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Luminescence and relaxation measurements on CdIn₂S₄ :Cr³⁺ Orfino, Francesco Paolo 1984

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LUMINESCENCE AND RELAXATION MEASUREMENTS ON CdIn 2S 4 by FRANCESCO PAOLO ORFINO B . S c , The University of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department of Physics) We accept t h i s thesis as confirming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1984 ®Francesco Paolo Orfino, 1984 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 fo r 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 a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis f o r 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 1956 Main Mall Vancouver, Canada V6T 1Y3 . / -6 (3/81) Abstract The luminescence and the relaxation rate of CdIn 2Si +:C r i + has been investigated. The R-line spectra s t a r t s at 12,996 cm - 1 and extends to lower energies. The R-line separation at T = 2K was measured to be 30.3 cm - 1. Also, the phonon sidebands associated with the R-lines are i d e n t i f i e d and tabulated. In addition, an energy l e v e l scheme for CdIn 2S i + : C r 3 + with the octahedral co-ordinated chromium ion i s proposed. No evidence of luminescence due to the tetrahedral co-ordinated chromium ion was observed. The broad peak was found to be composed of various t r a n s i t i o n s whose relaxation rates were i n the range (160-210) usee. Time-resolution measurements of the R-lines indicated that to within experimental error both l i n e s had the same rel a x a t i o n rate which was found to be (10.45 ± 0.45) msec. - i i i -Table of Contents Abstract i i Table of Contents i i i L i s t of Tables • v L i s t of Figures ••• v i Acknowledgements v i i Chapter 1: Introduction 1 1.1 Background 1 1.2 Thesis Motivation 2 1.3 Thesis Outline 2 Chapter 2: Theory of Photoluminescence of CdIn 2S l t: C r 3 + 4 Chapter 3: Photoluminescence of CdIn 2Si +:Cr 3 + 8 3.1 Experimental D e t a i l s 10 3.1.1 Experimental Set-Up 10 3.1.2 Samples 10 3.1.3 Data A c q u i s i t i o n 11 3.2 Experimental Results and Discussion 13 3.3 Conclusions 25 - i v -Chapter 4: Time Resolved Measurements 28 4.1 Experimental Technique 30 4.2 The Acousto-Optic E f f e c t 31 4.3 Experimental Det a i l s 35 4.3.1 The Modulator 35 4.3.2 The Experimental Arrangement 36 4.4 Estimate of the 2Eg Lifetime 37 4.5 Nu l l i n g Techniques and Results 38 4.5.1 Method #1 38 4.5.2 Method #2 42 4.6 Lifetime Determinations 47 4.6.1 MCS Arrangement 47 4.6.2 MCS Data and Results 50 4.7 Concluding Remarks 53 Chapter 5: Concluding Remarks 55 Bibliography 57 Appendix A • 60 -v-L i s t of Tables Table Page I The Cdln^S^ peak p o s i t i o n as a function of temperature and C r 3 + - i o n concentration 16 II Values f o r D and AR for various c r y s t a l s 21 III -^ E-^ Ao lumlinescence and v i b r o n i c assignments 24 - v i -L i s t of Figures Figure Page 2.1 Correlation diagram showing the e f f e c t of the c r y s t a l f i e l d combined with the a x i a l d i s t o r t i o n and the spin-or b i t e f f e c t on the " f r e e - i o n " e l e c t r o n i c states 7 3.1 Experimental set-up for the detection of the photoluminesce of CdIn 2S 1 +:Cr 3 + 9 3.2 Data flow of the photoluminescence s i g n a l 12 3.3 The photoluminescence spectra of stoichiometric CdIn 2S l + at 4K(a); of CdIn 2S i +:Cr 3 + (0.04 M%) at 2K (b'); and of CdIn 2S 1 +:Cr 3 + (0.5 M%) at 2K (b) 14 3.4 The absorption spectrum (a) and the e x c i t a t i o n spectrum (b) of Cr-doped C d l n ^ 17 3.5 The photoluminescence spectra of C d I n 2 S 4 : C r 3 + (0.5 M%) at (a) 77K and at (b) 2K 19 3.6 Proposed energy l e v e l scheme for C r 3 + s u b s t i t u t i n g for I n 3 + at an octahedrally co-ordinated B-site i n CdlnjS^. ... 26 4.1 The acousto-optic d i f f r a c t i o n process , 33 4.2 Generated pl o t of A D vs. t ^ ^ 39 4.3 Generated plots of vs. t y y D for (a) T y ^ D = 40 T n and for (b) t u / D < 4.0 x N 41 4.4 Spectrum for the nulled broad peaks 44 4.5 Graphs generated to aid i n estimating the n u l l i n g decay rate - 46 4.6 Experimental arrangement to measure l i f e t i m e s using the MCS 48 4.7 Data obtained using the MCS 51 A.l Photon counter pulse sequence necessary to load data i n computer memory 61 - v i i -Acknowledgements I wish to thank the many people who contributed to the completion of t h i s t h e s i s . In p a r t i c u l a r , I wish to thank: Dr. C.F. Schwerdtfeger for his supervision and assistance i n the preparation of the thesis and i n the performance of the experiments. Dr. N. Graber for c o l l e c t i n g some of the data and for many h e l p f u l discussions. Dr. M.L.W. Thewalt for his advice regarding his modulation technique. My friends Warren Lee, Zoran Ninkov and others who provided support at times when circumstances seemed to conspire against my f i n i s h i n g t h i s t h e s i s . My family, without whose constant support t h i s thesis would not have been possible at a l l . And f i n a l l y , Darlene Crowe for her patient and d i l i g e n t typing of t h i s t h e s i s . - v i i i -In memory of my g r a n d f a t h e r . 1 Chapter 1 Introduction 1.1 Background One of the most studied non-magnetic spinel-type semiconductor i s CdIn 2S l t. Apart from i t s i n t e r e s t i n g photoconducting properties, i n t e r e s t i n CdIn 2Si + and i n chromium doped CdIn 2S 1 + arose from a need to understand the band structure of the magnetic spinels (e.g. CdCr 2S 1 +). Thus, from a t h e o r e t i c a l point CdlngS^ was a good s t a r t i n g point. D i f f e r e n t methods have been applied to the c a l c u l a t i o n of the band structure ranging from semiquantitative approaches [1,2] to f u l l pseudopotential band c a l c u l a t i o n methods [3,4,5]. These re s u l t s have been applied towards the c a l c u l a t i o n of the band structures of magnetic spinels with p a r t i c u l a r success on CdCrjS^ and CdCr^e^ [6]. Experimental r e s u l t s which are the basis of any t h e o r e t i c a l c a l c u l a t i o n have tended to support the band structure c a l c u l a t i o n of CdIn 2S 1 +. In p a r t i c u l a r , the experimental determination of the CdlnjS^ o p t i c a l constants [7] have tended to support t h i s c a l c u l a t i o n . Also, over the years a small controversy regarding the structure of CdIn 2S t t seems to have been resolved. I n i t i a l l y the CdIn 2S l + structure was thought to be that of a d i r e c t s p i n e l [8]; however, further i n v e s t i g a t i o n s have shown th i s compound to c r y s t a l l i z e i n a p a r t i a l l y inverted s p i n e l . The problem o r i g i n a l l y arose from the fact that the Cd^ + and the I n 3 + ions are i s o e l e c t r o n i c so that x-ray d i f f r a c t i o n measurements could not be used to determine the i o n i c s i t e s . 2 Measurements on s p e c i f i c heat [9], electron paramagnetic resonance (EPR) [10-12] and photoluminescence [13] have shown that the CdlnjS^ c r y s t a l structure i s that of a p a r t i a l l y inverted s p i n e l . This structure i s given by Cd^/2T-ni/2^<^l/2-'-n3/2^i+» where the octahedral symmetry s i t e s are indicated by the brackets and the other s i t e s have tetrahedral symmetry. By inspection, the C d 2 + ions occupy both s i t e s - tetrahedral (A-site) and octahedral (B-site) - equally; the I n 3 + ions are more l o c a l i z e d on the B - s i t e s . The l o c a l symmetry of these s i t e s has been reported as being T, for the A-sites and D„, d Jd for the B-sites [10]. 1.2 Thesis Motivation The goals for t h i s thesis are twofold. F i r s t l y , the p o s s i b i l i t y that a spectral response for C d l n j S ^ : C r 3 + - i n the v i s i b l e region of the spectrum - at a much better r e s o l u t i o n than already found i n the l i t e r a t u r e [14] would be obtained. Secondly, once the s p e c t r a l response was obtained and analyzed then one would measure the l i f e t i m e of the doubly degenerate excited state of the C r 3 + ion, namely the 2Eg s t a t e . 1.3 Thesis Outline Chapter 2 consists of a t h e o r e t i c a l background for C d l n j S ^ : C r 3 + . Chapter 3 i s devoted to the d e s c r i p t i o n of the experimental equipment as w e l l as the experimental r e s u l t s of the photoluminescence of Cdl^S^^ : C r 3 + . Chapter 4 deals e x c l u s i v e l y with the e f f o r t s to determine the l i f e t i m e of the doubly degenerate excited state 2Eg of the t r a n s i t i o n metal ion C r 3 + . 3 And, Chapter 5 consists of a few concluding remarks with suggestions for refinements and/or other experiments which would further c l a r i f y t h i s subject. 4 Chapter 2 Theory of Photoluminescence of CdIn~S u:Cr The t h e o r e t i c a l considerations f o r C d I n 2 S u : C r 3 + deal mainly with the chromium energy l e v e l s . These are observed i n d e t a i l and are discussed i n the next chapter. The chromium atom i s a member of a group c o l l e c t i v e l y c a l l e d the i r o n group. This group encompasses atoms with atomic numbers 21 through 30. When these atoms are present as impurities i n host c r y s t a l l a t t i c e s they are commonly referred to as t r a n s i t i o n metal ions of the 1st series [15]. The des c r i p t i o n of the e l e c t r o n i c structure of an atom, where the proper number of electrons are placed i n the lowest l y i n g hydrogen-like o r b i t a l s according to the Pauli Exclusion P r i n c i p l e , i s c a l l e d the e l e c t r o n i c configuration. The el e c t r o n i c configuration f o r the ir o n group i s : (Ar c o r e ) 1 8 3 d n 4 s m , where m = 1,2 and n = 1,2,...,10. I t i s r e a d i l y apparent that f o r almost a l l of these ions the i n t e r a c t i o n with the c r y s t a l l i n e environment i s mediated through the 3d 1 1 o r b i t a l s . The ion of i n t e r e s t i n th i s thesis i s chromium. It substitutes f o r the t r i v a l e n t In-ion; therefore, the e l e c t r o n i c configuration of C r 3 + i s : (Ar c o r e ) 1 8 3 d 3 . The Hamiltonian for the electrons of a paramagnetic ion such as C r 3 + i n a c r y s t a l within an external magnetic f i e l d i s given by: + a I C.1 «s + I a j ' I [2.1] i i 5 where the f i r s t term denotes the k i n e t i c energy and the Coulomb a t t r a c t i o n between the nucleus and the electrons; the second term denotes the e l e c t r o s t a t i c repulsion between electrons; the t h i r d term denotes the c r y s t a l l i n e f i e l d acting on the paramagnetic ion; the fourth term denotes the spin - o r b i t i n t e r a c t i o n ; and, the f i f t h term denotes the hyperfine i n t e r a c t i o n . I f the s i t e symmetry i s known i t i s possible to predict how much of the degeneracy of the energy l e v e l s may be removed. This i s commonly re f e r r e d to as the c r y s t a l f i e l d s p l i t t i n g . The formalism of the c r y s t a l f i e l d can be categorized i n three groups: ( i ) the weak; ( i i ) the intermediate; and ( i i i ) the strong c r y s t a l f i e l d . The parameter which characterizes each group i s the strength of the c r y s t a l f i e l d i n comparison to the e l e c t r o s t a t i c i n t e r a c t i o n . In the f i r s t case the c r y s t a l f i e l d p o t e n t i a l i s weaker than the spin-orb i t coupling. In the second case the c r y s t a l f i e l d p o t e n t i a l i s stronger than the spin - o r b i t coupling but weaker than the e l e c t r o s t a t i c i n t e r a c t i o n . In the t h i r d case, the c r y s t a l f i e l d p o t e n t i a l i s stronger than the e l e c t r o s t a t i c i n t e r a c t i o n and electrons may be removed from the i o n . In a host l a t t i c e such as CdlnjS^ where the chromium t r i v a l e n t i o n substitutes for a t r i v a l e n t indium ion at an octahedrally co-ordianted B - s i t e the c r y s t a l f i e l d symmetry i s denoted as 0^ [16]. The intermediate c r y s t a l f i e l d formalism has been found to be the more accurate d e s c r i p t i o n applicable to the t r a n s i t i o n metal ions of the i r o n group. So, when the action of the 0^ f i e l d i s calculated some of the degeneracies of the "f r e e - i o n " states are 6 removed. In p a r t i c u l a r , the ground state and the 2G state degeneracies are p a r t i a l l y l i f t e d * . The ground state s p l i t s * * i nto three states l a b e l l e d : l*&2g' ^^Ig* a n c* ^ l g degeneracies of 4, 12 and 12 r e s p e c t i v e l y . As w e l l , the 2G state s p l i t s into three states l a b e l l e d : 2 E , 2 T . , and 2T. with g 2g' lg degeneracies of 2, 8 and 8 r e s p e c t i v e l y . When the e f f e c t of a t r i g o n a l c r y s t a l f i e l d of symmetry combined with the spi n - o r b i t i n t e r a c t i o n i s considered, further degeneracy removal of some states occurs. As noted i n figur e 2.1, the degeneracy of the 2 E state i s l i f t e d completely and the degeneracy of the ground state ^^2g ^ s r u r t n e r reduced. The s p l i t t i n g of the ground state i s usually much less than the s p l i t t i n g of the 2 E s t a t e . The e l e c t r o n i c t r a n s i t i o n s from the 2 E state to the ground state are going to be investigated i n t h i s t h e s i s , these are c a l l e d the R-li n e s . *The "f r e e - i o n " ground states of the t r a n s i t i o n metal ions may be found through the a p p l i c a t i o n of Hunds Rules [17]; for C r 3 + t h i s i s found to be the 4 F state with a t o t a l degeneracy of 28. **The c r y s t a l f i e l d s p l i t t i n g s of the "free - i o n " states as a function of the c r y s t a l f i e l d strength have been calculated and plotted by Tanabe and Sugano [32]. 7 free-ion O h D 3 d i ~ s .o Figure 2.1 Corr e l a t i o n diagram showing the e f f e c t of the c r y s t a l f i e l d combined with the a x i a l d i s t o r t i o n and spi n - o r b i t e f f e c t on the "fr e e - i o n " e l e c t r o n i c s t a t e s . 8 Chapter 3 Photoluminescence of CdlrijS^ : C r 3 + The t r a n s i t i o n metal ion Cr has been known to substitute for the t r i v a l e n t In-ion at the octahedral B-site when doped i n the CdIn 2S 1 + c r y s t a l [10]. In absorption, two peaks were observed by Wittekoek et a l . located at 14,900 cm - 1 and 18,500 cm - 1. These peaks were assumed to originate from the C r 3 + ion thus, they were assigned to the l i g a n d - f i e l d t r a n s i t i o n s 4 A „ -> **T„ and 4 A „ •* **T, , r e s p e c t i v e l y . More recent r e s u l t s by Sato et a l . confirm 2g l g ' 3 these r e s u l t s by photoluminescence as well as by photoconductivity measurements. Sato et a l . f i n d that by chromium-doping i n t r i n s i c CdlnjS^ the broad emission band centered at 15,000 cm - 1 (at 77 K and due to the i n t r i n s i c CdLn^S^) decreases i n i n t e n s i t y . Also, structured luminescence occurs i n the energy region between 12,500 cm-* and 13,000 cm - 1. This emission i s att r i b u t e d to the l i g a n d - f i e l d t r a n s i t i o n '•A- «- 2 E , 2T. of C r 3 + i n analogy 2g g' lg B y with r e s u l t s obtained from C d C ^ S ^ In the following the experimental set-up i s presented. Also, the data a c q u i s i t i o n method i s described. As w e l l , the experimental data obtained on i n t r i n s i c CdIn 2S l + and on chromium-doped CdIn 2S l + i s presented. A discussion of the r e s u l t s follows. 9 PM Figure 3.1 Experimental set-up f or the detection of the photoluminescence of CdIn 2Si +:Cr 3 +. The symbols have the following meaning: S i s the las e r source; F are the f i l t e r s ; Ml and M2 are the r e f l e c t i n g mirrors; LI i s the c o l l e c t i n g lens; L2 i s the focussing lens; D i s the dewar stock ( i n X-section) i n which the sample i s placed; SP i s the spectrometer; and, PM i s the photomultiplier. 10 3.1 Experimental Det a i l s 3.1.1 Experimental Set-up The experimental set-up which was used i n the determination of the photoluminescence of C d l i ^ S ^ : C r 3 + i s shown i n figure 3.1 The 488 nm l i n e at ~500 mW output power of a Spectra Physics 165 A r + - i o n laser was used as the e x c i t a t i o n source. The photoluminescence was detected with an RCA 7102 photomultiplier tube with selected Sl-photocathode. The luminescence was analysed with a Spex 1704 spectrometer - with a dispersion of 1.15 cm - 1 i n the spec t r a l region of i n t e r e s t , i . e . 16,667 cm - 1 - 11,111 cm - 1 (6000 A-9000 A) -i n conjunction with a Nova 2 computer co n t r o l l e d s i g n a l averaging system. The absorption measurements were made using an OSRAM LAMP @ 250 W power as a source instead of the A r + - i o n l a s e r . Of course, the or i e n t a t i o n of the source i s not as shown i n figure 3.1; rather, the sample i s illuminated from the d i r e c t i o n (see figu r e 3.1) of the reader. The e x c i t a t i o n measure-ments were made using as a source a 500 W PEK mercury lamp immediately follow-ed by a Bausch & Lomb monochrometer with a bandpass of ~150 cm - 1 (70 A). For low temperature measurements an e x i s t i n g low temperature dewar system with sapphire windows was u t i l i z e d . 3.1.2 Samples The samples used were c r y s t a l s grown from the melt by the Bridgeman method where the appropriate amount of C r 3 + had been added to the melt. Two concentrations, namely 0.04 Mol% and 0.5 Mol% of C r 3 + were investigated. These samples did not d i f f e r much from each other either i n colour or i n grainyness. The Cdln 2S^^:Cr 3 + samples were of a reddish-pink colour attributed to the C r 3 + doping, and smooth. 11 Having been cut from a boule they were of roughly c i r c u l a r geometry with a diameter of 0.8 cm and a thickness of 0.2 cm. The "pure" CdlnjS^ which was u t i l i z e d for i n t r i n s i c measurements d i f f e r e d markedly from the doped c r y s t a l s . These i n t r i n s i c c r y s t a l s resembled stacked flakes of roughly the same geometry as the doped c r y s t a l s . V i s u a l l y , the pure c r y s t a l s were mainly transparent with s l i g h t white d i s c o l o r a t i o n s . 3.1.3 Data A c q u i s i t i o n The data was c o l l e c t e d with the aid of a computer controlled s i g n a l averaging system already i n existence [18]. Since the computer co n t r o l l e d the spectrometer's wavelength by c o n t r o l l i n g the stepping motor which turned the grating, the data a c q u i s i t i o n sequence was begun by inputting on the computer terminal some i n i t i a l parameters. These parameters were the s t a r t , the end, the step si z e ( a l l i n Angstroms) of the sweep, the number of points as well as the dwell time per point. Thus the spectrum consisted of many points where each point was separ-ated i n wavelength from the previous one by the step si z e and each point represented the number of counts for a given time length. The data flow for each point of the spectrum i s as follows. The photoluminescence s i g n a l detected by the photomultiplier at a p a r t i c u l a r wavelength i s fed through some e l e c t r o n i c s for a m p l i f i c a t i o n purposes. The s i g n a l i s then fed to a photon-counting "black box"; the output i s subsequently fed through the i n t e r f a c e into the computer memory (see f i g u r e 3.2). This data may l a t e r be accessed v i a the computer software a v a i l a b l e . An important part of the data a c q u i s i t i o n equipment i s the photon-counting 12 PM PA > A D > TTL-PS PC R M PL COMP P U DISPL Figure 3.2 Data flow of the photoluminescence s i g n a l . The s i g n a l from the photomultiplier (PM) i s fed v i a the pre-amp (PA) to the a m p l i f i e r (A). From the discriminator (D) the signal i s fed to the rate meter (RM) where the counts per second may be viewed. In addi t i o n , the si g n a l i s fed v i a the TTL pulse shaper (TTL-PS) to the photon counter (PC) where the counts per unit time are stored d i g i t a l l y . Subsequently, these counts are stored i n the computer memory (COMP) and can be punched (PU) on a paper tape or plotted using a p l o t t e r (PL) or displayed on a CRT screen (DISPL). 13 "black box" so i t w i l l be useful to explain how i t works. This i s described i n d e t a i l i n Appendix A. 3.2 Experimental Results and Discussion A broad range spectrum of CdlnjS^ at 2K, i l l u s t r a t e d i n figure 3.3(a), reveals one luminescence peak centered at 14,170 cm-*. This broad peak i s considered to o r i g i n a t e from imperfections i n the c r y s t a l . This follows from the fact that the absorption edge of the c r y s t a l (CdIn 2S 1 +) i s about 5000 to 6000 cm - 1 above t h i s i n energy. Czaja et a l . have proposed that t h i s emission i s due to the p a r t i a l i n v e r s i o n of the Cd and In ions, i n p a r t i c u l a r , to Cd ions at the octahedral B-site and to the In ions at the tetrahedral A - s i t e s . Consequently, t h i s luminescence band i s a t t r i b u t e d to e f f e c t s of i n t r i n s i c CdlnjS^ . It should be noted that Czaja et a l . i n t h e i r i n t e r p r e t a t i o n of t h e i r r e s u l t s used emission spectra which showed two broad emission bands rather than the one found i n t h i s study. The two bands were centered at 7500 A and at 9400 A. With e x c i t a t i o n spectra i t was found that these emissions originated within the band gap and so were not due to band-to-band t r a n s i t i o n s . This fact coupled with t h e i r r e s u l t s f or mixed c r y s t a l s led to t h e i r proposal that the C d 2 + - i o n at the B-site with the I n 3 + - i o n at the A - s i t e and a sulphur vacancy formed a complex. The concentration of the sulphur vacancies would then somehow regulate the luminescence from the two centers. They found no evidence to indicate that the sulphur vacancies contribute to the luminescence i n a simple way. Further studies on CdlnjS^ have also revealed only one broad peak [14,19] rather than two. With one exception [20], no further studies have been found i n the l i t e r a t u r e which 14 (a) (b) —I 1 L_ 12.0 14.0 16.0 WAVEN UMBER (103 cm*1) Figure 3.3 The photoluminescence spectra of stoichiometric C d l n ^ at 4K (a); of CdIn 2S l t:Cr 3 + (0.04 M%) at 2K (b'); and of CdIn 2S 1 +:Cr 3 + (0.5 M%) at 2K ( b ) . Notice the diffe r e n c e i n the broad peak p o s i t i o n as a function of temperature and chromium concentration. 15 inves t i g a t e the role which the concentration of the sulphur vacancies plays i n the luminescence of CdIn 2S l t. Even t h i s i n v e s t i g a t i o n was inconclusive since a quantitative analysis proved immpossible. The e f f e c t of sulphur vacancy creation v i a oven heating was noted but no conclusions could be drawn about the role these play i n CdIn 2S 1 +. So, at present i t i s not known whether the apparent quenching of the 10,638 cm - 1 (\ = 9400 A) luminescence band i s due to the vacancies or to some other mechanism. Despite t h i s discrepancy the emission band observed occurs i n the spectral range due to t r a n s i t i o n s within the band gap so i t i s considered that t h i s band i s due to the p a r t i a l inversion of CdlngS^, hence i t i s a property of the i n t r i n s i c m a t e r i a l . A broad range spectrum of Cr-doped CdIn 2S l t at 2K i s i l l u s t r a t e d i n figure 3.3(b). This reveals two luminescence bands: the f i r s t shows a broad luminescence band centered at about 15,500 cm - 1; the second shows structured luminescence spanning about 500 cm-* from about 12,500 cm-* to 13,000 cm - 1. The emission spectra shown i s for 0.5 Mol.% of Cr-doping. Similar spectra were obtained for 0.04 Mol.% of Cr-doping with minor differences i n the i n t e n s i t y of some weak l i n e s ; however, the p o s i t i o n of the broad peak var i e d . The peak's p o s i t i o n seemed s e n s i t i v e to both temperature and concentration v a r i a t i o n as i s shown i n Table I. The peak's i n t e n s i t y r e l a t i v e to the structured luminescence was also dependent on the concentration of Cr. This can be understood i n terms of energy transfer between the c r y s t a l and the ion; a point which w i l l be discussed i n more d e t a i l l a t e r . The absorption spectrum of Cr-doped CdlnjS^shown i n f i g u r e 3.4(a) exhibits two peaks: the f i r s t i s centered at about 14,630 cm - 1; the second i s centered at about 11,800 cm - 1. The absorption peak at 14,630 cm - 1 i s assigned to the energy trans f e r process from the valence band to the 2 E state of the 16 TABLE I The CdIn 2S l t peak p o s i t i o n as a function of temperature and C r 3 + - i o n concentration Cdln 2 C d l n ^ r C r 3 * Pure 0.04 Mol.% 0.5 Mol.% T(K) MA) EUm" 1) T(K) MA) E(cm - 1) T(K) MA) E(cm _ 1) 2 7055 14,170 2 7004 14,270 4 6440 15,520 77 6837 14,620 - - - 77 6604 15,140 293 8500 11,760 293 8351 11,970 - - -1 1 1 1 1 1 1 1 1 1 (a) '.(••^••fj:' . . . . . . . •if r ,? '* * • * • • * \ . •f f V * (b) / / \ 1 1 1 1 1 1 1 1 1 1 10 13 16 19 W A V E N U M B E R ( 1 0 3 cm" 1) Figure 3.4 The absorption spectrum (a) and the e x c i t a t i o n spectrum (b) of Cr-doped Cdln^S^. 18 C r 3 + - i o n . To v e r i f y t h i s assignment the sample was excited by a 500W PEK mercury lamp followed by a Bausch & Lomb monochromator and a Corning 2-62 f i l t e r . The bandpass of the monochromator was ~150 cm - 1 (70 A). The only luminescence observed was i n the range of 12,500-13,000 cm - 1. In f a c t , t h i s luminescence was i d e n t i c a l , within experimental e r r o r s , to the spectrum recorded with l a s e r e x c i t a t i o n and shown i n figure 3.5(b). This r e s u l t places the ground state of the C r 3 + - i o n , the ^A. state, 1629 cm - 1 above the valence band as indicated i n figure 3.6. E x c i t a t i o n spectra of Cr-doped CdIn2Sl+ i l l u s t r a t e d i n figure 3.4(b) shows two peaks at 14,940 cm - 1 and 18,083 cm - 1. These correspond to the ligand f i e l d t r a n s i t i o n s 4 A „ •*• 4T„ and ^A. -*• ^ T, , r e s p e c t i v e l y . It should 6 2g 2g 2g l g ' be noted that the spectrum shown has not been corrected for the photomulti-p l i e r s p e c t r a l response. The reason for t h i s i s that even i f the spectrum were corrected for the spectral response of the photomultiplier the r e s u l t i n g spectrum would not show that the p o s i t i o n of the 18,083 cm - 1 peak had changed much. So, although t h i s peak would be s h i f t e d to higher energy i t would s t i l l not agree (to within 200-300 cm - 1) with the previously published value of 18,500 cm - 1 [14,21]. The absorption edge of the c r y s t a l was not seen due to the poor response of the photomultiplier i n the high energy range. The structured luminescence observed i n the range 12,500-13,000 cm"1 i s shown i n d e t a i l i n f i g u r e 3.5. The spectra, as indicated, were obtained at temperatures of 2K and of 77K and are assigned to the 2 E ^ •*• t r a n s i t i o n with i t s associated v i b r o n i c t r a n s i t i o n s . Similar spectra i n the same energy 19 T 1 1 1 r o z 0. (a)77K 6 UJ o z I—I 1 I I to z 5 3 (b)2K : v ' I W S2 SI I I J LZf L M2, V L2 (J2) Ql P l (Ml) L l Jl Gl —I—I U I i I R2 Fl El 0 | CIB,AI RI 12.6 12.7 12.8 12.9 13.0 13.1 WAVENUMBER (I03cm-') Figure 3.5 The photoluminescence spectra of C d I n 2 S 4 : C r 3 + (0.5 M%) at (a) 77K and at (b) 2K. The spectra for the 0.04 M% samples were i d e n t i c a l except f o r a few weak l i n e s which were presumably obscured because of the o v e r a l l lower i n t e n s i t y . A l l energies at 77K are s h i f t e d 7 cm - 1 lower from the 2K values. Also, the spectra are corrected for the system's response which i s almost f l a t i n t h i s region. 20 range were reported by Sato et a l . ; however, the better res o l u t i o n of the present data allows a much more exact i n t e r p r e t a t i o n of the e l e c t r o n i c t r a n s i -tions and attendant v i b r o n i c spectrum. The 2K emission spectrum s t a r t s at 12,996 cm - 1 and extends to lower energy. This value i s t y p i c a l for C r 3 + phosphorescence which i s i n the range of ~12,000 cm-* to ~15,000 cm - 1, i n p a r t i c u l a r f or sulphur co-ordinated Cr 3 + [22]. A l t e r n a t i v e l y , for oxygen co-ordinated C r 3 + i n other c r y s t a l l i n e structures such as: ruby [23], MgO [24], the aluminate spinels [25], emerald and various garnets [26], a l l phosphorescence occurs around 14,500 cm-*. The C r 3 + - i o n substitutes for an I n 3 + - i o n at an octahedrally co-ordinated B-site; however, the l o c a l symmetry i s that belonging to the point group. In general this l o c a l d i s t o r t i o n of the octahedral symmetry coupled with the s p i n - o r b i t coupling e f f e c t i s enough to l i f t the degeneracy of the 2 E excited state and the ^A„ ground state. The quartic spin degener-acy of the * * g r o u n d state s p l i t s into two Kramers doublets with mg = ±3/2 and ±1/2 with a t y p i c a l separation of 2D between 1 cm - 1 to 2 cm - 1 [26]. The double spin degeneracy of the 2 E excited state i s removed leav-ing two st a t e s . Whenever the e l e c t r o n i c t r a n s i t i o n s a r i s i n g from these two l e v e l s to the ground state are resolved, they are referred to as the R-lines and are l a b e l l e d RI and R2; the R2 l i n e i s higher i n energy. T y p i c a l values for the R-lines separation range between 6cm-* to 60 cm-* [25,26,28]. As shown i n fi g u r e 3.5(b) the two R-lines are resolved as indicated with a separation of 30.3 cm-*. A measure of the l o c a l d i s t o r t i o n i s given by the parameter D i n the f i t of the EPR spectrum to the spin Hamiltonian. The separation of the Kramers doublets may be obtained from -2D. In Table II the values of D and AR (the R-line separation) for CdlnjS^ are compared to some other c r y s t a l s . 21 TABLE I I Values of D and AR for various c r y s t a l s Crystal D(cm - 1) Ref. AR(cm - 1) Ref. Cdln 2 S k Ruby MgO Aluminate Spinels Emerald Garnets -0.187 -0.1916 n i l +0.915 +0.90 (0-261| to +0.3485 [10] [27] [24] [25] [28] [26] 30.3 28.0 n i l -6.5 58.0 12.4 to 28.0 Present work [28] [24] [25] [28] [26,28] 22 The e l e c t r o n i c t r a n s i t i o n s referred to as the R-lines are e l e c t r i c dipole forbidden i n an environment possessing a center of in v e r s i o n . In CdIn 2S 4 the C r 3 + - i o n i s located at the octahedrally co-ordinated B-site where the l o c a l t r i g o n a l d i s t o r t i o n reduces the symmetry from 0^ to D^* This d i s t o r t i o n coupled with in t e r a c t i o n s with odd low-symmetry vib r a t i o n s leads to the removal of the forbiddenness with respect to even p a r i t y and gives r i s e to t r a n s i t i o n s of e l e c t r i c dipole character. Detailed discussions of this v i b r o n i c mixing have been given i n many places [29]. This i n f e r s that the weak magnetic dipole allowed t r a n s i t i o n s (the R-lines) are accompanied by a v i b r a t i o n a l spectrum which i s e l e c t r i c dipole i n character. The ^A„ and 2 E states a r i s e from the same t 3 e l e c t r o n i c configur-2g g 2g ation therefore the minima of t h e i r p o t e n t i a l energy curves occur at very nearly the same value of the normal co-ordinates. This means that a l l the v i b r a t i o n a l related t r a n s i t i o n s are expected to be weak due to the near ortho-gonality of the v i b r a t i o n a l wavefunctions so that only the R-line t r a n s i t i o n w i l l be evident. C l e a r l y , from the spectra shown i n figu r e 3.5 th i s i s not the case. In f a c t , there i s a strong v i b r a t i o n a l spectrum with some apparent mirroring as shown by the peaks AA" and C C ( i n the 77K spectrum) which are equidistant from the point l a b e l l e d R2. The v i b r a t i o n a l spectrum can be explained i n terms of the i n t e r a c t i o n of the e l e c t r o n i c wavefunctions with odd pa r i t y v i b r a t i o n s of the c r y s t a l l a t t i c e . The i n t e n s i t y of these t r a n s i t i o n s i s larger than the R-lines owing to t h e i r e l e c t r i c dipole character. The mirroring e f f e c t cannot be explained i n terms of the Franck-Condon e f f e c t since the ^ A,, and 2 E states a r i s e from the same strong f i e l d configuration. 2g g Rather, i t i s due to the observation of t r a n s i t i o n s accompanied by the 23 absorption of phonons of which many are present at higher temperatures [27]. The l i n e at 12,996 cm - 1 i n the 2K spectrum i s thus assigned as the R2 l i n e (see figure 3.5(b)). It i s worth mentioning that a l l the l i n e s i n the 77K spectrum are s h i f t e d by ~7 cm - 1 to lower energy than those of the 2K spectrum. The i r r e d u c i b l e representations of the v i b r a t i o n a l modes i n a sp i n e l are as follows [30]: T = A. + E + T. + 3T„ + 2A„ + 2E + AT. + 2T„ . lg g lg 2g 2u u lu 2u The Raman-active modes are A, , E and T„ ; the T, modes are lg g 2g' lu Infrared-active. A comparison of the v i b r a t i o n a l spectra observed with the measured Raman and Infrared active modes energies f o r CdIn2S1+ [30] proved d i f f i c u l t . The phonon energies measured were at room temperature while the observed spectra, with many resolved l i n e s , were obtained at 2K. To resolve t h i s d i f f i c u l t y the v i b r a t i o n a l modes assigned to the C o 2 + spectrum i n CdIn 2S l t at 2K was used [19]. The v i b r a t i o n a l modes and t h e i r assignments are tabulated i n Table I I I . As mentioned, the two R-lines were resolved with a separation of 30.3 cm - 1 and each R-line had a v i b r a t i o n a l spectrum associated with i t . Only four l i n e s are unassigned i n figure 3.5. These could be due to combinations of phonons or other mechanisms. Although a time resolved study was undertaken to confirm the assignments and further c l a r i f y the or i g i n s of the unassigned l i n e s t h i s proved to be unsuccessful. In chapter four t h i s w i l l be discussed i n more d e t a i l . TABLE III !E - ^Aj luminescence and vib r o n i c assignments' Line Energy AE from RI Line Energy AE from R2 RI 12966 — R2 12996 -Al 12928 38 A2 12960 36 Bl 12917 49 B2 12950 46 42 b CI 12910 56 C2 12938 58 54 Dl 12892 74 D2 12917 79 71 El 12878 89 E2 12905 91 90 Fl 12850 116 F2 12884 112 110 Gl 12839 127 G2 12864 132 129 J l 12778 188 (J2) 12808 188 188 LI 12743 223 L2 12775 222 219 (Ml) 12705 261 M2 12735 262 261 PI 12670 296 P2 12697 300 298 Qi 12651 315 Q2 12685 312 315 SI 12607 359 S2 12637 360 358 K 12788 178 N 12729 237 | Unas T 12620 346 (see W 12569 397 Assignment a - l o c a l mode (?) 8 - l o c a l mode (?) Y - l o c a l mode (?) 68+0.5 T l u , I R c ' d 93±2 T 2 g,R [ 2E + J [ 2E + J 185±2 215±0.5 247±2 307±0.5 312±2 366±2 * A 2 + Q] lu ,IR T 2 g,R T l u » I R T 2 g,R L l g ,R a A l l energies are i n cm - 1 with errors < ± 2 cm' b C o 2 + assignments (see r e f . [19] and text), c See reference [30]. d IR-infrared active; R - Raman a c t i v e . 25 3.3 Conclusions On the basis of the above re s u l t s an energy l e v e l scheme f o r C d l i ^ S j , : C r 3 + may be proposed. Figure 3.6 shows such an energy l e v e l diagram. On the l e f t , i s the energy l e v e l scheme for CdlnjS^ which was determined from the broad band emission spectra. The cross-hatched band represents intermediate l e v e l s (IL) which are due to probable cation or anion vacancies, stacking f a u l t s , d i s l o c a t i o n s as well as to the p a r t i a l inversion of the s p i n e l l a t t i c e . On the r i g h t i s the energy l e v e l scheme for the C r 3 + - i o n at the octahedrally co-ordinated B - s i t e . The energy l e v e l s were determined from the absorption and the emission spectrum observed. The valence band and the conduction band are represented by V.B. and C.B., r e s p e c t i v e l y . It should be noted that no t r a n s i t i o n s occur between the two l e v e l schemes since t h i s would bring about a change i n the electron number and i n v a l i d a t e the diagrams. Energy transfer though, i s possible v i a h y b r i d i z a t i o n of the 3d o r b i t a l s of C r 3 + and of the 3p o r b i t a l s of S 2~ which form the valence band o r b i t a l s simultaneously. Evidence of t h i s type of energy transfer i s provided by the absorption band at 14,625 cm - 1 and by the quenching of the broad emission band at ~15,500 cm - 1. The f i r s t t r a n s i t i o n seems to populate s o l e l y the 2 E ^ l e v e l as measured by e x c i t a t i o n spectra. Because of t h i s , the ground state, , * s placed 1629 cm - 1 above the valence band. This r e s u l t i s s u r p r i s i n g l y s i m i l a r to that obtained for t e t r a h e d r a l l y co-ordinated C o 2 + i n CdIn 2Si + [19] where the ground state i s 1927 cm - 1 above the valence band. This second t r a n s i t i o n could transfer an electron to the l e v e l which could then relax v i a a r a d i a t i o n l e s s t r a n s i t i o n to the 2 E 2g g s t a t e . This would further enhance the R-lines' i n t e n s i t i e s at the expense of 26 CB 114,625 15,500 VB-! 18,500 •^A 14,900 L2g S 12,996 i 1629 2g Figure 3.6 Proposed energy l e v e l scheme for C r 3 + s u b s t i t u t i n g f or I n 3 + at an octahedrally co-ordinated B-site i n CdlnjS^... The symbols CB, IL, and VB stand for conduction band, intermediate l e v e l s , and valance band, r e s p e c t i v e l y . A l l t r a n s i t i o n energies are measured i n cm~l. The dashed l i n e s represent t r a n s i t i o n s i n absorption and the s o l i d l i n e s represent t r a n s i t i o n s i n emission. 27 the broad band emission peak observed i n CdIn 2S 4. This, i n f a c t , i s what i s observed (see figure 3.3(b)). An apparent d i f f i c u l t y l i e s with the fact that the conduction band has been reported to be at ~19,100 cm - 1 at 77K [13] and at 20,160 cm - 1 at OK [31]*; c l e a r l y , from fi g u r e 3.6 the **T l e v e l i s at 20,129 cm~l. It i s f e l t that since the i n d i r e c t band gap value changes l i n e a r l y with temperature that at 2K i t i s s t i l l at a value close to the OK value so that the ^T, l e v e l i s s t i l l below t h i s . Similar r e s u l t s for the lg energy l e v e l scheme for CdIn 2S l t : C r 3 + were obtained by Sato et a l . but they did not place the ground l e v e l above the valence band. Using the three C r 3 + t r a n s i t i o n s a more refined value of B, the Racah parameter, was possible. The revised value of B = 618 cm-* was obtained by f i t t i n g the three t r a n s i t i o n s to the Tanabe and Sugano theory [32] (for example see t h e i r figure 5 for Dq/B = 2.41). This value for B i s s i m i l a r to that found by others [19,33] although d i f f e r e n t from that found by Wittekoek and Bongers which was B = 320 cm-1-. The l a t t e r was obtained using a formula which at times gives r e s u l t s that are too low [34]. The photoluminescence r e s u l t s with the v i b r a t i o n a l assignments of t h i s i n v e s t i g a t i o n have been published [35]. *This value was arrived at by i n v e s t i g a t i n g the absorption c o e f f i c i e n t as a function of temperature. A l i n e a r r e l a t i o n s h i p was obtained over the temperature range studied and an i n d i r e c t band gap of 2.5 eV or 20,160 cm~l at OK was obtained. 28 Chapter 4 Time Resolved Measurements The impetus for time resolved measurements of the *E •*• 4 A „ t r a n s i -g 2g t i o n of the C r 3 + - i o n was sparked by the p o s s i b i l i t y to confirm the assignments made of the R-lines and the v i b r a t i o n a l sidebands as tabulated i n Table I I I . Also, information on the o r i g i n of the four unassigned l i n e s shown i n figure 3.5(b) (K, N, T and W) was expected to be gained. The relaxation times of the RI and R2 l i n e s should be s l i g h t l y d i f f e r e n t from one another owing to a difference i n t h e i r t r a n s i t i o n p r o b a b i l i t i e s . The l i f e t i m e of the v i b r o n i c sideband associated with RI i s expected to be the same as that for RI even though the sidebands are e l e c t r i c dipole i n character; s i m i l a r l y for R2. The quantity of i n t e r e s t which i s a measure of the t r a n s i t i o n prob-a b i l i t y i s the o s c i l l a t o r strength, f . The o s c i l l a t o r strength i s given by the following formula [15]: f = 1.51 [4.1] -c 0n 3 where XQ i s the wavelength of the emitted r a d i a t i o n i n vacuum; T q i s the r a d i -ative l i f e t i m e ; and n i s the index of r e f r a c t i o n . Typical values of f for the RI and R2 e l e c t r o n i c t r a n s i t i o n s are of the order of 1 0 - 9 [25,36] r e f l e c t i n g t h e i r magnetic dipole allowed o r i g i n . A s l i g h t difference i n the value of f for RI and R2 i s evidenced i n the aluminate spinels ZnAl 20 l t and MgAl 20 4 where f( R l ) = 1.0 x 10~ 9 and f(R2) = 0.8 x 10~ 9 [25] as well as i n ZnGa 20 4 where f( R l ) = 5.4 x 10~ 9 and F(R2) = 4.4 x IO - 9 [36]. The difference i n the values 29 of the o s c i l l a t o r strengths between the RI and R2 l i n e s indicates that the two states relax with a s l i g h t l y d i f f e r e n t time constant. Using equ. [4.1] a r a t i o of the o s c i l l a t o r strengths of R2 to RI y i e l d s : t 0(R2) f ( R l ) [ X 0 ( R 2 ) ] 2 x [ 4.2] X 0(R1) f(R2) [ X ( R 1 ) ] 2 v0' As equ. [4.2] i n d i c a t e s , the r a t i o on the righ t of the equality i s an important determining factor of whether the r a d i a t i v e r e l a x a t i o n rates for RI and R2 d i f f e r by an appreciable amount. Although workers i n the f i e l d [25,37-42] have usually reported a single l i f e t i m e measurement for both R-lines -t y p i c a l l y i n the range of 1.5 msec to 50 msec - equation [4.2] would indi c a t e that a difference should be measurable. In p a r t i c u l a r , for the spinels [25,36] t h i s r a t i o has a value of ~1.25 so that a difference could have been seen (Wood et a l . do not mention that they looked for t h i s difference rather they present data for the l i f e t i m e measurements of the "R-lines") although, i n the case of ZnAljO^ [25] the R2-line disappears at 4.2K.* In the spectra obtained for CdIn 2S 1 +:Cr 3 + at 2K (see f i g . 3.5(b)) the R2 l i n e i s weaker than the R l - l i n e but i t has not completely disappeared as i n the 77K spectra * I t should be noted that the two experimental values of f obtained by Wood et a l . were obtained through measuring the l i n e i n t e n s i t i e s and that a maximum error of 30% was given. Theoretical values were obtained from c r y s t a l f i e l d theory computations for comparison with the experimental values; these were: f(R l ) = 1.0 x 10" 9 and f(R2) = 0.9 x 10~ 9. Consequently, even though the value of the r a t i o calculated with experimental values may be i n error by about 50% the theory would support a measurable d i f f e r e n c e . 30 (see f i g . 3.5(a)). For th i s reason i t was thought that a measurement of the r a d i a t i v e l i f e t i m e of the RI and R2 l i n e s could be made. 4.1 Experimental Technique An experimental method which could confirm the assignments made i n Table III as well as possibly c l a r i f y the o r i g i n of the unassigned l i n e s i s one which could discriminate between the luminescence of the R-lines s o l e l y on the basis of t h e i r l i f e t i m e s ' d i f f e r e n c e . Just such a method was employed by Thewalt i n h i s analysis of bound multiexciton complexes [43]. The most impor-tant component of his set-up was an acousto-optic modulator which he used as a chopper for his l a s e r . The method he employed works i n the following manner. If the e x c i t a t i o n beam i s chopped at a frequency much above the r e c i p r o c a l of the decay times, the r a t i o of the A.C. to the D.C. component of the lumines-cence w i l l be larger for l i n e s which decay with a f a s t e r l i f e t i m e than for li n e s which decay with a slower l i f e t i m e . I f the luminescence giving r i s e to a p a r t i c u l a r r a t i o of A.C. to D.C. can be nulled out through the use of a phase s e n s i t i v e detector, then, l i n e s decaying at a fas t e r rate than the n u l l -ed l i n e w i l l give r i s e to a p o s i t i v e s i g n a l ; l i n e s decaying at a slower rate than the nulled l i n e s w i l l give r i s e to a negative s i g n a l . With t h i s method he was able to discriminate s u c c e s s f u l l y between luminescence l i n e s o r i g i n a t i n g at d i f f e r e n t l e v e l s . Methods s i m i l a r to the one described were used - a l b e i t less s u c c e s s f u l l y - with the C r 3 + - i o n luminescence l i n e s . These w i l l be discussed i n a l a t e r section along with the experimental r e s u l t s . F i r s t , the acousto-optic e f f e c t , which makes a device such as the acousto-optic modulator used i n the experiment possible, w i l l be discussed. 31 4.2 The Acousto-Optic E f f e c t Since the advent of the las e r i n t e r e s t has been refocussed on the acousto-optic i n t e r a c t i o n . These investigations have yielded a v a r i e t y of devices which are used i n numerous ap p l i c a t i o n s . * The acousto-optic i n t e r a c t i o n ( i . e . the i n t e r a c t i o n of a laser beam with an acoustic beam) i n a suitable medium produces various e f f e c t s which are of i n t e r e s t . Some of these e f f e c t s are: o p t i c a l beam d e f l e c t i o n and modulation of the phase or frequency. A c h a r a c t e r i s t i c of the i n t e r a c t i o n i s that i t occurs inside a medium hence the medium should be o p t i c a l l y transparent to the laser r a d i a t i o n and the medium should transmit sound with low l o s s . Devices which u t i l i z e t h i s i n t e r a c t i o n are c a l l e d bulk wave devices. Other devices which u t i l i z e the acousto-optic i n t e r a c t i o n but with surface acoustic waves (SAW) are c a l l e d SAW devices [44]. For the bulk wave case there are b a s i c a l l y three types of devices [45]: the def l e c t o r ; the modulator; and, the f i l t e r . These devices are characterized by the three d i s t i n c t regimes of i n t e r a c t i o n geometry described by a dimensionless parameter 'a'. The parameter 'a' i s defined as the r a t i o of the divergence angle of the o p t i c a l beam to the divergence angle of the aco u s t i c a l beam. The e f f e c t of present i n t e r e s t i s that of producing a grating with the acoustic waves and d i f f r a c t i n g the o p t i c a l laser beam from i t . This e f f e c t can be achieved through the use of modulators [46]. For modulators a ~ 1, for deflectors and *Overviews and works i n the i n v e s t i g a t i o n of the acousto-optic i n t e r a c t i o n may be found i n the following journals: Optical Engineer V o l . 16(5), 1977; SPIE Proc. V o l . 90, 1976; SPIE Proc. V o l . 202, 1979; SPIE Proc. V o l . 214, 1979; Methods of Experimental Physics V o l . 19, 1981. This l i s t i s by no means exhaustive but should serve as a s t a r t i n g point for the interested reader. 32 f i l t e r s a « 1 and a » 1, r e s p e c t i v e l y . The o p t i c a l divergence angle for a laser beam can be written as: 69 Q = 4\/itd, where X i s the wavelength of the o p t i c a l beam i n the medium and d i s the beam waist diameter for the las e r beam. The acoustic divergence angle i n the plane of i n t e r a c t i o n i s given by: 69 = A/A, where JI i s the transducer's width and A i s the acoustic wavelength. So the divergence r a t i o which characterizes the three regimes of i n t e r a c t i o n i s given by [45]: a - i 14.3) The r a t i o can be con t r o l l e d by the (Jl/d) r a t i o since I controls the acoustic d i f f r a c t i o n spread and d controls the o p t i c a l d i f f r a c t i o n spread. P h y s i c a l l y a modulator consists of a p i e z o e l e c t r i c transducer mech-a n i c a l l y coupled to an o p t i c a l l y transparent medium. An e l e c t r i c a l s i g n a l applied to the transducer produces stress waves which propagate i n the o p t i -c a l l y transparent medium. When such a s i t u a t i o n occurs a modulation of the index of r e f r a c t i o n v i a the e l a s t o - o p t i c a l e f f e c t occurs. This modulation produces what i s c a l l e d a moving phase grating which can d i f f r a c t portion of the incident l i g h t into one or more d i f f r a c t i o n orders. The geometry for the acousto-optic d i f f r a c t i o n process i s shown i n figure 4.1. D i f f r a c t i o n e f f e c t s predominate when the o p t i c a l beam waist diameter i s greater than the grating constant given by the acoustic wavelength, A. (If the o p t i c a l beam waist diameter i s less than the sonic wavelength then the enti r e laser beam i s deflected over a range of angles dependent on the sonic amplitude [47]). Chang has shown that there are two d i f f r a c t i o n regimes. A 33 Figure 4.1 The acousto-optic d i f f r a c t i o n process. The transducer (T) generates a sonic wave of ac o u s t i c a l divergence 69 a which in t e r a c t s with the laser beam of o p t i c a l divergence 69 Q. The la s e r beam i s incident at the Bragg angle of 9g. The sonic energy i s absorbed a f t e r the i n t e r a c t i o n by the acoustic absorber (AB). 34 parameter which aids i n d i s t i n g u i s h i n g the regime i s the c h a r a c t e r i s t i c length L 0 which i s given by: A 2 L Q = — cos9 0 [4.4] where 9 Q i s the angle of incidence i n the medium of the o p t i c a l beam onto the sonic beam which i s propagating as shown i n figure 4.1. So, the i n t e r a c t i o n length, A of the modulator r e l a t i v e to the c h a r a c t e r i s t i c length L Q completely determines the d i f f r a c t i o n regime. If A « L Q the i n t e n s i t y of higher d i f f r a c t i o n orders i s not n e g l i g i b l e so that several orders are p o s s i b l e . These are symmetrically spaced about the zeroth order and are separated i n angle by approximately X/A. This d i f f r a c t i o n regime i s c a l l e d the Raman-Nath regime. A l t e r n a t e l y , i f A » L Q then the higher order's d i f f r a c t i o n i n t e n s i t y i s vanishingly small except for where the Bragg condition i s s a t i s f i e d . This condition i s given by the r e l a t i o n : s i n 9 B = 2 T t 4 ' 5 1 So as the i n t e r a c t i o n length increases the amount of l i g h t coupled into one of the d i f f r a c t e d orders increases at the expense of the others. This way one may s e l e c t i v e l y couple l i g h t into only one order. Notice that for the small angles normally involved, equ. [4.5] may be rewritten i n terms of the d r i v i n g frequency f as: 29„ = \ f /v ,. Thus the angular separation i s c o n t r o l l e d n J s B s sound d i r e c t l y by the d r i v i n g sonic frequency which i s l i m i t e d by the band width given by: Af given by [48] = 2v A9T,/\. The d i f f r a c t i o n e f f i c i e n c y of the modulator i s ° J s s B n = s i n 2 ( a ) 1 / 2 2^2o P v s 3 ^ s 35 where n = index of r e f r a c t i o n ; p = e f f e c t i v e e l a s t o - o p t i c constant, p = mass density; v g = sonic wave speed; SL = acoustic beam width; H = acoustic beam height; P = Acoustic power. So, assuming that JL has been f i x e d so that one i s i n the Bragg* regime such that A > L 0 and that M2 which i s a function of the acoustic c e l l material parameters has been calculated then the d i f f r a c t i o n e f f i c i e n c y i s a function of the applied acoustic power. 4.3 EXPERIMENTAL DETAILS  4.3.1 The Modulator The modulator used throughout the experiments outlined i n th i s thesis i s a product of the HARRIS COMPANY. The modulator i s composed of two components: the acousto-optic modulator device (model H-211;A0D) and the acousto-optic modulator d r i v e r (model H-212;DR). In order f o r the l a t t e r to operate, three inputs are necessary: a 15 VDC input; a 24 VDC input; and a modulation input. A power supply with 15 VDC and 24 VDC outputs was b u i l t f o r thi s purpose while the modulation input was supplied by a pulser. The sole DR output i s an 80 MHz s i g n a l which drives the AOD whose modulation bandwidth i s 20 MHz. The AOD i s composed of the transducer and the medium (Te0 2) through which the sonic waves propagate. The AOD output was checked and was found to be accurate within experimental e r r o r s . Before using the modulator i n an experiment, the e f f i c i e n c y was checked. The d i f f r a c t i o n e f f i c i e n c y of a modulator may be defined as the r a t i o of the amount of ra d i a t i o n coupled to an order other than the zeroth order to the D.C. value of the amount of ra d i a t i o n of the zeroth order. *The s i m i l a r i t y of t h i s e f f e c t to the Bragg r e f l e c t i o n of x-rays from c r y s t a l l a t t i c e planes has prompted the adoption of t h i s nomenclature to this regime of i n t e r a c t i o n . 36 Maximum e f f i c i e n c y occurs when most r a d i a t i o n i s coupled into one order as i n the Bragg Regime. The maximum e f f i c i e n c y of the modulator was found to be ~80%. The manufacturer s p e c i f i c a t i o n s quote 85.2%. In the experiments envisoned one would be comparing r e l a t i v e i n t e n s i t y values so that a reproducible d i f f r a c t i o n e f f i c i e n c y of ~80% was acceptable. The v a l i d i t y of equ. [4.4] was also checked. The value of L Q was found to be i n the i n t e r v a l [0,0.028 mm]. Since the transducer length, 1 i s of the order of 1-2 cm then the condition for the Bragg Regime A » L Q i s s a t i s f i e d . S i m i l a r l y , i t was v e r i f i e d that d i f f r a c t i o n e f f e c t s predominate since the l a s e r beam diameter d = 0.2 cm and the d i f f r a c t i o n grating constant A = 0.00077 cm so that d » A i s s a t i s f i e d . 4.3.2 The Experimental Arrangement The experimental arrangement used i n a l l the time-resolved measurements on C d l n j S ^ : C r 3 + was s i m i l a r to that shown i n figure 3.1 and described i n sec. 3.1.1. The only difference was that the AOD was placed between the l a s e r f i l t e r s and the mirror Ml. Conventionally a focussing lens i s needed i n front of the entrance pupil of the AOD to focus the laser beam onto the i n t e r a c t i o n region. However, experiments with and without the lens showed that a focussing lens was unnecessary since the d i f f r a c t i o n e f f i c i e n c y of the modulator did not improve with a lens i n s e r t e d . In addition, when the lens was absent the image qu a l i t y was superior. For these reasons a focussing lens was not used; i t may be that i f a d i f f e r e n t laser with a larger diameter beam were used a lens would give an improvement. As mentioned i n sec. 4.3.1 a 37 modulation input to the DR i s a v a i l a b l e . It i s through t h i s input that the lase r l i g h t may be "chopped" at various frequencies. The procedure i s as follows. The modulation input of the DR i s fed a steady-state s i g n a l and the AOD output i s optimized such that the f i r s t order laser beam output i s incident on the sample. When the steady-state s i g n a l i s removed, the in t e n s i t y of the laser beam incident on the sample drops by ~90%. If a pulse i s fed to t h i s input instead of a steady-state s i g n a l the las e r w i l l mimic an on-off cycle, e f f e c t i v e l y chopping the laser beam at the desired frequency and thus modulating the incident r a d i a t i o n on the sample. 4.4 Estimate of 2Eg State Lifetime In order to u t i l i z e the n u l l i n g technique described i n section 4.1 i t i s necessary to know the approximate l i f e t i m e range of the 2Eg sta t e . To th i s end, the UP/DOWN (U/D) technique was used while photon counting with the laser beam chopped at the U/D frequency. The U/D technique consists of sampling the counting period at a p a r t i c u l a r frequency (period) and counting down for that f r a c t i o n of the period when the las e r i s on and counting up for the remainder of the period. Thus, i f the f r a c t i o n i s kept constant at one half-on and one h a l f - o f f and the sampling period i s short compared to the li f e t i m e then the r e s u l t of the U/D count w i l l be approximately zero. For very long periods the r e s u l t of the U/D count w i l l be approximately that of the down count alone. At the end of the counting period the r e s u l t i n g number i s the averaged difference between a l l the UP/DOWN cy c l e s . When the las e r beam i s chopped at the U/D frequency then the number obtained at the end of the counting period i s the averaged e f f e c t i v e area d i f f e r e n c e , A Q between the laser - o n / l a s e r - o f f cycle; i . e . the steady-state area minus the area under the decay curve. I f the counting period i s sampled at d i f f e r e n t U/D frequencies 38 an estimate of the decay time may be obtained from a graph of A vs. U/D D period ( t u / D ) . Care must be taken when estimating the 2Eg l i f e t i m e because i f i t i s much smaller than the U/D h a l f - c y c l e then the estimate w i l l be inaccurate. To i l l u s t r a t e t h i s , the graphs of figures 4.2(a) and 4.2(b) were generated using a normalized l i f e t i m e of 1.0 u n i t s . The U/D h a l f - c y c l e i s varied from 20 to 0.2 time units and the A^ i s calculated and plotted vs. time. Notice that a l i n e a r behaviour i s exhibited i n the graph of figure 4.2(a) u n t i l the U/D h a l f - c y c l e area s i z e i s comparable to the area under the decay curve when the r e s u l t of the U/D count i s not due to just the down count alone. This i s shown i n more d e t a i l i n figu r e 4.2(b). The l i f e t i m e estimate i s made from the 1/e point of the A^ axis ( t h i s i s so since the graphs were generated with a normalized unit time). By inspection, the l i f e t i m e i s seen to be 1.0 u n i t s . Using t h i s method the l i f e t i m e of the 2Eg state was estimated to be (1.2 ± 0.3) msec. The next section presents the methods used to chop the laser output and the re s u l t s of the n u l l i n g of the R-lines. 4.5 Nulling Techniques and Results  4.5.1 METHOD #1 A monostable IC c i r c u i t provided a pulse to the DR to cycle the laser on-and-off. While the las e r was i n the off mode the counting period was sampled using the UP/DOWN technique. At the end of the counting period the re s u l t was an averaged e f f e c t i v e area difference at that p a r t i c u l a r U/D f r e -quency, A^ for that p a r t i c u l a r wavelength of the spectrum. I f the wavelength was changed p e r i o d i c a l l y and the above repeated then a scan of the spectrum at that U/D frequency would r e s u l t . Various U/D frequencies were used ranging from 600 Hz to 40 kHz while the counting period t , ranged from 0.25 sec to 1.0 sec (notice that t i s greater than the U/D period for the ranges chosen). 39 AO A set of graphs were generated using a normalized l i f e t i m e x^ of 1.0 uni t , according to the method mentioned above. These graphs are shown i n figures A.3(a)-(b), I f t i s much larger than x^ then the curve of figure A.3(a) i s obtained (here t = 20 T \ t ) . It should be mentioned that f o r t > 8 T „ T N N figure A.3(a) i s e s s e n t i a l l y unchanged. If t i s comparable to x^ then curves II and III of figure A.3(b) are obtained, where t i s 2.0 x and 0.8 T re s p e c t i v e l y . Notice that as t gets smaller the maximum decay curve area measured i n the U/D mode gets smaller ( t h i s maximum i s e s s e n t i a l l y the t o t a l decay curve area for the period t ) ; t h i s l i m i t i s shown by curve IV of figure A.3(b). For n u l l i n g measurements one needs high countrates to minimize counting errors so that a t much larger than the estimated l i f e t i m e , x = (1.2±0.3) msec, was chosen. When the spectrum was scanned at the various U/D frequencies i t was found that the R-lines spectrum was not nulled at the expected U/D frequency of ~830 Hz but that the background on which i t was located was. At t h i s frequency, the R - l i n e s 1 counts, representing A^, were negative i n d i c a t i n g that the R-lines' l i f e t i m e was smaller than the U/D period. In f a c t , the R-lines were nulled at AO kHz but owing to the scatter of the data an accuracy of better than 25% was not possi b l e . Because of t h i s i t was not possible to determine i f the R-lines decay at d i f f e r e n t rates since one expects t h i s difference to be of ~25%. Another method used to n u l l the l i n e s i s described i n the following. 41 Figure 4.3 Generated plots of Af vs. t n / D for (a) t y / D = 40 t N and for (b) tU/D < TN* I n t* i e c o u n t i n g period i s t = 20 T n while i n (b) curve I i s reproduced for t y ^ D = 40 t N for comparison with: curve II for t n / D = 4.0 t N ; and curve III f o r t y ^ D =1.6 x N. Th counting period t for these curves i s half ty/D* Curve IV define the l i m i t of the maximum decay area measured as t gets smaller. 42 4.5.2 METHOD #2 A pulse from a monostable IC c i r c u i t was provided to the DR to turn the laser on-and-off. In addition, t h i s pulse was used as the U/D pulse. The pulse width was varied so that the counting method d i f f e r e d from the one used above. During the laser-on part of the cycle the counter counted DOWN (so that negative numbers were expected) and during the l a s e r - o f f part of the cycle the counter counted UP (adding p o s i t i v e numbers to the negative ones from the previous h a l f - c y c l e ) . At the end of the counting sequence the r e s u l t obtained was an averaged e f f e c t i v e area di f f e r e n c e , A^ at that p a r t i c u l a r pulse width and period, and at that selected wavelength. When a scan of the spectrum was made using t h i s p a r t i c u l a r pulse width and period the above procedure was repeated f o r every point of the spectrum. What one obtained was the Ap at various wavelengths. To n u l l out the spectrum or some l i n e s of the spectrum the pulse width was adjusted u n t i l a scan of the spectrum showed a n u l l . If any luminescence l i n e s were not nulled then t h e i r r elaxation rates T ,T, ,...,T , a b n were eit h e r f a s t e r or slower than the rel a x a t i o n rate % of the nulled l i n e ( s ) . T h a t i s , i f the R-lines decayed at a slower rate then, one would expect a p o s i t i v e spectrum; otherwise, one would expect a negative spectrum. Experiments were c a r r i e d out at T = 77 K where an extended range spectrum of the luminescence shows one broad peak at high energies and the R-l i n e s ' spectrum at lower energies (see figure 3.3). The broad peak was nulled 4 3 and the spectrum obtained i s shown i n figure 4 . 4 . As can be seen the large peak has been replaced by two smaller peaks and the R-line spectrum i s unchanged. The counts due to the f i r s t of the two broad peaks are negative while the counts of the other peaks are p o s i t i v e . This r e s u l t i s i n d i c a t i v e of the nature of the broad peak as explained i n chapter 3 ; i . e . due to impurities, d i s l o c a t i o n s , e t c . This r e s u l t indicates that t h i s luminescence peak i s the sum of various t r a n s i t i o n peaks with s l i g h t l y d i f f e r e n t decay rat e s . Those t r a n s i t i o n s decaying with a decay rate smaller than the n u l l i n g decay rate would give r i s e to a negative peak. Those t r a n s i t i o n s with larger decay rates than the n u l l i n g decay rate would give r i s e to a p o s i t i v e peak. The R-lines are seen to be on the shoulder or the " t a i l - e n d " of the broad peak and the countrates are p o s i t i v e . This indicates that the l i f e t i m e of the R-l i n e s i s longer than the relaxation rate T of the nulled broad peak. An attempt was made to n u l l out the R-lines using the same method but, at T = 4K. Although a spectrum s i m i l a r to that shown i n figure 4.4 was obtained i t was found to be very d i f f i c u l t to n u l l out the R-lines. Their i n t e n s i t y decreased but not to the extent that one could a f f i r m that a true n u l l i n g had occurred. The d i f f i c u l t y arose from the underlying background which changed when the period, as well as the pulse width, was changed. This e f f e c t can be a t t r i b u t e d to the d i f f e r e n t decay rates making up the t r a n s i t i o n s of the broad peak. This would imply that an approximate n u l l i n g could occur but interference from other s i m i l a r decay rates would make a t o t a l n u l l i n g improbable; therefore, a s a t i s f a c t o r y n u l l of the R-lines was not found. _J I I I I I L_ 13.0 15.0 17.0 19.0 WAVENUMBER (IO 3 cm"1) Figure 4.4 Spectrum f or the nulled broad peaks. N u l l i n g occured for T, = (184 ± 5) sec and t = (9.816 ± 0.005) msec, laser-on 45 An estimate of the l i f e t i m e of the broad peak can be made i f one observes the following. The n u l l occurs when the area counted during the pulse-on width i s equal to the area counted during the rest of the time period. A p p l i c a t i o n of elementary notions of Calculus y i e l d the following e q u a l i t y : T = T[l-exp(-t/x)] [4.7] where T i s the pulse width, (T+t) i s the period and, x i s the decay r a t e . The graphs of figu r e 4.5 were generated using eq. [4.7]. The following three conditions may r e a d i l y be deduced: 1) t » T then x = T 2) t = T then x > lOt or x > 10T (for 5.4% difference) 3) t ~ T then intermediate value of x. Figure 4.4 was obtained when condition 1) was v a l i d so that the n u l l i n g decay rate i s x = (18415) usee. The negative and p o s i t i v e peaks were also nulled and t h e i r decay rates were found to be (165 ± 5) usee and (202 ± 5) usee, r e s p e c t i v e l y . Since the R-lines' spectrum i s pos i t i v e then one can imply that the decay rate i s larger than x. This r e s u l t i s i n contradiction to that 46 r v o u n t i n g P e r i c d 4 5 6 Lifetime 9 16 9 1 2 3 Lifeline 5 6 7 8 9 18 Figure 4.5 Graphs generated to aid i n estimating the n u l l i n g decay r a t e . (a) i s a graph of the counting period t vs. T at constant pulse width T. Curves I to IV are for T = 1, 3, 5, 7. (b) i s a graph of the pulse width, T vs. t at constant t. Notice that as x gets larger T approaches the T = t l i m i t ; for the graph i l l u s t r a t e d t = l . 47 found previously with METHOD #1, where the R-lines' decay rate was found to be (25 ± 5) (isec, but i n agreement to that found i n sec. 4.4 where a l i f e t i m e of (1.2 ± 0.3) msec was found for the R-lines' decay rate. 4.6 Lifetime Determinations Owing to the fact that the R-lines could not be s a t i s f a c t o r i l y nulled out a d i r e c t measurement of the decay time was made i n order to confirm the values obtained i n the previous section. For t h i s measurement a D i g i t a l Signal Analyzer used i n the Multi-Channel Scanning (MCS) mode was employed. 4.6.1 MCS Arrangement The experimental set-up used i n conjunction with the MCS i s shown i n figure 4.6. As can be seen figures 3.1 and 3.2 have been incorporated to give an overview of the arrangement. The MCS i s a product of the Tracor Northern Inc. (Model NS-570A) and the pulser i s a B+K Precision Dynascan Corporation (Model 3300 Pulse Generator) product. A l l other components have been described above with the exception of the photomultiplier which was changed from an RCA 7102 to a Hamamatzu R928 because of i t s better e f f i c i e n c y i n the range of wavelengths used. The pulser has two output pulses available which i n Figure 4.6 are l a b e l l e d D^ (output pulse) and T^ ( t r i g g e r pulse). When the pulser i s used i n the Pulse Delay Mode the t r a i l i n g edge of T^ i s coincident with the r i s i n g edge of D ; the pulse width plus the pulse delay equal the period. This 48 Figure 4.6 Experimental arrangement to measure l i f e t i m e s using the MCS. The pulser (PULS) has two output pulses: Dp and Tp. Both pulses may be viewed on the dual trace scope (SC). T i s fed to the DR which v i a the AOD tr i g g e r s the laser on for the duration of T . On the t r a i l i n g edge of T p, Dp tr i g g e r s the MCS to s t a r t counting. The data may be viewed on a CRT which i s part of the MCS and/or may be viewed as hard copy from a teletype (TTY). A l l other components have been described i n figure 3.1 and 3.2 with the exception of the power supply (PS) to the photomultiplier (PM) and the s t r i p -chart recorder (RE) which i s used to pinpoint the l o c a t i o n i n wavelength on the spectrum where a decay measurement i s desired. 50 function serves a twofold purpose: f i r s t l y , i s fed to the DR so that the las e r can be turned on; secondly, on the t r a i l i n g edge of T , the MCS i s triggered by D^ and the counting sequence begins. The MCS has ava i l a b l e 512 channels or bins. Each bin has a v a r i a b l e but preset dwell time so that when the MCS i s triggered by D^ a sweep of the delay curve i n the time domain i s made. For a l l the experiments performed the lowest dwell time of 20 us per bin was used; the number of channels used and the number of sweeps taken were varied (the l a t t e r depending on the countrate). The f i n a l r e s u l t was an accurate depiction of the decay curve of the luminescence at a p a r t i c u l a r wavelength. Figure 4.7 gives an example of t h i s . 4.6.2 MCS Data and Results The data obtained with the MCS at a temperature of 77K i s shown i n figure 4.7. Figure 4.7(a) shows the decay curve of the R-lines (X = 7856 A) while figure 4.7(b) shows the decay curve of the bckground (X = 7650 A). As can be seen from the decay of the two curves, i n the f i r s t half of the data the background luminescence seems to decay much more quickly than the R - l i n e s 1 luminescence. This q u a l i t a t i v e observation confirms the r e s u l t s obtained i n sec. 4.5.2 where the R-lines' r e l a x a t i o n rate was i n f e r r e d to be greater than the range of the background's re l a x a t i o n rates of (160-210) usee. 51 ( m s e c ) F i g u r e 4 . 7 Data o b t a i n e d u s i n g the MCS. The d a t a shown i s the decay on a peak (a) and the decay on the background ( b ) . 52 The data was analyzed i n three steps.' F i r s t , using both decay curves a deconvolution was performed so that the e f f e c t s of the background were subtracted from the R-lines' decay. Second, the logarithm of the r e s u l t i n g data was taken and a l i n e was obtained. Third, the data reduction was performed using a program on the Nova 2 computer which e s s e n t i a l l y was a least-squares f i t t i n g routine adapted from Bevington's LINFIT Fortran program [49]. The least-squares f i t t i n g procedure yielded a slope and a y-intercept with good confidence l e v e l s . The decay rate calculated from the slope was found to be t = (10.45 ± 0.45) msec. This value compares favourably with the R l i f e t i m e s obtained f o r : MgO (~10 msec) [41]; the aluminate spinels (~30 msec) [25]; YAG (8.9 msec) [38]; and, ruby (4.3 msec) [50]. It should be noted that steps two and three above could be applied to each decay separately but the r e s u l t s are not conclusive. The reason for t h i s i s that one has to decide to what segment of the decay the least-squares f i t t i n g program could be a p p l i c a b l e . For example, a f t e r taking the logarithm of the decay curve data shown i n figure 4.7(a) the segment of points 150 to 320 seems reasonable to apply the least squares f i t t i n g program. In f a c t , the f i t t i n g routine y i e l d s a l i f e t i m e of (19 ± 2) msec. The point-by-point subtraction of the values obtained from the equation of the l i n e using the above l i f e t i m e was performed on the o r i g i n a l data. The r e s u l t of t h i s was what appeared to be a l i n e with scatter i n the f i r s t 150 points. Now, i f a l i f e t i m e i s obtained by applying the f i t t i n g procedure to t h i s data using the 53 f i r s t 50 points one gets t = (1.09 ± 0.5) msec;,alternatively, i f one uses the f i r s t 100 points one gets x = (1.95 ± 0.04) msec; instead, i f one uses the f i r s t 150 points one gets x = (2.18 ± 0.04) msec. It should be emphasized that these are not the only segments that could have been chosen since segments made up of points (15-50), (20-80), etc. would have served as well; even the i n i t i a l segment of points 150 to 320 i s not the only possible one. The point i s that there i s not an unambiguous way of choosing a segment of data points to which one applies the f i t t i n g routine and thus calculates a l i f e t i m e unless a deconvolution of the data i s performed f i r s t . 4.7 Concluding Remarks The o r i g i n a l goal for performing time-resolved measurements was to confirm the assignments of the R-lines and t h e i r v i b r o n i c sidebands made i n Table I I I . As we l l , an attempt would be made to i d e n t i f y the four unassigned l i n e s l a b e l l e d K, N, T, and W i n Table I I I . The re s u l t s presented i n this chapter show that although n u l l i n g of sp e c t r a l l i n e s , with the method used, i s possible, the n u l l i n g of the R-lines was not s a t i s f a c t o r i l y achieved; therefore the o r i g i n a l goal was not obtained. The broad peak att r i b u t e d to i n t r i n s i c CdIn 2S l t, to impurities, to d i s l o c a t i o n s , etc. and on whose shoulder the R-line luminescence i s exhibited, i s made up of various t r a n s i t i o n peaks. The relaxation rates of these are i n the range of (160-210) usee, the unsuccessful attempts to null-out the R-l i n e s stems from the relaxation rates of the background which i n t e r f e r e d with 54 the n u l l i n g process. The i n t e n s i t y of the background as compared to that of the R-lines i s not as i n s i g n i f i c a n t as i t was for Thewalt [43]. This means that when one i s doing the UP/DOWN counting, the background w i l l have a greater e f f e c t on the r e s u l t s . This, i n f a c t , i s what occurred; hence the R-lines could not be s u c c e s s f u l l y n u l l e d . When the MCS was used to determine the l i f e t i m e of the chromium excited state, there was no i n d i c a t i o n from the data obtained that more than one decay rate was present. This r e s u l t would imply that the difference i n the R-lines' relaxation rate could be of the order of the experimental e r r o r , ~4%, or l e s s . I t does not seem s u r p r i s i n g then, that a n u l l i n g of the R-lines was not achieved due to the relaxation rates of the background. 55 Chapter 5  Concluding Remarks In the introduction i t was stated that the motivation for t h i s t h e s i s was twofold. The two goals consisted of i n v e s t i g a t i n g the o p t i c a l s p e c t r a l response of chromium doped CdIn 2Si +, and of i n v e s t i g a t i n g the time-resolved response of chromium doped Cdln-^S^ The f i r s t goal was achieved with moderate success; the second proved more challenging. An i n t e r e s t i n g area of research which merits further study i s that of sulphur vacancies i n Cdln 2S l +. As noted i n sec. 3.2, the sulphur vacancy with the C d 2 + - i o n at a B-site and the I n 3 + - i o n at an A - s i t e form a complex. The luminescence from t h i s complex i s what has been referred to as the broad peak on which the R-line spectrum s i t s (see figure 3.3). Thus, further investigations i n the r o l e that the sulphur vacancies play i n the luminescence of Cdln-jS^ would be an asset i n understanding the properties of t h i s m a terial. Further studies on the time-resolved properties of CdIn 2S 1 +: C r 3 + would also be an asset. Throughout the experiments performed and described i n chapter 4 a modulator was used to "chop" the laser beam. Experience has shown that t h i s was not a proper choice. A better choice would have been a d e f l e c t o r . The reason for t h i s i s as follows. Whenever the DR was given a l a s e r - o f f pulse the f i r s t order d i f f r a c t e d laser beam impinging on the sample would not "shut-off", rather, i t would decrease i n i n t e n s i t y by ~90%. This means that whenever the UP/DOWN counting procedure was used a small error was introduced i n the data c o l l e c t e d . If a d e f l e c t o r were used t h i s problem would not e x i s t since the laser-beam would be deflected o f f the sample completely. 56 Preliminary r e s u l t s with the MCS arrangement show that t h i s method could be u s e f u l l y employed i n measuring r a d i a t i v e l i f e t i m e s . The s u b s t i t u t i o n of a d e f l e c t o r f o r the modulator could improve the performance of the system. This i s e s p e c i a l l y true when lack of s e n s i t i v i t y requires an accumulation of many sweeps and the sweep duty cycle i s comparable to the l i f e t i m e being measured. Further measurements could be made on C d I n 2 S 4 : C r 3 + at d i f f e r e n t temperatures to determine the temperature dependance of the l i f e t i m e . 57 Bibliography [1] W. Rehwald, Phys. Rev. 155, 861 (1967) [2] R. Meloni and G. Mula, Phys. Rev. B2, 392 (1970). [3] S. Katsuki, J . Phys. Soc. Japan 33, 1561 (1972). [4] M. Inoue and M. Okazaki, J . Phys. Soc. Japan 36, 780 (1974). [5] A. Baldereschi, F. Meloni, F. Aymerich and G. Mula, Ternary Compounds 1977: Inst. Phys. Conf. Ser. 35., 193 (1977). [6] T. Kambara, T. Oguchi and K.I. Gondaira, J . Phys. C j_3, 1493 (1980); see also: T. Oguchi, T. Kambara and K.I. Gondaira, Phys. Rev. B22, 872 (1980). [7] E. G r i l l i , M. Guzzi, A. Anedda, F. Raga and A. Serpi, S o l i d State Comm. 27, 105 (1978). [8] R.W.G. Wyckoff, Cr y s t a l Structures, V o l . 3, pg. 80 ( J . Wiley, London, 1965). [9] W. Czaja, Phys. Kondens. Materie _1_0, 299 (1970). [10] J.C.M. Henning, P.F. Bongers, H. van der Boom, and A.B. Voermans, Phys. L e t t . 30A, 307 (1969). [11] R.K. Kerr and C.F. Schwerdtfeger, J . Phys. Chem. Solids 3_3, 1795 (1972). [12] D. F i o r a n i and S. V i t i c o l i , S o l i d State Comm. 32, 899 (1979). [13] W. Czaja and L. Krausbauer, Phys. Stat. S o l . 33_, 191 (1969). [14] K. Sato, Y. Yokoyama and T. Tsushima, J . Phys. Soc. Japan 4_2, 599 (1977). [15] B. Di Bartolo, Optical Interactions i n Solids, John Wiley & Sons © 1968. [16] W.E. H a t f i e l d and W.E. Parker, Symmetry i n Chemical Bonding and  Structure, B e l l & Howell Company © 1974. [17] N.W. Ashcroft and N.D. Mermin, Solid State Physics, Holt, Rinehart and Winston © 1976. [18] M.L.W. Thewalt, M. Sc. Thesis, University of B r i t i s h Columbia, 1975. 58 [19] N. Graber, R.R. Parsons, C.F. Schwerdtfeger and W. Czaja, J . Luminescence 22, 129 (1981). [20] R.K. Kerr, Ph.D. Thesis, University of B r i t i s h Columbia, 1971. [21] S. Wittekoek and P.F. Bongers, S o l i d State Comm. _7, 1719 (1969). [22] H.L. Schiafer, H. Gausmann, H. Witzke, J . Chem. Phys. 4£, 1423 (1966). [23] S. Sugano and Y. Tanabe, J . Phys. Soc. Japan 13, 880 (1958); S. Sugano and I. Tsujikawa, J . Phys. Soc. Japan T3, 899 (1958). [24] G.F. Imbush, Ph.D. Thesis, Stanford University, 1964. [25] D.L. Wood, G.F. Imbush, R.M. Macfarlane, P. K i s l i u k and D.M. Larkin, J . Chem. Phys. 48, 5255 (1968). [26] G. Burns, E.A. Geiss, B.A. Jenkins and M.I. Nathan, Phys. Rev. 139, A1689 (1965). [27] E.O. Schulz-du Bois, B e l l Syst. Tech. J . 37., 271 (1959). [28] D.L. Wood, J . Ferguson, K. Knox and J.F. D i l l o n J r . , J . Chem. Phys. 39, 890 (1963). [29] D.H. Kuhner, H.V. Lauer and W.E. Bron, Phys. Rev. B5, 4112 (1972); S.L. Chodos and R.A. Satten, J . Chem. Phys. 62^ , 2411 (1975); CD. F l i n t , Coord. Chem. Rev. 1_4, 47 (1974); C.J. Ballhausen and A. Hansen, Ann. Phys. Chem. 23, 15 (1972); I. Ya Gerlovin, Opt. Spektrosk. 43, 896 (1977). [30] H. Shimizu, Y. Ohbayashi, K. Yamamoto and K. Abe, J . Phys. Soc. Japan 38, 750 (1975). [31] H. Nakanishi, E. Endo and T. I r i e , Japan J . Appl. Phys. _12, 1646 (1973). [32] Y. Tanabe and S. Sugano, J . Phys. Soc. Japan 9_, 766 (1954). [33] M. Veno, H. Nakanishi and T. I r i e , J . Phys. Soc. Japan 44_, 2013 (1978). [34] H. Witzke, Theor. Chim. Acta (Berlin) 20. 1 7 1 (1971). [35] N. Graber, F. Orfino and C.F. Schwerdtfeger, S o l i d State Comm. 36_, 407 (1980). [36] H.M. Kahan and R.M. Macfarlane, J . Chem. Phys. 54, 5197 (1971). [37] I . Ya Gerlovin, Opt. Spektrosk. 43, 896 (1977). 59 [38] J.P. Hehir, M.O. Henry, J.P. Larkin and G.F. Imbush, J . Phys. C7_, 2241 (1974). [39] B. Di Bartolo and R. P i c c e i , Phys. Rev. 137, A1770 (1965). [40] B. Di Bartolo and R.C. Powell, II Nuovo Cimento 66B, 21 (1970). [41] F. C a s t e l l i and L.S. Forster, Phys. Rev. B l l , 920 (1975). [42] R.C. Powell, B. Di Bartolo, B. Birang and C.S. Naiman, Phys. Rev. 155, 296 (1967). [43] M.L.H. Thewalt, Proc. 15th Int. Conf. Physics of Semiconductors, Kyoto (1980) J . Phys. Soc. Japan 49 Suppl. A, 437 (1980). [44] R.V. Schmidt, IEEE Trans. Sonic Ultrason. SU-23, 22 (1976); G.I. Stegeman, IEEE Trans. Sonic Ultrason.SU-23, 33 (1976); G.I. Stegeman, Op t i c a l Engineering 1_6, 446 (1977). [45] I.C. Chang, IEEE Trans. Sonic Ultrason. SU-23, 2 (1976). [46] D.E. Flinchbaugh, Acoustic Surface Wave and Acousto-Optic Devices, (Thomas K a l l a r d , ed.) Optosonic Press, 1971, pp. 139-150. [47] D.E. Flinchbaugh, Laser Focus September 1967, pp. 25-29. [48] E.I. Gordon, Proc. IEEE 54, 1391 (1966). [49] P.R. Bevington, Data Reduction and Error Analysis for the Physical  Sciences^ McGraw-Hill Book Company, ® 1969. [50] E.E. Bukke and Z.L. Morgenshtern, Optics and Spectr. (English t r a n s l a t i o n ) 14, 367 (1963). 60 Appendix A The Photon Counter After s e t t i n g the spectrometer at the desired wavelength the counting procedure can be i n i t i a t e d . This procedure may best be i l l u s t r a t e d i f presented i n steps. The sequence consists of four steps; these are: (1) The binary number i s stored i n the counter - t h i s i s accomplished by s e t t i n g the counter's LOAD/RESET to HI; the UP/DOWN and the CLOCK to LO. The above i s the i n i t i a l i z a t i o n sequence. The data i s accumulated v i a the Programmable Input Timer (PIT) of the computer which allows data to accumulate for a predetermined i n t e r v a l (the dwell time mentioned i n section 3.1.3). ( i i ) the binary number i s loaded i n the s h i f t r e g i s t e r - t h i s i s accomplished by brining the LOAD/RESET from HI to LO b r i e f l y , ( i i i ) The binary number i s read by the computer - t h i s i s accomplished by s e r i a l l y reading the binary b i t s by the computer. A two step process repeated as many times as necessary i s required: (a) the computer sums the channels that are HI ( c a l l t h i s Q(x)); (b) the next b i t i s clocked to the output (see figure A.1). Since the s h i f t r e g i s t e r i s a 20-bit r e g i s t e r parts (a) and (b) above are repeated twenty times (from 0 to 19). ( i v ) The binary number i s converted to decimal - t h i s i s accomplished by c a l c u l a t i n g the decimal number from information obtained i n part ( i i i ) through the use of the formula: Y = Y + 2t(19-x)*Q(x), where x varies from 0 to 19. This decimal number i s then stored i n the computer memory. To r e c a p i t u l a t e , for each point at a p a r t i c u l a r wavelenth, each photon impinging on the photomultiplier's cathode i n i t i a t e s a cascade of electrons giving r i s e to a current. The current thus obtained i s then amplified v i a e l e c t r o n i c s and transmitted to the photon counter where the counters are increased by one; this i s done for every photon detected. At t end of the counting sequence the photon counter releases the number - which represents the number of photons impinging on the photomultiplier i n the giv time - to the computer where i t i s converted to a decimal equivalent and the stored i n memory. The computer then moves to the next point and the sequenc repeats. When the sequence of points as stated i n the i n i t i a l parameters ar sampled the computer signals a halt e l s e , i t continues on another sweep averaging with the previous one. While the data i s being gathered i t i s a l s being displayed on a display screen so that anomalities and/or i n t e r e s t i n g features may be e a s i l y and quickly discerned. The option e x i s t s of i n t e r r u p t i n g the data gathering process or to increase the number of sweeps a spectral region. In the l a t t e r case a s i g n a l averaging process i s employe and i s e s p e c i a l l y u s e f u l i n the minimization of noise from the data. Once t spectra i s c o l l e c t e d and deemed i n t e r e s t i n g and/or important i t may be punch on a paper tape. This way i t may be reviewed at a l a t e r date. Also, a p l o t t e r i s a v a i l a b l e so as to plot i n t e n s i t y vs. wavelength or i n t e n s i t y vs. wavenumber spectra. |<J serial read— H CLOCK n n n n .._n LOAD Lj U/D ! ! PIT — 1 H>! re- convert to )H> load decimal pulse START END Figure A.1 Photon Counter pulse sequence necessary to load data i n computer memory. 

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