une width Finite line width -77-APPENDIX 6 SECOND ORDER g-VALUE CORRECTIONS FOR Co 2 + 2+ The second order corrections to g^ _ and g(1 for Co due to admixing of upper levels may be written (Abragam and Pryce, 1970); g„(2) = (3a 2 - c 2)P, + b 2v^ + (6 l / 2ab - 8l/2bc)v>, g (2) = b 2vJ. + C 2 U + 31//2acv>t + 21/'2bcv^ . 6 l / 2 8 1 / 2 where the parameters a, b and c are related to x by; a:b:c = ~:-1 2 2 2 and a" + b + c =1 (see section 4.4b). Assuming x^1 and considering only the next nearest orbital level, "4" (see Figure 4.5), we calculate a= -0.870, b= +0.356 and c= -0.336. For a trigonal f i e l d the coefficients, Vl , may be written as; P, = 5/2y, Vi= 10y, V,= 15/2y, V>= 5y, Vs= 5y, and v>= Y}= 0, where y = - VSE and BE is the energy separation between the ground state and <H". _ -1 v -1 * If we further assume bE ^3000 cm. and A- -180 cm. , then y = 0.06 and the g-value corrections are; g u(2) = 0.210 gj_(2) = 0.072 . Thus, to second order, the theoretical curve for g M vs. g ^ w i l l be shifted to higher g-values. The second assumption is certainly a good one (the free ion value) while the other one uses a representative value for £>E taken from Abragam and Pryce's paper. 


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