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Optical absorption and photoconductivity in magnesium oxide crystals Peria, William Thomas 1957

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%[\t P«tlier0rtg of ^rtttslj Columbia Faculty of Graduate Studies PROGRAMME OF THE F I N A L O R A L E X A M I N A T I O N FOR THE DEGREE OF D O C T O R O F P H I L O S O P H Y WILLIAM T H O M A S PERIA M. A. Sc., University of British Columbia, 1951 TUESDAY, AUGUST 6th, 1957, at 2:30 p.m. IN ROOM 300, PHYSICS BUILDING C O M M I T T E E I N C H A R G E D E A N G . M . S H R U M , Chairman A. M. CROOKER K. C. MANN R. E . BURGESS J. B. GUNN J. NORRIS F. NOAKES R. D. JAMES G. B. PORTER External Examiner Dr. EUGENE B. HENSLEY University of Missouri OPTICAL ABSORPTION AND PHOTOCONDUCTIVITY IN MAGNESIUM OXIDE CRYSTALS A B S T R A C T The purpose of this investigation was the determination of the nature of certain imperfections in magnesium oxide crystals. Optical absorption and photoconductivity spectra of specimens cleaved from a number of larger pieces were measured. The effect of vacuum heating, of non- stoichiometry and of ultraviolet and x-ray irradiation were investigated. The nature of the imperfections could not be inferred from the experi mental results but an energy level diagram consistent with all the data has been deduced. A comparison of the present work with pertinent data from the litera ture is presented and a basic error in previous photoconductivity mea surements is pointed out. A method for the determination of the sign of the charge carriers excited during photoconductivity measurements is described. GRADUATE STUDIES Field of Study: Physics Electromagnetic Theory . . . . . . W. Opechowsh- Theory of Measurement .. . _. A. M. Crook;', Quantum Mechanics . . . . . . G. M. Volkoff Nuclear Physics . . . . . .• K. C. Mam-, Dielectrics and Magnetism . . . . . A. J . Dekker and C. G. Eicholtz Spectroscopy ... . A . M . Crooker Chemical Physics .... . . . A. J . Dekker Other Studies: Advanced Quantum Mechanics . . . . . . . L. Teng Mathemetical Foundations of Statistical Mechanics . P. C. Eosenbloom OPTICAL ABSORPTION AND PHOTOCONDUCTIVITY IN MAGNESIUM OXIDE CRYSTALS by Williara Thomas Peria M.A. Sc. University of B r i t i s h Columbia, 1951 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1957 In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements f o 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 available f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representative. It i s understood that copying or publication 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. The University of B r i t i s h Columbia, Vancouver £, Canada. Department Date i i ABSTRACT The purpose of t h i s investigation was the determination of the nature of certain imperfections i n magnesium oxide c r y s t a l s . Optical absorption and photoconductivity spectra of specimens cleaved from a number of larger pieces were measured. The e f f e c t s of vacuum heating, of non-stoichiometry and of u l t r a  v i o l e t and X-ray i r r a d i a t i o n were investigated. The nature of the imperfections could not be i n f e r r e d from the experimental results but an energy l e v e l diagram consistent with a l l the data has been deduced. A comparison of the present work with pertinent data from the l i t e r a t u r e i s presented and a basic error i n previous photoconductivity measurements i s pointed out. A method for the determination of the sign of the charge c a r r i e r s excited during photoconductivity measurements i s described. i i i TABLE OF CONTENTS Section : :, Introduction . . . . . . . . . . . . . . . . 1 A Experimental Details . . . . . . . . . . . . . 5 B Results 10 B. l * O p tical Absorption Measurements . . . 10 2 Analysis of Photoconductivity Data . . 11 3 Dependence of Photocurrent on Light Intensity and E l e c t r i c F i e l d . . . . 14 4 Evidence that Photocurrents are a Bulk Effect . , 14 5 Space Charge Formation . . . . . . . . 15 6 Properties of Crystals as Received . . 16 7 Heat Treatment Studies 20 8 Excess Magnesium Crystals . . . . . . 21 9 The E f f e c t of U l t r a v i o l e t I r r a d i a t i o n . . . . . 22 10 The E f f e c t of X-Irradiation 23 11 Sign of the Charge Carrie r s 26 C Discussion . . . . . . . . . . . . . . . . . 2 9 C. l Optical Absorption 29 2 Discussion of the Factors Involved in the Photoconductive Y i e l d . . . . . 30 3 The Dependence of the Photocurrent on Light Intensity and E l e c t r i c F i e l d 33 4 Evidence that the Photocurrents are Due to a Bulk E f f e c t 37 5 Formation of Space Charge F i e l d s . . . 38 •Sections B and C are divided into 11 subsections, each i n such a way that the results described i n B.l are d i s  cussed i n C.l and so on. i v TABLE OF CONTENTS (continued) Section Page C„6 Properties of Crystals as Received . . . . 43 7 Heat Treatment Studies 47 8 Excess Mg Crystals 50 9 U l t r a v i o l e t I r r a d i a t i o n .• 52 10 X-Ray I r r a d i a t i o n 56 11 Sign of the Charge C a r r i e r s 64 D Conclusions .69 E Comparison with Previous Work . . . . . . . . . 7 4 T i t l e INDEX TO FIGURES v F i g u r e No. S c h e m a t i c Arrangement o f the P h o t o c o n d u c t i v i t y A p p a r a t u s 1 Mounting o f the C r y s t a l f o r P h o t o c o n d u c t i v i t y Measurements 2 Development and Removal o f Space Charge 3 T y p i c a l A b s o r p t i o n S p e c t r a o f MgO C r y s t a l s as R e c e i v e d 4 T y p i c a l P h o t o c o n d u c t i v i t y and A b s o r p t i o n S p e c t r a 5 R e s o l u t i o n of a T y p i c a l P h o t o c o n d u c t i v i t y Spectrum i n t o Two G a u s s i a n Bands 6 E f f e c t o f Heat Treatment on the Background A b s o r p t i o n 7 P h o t o c o n d u c t i v i t y and A b s o r p t i o n o f C r y s t a l s Heated i n Vacuum a t D i f f e r e n t Temperatures 8 A b s o r p t i o n Spectrum Due t o H e a t i n g i n Magnesium Vapor 9 The E f f e c t o f E x c e s s Magnesium on the Background A b s o r p t i o n o f MgO 10 The E f f e c t o f E x c e s s Magnesium on the Background A b s o r p t i o n o f MgO 11 The E f f e c t o f E x c e s s Magnesium on the Background A b s o r p t i o n o f MgO 12 E f f e c t o f E x c e s s Mg on P h o t o c o n d u c t i v i t y 13 O p t i c a l A c t i v a t i o n o f P h o t o c o n d u c t i v i t y 14 E f f e c t o f U l t r a v i o l e t I r r a d i a t i o n on Photoconduc t i v i t y i n MgO 15 I n c r e a s e i n O p t i c a l D e n s i t y by I r r a d i a t i o n i n 5 ev Band 16 Induced O p t i c a l A b s o r p t i o n Due t o I r r a d i a t i o n i n 4 ev Band 17 B u i l d u p o f X-Ray Induced A b s o r p t i o n 18 A b s o r p t i o n S p e c t r a o f X-Rayed C r y s t a l s 19 Decay o f X-Ray Induced A b s o r p t i o n 20 P h o t o c o n d u c t i v i t y i n X-Rayed MgO 21 VI INDEX TO FIGURES -(continued) T i t l e Figure No, Photoconductivity i n X-Rayed MgO 22 Effect of X-Irradiation on the Photoconductivity of U l t r a v i o l e t Activated MgO 23 Bleaching of Xr-Ray Induced Absorption at 4.2 ev by 2.3 ev Quanta 24 Bleaching of X-Ray Induced Absorption at 2.3 ev by 2.3 ev Quanta 25 Bleaching of X-Ray Induced Photoconductivity by 2.3 ev Quanta 26 Determination of the Sign of Charge Ca r r i e r s Excited i n 4 ev Band 27 Determination of the Sign of Charge Ca r r i e r s Excited i n 5 ev Band 28 Determination of the Sign of Charge Carrie r s i n an X-Rayed Cryst a l 29 Possible Mechanisms for the Loss of Free C a r r i e r s 30 Proposed Energy Level Schemes for MgO 31 Thermal Decay of X-Ray Induced U l t r a v i o l e t Absorption at Room Temperature 32 -Idealized F i e l d D i s t r i b u t i o n s I l l u s t r a t i n g the Method of Determining the Sign of the Charge Carrie r s 33 INDEX TO TABLES T i t l e Absorption and Photoconductivity at 5.0 ev Photoconductive Y i e l d of a Number of Specimens Fractional Change in Photoconductive Y i e l d by Bleaching with 2.3 ev Quanta Calculated Thermal Ionization Energies of the Shallow Electron Traps v i i i ACKNOWLEDGEMENTS Support for t h i s work was provided by the United States Army Signal Corps through contracts with the University of Minnesota Electron Tube Research Laboratory. The author wishes to express his gratitude to Professor W. G. Shepherd, di r e c t o r of the Laboratory, for the provision of f a c i l i t i e s and f o r he l p f u l discussions. Thanks are due also tboProfessor A. J. Dekker whose encouragement enabled the writer to proceed to graduate study and who discussed a l l phases of the work. B. V. Haxby, R. G. Lye, R. W. Soshea and P. Wargo have provided a b e n e f i c i a l exchange of ideas. Appreciation to Joan Theresa Peria f o r her encouragement and forbearance i s hereby a f f e c t i o n a t e l y extended. 1 INTRODUCTION The increasing importance of semiconductors and i n s u l a t o r s i n the modern technology need hardly be emphasized. S o l i d state devices are finding more and more app l i c a t i o n i n most en deavors involving the use of e l e c t r o n i c c i r c u i t s . As i s always the case, increased a p p l i c a t i o n c a l l s f o r increased understand ing of the physical properties of the materials involved. Since many of the useful and i n t e r e s t i n g properties of these solids stem from the presence of deviations of the l a t t i c e from s t r i c t p e r i o d i c i t y , a study of such s o l i d s nearly always consists of a study of the l a t t i c e imperfections, whether they occur naturally or are purposely introduced. Deviations from p e r i o d i c i t y can introduce, into the f o r  bidden energy region c h a r a c t e r i s t i c of the unperturbed l a t t i c e , l o c a l i z e d energy l e v e l s , i . e . , the imperfect s o l i d has some eigenstates whose eigenvalues l i e i n the normally forbidden region of energy and whose eigenfunctions are l o c a l i z e d i n the region of the imperfection rather than extending through out the whole l a t t i c e . The determination of the l o c a t i o n of such l e v e l s on the energy scale i s a f i r s t step i n the study of the nature of the corresponding imperfections. However, i t i s possible that the i n v e s t i g a t i o n of the energy l e v e l scheme for a p a r t i c u l a r imperfect s o l i d may have some importance beyond the understanding of the physical properties of t h i s s o l i d alone. One has only to consider the v i t a l role that the determination of atomic and nuclear energy l e v e l schemes has played i n the development of physics to r e a l i z e the 2 significance of t h i s statement. Of course, a knowledge of the scheme alone does not permit the deduction of the nature of the imperfections. Inferences as to the constitution of a p a r t i c u l a r imperfection may be made i n a number of ways; (1) By studying the properties of t h i s imperfection by i t s e l f and comparing the observed behavior with the properties predicted by various t h e o r e t i c a l models, (2) By observing reactions of the imperfections among themselves and with other types, (3) By introducing imperfections i n such a way as to favor the production of a s p e c i f i c type. The f i r s t group of compounds to receive a thorough investigation of i t s structure sensitive ( i . e . , imperfection- controlled) properties was the monovalent i o n i c a l k a l i halide group. These materials were studied extensively by the Gottingen school under Pohl, beginning about 1930. These experiments might be regarded as the beginning of semiconduc tor physics. Many of the concepts employed i n current research on semiconductors arose i n connection with the work on these a l k a l i halides. Of course many other groups of s o l i d s are currently receiving much attention. Of these the group which i s probably;-most closely related to the a l k a l i halides i s the group of alk a l i n e earth oxides, i . e . , divalent i o n i c compounds. In addition to the interest i n these compounds because of t h e i r analogy to the better known monovalent i o n i c compounds, they a l l have important•device applications. Barium and strontium oxides are used i n thermionic cathodes while magnesium oxide i s a 3 very e f f i c i e n t secondary electron emitter. Of these three compounds magnesium oxide i s by f a r the easiest to obtain and work with i n single c r y s t a l form. A concerted e f f o r t to understand the secondary emitting c h a r a c t e r i s t i c s of t h i s material has been underway i n the Electron Tube Laboratory of the University of Minnesota for several years. Because i t was believed that the secondary emission i s influenced by certain types of imperfections, studies of the e l e c t r i c a l and o p t i c a l properties of these imperfections have been car r i e d out as an i n t e g r a l part of t h i s program. As mentioned previously, c r y s t a l l i n e imperfections lead to l o c a l i z e d energy l e v e l s l y i n g i n the forbidden energy gap. E x c i t a t i o n of electrons to or from these l e v e l s leads of course to o p t i c a l absorption bands which would not be present i n the perfect c r y s t a l . The absorption processes may lead to free charge c a r r i e r s (electrons or holes) either d i r e c t l y or by subsequent thermal steps. In e i t h e r case photoconductivity measurements may lead to a d d i t i o n a l information which w i l l a i d i n the construction of an energy l e v e l diagram. It i s also conceivable that imperfections not detectable i n o p t i c a l absorption may be detected i n photoconductivity (or vice versa) since the l i m i t s of detection i n the two cases are governed by d i f f e r e n t properties of the center and the host c r y s t a l . This w i l l be discussed i n more d e t a i l below. The work to be described i n t h i s thesis was aimed at a 4 determination of the nature of certain of the color centers commonly observed i n MgO c r y s t a l s , by the measurement of o p t i c a l absorption and photoconductivity of specimens treated i n various ways. Insofar as an unambiguous energy l e v e l scheme has not been determined, not even the f i r s t step i n the o r i g i n a l purpose has been achieved. On the other hand, by proceeding i n each of the three fashions enumerated previous l y , i t has been possible to make certain inferences concerning the properties of some of the color centers and the r e l a t i o n s between them which at the very l e a s t , suggest further, more c r u c i a l experiments. 5 A. EXPERIMENTAL DETAILS Unless otherwise noted the c r y s t a l s used i n these experi ments were obtained from the Norton Company, Niagara F a l l s , New York. Only those pieces which showed no v i s i b l e absorp t i o n were used. From these larger pieces th i n slabs could be e a s i l y cleaved out. These were usually about 5 x 10 mm on the faces and from 0.2 to 1.0 mm thick. Some of the c r y s t a l s were heated i n vacuum before use. Such heat treatments were carried out i n a small furnace operating inside a b e l l j a r . The pressure was usually about 5 x 10 ^ mm Hg. To prevent contamination of the c r y s t a l faces during the heat treatment, they were placed i n a boat ground from a large MgO c r y s t a l and a MgO slab l i d was t i e d on with molybdenum wire. Specimens were ad d i t i v e l y colored with Mg by heating them in steel bombs containing Mg metal. Two-chamber bombs with independent temperature controls were used. In t h i s way the temperature of the c r y s t a l s ( i n the hotter chamber) and the vapor pressure of the metal could be varied independently. The bombs were assembled i n a i r by means of a tapered conical j o i n t . Evacuation was not necessary since the metal r e a d i l y combined with the oxygen and nitrogen at the temperatures employed. The crystals were heated at temperatures i n the range 1100°C to 1350°C, i n Mg pressures from 1 to 7500 mm Hg, and f o r times from 1 to 50 hours. On some occasions the bombs were quenched by dropping into water, on others they were allowed to cool slowly. 6 The apparatus employed for the measurement of photoconduc t i v i t y i s shown schematically i n Figure I. Light from the source A was focused by the 12-inch diameter e l l i p t i c a l aluminum mirror B onto the entrance s l i t of a Bausch and Lomb- grating monochromator C, having a dispersion of 33 angstrom/mm. The monochromator was normally used with s l i t s of 3 mm or l e s s i n o width so that the band width was normally about 100 A or l e s s . At 5 ev t h i s corresponds to an energy range of 0.2 ev i n the monochromator output. To remove the higher order dispersions from the monochromator output, sharp-cut glass f i l t e r s could be inserted at D. These were prevented from overheating when necessary by 2 cm of water between fused quartz plates (E). The output from the monochromator passed through the fused quartz plate F, from which a f r a c t i o n of the beam was focused onto a type 935 photocell, G, by the front surface aluminized mirror, H. The main portion of the beam was focused onto the cry s t a l J by means of a second front surface mirror, K. The l a t t e r was pivoted so that i t could be moved i n a horizontal plane by means of micrometer screw, L. A l l the parts follow ing the e x i t s l i t of the monochromator were enclosed i n a l i g h t - t i g h t box with a fused quartz entrance window. The box could be desiccated when necessary. Three l i g h t sources were employed to cover the energy range from 1.7 to about 5.6 ev. A carbon arc, using a National Carbon Company Type W cored anode, operating at 40 V, 60^, could be used over the entire range. More stable output was obtained from a General E l e c t r i c Company Type AH6 high 7 pressure mercury arc (2.3 - 4.6 ev) or a tungsten lamp (1.7 - 2.3 ev). At energies greater than 5.0 ev there was an appreciable amount of stray l i g h t i n the monochromator output. This was accounted for by measuring the decrease i n photocurrent and l i g h t i n t e n s i t y when a Corning 9700 f i l t e r was placed i n the beam. This f i l t e r cut o f f the energy at which the measurement was being made but passed p r a c t i c a l l y a l l the stray radiation. The photocell G was cal i b r a t e d i n a separate- experiment by placing a cal i b r a t e d thermopile i n the sample p o s i t i o n and measuring the output of both photocell and thermopile as a function of wavelength. The photocell output was detected by a D.C. amplifier constructed according to the design of Lander 1 while a Perkin Elmer Model 53 breaker ampl i f i e r measured the thermopile output. The thermopile used had a time constant of approximately 1 s e c , so that the c a l i b r a t i o n procedure would normally have required s t a b i l i t y of the l i g h t source over periods of several seconds. This condition could not be met when the carbon arc was employed. This d i f f i c u l t y was overcome, however, by placing, i n the photocell c i r c u i t , a network having an e l e c t r i c a l time constant equal to the thermal time constant of the thermopile. Under these conditions a comparison of thermopile and photo c e l l outputs at a given time provides the required c a l i b r a t i o n , despite fluctuations i n the l i g h t source. To f a c i l i t a t e the comparison, the two outputs were recorded on a Sanborn Model 64-1300 A multi-channel recorder. 8 Due to the lack of s e n s i t i v i t y , the photocell could not be used at quantum energies below 2.30 ev. By using the calibrated thermopile the v a r i a t i o n of the output of the tungsten lamp with energy was determined. Then under a given set of conditions the i n t e n s i t y could be measured at 2.3 ev using the photocell and the i n t e n s i t y at lower quantum energies calculated from t h i s . Crystals were prepared for photoconductivity measurements by painting electrodes of air - d r y i n g s i l v e r paint (DuPont No. 4817) on two of the edges. They were held between Teflon blocks, which were also coated on one face with the same s i l v e r paste (Fig. 2). The e l e c t r i c f i e l d was applied to the c r y s t a l by a number of 300^ dry c e l l s , while the current was measured by a d i r e c t - coupled feedback amplifier whose f i r s t stage was mounted near 19 the c r y s t a l . An input r e s i s t o r of 10 ohms could be employed and currents of 5 x l O - " ^ amperes were re a d i l y measurable. With t h i s input r e s i s t o r the time constant of the system was about 2 seconds. The s e n s i t i v i t y and l i n e a r i t y of the system were checked by applying the accurately known voltages from a Rubicon potentiometer to the input. In a l l the photocurrent measurements, the exposure of the c r y s t a l to l i g h t , when the e l e c t r i c f i e l d was applied, was kept as small as possible i n order to minimize the formation of space charge f i e l d s . The l i g h t was allowed to f a l l on the cr y s t a l i n single "pulses" varying from .05 to about 5 seconds depending on the s e n s i t i v i t y (and hence response time) of the 9 apparatus. A magnetically operated shutter was set up to provide the shorter l i g h t pulses, but t h i s was o r d i n a r i l y found to be unnecessary since the currents were small enough to require the use of the largest input r e s i s t o r s . Under these circumstances the longer response time of the amplifier required l i g h t flashes of durations e a s i l y obtained by means of a manually operated shutter. The flashes were s t i l l too short, however, to permit the photocurrent and l i g h t i n t e n s i t y to be read from meters. Consequently, both quantities were recorded simultaneously on the previously; mentioned recorder. Aside from the prevention of space charge formation, the use of short pulses of l i g h t was desirable because of the poor long-term s t a b i l i t y of the carbon arc and the ef f e c t of pro longed UV radiation on the photoconductive response. 10 B. RESULTS B . l * Optical Absorption Measurements Absorption spectra were measured with a Beckman Model DU quartz spectrophotometer. The data are usually presented i n terms of the absorption c o e f f i c i e n t , K, defined by T „ — Kd ., ^.2 I a I Q e (1-R&/ where I 0 and I are the incident and transmitted i n t e n s i t i e s , respectively, d i s the specimen thickness and R i s the r e f l e c  t i o n c o e f f i c i e n t . The above expression allows for the losses at the f i r s t and second p a r t i a l r e l f e c t i o n s l o n l y . Since R i s small, t h i s approximation i s s u f f i c i e n t l y accurate for our purposes. R was calculated from the index of r e f r a c t i o n data 2 of Strong and Brice , which was extrapolated into the short 3 wavelength region using the Sellmaier equation , u.2 - 1.945 X 2 X 2 - 1.251 x 10 b where u. i s the index of r e f r a c t i o n and X the wavelength o expressed i n Angstrom u n i t s . Since the cleaved surfaces of the c r y s t a l s were not p e r f e c t l y smooth but had a "wavy" appearance, these calculated r e f l e c t i o n losses were no doubt too low. Where absorption changes (AK) are presented, t h i s l o s s , of course, cancels out. •Sections B and C are divided into 11 subsections each i n such a way that the r e s u l t s described i n B.l are discussed i n C.l and so on. 11 On some occasions, the change in o p t i c a l density (AD) i s pl o t t e d rather than the change i n absorption c o e f f i c i e n t . Since I D = l o g i o " I ' then 2.3 AE = — j - AD B.2 Analysis of the Photoconductivity Data For reasons which w i l l become evident i n l a t e r sections, the photoconductivity data had to be analyzed i n a somewhat d i f f e r e n t fashion from that normally employed. The analysis used i s presented below: Consider a c r y s t a l with an absorption c o e f f i c i e n t K(E), where E designates the quantum energy. K may be a composite c o e f f i c i e n t which defines the t o t a l absorption, at a given energy, due to several d i f f e r e n t absorption processes, K^(E), i . e . , K(E) = £ YL±{E) i If the c r y s t a l absorbs a f r a c t i o n , a_, of the incident radiation, the f r a c t i o n absorbed by o p t i c a l t r a n s i t i o n s of K-i a the i th kind i s — i — . Let p i be the p r o b a b i l i t y that such K a t r a n s i t i o n leads to a free charge c a r r i e r . Then the f r a c t i o n of the incident radiation which produces free charge c a r r i e r s , by a l l possible types of t r a n s i t i o n s , i s - Z p, K K i l i 12 Let the c a r r i e r s move an average distance x^ i n unit f i e l d (we use the subscript here to allow for the p o s s i b i l i t y that both electron and hole e x c i t a t i o n occur at the same energy, i . e . , x^ takes on either one of two possible values). Then each contributes a charge, _iZZZ.e, to the external c i r c u i t , w where w i s the distance between the electrodes and V i s the applied voltage. Then i f N quanta per sec. f a l l on the c r y s t a l , the observed photocurrent w i l l be or i K w2 v 2 x.p.K, = — . _ . — = Y, say. (1) i 1 1 i N a eV K was determined by o p t i c a l absorption measurements on each c r y s t a l and a calculated therefrom. Thus, from a'combination of o p t i c a l absorption and photoconductivity measurements, the quantity Y(E) could be determined. In the l i t e r a t u r e , photoconductivity data i s usually presented by p l o t t i n g e i t h e r X/N versus E or 1/Na versus E. The former method ignores the fact that some of the radiation may be l o s t by transmission through the sample, while the second does not allow f o r the p o s s i b i l i t y that the major absorption processes may not contribute to the photoconductivity. That these assumptions may lead to serious error w i l l be shown below. An expression f o r a_ which accounts for the l i g h t absorbed on the f i r s t t raversal through the c r y s t a l and also f o r that absorbed on the second t r a v e r s a l ( i . e . , a f t e r p a r t i a l r e f l e c t i o n 13 at the second MgO-air interface) may e a s i l y be shown to be a = ( l - R ) ( l - e ~ K d ) ( l + R e * " K d ) (2) where R(E) i s the r e f l e c t i o n c o e f f i c i e n t of MgO and d i s the c r y s t a l thickness. Then the correction factor /a i n equation (1) i s — - ^ (3) a ( l - R ) ( l - e - ^ d ) ( l + R e - ^ d ) Now for Kd s u f f i c i e n t l y small (say < 0.1), a good approximation to (3) i f R ^ 0.1, i s £ = I (4) a d Hence, t h i s correction factor w i l l have no influence on the spectral dependence of Y i n that region of the spectrum where the absorption c o e f f i c i e n t of the c r y s t a l i s small enough to s a t i s f y the inequality, Kd< 0.1. On the other hand, for Kd s u f f i c i e n t l y large (say > 2.5) a good approximation to (3) i s 1 = T^~ (5) a 1-R In t h i s case, the correction factor i s of the utmost impor tance i n the determination of the spectral dependence of Y. The neglect of t h i s factor i s equivalent to the assumption that the photoconductivity i s due to those centers which are responsi ble for most of the o p t i c a l absorption. This i s not always a j u s t i f i a b l e assumption and i t may lead to erroneous r e s u l t s . 14 A l l the photoconductivity y i e l d s quoted here were calculated i \ according to equations (1), and (3), (4) or (5). B.3 Dependence of Photocurrent on Light Intensity and E l e c t r i c  F i e l d In untreated crystals the photocurrents were found to be proportional to the e l e c t r i c f i e l d up to about 6*000 volts/cm. In t h i s range of f i e l d s , the dark current was n e g l i g i b l e , i . e . , less than 10 ^ 5 amperes. However, for f i e l d s greater than some c r i t i c a l value (ca. 6,000 volts/cm.), the dark current rose sharply to 10""^ amperes or more. This current was s u f f i c i e n t l y unstable that photoconductivity measurements were impossible. Usually, the photocurrents were small enough at f u l l l i g h t i n t e n s i t y to prevent an investi g a t i o n of the dependence of current on i n t e n s i t y . However, because of the larger currents available i t was possible to perform the'experiment on an X-rayed c r y s t a l , using 2.3 ev quanta. In t h i s case, the photocurrent was propor t i o n a l to i n t e n s i t y for a 40 to 1 v a r i a t i o n of i n t e n s i t y . Because of the i r r e g u l a r spectral output of both the carbon arc and the mercury arc, i t i s believed that any s i g n i f i c a n t deviations from pr o p o r t i o n a l i t y i n the cases of other types of c r y s t a l s would have led to corresponding i r r e g u l a r i t i e s i n the calculated y i e l d curves. Since the l a t t e r i r r e g u l a r i t i e s were not observed, we conclude that i n the range of i n t e n s i t i e s used (at least 1,000 to 1) the photocurrent was proportional to l i g h t i n t e n s i t y . B.4 Evidence that Photocurrents are a Bulk E f f e c t In view of the fact that the observed currents were so small, the p o s s i b i l i t y that they were due to a surface e f f e c t 15 must be considered. To investigate t h i s p o s s i b i l i t y the photo conductivity of a thick c r y s t a l was measured. A section was cleaved o f f and the remainder remeasured. This procedure was repeated several times, measuring the photoconductivity and absorption at each step. Table I shows Y and K for the d i f f e r  ent sections of the same o r i g i n a l c r y s t a l . Table I Absorption and Photoconductivity at 5.0 ev Thickness (cm) i / N e l e c t r o n s x 1 Q 1 0 y x 1 Q10 _cm K ( c m - 1 ) .814 7.1 1.85 1.92 .498 4.5 1.61 2.27 .346 5.5 2.18 1.72 .211 3.3 1.83 1.30 .133 2.3 1.99 1.85 .101 1.3 1.45 2.03 As discussed i n Section C.4 the approximate constancy of the t h i r d column r e l a t i v e to the second, implies that the measured photocurrents are the result of o p t i c a l e x c i t a t i o n i n the bulk of the c r y s t a l . B.5 Space Charge Formation As explained previously, the exposure of the c r y s t a l to l i g h t was held to a minimum i n order to prevent the formation of space charge f i e l d s . In order to demonstrate the develop ment of such f i e l d s , the following experiment was performed. With an e l e c t r i c f i e l d applied to a c r y s t a l , a portion 16 i of the volume between i t s electrodes was i r r a d i a t e d with 4.4 ev quanta and the photocurrent measured as a function of time. At i n t e r v a l s the e l e c t r i c f i e l d was removed, the electrodes were brought to the same potential by connecting them through the input r e s i s t o r , and the photocurrent measured under t h i s condition. Figure 3(a), curve A shows the v a r i a t i o n , with time of i r r a d i a t i o n , of the photocurrent with applied f i e l d , while curve B gives the current when measured with no applied f i e l d . The photocurrents of curve B flow i n the opposite d i r e c t i o n to those i n curve A. The i r r a d i a t i o n was then continued with no applied e l e c t r i c f i e l d (electrodes connected) and the photocurrent measured as a function of time. At i n t e r v a l s the e l e c t r i c f i e l d was applied and the photocurrent measured under t h i s condition. The corresponding curves are presented i n Figure 3(b). In each case curve C i s the sum of curves A and B. It i s evident from the curves that the flow of photo current i n the applied f i e l d produces space charge f i e l d s which p e r s i s t a f t e r the i n i t i a l exposure to l i g h t and a f t e r the removal of the poten t i a l difference between the electrodes. These r e s u l t s are discussed i n a more quantitative fashion i n Section C.5. B. 6 Properties of Crystals as Received In view of the reasonable agreement among the results from d i f f e r e n t c r y s t a l s (Table II) l i t t l e attempt to correlate o p t i c a l absorption or photoconductivity data with impurity content has 17 been made. Spectrographic analyses of MgO c r y s t a l s obtained from the Norton Company have, however, been made in t h i s laboratory . These analyses show that the p r i n c i p a l impurity i s iron (.01 - .05%) with somewhat smaller concentrations of manganese, chromium, calcium and s i l i c o n . As received from the Norton Company, most of the MgO crystals employed i n t h i s i nvestigation showed an o p t i c a l absorption spectrum as shown i n Figure 4, curve A. The exceptions to t h i s rule had a spectrum as shown by curve B. The actual magnitude of the absorption varied considerably from c r y s t a l to c r y s t a l but these two shapes were nearly always found. The photoconductivity spectra of c r y s t a l s characterized by absorption spectra of e i t h e r type A or type B (Figure 4) were as shown i n Figure 5, which gives two t y p i c a l photoconduc- ti v e y i e l d curves along with the corresponding absorption curves. A l l spectra obtained on untreated crystals were of one or the other of these two types, which d i f f e r i n shape p r i n c i p a l l y in, the energy region above 5.0 ev. The l a t t e r difference could not be correlated with any known difference among c r y s t a l s . The photoconductivity i n the region below 5.0 ev could be well accounted f o r i n most cases by a superposition of two Gaussian bands centered about 4.05 ev and 5.05 ev. The decomposition of a t y p i c a l spectrum into these two bands i s shown i n Figure 6. The locations of these peaks do not correspond to the positions of any of the previously known o p t i c a l absorption bands in MgO. The r e p r o d u c i b i l i t y of the magnitude of these bands from c r y s t a l to cr y s t a l i s i l l u s t r a t e d i n Table II, where the y i e l d s at 3.8 and 4.6 ev and t h e i r ratio are presented f o r a number 18 of specimens. These energies were chosen as being representa t i v e of the magnitudes of the low and high energy peaks, respec t i v e l y . Considering that the measured y i e l d depends both on the density of photoionizable centers and on the range of the free c a r r i e r s , both of which may depend upon impurity concentration, i t i s perhaps surprising that the magnitude of the y i e l d does not show a greater v a r i a t i o n from c r y s t a l to c r y s t a l . The magnitude variations which d i d occur could not be correlated with variations of magnitude nor type i n the o p t i c a l absorption spectrum. 19 Table II Photoconductive Y i e l d of a Number of Specimens ,8 x 1 3  Y4.6 * 1 0 1 1 10 (cm/volt) Y4.6/ Y3.8 Type of Absorption Spectrum (See F i g . 4) Comments 43 14.8 34 B 11.5 6.0 52 B 4.1 2.53 62 14.0 7.12 51 B * 3.81 B * 12.4 6.0 48 B * CO. 9 5.74 640 A 6.2 4.89 79 A Lower Purity 70.0 17.7 25 B 4.40 B * 13.5 6.34 5.45 47 B A 6.3 3.4 54 A 14.4 4.08 28 A 8.5 4.6 54 B 6.6 4.52 68 B 9.1 5.0 55 B NOTES: 1. Samples marked* were cut from the same larger piece. 2. The sample designated "lower p u r i t y " was impure enough to be v i s i b l y colored. The p r i n c i p a l impurity was probably iron. The photoconductive y i e l d at 4.8 ev ( i . e . i n the 5 ev band) was found to be approximately twice as great at 250°C as at room 20 temperature. With the experimental arrangement employed the ; temperature v a r i a t i o n of the 4 ev band could not be measured. B.7 Heat Treatment Studies As has been previously mentioned (Section B.6 and F i g . 4A) most of the cr y s t a l s as obtained, possessed an u l t r a v i o l e t absorption spectrum consisting of two obvious bands. For c r y s t a l s of normal thickness (0.2 to 0.7 mm) the two absorption bands could be removed by heating i n vacuum at 1400°C for several hours. Such a treatment resulted i n spectra l i k e that shown i n Figure 4, curve B. Further heating at the same temperature d i d not change the shape of the spectrum. For convenience we w i l l refer to cr y s t a l s with t h i s type of absorption spectrum as "stoichiometric" although, admittedly, we cannot be sure that t h i s spectrum i s not c h a r a c t e r i s t i c of a small deviation from stoichiometry, i n equilibrium at the high temperature. The spectrum i t s e l f w i l l be termed the "background" absorption. The ef f e c t of heat treatment at various temperatures on the absorption of stoichiometric c r y s t a l s was studied i n some d e t a i l . Since no conclusions could be drawn from the d e t a i l e d behavior of the absorption at the various temperatures, only the most important observations w i l l be given here. Figure 7, curve C shows the spectrum of a specimen which was cooled slowly from 1400°C. This type of spectrum was also c h a r a c t e r i s t i c of specimens heated at 1000°C or 1100°C and quenched therefrom. The following observations summarize the experiments performed at 1000°C and 1100°C. 1. The change of spectral shape from that of curve A to 21 that of curve C (Fig. 7); was re v e r s i b l e . That i s , the curve A could be regained by reheating at 1400°C and quenching from t h i s temperature. 2. The rate at which the equilibrium shape C (Fig. 7) was approached was e s s e n t i a l l y the same at 1000°C as i t was at 1100°C. At both temperatures t h i s rate was found to be independent of cr y s t a l thickness. 3. The change i n shape of the o p t i c a l absorption curve was not accompanied by a change i n the spectral dependence of the photoconductivity. This point i s i l l u s t r a t e d by F i g . 8 which shows the y i e l d curves for two c r y s t a l s , one heated at 1400°C for 2 hours, the other at 1000°C for 230 hours. The absorption spectra were of the types A and C (Fig. 7) respectively. B.8 Excess Mg Crystals A t y p i c a l absorption spectrum f o r a cry s t a l heated i n Mg vapor i s shown in Figure 9, curve B. Since the shape of the curve d i f f e r e d somewhat for d i f f e r e n t coloring conditions, two experiments designed to determine the cause of t h i s change of shape were carried out, v i z . , 1, A cr y s t a l .068 cm thick was heated for 1 hour at 1115°C i n a Mg pressure of approximately 2 atmospheres. The spectra before and afte r t h i s treatment are shown i n Figure 10. Figure 11 shows similar curves for a c r y s t a l .074 cm thick treated i n a similar fashion for 3 hours. Both of these crystals were l i g h t l y colored compared to that shown i n Figure 9. 2. A cr y s t a l .077 cm thick was heated 4 hours at 1115°C 4 22 in about 2 atmospheres pressure of Mg. The absorption change I s shown by curve A of Figure 12. A further similar t r e a t - v ment of 5 hours was carried out. Curve B shows the extra absorption induced by the second treatment only. .v-.v: The above two experiments show that the true induced absorption could not be calculated by simply subtracting the absorption measured before heating i n Mg vapor from that measured a f t e r heating. This point i s discussed more thoroughly i n Section C.8. The photoconductivity of therrmore strongly colored c r y s t a l of Figure 9 i s shown i n Figure 13, curve B. This specimen had been treated f o r 48 hours at 1200°C i n a Mg pressure of 1 mm Hg. For comparison, the spectrum of a t y p i c a l stoichiometric or excess oxygen c r y s t a l i s also included (curve A). B.9 The Effect of U l t r a v i o l e t I r r a d i a t i o n The e f f e c t of u l t r a v i o l e t i r r a d i a t i o n on the photoconductivity of stoicrrdometric c r y s t a l s was studied by i r r a d i a t i n g a c r y s t a l with low energy quanta, measuring the y i e l d at fiwe d i f f e r e n t energies, i r r a d i a t i n g at a higher energy, remeasuring, etc. Figure 14 shows the r e s u l t s of t h i s experiment. The numbers along the horizontal axis indicate the energy of the quanta leading to the photoconductivity spectrum with the corresponding number. In view of the apparent presence of two absorption bands which lead to appreciable photoconductivity (Figure 6), the u l t r a v i o l e t i r r a d i a t i o n experiments were repeated on two other c r y s t a l s one of which was i r r a d i a t e d at 3.8 ev, (1.6 x I O 1 9 quanta/cm 2) the other at 4.6 ev (4 x 1 0 1 7 quanta/cm 2). These 23 energies were chosen so that the a c t i v a t i o n would i n each case be due to absorption i n only one of the two bands. The results of these experiments are -shown in Figure 15, which also shows for comparison a t y p i c a l spectrum before i r r a d i a t i o n . The absorption changes produced by such i r r a d i a t i o n s are shown i n Figures 16 and 17. B.10 The Effect of X-Irradiation The e f f e c t of X - i r r a d i a t i o n on the o p t i c a l absorption and photoconductivity was studied by exposing stoichiometric c r y s t a l s to the beam from an X-ray tube with a tungsten target and beryllium window. The samples were placed about 8 cm from the target and the tube was operated at 50 kv and 15 ma. During the i r r a d i a t i o n the specimens were covered with aluminum f o i l - t o protect them from o p t i c a l radiation. Figure 18 shows the induced absorption at two quantum energies as a function of the i r r a d i a t i o n time. S i m i l a r curves were obtained for a l l quantum energies so that to a good approximation i t may be said that the shape of the induced absorption spectrum does not vary during the period of X-ray i r r a d i a t i o n . The saturated induced absorption spectrum at room temperature i s shown in Figure 19, curve A. The specimen was stored i n the dark at room temperature and the absorption measured at i n t e r v a l s . Figure 19, curve B, shows the induced absorption a f t e r 95 hours of dark decay while the absorption at two quantum energies i s plotted as a function of time i n Figure 20. Figure 21 shows the effect of X-rays on the photoconductivity. 24 Curve A corresponds to the untreated c r y s t a l . The 5.0 ev band i s obvious but the 4.0 ev band i s just resolved i n t h i s p a r t i c u l a r case. The cr y s t a l was exposed to X-rays f o r 40 minutes and curve B measured immediately aft e r t h i s i r r a d i a  t i o n while curve C was measured 4 hours l a t e r . A f t e r 50 hours the y i e l d had changed to curve D and changed only very slowly thereafter. Figure 22 shows sim i l a r data for the same c r y s t a l in the low energy region of the spectrum. Curve A was obtained immediately a f t e r i r r a d i a t i o n ; curve B, 72 hours l a t e r . The change i n absorption c o e f f i c i e n t during the same period i s shown by the dotted curves i n the same figure. By comparing Figure 15, curve C, with Figure 21, curve D, i t may be seen that the photoconductivity of a specimen activated by i r r a d i a t i o n i n the 5.0 ev band i s similar to the photocon d u c t i v i t y of specimens i r r a d i a t e d with X-rays and allowed to decay thermally. The ef f e c t of subsequent X - i r r a d i a t i o n on a previously UV-irradiated c r y s t a l i s shown i n Figure 23. Curve A was obtained by i r r a d i a t i o n with 4.4 ev quanta, i . e . , the i r r a d i a t i o n was i n the 5 ev band and the spectrum i s therefore s i m i l a r to that of Figure 18, curve C. Curve B resulted from the X-ray exposure, while- curve C was obtained a f t e r 96 hours of subsequent thermal decay. The extra absorption and photoconductivity induced by X - i r r a d i a t i o n can be reduced by o p t i c a l i r r a d i a t i o n . A thorough study of t h i s e f f e c t has not been made but the e f f e c t of 2.3 ev quanta has been studied to some extent. Figure 24, curve A, shows the v a r i a t i o n with time of the 25 o p t i c a l absorption at 4.2 ev, when a freshly X-rayed c r y s t a l 15 2 was i r r a d i a t e d with 3 x 10 quanta/cm -sec. Curve B i s for a control sample X-rayed at the same time but stored i n the dark at room temperature. Similar curves for the absorption at 2.3 ev are shown i n Figure 25. The absorption at a l l other quantum energies was likewise reduced by the i r r a d i a t i o n . The v a r i a t i o n with integrated l i g h t flux, of the photo conductive y i e l d of a p a r t i a l l y decayed, X-rayed c r y s t a l , i s shown in Figure 26. In t h i s case the o p t i c a l absorption was not measured during nor aft e r the i r r a d i a t i o n . The data on Figure 26 was p l o t t e d assuming that the factor /a i n equation (1) remained constant during the i r r a d i a t i o n . Since we know from Figures 24 and 25 that t h i s factor a c t u a l l y did decrease during i r r a d i a t i o n ( e s p e c i a l l y for the high energies), i t may be seen that the l e f t hand sides of the curves i n Figure 26 should be raised r e l a t i v e to the right hand sides. Since the amount of t h i s increase i n largest for the energies 3.5, 4.0 and 4.5 ev, i t would tend to make the shapes of a l l curves more nearly the same. Since the o p t i c a l absorption at the beginning of the i r r a d i a t i o n was known, the true y i e l d (Y) at t h i s time could be calculated. Then, by assuming that the i r r a d i a t i o n reduced the absorption to a small value, /a a f t e r the i r r a d i a t i o n was calculated from equation (4). Since t h i s assumption gives a lower l i m i t to K / a , the t o t a l f r a c t i o n a l change i n y i e l d calculated therefrom w i l l be an upper l i m i t . Thus the true values of t o t a l f r a c t i o n a l change i n y i e l d l i e between those i n the two columns of the table following. Table III Ene rgy (e.v.) Total Fractional Changes i n Y i e l d (%) Uncorrected Over-Corrected 2.3 61 61 3.0 61 63 3.5 57 60 4.0 56 65 4.5 53 70 The s i g n i f i c a n t point i l l u s t r a t e d by Table III i s that the reduction i n photoconductive y i e l d i s - e s s e n t i a l l y independent of energy. As discussed i n section C.10 t h i s implies that the main e f f e c t of 2.3 ev i r r a d i a t i o n i s to empty some l e v e l s which have been f i l l e d during t h i s X-ray ex c i t a t i o n , thus reducing the e l e c t r o n i c range. B.11 Sign of the Charge C a r r i e r s In order to determine the sign of the o p t i c a l l y induced current c a r r i e r s , the f i e l d d i s t r i b u t i o n due to the photo- e l e c t r i c a l l y produced space charge regions (see section C.5) was studied. For each spectral region of int e r e s t a central region (such as b i n Figure 3(c) of a c r y s t a l was i r r a d i a t e d with the e l e c t r i c f i e l d applied for periods ranging from 20 minutes to several hours. When the photocurrent was reduced to a low value by theJformation of the space charge f i e l d , the applied voltage was removed, the two electrodes of the cr y s t a l were connected together through the amplifier input r e s i s t o r (see Figure 1) and a narrow beam of l i g h t of the 27 same quantum energy was moved across the c r y s t a l by means of the micrometer L (Figure 1). In t h i s way the photocurrent could be measured as a function of the p o s i t i o n of the l i g h t beam on the c r y s t a l . If the photoconductive s e n s i t i v i t y of the c r y s t a l were unaffected by the i r r a d i a t i o n , the plot of photocurrent versus position would also be a plot of space charge f i e l d versus po s i t i o n . The e f f e c t s of i r r a d i a t i o n - induced changes i n p h o t o s e n s i t i v i i t y could be minimized i n a number of ways and therefore approximate space charge f i e l d d i s t r i b u t i o n s could be obtained. To determine the sign of the charge c a r r i e r s produced by quanta i n the 4.0 ev band, the following experiment was performed: An untreated stoichiometric specimen was i r r a d i a t e d over i t s whole volume for a period of 42 hours, with no applied e l e c t r i c f i e l d ; 3.9 ev quanta were used for t h i s i r r a d i a t i o n to ensure that l i t t l e absorption occurred i n the 5.0 ev band. The spectral d i s t r i b u t i o n of photoconductivity aft e r t h i s i r r a d i a t i o n has already been given i n Figure 15, (curve B). An e l e c t r i c f i e l d was then applied to the c r y s t a l and the central region i r r a d i a t e d with 3.8 ev quanta to create a space' charge f i e l d . The electrodes were then brought to the same po t e n t i a l and the f i e l d d i s t r i b u t i o n was determined as described above, using a l i g h t beam 1/3 of the width of that used i n the i r r a d i a t i o n . This f i e l d d i s t r i b u t i o n i s shown i n Figure 27, curve A. The i r r a d i a t i o n was then con tinued, using the wider beam, u n t i l the photocurrent was again reduced to a small value. The r e s u l t i n g f i e l d d i s t r i  bution i s shown by curve B of Figure 27. The most 28 s i g n i f i c a n t feature of the l a t t e r curve i s the s h i f t of the f i e l d minimum towards the negative electrode with respect to the minimum of curve A. This was a reproducible feature of the experiment. A si m i l a r experiment was performed on a d i f f e r e n t c r y s t a l t h i s time using 4.6 ev quanta i . e . i r r a d i a t i n g i n the 5.0 ev absorption band. In t h i s case, however, the sample was not given an i n i t i a l o v e r a l l i r r a d i a t i o n to homogenize the sensi t i v i t y . For t h i s reason the photocurrent d i s t r i b u t i o n s ob tained represented e l e c t r i c f i e l d d i s t r i b u t i o n s only when the scanning beam was within the l i m i t s of the i r r a d i a t e d region. The d i s t r i b u t i o n s obtained are shown in Figure 28, curve A a f t e r one i r r a d i a t i o n with e l e c t r i c f i e l d applied, curve B, a f t e r a subsequent i r r a d i a t i o n with no applied f i e l d , and curve C after a further i r r a d i a t i o n also without f i e l d . ("No applied f i e l d " always implies that the electrodes were maintained at the same potential.) The sign of the charge c a r r i e r was also determined for the X-rayed cr y s t a l corresponding to curve D of Figure 21. The f i e l d d i s t r i b u t i o n s are shown i n Figure 29. In t h i s case 4.4 ev quanta were used to form and to detect the space charge. In t h i s experiment the most s i g n i f i c a n t feature i s the appearance i n curve B of a minimum displaced toward the po s i t i v e electrode from another minimum corresponding i n p o s i t i o n to the minimum i n curve A. The interpretation of these experiments i s presented in section G . l l . 29 C. DISCUSSION C.l Optical Absorption The usual model used i n discussing the properties of soli d s involves the introduction of a pe r i o d i c p o t e n t i a l due to a l l nuclei and a l l the electrons but one. The eigenvalues and eigenfunctions of the remaining electron are then given by the solutions of the Schrodinger equation with t h i s p o t e n t i a l . The most important feature of t h i s model i s the occurrence of quasicontinuous groups of energy eigen values spearated by energy regions which are forbidden. The disruption of the perio d i c p o t e n t i a l by some type of imperfection results i n the occurrence of l o c a l i z e d energy leve l s i n the normally forbidden region. It i s the e x c i t a t i o n of electrons to or from such l e v e l s i n MgO that i s the main concern of t h i s thesis. Since the region of the c r y s t a l i n which the deviation from p e r i o d i c i t y occurs (hereafter referred to as the "center") w i l l usually have associated with i t more than one energy 29 l e v e l in the normally forbidden band , we may expect that t r a n s i t i o n s between these l e v e l s may be of some importance. Thus one may expect to f i n d associated with the centers certain absorption bands. There are many examples of t h i s O A type of absorption i n the l i t e r a t u r e . The fact that bands occur rather than l i n e s , (as might be expected for t r a n s i t i o n s between discrete states) has been well explained as due to in t e r a c t i o n between the l o c a l  's "I ized electron and the thermal vibrations of the l a t t i c e . 30 Calculations of the v a r i a t i o n of absorption with quantum energy have been made on a similar basis. It i s found that under most circumstances the absorption bands can be well approximated by Gaussian curves. Optical t r a n s i t i o n s which take electrons between l o c a l  ized l e v e l s and energy bands of the perfect c r y s t a l are of course also possible. Numerous examples of t h i s type of 3? absorption have also been reported . The absorption i n these cases has usually been detected by photoconductivity measurements. Since the f i n a l state of the t r a n s i t i o n i s not discrete the absorption may be expected to extend over a wider range of energy than i n the previous case and i n addition w i l l not be symmetrical about some central energy. C.2 Discussion of the Factors Involved i n the Photoconductive  Y i e l d In the analysis of the photoconductivity data described i n section B.2, a factor p was introduced to represent the p r o b a b i l i t y that, following an e l e c t r o n i c e x c i t a t i o n , a free charge c a r r i e r be formed. Such a factor i s necessary i n order to take account of the p o s s i b i l i t y that the e x c i t a t i o n may take place, not to an energy band but rather to another discrete l e v e l belonging to the same absorption center. In t h i s case, the formation of a free charge c a r r i e r requires a subsequent process by which the p a r t i c l e i n the excited state may gain s u f f i c i e n t l y more energy that i t may be transferred to an energy band. The extra energy may be obtained by the absorption 31 of l a t t i c e phonons, for example. Under these conditions the photoconductivity may be expected to contain a strong tempera ture dependence i n a certain temperature i n t e r v a l . A good example of such behavior i s given by KC1 cr y s t a l s containing a stoichiometric excess of potassium^. In contrast to the weak temperature dependence mentioned i n section B.6, Day^ has reported that the photoconductivity i n MgO decreased 10^ times on lowering the temperature to 90°K. Although we cannot determine d e f i n i t e l y from Day's paper whether t h i s result applies to the untreated c r y s t a l (as does the present result) i t i s believed that i t applies to neutron i r r a d i a t e d samples so that there may be not d i s  p a r i t y between the two r e s u l t s . The quantity x introduced i n equation (1) was defined as the mean distance a charge c a r r i e r moves during i t s l i f e  time, when the e l e c t r i c f i e l d i s unity. This quantity can be written x - u.T where a. i s the mobility of the c a r r i e r s and T t h e i r mean l i f e t i m e . The l a t t e r , of course, i s determined by the density and capture cross-section of l e v e l s i n which the c a r r i e r s may be trapped. This trapping may be temporary or permanent, i . e . , thermal release from the trap may occur within the time of a measurement or only af t e r a time which i s long compared to the l a t t e r . In the former case, the photocurrent w i l l be observed to increase during the time of the measurement. Since no such "secondary" e f f e c t s were 32 noted i n these experiments, the trapping i n MgO may be regarded as permanent. Indeed i t i s concluded i n a l a t e r section that some electrons may be trapped f o r many months. In equation;(1) we have employed the fact that a charge e displaced a distance x i n the e l e c t r i c f i e l d w i l l be ob- served externally as the passage of a charge ~ . This fact follows from simple e l e c t r o s t a t i c s but the derivation w i l l be deferred u n t i l section C.5 where the appropriate equations are developed for another purpose. The equation f o r the photoconductive y i e l d developed i n section B.2 gives for a given (crystal, constant e l e c t r i c f i e l d , and spectral region of strong absorption (equation (5), the pr o p o r t i o n a l i t y Y~ — K. N Thus i f the r a t i o of photocurrent to incident l i g h t f l u x (1/N) i s p l o t t e d against quantum energy a d i s t o r t e d picture of the true absorption, spectrum of the photoionized centers w i l l be obtained since L~ 1 N K " It can e a s i l y be seen that i n spectral regions where peaks i n the t o t a l absorption (K) e x i s t and where the photo- i o n i z a t i o n varies r e l a t i v e l y slowly with energy, spurious minima i n X/N may be obtained. It i s believed that the d i s  agreement between the present r e s u l t s and those of Day^ are completely due to t h i s cause. A more d e t a i l e d comparison of 33 the two sets of results w i l l be given i n a l a t e r section. C.3 The Dependence of the Photocurrent on Light Intensity  and E l e c t r i c F i e l d The threshold e l e c t r i c f i e l d above which a large increase in dark current occurred (see section B.3) was not observed by Day^f although fieldsuupifeo 14,000 volts/cm were employed. In the present work the c i r t i c a l f i e l d was about 6,000 volts/cm. The reason for t h i s discrepancy i s not known although two pos s i b i l i t i e s have been considered. In the f i r s t place, the electrodes used i n Day's work and the present work were Aguadag ( c o l l o i d a l graphite applied i n water suspension) and s i l v e r paste, respectively. It i s d i f f i c u l t to define a work function for such materials but i t i s l i k e l y that the " e f f e c - t i v e work function" for strong f i e l d emission i s d i f f e r e n t for the two cases. If the sudden onset of a large dairk current were due to strong f i e l d electron emission from the negative electrode, the threshold f i e l d would be expected to be d i f f e r e n t in the two cases. Secondly, although i n the work of Day the c r y s t a l s were measured i n dry a i r , i n most of the present measurements i t was not found necessary to desiccate the sample chamber during the measurement of the photoconductivity spectra. Consequently, a surface breakdown might occur at a smaller e l e c t r i c f i e l d due to a surface f i l m of e.g. hydroxide. In any case, whatever the cause of the high dark currents they could be readily avoided simply by maintaining an e l e c  t r i c f i e l d less than the c r i t i c a l value. The small dark 34 current which d i d flow under the l a t t e r circumstances d i d not cause measurable space charge development. The experimental observation of the lin e a r r e l a t i o n between photocurrent and e l e c t r i c f i e l d strength i s a j u s t i f i c a t i o n for equation (1) and the assumption i m p l i c i t therein, v i z . that none of the excited c a r r i e r s reach the electrodes, for i f they did, a tendency f o r the photocurrent to saturate with increas ing f i e l d would have been observed. Thus, knowing the d i s  tance from the edge of the i r r a d i a t i o n region to the electrode, an upper l i m i t on x may be obtained. This l i m i t i s x < l ( f 5 cm 2/volt for untreated c r y s t a l s . Similar experiments have not been performed on X-rayed or UV i r r a d i a t e d specimens. As mentioned above, x i s determined by the l i f e t i m e of the excited c a r r i e r s . A c a r r i e r may end i t s l i f e by one or other of the following mechanisms: (see F i g . 30) (a) Direct recombination with a free c a r r i e r of the opposite type, (b) recombination with a free c a r r i e r of the opposite type through some imperfection-contributed intermediate state, (c) return to a l e v e l of the same type as that from which i t came or, (d) trapping by a l e v e l other than that from which i t came. Process (a) (Figure 30(a) i s of no importance when e x c i t a  t i o n occurs i n a single absorption band, assuming of course, 35 that the quanta are not s u f f i c i e n t l y energetic to cause band- to-band t r a n s i t i o n s and thus create electron-hole p a i r s . Since the forbidden energy region i s 10.5 ev wide ' t h i s condition i s met i n a l l the present measurements. In the energy region of band overlap (Figure 6), however, i t i s conceivable that both electrons and holes may be simultaneously excited and di r e c t recombination must be considered. Such recombination, however, leads to a non-linear relationship between photo- current and l i g h t i n t e n s i t y . Since we have concludedi(section B.2) that, for the range of i n t e n s i t i e s used and the spectral region investigated, the photocurrent was proportional to l i g h t i n t e n s i t y , we conclude also that di r e c t recombination i s not a dominant mechanism. Recombination through intermediate states (Figure 30(b) would again be important only i n a spectral region where both free electrons and free holes were being generated. For the low excitations obtained i n these experiments, a l i n e a r dependence of photocurrent on l i g h t i n t e n s i t y would be expected i n t h i s case^. Thus mechanism (b) cannot be ruled out by the same argument used to eliminate (a). However, i f t h i s mechanism were important one would expect to f i n d an abnormal decrease i n photoconductive response as the quantum energy reached the spectral region of absorp t i o n band overlap. It may be seen from Figure 6 that such a decrease was not observed i n untreated or vacuum heated c r y s t a l s . Therefore, i t i s believed that free hole-electron recombination i s not an important mechanism i n such c r y s t a l s . 36 Since UV or X-ray e x c i t a t i o n can hardly be expected to change the number or type of l e v e l s through which the recombination can occur the same conclusion may be applied to such c r y s t a l s . The t h i r d mechanism l i s t e d above was the return of excited c a r r i e r s to the same type of center from which they came. If t h i s center had previously been emptied by o p t i c a l e x c i t a t i o n , such a trapping event would assure that the net effe c t on the properties of the c r y s t a l would be zero. Since the r e s u l t s of section B.9 show that the photoconductive spectrum was altered by prolonged UV i r r a d i a t i o n i n e i t h e r of the two bands i t must be concluded that t h i s type of trapping event i s not the only one which can occur. Also, simple considerations show that t h i s mechanism leads to a non-linear dependence of current o n l l i g h t i n t e n s i t y . For t h i s reason one can make the stronger conclusion that the trapping of c a r r i e r s i n already ionized centers of the type from which they came i s not the dominant recombination mechanism. If on the other hand the excited c a r r i e r s were to be trapped i n centers exactly similar ( i . e . s t i l l occupied) to those from which they came (Figure 30(c), a change i n spectral response would be expected and a linear^dependence on i n t e n s i t y Would be o b t a i n e d . Trapping by previously unoccupied l e v e l s (Figure 30(d) would also f u l f i l l the two conditions required by the experi mental results and discussed above. The occupancy of such l e v e l s comprises a thermodynamically unstable s i t u a t i o n which w i l l revert to the o r i g i n a l state, given enough time. In view of the fact that space charge d i s t r i b u t i o n s which l a s t 37 for considerable periods of time can be formed (section B.5) i t can be concluded that at least some of the trapped c a r r i e r s have release times much greater than 0.5 seconds. It i s con cluded i n section C.10 that at least some of the electrons remain trapped for several months. Thus, the most l i k e l y recombination mechanisms seem to be the trapping of excited c a r r i e r s by centers of the same type as those from which they were excited and/or by other, normally empty, more shallow l e v e l s . It i s t e n t a t i v e l y con cluded i n section C.6 that for untreated c r y s t a l s both mechanisms are operative. C.4 Evidence that the Photocurrents are Due to a Bulk Eff e c t The question of photocurrents excited i n surface films (e.g. magnesium hydroxide) arises because of the low sensi t i v i t y of the MgO c r y s t a l s to o p t i c a l i r r a d i a t i o n . If the currents were primarily due to surface conduction, the contribu t i o n from the front surface ( i . e . the side on which the l i g h t beam was incident) would remain constant as the thickness of the specimen was reduced. If the surface layer were to form rapidl y ( i n c. 1 hour, say) then the contribution from the back, freshly cleaved, face would be proportional to the l i g h t incident on i t and would thus increase somewhat as successive pieces of the specimen were cleaved o f f . Thus the quantity X/N would be expected to increase s l i g h t l y as the thickness of the specimen was reduced. On the other hand, i f the photosensitive surface layer 38 r e q u i r e d a very l o n g time to form, o n l y the t r i a l r e p r e s e n t e d by the f i r s t l i n e of Table I would be expected t o c o n t a i n a c o n t r i b u t i o n from both s u r f a c e s . In t h i s case X/N would decrease by l e s s than a f a c t o r 2 a f t e r the f i r s t r e d u c t i o n i n t h i c k n e s s and remain constant t h e r e a f t e r . I f the measured p h o t o c o n d u c t i v i t y were e x c l u s i v e l y a b u l k e f f e c t , the c a l c u l a t e d y i e l d Y would be expected to be constant, independent of t h i c k n e s s . The q u a n t i t y 1/N d i d not vary i n e i t h e r of the above d i s c u s s e d f a s h i o n s (see Table I ) . The observed v a r i a t i o n i n Y was s l i g h t l y g r e a t e r than the experimental e r r o r . However, the n o n - u n i f o r m i t y of the c r y s t a l , as e v i d e n c e d a l s o by the o p t i c a l a b s o r p t i o n ( l a s t column, Table I) may be r e s p o n s i b l e f o r t h i s v a r i a t i o n . I t s h o u l d be emphasized t h a t such a volume non-uniformity would not a f f e c t a s u r f a c e p h o t o s e n s i  t i v i t y . I t i s b e l i e v e d t h a t the above d i s c u s s e d experiment pro v i d e s c o n v i n c i n g evidence t h a t the major p o r t i o n of the photocurrent was e x c i t e d i n the volume of the c r y s t a l . A l l f u r t h e r d i s c u s s i o n w i l l be p r e s e n t e d on t h i s b a s i s . C.5 Formation of Space Charge F i e l d s The r e s u l t s p r e s e n t e d i n F i g u r e 3 can be e x p l a i n e d i n v terms of a simple model, which w i l l be d i s c u s s e d by r e f e r e n c e to F i g u r e 3 ( c ) . The YZ planes of the c r y s t a l c o n s t i t u t e the e l e c t r o d e s . A p o r t i o n of the XZ plane was i l l u m i n a t e d with a beam of 39 l i g h t p a r a l l e l to the Y axis. Upon ill u m i n a t i o n , some excited c a r r i e r s t r a v e l to the edge of the illuminated region and even outside i t . If the range of the c a r r i e r s i s small compared to the width of the i r r a d i a t e d region, the net result of the i r r a d i a t i o n with f i e l d can be considered as the formation of a sheet of charge at either side of the i r r a d i a t e d region. 2 Let the charge i n each sheet be + ne per cm . Then i f E(x) i s the e l e c t r i c f i e l d and e the d i e l e c t r i c constant, we have from Poisson's equation AE = + — ne (6) e" where AE i s the discontinuity i n the e l e c t r i c f i e l d at eithe r side of the i r r a d i a t e d region. We also have % • a l + E b • b + \ • a2 = V ( 7 ) where; E & and E^ are the e l e c t r i c f i e l d s in t h e i r respective regions, V i s the pot e n t i a l difference between the electrodes and d i s the c r y s t a l thickness. From equations (6) and (7) and the d e f i n i t i o n of AE we obtain With the electrodes at the same potential = - iHLSL ( i - k) ( 9 )  b e d When the condition E h = - E ' has been achieved, the photo- b currents measured with and without the applied e l e c t r i c f i e l d should be equal i n magnitude but opposite i n sign. The time, 40 T, at which t h i s condition held can be obtained from Figure 3(a) and we have from (8) and (9), n(T) = ^ (10) 8ire (d-b) For the experimental conditions employed i t was calculated that n(T) = 8.7 x 10 9 electrons/cm 2. Now the formation of t h i s space charge i s equivalent, as far as the external c i r c u i t i s concerned, to the transfer of a charge n(T)Ae from one side of the illuminated region to the other, a distance b (A i s the cross sectional area of the c r y s t a l i n the YZ plane). T i . d t = n(T) ^ (11) d The reason for the factor — on the right hand side of d Equation 11 i s explained l a t e r i n t h i s section. By integrating under the experimental curve A of Figure 3(a) the l e f t hand side of Equation (11) was determined and n(T) c a l  culated to be 9 n(T) = 9.0 x 10 9 electrons/cm 2 Thus the two values of n(T) agree within the experimental e r r o r . The curves of Figure 3 are approximately exponential i n character. A simple analysis would show that they should be 41 p r e c i s e l y exponential i f the UV i r r a d i a t i o n had no e f f e c t on the c r y s t a l (except, of course for the formation of the space charge f i e l d ) . If the l a t t e r were the case the absolute values of the photocurrents measured with and without e l e c t r i c f i e l d should have a constant sum (see equations 8 and 9 ) . Curves C of Figure 3(a) and (b) show that t h i s i s not so. From the res u l t s of section B.9, however, an a c t i v a t i o n of the c r y s t a l was to be expected i n t h i s experiment, so that curves C of Figure 3 should increase as a function of time. The maximum i n Figure 3(a) and the minimum i n Figure 3(b) are not explained. It should be emphasized that the presence of t h i s a c t i v a  t i o n e f f e c t has ho influence on the foregoing calculations of space charge density (equations (10) and (11). Indeed the comparison with experiment was done i n the above fashion i n 'order to eliminate the eff e c t of the changing photosensitivity with time of- i r r a d i a t i o n . In the work of Day^, i t was found that when a narrow region i n the center of a c r y s t a l was illuminated, the photocurrent decreased i n i t i a l l y by a fac t o r two, then remained constant for many hours. The i n i t i a l decrease may have been due to the development of space charge f i e l d s as described above. The fact that the current was not reduced to zero i s i n agreement with the results obtained, i n certain cases, i n the present experiments. A possible explanation of t h i s non-reproducible resu l t i s as follows: As the e l e c t r i c f i e l d i n the illuminated region i s decreased due to the formation of the space charge, that i n the dark region i s increased (equation (7). Thus, , 42 depending on the magnitude of the i n i t i a l e l e c t r i c f i e l d and the r e l a t i v e magnitudes of b and d (equations (7) and (8), the e l e c t r i c f i e l d i n the dark region may increase to the c r i t i c a l value (section C.3) even though the i n i t i a l , uniform, f i e l d was well below t h i s value. If t h i s were the case, the equilibrium current observed would consist i n part of "dark current" and the question, raised by Day, as to the mechanism allowing the passage of continuous photocurrents would be revolved into the same question concerning the passage of continuous dark currents. From t h i s experiment i t may be concluded that the photo conductivity mechanism may be the most obvious one, v i z . , the e x c i t a t i o n of c a r r i e r s to an energy band, t h e i r motion therein, and t h e i r subsequent trapping with consequent formation of space charge layers at the boundaries of the i r r a d i a t e d region. From the above equations i t i s e a s i l y shown that the motion of a charge between the electrodes i s measured by the external c i r c u i t as a smaller charge by the ratio of the d i s  tance moved to the electrode separation. (This was assumed i n equation (1).) To see t h i s we f i r s t apply Gauss' Theorem to a rectangular p a r a l l e l e p i p e d containing the l e f t hand electrode of the c r y s t a l (see Figure 3(c) and having two of i t s faces p a r a l l e l to t h i s electrode. Then ignoring the f r i n g i n g of the e l e c t r i c f i e l d (as i n the derivation of equations (8) and (9) we obtain eE^, A = 4-n-q-^  (12) 43 where q^ i s the charge on the electrode. A charge e i s noxtf moved from x = a-^  to x = a^ + b where a^ and b are now a r b i t r a r y . From (12) sA (13) and of course the passage of Aq-^  i s observed externally. Now from (6) and (7) a l d V + 4irneb e and 4irne b d (14) For the case under consideration the charge /cm , ne must be replaced by e/A so that (14) becomes AE." ali 4ire b_ eA ' d (15) and combining (13) and (15) b d Aq-^  = — . e (16) which i s the desired r e s u l t . C.6 Properties of Crystals as Received The two obvious absorption peaks i n spectra such as curve A, Figure 4 were shown by Weber"^ to be c h a r a c t e r i s t i c of the presence of a stoichiometric excess of oxygen i n the c r y s t a l . This fact has been v e r i f i e d by Soshea^l and i n addition he has shown that such spectra also contain a peak 44 centered at 4.8 ev which i s masked by those at 4.3 and 5.7 ev. None of these three bands were observed i n the photocon d u c t i v i t y spectra. Consequently i t must be concluded that the p r o b a b i l i t y p of thermal i o n i z a t i o n of the excited state i s considerably smaller than for the 4.0 and 5.0 bands which were observed i n photoconductivity. Since the mean range, x, i s s u f f i c i e n t l y large for conduction by ei t h e r holes or electrons to be observed (section C . l l ) i t cannot be argued that t h i s i s the factor which prevents the observation of the three excess oxygen bands i n photoconductivity measurements. Si m i l a r l y in many of the specimens measured the t o t a l absorp ti o n was dominated by these bands. Thus as has already been stated, p must be very small f o r the excess oxygen centers. Since i t i s reasonable to expect that the excess oxygen i s incorporated s u b s t i t u t i o n a l ^ as a divalent ion, the observed o p t i c a l t r a n s i t i o n s thus produced may be expected to result from e l e c t r o n i c t r a n s i t i o n s to l e v e l s which have been emptied to complete the outer s h e l l of the i o n i c excess oxygen. Thus, i f the t r a n s i t i o n s took place from the valence band they might be v i s u a l i z e d as i n Figure 31(a). However, i t has been argued above that the t r a n s i t i o n produces a free hole with very small p r o b a b i l i t y . Hence, we v i s u a l i z e transi tions such as that i l l u s t r a t e d by Figure 31(b). It has been observed by several workers"*"^'^'^ that the ra t i o of the i n t e n s i t i e s of the 4.3 and 5.7 ev bands i s 45 s t r i k i n g l y constant under rather widely varying conditions, while the 4.8 ev band has a d i f f e r e n t intensity r e l a t i v e to the other two, depending on the conditions of formation of the bands. These facts strongly suggest that the 4.3 and 5.7 ev tr a n s i t i o n s occur i n the same center while the 4.8 ev t r a n s i  t i o n may be c h a r a c t e r i s t i c of a d i f f e r e n t center. The 4.0 and 5.0 ev t r a n s i t i o n s observed i n the photo conductivity measurements had not been observed previously. 13 Recently, however. Lye has d e f i n i t e l y i d e n t i f i e d the 5.0 ev tr a n s i t i o n i n the absorption spectra of stoichiometric c r y s t a l s and has also observed a small absorption which may be i d e n t i  f i a b l e with the 4.0 ev t r a n s i t i o n . The magnitude of the absorption was very nearly the same for a l l cr y s t a l s and had the approximate values K5.0 " °-7 c*'1 Q .05 cm These values enable an estimate of the product xp to be made. For t h i s the data of Figure 6 can be employed. We obtain x p 5 > 0 = 2 x 10~ 1 0 cm 2/volt. (17) x p 4 < 0 3 x 10" 1 1 cm 2/volt. The fact that most of the specimens l i s t e d i n Table II show values of the photoconductive y i e l d of the same order of magnitude i n spite of the fact that they were cut from several 46 d i f f e r e n t samples obtained from two d i f f e r e n t sources, i s a very important one. The implications of t h i s fact w i l l now be discussed. In section C.2 i t was concluded the most l i k e l y trapping mechanisms were (a) Capture of the free c a r r i e r by a center of the same type as that which i n i t i a l l y provided the c a r r i e r (Figure 30(c) and, (b) Capture of the free c a r r i e r by previously unoccu pied, shallower l e v e l s (Figure 30(d). Consider for the moment that mechanism (a) i s the dominant one. We have K<~ n where n i s the density of the centers i n question. Since, according to (a) above the same centers dete 'the mean range x, we have 1 x ^ **- n Therefore the y i e l d Y = xpK p and i s independent of the density of the centers. If, on the other hand, mechanism (b) were to dominate, K and x would be independently controlled by the density of absorbing centers and the d e n s i t i e s of the shallower l e v e l s , respectively. Thus the postulate of a constant number of absorbing centers independent of the c r y s t a l source would not 47 su f f i c e to explain the reproducible photoconductive y i e l d . Since the postulate of reproducible d e n s i t i e s of both absorb ing centers and shallow l e v e l s ("trapping centers") seems somewhat unlikely, we are l e d to the hypothesis that the main trapping mechanism i s (a). That (b) also occurs i s manifested by some v a r i a t i o n i n the y i e l d from c r y s t a l to c r y s t a l , and also by the results of the UV a c t i v a t i o n experiments discussed i n section C.9. Further discussion as to the nature of the 4 and 5 ev centers w i l l be deferred u n t i l the sign of the charge c a r r i e r has been deduced from the experiments of section B . l l . Lower l i m i t s on the values of p can, however, be made, using egua- t i o n (17) and the l i m i t x < 10 cm /volt given i n section C.3. We obtain P 5.0 > 2 x 1 0 ~ 5 (18) p 4 > 0 > 3 x 10" 6 C.7 Heat Treatment Studies Optical absorption occurring near the fundamental edge 14 m a l k a l i halide c r y s t a l s i s known to be a structure sensi t i v e property. The fundamental absorption edge i t s e l f i s believed to be due to e l e c t r o n i c t r a n s i t i o n s from negative ions to neighboring p o s i t i v e ions, i n such a way that the ele c  tron and i t s corresponding "hole" on the negative ion remain i n i n t e r a c t i o n . Thus the energy for t h i s t r a n s i t i o n i s lower 48 than that for complete removal of theselectron. Since a l l the ions of the lattice can contribute to this absorption, the absorption coefficient is very high (10 - 10° cm ). However, at energies slightly less than that required for this "exciton" transition, the structure sensitive absorption referred to above is always found. It has been suggested that such absorption is due to exciton transitions in ions situated near crystalline imperfections such that a smaller energy is required to transfer the electron. Experimentally i t has been shown^ that the magnitude of the absorption is increased by plastic deformation which is believed to intro duce dislocations and vacancies. Thus a study of the optical absorption near the fundamental edge may be considered use ful in any investigation of imperfections in ionic crystals. The first fundamental absorption edge in MgO was located 15 at about 7.5 ev by Johnson and was later ascribed to exciton 16 formation by Krumhansl . In stoichiometric crystals a measur able absorption occurs, however, at energies as low as 4 ev (Figure 7, curve A) i . e . , at roughly one-half the exciton energy. Thus the ultraviolet absorption begins much further from the fundamental edge than it does in typical alkali halide crystals. It can then be argued that either, (a) The ultraviolet absorption in stoichiometric MgO is not due to "perturbed" exciton transitions but rather to absorption by impurity atoms, or, (b) The absorption is due to perturbed exciton transi tions and crystalline imperfections have a much greater 49 influence on the energy of the exciton t r a n s i t i o n i n MgO than i n a l k a l i halide c r y s t a l s . It does not seem possible to disting<uisrfo between these two p o s s i b i l i t i e s on the basis of the available experimental evidence. A comparison of curves A and B, Figure 7 seems to i n d i  cate that the magnitude of the background absorption was decreased by cooling slowly and thus allowing the c r y s t a l to approach equilibrium at a temperature lower than 1400°C, the temperature of the treatment. Curve C however implied that the shape of the absorption spectrum changes with tempera ture and therefore implies that curve B was merely a non- equilibrium state between the states represented by A and C. This implication was further brought out by the subsequent experiments, the d e t a i l s of which were omitted from section B.7. Such a change i n the absorption spectrum indicates the formation of new types of imperfections. The fact that more of the l a t t e r were formed at lower temperatures suggests that the new imperfections may be formed from the o l d , e.g. by aggregation. The lack of influence of the c r y s t a l thickness on the rate at which the new state i s achieved i s i n accord with t h i s suggestion. Since the spectral dependence of photoconductivity d i d not change with heat treatment i t must be concluded that the background absorption makes a n e g l i g i b l e contribution to the photoconductivity. For t h i s reason we have represented 50 (Figure 31(d) the t r a n s i t i o n s involved i n such a way that the absorption process w i l l lead to no free c a r r i e r s . C.8 Excess Mg Crystals The experiments described i n section B.8 and i l l u s t r a t e d by Figures 10, 11 and 12 show that the o p t i c a l absorption c h a r a c t e r i s t i c of the stoichiometric c r y s t a l i s reduced by the addition of excess Mg. The actual form of the induced o p t i c a l absorption can therefore only be deduced from an experiment l i k e that i l l u s t r a t e d by Figure 12; assuming that the absorption decrease i s e s s e n t i a l l y complete a f t e r the f i r s t treatment, the change on the second treatment, curve B, gives the actual spectral dependence of the o p t i c a l absorption. Thus i n Figure 9, for example, the t o t a l absorption spectrum a f t e r the heating i n Mg vapor i s approximately the induced absorption spectrum. It i s then clear from Figure 9 that the induced spec trum contains no obvious strncture and cannot be resolved into "bands". For t h i s reason we postulate that the spectrum con s i s t s of a superposition of several bands; a s u f f i c i e n t number, i n f a ct, that the composite absorption curve shows none of the extrema nor double i n f l e c t i o n s which would be expected for the superposition of bands centered about energies s u f f i c i e n t l y d i f f e r e n t from one another. The most obvious manner i n which the excess metal can be accommodated into the l a t t i c i s s u b s t i t u t i o n a l ^ as doubly charged positive ions. Thus the extra absorption may be ascribed to the f i l l i n g of c e r t a i n unoccupied l e v e l s by the 51 extra electrons. Such a set of l e v e l s i s shown in Figure 31(d). Since the f i l l i n g of these lev e l s reduced the background absorp t i o n as discussed above, we associate a f i l l e d ground state with each of them. The reduction of the background absorption then follows i f t r a n s i t i o n s such as that i l l u s t r a t e d i n Figure 34(d) are supposed to account for t h i s absorption, as mentioned i n the previous section. It might be concluded from the above that when the back ground absorption has e s s e n t i a l l y disappeared ( i . e . , the empty leve l s have been f i l l e d ) the t o t a l absorption w i l l not change further. Experimentally, however, the absorption con tinues to increase af t e r the i n i t i a l decrease. It i s there fore necessary to assume that the process of adding excess Mg also provides the l e v e l s i n which the extra electrons are to be assommodated. This may be accomplished, for example, by the d i f f u s i o n of negative ion vacancies into the body of the c r y s t a l . If the photoconductivity (Figure 13) i s to be ascribed to the centers responsible f o r the bulk of the o p t i c a l absorp t i o n (Figure 9), i t can be concluded that the low energy- absorption contributes very l i t t l e to the photoconductivity. This low energy absorption then cannot be i d e n t i f i e d with that discussed i n connection with X-rayed cr y s t a l s (section C.10). The l a t t e r absorption contributed a measurable photo conductivity. . The major f r a c t i o n of the o p t i c a l absorption may, how ever, contribute nothing to the photoconductivity. In t h i s 5 2 case two sets of l e v e l s such as that shown i n Figure 31(d) would have to be postulated. One of these would be required to .account for the absorption spectrum as discussed above while the other would account for the structureless photoconductivity spectrum. None of the evidence so f a r presented allows one to choose between the above two a l t e r n a t i v e s . At t h i s point we a r b i  t r a r i l y select the f i r s t p o s s i b i l i t y since i t requires the introduction of fewer l e v e l s . As mentioned above, the low energy absorption then must be ascribed to t r a n s i t i o n s which do not result i n free c a r r i e r s . No attempt has been made to indicate such t r a n s i t i o n s on Fgiure 31(d). It i s believed that the transitions g i v i n g the photoconductivity (and accord ing to our postulate the absorption) at higher energies may be i d e n t i f i e d with t r a n s i t i o n s observed i n c r y s t a l s treated i n other ways. These are discussed i n section C.9 and C.10. C.9 U l t r a v i o l e t I r r a d i a t i o n I r r a d i a t i o n with u l t r a v i o l e t l i g h t of an appropriate energy may be expected to empty certain l e v e l s , placing the corrsponding c a r r i e r s i n shallower l e v e l s or i n other, as yet unexcited, deeper l e v e l s . These two trapping mechanisms were discussed e a r l i e r (section G.3). The e f f e c t of the pro longed i r r a d i a t i o n on the photoconductive y i e l d at the energy  of i r r a d i a t i o n may be (a) A decrease due to a depletion i n the number of centers which can be ionized by t h i s quantum energy or (b) An increase, i n spite of (a), due to the fact 53 that the density of trapping centers i s decreased and hence the range increased. The occurrence of (a) would required, of course, that the range be l i t t l e a f fected by the f i l l i n g of traps, i . e . , that the density of ionizable centers be much less than the density of trapping ccent'ersj. ^Experimentally, however, (b) was observed for i r r a d i a t i o n i n e i t h e r the 4.0 or 5.0 ev bands. Thus i t can be concluded that the depletion of the ionizable centers i s more than o f f s e t by the increase i n range afforded by the f i l l i n g of the trapping centers.isFrom t h i s i t follows that the density of trapping centers i s less than the density of ionizable (5 ev) centers and "therefore >ithat the l a t t e r cannot themselves provide the only trapping mechanism. A similar conclusion follows from the e f f e c t of the pro longed i r r a d i a t i o n on the photoconductive y i e l d at quantum energies other than that of the i r r a d i a t i o n . For the large r e l a t i v e increase that occurred at the lower energies (Figure 15) can be explained by the increased occupancy of l e v e l s which would be empty i f the c r y s t a l were in thermal equilibrium. The lack of obvious structure i n the spectrum of Figure 15, curve C, may simply be due to presence of a number of overlapping bands. The experimental curves could probably be explained by the superposition of 4 or 5 bands with widths of 0.6 to 0.8 ev. The low energy section of curve B, however, does not appear to require the assumption of as many l e v e l s . This spectrum appears to show that no l e v e l s are f i l l e d which have o p t i c a l e x c i t a t i o n energies as low as some 54 of those which can be f i l l e d by the 5.0 ev i r r a d i a t i o n . According to Figure 14, the e f f i c i e n c y of the a c t i v a t i o n increased abruptly when the energy of i r r a d i a t i o n was changed from 3.4 to 3.9 ev. This, of course, i s in agreement with the previously determined spectral dependence of photosensi t i v i t y (see Figure 6). The difference between curves 5 and 6 was not expected but i n view of the fact that curves 5 and 6 were brought about by i r r a d i a t i o n s i n the 5 ev band, following previous i r r a d i a t i o n s i n the 4 ev band, we may expect the situ a t i o n to be quite complicated. This w i l l be es p e c i a l l y true i f e x c i t a t i o n i n the two bands does not lead to the same type of c a r r i e r . In f a c t , since the photoconduc t i v i t y spectra induced by the two i r r a d i a t i o n s were not the same, i t may be concluded that the two excitations do not produce the same type of c a r r i e r . This conclusion i s strengthened by the res u l t s of section B . l l . From the absorption change which occurred under 5.0 ev i r r a d i a t i o n (Figure 16) i t i s evident that such i r r a d i a t i o n introduced the centers c h a r a c t e r i s t i c of excess oxygen (cf. Figure 4). Now according to the discussion to be given i n i section C . l l , the 5.0 ev t r a n s i t i o n leads to free electrons, so that the only obvious t r a n s i t i o n which could lead to the formation of the excess oxygen centers i s that indicated i n Figure 31(e). This model associates the:5 ev t r a n s i t i o n with a p o t e n t i a l excess oxygen center. The ex c i t a t i o n of t h i s center by the absorption of a 5 ev quantum and i t s subsequent 55 thermal i o n i z a t i o n would result i n the l e v e l configuration of Figure 31(c) which we ascribed to the excess oxygen center. It should be noted that the induced absorption shown i n Figure 16 has a long t a i l extending well into the v i s i b l e region. This part of the spectrum cannot be associated with the excess oxygen type centers. It i s suggested that i t can be ascribed to those centers which also provide the photo conductivity i n t h i s part of the spectrum (Figure 15, curve C). According to section C . l l the i r r a d i a t i o n at 4.0 ev creates free holes. It i s not possible to associate the o r i g i n of these holes with potential metal-excess centers, since the absorption.spectrum of the l a t t e r i s not very s p e c i f i c (Figure 9). Moreover, the absorption change on i r r a d i a t i o n was s u f f i  c i e n t l y small that poor accuracy was obtained i n these measure ments (Figure 17). In any case, a comparison of Figures 9 and 17 shows that there i s some difference between the i r r a d i a  t i o n induced absorption and that induced by heating i n Mg vapor. A l l that can be said with certainty i s that the holes produced by the 4 ev radiation are not trapped to form oxygen- excess centers (Figure 17). One other important feature of curve B, Figure 15, should be mentioned. I r r a d i a t i o n i n the 4 ev band reduced the photo- conductive y i e l d i n the 5 ev band. It seems reasonable to suppose that the holes, trapped i n shallower l e v e l s a f t e r being excited by 4 ev radiation, can then provide an additional trapping mechanism for electrons excited by 5 ev radiation. 56 Thus the electron range would be reduced and the magnitude of the y i e l d i n the 5 ev band would decrease as observed. To summarize, we suppose that i r r a d i a t i o n i n the 5 ev band excites electrons to the conduction band and that at least some of these are subsequently trapped i n a number of previously unoccupied l e v e l s (see Figure 31(e). The electron range i s thereby increased and i n addition, since o p t i c a l e x c i t a t i o n of these shallow l e v e l s i s now possible, photo- conduction i s observable at lower quantum energies. At the same time e x c i t a t i o n to the states emptied by the i r r a d i a t i o n becomes possible and an increase i n o p t i c a l absorption i n the excess oxygen bands i s observed (Figure 16). On the other hand, i r r a d i a t i o n i n the 4 ev band creates free holes which are than trapped by leve l s (Figure 31(f) previously occupied by electrons. The pote n t i a l excess oxygen type centers do not, however, take part i n the hole trapping process. C.10 X-Ray I r r a d i a t i o n The X-ray induced absorption spectrum of Figure 19, curve A, shows c l e a r l y the 5.7, 4.3 and 2.3 ev bands. Weber 1 0 has shown that the 4.8 ev band i s also present and t h i s result has been confirmed by Soshea 1 1. The l a t t e r author has also obtained evidence that there i s more absorp t i o n to the high energy side of the 5.7 ev peak than can be accounted for by a symmetrical band centered at 5.7 ev. It appears, therefore, that the 5.2 ev band, found by Johnson 1 5 i n excess oxygen c r y s t a l s , may also be produced by X - i r r a d i a t i o n . 57 Thus the spectrum of Figure 19, curve A, contains a l l , or a l l but one, of the bands c h a r a c t e r i s t i c of excess oxygen plus some extra absorption l y i n g i n the v i s i b l e region of the spec trum. The band at 2.3 ev i s e a s i l y defined but i n the region between the l a t t e r and the 4.3 ev band there i s no obvious resolved structure. In f a c t , i t has been shown, again by Soshea 1 1, that a f t e r the thermal decay of the 2.3 ev band there remains i n the same spectral region some unresolved absorption of rather small magnitude. Consequently, i t appears that the absorption, over and above that also found i n excess oxygen c r y s t a l s , consists of the 2.3 ev band plus a small more or l e s s continuous absorption extending from about 2 ev to at least 3.6 ev. This may be due to the super p o s i t i o n of a number of r e l a t i v e l y broad bands as suggested i n the previous section incconnection with. UV excited speci mens (cf. Figure 15). As shown in Figure 20 most of the v i s i b l e absorption decays rather rapidly at room temperature while the u l t r a  v i o l e t absorption decays rapidly at f i r s t then more and more slowly u n t i l the decay rate becomes immeasurably small. These bands were observed to the extent of 40 percent of t h e i r saturation i n t e n s i t y 4 months a f t e r t h e i r formation. Thus some of the centers appear to have higher thermal a c t i v a t i o n energies than others. This type of observation has been made previously i n the sase of X-rayed a l k a l i hal'ide c r y s t a l s 1 8 . It has been variously assumed fo r the l a t t e r that (a) The thermal bleaching occurs by the thermal release 58 of a trapped electron- and i t s subsequent recombination with a trapped hole. Both the electrons and holes are believed to be connected with centers which evidence themselves i n the absorption spectrum. Thus the decays of the absorption i n dif f e r e n t spectral regions must be correlated. An alternative decay mechanism i s (b) The recombination of trapped electrons and holes by the quantum mechanical tunneling process. The decay of the various absorption bands must again be correlated. With hypothesis (a) the large v a r i a t i o n of decay rate with time has been taken to imply that the centers have di f f e r e n t thermal io n i z a t i o n energies i n spite of t h e i r common 18 o p t i c a l e x c i t a t i o n energy. Se i t z , however, prefers hypo thesis (b) and i n t h i s case explains the decay rate v a r i a t i o n by a non-uniform d i s t r i b u t i o n of trapped electrons and holes. Such a d i s t r i b u t i o n of course, leads to a wide d i s t r i b u t i o n i n the distances between centers of opposite type and there fore also to large variations i n the tunneling p r o b a b i l i t y . Postulate (b), however, does not seem to explain i n a simple fashion the commonly observed dependence of the thermal s t a b i l i t y of tie X-ray induced centers on the temperature at which the i r r a d i a t i o n i s ca r r i e d out. It i s generally found, for example 1 9, that samples i r r a d i a t e d at low temperature hawe a higher i n i t i a l decay rate at room temperature than those i r r a d i a t e d at room temperature. A similar r e s u l t was recently 20 obtained by Sturtz for MgO c r y s t a l s . The i n i t i a l decay rate at room temperature was found to be much greater for c r y s t a l s 59 i r r a d i a t e d at that temperature than f o r those i r r a d i a t e d at higher temperatures. It i s believed that these facts may be q u a l i t a t i v e l y explained by the model developed l a t e r i n t h i s section. The e f f e c t of X-rays on the photoconductivity (Figure 21) was not correlated with the absorption change at high energies obtained by the same means (Figure 19). It seems reasonable to postulate that the photoconductivity i s associated with the unresolved absorption discussed e a r l i e r i n t h i s section. fi's^shown in Figure 23, the photoconductivity spectrum induced by prolonged i r r a d i a t i o n i n the 5.0 ev band i s s i m i l a r to that of an X-rayed specimen which had undergone a p a r t i a l thermal decay (by " s i m i l a r " we imply that the spectra d i f f e r only by a factor which i s independent of quantum energy) a Since the former i r r a d i a t i o n can only introduce one type of trapped c a r r i e r i t i s concluded that the p a r t i a l l y decayed X-rayed cry s t a l also contains oniy one type of c a r r i e r capable of photoionization. The dir e c t determination of c a r r i e r type (section C . l l ) shows that i n both cases the spectra are due to trapped electrons. Thus the photoionizable trapped holes decay very readily at room temperature, at a rate which i s comparable to that of the decay of the resolved absorption band at 2.3 ev (Figure 22). It then seems reasonable to suppose that these trapped holes disappear by recombination with electrons from the 2.3 ev.centers. Since the o p t i c a l a c t i v a t i o n energy of the l a t t e r i s smaller than that for the trapped holes (Figure 15, curve B) i t i s also reasonable to 60 suppose that the rate of decay of both types of centers i s determined by the thermal io n i z a t i o n rate of the 2.3 ev centers. The disappearance of the trapped holes can, on the basis of previous considerations, be expected to have two other consequences. In section C.9 i t was concluded that the pro duction of trapped holes provided an additional trapping mechanism which appreciably reduced the electron range. Thus in the present case the decay of the trapped holes can be expected to increase the photoconductive y i e l d i n that region of the spectrum where e l e c t r o n i c e x c i t a t i o n predominates, i . e . above 4„ev. Secondly, a decrease i n y i e l d can be expected at lower energies because the above discussed recombination of shallow trapped electrons with the trapped holes leaves fewer centers which can be ionized by quanta i n t h i s energy region. Both of the required features are shown by Figure 21 (compare curves B and D). After the r e l a t i v e l y rapid processes discussed above have taken place the UV absorption bands can only decay by combina t i o n withhthermally released electrons from the centers giv i n g r i s e to the remaining photoconduction. Since the photoconduc t i v i t y spectrum must be due to a number of d i f f e r e n t types of centers, the decay curves for the UV bands may be expected to be complicated. In fact since each type of trapped electron w i l l be expected to decay monomolecularly with i t s own time constant, the decay curve should be resolvable into a number of simple exponential terms. An analysis of t h i s type has been given for the decay of X-ray induced luminescence i n KBr. 61 by Williams et a l , who apparently have located several l e v e l s i n which c a r r i e r s can be trapped. A s i m i l a r analysis of the decay of o p t i c a l absorption i n MgO i s shown i n Figure 32 where 3 c h a r a c t e r i s t i c time constants are also given. In order to calculate thermal i o n i z a t i o n energies from these, the value 99 of ~V i n the expression o 1 -E/kT - = v e r ° must be known. Here T i s the time constant to be associated with a thermal io n i z a t i o n energy E. Table IV shows the c a l  culated values of E for various assumed values o f v . o Table IV Calculated Thermal Ionization Energies  of the Shallow Electron Traps ^ = 10 9 sec" 1 v o»10 1 2sec~ 1 "10 sec 1230 hrs. 44 hrs. 5 hrs. .90 ev .82 .76 1.07 ev 1.00 0.93 1.19 ev 1.10 1.05 Thus the traps which decay i n reasonable times at room temperature have thermal a c t i v a t i o n energies i n the v i c i n i t y of 1 ev. The o p t i c a l i o n i z a t i o n energies should be somewhat greater than these. We may estimate on the basis of various 62 23 t h e o r e t i c a l and experimental r e s u l t s that the o p t i c a l energies should be grouped around 2 ev for these, the shallowest traps, which can be f i l l e d by excitation at room temperature. Then the photoconductivity i n an X-rayed ( i . e . , traps f i l l e d ) specimen should begin to drop sharply i n t h i s energy region. Figure 22 shows that t h i s i s approximately so. Those traps which have thermal i o n i z a t i o n energies apprecia bly greater than 1 ev (opt i c a l energies greater than about 2 ev) do not decay to a measurable extent at room temperature. Consequently, neither the magnitude nor the spectral dependence of the photoconductivity i n the high energy region would be expected to change with time, once the trapped holes and the shallow trapped electrons have e s s e n t i a l l y disappeared. To summarize, the proposed model at t r i b u t e s the large increase i n photoconductive y i e l d induced by X - i r r a d i a t i o n to (a) A large increase i n x (see section B.2 for the meaning of the symbols) because many of the electron and hole traps are f i l l e d and (b) An increase i n the because e x c i t a t i o n from the newly f i l l e d l e v e l s becomes possible. The change i n spectral dependence (curves B, C, D, Figure 21) with thermal decay i s attributed to the l i b e r a t i o n of trapped holes which also annihilate the electrons which gave the 2.3 ev band absorption (Figure 22). The fact that the y i e l d at high energies actually increases during the thermal decay (curve D, Figure 21) may be evidence that the trapped holes act 63 as electron traps as previously suggested. An increase i n x for electrons would then occur as the holes decayed. The experiment i l l u s t r a t e d by Figure 23 i s i n accord with the above model i n that i t shows that a specimen excited i n the 5.0 ev band (curve A) can be returned to the same state C (except for an increase i n x a f t e r a subsequent X - i r r a d i a t i o n , by simply allowing a few hours of thermal decay to take place. The fact that i r a d i a t i o n at 2.3 ev reduced the photo- conductive y i e l d by approximately the same f r a c t i o n a l amount at a l l energies (Figure 26) implies that the reduction i s due to a decrease i n x. This decrease presumably occurs because the 2.3 ev quanta ionize some of the shallow f i l l e d l e v e l s thus providing more l e v e l s for trapping. The electrons from these l e v e l s can re combine with the trapped holes i n the excess oxygen type l e v e l s (Figure 31(c), thus reducing the o p t i c a l absorption i n the 5.7, 4.8 and 4.3 ev bands (Figure 24). Since the photoconductive y i e l d at 2.3 ev was not p r e f e r e n t i a l l y bleached, i t must be concluded that only a small f r a c t i o n of the f i l l e d l e v e l s of t h i s energy were emptied in the course of t h i s experiment. The few extra empty le v e l s must, of course, increase the trapping p r o b a b i l i t y s u f f i c i e n t l y to decrease the range by 60 percent (Table I I I ) . Although Figure 25 shows a rather large f r a c t i o n a l decrease i n absorption at 2.3 ev, i t does not contradict the statements made above i n connection with Figure 26. The crystal of Figure 25 was freshly X-rayed and therefore contained a prominent absorption band at 2.3 ev (cf. Figure 29, curve A). It i s believed that the absorption decrease shown i n Figure 25 i s due p r i n c i p a l l y to the disappearance of t h i s band. In the case of the p a r t i a l l y decayed c r y s t a l , however, t h i s band has already decayed thermally to a very low l e v e l . The bleaching of the photoconductivity by quanta of t h i s energy i s then attributed to the ex c i t a t i o n of electrons from l e v e l s which are evidenced by the previously discussed (Section C.9) unresolved absorption superimposed on the 2.3 ev absorption band (Figure 16). C.11 Sign of the Charge Carrie r s In order to provide an inte r p r e t a t i o n of the r e s u l t s presented i n section B . l l , some discussion of the space charge f i e l d d i s t r i b u t i o n w i l l be given for a very i d e a l  ized case. Consider the experimental s i t u a t i o n as i l l u s t r a t e d by Figure 3(c) wherein the ZY planes constitute the electrodes of a cry s t a l with the l i g h t beam incident on the XZ plane and illuminating a f r a c t i o n of the volume, b wide as shown i n the figure. Assuming that the distance moved by each excited c a r r i e r i s small compared to a-^ , ag and b, the result of an i r r a d i a t i o n , during which the e l e c t r i c f i e l d i s applied, i s to give the f i e l d d i s t r i b u t i o n shown by the s o l i d l i n e i n Figure 33(a). The dotted l i n e shows the f i e l d before i r r a d i a t i o n , i . e . , that which would be calculated from the applied voltage and the electrode separation. The second step i n t h i s i d e a l i z e d experiment i s to 65 remove the applied voltage and bring the electrodes to the same pot e n t i a l . The f i e l d d i s t r i b u t i o n i s then as shown i n Figure 33(b) which i s simply a v e r t i c a l displacement of the previous diagram. For definitness i t i s assumed at t h i s point that the excited c a r r i e r s are electrons. The discussion can be e a s i l y altered to f i t the case of hole e x c i t a t i o n . In t h i s ease the f i e l d d i s t r i b u t i o n s of Figures 33(a) and (b) are the result of the space charges indicated on the diagrams. The important fact here i s that the electron excess l i e s outside the illuminated region while the electron deficiency l i e s within t h i s region. The t h i r d step of the experiment consists i n the e x c i t a  t i o n of more c a r r i e r s (within the same volume as previously irradiated) and t h e i r motion under the influence of the space charge f i e l d alone. Under these conditions the motion of the excited electrons i s to the right and the tendency i s for the former electron deficiency to be neutralized and a new deficiency to form at the .-left hand side of the i r r a d i a t e d region. (Notice that the electron excess i s not disturbed because i t l i e s outside the i r r a d i a t e d region.) If t h i s process could be carried to completion the space charge d i s - t r i b u t ion would be as shown i n Figure 33(c) with the cor responding e l e c t r i c f i e l d having an appreciable value only at the l e f t hand edge of the illuminated region. If the photocurrent were carried by holes rather than by electrons the "dipole" layer would exi s t at the opposite edge of the 66 illuminated region ( i . e . , the edge nearest the electrode which was held negative during the f i r s t step of the experiment). According to the foregoing discussion the sign of the charge c a r r i e r s can be determined i f the dipole layer can be located. This can be done i n practice by moving a narrow beam of l i g h t across the c r y s t a l and measuring the photocurrent as a function of the beam p o s i t i o n . If the electrodes are at the same po t e n t i a l during t h i s "scanning" the photocurrent observed w i l l be due to the motion of c a r r i e r s i n the pre viously developed space charge f i e l d and hence w i l l be a measure of t h i s f i e l d . The measured dependence of photo current on beam position w i l l , of course, only be a true representation of the e l e c t r i c f i e l d d i s t r i b u t i o n i f the s e n s i t i v i t y of the crys t a l i s uniform; that i s i f the UV i r r a d i a t i o n has not appreciably activated the c r y s t a l . This condition very l i k e l y cannot be met i n practice but nevertheless t h i s e f f e c t does not inter f e r e with the loca t i o n of the dipole layer. In an actual experiment the results may be expected to deviate from those shown schematically i n Figures 33(a) to (c). There are several obvious reasons for t h i s ; (a) The c a r r i e r range may not be small compared to the width of the i r r a d i a t e d region. (b) The c a r r i e r range may vary during the course of the experiment by means of the a c t i v a t i o n e f f e c t discussed above and also because the e l e c t r i c f i e l d i s not constant during the experiment. (c) The term, "range", as used above should a c t u a l l y read "mean range" since the displacement of a given electron 67 can vary between zero and a distance comparable to the d i s  tance between the electrodes, (d) The width of the scanning beam i s not n e g l i g i b l e compared to the width of the i r r a d i a t e d region, (e) It i s d i f f i c u l t to estimate the optimum duration of the second i r r a d i a t i o n (no applied f i e l d ) . If i n s u f f i c i  ent time i s employed the f i e l d due to the dipole layer may be masked by that due to the unneutralized charges at e i t h e r edge of the illuminated region. If the second i r r a d i a t i o n i s prolonged to avoid the former e f f e c t , the dipole i t s e l f may be destroyed, by the continuous dark current, f o r example. In spite of the above l i s t e d d i f f i c u l t i e s , i t i s believed that the results of section B . l l may be used to determine the sign of the charge c a r r i e r s excited under various conditions. For, even i f a c l e a r l y defined f i e l d minimum, corresponding to the "dipole" of Figure 33(c), cannot be discerned, the location of the "dipole" can be deduced from the asymmetry of the f i e l d d i s t r i b u t i o n . Thus i n Figure 27, curve B, the f i e l d minimum was shi f t e d towards the negative electrode by the formation of the dipole layer. It i s therefore concluded that e x c i t a t i o n i n the 4.0 ev band creates free holes. In Figure 28, curve B, there i s no obvious minima corres ponding to that of curve A. However, since further i r r a d i a t i o n (curve C) brings out the l e f t hand minimum p r e f e r e n t i a l l y , we ascribe the l a t t e r to the dipole layer. Thus the dipole was formed nearest to the p o s i t i v e electrode and i t i s concluded that e x c i t a t i o n i n the 5.0 ev band creates free electrons. 68 The interpretation of Figure 29 i s more obvious since the right hand minimum of curve B i s readily associated with that of curve A. Thus, the l e f t hand minimum of curve B i s ascribed to the dipole and i t i s concluded that 4.4 ev quanta create free electrons i n a p a r t i a l l y decayed X-rayed c r y s t a l . by D. CONCLUSIONS Much of the material presented here consists of prelimin ary investigations of the o p t i c a l absorption and photoconduc t i v i t y i n MgO c r y s t a l s of i n f e r i o r purity. The i n t e r p r e t a t i o n of the results required the introduction of a large number (or even continua) of energy l e v e l s i n the normally forbidden gap. It i s recognized that interpretations made on such a basis are not very s a t i s f y i n g . However, i t should be pointed out that even i n some other, much more thoroughly explored areas (e.g. 94 the properties of CdS and similar photoconductors ), s i m i l a r postulates are found to be necessary. Furthermore, the ob served properties were found to be reasonably reproducible among the several l o t s of MgO a v a i l a b l e . Thus i t i s believed that these properties, although they are probably determined to a large extent by the large impurity content, should also apply to many of the specimens for which data appear i n the l i t e r a t u r e . The following are the more important tentative conclusions r e s u l t i n g from t h i s work. (1) The most prominent UV absorption bands — those characteris t i c of excess oxygen and occurring at 4.3, 4.8, and 5.7 ev — have no photoconductivity associated with them (section 6). (2) The photoconductivity i n stoichiometric or excess oxygen c r y s t a l s l i e s p r i n c i p a l l y i n two Gaussian shaped peaks centered at 4.05 ev and 5.05 ev. E x c i t a t i o n i n these peaks i s found to res u l t i n free holes and .free electrons respectively. (Sections 70 6 and 11). (3) Addition of an excess of Mg to stoichiometric c r y s t a l s reduces or eliminates the o p t i c a l absorption c h a r a c t e r i s t i c of the stoichiometric state-. (Section 8) For t h i s reason i t i s te n t a t i v e l y concluded that the absorption spectra of s t o i c h i o  metric crystals and of excess Mg c r y s t a l s are associated with the same centers (Figure 31(d). With t h i s model the background absorption i s interpreted as being due to the t r a n s i t i o n s shown in the fi g u r e . The addition of excess Mg i s then considered to provide electrons which f i l l the upper states, thus eliminat ing the p o s s i b i l i t y of the t r a n s i t i o n s shown and therefore reducing the background absorption. At the same time t r a n s i  tions from the upper states to the conduction band are made possible, thus providing the extra absorption and photocon d u c t i v i t y observed in excess Mg c r y s t a l s . It seems necessary to postulate a near continuum of l e v e l s to explain the absorp t i o n i n eith e r stoichiometric or excess Mg cr y s t a l s and also to explain the photoconductivity of the l a t t e r . (4) Excitation of free electrons r e s u l t s i n the f i l l i n g of a number of shallow l e v e l s (Figure 31(e) some of which seem to contribute strongly (when empty) to the electron trapping process (section 9). Those of high energy (with e x c i t a t i o n energies greater than say 3 ev) may be those which are also f i l l e d by the addition of excess Mg. The lower energy ones are believed to be responsible for the absorption i n the v i s i b l e regions of Figure 16 ( i r r a d i a t e d i n 5 ev band) and for part of that i n the v i s i b l e region of Figure 19, curve A (X-rayed). 71 (5) Irr a d i a t i o n i n the 5 ev band introduces the absorption bands c h a r a c t e r i s t i c of excess oxygen. The 5 ev t r a n s i t i o n i s believed to be associated with a pote n t i a l ©enter of the l a t t e r type. (Figure 31(e). (6) The e x c i t a t i o n of free holes (e.g. by 4 ev band i r r a d i a  tion) causes a small increase i n UV absorption. No structure i s obvious i n t h i s spectrum. Some l e v e l s l y i n g nearer to the valence band than the 4 ev l e v e l trap these holes, making possible photoconduction at somewhat lower energies. (Section 9). These trapped holes can act as electron traps so that as they are formed, the e f f i c i e n c y of e l e c t r o n i c photoconduc- t i o n decreases (Figure 15) and as they are thermally ionized the e l e c t r o n i c y i e l d increases (Figure 21, curve D). (7) X - i r r a d i a t i o n excites both electrons and -holes and pro vides the following changes i n l e v e l occupancy. (a) The upper f i l l e d l e v e l s of Figure 31(e) are emptied thus providing the excess oxygen absorption bands at 5.7, 4.8 and 4.3 ev and at the same time decreasing the number of 5.0 ev excitations (Figure 21). (b) The series of shallow l e v e l s of Figure 31(e) i s f i l l e d with electrons thus increasing the range of free elec trons and providing o p t i c a l absorption i n the v i s i b l e region of the spectrum. Part of t h i s absorption l i e s i n a well defined band (Figure 19) while the remainder shows no obvious structure and corresponds to the photoconductivity of the c r y s t a l a f t e r a p a r t i a l thermal decay (Figure 21(d). (c) The series of low l y i n g l e v e l s of Figure 31(f) are 72 emptied thus providing photoconductivity at lower energies (Figure 21, curve B) and at the same time providing additional electron traps. (8) The thermal decay proceeds by: (a) The thermal release of electrons from the centers which give rise to the 2.3 ev absorption band. These e l e c  trons then combine with the trapped holes i n the le v e l s of Figure 31(f). By t h i s means the hole photoconductivity i s reduced and the electron range increased (compare curves B and D, Figure 21), while the v i s i b l e absorption decreases. (b) The UV absorption centers (Figure 31(c) decay by combination with electrons thermally released from the series of lev e l s of Figure 31(e). Since a number of thermal a c t i v a  t i o n energies are involved i n t h i s release, the dependence of UV absorption on time can be decomposed i n a number of simple exponential terms (Figure 32). (9) Bleaching of the UV absorption may be accomplished by using any wave length which can excite e l e c t r o n i c photoconduc ti o n , i . e . , any energy from about 2 ev to about 6 ev or higher. The higher energies may however, produce complicating side e f f e c t s . When the bleaching radiation l i e s i n the 2.3 ev absorption band electrons may be excited e i t h e r from the l e v e l s responsible for t h i s band or from those which also l i e at t h i s energy but are part of the quasi-continuous d i s t r i b u t i o n shown i n Figure 31(e). Thus, i n the bleaching experiment described in section B.10, no simple relationship between the absorption changes in the 2.3 ev band and i n the UV absorption bands may 73 be expected. (10) Bleaching of the X-ray induced photoconductivity can be achieved by i r r a d i a t i o n with 2.3 ev quanta. The e f f e c t i s due to the emptying of electron traps by o p t i c a l i o n i z a t i o n as discussed above and the consequent reduction i n electron range. 74 E. COMPARISON WITH PREVIOUS WORK The only previously reported measurements of photoconduc t i v i t y i n MgO c r y s t a l s were made by Day^. Since the two sets o f r e s u l t s are i n c o n f l i c t on a number of points Day's results w i l l be discussed i n some d e t a i l . The most important differences are: 1. The peaks at 3.6 and 4.8 ev obtained by Day i n neutron  i r r a d i a t e d c r y s t a l s were not found i n X-rayed c r y s t a l s i n the  present work. This fact alone i s not cause for alarm, but i t does seem reasonable to expect that any means of e x c i t a t i o n which i s capable of e x c i t i n g both electrons and holes w i l l result i n the formation of similar absorption and photoconduc t i v i t y bands. The apparent discrepancy can, however, be re solved by a consideration of the geometry used by Day and the fact that the correction factor /a (equation (1) was omitted i n his calculations. The dimension of h i s c r y s t a l i n the d i r e c t i o n p a r a l l e l to the l i g h t beam was about 1 cm. Thus the quantity a_ (equation (2) achieved a constant value at r e l a t i v e l y low quantum energy (say about 3.6 ev) compared to the case of a thinner specimen where the constancy of a would not be' achieved u n t i l the quantum energy was well into the 4.3 ev o p t i c a l absorption band. The spectrum (Day, ref. 5, Figure 1) should therefore be m u l t i p l i e d by a fa c t o r proportional to K for quantum energies greater than 3.6 ev. Since K i s expected to peak at 4.3 ev (Figure 22) the " v a l l e y " at 4.3 ev i n Day's spectrum would tend to be 75 eliminated and the 3.6 and 4.8 ev peaks thus disappear. The spectral dependence of photoconductivity would then esse n t i  a l l y agree with the re s u l t s of the present measurements. 2. The f a i l u r e to recognize i n the e a r l i e r work 5 that  the photoconductivity i n stoichiometric c r y s t a l s l i e s i n two  bands. The UV a c t i v a t i o n experiments were performed with a quantum energy of 4.0 ev. According to Figure 6 the a c t i v a  t i o n obtained by t h i s UV i r r a d i a t i o n should have been due i n part to absorption i n the 4 ev band and i n part to 5 ev band absorption. The spectral dependence of the photoconductivity i n the activated c r y s t a l (ref. 5, Figure 2) shows that the ac t i v a t i o n obtained was more c h a r a c t e r i s t i c of 5 ev band i r r a d i a t i o n . 3. The sign of the charge c a r r i e r s released by 4 ev  i r r a d i a t i o n . Day attempted to determine the sign of the charge released by 3.7 ev radiation by detecting the displacement by the e l e c t r i c f i e l d of a narrow UV activated region of the c r y s t a l . The location of the activated region was determined by scanning the activated c r y s t a l with a narrow l i g h t beam. The procedure involved the i m p l i c i t assumption that a plo t of photocurrent versus distance across the c r y s t a l ( i n a d i r e c t i o n p a r a l l e l to the f i e l d ) comprised a determination of the pro f i l e of the photosensitivity. However, since the i r r a d i a t i o n was of necessity performed with the e l e c t r i c f i e l d applied to the c r y s t a l , space charge f i e l d s were presumably developed as discussed i n section 5. Therefore, the v a r i a t i o n of photo current with distance i s a measure of the p r o f i l e of the product 76 of e l e c t r i c f i e l d and photosensitivity. Thus the interpreta t i o n of t h i s type of experiment i s confused by the formation of space charge f i e l d s . In spite of the above objection Day's conclusion that the c a r r i e r s produced by 3.7 ev i r r a d i a t i o n are holes i s i n agreement with the result o f section B . l l . However, his conclusion that the c a r r i e r s excited during his a c t i v a  t i o n experiment were therefore also holes i s not warranted (activating i r r a d i a t i o n was at 4.0 ev, i . e . i n the t a i l of the 5 ev band) and in f a c t , according to the present work, incorrect. The o p t i c a l absorption spectrum of the excess Mg c r y s t a l shown by Figure 9 i s similar to that obtained by Weber1^. The l a t t e r author, however, believed that t h i s spectrum could be decomposed into 3 bands centered at 4.8, 3.6 and 2.3 ev. The structure i s , however, not obvious i n Weber's data and i t i s believed that he was misled on two counts. (a) The decreasing background absorption discussed i n section G.8 makes the calculated induced absorption f a l l o f f i n the range of quantum energies where the background absorp ti o n has, before treatment, an appreciable magnitude (see Figure 12, curve A). If the induced absorption i s neverthe less calculated i n t h i s way, i t i s possible to postulate a 4.8 ev absorption band, whereas the true induced absorption would show no such f a l l i n g o f f at high energies and would therefore not indicate "the presence of such a band. (b) Weber was also convinced that the absorption spectrum 77 of an excess Mg c r y s t a l should consist of those bands which are found i n X-rayed c r y s t a l s but not i n excess oxygen c r y s t a l s . Since he was not aware that the 4.8 ev band was present i n excess oxygen cry s t a l s he believed that i t should be present i n excess Mg crystals since i t was quite obvious i n X-rayed c r y s t a l s . Having a t t r i b u t e d the absorption at high quantum energies in excess Mg c r y s t a l s to the 4.8 ev band, Weber could then decompose the remainder of the spectrum into 3.6 and 2.3 ev bands, both of which he believed were present i n the X-ray induced spectra. There seems to be no doubt about the e x i s  tence of an absorption peak at 2.3 ev i n X-rayed c r y s t a l s . However, there seems to be no good evidence for i t s existence i n excess Mg crystals nor for the existence of a 3.6 ev band i n c r y s t a l s treated i n any fashion. It i s believed that only the erroneous assumption of a 4.8 ev band i n the excess Mg cr y s t a l s would lead one to postulate the existence of the 3.6 ev band. 9 5 Hibben found that MgO crystals were v i s i b l y colored by exposure to 4.9 ev radiation. This i s presumably the same e f f e c t as i l l u s t r a t e d by Figure 16. 26 Eisenstein studied the X-ray induced phosphorescence of MgO c r y s t a l s . An emission band at 3.6 ev wasJTound to have a very long decay time. This band may be connected with the decay of the excess oxygen type absorption centers. The long .decaya'time v isoxsoiisistent with the long term absorption decay shown by Figure 20. 78 Yamaka and Sarwamoto have determined the sign of excited c a r r i e r s by measuring the H a l l e f f e c t . It does not seem p r o f i t  able to discuss t h e i r work i n terms of the present r e s u l t s since no attempt was made to determine which photoconductivity bands were present i n t h e i r samples. Radiation of a p a r t i c u l a r wave length (provided by f i l t e r s ) was assumed to provide e x c i t a t i o n i n a "band" centered at the same energy. In t h i s manner they determined that e x c i t a t i o n i n the 4.8, 3.6 and 2.3 ev "bands" provided hole conductivity i n excess Mg c r y s t a l s . Although t h i s conclusion i s i n doubt i n view of the doubt concerning the presence of these bands i n such c r y s t a l s , the fact that hole conduction was detected i s in contradiction to the d i s  cussion of Section C.l-1. 2 8 Yamaka detected, by measurements of thermoluminescence, the presence of a number of traps whose thermal a c t i v a t i o n energies he estimated to f a l l i n the region .56 to 1.58 ev. Since the same results were obtained both by X-ray and 4.9 ev o p t i c a l i r r a d i a t i o n the traps are according to the present work electron traps. These are presumably the traps which are responsi ble for the photoconductivity i n X-rayed and p a r t i a l l y decayed cry s t a l s (Figure 22, curve B, and Table IV). BIBLIOGRAPHY 1. Lander, Rev. S c i . Inst., 24., 331 (1953). 2. Strong and Brice, J. Opt. Soc. Am., 25_, 207 (1935). 3. Jenkins and White, Fundamentals of Physical Optics, (McGraw-Hill, 1937) p. 294. 4. S e i t z , Rev. Mod. Phys., 26., 44 (1954). 5. Day, Phys. Rev., 91_, 822 (1953). 6. G e l l e r , Phys. Rev., 101, 1685 (1956). 7. H a l l , Phys. Rev., 8_7, 387 (1952). 8. Rose, Proc. IRE, 43, 1850 (1955). 9. PBube, Proc. IRE, 4_3, 1846 (1955.). 10. Weber, Z e i t s f. Physik, 130, 392 (1951). 11. Soshea, M. S. Thesis, E l e c t r i c a l Engineering Department, University of Minnesota, (1956). 12. Molnar and Hartman, Phys. Rev. 91, 1015 (1950). 13. Lye, S c i e n t i f i c Report No. 1, U. S. A i r Force Contract No. 33(616)-3325 (1956). 14. Blakney and Dexter, Defects i n C r y s t a l l i n e Solids (The Physical Society, London, 1955), p. 108; Phys. Rev. 96, 227 (1954). 15. Johnson, Phys. Rev. 94_, 845 (1954). 16. Krumhansl, Photoconductivity Conference (Wiley, 1956) p. 455. 17. Seitz, Rev. Mod. Phys. 26., 53 (1954). 18. Ibid, p. 68 19. Ibid, p. 68, F i g . 34. 20. Sturtz, E l e c t r i c a l Engineering Department, University of Minnesota; private communication. 21. Williams, Usiskin and Dekker, Phys. Rev. 92_, 1398 (1953). 22. Mott and Gurney, El e c t r o n i c Processes i n Ionic Crystals, Oxford, 1948), p. 130. 23. Lehovec, Phys. Rev. 92, 253 (1953). 80 V a s i l e f f , Phys. Rev. 96_, 603 (1954). 24. -Rose, Proc. IRE 43, 1857 (1955). 25. Hibben, Phys. Rev. 51, 530 (1937). 26. Eisenstein, Phys. Rev. 9_4, 776 (1954). 27. Yamaka and Sawamoto, Phys. Rev. 101, 565 (1956). 28. Yamaka, Phys. Rev. 96, 293 (1954). 29. Mott and Gurney, E l e c t r o n i c Processes i n Ionic Crystals, (Oxford, 1948) p. 82. 30. Seitz, ref. 4. Burstein et a l . , ref. 16, p. 384. 31. Lax, ref. 16, p. 111. Pekar, Z. exptl. teor. phys., 20, 267 (1950). 32. Burstein et a l . , Photoconductivity Conference (Wiley, 1956) pp. 379-382. 33. Bernard V. Haxby, E l e c t r i c a l Engineering Department, University of Minnesota, private communication. 34. Lipson et a l . , Phys. Rev. 99, 444 (1955). MOUNTING OF THE CRYSTAL FOR PHOTOCONDUCTIVITY MEASUREMENTS SCHEMATIC ARRANGEMENT OF THE PHOTOCONDUCTIVITY APPARATUS FIG. 2 FIG. I I2r or < or or < UJ or or O o H O I CL 8 12 16 TIME OF IRRADIATION (min) 4Z -7—r I (O FIG. 3 100 80 2 o UJ o u . UJ o o g r-0-tr o oo < 60 40 20 0 * 6.0 TYPICAL ABSORPTION SPECTRA OF MgO CRYSTALS AS RECEIVED \ \ x—x"^x. * X \ x - ^ y - x ^ \ \ \ 5.0 4.0 QUANTUM ENERGY(ev) FIG. 4 b o a N n >- o UJ >- .16'° y 10' 111 > o O z o o o o 10 12 10 13 1 RESOLUTION OF A TYPICAL 5. PHOTOCONDUCTIVITY. SPECTRUM INTO TWO GAUSSIAN BANDS X* 05 e.v. o Q / Half • / 0.6 -width \ 9 e.v. \ / (Point > Curve s are expi s are calci erimental, jlated.) / 4. 05e.v. / < o/j v / / / / 7v /Half - width ^  >7 e.v. \ 7 » / / / \ \ \ \ \ \ \ \ \ \ 3.0 3.5 4.0 4.5 5.0 QUANTUM ENERGY (e.v.) FIG. 6 5.5 6.0 EFFECT OF HEAT TREATMENT ON THE BACKGROUND ABSORPTION QUANTUM ENERGY(eV) FIG. 7 IO9 t j l f l f 0 o > o XL Q. K w M >- UJ >\ba UJ > r- O z o o o & a I Q_ ^13 PHOTOCC OF CRY! - A T D1FF )NDUCTIVP 5TALS HE ERENT TE ~ , , FY AND A ATED IN V :MPERATUF c -• - "1 ^BSORPTIO 'ACUUM IES Y ^ o ^ r N / - J 1 1 V r * 1 > —X" lOooo^c /# * fa! 1 K, I400*C 10 E o UJ g Li-Li- 1.0 g O z g 01 o CD < 3.5 4.0 4.5 5.0 5.5 FIG. 8 QUANTUM ENERGY (e.v.) 6.0 0.1 ABSORPTION SPECTRUM DUE TO HEATING IN MAGNESIUM VAPOR (THICKNESS .036 cm.) B A - B E F O R E HEATING B - A F T E R HEATING 8 2 0 2.4 2.8 32 36 4.0 4.4 QUANTUM ENERGY(ev) FIG. 9 4.8 5.2 5.6 THE EFFECT OF EXCESS Mg ON THE BACKGROUND ABSORPTION OF Mg 0 A "BEFORE TREATMENT - \ B -AFTER IHR. AT I I I5°C C -CHANGE DUE TO HEATING 5.4 / i i — • 1 i = 1 — ^5.0 4.6 4.2 3.8 3.4 'A, QUANTUM ENERGY(ev) FIG. 10 THE EFFECT OF EXCESS Mg ON THE BACKGROUND ABSORPTION OF Mg 0 FIG. II 3 2 0 UJ O LT 16 U. UJ O O Z 12 o I- Q_ CC O 8 C/) CD < UJ e> z < 5 o EFFECT OF EXCESS Mg ON ABSORPTION OF MgO A" CHANGE BY HEATING 4 HRS. AT 1115* C B -CHANGEBY HEATING AN ADDITIONAL 5HRS. AT 1115° C 5.8 5.4 5.0 4.6 4.2 3.8 3.4 QUANTUM ENERGY (ev) 3.0 2.6 2.2 FIG. 12 T T 10 101 O -II £ 10 E o CL X w -12 10 -13 10 EFFECT OF EXCESS MG ON PHOTOCONDUCTIVITY x B / / X / X 7 > 7 / A - UNTREATED B - EXCESS Mg 2.5 3.0 4.0 , . 5.0 QUANTUM ENERGY (ev.) FIG. 13 \pPTICAL ACTIVATION OF PHOTOCONDUCTIVITY l ^ l ^ ~ r - IN MgO ^ S ^ - - ^ ^ ^ ^ ^ ^A^/ 4 " 7 ill l a "'•I 1 7 / i c • • - 1 " 1 2 3 1 \ 4 J 5 6 1 1 .0 2.5 3.0 3.5 4.0 4.5 FIG. 14 QUANTUM ENERGY (e.v.) QUANTUM ENERGY (EV) FIG. 15 Q <3 t .040 z UJ Q < .030 Q. O UJ CO z < I o .020 .010 INDUCED OPTICAL ABSORBTION D U E T O IRRADIATION IN 4 ev. B A N D IRRADIATION ENERGY (3Bev) THICKNESS (0.65 Cm ) x — - x X X^ - x - x - s r x X 'X 3.2 3.6 4.0 44 4.8 5.2 5.6 6.0 6.4 QUANTUM ENERGY (ev) FIG. 17 BUILD-UP OF X-lRAY INDUCED ABSORPTION FOR 50 K.V. X - R A Y S (I5ma.) * I36 (0.40 mm.) TIME (HOURS) FIG. 18 ABSORPTION SPECTRA OF X-RAYED CRYSTALS >- H CO z UJ o _l < o I— CL o o UJ O Z) Q 0.8 " 0.6 " 0.4 - 0.2 - 0.0 6.0 A"AFTER X-RAY (SEE FIG. 21) B -AFTER 95HOURS THERMAL DECAY (d = .040CM) 5.0 4.0 3.0 QUANTUM ENERGY(ev) 2.0 FIG. 19 PHOTOCONDUCTIVITY IN X-RAYED MgO 'A- UNTREATED B-AFTER 40MIN. OF X-IRRADIATION C-AFTER 4HRS. THERMAL DECAY —| D-AFTER 50HRS. THERMAL DECAY I I • J _ 1.5 3.0" 3.5 4.0 4.5 5.0 QUANTUM ENERGY (e.v.) 5.5 6.0 FIG. 21 2.0 2.2 2.4 QUANTUM E N E R G Y (ev.) F IG. 22 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 QUANTUM ENERGY (e.v.) F IG. 2 3 1.000 - OPTICAL DENSITY AT4.2eV. VS BLEACHING TIME (IRRADIATION ENERGY = 2.3ev.) d = .IICM .800- .600- .400 A - IRRADIATED B - THERMAL DECAY ONLY .200 OPTICAL DENSITY BEFORE X-IRRADIATION .000 30 60 90 120 TIME IRRADIATED (MINUTES) FIG. 24 .200H OPTICAL DENSITY AT 2 3 e v VS BLEACHING TIME (IRRADIATION ENERGY = 2.3eV.) d = .IICM. .160 > ro cvi < .120 >- CO U J o < g C L o .080 040 A - IRRADIATED B-THERMAL DECAY ONLY C-DIFFERENCE OPTICAL DENSITIES BEFORE X - IRRADIATION A_ B 60 90 TIME IRRADIATED (MINUTES) 120 150 FIG. 25 0 I 2 3 . ^ 4 FIG. 26 QUANTA/CM 2 x|0~ 1 9 (Approximate) DETERMINATION OF THE SIGN OF CHARGE CARRIERS EXCITED IN 4 EV BAND POSITION F IG. 27 FIELD DISTRIBUTIONS AFTER IRRADIATION IN 5 EV BAND A - A F T E R I R R A D I A T I O N W I T H A P P L I E D E L E C T R I C F I E L D B - A F T E R S U B S E Q U E N T I R R A D I A T I O N W I T H N O A P P L I E D E L E C T R I C F I E L D C - A F T E R F U R T H E R I R R A D I A T I O N W I T H N O A P P L I E D E L E C T R I C F I E L D POSITION FIG. 28 DETERMINATION OF THE SIGN OF CHARGE CARRIERS IN AN X-RAYED CRYSTAL POSITION FIG. 29 POSSIBLE MECHANISMS FOR THE LOSS OF FREE CARRIERS CONDUCTION BAND / / 77TTTTT7JT77T777777 VALENCE BAND (a ) ( c ) («0 FIG. 30 CONDUCTION BAND 5.05 ev. 4.3 ev. 5.7 ev. 4.05ev / / / / / / / / / / / / / / / / / / / / / / / / . / / / / / / / VALENCE B A N D 7 / 7 (a) (b) (c) (d) (e) ( f ) P R O P O S E D ENERGY L E V E L S C H E M E S FOR Mg 0 FIG. 31 THERMAL DECAY OF X - R A Y INDUCED ULTRAVIOLET ABSORPTION AT ROOM TEMPERATURE O 100 2 0 0 3 0 0 4 0 0 500 6 0 0 TIME AFTER X-IRRADIATION (HRS.) FIG. 32 9 I D E A L I Z E D F I E L D DISTRIBUTIONS ILLUSTRATING T H E M E T H O D O F DETERMINING T H E SIGN O F T H E C H A R G E C A R R I E R S X=0 X=Q POSITIVE ELECTRODE x=a+b x=2a+ b NEGATIVE ELECTRODE x=o x=a POSITIVE ELECTRODE x*a+b x«2a+b NEGATIVE ELECTRODE Q _ J LU (a ) (b) + + + x=o x= a POSITIVE ELECTRODE x=a+b x*2a+b NEGATIVE ELECTRODE ( c ) FIG. 33 

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