Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Kinetics of bound excitons and multi-exciton complexes in Si (B) Sullivan, Brian Thomas 1982

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

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1982_A6_7 S84.pdf [ 2.84MB ]
Metadata
JSON: 831-1.0085045.json
JSON-LD: 831-1.0085045-ld.json
RDF/XML (Pretty): 831-1.0085045-rdf.xml
RDF/JSON: 831-1.0085045-rdf.json
Turtle: 831-1.0085045-turtle.txt
N-Triples: 831-1.0085045-rdf-ntriples.txt
Original Record: 831-1.0085045-source.json
Full Text
831-1.0085045-fulltext.txt
Citation
831-1.0085045.ris

Full Text

KINETICS OF BOUND EXCITONS AND MULTI-EXCITON COMPLEXES IN S I ( B ) by BRIAN THOMAS SULLIVAN B . S c , The U n i v e r s i t y of A l b e r t a , 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of P h y s i c s We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1982 ® B r i a n Thomas S u l l i v a n , 1982 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 Li b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for 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 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 f!ji«M/£<# The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 - i i -Abstract The kinetics of the free exciton, bound exciton and multi-exciton complexes have been investigated for Si(B) by using the rate equations to analyze the experimental transient responses of these luminescent species. From th i s analysis, the B capture cross section for an exciton to bind upon a neutral impurity has been determined, as well as the B capture cross sections ra t i o s for higher order complexes. Furthermore, the lif e t i m e s for the BE, BMEC-2 and BMEC-3 have been determined. From the low temperature l i f e t i m e s , the BMEC-m/BE l i f e t i m e r a t i o appears to form a simple integer series for increasing m. The computer programs used to analyze the experimental data and generate the the o r e t i c a l transient responses, along with technical information concerning the experiment, are l i s t e d in the appendices. - i i i -TABLE OF CONTENTS Page Abstract i i Table of Contents i i i L i s t of Tables iv L i s t of Figures v Acknowledgements v i Chapter I. Introduction and Experimental Information 1 Chapter I I . Experimental Data 5 Chapter I I I . Theoretical Analysis 10 Chapter IV. Results 16 Chapter V. Conclusions and Future Research 42 Appendices Appendix A. Technical and Programming Information 45 Appendix B. Computer Programs 52 Bibliography 69 - i v -LIST OF TABLES  Tables P a 9 e 1 Parameters used to generate the t h e o r e t i c a l responses 18 -v-LIST OF FIGURES  Figures Page 1 GaAs laser and photoluminescence spectrum of Si(B), and their associated transient responses 8 2 BMEC-3 experimental and the o r e t i c a l transient responses 19 3 BMEC-2 experimental and theoreti c a l transient responses 22 4 BE, T=4.2K experimental and the o r e t i c a l transient responses 25 5 Photoluminescence spectra of Si(B) measured during and after the i n i t i a l excitation pulse 27 6 BE, T=1.8K experimental and th e o r e t i c a l transient responses 31 7 • FE, T=4.2K experimental and the o r e t i c a l transient responses 34 8 FE, T=1.8K experimental and th e o r e t i c a l transient responses *. 37 9 BE experimental transient response measured during low and high exc i t a t i o n intensity and the FE transient response measured at T=1.8 and 4.2K 39 10 Experimental Setup 47 - v i -Acknowledqments I would l i k e to thank my supervisor Dr. R.R. Parsons Parsons for the friendship, knowledge and help that he gave during the course of my research. Thanks are also due to Dr. U.O. Ziemelis and Dr. M.L.W. Thewalt for th e i r p a r t i c i p a t i o n in several useful discussions and for their help in obtaining the time-resolved spectra, and to Dr. R, Barrie for his useful comments. I would l i k e to thank the National Sciences and Engineering Research Council as well as the University of B r i t i s h Columbia for f i n a n c i a l support during my research. F i n a l l y , special thanks to Susanne, even though she set back my research by six months! -1-CHAPTER I_ INTRODUCTION AND EXPERIMENTAL INFORMATION -2-Introduction S i l i c o n , doped with impurities such as B and P, e x h i b i t s sharp luminescence l i n e s at energies s l i g h t l y lower than that of the bound exciton (BE) l i n e when excited by above-band-gap r a d i a t i o n [1-4]. The i n t e r p r e t a t i o n that these l i n e s are due to r a d i a t i v e recombination of an e l e c t r o n and a hole i n s i d e a bound multi-exciton complex (BMEC) has been well established by Kosai and Gershenzon [5], Sauer [6] and Thewalt [7-10]. However, due to the nature of the coupled, non-linear rate equations, the kinematics i n v o l v i n g the free exciton (FE), BE and BMEC's have not been investigated i n d e t a i l . Such an i n v e s t i g a t i o n i s c a r r i e d out here by observing the transient c h a r a c t e r i s t i c s of the FE, BE, BMEC-2 and BMEC-3 during and a f t e r pulsed e x c i t a t i o n and comparing these experimental curves to the t h e o r e t i c a l curves given by the rate equations. F i t t i n g the t h e o r e t i c a l t r a n s i e n t response to the experimental responses f o r T=1.8 and 4.2K leads to a determination of the capture cross section of the FE onto a n e u t r a l acceptor, the r a t i o of capture cross sections f o r higher order complexes and the decay times f o r BE, BMEC-2 and BMEC-3. Experimental Considerations 14 -3 A S i sample l i g h t l y doped with boron (N«lxl0 cm ) was used i n t h i s study. This impurity concentration was large enough to produce strong BMEC's, but s u f f i c i e n t l y low to e s s e n t i a l l y eliminate impurity-impurity i n t e r a c t i o n s , which are revealed by l i n e broadening s t a r t i n g 16 3 at about 5x10 B/cm . The sample was immersed i n l i q u i d He at temperatures -3-of 4.2K or 1.8K. The e x c i t a t i o n source was an R.C.A. C30007 GaAs l a s e r diode array, operating at a temperature of 80K, with a pulse width of approximately 400 ns and at a r e p e t i t i o n rate of 30 kHz. The i n f r a r e d output (.85 to .86 ym) of the array was passed through a Corning f i l t e r (7-69) to reduce background luminescence and then focussed onto the sample. Sample heating was not s i g n i f i c a n t since the sample was i n d i r e c t contact with the l i q u i d He and the power per pulse was determined to be l e s s than 20 mW (using a p y r o e l e c t r i c radiometer). The photoluminescence from the sample was passed through a 1.0 to 1.75 um bandpass f i l t e r , analyzed by a Perkin-Elmer E l double-pass spectrometer, and then detected with a Varian VPM-159A3 photomultipler operated at -78°C. The detector s i g n a l was processed i n the photon-counting mode f o r both photoluminescence and transient measurements. To measure the transient c h a r a c t e r i s t i c s of the photoluminescence during and a f t e r pulsed e x c i t a t i o n , a LeCroy 3001 Multichannel Analyzer (MCA) operating i n the Time(Start/Stop) mode was used. The MCA has 1024 bins; each bin representing a c e r t a i n time i n t e r v a l i n ns between Start/Stop pulses (except f o r the l a s t bin which i s an overflow counter). During a sweep, the time between the s t a r t pulse (synchronized to the t r i g g e r i n g of the GaAs laser) and the stop pulse (a photon) was recorded by incrementing the appropriate time b i n . Thus, over a s u f f i c i e n t l y long period of data a c q u i s i t i o n , depending upon the photon count rate, the t r a n s i e n t response f o r a p a r t i c u l a r l i n e was b u i l t up and displayed on an o s c i l l o s c o p e . A f t e r the data had been c o l l e c t e d , i t was stored on magnetic tape f o r l a t e r a n a l y s i s . -4-It v a 6 Important to keep the photon counting rate below approximately 4000 counts/sec (for our repetition rate) i n order to avoid distortion of the data. This distortion occurs whenever there is a significant probability (proportional to the photon count rate) that two photolumlnescence photon pulses reach the MCA during i t s time sweep. Gated (photon counting) acquisition permitted the photolumlnescence spectra to be measured at any given delay time after the triggering of the excitation pulse. With gate widths of 500 ns, the spectra were measured for six consecutive intervals in order to ensure that the transient reponse measured at a certain line was not due to another line or the background (Fig. 5). The MCA, the spectrometer and the data acquisition were a l l controlled using a minicomputer. See appendix A and B for further t e c h n i c a l d e t a i l s and the computer programs used i n the a n a l y s i s . -5-CHAPTER II EXPERIMENTAL DATA -6-Data The e x c i t a t i o n i n t e n s i t y was varied so that the t r a n s i e n t response of the FE and BE l i n e s could be measured with and without the presence of BMEC's. Transient measurements were made on the FE, BE, BMEC-2, -3 l i n e s (the BMEC-4 l i n e was very weak), and of the background luminescence near these l i n e s . Then, lowering the e x c i t a t i o n i n t e n s i t y u n t i l only a small BMEC-2 contribution was present, with no BMEC-3 l i n e , the t r a n s i e n t responses of the FE, BE and background luminescence l i n e s were remeasured. The BMEC-2 could not be eliminated e n t i r e l y , since the FE t r a n s i e n t response would be exceedingly d i f f i c u l t to measure at such low e x c i t a t i o n i n t e n s i t y . In order to remove the noise present in a transient response, the data was smoothed using a 40 point moving average procedure. Since the actual t r a n s i e n t response of a l i n e can be affected by background or other l i n e s , i t i s necessary to subtract from the former the transient response of the background, with both sets of data being obtained under the same experimental conditions. This c o r r e c t i o n i s e s p e c i a l l y important for the FE t r a n s i e n t response, because of the close proximity of the FE (TO) l i n e to the BE(LO) l i n e . As shown i n F i g . l a , the output spectrum (1440-1460 meV) of the l a s e r diode array consists of a s e r i e s of sharp peaks imposed over a broad background. Since the t r a n s i e n t c h a r a c t e r i s t i c s of the spectrum can d i f f e r s l i g h t l y for various peaks, the transient response of the e n t i r e l a s e r spectrum was measured. This average response was obtained by summing together a l l the t r a n s i e n t responses of the l a s e r peaks. A t y p i c a l photolumlnescence spectrum of B taken at 4.2K i s shown i n F i g . l b . Apart from a small phosphorus re l a t e d shoulder on the BE(TO) l i n e and a weak unknown l i n e at 1099.6 meV (discussed i n Chap. IV) , there was no a d d i t i o n a l evidence i n d i c a t i n g the presence of impurities other -7-than boron. Electron-Hole Droplet (EHD) l i n e s [ll] were not observed at the e x c i t a t i o n i n t e n s i t i e s used i n t h i s study. The transient responses associated with the photoluminescence as well as the e x c i t a t i o n pulse are shown in F i g . l c . As expected from the BMEC model, the FE photolumines-cence appears f i r s t , followed i n succession by the BE, BMEC-2 and BMEC-3 photoluminescence. This i s required as the lower order complexes have to be created before higher order complexes can be formed. Further examples of the experimental t r a n s i e n t responses for the BMEC-3, -2 and BE and FE l i n e s are shown i n Figs. 2-4, 6-9 along with the t h e o r e t i c a l l y generated t r a n s i e n t responses for those complexes (discussed i n the next chapter). L -8-Figure 1. (a) The l a s e r spectrum of the GaAs l a s e r diode array. (b) A t y p i c a l photoluminescence spectrum of Si(B) taken at 4.2K. (c) The experimental t r a n s i e n t responses f o r the FE, BE, BMEC-2 and BMEC-3 l i n e s as w e l l as the pulsed e x c i t a t i o n . A l l t r a n s i e n t responses have been normalized with respect to t h e i r peak values. -9-0> o u g 1440 c PHOTON ENERGY (meV) 1460 >-H CO z UJ UJ o UJ o CO UJ i => _J o I-o 1 I 1 1 1 1 1 1 1 1 1 1 PHOTOLUMINESCENCE SPECTRUM OF Si(B) l l l l i l i l i T — 1 — BE (TO) T-4.2 K BMEC-2 \ > BMEC-3 \ __l . J J J 1 1 I I I I 1/ 1 • f& FE(TO) 1 1 1 1 1 1 1 1 1 1 1 1080 PHOTON ENERGY (meV) 1104 Si(B) T-4.2 K 300 600 TIME (nsec) 900 -10-CHAPTER III THEORETICAL ANALYSIS -11-T h e o r e t l c a l Considerations Considering exciton capture, together with evaporation and decay of e x c i t o n i c complexes based on a BMEC model, the rate equation f o r a BMEC can be written as follows, d T " " ^  + C i - 1 n o n i - l ' C i n o n i + Ri+1 n i + l ( 1 ) f o r i-2,3..., where n. i s the BMEC-i concentration, n i s the FE concen-i o t r a t i o n , and are the capture and release rates of an exciton with respect to an n^-complex and i s the l i f e t i m e (combined r a d i a t i v e and non-radiative) of an n^-complex. Due to the non-linear coupling of the various complexes i t i s d i f f i c u l t to determine the rate c o e f f i c i e n t s unless one makes c e r t a i n assumptions (such as ignoring the non-linear terms) which may not be j u s t i f i a b l e . To circumvent these d i f f i c u l t i e s , the t h e o r e t i c a l response f o r a c e r t a i n complex, n^, was generated by using the experimental transient curves measured f o r the other complexes, n i + l ' n i - l n o 1 1 1 t l i e r a t e equation. Employing the f i r s t order Taylor s e r i e s expansion, fdn. n^t+At) - n ± ( t ) + dt At (2) -12-(where At is much shorter than the fastest physical process involving excitons in Si(B)), the theoretical response is generated for tml,2,3...1023 ns in an iterative procedure. In knowing the experimental transient responses of the complexes any physically unrealistic approxi-mations to the rate equations are avoided and only 2 to 3 parameters at most have to be varied in order to obtain the best f i t to an experimental curve. One must, of course, be careful to ensure that the transient responses measured are accurate (i.e., that background Influences have been properly taken into account). Since the absolute intensities of the photoluminescence lines are unknown, the measured transient characteristics are arbitrary to within a multiplicative factor. Thus equation (1) has not 4 parameters, but 3, because the other parameter can be factored out (since the absolute . % % intensity is not relevant). Letting n.. - = a.,.n.,,, n = a n , ' . ° i+1 i+1 i+1' o o o n^_^ = ^n^ ^  (where n^ is the normalized transient curve) and n^ = C i - l a o a i - l n i ' ^  becomes, i n i ^ 'v. a, % ^ _ ^ + V i - i ' B i n o n i + Vi+i ( 3 ) R i + l a i + l where g. • C.a and y. = -z . 1 1 ° 1 C i - l a o a i - l cannot be determined since 8^  depends upon the intensity of the n Q curve; however, the ratio C^+]/C^ = ^ i + l ^ i c a n ^ e e v a ^ u a t e ^ * ^h e parameters are not relevant quantitatively because of the unknown relative intensities of the various complexes. -13-For the BE(n-), the rate equation i s as follows, dn, n, ( 4 ) 1 = . _1 + C o n o ( N - n r n 2 ) - C ^ n ^ + dt ^ where i s the l i f e t i m e f o r the BE and C Q i s the capture rate f o r an exciton to bind on a ne u t r a l B impurity. BE formation through a n e u t r a l acceptor capturing f i r s t a hole and then an el e c t r o n i s assumed to be n e g l i g i b l e compared to the process where the ne u t r a l acceptor captures an exciton (since most electron-hole p a i r s are bound as excitons at such low temperatures). The second term includes saturation e f f e c t s , ( i . e . , to r e f l e c t the f a c t that the number of impurity s i t e s decrease), however, assuming that they are not important to order n (which i s v e r i f i e d ) , (4) i s , a f t e r normalizing, rewritten as d n l n l % * * dt o 1 o 1 1 2 where ^ = ( C + C ^ a , and ^ = . Note that i n the t h i r d term one V_2 x C o o cannot d i s t i n g u i s h between saturation e f f e c t s and the capture process of excitons onto BE to form BMEC-2. F i n a l l y , the rate equation f o r the FE, i n i t s most general form, can be written as, dn n 9 __o = _ _° _ C n (N-n.) + g^(t) + R,n + rUn, + l U ^ . (6) dt T O O l J. A * * J J o -14-This equation assumes that saturation effects beyond order n Q n2 a r e negligible and that no EHD lines are present. The function g(t) represents the pulse excitation which optically generates the carriers. Physically, the electron (n£) and hole (n^) concentrations are expected to be propor-tional to g(t), since the main decay channel of carriers is through deep traps caused by defects. Thus, the second term, which is proportional to n e n n » represents the FE generation rate. The third term represents loss of excitons via capture onto a neutral B acceptor, while the remaining terms take into account any release of excitons from complexes by thermalization. For Si, the FE recombination lifetime, x , has recently been measured by Ohyama [12] and found to be around 3.5 us in the temperature range 2 to 10K. From previous measurements of the B capture cross section at 4.2K [13,15,16], and for the impurity concentration level in this study, it can be assumed that x >> x (where C N = 1/x ). Thus the first term in o c o c rate equation (6) can be ignored, so (6) becomes, after normalizing, d^ % o no 2, ^  x x x x x ,_. - - _ + g (t) + W l + + t 2 n 2 + e 3n 3 (7) c The capture time, x , is the only quantitatively significant parameter, the other parameters being only qualitatively indicative of a physical process that is occurring (since the relative intensities of the lines are unknown). For instance, g is varied in order to simulate saturation effects while controls the evaporation of excitons from an n^-complex. Thus, by generating the response for the FE line from this equation, the capture time, x£, can be determined and compared with previous results. -15-At low e x c i t a t i o n i n t e n s i t y , only 2 parameters are required to get a good f i t . After determining these parameters, they are held con-stant i n the higher e x c i t a t i o n case, while the other parameters are varied. To achieve the best f i t , the standard deviation between the normalized experimental and t h e o r e t i c a l curves i s minimized. -16-CHAPTER IV RESULTS -17-Resuits The values f o r the parameters which r e s u l t i n the best f i t f o r the various rate equations are summarized i n Table 1 along with t h e i r e r r o r estimates. These estimates were obtained by varying one parameter (holding the r e s t constant), u n t i l the t h e o r e t i c a l response was outside the e r r o r l i m i t s (due to background influences) imposed upon the ex p e r i -mental response. The BMEC-3 transient response i s analyzed f i r s t , since the BMEC-4 release term can be neglected (due to i t s weak luminescence i n t e n s i t y ) . Thus the s i m p l i f i e d rate equation has only two parameters, 3 n 3 ^ ^ xx - j — *= + n n - p n n. dt o 2 3 o 3 A l t e r the t h e o r e t i c a l curve f o r BMEC-3 i s generated, i t i s compared to the experimental curve f o r T«4.2K. I n i t i a l l y , with 6^ • 0 the best o v e r a l l f i t i s obtained with T 3 - 110 ns ( F i g . 2a). While the f i t i s quite good f o r the t a i l region, the t h e o r e t i c a l build-up does not match the experimental build-up. However, by adjusting fJ^ an ex c e l l e n t f i t i s obtained with « 103 ns and p\j • .015 as seen i n F i g . 2b (remember that the B-coeff i c i e n t 6 depend upon the n Q i n t e n s i t y ) . -18-TABLE J, Para m e t e r s used t o g e n e r a t e t h e o r e t i c a l r e s p o n s e ( B e s t F i t ) Complex T = 1.8K T = 4.2K BMEC-3 T - =1 44 ± 1 0 ns Bo =.017±.004 yi = .0 T = 180 ns T - =103 ±10 ns 6, =.015±.005 Yo =.0 T = 212 ns BMEC-2 T - =343 +20 ns B, =.009±.003 Yo - . 0 T = 390 ns T , =203 ± 30 ns 6, =.018±.004 yZ =.075*.025 T = 435 ns BE * T =1053±100 ns B, =.0015 ±.0005 Y^  =.0 T = 1300 ns T . = 620 ± 60 ns B7 =.0006±.0006 yi c-0 T = 1000 ns BE ** T =1050±100 ns BZ =.006± .002 yt =.026 T = 1265 ns T . =600 ± 60 ns B, =.009±.003 y] =-06 T = 1100 ns FE T =35 ± 10 ns B c =.005* .005 e° =.03 T =50 ±15 ns B c =.004±.004 T = Luminescence decay time - o b t a i n e d w i t h o u t the p r e s e n c e of h i g h e r o r d e r complexes. - o b t a i n e d i n t h e p r e s e n c e of h i g h e r o r d e r complexes. -19-Flgure 2. BMEC-3i (a) The BMEC-3 experimental transient response, ob-tained at 4.2K, is shown along with two theoretical responses. The parameters governing these responses are: (i) x« - 37 ns, 6,-0 and (ii) x 3 « 110 ns, B3 - 0 where x, is the BMEC-3 lifetime and B3 controls the loss of BMEC-3*s through BMEC-4 creation. Neither response gives a good overall f i t . (b) By adjusting {$3, an excellent f i t with respect to the 4.2K experimental transient response is achieved with x 3 • 103 ns and p*3 * .015. (c) The BMEC-3 transient response measured at 1.8K and the theoretical response with parameters x. • 144 ns and 6, - .017 are shown here. -20-0 200 400 600 800 1000 TIME (nsec) -21-I t should be emphasized that i n order to determine the rate parameters accurately, i t i s necessary to examine the e f f e c t such parameters have on both the build-up and decay regions. For example, i f only the build-up region had been examined a good f i t would have been obtained f o r = 37 ns and 8^  = 0, but there would have been a large deviation i n the decay p o r t i o n of the curve ( F i g . 2a). For T = 1.8K, the best f i t i s obtained with » 144 ns and 6^  = -017 ( F i g . 2c). Thus, the l i f e t i m e increases going to a lower temperature, i n d i c a t i n g that evaporation of excitons i s probably occurring from the BMEC-3 complexes. At both temperatures, as seen i n Table 1, the l i f e t i m e i s l e s s than the measured luminescence decay time. Next, the BMEC-2 curve was generated (the r e s u l t s are given i n Table 1). I n i t i a l l y , f o r T=4.2K (holding B 2 = 0), the best f i t was obtained with x 2 = 257 ns, but again there existed a large deviation i n the build-up region (see F i g . 3a). With the parameters x 2 ~ 253 ns, B 2 = »015 a good f i t was obtained, but the t h e o r e t i c a l and experimental peaks were not in the same p o s i t i o n . Due to t h i s s h i f t i n the peaks, x 2 * 200 ns and 6 2 * .020 are i n fac t b e t t e r parameters, i f one demands that the t a i l regions of the generated and experimental curves be p a r a l l e l ( F i g . 3a). To correct the peak s h i f t , a release term was included and the best o v e r a l l f i t was achieved with x 2 = 203 ns, B 2 • .018 and Y 2 = .075 as i l l u s t r a t e d i n F i g . 3b. S i m i l a r l y , f o r T=1.8K the best f i t was obtained f o r x 2 • 345 ns and 82 •= .009 ( F i g . 3c). The longer l i f e t i m e at T=1.8K compared to 4.2K again seems to i n d i c a t e that evaporation of excitons i s taking place, t h i s time from BMEC-2's. -22-Flgure 3. BMEC-2. (a) The BMEC-2 experimental transient response mea-sured at 4.2K as well as two theoretical responses are shown here. The parameter values for these responses are: (i) T 2 - 200 ns, 32 - .02 and (ii) T 2 « 257 ns, 62 - 0. Examining the experimental response and the (ii) curve, a large deviation between the two responses is observed in the build-up region. A better f i t is obtained with the (i) curve, but a shift between the experimental and theoretical peaks now exists, (b) Including a BMEC-3 to BMEC-2 release term in the rate equation (by adjusting y^) * corrects the peak shift in the theoretical response and a very good f i t is obtained with T 2 • 203 ns, B2 » .018 and Y 2 • '.075. (c) At 1.8K, a very good f i t between the experimental and theoretical response is obtained with T 2 - 345 ns and B2 » .009. -23-0 200 400 600 800 1000 TIME (nsec) -24-For the same excitation intensity, the ratios of the 3-coefficients for the BMEC-2, -3's yield capture cross section information. At T-1.8K, C3/C2 = .017/.009 - 1.8 + 1.0, while for 4.2K, C3/C2 - .015/.018 = .8 + .5. The relative cross sections appear to have increased only slightly with a lowering of temperature. The transient response of the BE line was measured with and without the presence of higher order complexes. Since the response without the presence of higher order complexes is less complicated, the parameters determined for this case can be held constant in the higher excitation case. At T=4.2K an excellent f i t was obtained (as seen in Fig. 4a) with T 1 = 620 ns and = .006. Setting 8 1 » 0 would not visibly alter the f i t , which indicates saturation effects are not important. This value of x^  is less than the luminescence decay time (approximately 1000 ns) obtained by fitting the decay transient response to an exponential. The difference is due to the t a i l region of the FE curve, which indicates that BE's continue to be generated after the end of the excitation pulse. The importance of properly eliminating background effects is seen here; i f there were no t a i l on the FE curve, then x^  would equal the luminescence decay time. To ensure that this t a i l is real, the photolumlnescence spectrum was examined for 3 ys (with .5 ws increments) during and after the i n i t i a l excitation. As seen in Fig. 5(a), the FE(TO) line is definitely visible at T - 4.2 K for a l l the observed times. In Fig. 5(b), however, the FE(TO) line is not visible at T=1.8K in any spectra measured with a delay time greater than 1.0 us. This thermal dependence seems to indicate that the FE's are being evaporated from a complex, most likely a BE. To correct the FE(TO) response, which is distorted by the BE(LO) line, the transient response of a point between -25-Figure 4. BE, T-4.2K (a) The BE transient response measured without the presence of higher order complexes is shown along with a theore-tical response (T^ « 620 ns, 6, • .0006) and an excellent f i t is observed. Setting - 0 would not visibly alter the f i t , which indicates that saturation of the impurity sites is not occuring. (b) Next, the BE transient response in the pre-sence of BMEC-2, -3's was measured. The best f i t , with B 1 • 0 (neglecting saturation and loss of BE's through BMEC-2 creation) was obtained with T. * 597 ns, but a large deviation between the two responses is evident in the build-up region, (c) To correct this, 6^  was adjusted and a BMEC-2 to BE release term was added to give a good f i t to the BE transient response (t1 - 600 ns, $2 - .009 and - .06). TIME (nsec) -27-Figure 5. The photoluminescence spectrum for Si(B) showing the BE(LO), FE(TO) and FE(LO) lines was examined for 3 ps during and after the i n i t i a l excitation. The spectra measured after a delay time of 1.0 us, were scaled by a multiplicative factor for display purposes, (a) At T»1.8K the FE(TO) line is not visible in any spectra with a delay time greater than 1.0 us. (b) At 4.2K, however, the FE(TO) is definitely visible for a l l observed times. To correct the FE(TO) response for distortion caused by the BE(LO) line, the transient response of a point between the two lines is measured and this is subtracted from the FE(TO) response. A weak, long-lived line of unknown origin centered at 1099.6 meV is evident in both (a) and (b), and begins to dominate over the FE(LO) line after the end of the excitation pulse. A weaker line,.also of unknown origin, appears at 1101.7 meV. PHOTOLUMiNESCENCE INTENSITY (linear scale) PHOTOLUMINESCENCE INTENSITY (linear scale) o -83--29-the two l i n e s i s measured, and t h i s i s subtracted from the FE(TO) response. While one may be tempted to use the FE(LO) tr a n s i e n t response ( i d e n t i c a l to the FE(TO) response) because i t i s further from the BE(LO) l i n e , F i g . 5 ind i c a t e s that t h i s cannot be done (at l e a s t not f o r the sample under study). In F i g . 5(a) and 5(b) a new l i n e centered at 1099.6 meV i s evident; i t begins to dominate over the FE(LO) l i n e a f t e r the end of the e x c i t a t i o n pulse. The exact o r i g i n of the l i n e i s not cl e a r at t h i s time, as no known e x c i t o n i c or i s o e l e c t r o n i c centre i s known to luminesce at t h i s energy. A weaker l i n e , also of unknown o r i g i n , appears ( s h i f t e d by approximately the TO-LO energy separation, 2.1 meV) at 1101.7 meV, a f t e r the end of the e x c i t a t i o n . The BE response with BMEC-2 and BMEC-3's present i s now analyzed. Setting = 0, the best f i t i s obtained with = 597 ns, but there e x i s t s a s i g n i f i c a n t deviation i n the build-up region ( F i g . Ab). This can be corrected f o r by including a n Qn^ term (S^ = .008, i n d i c a t i n g l o s s of BE's through BMEC-2 creation or sa t u r a t i o n ) , but t h i s leads to a s h i f t between the t h e o r e t i c a l and the experimental peak p o s i t i o n s . A BMEC-2 to BE release term can p a r t i a l l y correct t h i s , and the best f i t i s obtained with = 600 ns, ^ - .009 and y^ = .06 as shown i n F i g . Ac. As required by the f i t t i n g procedure, the values f o r the parameter are i n close agreement i n both cases (both with and without higher order BMEC's), while 6^  i s approximately 10 times greater with the higher e x c i t a t i o n than with the lower e x c i t a t i o n , which r e f l e c t s the higher FE i n t e n s i t y . The d i f f e r e n c e i n the build-up region of the BE transient response at low and high e x c i t a t i o n can be seen c l e a r l y i n F i g . 9a. -30-Comparing the r a t i o of = .009 with B 2 = .018 (obtained at the same e x c i t a t i o n i n t e n s i t y at 4.2K), the C 2/(C +1^) « 2.0 ± 1.0. Thus, the capture cross section f o r an exciton to bind upon a BMEC-2 would appear to be at l e a s t twice that of the cross section f o r an exciton to be captured by a n e u t r a l acceptor. The same analysis f o r T=1.8K was c a r r i e d out on the BE (with only a small BMEC-2 contr i b u t i o n present) and the best o v e r a l l f i t was obtained with = 1053 ns and = .0015 ( F i g . 6a). At t h i s low temperature, the decay l i f e t i m e should equal the Auger time, and, indeed, t h i s value i s i n close agreement with the Auger time determined experi-mentally by Schmid [14]. In the presence of higher order complexes, the best f i t ( F i g . 6b) i s achieved with t = 1050 ns, ^ = .006 and y = .025. The di f f e r e n c e between the two l i f e t i m e s at T~1.8K and 4.2K can be a t t r i b u t e d to thermalization of excitons from the BE. Comparing the 1.8 and 4.2K r e s u l t s , i t i s cl e a r from the above that the role of BMEC's i n BE kinematics cannot be neglected above a c e r t a i n e x c i t a t i o n i n t e n s i t y . Examining the r a t i o &2^1 f o r T=1,8K> o n e s e e s t h a t  C 2 ^ C o + C l ^ = • 0 0 6 / * 0 0 9 = * 7 1 A t t h i s temperature, C 2 i s of the order of C q or greater. Therefore, i t appears, that the capture cross section increases with the number of excitons bound onto a complex. As seen from Table 1, the luminescence decay times (obtained by f i t t i n g the decay region to an exponential) do not agree with the l i f e t i m e determined v i a the rate equations. This i s to be expected because higher order complexes decay to lower order complexes and because excitons evaporated from BMEC's are recaptured. -31-Figure 6. BE, T-1.8K (a) With only a small BMEC-2 contribution present, the BE transient response was measured and best overall f i t was achieved with the theoretical response using the parameters T. - 1053 ns and 6- * .0015. (b) In the presence of BMEC-2, -3's, the best f i t was obtained with - 1050 ns, 6, - .006 and YX - -025. -32-TIME (nsec) -33-Comparing the lifetimes obtained at T=1.8K, for the exciton complexes, a simple integral ratio is suggested. Letting = BMEC-m lifetime m BE lifetime we obtain r m = 1,3,7.2 with m = 1,2,3. In a situation where the lifetime is inversely proportional to the number of electrons times the number of holes in th« complex, one expects rffi = 1,3,6. The closeness of this prediction with the experimental result appears to contradict the accepted model for non-radiative decay, namely Auger recombination which involves combinations of three particles. By examining the lifetimes for other impurities such as Li or P, i t would be interesting to see whether or not the same ratio pattern is followed. Finally the FE transient response is examined. First the theoretical response is generated to try and match the T=4.2K experimental response obtained in the presence of higher order complexes. With B o =0 and £ 2 = n the build-up region can be fitted reasonably well with Tc=60 ns, but the theoretical response for the t a i l region falls off far quicker than the experimental response. Introducing a release term for excitons from a BE improves the f i t with xc«56 ns, BQ-0 and e^.13 (Fig. 7a). However, i f one employs the BQ term to include possible saturation effects, an acceptable f i t is achieved with T = 35ns, B = .006 and e,= .14 as seen in r c o l Fig. 7b, although the previous f i t was better. Thus from this data for T-4.2K, for T c within 50 + 15 ns, a good f i t would be obtained. Next the corresponding FE response obtained (at T-4.2K) with a lower excitation intensity is examined. With T -70 ns, B -0 and e.-.l a good f i t is c o i -34-Figure 7. FE, T=4.2K The FE experimental transient response (with BMEC-2, -3's also present) is shown in (a) and (b) along with the theoretical responses, (a) Setting $ » 0 (neglecting saturation effects), the best f i t is obtained w?th T • 56 ns and e, - .13. c X (b) Adjusting B , a good f i t can also be achieved with T • 35 ns, 6 • .006 and .14. The FE experimental transient response, obtained under excitation conditions such that only a small BMEC-2 contribution was present is shown along with theoretical responses in (c) and (d). (c) With T • 70 ns, BQ - 0 and e^^ - .1 a good f i t is obtained, but ihe best overall f i t is achieved in (d), with the parameters T £ • 45 ns, 6q • .007 and - .09. PHOTOLUMINESCENCE INTENSITY (linear scale) -se--36-obtalned (Fig. 7c), but the best overall f i t is achieved with i =45 ns, c 6o=.007 and (Fig. 7d). Release terms involving BMEC-2,-3's did not improve the f i t significantly. For T=1.8K, in the presence of BMEC's, the effects of different sets of parameters on the theoretical response are shown in Figs. 8a-c. From these results, the best estimate for the capture time is Tc™35 + 10 ns. Saturation effects appear to be minimal while a small BE release term is required in order to f i t the BE t a i l region. In a l l these cases, i t was difficult to achieve a good f i t in the build-up region of the transient response. In particular, the sinusoidal variations present in the excita-tion pulse, are also evident in the theoretical response, but absent from the experimental response. It is not clear physically how these fluctua-tions were smoothed out (the sinusoidal variations were definitely due to the laser output and not associated with other aspects of the apparatus, which was verified by substituting the sample by a tungsten lamp but keeping a l l other parts of the experiment unchanged). The FE transient responses at IVl.BK and 4.2K are shown together in Fig. 9b. Examining the leading edge and the region where the laser pulse shuts off, a time shift between the two curves of approximately 15 ns is evident. Physically, one can attribute this shift to a difference in capture times for an exciton, which would be in agreement with the results obtained above. The capture times for the two temperature cases are related to capture cross sections, on, by -37-Fiaure 8. FE, T-1.8K for (a), (b) and (c), the experimental transient was measured in the presence of BMEC-2, -3's. The values for the parameters used in the theoretical responses are: (a) T £ - 29 ns, *. r-i . /.\ _ _ a m f\ c m .037 and 6 - .005, c. - .04; (b) T - 36 ns, 8 - 0, E l - .037 (8) T c - 42 ns, 6o - 0, c x c- 0. -38-0 200 400 600 800 1000 TIME (nsec) -39-Figure 9. (a) The BE experimental transient responses obtained under different excitation intensities. The main effect is apparent in the build-up region, where the BE response under "high" excitation has become partly saturated while in the "low" excitation case i t has not. (b) The FE experimental transient responses obtained at T=1.8 and A.2K are displayed. A time shift of approximately 15 ns is evident between the leading edge of the two responses and this can be attributed to the difference in capture times for an exciton to bind upon a neutral Boron acceptor. TIME (nsec) where v ^ i s the mean FE thermal v e l o c i t y . Thus, B capture cross sections of 2.7 + 1.0 x 1 0 " 1 3 cm 2 at T=1.8K and 1.2 + 1.0 x 1 0 - 1 3 cm 2 at T-4.2K are obtained. This i s the f i r s t reported value f o r the B cross section at T=1.8K. Previously Feenstra and M c G i l l [13] determined the B cross section —13 2 % to be about 10 cm f o r T 'v. 5K, which i s i n close agreement with the T=4.2K value obtained above. Nakayama, et a l . , [15] obtained at 4.2K, a -14 2 B cross section of 1.51 x 10 cm . Hammond and S i l v e r [16], through t h e i r measurements of the FE l i f e t i m e s and BE to FE i n t e n s i t y r a t i o s , assigned a -13 2 cross section of about 7.5 x 10 /T cm /K to B, f o r T - 2 to 16K. The cross sections obtained i n t h i s study are i n good agreement, but l i e j u s t below t h e i r r e s u l t s . -42-CHAPTER V CONCLUSIONS AND FUTURE RESEARCH -43-Conelusion The experimental t r a n s i e n t responses of the FE, BE and BMEC's luminescence have been analyzed by t h e i r coupled rate equations. Two goals have been achieved; ( i ) the v e r i f i c a t i o n of the rate equations themselves and ( i i ) the determination of the rate parameters f o r processes that u n t i l now have not been analyzed. The B capture cross section of -13 2 1.2 + 1.0 x 10 cm obtained at A.2K i s i n close agreement with previous r e s u l t s and t h i s cross section measurement has been extended down to -13 2 1.8K f o r the f i r s t time, g i v i n g a value of 2.7 + 1.0 x 10 cm . The l i f e t i m e s f o r the BE, BMEC-2 and BMEC-3 have been determined. The BE l i f e t i m e at 4.2K (600 + 60 ns) was l e s s than that at 1.8K (1050 + 100 ns) due to thermal d i s s o c i a t i o n of the complex. From the low temperature l i f e t i m e s , the BMEC-m/BE l i f e t i m e r a t i o appears to form a simple integer s e r i e s f o r i n c r e a s i n g m. F i n a l l y , the B capture cross sections f o r the higher order complexes were shown to increase with the number of excitons bound to an impurity. -44-Future Research This research could be extended by varying excitation conditions such as pulse width or intensity in order that d i f f -erent transient responses could be f i t t e d , which would lead to an improvement in the error estimates for the parameters. There are no apparent temperature or excitation l i m i t -ations that would prohibit use of the transient response method to obtain kinetic information involving higher order complexes (provided they exist at that temperature), other than the fact that new processes (such as EHD li n e s ) may complicate the actual analysis of the data. If the r e l a t i v e i n t e n s i t i e s of the photoluminscence l i n e s were known, then the capture cross sections and release rates of the BMEC's could be obtained from the rate parameters di r e c t l y . After investigating Si(B) more thoroughly, i t would then be useful to examine other impurities such as lithium or phosphorus. It would be interesting to see i f the BMEC-m/BE lif e t i m e s for these impurities measured at low temperatures, formed the same integer series for increasing m, as for boron. -45-APPENDIX A TECHNICAL AND PROGRAMMING INFORMATION -46-Th i S appendix d i s c u s s e s how the e x p e r i m e n t a l t r a n s i e n t d a t a was c o l l e c t e d and the programs used t o a n a l y z e the d a t a . The computer programs the m s e l v e s a r e g i v e n i n appendix B. In o r d e r t o u t i l i z e t h e m u l t i - c h a n n e l a n a l y z e r (MCA), the TRIUMF BASIC OBJECT code must f i r s t be r e a d i n , f o l l o w e d by the TRIUMF SUBROUTINE code which c o n t a i n s the s u b r o u t i n e CALL 27. Then the photon c o u n t i n g program, m o d i f i e d f o r the MCA, has t o be r e a d i n (when l o a d i n g , i f any e r r o r t y p e 8 messages are. p r i n t e d , j u s t t y pe i n Load and c o n t i n u e ) . For f u r t h e r d e t a i l s c o n c e r n i n g the Nova-2 s u b r o u t i n e s , see [ 1 7 ] . A p u l s e g e n e r a t o r , which t r i g g e r s the GaAs l a s e r a r r a y , i s a l s o used t o t r i g g e r the S t a r t i n p u t on the MCA. A p u l s e from the d e t e c t o r (due t o the p h o t o l u m i n e s c e n c e ) i s sent t h r o u g h a d i s c r i m i n a t o r and then goes t o a r a t e m o n i t o r and the STOP gate on the MCA. Thus the d a t a i s then c o l l e c t e d over a p e r i o d of t i m e . When f i n i s h e d , the d a t a i s then s t r o b e d over t o the Nova mini-computer (See F i g . 10). A f t e r the t r a n s i e n t d a t a has been c o l l e c t e d on the MCA and then sent over t o the Nova m i n i c o m p u t e r , the d a t a i s punched onto a paper tape f o r t r a n s f e r t o t h e computer c e n t r e . The d a t a i s then r e a d o f f the paper tape and s t o r e d onto a d i s k f i l e on MTS, where i t can then be a n a l y z e d . -47-Figure 10. Schematic diagram of the experimental setup as described i n the text. The system was used i n the photon counting mode i n order to perform photolumlnescence and t r a n s i e n t measurements. OPTICAL FIBER BUNDLE EXPERIMENTAL SETUP -49-To a c c o m p l i s h t h i s , i t i s n e c e s s a r y t o know how the e x p e r i m e n t a l d a t a i s s t o r e d on the paper tape and how i t i s l a t e r r e ad i n t o a MTS f i l e . On the Nova m i n i c o m p u t e r , each i n t e g e r i s r e p r e s e n t e d by two b y t e s : a L e a s t S i g n i f i c a n t B yte (LSB) and a Most S i g n i f i c a n t Byte (MSB). T h e r e f o r e , when d a t a i s punched onto a paper t a p e , two p h y s i c a l frames on the tape a r e n e c e s s a r y t o form an i n t e g e r . The d a t a i s i n B i n a r y Coded Deci m a l and not i n ASCII code, w i t h no p a r i t y c h e c k s . In t h i s e x p e r i m e n t , our d a t a t a k e s the form of 1024 i n t e g e r s , r e p r e s e n t i n g the t r a n s i e n t response of a p a r t i c u l a r p h o t o l u m i n e s c e n c e l i n e , so t h a t t h e s e 1024 d a t a p o i n t s comprise one " r e c o r d " . In o r d e r f o r the paper tape r e a d e r (PTPR) t o r e c o n i z e what i s a c t u a l l y d a t a , the d a t a r e c o r d has t o have end of r e c o r d (EOR) sequences b e f o r e and a f t e r i t . An EOR=4FFFFFFFF was chosen, which r e p r e s e n t s p h y s i c a l l y 4 t o t a l l y punched PT frames. Suppose our d a t a r e c o r d i s i n memory l o c a t i o n s 2003-3027, then i n o r d e r t o form the EOR sequence, the i n t e g e r '65535' i s s t o r e d i n l o c a t i o n s 2001,2002,3028 and 3029 w h i l e a '0' i s p l a c e d i n t o l o c a t i o n 2000. The l o c a t i o n s 2000-3029 a r e then punched onto paper t a p e , w i t h the a p p r o p r i a t e l e a d e r and t r a i l e r t o form the d a t a r e c o r d w i t h EOR's. The paper tape i s then taken over t o the computing c e n t r e where i t i s a s s i g n e d a rack number f o r l a t e r i d e n t i f i c a t i o n . To r e a d the paper t a p e , a b a t c h j o b i s performed a t low p r i o r i t y , which mounts the tape o n t o a PTPR and reads i t u n t r a n s l a t e d i n t o a MTS f i l e ( s t i l l i n b i n a r y f o r m a t ) . The f o l l o w i n g f i l e was used -50-t o r ead i n the paper t a p e : F i l e S2.READ $Signon CCID Time=3sec Pages=5 P r i o r i t y = L o w Password $Mount PTnnnn PTPR * t a p e * p a r i t y = n o n e t r a n = o f f rod=off nd=off size=25000 EOR=4FFFFFFFF $Copy * t a p e * t o D a t a . f i l e $ S i g n o f f By u s i n g the command "$Copy S2.READ t o * b a t c h * " , the paper tape w i t h r a c k number PTnnnn i s then read i n t o the dummy f i l e • t a p e * , which then i s c o p i e d i n t o the permanent f i l e " D a t a . f i l e " . The "Mount" command . i s e x p l a i n e d f u r t h e r i n the UBC documents TAPE or PAPER TAPE USER'S GUIDE. The para m e t e r s a r e a l s o e x p l a i n e d i n the l a s t document as w e l l . I f t he f i l e D a t a . f i l e i s now examined, t h r e e l i n e s w i l l be seen, the f i r s t one c o r r e s p o n d i n g t o the b l a n k l e a d i n g edge of the t a p e , the second t o the d a t a r e c o r d and the t h i r d l i n e t o the b l a n k t r a i l i n g edge of t h e paper t a p e . In o r d e r t o r e a d the d a t a i n h e x a d e c i m a l f o r m a t , e n t e r the e d i t mode u s i n g the m o d i f i e r Hex. Next, i t i s n e c e s s a r y t o t r a n s l a t e the b i n a r y format i n t o a r e a l format i n o r d e r t o check the d a t a . To a c c o m p l i s h t h i s , the program S2.PAPC0N was used. In t h i s program, the e x p e r i m e n t a l d a t a i s w r i t t e n i n t o a 2x1 l o g i c a l a r r a y one b y t e a t a t i m e , and t h i s a r r a y i s then made e q u i v a l e n t t o an I n t e g e r * 2 a r r a y . -51-However, as two b y t e s a r e re a d i n t o form an i n t e g e r , they must f i r s t be t r a n s p o s e d . A f t e r t h i s has been done, the i n t e g e r a r r a y i s used t o c r e a t e a r e a l a r r a y and t h i s i s o u t p u t t e d onto a permanent f i l e u s i n g a f i x e d f o r m a t . A l l f u t u r e programs use the same format f o r i n p u t and o u t p u t . The a c t u a l d a t a a n a l y s i s can b e g i n now. I f the d a t a has t o be smoothed i n o r d e r t o remove any n o i s e , the program S2.NSMOOTH i s used. In t h i s program, an N - p o i n t moving average i s performed on the d a t a . U s u a l l y , a 2 0 - p o i n t moving average i s s u f f i c i e n t f o r the t r a n s i e n t response d a t a . To g e n e r a t e the t h e o r e t i c a l r e s p o n s e , based upon the r a t e e q u a t i o n s (and the v a l u e s a s s i g n e d t o the r a t e p a r a m e t e r s ) , f o u r programs a r e a v a i l a b l e : S2.GENFE, S2.GENBE, S2.GENM2 and S2.GENM3 which c a l c u l a t e the FE, BE, BMEC-2 and BMEC-3 t h e o r e t i c a l r e s p o n s e s r e s p e c t i v e l y . As d i s c u s s e d p r e v i o u s l y , the programs use the e x p e r i m e n t a l t r a n s i e n t r e s p o n s e s i n the r a t e e q u a t i o n s t o compute the t h e o r e t i c a l r e s p o n s e . To p l o t the e x p e r i m e n t a l r e s p o n s e s a l o n g w i t h the t h e o r e t i c a l r e s p o n s e s , the program S2.XPLOT i s used, which w i l l p l o t up t o f o u r p l o t s on the same g r a p h . To f i t an e x p o n e n t i a l l i n e t o the decay r e g i o n of the t r a n s i e n t c u r v e , the program S2.LOGEXP can be used. T h i s program prompts the user t o e n t e r the d a t a range t o be f i t t e d and w i l l p l o t the c o r r e s p o n d i n g e x p o n e n t i a l l i n e a l o n g w i t h t h e d a t a . -52-APPENDIX B COMPUTER PROGRAMS -53-F i l e S2.READ. T h i s f i l e i s copied t o *batch* i n order t o read i n a paper tape (PT) and copy i t t o a permanent MTS f i l e . The data record i s separated from the r e s t of the tape by end-of-record (EOR) sequences. The data i s assumed t o be in b i n a ry format and wi t h no p a r i t y checks. Each i n t e g e r on the Nova minicomputer i s represented by two bytes, which takes up two frames on the PT. A f t e r the data has been punched out wit h EOR's, the PT i s taken over t o the computing cent r e and assigned a rack number, f o r i d e n t i f i c a t i o n purposes. The §Mount command i s then used t o read i n the tape. More inform-a t i o n can be obtained from the UBC manuals TAPE and PAPER TAPE USER'S GUIDE. The i n f o r m a t i o n on the PT i s s t o r e d on a dummy f i l e *tape* and must be copied to a permanent f i l e before the batch job i s completed. ***********************************************************" $Signon CCID Time=3sec P r i o r i t y = l o w Password $Mount PTnnnn PTPR *tape* parity=none tran=off rod=off nd=*off size=25000 EOR=4FFFFFFFF 'message t o operator' $Copy *tape* D a t a . f i l e $Signoff ************************************************************* In the $Mount command, the parameters are as f o l l o w s : PTnnnn - Rack number assigned to PT at computing c e n t r e . *tape* - Dummy f i l e , where data i s t e m p o r i a l l y s t o r e d . parity=none - no p a r i t y checking i s performed on data. tran=off - Data i s i n bi n a r y format, not ASCII code. size=25000 - maximum s i z e of record E0R=4FFFFFFFF - EOR sequence which i s placed before and and a f t e r the data r e c o r d . Note, s i n c e the experimental data i s s t i l l i n b i n a r y format i n the f i l e ' D a t a . f i l e ' , i t has to be converted to a r e a l format i n order t o check the data and use i t f o r f u t u r e programs. T h i s conversion i s performed using the program S2.PAPCON. -54 -C Program S2.PAPC0N. This program i s used to t r a n s l a t e the C experimental data which i s i n binary format i n t o a C r e a l f l o a t i n g point format. The input f i l e assigned C to u n i t 1 i s assumed to have the data on l i n e #2. C This program f i r s t reads the data i n t o a 2x1 l o g i c a l C a r r a y , one byte at a time. I t takes two bytes to C form an integ e r and so the l o g i c a l a r r a y i s made C equivalent to an Integer*2 a r r a y . Since the data i s C i n reverse order, the informa t i o n i n the Integer*2 C array i s st o r e d i n a Real array i n reverse order. C The data i n the r e a l a r r a y i s then outputted to C the f i l e assigned to u n i t 2 w i t h format 4F12.5. C This format i s used i n a l l subsequent programs that C begins with the l e t t e r s S2. C LOGICAL*1 LY,TEST INTEGER*2 NY REAL SYO023) DIMENSION LY(2,1024), NY(1024) C The next statement makes the ar r a y s LY and NY e q u i v a l e n t EQUIVALENCE(LY,NY) N=1024 M=1023 C Read i n the f i r s t l i n e , which corresponds to the C le a d i n g blank edge of the paper tape and d i s c a r d . READ(1,150) TEST 150 FORMAT(A1) C Read i n the data and sto r e i n the array LY. Since C the Nova punched out the Least S i g n i f i c a n t Byte (LSB) C and the Most S i g n i f i c a n t Byte (MSB) that form an integ e r C transposed to the MTS forms an i n t e g e r , the bytes have C to be transposed as they are read i n . READ(1,100) (L Y ( 2 , J ) , L Y ( 1 , J ) , J=1,N) 100 FORMAT(250A1,250A1,250A1,250A1,250A1,250A1,250A1,250A1,250A1,250A1) C The format statement cannot be made any shorter s i n c e C you can d e c l a r e only 256 c h a r a c t e r s at any time. C C Next, the data from the ar r a y NY i s read i n t o the C r e a l a rray SY i n reverse order. Note that the 1024'th C element i n array NY i s not kept, as i t corresponds t o C the overflow counter (the l a s t MCA b i n ) . DO 50 1=1,M J=(N-I) NINT=NY(J) SY(I)=FLOAT(NINT) 50 CONTINUE C Write out the r e a l a rray to the f i l e assigned to u n i t 2. WRITE(2,300) SY 300 FORMATUF12.5) STOP END ) 55-C Program S2.NSM0OTH. This program w i l l perform a running or C s l i d i n g average over N p o i n t s . The input f i l e i s C assigned t o u n i t #1 and the output f i l e i s assigned to C u n i t #2. The user i s f i r s t prompted f o r the range of C the s l i d i n g average (N). The s l i d i n g average i s per-C formed by summing up the f i r s t N elements and d i v i d i n g C by N, and t h i s number i s assigned t o the N/2 element C i n the a r r a y SMOOTH. Next, the N+1 data element i s C added t o the f i r s t sum wh i l e the 1 element i s subtracted C and then t h i s number i s d i v i d e d by N and becomes the C N/2+1 element i n the a r r a y SMOOTH, and so on. C For the elements I < N/2, SMOOTH(I)»DATA(I). C DIMENSION DATA(1023).SMOOTH(1023) C Read i n the experimental data and s t o r e i n array DATA. READ(1,50) DATA 50 FORMATUF12.5) C Prompt user f o r degree of smoothing. WRITE(6,60) 60 FORMAT('Degree of smoothing? (even number)') READ(5,70) N 70 FORMAT(12) N2*IFIX((FLOAT(N)/2) C D i s p l a y N2 t o operator as a check. WRITE(6,80) N2 80 FORMAT('N2« ',12) C Read the arr a y element < N2 from DATA d i r e c t l y i n t o the C arr a y SMOOTH. DO 150 1=1,N2 150 SMOOTH(I)-DATA(I) C Assign SMOOTH(N2)»0 and begin to sum the f i r s t N elements C from array DATA i n t o SMOOTH(N2). SMOOTH(N2)«0.0 DO 100 1-1,N 100 SMOOTH(N2)=SMOOTH(N2)+DATA(I) C The f o l l o w i n g are the l i m i t s of the smoothing o p e r a t i o n . N1-N2+1 N3=!023-n2 C The f o l l o w i n g procedure now performs the s l i d i n g average. DO 200 I«N1,N3 J1-I+N2 J2=I-N2 200 SMOOTH(I)"SMOOTH(I-1)+DATA(J1)-DATA(J2) N4-N3+1 C Next, f i l l up the a r r a y SMOOTH from N3+1 t o 1023 from C the ar r a y DATA. DO 300 I«N4,1023 300 SMOOTH(I)«DATA(I) C Now the elements from the a r r a y SMOOTH which were C obtained from the s l i d i n g average are now d i v i d e d C by N. DO 400 I-N2.N3 400 SMOOTH(I)-SMOOTH(I)/FLOAT(N) C Write the arr a y SMOOTH onto the f i l e assigned t o u n i t #2. WRITE(2,50) SMOOTH STOP END -56-C Program S2.GENFE. T h i s program w i l l compute the t h e o r e t i c a l C response f o r FE based upon the e x c i t a t i o n pulse and C experimental BE and BMEC-2 t r a n s i e n t responses. The C operator i s prompted t o enter the values f o r the r a t e C parameters t o c a l c u l a t e the t h e o r e t i c a l response. C The standard d e v i a t i o n between the experimental and C t h e o r e t i c a l responses i s c a l c u l a t e d and d i s p l a y e d to C the operator. F u r t h e r responses can then be computed C i n order t o minimize the standard d e v i a t i o n , or i f the C operator i s s a t i s f i e d , the program w i l l w r i t e out the C l a s t t h e o r e t i c a l response i n t o the f i l e -FEGEN by C e n t e r i n g -1 as the value of f i r s t r a t e parameter CAP. C DIMENSION SPULSE(1023),FE(1023),EXPFE(1023),BE(1023),SN2(1023) C The experimental t r a n s i e n t responses used i n t h i s C computation are assigned i n the program i n order to C ensure that the r i g h t responses have been used and C t o save time i n the running of the program. C The experimental e x c i t a t i o n pulse i s i n a r r a y SPULSE C The experimental BE response i s i n a r r a y BE. C The experimental BMEC-2 response i s i n a r r a y SN2. C The t h e o r e t i c a l FE response i s i n a r r a y EXPFE. CALL FTNCMD('ASSIGN 7»-FEGEN;') CALL FTNCMD('ASSIGN 1"RSX15LP;') CALL FTNCMD('ASSIGN 2-RSCX3FE;') CALL FTNCMD('ASSIGN 3-RSCX7BE;') CALL FTNCMD('ASSIGN 4-RSCX8M2;') C Read i n the experimental data. READ(1,50) SPULSE READ(2,50) EXPFE READ(3,50) BE READ(4,50) SN2 C Normalize a l l a r r a y s t o t h e i r peak v a l u e s . CALL NORM(SPULSE,1023) CALL NORM(EXPFE, 1023) CALL NORM(BE,1023) CALL NORM(SN2,1023) C TT i s the time increment i n ns. TT*1.0 C Prompt the operator f o r the ra t e parameter v a l u e s . 400 WRITE(6,20) C Read i n the r a t e parameters. READ(5,30) CAP,BETA,GAMMA,DELTA C Cap - Capture l i f e t i m e of the FE. C Beta - governs the s a t u r a t i o n of imp u r i t y s i t e s . C Gamma - governs the r e l e a s e of BE t o FE. C D e l t a - governs the r e l e a s e of BMEC-2 t o FE. C I f the f i r s t parameter CAP i s < z e r o , w r i t e out C the FE t r a n s i e n t response onto the f i l e -FEGEN C IF (CAP.LT.0) GOTO 300 CONST-(1.0-TT/CAP) C FE i s the FE t h e o r e t i c a l response. F E ( l ) - 0 i s the C i n i t i a l c o n d i t i o n . FE(1)-0.0 C Compute the FE t r a n s i e n t response i n the f o l l o w i n g C i t e r a t i v e process using the FE r a t e equation. C DO 100 I«1,1022 -57-SQPUL«SPULSE(I)**2 100 FE(I•1)-FE(I)*CONST+SQPUL+BETA*BE(I)*FE(I)•GAMMA*BE(I)+DELTA*SN2(I] C Normalize the t h e o r e t i c a l response and then c a l c u l a t e C the standard d e v i a t i o n between the FE experimental and C t h e o r e t i c a l responses u s i n g the s u b r o u t i n g LSTDEV. CALL NORM(FE,1023) CALL LSTDEV(FE,EXPFE,1023,1,1023,DEV) WRITE(6,60) DEV C Prompt the operator f o r new parameters. GOTO 400 C Operator has decided t o q u i t program. Write out C the l a s t t h e o r e t i c a l response onto the f i l e -FEGEN. 300 CONTINUE WRITE(7,50) FE 20 FORMAT('CAPTURE TIME,BETA,GAMMA,DELTA?') 30 F0RMAT(4F12.6) 60 FORMAT('THE STANDARD DEVIATION - * , F 1 2 . 5 ) 50 FORMAT(4F12.5) STOP END - 5 8 -C PROGRAM S2.GENBE. T h i s program w i l l compute the t h e o r e t i c a l C curve f o r the BE based upon the experimental FE and C BMEC-2 t r a n s i e n t responses. The operator i s prompted C t o enter the r a t e parameters t o determine the t h e o r e t i c a l C t r a n s i e n t response. The standard d e v i a t i o n between the C experimental and t h e o r e t i c a l responses i s c a l c u l a t e d C and p r i n t e d . Further responses can then be computed C i n order to minimize the standard d e v i a t i o n , or i f the C operator i s s a t i s f i e d , the program w i l l w r i t e out the C l a s t t h e o r e t i c a l response onto the f i l e 'BEGEN' by C e n t e r i n g -1 as the value of the f i r s t r a t e parameter, REL. C DIMENSION FE(1023),BE(1023),EXPBE(1023),SN2(1023) C The experimental t r a n s i e n t response used i n t h i s C c a l c u l a t i o n are assigned i n the program i n order to C ensure that the r i g h t responses have been used and t o C save time. C The experimental FE response i s i n a r r a y FE. C The experimental BE response i s i n a r r a y EZPBE. C The experimental BMEC-2 response i s i n a r r a y SN2. C The t h e o r e t i c a l BE response i s i n a r r a y BE. C CALL FTNCMD('ASSIGN 1-RSSCU2FE;') CALL FTNCMD('ASSIGN 2-RSCU3BE;') CALL FTNCMD('ASSIGN 3-RSCJ11M2;') CALL FTNCMD('ASSIGN 7--BEGEN;') C Read i n the experimental data READ(1,50) FE READ(2 ,50) EXPBE READ(3,50) SN2 C Normalize a l l the ar r a y s t o t h e i r peak v a l u e s . CALL NORM(FE,1023) CALL NORM(SN2,1023) CALL NORM(EXPBE,1023) C TT i s the time increment i n ns. TT=1.0 C Prompt the operator f o r r a t e parameters. A f t e r C each t h e o r e t i c a l c a l c u l a t i o n , prompt f o r new C parameters. 400 WRITE(6,20) C Read i n the r a t e parameters. READ(5,30) REL,BETA,GAMMA C R el 1 / l i f e t i m e of BE C Beta - governs the capture of FE onto BE t o form C BMEC-2 and the s a t u r a t i o n of imp u r i t y s i t e s . C Gamma - governs the r e l e a s e of BMEC-2 t o BE. C I f the f i r s t parameter REL i s < zero, w r i t e out the C BE t h e o r e t i c a l response onto the f i l e '-BEGEN'. C IF (REL.LT.0) GOTO 300 DECAY-1.0/REL CONST-(1.0-TT*DECAY) C BE i s the BE t h e o r e t i c a l response. BE(1)»0.0 i s the C i n i t i a l c o n d i t i o n . BE(1)-0.0 C C C a l c u l a t e the BE t h e o r e t i c a l response i n the f o l l o w i n g C i t e r a t i v e process using the BE r a t e equation. DO 100 1-1,1022 -59-100 BE (I «• 1 ) -BE (I ) *CONST+FE (I) -BETA*FE (I) *BE (I ) +GAMMA*SN2 (I ) C Normalize the t h e o r e t i c a l response and then c a l c u l a t e C the standard d e v i a t i o n between the experimental and C t h e o r e t i c a l BE response u s i n g the subrouting LSTDEV. CALL NORM(BE,1023) C C CALCULATE THE STANDARD DEVIATION BETWEEN THE THEORETICAL C CURVE AND THE EXPERIMENTAL CURVE C CALL LSTDEV(BE,EXPBE,1023,1,1023,DEV) WRITE(6,60) DEV C Prompt f o r new parameters. GOTO 400 C Operator has decided t o q u i t program. Write out the C l a s t t h e o r e t i c a l response onto f i l e -BEGEN. 300 CONTINUE WRITE(7,50) BE 20 FORMAT('DECAY TIME,BETA,GAMMA?') 30 F0RMAT(3F12.6) 50 FORMAT(4F12.5) 60 FORMAT('THE STANDARD DEVIATION = ',F12.5) STOP END - 6 0 -Program S2.GENM2. This program w i l l c a l c u l a t e the t h e o r e t i c a l curve f o r BMEC-2 based upon the experimental FE, BE and BMEC-3 t r a n s i e n t responses. The operator i s prompted t o enter the r a t e parameters t o c a l c u l a t e the t h e o r e t i c a l t r a n s i e n t response. The standard d e v i a t i o n between the experimental and t h e o r e t i c a l responses i s c a l c u l a t e d and shown t o the operator. Further curves can be then com-puted t o minimize the standard d e v i a t i o n , or i f the operator i s s a t i s f i e d , the program w i l l w r i t e out the l a s t t h e o r e t i c a l response i n t o the f i l e '-M2GEN* by e n t e r i n g -1 as the f i r s t r a t e parameter. DIMENSION BE(1023),SN2(1023),EXPM2(1023),FE(1023),SN3(1023) The experimental t r a n s i e n t responses used i n t h i s c a l c u l a t i o n are assigned i n the program i n order to C ensure that the r i g h t responses have been used and t o C save time i n the running of the program. C The experimental FE response i s i n a r r a y FE C The experimental BE response i s i n a r r a y BE C The experimental BMEC-2 response i s i n a r r a y EXPM2 C The experimental BMEC-3 response i s i n a r r a y SN3 CALL FTNCMD('ASSIGN 1-RSCJ8FE;') CALL FTNCMD('ASSIGN 2-RSCJ10BE;') CALL FTNCMD('ASSIGN 3-RSCJ12M3;') CALL FTNCMD('ASSIGN 4--M2GEN;') CALL FTNCMD('ASSIGN 7-RSCJ11M2;') C Read i n the experimental data. READ(1,50) FE READ(2,50) BE READ(3,50) SN3 READ(7,50) EXPM2 C Normalize a l l the a r r a y s t o t h e i r peak v a l u e s . CALL NORM(BE,1023) CALL NORM(FE,1023) CALL NORM(SN3,1023) CALL NORM(EXPM2,1023) C TT i s the time increment i n ns. TT=1.0 C Prompt the operator f o r rat e parameters. 400 WRITE(6,20) C Read i n ra t e parameters. READ(5,30) REL,BETA,GAMMA C R e l - 1 / l i f e t i m e of BMEC-2 C Beta - governs the capture of FE onto BMEC-2 t o form C BMEC-3. C Gamma - governs the r e l e a s e of BMEC-3 t o BMEC-2. C I f the f i r s t parameter REL i s < zer o , w r i t e out the C BMEC-2 t h e o r e t i c a l response onto the f i l e -M2GEN. IF (REL.LT.0) GOTO 300 C SN2 i s the BMEC-2 t h e o r e t i c a l response. SN2(1)-0.0 DECAY-1.0/REL CONST-(1.0-TT*DECAY) C C a l c u l a t e the BMEC-2 t h e o r e t i c a l response i n the f o l l o w i n g C i t e r a t i v e process using the BMEC-2 r a t e equation. DO 100 1-1,1022 100 SN2(I+1)-SN2(I)*CONST+FE(I)*BE(I)-BETA*FE(I)*SN2(I)•GAMMA*SN3(I) C C Normalize the t h e o r e t i c a l response and then c a l c u l a t e -61-C the standard d e v i a t i o n between the BMEC-2 experimental C and t h e o r e t i c a l response using the subrouting LSTDEV. CALL NORM(SN2,1023) C CALL LSTDEV(SN2,EXPM2,1023,1,1023,DEV) C Write the standard d e v i a t i o n t o the operator and then C request new parameters f o r a new t h e o r e t i c a l response. WRITE(6,60) DEV C Prompt f o r new parameters. GOTO 400 C Operator has decided t o q u i t program. Write out l a s t C l a s t t h e o r e t i c a l curve onto f i l e -M2GEN. 300 CONTINUE WRITE(4,50) SN2 C The f o l l o w i n g are format statements. 20 FORMAT('DECAY TIME,BETA,GAMMA?') 30 FORMAT(3F12.6) 50 FORMAT(4F12.5) 60 FORMAT('THE STANDARD DEVIATION « *,F12.5) STOP END - 6 2 -C Program S2.GENM3. Th i s program w i l l c a l c u l a t e the t h e o r e t i c a l C curve f o r BMEC-3 based upon the experimental FE and BMEC-2 C t r a n s i e n t responses. The operator i s prompted to enter C the r a t e parameters t o c a l c u l a t e the t h e o r e t i c a l C t r a n s i e n t response. The standard d e v i a t i o n between the C experimental and t h e o r e t i c a l responses i s c a l c u l a t e d and C shown t o the o p e r a t o r . Further curves can be then com-C puted t o minimize the standard d e v i a t i o n , or i f the C operator i s s a t i s f i e d , the program w i l l w r i t e out the l a s t C t h e o r e t i c a l response i n t o the f i l e '-M3GEN' by e n t e r i n g C -1 as the f i r s t r a t e parameter. DIMENSION SN2O023),SN3(1023),EXPM3(1023),FE(1023) C C The experimental t r a n s i e n t responses used i n t h i s C c a l c u l a t i o n are assigned i n the program i n order to C ensure t h a t the r i g h t responses have been used and t o C save time. CALL FTNCMD('ASSIGN 1-RSCJ11M2;') CALL FTNCMD('ASSIGN 2-RSCJ12M3;') CALL FTNCMD('ASSIGN 3-RSCJ8FE;') CALL FTNCMD('ASSIGN 4--M3GEN;') C The experimental FE response i s i n a r r a y FE C The experimental BE response i s i n a r r a y BE C The experimental BMEC-3 response i s i n a r r a y EXPM3 C Read i n the experimental data. READ(1,50) SN2 READ(2,50) EXPM3 READ(3,50) FE C Normalize a l l the a r r a y s t o t h e i r peak v a l u e s . CALL NORM(FE,1023) CALL NORM(SN2,1023) CALL NORM(EXPM3,1023) C TT i s the time increment i n ns. TT=1 .0 C Prompt operator f o r the rat e parameters. A f t e r the C t h e o r e t i c a l response has been computed, prompt again C f o r new parameters. 400 WRITE(6 r20) C Read i n the rat e parameters. READ(5,30) REL,BETA C R e l - 1 / l i f e t i m e of BMEC-3 C Beta - governs the capture of FE onto BMEC-3 to form C BMEC-4. C I f the f i r s t parameter REL i s < z e r o , w r i t e out the C BMEC-3 t h e o r e t i c a l response onto the f i l e -M3GEN. IF (REL.LT.0) GOTO 300 CON 1« (1 .0-TT/REL) SN3(1)«0.0 C SN3 i s the BMEC-3 t h e o r e t i c a l response. C C a l c u l a t e the BMEC-3 t h e o r e t i c a l response i n the f o l l o w i n g C i t e r a t i v e process using the BMEC-3 r a t e equation. C DO 100 1-1,1022 100 SN3(I+1)«SN3(I )*CON1«-FE(l)*SN2(I)-BETA*FE(I)*SN3(I) C C Normalize the t h e o r e t i c a l response end then c a l c u l a t e C the standard d e v i a t i o n between BMEC-3 experimental C and t h e o r e t i c a l responses using the subrouting LSTDEV. CALL NORM(SN3,1023) 63-CALL LSTDEV(SN3,EXPM3,1023,1,1023,DEV) C Write the standard d e v i a t i o n t o the operator and then C request new parameters f o r a new t h e o r e t i c a l response, WRITE(6,60) DEV C Prompt operator f o r new parameters. GOTO 400 C Operator has decided t o q u i t program. Write out l a s t C l a s t t h e o r e t i c a l curve onto f i l e -M3GEN. C The f o l l o w i n g are format statements. 300 CONTINUE WRITE(4,50) SN3 20 FORMAT('RELEASE TIME,BETA?') 30 F0RMAT(2F12.6) 50 FORMATUF12.5) 60 FORMAT ('DEVIATION FROM EXP CURVE «= ',F12.5) STOP END - 64 -C Program S2.XPL0T. T h i s program w i l l p l o t up t o four f i l e C of data on the same graph provided the data i s assigned C t o u n i t s 1-4. The format f o r the data i s assumed to C be 4F12.5 and t h a t each f i l e holds l e s s than 1023 C data p o i n t s . The operator t h e r e f o r e a s s i g n s the f i l e s C to be p l o t t e d onto u n i t s 1-4 and he i s then prompted C f o r the number of f i l e s t o be p l o t t e d ( <4 ). C REAL DATAO023), SINT(1023) C I n i t i a l i z e the a r r a y SINT which w i l l be the h o r i z o n t a l C a x i s f o r the graph and represents the time i n ns. DO 100 1 = 1,1000 100 SINT(I)=FLOAT(I) C C I n i t i a l i z e the p l o t t i n g r o u t i n e by s e t t i n g the s c a l e C of the graph, l a b e l l i n g the a x i s and a l s o s e t t i n g the C s i z e of the graph. CALL ALSIZE(10.,7.0) CALL ALAXIS ('TIME Scale (nsec)',17,'INTENSITY',9) CALL ALSCALC0.,1000.,0.,1.0) C Next, the user i s prompted f o r the number of f i l e s C t o be p l o t t e d . WRITE(6,20) 20 FORMAT(' ENTER « OF PLOTS') C Read i n the number of f i l e s . READ(5,30) M 30 FORMAT(12) 40 F0RMAT(4F12.5) C C S t a r t i n g from u n i t 1 ( i t i s assumed that at l e a s t one C f i l e w i l l be p l o t t e d using t h i s program), the data i s C f i r s t read i n from that f i l e and s t o r e d i n the array C DATA. DO 500 L=1,M READ(L,40) DATA SDATA*0.0 C Next the data i n the array DATA i s normalized. C DO 200 1 = 1 , 1023 IF (DATA(I).GT.SDATA) SDATA-DATA(I) 200 CONTINUE DO 300 1=1,1023 DATA(I)-DATA(I)/SDATA 300 CONTINUE C The data i s then p l o t t e d using the subrouting ALGRAF. C Only the f i r s t 1000 p o i n t s are p l o t t e d . Each subsequent C p l o t i s then placed on the same graph. CALL ALGRAF(SINT,DATA,-1000,0) C I f M > 1, then t h i s procedure i s repeated and another C f i l e i s p l o t t e d . T h i s continues u n t i l a l l M f i l e s have C been p l o t t e d . 500 CONTINUE C The subroutine PLOTND i s now c a l l e d t o terminated the C p l o t r o u t i n e s . CALL PLOTND STOP END -65-C Program S2.LOGXP. T h i s program w i l l f i t an e x p o n e n t i a l l i n e C t o the data range s p e c i f i e d by the op e r a t o r . Subroutine C LEAST i s a program which computes a s t r a i g h t l i n e by C l e a s t squares d e v i a t i o n . Two p l o t s are then made, C one f i r s t of the data region which has been f i t t e d C along w i t h the e x p o n e n t i a l l i n e and then a p l o t of the C whole t r a n s i e n t response. DIMENSION X(1000),Y(1000),DATA(1023),TIME(1000) C I n i t i a l i z e the a r r a y TIME, which i s the h o r i z o n t a l C a x i s used i n the p l o t t i n g r o u t n i n e s . DO 400 1-1,1000 TIME(I)-FLOAT(I) 400 CONTINUE C Prompt operator f o r data range to be f i t t e d t o an C e x p o n e n t i a l l i n e . WRITE(6,10) 10 FORMAT('SPECIFY BOUNDARY (START AND FINISH)') READ(5,20) NI,N2 20 F0RMAT(2I5) C Read i n the experimental data. READ(1,30) DATA 30 FORMAT(4F12.5) C Assign the data from the range s e l e c t e d t o the ar r a y s C X and Y, f i r s t t a k i n g the Log of the data before s t o r i n g C i t i n Y. N-N2-N1+1 DO 100 1-1,N Y(I)»ALOG(DATA(I+N1-1)) X(I)-FLOAT(l+N1-1) 100 CONTINUE C Compute the best f i t to the data using the leas t - s q u a r e s C technique. CALL LEAST(N,X,Y,SLOPE,SINT,DEVS,DEVI) C D i s p l a y the slope (which i s the negative inverse of C e x p o n e n t i a l time constant) and the i n t e r c e p t (a m u l t i -C p l i c a t i v e constant) and t h e i r a s s o c i a t e d e r r o r s . WRITE(6,40) SLOPE,DEVS,SINT,DEVI 40 FORMAT('THE SLOPE=',F10.5,'DEV-',F10.5,'INT=*,F10.5,*DEV=',F10.5) WRITE(6,60) C The p l o t t i n g i s now performed. 60 FORMAT('HIT RETURN TO CONTINUE') C C a l c u l a t e the data range t o be p l o t t e d . M1-N1-40 M2-N2+40 M-M2-M1 C Operator requests f i r s t p l o t . READ(5,50) N3 50 FORMAT(12) DO 300 I-M1,M2 J-I-M1+1 X(J)-FLOAT(I) Y(J)«DATA(I) 300 CONTINUE C The data i s now p l o t t e d . The subroutine ALPLOT C uses the ALGRAF r o u t i n e s . CALL ALPLOT(X,M,Y,M,6.,3.,*TIME',4,'DATA',4) DO 200 I-M1,M2 J-I-M1+1 Y(J)-EXP(SLOPE*FLOAT(I)+SINT) -66-200 CONTINUE C The ex p o n e n t i a l l i n e i s next p l o t t e d . CALL ALGRAF(X,Y,-M,0) C A second p l o t i s now made u t i l i z i n g the e n t i r e C t r a n s i e n t response. CALL ALPLOT(TIME,1000,DATA,1000,6.,3.,'TIME',4,'DATA',4) CALL ALGRAF(X,Y,-M,0) C P l o t r o u t i n e s are now terminated. CALL PLOTND STOP END - 6 7 -C Subroutine ALPLOT. T h i s subroutine i s a p l o t package C t o provide quick p l o t s , w i t h the input parameters C s p e c i f y i n g the s i z e and a x i s l a b e l s . The ALGRAF C r o u t i n e s are u t i l i z e d i n t h i s program. C SUBROUTINE ALPLOT(X,MX,Y,MY,SX,SY,XMESS,NX,YMESS,NY) C C T h i s subrouting w i l l p l o t the two a r r a y Z and Y C using the ALGRAF r o u t i n e s . C X - H o r i z o n t a l line,NX»# of p o i n t s , SX»size of X-axis C Y - V e r t i c a l l i n e , NY«# of p o i n t s , SY-size of Y-axis C XMESS - message w r i t t e n t o X-axis,NX - l e n g t h of mess C YMESS - message w r i t t e n t o Y-axis,NY - l e n g t h of mess DIMENSION X(MX),Y(MY) LOGICAL*! XMESS(NX),YMESS(NY) RX1=X(1) RX2=X(MY) CALL ALSIZE(SX,SY) CALL ALAXIS(XMESS,NX,YMESS,NY) CALL ALSCAL(RX1,RX2,0.0,0.0) CALL ALGRAF(X,Y,MY,0) RETURN END -68-A l l f i l e s are sto r e d on the *FS tape RE0280 Vol=BACKUP (see Lab notebook f o r f u r t h e r d e t a i l s ) F i l e s used i n the programs S2.GENFE,-BE,-M2,-M3. T»4.2K Laser P u l s e : RSX15LP FE - RSCX3FE c o r r e c t e d : RSX3FE - RSX2B1 BE - RSCX7BE RSX7BE - RSX2B1*scale f a c t o r BMEC-2 - RSCX6M3 RSX6M3 - RSX2B1 BMEC-3 - RSCX8M2 RSX8M2 - RSX2B1*scale f a c t o r Scale f a c t o r « 597/6974 F i l e s used i n the programs S2.GENFE,-BE,-M2,-M3. T=4.2K (low e x c i t a t i o n ) Laser P u l s e : RSU7LP FE - RSCCU2FE c o r r e c t e d : RSU2FE - RSU1B1 BE - RSCU3BE RSU3BE - RSU1B1 BMEC-2 - RSCU2M2 RSU2M2 - RSU1B1 F i l e s used i n the programs S2.GENFE,-BE,-M2,-M3. T*1.8K Laser P u l s e : RSJ7LP FE - RSCJ8FE c o r r e c t e d : RSJ8FE - RSJ9B3 BE - RSCJ1OBE RSJ10BE - RSJ9B3 BMEC-2 - RSCJ11M2 RSJ11M2 - RSJ9B3 BMEC-3 - RSCJ12M3 RSJ12M3 - RSJ9B3 F i l e s used i n the programs S2.GENFE,-BE,-M2,-M3. T=1.BK (low e x c i t a t i o n ) Laser P u l s e : RSJ7LP FE - RSCJ8FE BE - RSCJ14BE RS - i n d i c a t e s that the experimental data has been smoothed t o some e x t e n t . For f u r t h e r inform-a t i o n on the above f i l e s , see Lab notebooks. - 6 9 -BIBLIOGRAPHY -70-1. A. S. KAMINSKII and YA. E. POKROVSKII. Zh. Eksp. Teor.Fiz.Pis'ma Red. J J _ , 381 ( 1 9 7 0 ) ; Engl.transl.Sov. Phys. JETP Lett. J J _ , 225 ( 1 9 7 0 ) . 2 . A. S. KAMINSKII, YA. E. POKROVSKII, and N. V. ALKEEV. Zh. Eksp. Teor. F i z . 5 9 , 1937 ( 1 9 7 0 ) ; Engl, t r a n s l . Sov. Phys. JETP, 3_2, 1048 ( 1 9 7 1 ) . 3. YA. E. POKROVSKII, A. S. KAMINSKII, and K. SVISTUNOVA. In Proceedings of the Tenth International Conference on the Physics of Semiconductors. Cambridge, Mass. 1 9 7 0 . Edited by S. P. K e l l e r , J.C. Hensel, and F. Stern. USAEC Division of Technical Information, Oak Ridge, TN. 1 9 7 0 . p.5 0 4 . 4 . YA. E. POKROVSKII. Phys. Status S o l i d i a, J J _ , 3 8 5 ( 1 9 7 2 ) . 5 . K. KOSAI and M. GERSHENZON. Phys. Rev. B, 9 , 723 ( 1 9 7 4 ) . 6 . R. SAUER. Phys. Rev. Lett. 3J_, 376 ( 1 9 7 3 ) . 7 . M.L.W. THEWALT. So l i d State Commun. 2J_, 937 ( 1 9 7 7 ) . 8 . M.L.W. THEWALT. Can. J. Phys. 5 5 , 1463 ( 1 9 7 7 ) . 9 . M.L.W. THEWALT. Ph.D. Thesis. University of B r i t i s h Columbia, Vancouver, B.C. 1 9 7 7 . 1 0 . M.L.W. THEWALT. Phys. Rev. Lett. 3 8 , 521 ( 1 9 7 7 ) . 1 1 . See, for instance, S o l i d State Physics, Vol 3 2 . Edited by H. Ehrenreich, F. Seitz and D. Turnbull, Academic Press, New York ( 1 9 7 7 ) . 1 2 . T. OHYAMA, Phys. Rev. B, 2 3 , 5 4 4 5 ( 1 9 8 1 ) 1 3 . R. M. FEENSTRA and T. C. McGILL. Solid State Commun. . 2J[, 937 ( 1 9 7 7 ) . 1 4 . W. SCHMID, Phys. Stat. Sol(b) 8 4 , 529 ( 1 9 7 7 ) . 1 5 . H. NAKAYAMA, T. NISHINO and Y. HAMAKAWA, Jap. J . of Appl. Phys. J_9, 501 ( 1 9 8 0 ) . 1 6 . R. B. HAMMOND and R. N. SILVER, S o l i d State Commun. 2 8 , 993 ( 1 9 7 8 ) . 1 7 . M.L.W. THEWALT. M.Sc. Thesis. University of B r i t i s h Columbia, Vancouver, B.C. 1 9 7 5 . 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0085045/manifest

Comment

Related Items