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Conduction processes in crystals Williams, Robert Leroy 1952

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CONDUCTION PROCESSES IN CRYSTALS by ROBERT LEROY WILLIAMS A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of PHYSICS We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF ARTS. Members of the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA October, 1952 ABSTRACT . Two problems have been investigated i n connection with t h i s thesis. The f i r s t was a search f o r cr y s t a l s which detect alpha p a r t i c l e s by the transient conductivity produced. The second involved the measurement of H a l l voltages and conductivity to determine properties of lead sulphide. A few cry s t a l s have been made to count alpha p a r t i c l e s , some.at room temperature, and others at l i q u i d a i r temperatures. As I t i s inconvenient to cool c r y s t a l s , an attempt was made to f i n d a suitable room temperature counter. A few c r y s t a l s were t r i e d , but most of the time was spent investigating p e r i c l a s e . I t was thought that p e r i c l a s e , being transparent i n the u l t r a -v i o l e t , v i s i b l e and i n f r a red, should be trap-free and thus might possess good counting properties. Some time was spent i n v e s t i -gating associated effects i n germanium. In the second problem i t was hoped to derive a method of producing lead sulphide i n non-stoichiometric, proportions so that reproducible samples could be made. I f the properties of one sample were determined by using H a l l voltage and conductivity measurements, then the properties of a l l samples would be known. At present, as there are no methods of making lead sulphide with given properties, t h i s would be advantageous. ACKNOWLEDG-EMMTS The research described i n t h i s thesis has been supported by grants from the Defence Research Board. The author i s personally indebted to the Research Coun-c i l of Ontario f o r a bursary held during 1951 - 52. Also, the author wishes, to express his gratitude to Dr. U.F. Gianola under whose supervision the c r y s t a l counter portion of the thesis was c a r r i e d out, and to Dr. A.J. Dekker who supervised the H a l l effect portion of the t h e s i s . INDEX PART I • INVESTIGATION OF BOMBARDMMT CONDUCTIVITY IN CRYSTALS . Pag©. A. INSULATORS , . Introduction 1 Band Theory. . 2 Theory of Pulse Production..... 5 Discussion of n Q . 10 P o l a r i z a t i o n Effects.................... 11 Apparatus - Cr y s t a l Holder......... .. 12 Alpha Source 15 C i r c u i t Components 16 Crystal Contacts.... 17 Theoretical Calculations. 20 Crystals Used and Results Obtained......., 25 Discussion.. 28 B. SEMICONDUCTORS Introduction 31 Band Theory 31 . Germanium as a C r y s t a l . . ; • ••• 33 Apparatus 34 Experimental Results. 34 Extension of Counting Area 35 Increase of Pulse Size. 36 Discussion..... 36 PART I I CONDUCTION PROCESSES OF A SEMICONDUCTOR Introduction. 40 Theory of H a l l E f f e c t . . . . . . 40 Production of Lead Sulphide Layers... 42 H a l l Voltage Apparatus 44 Discussion 46 BIBLIOGRAPHY. • 48 ILLUSTRATIONS Figure following page 1 Band Picture of S o l i d s . . . 2 2 Ionic C r y s t a l L a t t i c e 3' 3 Crys t a l Holder.. 12 4 Crys t a l Holder..... .13 5 Heat Conduction Down a Cylinder... 13 6 C i r c u i t Diagram 16 7 E f f e c t of Heating Crystal 16 8 Evaporating Apparatus 18 9 Band Picture i n Semiconductors '32 10 Crystal Mounting. 36 11 Lead Evaporating Apparatus.. 42 12 Sulphur Reaction Chamber. 43 13 S p l i t Samples 45 GRAPHS Graph following' page 1 Voltage-Pulse Height . 26 2 Voltage-Pulse Height.... 34 3 Voltage-Pulse Height 1 34 4 Diode Characteristics 36 PART I INVESTIGATION OF BOMBARDMENT CONDUCTIVITY IN CRYSTALS A. INSULATORS Introduction In 1913 Rontgen and Joffe (1) showed that bombardment with ions could produce conductivity i n a c r y s t a l . S c h i l l e r (3) and J a f f e (3) also investigated these e f f e c t s . However i t was not u n t i l 1945 that van Heerden (4), working with s i l v e r chloride, showed that_Crystals-might be used to detect single p a r t i c l e s . This work has been extended by Street (5) and Hofstadter (6,7). Beta p a r t i c l e and gamma ray i o n i z a t i o n currents were detected by Frerichs and Warminsky (8) using cadmium sulphide, but because of th e i r lack of amplifying equipment they did not detect i n d i v i d u a l p a r t i c l e s or rays. Goldsmith and Lark-Horovitz (9) have since shown that cadmium sulphide i s a very good detector of i n d i v i d u a l p a r t i c l e s . Later Stetter (10) working with diamonds was able to detect i n d i v i d u a l p a r t i c l e s but did no extensive work. His work was confirmed by Woolridge, Ahearn and Burton (-1-1) i n 1947. At about t h i s time wide in t e r e s t developed i n the p o s s i b i l i t y of a cr y s t a l counter. The main advantages of a c r y s t a l counter are the large stopping power and small resolving time. The large stopping power compared with a g a s - f i l l e d tube makes i t possible to have a muoh more compact counter, and cry s t a l s would be more e f f i c i e n t i n detecting penetrating gamma rays and beta p a r t i c l e s . A small resolving time allows for the fast counting required i n coincident z and other work. Because of these advantages a search has been made i n recent years f o r s u i t a b l e c r y s t a l s . At present there e x i s t wide discrepancies i n reports on c r y s t a l s . Some c r y s t a l s work at l i q u i d a i r temperature while others work at room, temperature. Because of the inconvenience i n working at l i q u i d a i r temperature most of our invest igat ions have been c a r r i e d out w i t h c r y s t a l s at room tempera-t u r e . Band Theory A s a t i s f a c t o r y explanation of the mechanism of bombard-ment induced currents i s given by the band p i c t u r e of c r y s t a l s . Quantum mechanical theory p r e d i c t s that i n a c r y s t a l l a t t i c e the electrons of the system take energy l e v e l s i n d i s c r e t e bands. Up to a c e r t a i n energy l e v e l the bands are completely f i l l e d , that i s , each-available s i t e , or energy l e v e l , i n the band i s occupied by an e l e c t r o n . I n the case of an i n s u l a t o r , the next band, the conduction band, w i l l be completely empty, F i g . 1 (a) . Conse-quently, conduct iv i ty can only be produced i n an i n s u l a t o r i f an e lectron i n the f u l l band can be ra ised to an energy l e v e l i n t h i s empty band, where the e lec tron i s free to -move about the c r y s t a l , F i g . 1 (b) . The e lectron w i l l stay i n the conduction band u n t i l i t f a l l s back to i t s o r i g i n a l s i t e , or other vacant s i t e s i f they e x i s t . The e l e c t r o n , on l e a v i n g a f u l l band, leaves what i s known as a ho le , a l a t t i c e s i t e or energy l e v e l with no e l e c t r o n occupying i t . Neighbouring electrons i n the f u l l band may?now transfer t h e i r s i t e s . As a r e s u l t the hole could e f f e c t i v e l y move through the l a t t i c e . I t . h a s been found that holes remain empty band u © G 0) empty conduc- • _ ^ J f r e e tion band " electron """trap ///I /-7'- b i l l e d band /T/ /y7"~hole / / / / / - / - — / / / / / / T : 0° absolute T > 0° absolute (a) (b) F i g . 1 Band picture of so l i d s . to follow p. 2 fixed i n some cases and mobile in others. If mobile they act as a positively charged particle, of mass equal to the electron. If an electric f i e l d i s applied to a crystal which has electrons in the conduction band and holes that are mobile, the electrons w i l l move i n the direction of the f i e l d , and the holes in the opposite direction. However, because of interaction with the lattice, and electron traps, the electrons and holes w i l l be prevented from acting as i f only, the f i e l d were present. To understand the action of an electron trap in an ionic crystal one has to consider the l a t t i c e of a pure crystal. An ideal crystal at absolute zero would have an ion occupying every l a t t i c e point, Fig. 2 (a). At higher temperatures some of the ions are able to move from their l a t t i c e points leaving what is known as a trap, Fig. 2 (b). These ions may travel to the out-side of the crystal, extending the l a t t i c e , or go to i n t e r s t i t i a l positions between other ions of the l a t t i c e . A vacant l a t t i c e point would have an effective charge,-as removing an ion i s equivalent to adding an equal but opposite charge. This results in a change, of the potential i n the vi c i n i t y of the trap, such that electrons or holes, depending on the charge of the ion removed, can be attracted and_trapped, Fig. 2 (c). In the band picture this gives rise to energy levels below the conduction band, Fig. 1 (b) and free electrons in the conduction band can drop into these vacant sites. If the energy levels are close enough to the conduction band, trapped electrons can be excited to i t thermally. Depending on the level, light waves of various frequencies may also raise the trapped electrons to the conduction band. - + - + -+-- * • - + - + -+- - + - 4 - - + •I -i 4- — 4-+* - positive ion — - negative ion Ideal ionic l a t t i c e , (a) -+ - 4--- +-4-- f -+ — *•— + ^4.^-.- vacant l a t t i c e - + - f - point , •K-.t - j- - + - ^ - ^ - - • • ' ^ - +V> - 4-- path of ion ' i n t e r s t i t i a l atom Possible ionic l a t t i c e , (b) t- - + - *£_-^± trapped t- — + - fs^- +• - - e l e c t r i c f i e l d - + - 4- - 4- - hole _ 4> ~ ~ ^XLT->*.possible path - 4- — +* — of electron - + - +• - + — + "t__4_ 1 trapped 4- - + —-»- — 4- electron 4- - 4- - + - 4-(c) (d) F i g . 2 Ionic c r y s t a l l a t t i c e . to follow p. 3 4 The contribution of an electron to the conduction cur-rent w i l l depend on the distance i t tr a v e l s before being trapped. The density d i s t r i b u t i o n of the traps and t h e i r trapping cross-section w i l l thus p a r t l y determine the effectiveness of the conduc-t i o n electrons. The contribution of a f r e e electron to the current depends not on the t o t a l distance t r a v e l l e d , but on the component of the distance i n the d i r e c t i o n of the e l e c t r i c f i e l d . An elec-tron, although i n the conduction band, s t i l l reacts with the l a t -t i c e . C o l l i s i o n s with-ions w i l l d e f l e c t the electron, giving i t ve l o c i t y components not i n the d i r e c t i o n of the f i e l d , F i g . 2 (a). Thus, as an electron only travels an average t o t a l distance before being trapped, the more devious the path the shorter the distance t r a v e l l e d i n the d i r e c t i o n of the f i e l d . This r e s u l t s i n a smaller e f f e c t i v e transfer of charge. The average t o t a l distance that an electron travels between c o l l i s i o n s i s c a l l e d the mean free path, and i s related to the mobility, the average v e l o c i t y per unit f i e l d of the electron through the l a t t i c e . I t i s now possible to explain the action of bombardment conductivity. An alpha p a r t i c l e on entering the c r y s t a l i n t e r a c t s with the ions of- the l a t t i c e , i o n i z i n g some, exc i t i n g others, u n t i l a l l i t s energy has been expended and i t comes to r e s t . As a r e s u l t a number of electrons are raised from the f u l l band to the conduc-t i o n band. The excited electrons would f a l l to lower energy l e v e l s , giving o f f energy, either i n the-form of heat to the l a t t i c e or as radiation. The alpha p a r t i c l e s are stopped within about ten microns of the point of entry into the c r y s t a l , r e l e a s i n g a-cloud of electrons along t h e i r path. The distance the freed electrons 5 t r a v e l depends on t h e i r mobility, and on the density and cross-section of the traps. An equal number of holes w i l l be produced, which may or may not be mobile. In the following theory i t w i l l be assumed that the holes are immobile. I t should be mentioned that under ce r t a i n conditions trapped electrons may be released by thermal e x c i t a t i o n . In addition, free electrons, i f s u f f i c i e n t l y accelerated, may produce secondaries when c o l l i d i n g with the l a t t i c e . Both these effects are secondary to the primary action of the alpha p a r t i c l e s , and w i l l be neglected i n the following analysis. Theory of Pulse Production Let us suppose that freed electrons remain i n the con-duction band f o r a time T independent of the f i e l d . Then, i f dt i s a small i n t e r v a l of time, the p r o b a b i l i t y that an electron w i l l be trapped i n t h i s i n t e r v a l i s proportional to dt. I f there are n free electrons at time t then the number trapped i n time dt i s dn s ndt or i f n 0 i s the number of electrons at t equal to zero, then the number free a f t e r a time t i s t n a n Q e -7p (1) I f v i s the mobility or d r i f t v e l o c i t y f o r unit f i e l d , and E i s the f i e l d , then the average distance, & , that electrons cover before being captured i s given by 6 = vET (2) When an electron travels a distance i n a c r y s t a l , the e f f e c t i v e transfer of charge across the c r y s t a l i s given by q 6 f f * e £ i [ - ( 3 ) where d i s the thickness of the c r y s t a l . In the event that both holes and electrons conduct, t h i s becomes <leff = e * x r+ A X - ( 4 ) d A and A x _ being the distance the holes and electrons move respectively. The voltage produced across the input dropping r e s i s t o r of an amplifier would then be V 6 f f = 8 A 3 C (5) where C i s the input capacity-of the amplifier. I f we consider alpha p a r t i c l e s s t r i k i n g a c r y s t a l we can calculate what Veff should be. As the alpha p a r t i c l e s pene-tr a t e only a short distance into the c r y s t a l compared with i t s thickness, we can assume the conduction electrons s t a r t at the edge of the c r y s t a l . The electrons which are freed go varying distances x from the incident surface before being trapped. The number that are trapped i n a region dx at x are given by equation (1) and (2) together with the equation x m vET namely dn = Jo e - - ~ ( 6 ) Expressed as a function of x t h i s i s 7 dn no e - f ^ 6 5 Accordingly, electrons captured by traps i n a range dx at x w i l l contribute a charge ex * l e t t = i f dn exn, 6 d 2 © T dx Summing over the whole crystal, x = o to x = d, we get ' * e f f ^ n o e -2_e~f d-*. £ s S Now i n addition to these electrons there are those which would have gone a greater distance than d i f the c r y s t a l had been larger. Each of these contributes a charge e, so adding them to the other charge we obtain Qeff <S n Ge dx or Qeff = n o e d ( l - e ^ f - •) . * ( f i ! . x d (7) This would give r i s e to a pulse 7 given by " ~ ~ C T - (7a) From equation (7) i t can be shown that as h increases ^ e f f n 0e 8 approaches the l i m i t unity. Thus as & i s proportional to E, the pulse height should saturate with increasing e l e c t r i c f i e l d . The theory above i s based on the assumption that the c r y s t a l i s perfect. I f cracks are present, the equation becomes Qeff = a©© (1 - ej ) (8) d where s i s the distance x that the crack, a po t e n t i a l b a r r i e r , i s situated from the bombarding surface. The saturation value f o r a perfect c r y s t a l would be Qeff = no© O) while f o r a cracked c r y s t a l i t becomes s Qeff a a©®! <9*) From equation (7) we see that the a b i l i t y of a c r y s t a l to detect alpha particles-depends on 6 • I f <5 i s small, equation (7) reduces to I Qeff a 20*1 (10) Mott and Gurney (13) have calculated t h e o r e t i c a l l y a value f o r <$ , the mean free path r e l a t i v e to trapping centers. This i s given i n the form 6 = E e l 6kTP cr I1* where T i s the absolute temperature, 1 i s the mean free path with respect to l a t t i c e v i b r a t i o n s , P i s the number of randomly d i s -tributed trapping centers per unit volume, and G~ i s the cross-section f o r capture of an electron by a trapping center. F r o h l i c h and Mott (12) have calculated values f o r 1, but l i t t l e i s known of T- and P. A value of 3 x 10"*15cms.2 has been estimated f o r by Mott and Gurney (13) f o r s i l v e r chloride. The c r y s t a l we have been interested i n i s per i c l a s e , a c r y s t a l form of magnesium oxide, which has a cubic structure and i s an i o n i c c r y s t a l . Because of these s i m i l a r i t i e s <T" would probably be of the same order of mag-nitude as f o r s i l v e r chloride. P i s a l i t t l e known quantity, but using the method of S e i t z (14) an upper l i m i t can be determined. For t h i s , one needs to know the o s c i l l a t o r strength, f, of a trap-ping center, the width at h a l f maximum of the i n f r a red absorption peak i n energy units, the index of r e f r a c t i o n , and the absorption c o e f f i c i e n t at the peak of the absorption band. Unfortunately few of these data are available. I t would be possible to determine P i f measurements could be made of pulses, thus obtaining S from them. The & could be calculated using two-crystals of d i f -i t ferent thickness cleaved from the same c r y s t a l . I f the temperature and e l e c t r i c f i e l d are the same f o r both cr y s t a l s they w i l l have the same -6 by equation (2). The voltage, V, produced by an alpha p a r t i c l e i s related to the height, h, of the pulse observed on the oscilloscope by the c a l i b r a t i o n factor G', so that ¥ 3 C'h Then by equation (7a) <W = CC'h The f a c t o r CC 1 i s determined completely by the ampli-f y i n g c i r c u i t , so i t i s independent of the thickness of the c r y s t a l . I f the subscripts 1 and 2 r e f e r to two c r y s t a l s of d i f -ferent thickness, by taking the r a t i o of the e f f e c t i v e charges e > and assuming equal a s , we obtain the expression d l >L _ d 2 (1 - e " — ) V d l " e T } As S i s the only unknown, a value can be determined f o r i t * Discussion of n Q When a c r y s t a l i s bombarded with alpha p a r t i c l e s i t i s important to know what f r a c t i o n of the energy i s used i n actually producing electrons. If H i s the t o t a l energy of the incident p a r t i c l e , p the energy required to free an electron, i . e . the energy gap between the empty and f u l l band, then the maximum number of free electrons would be H • We can equate no .to H ? by the equation n 0 = _H_ -y (12) y being the f r a c t i o n of the energy used to produce electrons. I f one has a crack-free c r y s t a l t h i s value could be determined. From equation (9) Qeff - ^oe» Qeff e a r e fca°wn» H should be known, and Q would be the i o n i z a t i o n p o t e n t i a l . Van Heerde^s work (4) indicates a X of 0.6 f o r s i l v e r chloride. I f f i s not available, the energy per free electron would serve as an i n d i c a t i o n of how e f f i c i e n t a c r y s t a l Is i n producing free elec-trons. This energy i s the f r a c t i o n of the t o t a l energy l o s t i n producing one free electron, which equals , and could be n 0 calculated from saturation pulses. This value f o r a gas i s of the order of 32 electron v o l t s , while f o r a c r y s t a l i t i s only approximately 7.6 electron v o l t s . The energy not used to produce electrons i s l o s t to the l a t t i c e . P o l a r i z a t i o n E f f e c t s When alpha p a r t i c l e s release electrons they t r a v e l an average distance £ before being trapped; After a continued bom-bardment there w i l l be a large number of electrons trapped about some plane approximately a distance & from the bombarded surface. This w i l l produce i t s own f i e l d which tends to neutralize the applied f i e l d . I f the holes are f i x e d they w i l l a l l be clustered i n the area where they were created, thus also tending to neutra-l i z e the f i e l d w i t h i n the c r y s t a l . I f the holes are mobile they get trapped about some plane and reduce the f i e l d . The trapped electrons and holes both reduce the f i e l d i n the area where they were freed. As was shown e a r l i e r , £ depends on the f i e l d , and the pulse height on & , therefore i f the f i e l d i s reduced, so are & and the pulse height. As these e f f e c t s , known as p o l a r i z a t i o n , increase, the pulse height decreases and eventually disappears. These p o l a r i z a t i o n effects lessen the e f f i c i e n c y of c r y s t a l counters and have been the subject of much i n t e r e s t , r e f . 15, page 11. The p o l a r i z a t i o n cannot be avoided but a c r y s t a l may be returned to i t s o r i g i n a l state by heating i t , reversing the f i e l d , or by continued bombardment with no f i e l d . Heating a c r y s t a l increases the p o s s i b i l i t y of a trapped electron or hole being 12 excited to the conduction band so that a uniform d i s t r i b u t i o n of traps, holes-and electrons may be restored i n the c r y s t a l . This may take place i n some cr y s t a l s at room temperature-if the f i e l d i s removed. I r r a d i a t i n g the c r y s t a l produces free electrons and holes which can neutralize the p o l a r i z a t i o n f i e l d i f no applied f i e l d i s present. P o l a r i z a t i o n i s only serious i f the p o l a r i z a -t i o n time i s of the order of magnitude of the duration of an experiment. Apparatus - Cryst a l Holder The f i r s t attempts to get c r y s t a l s to count were made with the apparatus shown i n F i g . 3. This was made small so that i t could be put i n a glass tube-and evacuated. I t was hoped that i t would be possible to work with temperatures ranging from that of l i q u i d a i r to about 300°C. I f the apparatus were placed i n the evacuated-tube and then immersed i n l i q u i d a i r i t should reach l i q u i d a i r temperature. The heater could then be used to r a i s e the temperature to the value required. This arrangement had some unfortunate defects. P o l a r i -zation, which seems to be present i n most c r y s t a l s , i s corrected i n many cases by i r r a d i a t i n g the c r y s t a l with l i g h t . This was not possible i n t h i s case. The smallness of the holder made i t d i f f i c u l t to put an e f f e c t i v e s h i e l d inside the holder, and i t was impossible to remove the source when the system was sealed i n a vacuum. The heater on the outside of the holder had to be well shielded to prevent the 60-cycle mains from producing a stray si g n a l i n the a n p l i f i e r . To surmount these obstacles the apparatus shown diagram-_ e l e c t r i c a l lead - - aluminum . - micalex - - c r y s t a l - - clamp i • - source ; - aluminum ! — h e a t e r 2 mica -micalex Fig . 3 Crystal holder. to follow p. 12 matically i n F i g . 4 was constructed. This unit embodies many of the features of the apparatus used by Hofstadter (15) with some modifications to overcome some of the d i f f i c u l t i e s he encountered. The main d i f f i c u l t y Hofstadter found was that when he heated h i s c r y s t a l the whole holder became hot - hot enough to a f f e c t h i s vacuum seal s . This d i f f i c u l t y was overcome i n our apparatus by using a long t h i n walled cylinder connecting the c r y s t a l and the heater to the main body of the apparatus. A simple c a l c u l a t i o n can be made to show approximately how e f f e c t i v e t h i s would be. With a cylinder as i n F i g . 5, 1 being the length, r the radius of the cylinder, a the thickness of the wall, the high temperature, Q 2 the temperature of the cool end, K the c o e f f i c i e n t of thermal conductivity, A the cross sectional area, and using the heat flow equation, d Q = KA (°1 " °2) at the heat flow down the cylinder per second i s given by Here Q i s the number of c a l o r i e s , and t i s the time i n seconds. The cylinder was of s t a i n l e s s s t e e l which has a K of 0.107 c a l . / sec./cm./deg. The radius of the cylinder was one inch and the thickness was twenty thousandths of an inch. I t was s p e c i f i e d that the holder should not exceed 50°C and that the c r y s t a l would not be heated above 400°C. Using these values f o r a three-inch piece of pipe, the heated conducted i s . - - • I stainless stee •020" thick va cuum sea crystal holder window shield source holder to pump •va ive vacuum joint F i g . 4 C r y s t a l holder. to follow p. 13 ' 1 heat flow \ F i g . 5 Heat conduction down a cylinder. * a to follow p. 13 14 -|&- = 3.7 cal./sec. The main heat loss i s ra d i a t i o n from the hot piece of s t e e l tubing. The radiation loss as given by the Stefan-Boltzman Law i s = A ^ e <e h 4- O where A i s the area of radiating surface, CT i s the Stefan-Boltz-man constant . s 5.73 x 10- ergs/sec. cm. deg., e i s the emissivity o of s t e e l s 0.2, 9^ i s the temperature of the r a d i a t i n g body i n A, and 0 0 i s the temperature of the surrounding medium. As an approximation, a l i n e a r temperature gradient was assumed i n order to determine the average temperature over three one-inch sections of the cylin d e r . This gave f o r the temperatures of the respective sections 600°A, 480°A and 370 GA. From t h i s the ra d i a t i o n l o s s i s found to be = 1.88 cal./sec. dt As a l i n e a r temperature gradient was assumed, t h i s figure i s on the low side. I f one also includes the radiation from the chamber at50°C and the convection around the whole apparatus, the figure would be greatly raised. A fi g u r e of 100°C f o r the main body of the chamber y i e l d s 3.2 cal./sec. This was thought a s u f f i c i e n t approximation and indeed proved to be so. The c r y s t a l when heated to over 350°C did not r a i s e the temperature of the holder above 50°C. 1 5 Alpha Source. The source holder was made of one-quarter inch diameter aluminium rod about four to s i x inches long,.„fitted. with a pro-t e c t i v e cap. A s i l v e r button was fastened to the holder and then activated. Two types of cement, C.I.L. and Sauereisen, were t r i e d but not found very s a t i s f a c t o r y . To secure some s i l v e r to the holder a small hole was bored into the end of i t and the s i l v e r wedged t i g h t l y into the hole by small pieces of tungsten wire. Enough s i l v e r was l e f t out of the hole to be flattened over the end to form the button. The s i l v e r button was activated by allowing i t to touch the surface of a solution of radium D i n one-half normal hydro-c h l o r i c acid. Radium F, which i s a decay product from radium D v i a radium E, was deposited on the button by electrochemical exchange of the s i l v e r and radium. The button was l e f t i n con-tact with the solution f o r about twenty minutes, then washed thoroughly and dried before being capped. The cap had a hole about one-half a millimeter i n diameter to allow a beam of par-t i c l e s to come through. In most cases the source was used with the cap o f f i n order to get a stronger beam of p a r t i c l e s . With the cap on, a s c i n t i l l a t i o n counter detected about 400 alpha p a r t i c l e s per second. To ensure that there are only alpha p a r t i c l e s emitted from-.the source, a piece of n i c k e l should be dipped into the solutio n f i r s t to take out radium E, a decay product of radium D, and a source of beta p a r t i c l e s . In a l l cases, the s i l v e r button was placed as close to the c r y s t a l as possible i n order that the maximum amount of energy would be dissipated i n the c r y s t a l and' as l i t t l e as possible i n the a i r . C i r c u i t Components The c i r c u i t that was used f o r the detection of conduc-t i o n pulses i s shown i n F i g . 6. The preamplifier i s an Atomic Model E05, the main amplifier i s a l i n e a r Atomie Model SG4C and the oscilloscope i s a Tektronik Model 511AD. The amplifiers were calibra t e d with a square wave generator which delivered a pulse of 0.2 microseconds r i s e and decay time, and of 2 microseconds duration. With t h i s pulse the preamplifier had a gain of about 20 and the main amplifier a gain of about 70. The r i s e time of the main amplifier could be varied from 0.2 microseconds to 2 microseconds. The r i s e time of the pulses produced by alpha p a r t i c l e s i s believed to be of t h i s order or less so that detec-t i o n should be possible, but i t would be advantageous i f the r i s e time were a l i t t l e f a s t e r . I f , f o r example, the r i s e time of the conduction pulse was about 1/10 of the r i s e time of the amplifier, only a portion of the pulse height would be detected, F i g . 7. I t was thought that by heating the c r y s t a l the length of the pulse could be extended and would compensate f o r the r i s e time of the amplifier. As electrons can generally be excited from traps by heating, i t was hoped that a temperature might be reached where the traps would be emptied almost as soon as f i l l e d . In t h i s way the length of the pulse could be extended so that the amplifier would have time to r i s e closer to the maximum of the pulse. Another alt e r n a t i v e i s of course to b u i l d equipment battery Fig. 6 C i r c u i t diagram to, follow p. 16. \ to follow p.' 16 which has a f a s t e r r i s e time. This would be a b i g advantage, as the mean free path of an electron i n a c r y s t a l decreases with increasing temperature. I f an amplifier.could be b u i l t of f a s t enough r i s e time to follow the pulse, the mean free path could be extended and the pulse height raised by lowering the temperature. Using existing equipment one would have to choose a temperature which compromised between mean free path and length of pulse to give the maximum response. In the f i r s t experiments Eveready minipac batteries were used f o r the voltage supply. These were arranged with selector switches and dropping resistances so that voltage steps of about 6 volts could be obtained i n the.range 0 - 720 v o l t s . This was replaced l a t e r by a two k i l o v o l t C i n t e l power supply. The regu-l a t i o n was such that when the power supply was connected to the preamplifier, no noise appeared on the oscilloscope, over the open c i r c u i t noise. I t i s believed that the capacity of the holder and the c r y s t a l i s as small, i f not smaller, than the input capacity of the preamplifier, so l i t t l e can be done to reduce i t . Care had to be taken i n a l l eases to guard against pick-up, and f o r t h i s reason coaxial cable was used f o r a l l the connections. Cr y s t a l Contacts A l l the cr y s t a l s used were t r i e d with three types of contacts, evaporated electrodes on opposite sides of the crystals,, point probes and s p l i t layers on one surface. Aquadag, which has been successfully used by other workers, was t r i e d but not used much as i t i s d i f f i c u l t to know how thick the layer i s , and i f 18 too thick i t would stop the alpha p a r t i c l e s . Most people i n the f i e l d have found that the noble metals, platinum and gold, when evaporated onto the surfaces made good contacts. In l i n e with t h i s , gold l e a f was t r i e d as a con-tact by f l o a t i n g i t on with methyl alchohol. For the most part platinum was used for contacts, t h i s being evaporated from a hot filament i n a vacuum. This proved rather d i f f i c u l t as the tungsten, used as a filament, appeared to dis s o l v e or a l l o y . a t the edges of the molten b a l l of platinum as i t was heated, eventually parting the wire. Using a sing l e tungsten filament of 0.0E0 inch diame-t e r about twenty-five minutes were required to get a good coating. Approximately 70 milligrams of sheet platinum were r o l l e d around the filament. The c r y s t a l s being mounted about 1.5 cms. from the -4 filament would receive a coating about 10 cms. thick i f a l l the platinum evaporated. In actual practice only a small f r a c t i o n of the platinum was evaporated so the alpha p a r t i c l e s should not have -3 been stopped as t h e i r range i n platinum i s about 10 cms. To f a c i l i t a t e evaporation a holder was constructed. Two copper bars 1/4 by 1/2 inch i n cross, section were used as current leads. One-quarter inch bolts held the bars to a micalex base and acted as binding posts, F i g . S . This made i t possible to cross two pieces of tungsten wire using one on each side of the bol t s . The crossed section of the wires, became hotter than a single wire, and platinum placed at the junction when melted spread out over a larger area so that more evaporated i n a much shorter time. Even with t h i s only a small portion of the platinum used was evaporated. To evaporate the platinum the cr y s t a l s were mounted i n o o o - binding post - copper bar _ c r y s t a l holder • - micalex - tungsten wire _ current leads F i g . 8 Evaporating apparatus. to follow p. 18 19 brass holders made by d r i l l i n g holes, of the size wanted f o r elec-trodes, i n the center of pieces of brass. One end of the brass holder was bent around to act as a spring clamp to hold the crys-t a l , while the other was bent to make i t convenient f o r clamping; With the holder described above the crystals were mounted upright, the brass being bolted to the micalex. An electrode about 1/4 inch i n diameter was used for the high tension side of the c r y s t a l , and i n an e f f o r t to keep capacity small a 1/8 inch diameter el e c -trode was used on the amplifier side. The c r y s t a l was placed on a piece of copper which made contact with the large electrode and held there by a brass clamp, the clamp making contact with the small electrode, the bombarded surface. A small dot of s i l v e r paint on the edge of the platinum spot made good contact with the platinum and was hard enough to be undamaged by the clamp. I f the clamp was put d i r e c t l y on the platinum i t would scratch the surface and made a good contact more improbable. To make contact from the platinum to the brass a l i t t l e piece of tine f o i l proved very e f f e c t i v e . When i t was heated the t i n melted and i n many cases stuck the c r y s t a l to the metal. < -A few spots of s i l v e r paint also seemed to work s a t i s f a c t o r i l y as they held ..the c r y s t a l away from the copper, thus being the only points i n contact. Aluminium f o i l was also used but was ques-tionable as i t was rather s t i f f and may not have made good contact. A spot of Aquadag, too, when put on the c r y s t a l stuck i t to the metal. When using probes, two pieces of tungsten wire were sharpened to f i n e points by using them as electrodes i n a one percent sol u t i o n of sodium hydroxide. The probes fastened to the 20 clamp binding posts of the c r y s t a l holder, F i g . 4, served to hold the c r y s t a l i n place. The points were placed on the surface of the c r y s t a l as close to each other as possible. In an e f f o r t to get a very short distance between two electrodes, films were evaporated onto the surfaces of a few crys-t a l s with 0.005 inch tungsten wires stretched across the c r y s t a l s . This gave two electrodes of platinum separated by something l e s s than f i v e thousandths of an inch. Theoretical Calculations Champion (16) has found that diamonds which transmitted both i n f r a red and u l t r a v i o l e t l i g h t make e f f e c t i v e counters. As p e r i c l a s e has very good i n f r a red transmission properties, i s transparent to the v i s i b l e and u l t r a v i o l e t , i t was thought that i t might act as a eounter. Calculations have been made f o r the electron mean free path and the mobility i n p e r i c l a s e . F r o h l i c h and Mott (12) have calculated a t h e o r e t i c a l value for the mobility, v, given by 3 7 K - K0t-1 0 where K . -• • d i e l e c t r i c constant f o r s t a t i c f i e l d K 0 s d i e l e c t r i c constant f o r high frequency f i e l d s —28 m - mass of electron = 9.1 x 10 gms. e = charge of the electron = 4.8 x 1 0 " 1 0 e.s.u, a " 9 1 1 = f i r s t Bohr o r b i t 0.5 x 1 0 " 8 i f m s m^ m e m = e f f e c t i v e mass of electron T s temperature i n degrees K e l v i n 0 = k k s Boltzman's constant s 1.38 x 10~ 1 6deg.~irg h = Plank 1s constant = 6.6 x 10""27 erg-sec. • V t ^ 7 T M - 0 -3 s volume of .unit c e l l = 2a a a Interatomic distance ^ = o p t i c a l frequency t M Ml'-t* M l & M 2 = component masses of the ions In the derivation of the above equation i t i s assumed that T ^ 9. For a value of 9 we need-0- , M and P^, i s defined as the value of a unit c e l l which i n the case of mag-nesium oxide i s 2a 3. The International C r i t i c a l Tables (17) give fo r a, 4.2 Angstroms. Accordingly, -0- = 2 x 4.2 3x 10 2 4cms? Willmott (18) gives f o r p e r i c l a s e a value of JJ^ equal 12 to 17.3 x 10 cycles/sec. In order to calculate the mass of the ions we w i l l use the rel a t i o n s h i p atomic weight of proton - atomic weight of ion mass of proton mass of ion Taking the atomic weight of the proton to be 1.007, the mass of the proton as 1.67 x 10"24gms., the atomic weight of magnesium as 24.3, and the atomic weight of oxygen as 16.0, we get the mass 22 of the magnesium ion as 40.6 x 10 gms., the mass of the oxygen ion as 26.7 x 10 'gms., and a value f o r M, the composite mass, -24 as 16.2 x 10 gms. Consequently, 2 , 2 2 P Z 2) + g t ft M — ° -gives a value of \) = 1.82 x 10 cycles/sec. 0 then has a value of 875°K. Thus these calculations are v a l i d i n any tem-perature range below 600°C. In order to calculate v we must know K and K 0. values of I^are known but none of K. The value K - K Q i s the only way the d i e l e c t r i c constants enter into the equation, and this d i f -ference can be calculated from the compressibility, which i s known. The following development i s outlined i n Mott and Gurney (13)i In an io n i c c r y s t a l there are a t t r a c t i v e forces or Coulomb forces i n the form (r) Z z e r Z denoting the number of electrons i n the atom, e the e l e c t r o n i c charge, < ^ i s the Madelung constant related to the structure and r i s the distance between two ions. The repulsive or overlap forces have been found to have a form w(r) = Ae~ r /f where A and P are two unknown constants depending on the substance i n question. 23 For a cubic structure the t o t a l energy, U(r), i s Tj(r) = -T- 6 A e - r ^ (1) r Z being unity as there i s a single electron difference between the ions and the factor of 6 comes i n from the number of nearest neighbouring atoms. The equilibrium condition f o r t h i s equation i s that at r s a, the interatomic distance, the t o t a l force must be equal to zero. This equilibrium condition requires that d U(r) , = 0 (3) r«a dr The compressibility y i s given by • ( TP/ t where 7 i s the volume, P i s the pressure and T i s the temperature, Using the energy equation PdV - -dU we can equate y 1 - Vdftj Now V = 2Nr 3 , N being the number of atoms per unit volume. Then we get f o r the y. the expression 1 _ • I / d^J , v- • ' ' (3) y 18Nr V dr*5 1 24 Using equation (2) and (3) to solve f o r p and A i n equation (1), we get I = e 2 *M / l ' - -2 , ... ( r -J M Mott and Gurney give f o r a value of K - Kft, page 22, K - Kn - 4- 7 r (^" = Ne 8 0 i - 4 3 2 <*„. e 2 / , M / I - 8 | (5) 3 a 2 f Comparing equations (4) and (5) we see that' K - K Q = — £ B 2 r r N e 2 T 1 - B • ' • ~ 3" a The International C r i t i c a l Tables (19) give f o r y. a value.0.72 x 1 0 ~ 1 2 degrees/cm. 2 . This i s f o r O^C and 125 atmo-spheres. This value, according to the tables, i s p r a c t i c a l l y independent of temperature and pressure. For N we take w Avogadro's number $ x density a gm molecular volume - molecular weight = 5.88 x 1 0 2 3 As before, a = 4.02 x 10" 8 cms. Substituting we get B = 1.46 or K - K Q = 2.84 Using T = 300°K we obtain f o r v 62 cms./volt-second. The mean free path i s related to the mobility, according to F r o h l i c h and Hott, by 1 = Q* / 3mKT v - 41 Angstroms Calculating v and 1 at 600°K give v - 12.9 cms. /volt-second 1 = 12.3 Angstroms Compared with s i l v e r chloride which has an electron mean free path of 530 Angstroms at l i q u i d a i r temperature (15) mag-nesium oxide should be a moderate counter at room temperature. Crystals Used and Results Obtained Small c r y s t a l s of p e r i c l a s e were cleaved from larger c r y s t a l s , or the larger c r y s t a l s were ground with carborundum to get t h i n samples of the order of ten thousandths of an inch t h i c k . The cleaved c r y s t a l s had thicknesses of ten to twenty thousandths of an inch. When probes were used they were placed on a cleaved surface. The periclase was a commercial c r y s t a l and l i t t l e i s known of i t s impurity content. I t i s not certa i n that p e r i c l a s e ever gave true conduc-t i o n pulses but some pulses were observed while i t was mounted. Pe r i c l a s e was cooled using the holders of F i g . 3 and F i g . 4, but f a i l e d to give pulses. When the c r y s t a l was heated, using the old holder, pulses were observed along with a l o t of noise. The 36 noise at t h i s time was accredited to breakdown i n the c r y s t a l . •"•.•:> With the o r i g i n a l apparatus i t was d i f f i c u l t to be sure that the pulses were due to alpha p a r t i c l e s . I t was found that i f the source was set about 4 centimeters or better away from the c r y s t a l and i f the system was evacuated, that pulses appeared when the cr y s t a l was heated, but disappeared when the a i r was allowed i n . As the range of alpha p a r t i c l e s i s about 3.4 centimeters i n a i r , t h i s was taken to indicate alpha conduction. We also found that i f we evacuated and heated the system without the source that we got no pulses. In addition, effects which appeared to be due to po l a r i z a t i o n were observed. The contradictory part occurred when we put a brass s h i e l d i n the chamber and found that i t made no difference to the pulses. At t h i s time some very good pulses were found, which i n one respect were i n agreement with theory, that i s they varied i n height with the f i e l d . A series of readings were taken with one sample which proved quite promising at the time. Some of the re s u l t s are given i n Graph 1. These were of int e r e s t because of the plateaus which were exhibited. The graph at 385°G e x h i b i t i n g smaller pulse heights than those on the other graphs seemed to prove p o l a r i -zation e f f e c t s as the readings were taken some time a f t e r the others, about eight hours, with the f i e l d on continuously. I t was to study t h i s more closely that the second holder was made. The f i r s t t r i a l s c a r r i e d out with the new holder were done i n a vacuum provided by the backing pump that had been used with the old apparatus. I t was found that, when heated and evacuated, broader pulses were obtained, but through the windows 27 of the apparatus one could see that the chamber was f i l l e d with discharge. To overcome t h i s , the chamber was connected to a high vacuum system. With t h i s we found we could not get better than 0.1 micron, but the discharge disappeared. With the new apparatus the c r y s t a l s were observed from l i q u i d a i r temperature to about 325°C. About eight or nine c r y s t a l s have been t r i e d since but no pulses have been observed. A few samples showed some i n t e r e s t i n g e f f e c t s . A = thousand v o l t s applied to the system o r d i n a r i l y appeared across the c r y s t a l and nothing across the series resistance. It was found that with some of the c r y s t a l s a small voltage, varying between 1 volt and 8 v o l t s with d i f f e r e n t samples, developed across the series resistance.as the system was heated. This meant that the resistance of the c r y s t a l had dropped to about 4000 megohms. When the c r y s t a l was cooled, the voltage dropped to l e s s than l/50th of a v o l t . This happened with some but not a l l of the p e r i c l a s e samples. This can be interpreted i n two ways. As p e r i -clase i s an i o n i c c r y s t a l , i t may be that a high enough tempera-ture was reached so that i o n i c conductivity was taking place. As w i l l be shown i n the next section, an insulator with impurities makes a semiconductor which has a p o s i t i v e temperature-resistance c o e f f i c i e n t . As the c r y s t a l s t r i e d were not a l l from the same parent c r y s t a l , they could quite e a s i l y have d i f f e r e n t impurity contents, and so give d i f f e r e n t resistances at the same tempera-ture used. This would explain why some c r y s t a l s showed these ef f e c t s and not others. I f i t were ioni c conductivity one would expect the effect to be about the same f o r a l l c r y s t a l s . Sections were cut from a natural c r y s t a l of sphalerite, 28 a form of zinc sulphide, and polished with jeweler's rouge. Probes were t r i e d on these surfaces but no pulses were observed. Thin samples were made by mounting a small c r y s t a l i n l u c i t e , to f a c i l i t a t e handling, and the whole ground with carborundum to the thickness desired. Crystals about ten thousandths of an inch thick could be prepared quite e a s i l y t h i s way. Again, no pulses were observed. As the c r y s t a l s were natural forms, l i t t l e i s known of t h e i r impurity content, but i t i s thought to be large. Two commercial diamonds were t r i e d using a f l a t surface for probes and evaporated contacts on two sides. After unsuccess-f u l attempts to make the diamonds detect alpha p a r t i c l e s , the sam-ples were examined f o r u l t r a v i o l e t transmission properties and i t was found that one completely absorbed the u l t r a v i o l e t l i g h t while the other transmitted only a small f r a c t i o n . A sapphire o p t i c a l f l a t was t r i e d but with no success. Discussion The impurity content was not known f o r any c r y s t a l investigated. This was a serious drawback, as most of the c r y s t a l s reported as counters have been of high p u r i t y . For s a t i s f a c t o r y work, the c r y s t a l s should be grown under conditions such that the amount of impurity i s known. With the diamonds used i t was found that one completely absorbed u l t r a v i o l e t l i g h t and the other transmitted very l i t t l e . I t has been found by Friedman, Birks and Gauvin (20) t h a t ' d i a -monds which do not transmit u l t r a v i o l e t l i g h t do not count. This appears to be borne out by the negative r e s u l t s f o r the diamonds. Zinc sulphide has been made to count by Ahearn (21) whose samples were natural c r y s t a l s of high p u r i t y . I t Is 29 believed that impurities were the reason f o r our i n a b i l i t y to get ours to count. Champion (16) has found that diamonds which transmitted both i n f r a red and u l t r a v i o l e t l i g h t are counters. As periclase has very good i n f r a red transmission properties, and i s trans-parent to the v i s i b l e and u l t r a v i o l e t , i t was thought i t would be worthwhile in v e s t i g a t i n g i t s counting properties i n spite of i t s short mean fre e path. This assumption was based on the fac t that traps have an absorption spectra and i f a c r y s t a l absorbs l i t t l e l i g h t i t might have fewer traps. The resistance change of some of the samples of p e r i -clase when heated indicated that i t was a semiconductor. As i s shown i n the next section, an insulator with impurities i s a semiconductor. This being the case, l i t t l e hope i s held f o r a c r y s t a l unless a sample of a given p u r i t y can be grown. Working with diamonds, Champion (16) has found that the surface of a c r y s t a l i s more densely populated with traps than the i n t e r i o r . This i s i n q u a l i t a t i v e agreement with theory. Mott and Gurney (13) i n Chapter 2, t e l l how ions may migrate to the surface leaving traps. This can be considered as a vacuum d i f f u s i n g into the c r y s t a l . Considered t h i s way, the density of vacant l a t t i c e points would probably increase i n the outer l a s t few interatomic distances of the c r y s t a l . With alpha p a r t i c l e s the energy i s l o s t i n a very short distance so that i f there i s a layer of traps close to the surface, the freed electrons would never get into the main part of the c r y s t a l . The density of traps i n any c r y s t a l depends on the energy required to move an ion from i t s l a t t i c e point and on the frequency of the l a t t i c e . Thus i t i s possible that c e r t a i n c r y s t a l s might have larger layers of traps and ,so be very poor counters. A layer of traps on the surface of a c r y s t a l i s not such a detriment f o r beta p a r t i c l e s and gamma rays as most of the freed electrons are released i n s i d e the c r y s t a l . Hofstadter (22) has suggested a reason to explain why cry s t a l s with good t h e o r e t i c a l p o s s i b i l i t i e s do, not count. X-ray work beginning with Darwin and Moseley (23) has revealed that most crys t a l s are not single c r y s t a l s but are composed of many t i n y c r y s t a l l i n e blocks each of which i s a single c r y s t a l . The blocks are oriented nearly p a r a l l e l to each other but Mark (24) has found sodium chloride with f i f t e e n minutes of arc Disorientation. He also found that a t y p i c a l edge of a block was about one micron i n length. Wide v a r i a t i o n i n the orientation i s found from sample to sample. In the theory, the eff e c t of a erack was mentioned, and i f the c r y s t a l were made up of a great number q£ small c r y s t a l s , the t o t a l distance an electron could t r a v e l would be extremely small. I t i s f e l t by Hofstadter (22) that c r y s t a l s such as l i t h -ium f l u o r i d e and sodium.chloride i n which electrons have long mean free paths but which do not count, must be made of thi s mosaic c r y s t a l structure. This appears to be confirmed, as excel-lent samples of diamond, c a l c i t e and zinc sulphide, which count, show tendencies of being p e r f e c t l y regular sing l e c r y s t a l s . Accordingly, to have a c r y s t a l count alpha p a r t i c l e s i t i s necessary that i t be a single c r y s t a l which i s not mosaic has few traps, cracks or impurities, and has a long electron mean free path. The energy gap between the f u l l and empty bands would have to be small, along with a high percentage of the energy used to create free electrons. • ' B. • SEMIGONDUGTORS Introduction In a search f o r an e f f i c i e n t p a r t i c l e counter, the pro- , perties of a ba r r i e r layer of a semiconductor have been i n v e s t i -gated. Bombardment of such a layer causes i t s e l e c t r i c a l break-down, r e s u l t i n g i n a conduction pulse. Any semiconductor which has r e c t i f y i n g properties would display t h i s e f f e c t , but i n a ' junction such as the copper cuprous oxide junction, the large s e l f capacity makes i t i n e f f e c t i v e i n detecting p a r t i c l e s or rays. Germanium used with a point probe has a small s e l f capacity so i t has been used as a counter. The greatest defect of the germanium P-n junction i s the very small counting area. I t was hoped that a method could be devised f o r extending the area. Band Theory To understand the mechanism of a p-n junction i t i s necessary to turn again to the band theory. A semiconductor, as the name implies, can conduct but i t s conductivity i s quite low. In order to r e a l i z e t h i s , there must be electrons i n the conduc-t i o n band. With some semiconductors at ordinary temperatures the thermal e x c i t a t i o n i s s u f f i c i e n t for a large number of electrons to get to the conduction band. There w i l l also be an equal number of holes created, which again may be mobile or f i x e d . T h i s . i s c a l l e d an i n t r i n s i c semiconductor. In e x t r i n s i c semiconductors two other processes may take place, excess conduction, or deficiency conduction. In excess con-duction an impurity atom i n the c r y s t a l has energy l e v e l s near, but below, the conduction band. As each of these l e v e l s has an electron which i s eas i l y raised thermally to the.empty band, the electron spends most of i t s time i n the conduction band, Pig. 9(a). This process produces the greatest proportion of the freed e l e c -trons. In general there are always a few electrons excited from the f u l l band but these are generally i n s i g n i f i c a n t compared with the electrons from the excess l e v e l s . I f t h i s type of conduction i s present, electrons do the conducting. This i s also known as an n-type semiconductor. I f an impurity has energy l e v e l s close to the f u l l band, then i t can easily receive electrons from the band, F i g . 9 (b). This would leave holes which, i f mobile, give r i s e to a current. This i s c a l l e d p-type conduction. The word impurity as used above can mean a foreign sub-stance or i t may mean an excess or deficiency of one of the com- i ponents of an ioni c c r y s t a l . For example, germanium can have the impurity phosphorous to make i t a semiconductor. On the. other hand a substance l i k e lead sulphide can be an excess or deficiency con-ductor by having lead or sulphur i n excess of the stoichiometric proportions. I f an n-type c r y s t a l and a p-type c r y s t a l are grown t o -gether, a p-n junction r e s u l t s with a common surface. The d i f -ferent conduction processes r e s u l t i n a drop or r i s e i n the poten-t i a l of the energy bands at the junction, F i g . 9 (e). I f a f i e l d i s applied i n the d i r e c t i o n so that the electrons have to climb t h i s p o t e n t i a l there w i l l be a resistance to t h e i r motion. I f the f i e l d i s applied- i n the opposite d i r e c t i o n , the electrons move ea s i l y down the pot e n t i a l gradient and no extra resistance i s measured..above that of the crystals themselves. . For the holes a similar picture holds, but now for a — — — — •—impurity l e v e l s — — — — impurity / / / / / / / / - / / A / 7 7 — n-type p-type (a) (b) p-type _ _ p-n junction (c) F i g . 9 Band picture i n semiconductors. to follow p. 32 given f i e l d the holes encounter a drop i n potential instead of a r i s e . As they are p o s i t i v e l y charged t h i s w i l l also oppose t h e i r motion. For the reverse f i e l d there would be no opposition. A voltage, which i s applied to the c r y s t a l so that the electrons and holes flow f r e e l y across the junction, i s c a l l e d a forward voltage A back voltage i s applied i n the reverse d i r e c t i o n . Germanium as a Crystal Counter Germanium i s o r d i n a r i l y an n-type semiconductor. I f a point contact i s placed on a surface of a c r y s t a l and a high cur-rent passed, the c r y s t a l being e l e c t r i c a l l y negative r e l a t i v e to the contact, a high back impedance develops. Bardeen and Brattain (25) found that with increasing forward bias the concentration of c a r r i e r s , holes, and electrons, changed i n the v i c i n i t y of the point contact. This produced an e f f e c t i v e potential b a r r i e r which acts as a p-n junction. Such a junction can be compared with two conductors separated by an i n s u l a t i n g l a y e r . Thus v i r t u a l l y a l l the voltage drop occurs across the junction. I f now, electrons are released or holes produced i n t h i s region, they w i l l be swept away by the strong f i e l d . This w i l l r e g i s t e r i n the external c i r c u i t as a conduction pulse, and the r e s u l t i n g electrons and holes w i l l be dispersed i n the conducting germanium. Although the f i e l d may not be too uniform, t h i s w i l l not be important as long as few electrons or holes, get trapped or recombine i n the area of the junction. No evidence has been found to indicate that there i s recombination i n germanium. Apparatus ' > A p-n junction was obtained by using a Kemtron IN34 ,germanium diode. In order to expose the junction, most of the casing was cut away and the i n s u l a t i o n removed from around the ger manium and the cat's whisker. As the junction i s already formed, one has only to apply a back voltage. I f too high a back voltage i s applied to the diode, the junction i s damaged, reducing i t s back impedance. The junction may be restored by moving the point contact and passing a forward current. About 90 v o l t s applied i n the forward d i r e c t i o n f o r a few seconds produced a back impedance of the order of 100K - 300K. The c i r c u i t used was b a s i c a l l y the same as that des-cribed In the previous section, with the 4.7 megohm dropping 1 resistance replaced by a resistance of the. same order as<the im-pedance of the diode, about 250K being used most of the time. The battery box was also used i n order to get the small voltages required. The diode was mounted on a piece of l u c i t e with the source held as close to the junction of the germanium and cat's whisker as possible. The leads were kept short to keep down capacity and the complete apparatus was placed insi d e a galva-nized i r o n s h i e l d . Experimental Results Graph 2, showing a set of maximum pulse heights obtained i n the range 2.3 v o l t s to 14.9 v o l t s , i s rather t y p i c a l of many readings obtained, but there is quite a large v a r i a t i o n from sample to sample, depending on.the condition of reforming. Graph 3 i s taken over a l a r g e r voltage range, but the bottom > 20+ a ~ 164 £ 14 * 12 o> m •1 24-Voltage - Pulse height _ . _ noise •f-0 2 4 6 8 10 12 14 16 Voltage across c r y s t a l and r e s i s t o r (volts) Graph 2 to follow p. 34 points axe most in t e r e s t i n g . As the pulse height was 1.7 cms. at 0.08 vo l t s across the c r y s t a l , the pulses had nearly reached t h e i r , saturation value at t h i s voltage. McKay's r e s u l t s (E7) agree well with t h i s graph, especially i n that the noise l e v e l remained low u n t i l the pulse height had saturated. This graph also confirms McKay's theory that few.electrons recombine or become trapped i n the junction. A' new c r y s t a l which had just been formed had a back resistance of about 300K. I f the junction were reformed by f i r s t moving the point contact and then passing a small current, the back impedance could be made as low as 1000 ohms or l e s s . Extension of the Counting Area McKay (27) found a p-n type junction formed by a point -5 contact has a s e n s i t i v e area with a diameter of the order of 10 —2 to 10 centimeters. The probe being i n the center of t h i s area covers some of i t and shadows some more. Such a small area would detect only a small portion of the alpha p a r t i c l e s emitted from any source. With the source used at about 1/2 a centimeter from the junction, about f i v e or six pulses per second were observed, while a s c i n t i l l a t i o n counter indicated an emission of about 400 alpha p a r t i c l e s per second from the 3 millimeter diameter button. In order to enlarge t h i s area a large surface contact was pro-posed. For t h i s purpose the complete casing was taken from a diode leaving the c r y s t a l of germanium mounted on the base con-t a c t . A small c o l l a r was made to screw on over the c r y s t a l so that i t would come i n contact with the very edge of the top surface. I f a layer of platinum i s evaporated on the c r y s t a l and the c o l l a r screwed on, a contact can be made with the. platinum by making contact with the c o l l a r . The c o l l a r was insulated from the c r y s t a l mounting plate by putting a piece of threaded l u e i t e on the mounting, F i g . 10. This was t r i e d using the same c i r c u i t as was used f o r a p-n junction, but pulses could not be detecfed. I t was found that when a current was passed to form the junction, the difference i n resistance was almost n e g l i g i b l e . I f any pulses were produced they were probably swamped by the steady current. An attempt made to detect D.C. photo conduction was unsuccessful. Increase of Pulse Size As Benzer' (28) shows, i f the back voltage i s increased, a point w i l l be reached where the voltage across the c r y s t a l drops, Graph 4.~ I f the c r y s t a l could be mounted so that the back voltage was just on the maximum of the curve, i t i s possible that a conduction pulse might be enough to make the voltage go around the curve and onto the negative resistance slope. I f t h i s hap-pened i t would be possible to get large conduction pulses pro-duced by a single alpha p a r t i c l e . No such large pulses were observed, but the noise l e v e l which had, been raised considerably by the increased voltage may have masked any e f f e c t s . Discussion The small e f f e c t i v e counting area of the germanium diode and the probe being over the sensitive area, make the germanium point contact system poor f o r e f f i c i e n t detection of alpha par-t i c l e s . The small volume where electrons or holes can be r e -leased to be detected r e s t r i c t s the use of such-a system. For platinum- .copper c o l l a r germanium - l u c i t e mounting base Pig. 10 Crys t a l mounting, to follow p. 36 to f o l l o w p. beta p a r t i c l e s and gamma rays which go long distances i n c r y s t a l s because of t h e i r small s p e c i f i c i o n i z a t i o n , few electrons or holes would be released i n the sensitive volume. A p-n junction formed by McKay (26) might be used i n these cases. He made a p-n junc-t i o n by growing a rod of n-type and a rod of p-type germanium t o -gether. Alpha p a r t i c l e s entering the side of the c r y s t a l t r a v e l •0 along the junction so that a l l the c a r r i e r s are released i n the junction. This requires that the beam of incident p a r t i c l e s or rays be collimated f o r i f they pass through the c r y s t a l at an appreciable angle, t h e i r effectiveness would be reduced. McKay believed that i f the electrons are produced close to the junction, the weak f i e l d w i l l cause, them to move to the junction before the cloud of freed electrons spreads out appreciably. Thus a p a r t i c l e or ray entering the c r y s t a l close and p a r a l l e l to the junction, would produce a pulse a short time af t e r entering the c r y s t a l . I f a p a r t i c l e or ray entered the c r y s t a l at a small angle, t h i s effect would probably broaden the pulse, as the current c a r r i e r s freed i n the junction would pass through the junction immediately, while those outside would pass through as soon as they d r i f t e d to i t . In spite of the increase i n the sensitive volume obtained by McKay, the surface area was not appreciably increased. The sensitive area on the surface of the germanium was a rec-tangle which he believed to be about 5 x 10" 4 cms. wide at a few 5 v o l t s reverse bias. Using a beam of alpha p a r t i c l e s 3.5 x 10 cms. wide, he believes he obtained one hundred percent detection. Our unsuccessful attempt to extend the counting area might be attributed, to the large area of contact decreasing the - • 3 ' resistance. For a sensi t i v e area of about 10 cms. i n diameter, such as i s obtained with a probe, the resistance i s of the order of 300K. I f the whole surface of the c r y s t a l i s covered with the junction, the area* i s increased by a factor of about 1000 to 5000, so the impedance i s decreased by t h i s f a c t o r . As Shockley (29) explains, part of the resistance drop developed when using a point probe i s due to what i s c a l l e d the spreading resistance, given by the expression, R - 1 , where <r~ i s the conductivity, and r i s 4 o~ x the diameter of the point. As r increases, the resistance de-creases. The radius of the point would be l e s s that 10" 4 cms., so that a factor of about 1000 enters again* A combination of the spreading resistance and the actual resistance of the junction would probably account f o r the resistance change obtained. ^ Using the germanium at the maximum of the voltage-cur-rent curve has two disadvantages.. Once the voltage passes over the maximum the resistance i s negative so the current increases, and unless the voltage i s cut o f f , the junction w i l l be damaged. To overcome t h i s one would have to have an a u x i l i a r y c i r c u i t f o r resetting the voltage on the maximum. Secondly, i f a c r y s t a l with a curve such as that i l l u s t r a t e d i n Graph 4 i s used, a very accurate voltage s e t t i n g would be required. However, i f the cha r a c t e r i s t i c curve has a sharp point such as Benzer (28) i l l u s t r a t e s , the voltage s e t t i n g would not be so c r i t i c a l , as a pulse could produce enough current change to drop the operating point to the negative part of the curve. The response time of such a system also would have to be studied before i t could be determined i f such a system could be used effectively,^and a junction with the required characteris-PART I I CONDUCTION PROCESSES OF A SEMICONDUCTOR Introduction As explained i n the previous section, a semiconductor always has a number of free electrons and an equal number of holes which may or may not be mobile. The properties of a semiconduc-tor are determined by the number of holes and electrons and t h e i r respective m o b i l i t i e s . The H a l l e f f e c t and conductivity are used to study these properties. I t was hoped to devise a method of producing lead s u l -phide i n reproducible non-stoichiometric proportions. The H a l l voltage and the conductivity would be used to determine the pro-perties of the sample. A sample could then be made up of known properties. Theory of H a l l E f f e c t I f a conductor carrying a current i s placed i n a mag-netic f i e l d at right angles to the current, a pote n t i a l difference, V, develops across the conductor, i n a d i r e c t i o n perpendicular to both the magnetic f i e l d and the current flow. The p o t e n t i a l d i f -ference i s known as the H a l l voltage and i s given by V - RIH x 10" 9 (1) t where I i s the current i n amperes, H i s the. magnetic f i e l d i n Gauss, t i s the thickness of the conductor i n the d i r e c t i o n of the magnetic f i e l d , and R i s the H a l l c o e f f i c i e n t of the con-t i c s would have to be produced. The serious defect of the germanium junction i s the small sensitive area, and some such device as McKay has used would be required f o r a p r a c t i c a l counter. 4 ducting material i n c.g.s. magnetic u n i t s . As Shockley (29) shows, the H a l l c o e f f i c i e n t also may he expressed i n terms of the number of holes and electrons and t h e i r m o b i l i t i e s i n the form 3 nfiC - n n R = - — ? (2) 8e (n QC 4- nnr where e i s the electronic charge, n Q i s the number of electrons i n the conduction band, n n i s the number of holes, and C = u e / u h » where u e i s the mobility of the electrons and u n i s the mobility of the holes. The parameters are i n c.g.s. u n i t s . He also gives an expression f o r the conductivity a ~ , namely, (T s n ee u e 4- n ne u n (3) i n c.g.s. p r a c t i c a l u n i t s . From the determination of the H a l l c o e f f i c i e n t R along with i t s sign, from equation (1), and the conductivity, one can calculate the number of various c a r r i e r s and t h e i r m o b i l i t i e s . Further, the mean f r e e path and the e f f e c t i v e mass can be determined by using the equation -1/2 u = 4 el(27T mekT) 3 i n es.u; units, 1 being the mean free path, me the e f f e c t i v e mass, k the Boltzman constant, T the temperature i n degrees Kelv i n , and u the mobility of the electron. A very good example of the i n t e r -pretation that can be derived from the above r e s u l t s i s given by Pearson and Bardeen (30). Production of Lead Sulphide Layers Lead sulphide layers were formed hy f i r s t evaporating a th i n f i l m of lead onto a microscope s l i d e and then exposing the plate to sulphur i n an evacuated, sealed, heated glass tube. The t h i n films were evaporated i n a device i l l u s t r a t e d i n F i g . 11. Part B i s a two-inch pyrex glass tube which connects to the vacuum system and has the evaporating tubing, part A, attached to the top of i t . A l l the evaporating tubing i s vycor glass as i t must stand temperatures up to about 1000°C. The ves-s e l containing the lead i s a piece of vycor tubing blown into a bubble. I t was found that i f a straight tube was used the expan-sion of the lead would crack the glass. Even with a bulb, only small quantities could be used without causing trouble. To evaporate the f i l m a small furnace was placed over part A. The pyrex glass was covered with insul a t i o n to protect i t from the heat and to t r y to keep the microscope s l i d e cold. The lead evaporated, passed down through the tubing, and deposited quite uniformly on the plate. The whole system was evacuated to better than 0.1 micron during the evaporation. With the furnace at 1000°C before being placed over part A, a thickness of about 0.5 micron of lead was deposited i n approximately two minutes. The conductivity of lead sulphide depends on the number of c a r r i e r s and t h e i r m o b i l i t i e s . As the various proportions of sulphur would produce varying numbers of energy l e v e l s , a r e s i s -tance measurement at any time should indicate how much sulphur had reacted with the lead. Using t h i s fact, i t was thought that resistance measurements could be used as a control to determine the proportions of -lead and sulphur i n the sample. to follow p. 42 The plate to be exposed to sulphur was held onto a backing of micalex by clamps, which also acted as contacts. The leads acted as supports f o r the plate which was mounted i n a one and one-quarter inch diameter pyrex glass tube. A small c a p i l l a r y having a bulb of sulphur on one end was joined to the main glass chamber, F i g . 12. The tube was evacuated and then placed inside a c i r c u l a r furnace. The furnace was so arranged that the tempera-ture of the bulb of sulphur could be varied independently of the temperature of the plate being exposed. This was achieved by having two furnaces, one surrounding the main body of the tube, and a second, which could be removed, placed over the bulb of sulphur. Rock wool was packed around the top of the one and one-quarter inch tube to prevent heat convection. As the vapour pressure i n a system i s controlled by the coolest point i n the system, the vapour pressure of the sulphur could be controlled by varying the temperature of the coolest point. The bulb was used as a control of the sulphur vapour pres- . sure, the plate being at a higher temperature to speed the reaction: Resistance measurements proved unsatisfactory as there seemed to be a large resistance drop at the junction of the lead ® sulphide and the contact. Brass contacts had been used at f i r s t , but platinum was used l a t e r to ensure that the sulphur would not react with the contact. As resistance measurements were unsatis-factory, i t was believed that i f the vapour pressure of the s u l -phur and temperature of the plate were kept the same f o r two - 9 plates, equal composition could be produced. In Order to ensure uniform layers, the plates were l e f t f o r approximately a day so that the reaction would be completed. I Fig. 12 Sulphur reaction chamber to follow p. 43 The samples were cooled i n approximately one hour so that the composition would not change. I f more rapid cooling was used the layer of lead sulphide flaked o f f . A few test samples were made with the plate and bulb at 250°C. This gave a sample resistance of IOOK, a conductivity' of about 1 ohm-1- cm"-*-. H a l l Voltage Apparatus Early workers used D.C. magnetic f i e l d s and D.C. currents f o r measuring H a l l voltages. A D.C. H a l l voltage r e s u l t s , but an extra voltage c a l l e d the Ettingshausen voltage a r i s e s . This i s produced by a temperature gradient which develops across the sample, and i f the H a l l voltage contacts to the sample are not of the same material as the samples, a thermal E.M.F. develops. The Ettingshausen voltage could be overcome by measuring i t separately and subtracting t h i s from the H a l l voltage, or eliminating i t by using a contact of material similar to the sample. Either of these methods are very d i f f i c u l t , so to circumvent them, an A.C. current was used i n the sample. With t h i s method, Smith (31) found that the H a l l voltage remained the same for frequencies as high as 10,000 to 12,000 cycles, and Busch (32) detected no Ettings hausen voltage at 50 cycles. Dekker and Leverton (33) had set up a H a l l apparatus using a D.C. f i e l d and an A.C. current for'work with antimony and bismuth. .It was hoped to use t h i s f o r lead sulphide. The samples of antimony that were used had a sample resistance of about 5 ohms and drew about a milliamp. In order to keep the parameter of the same order i n equation (1), the 5 voltage was raised by a factor of 10 to give about 100 v o l t s across the three-inch sample. This produced a voltage gradient of about 33 v o l t s / i n c h . A misplacement of the H a l l probes on the sides of the sample by about 3 x 10 inches would produce a v o l -tage difference of the order of a m i l l i v o l t , which i s approximately the order of the H a l l voltage. On the other hand, with the small voltage gradient of 1.3 x 10" 3 v o l t s / i n c h for the antimony samples, probes could be adjusted by hand accurately enough. To overcome t h i s problem a sample was s p l i t i n two by scratching a l i n e down the center. For'each side of the sample to have a current which i s i n phase, a double tap transformer was used on the output of the power supply. The current i n each hal f of the sample was controlled by a variable series, r e s i s t o r of the order of the resistance of the h a l f sample, F i g . 13. The only common point of the two halves was a point i n the center of the sample made by a spot of s i l v e r paint. Contacts were made with the H a l l probes as before, and resistances were adjusted to give a zero reading on the probes. This reading could be achieved when the voltage gradients had been changed, so that the voltage gradient on one side times the distance the probe i s from the common point, equals the voltage gradient on the other side times A the'distance i t i s from the common point. For each h a l f of the sampLe there would be a H a l l v o l -tage produced, V 1 and Vg, and the t o t a l voltage measured would then be 7 = Vl+Vg. As the two halves have the same magnetic f i e l d , H, the same H a l l c o e f f i c i e n t , R, and the same thickness, we get f o r Y the expression _ RH , _ _ . V = ( I n f" I 0 ) variable resistance s p l i t sample common point — A A A A A M from double tap -'transformer to a m p l i f i e r o F i g . 13 S p l i t sample. to follow p. 45 46 so f o r a measurement the two half sample currents, and I 2 , would have to be known. The above method was t r i e d and i t was found that the voltage across the probes could be reduced but not made low enough to take readings. •Discussion In the above work i t was stated that gradient^ times distance^ equals gradient 2 times di s t a n c e 2 » or g r d ^ _ d 2 grd. 2 d-j^  i s the condition for balancing out the voltage. As the gradient can only be altered by about a factor of 2, we get dg/d-^ - 2. That i s , i f the r a t i o of the distances of the probes i s any greater than 2, the voltage cannot be balanced out. I t was believed that t h i s f a c t , and possible phase s h i f t , were probably the reasons f o r the ineffectiveness of the s p l i t sample method. I f the phase s h i f t i s not too strong, the voltage probably could be reduced by moving the common point towards one end, and the probes toward the other. The farther the probes are separated, the easier i t i s to balance out the voltage, but a reasonable distance should be l e f t at the end of the sample as end effects may occur. The above problem could be avoided by using an A.C. magnetic f i e l d and a D.C. current through the sample. This would give an A.C. H a l l voltage, and a D.C. voltage due to a mismatch of the probes, which would not a f f e c t the H a l l voltage readings. 47 I t i s hoped that an opportunity w i l l a r i s e to check the above methods as they seem to show promise, and no apparatus seems to have been developed f o r measuring H a l l voltages of high r e s i s -tance materials. 48 BIBLIOGRAPHY (1) W.C. Rc-ntgen, A. Joff e ; Ann. Physik 41, 449 (1913) (2) H. S c h i l l e r , Ann. Physik 81, 32 (1926) (3) G. J a f f e , Physik. Z. 33, 393 (1932) (4) P.J. van Heerden. Physica 16, 505 and 517 (1950) (5) J.G. Street. Brookhaven Conference Report on High Speed Counters, August 14-15, 1947. (6) R. Hofstadter, Phys. Rev. 72, 749 (1947) (7) R. Hofstadter, J.C. Street. Brookhaven Conference Report on High Speed Counters, August 14-15, 1947. (8) R. Frerichs, Ri Warmihsky, Naturwissenschaften 33, 251 (1946); R. Frer i c h s , Naturwissenschaften 33, 281 (1926). (9) G.J. Goldsmith, Lark-Horovitz, Phys. Rev. 75, 526 (1949) (10) G. Stetter, Verhandl. deut. physik. Ges. 22, 13 (1941) (11) D.E. Wooldridge, A.J. Ahearn, J.A. Burton, Phys. Rev. 71, 913 (1947) (12) H. Frohlieh, N.F. Mott, Proc. Roy. S o c 171A, 496 (1939) (13) N.F. Mott, R.W. Gurney, "Electronic Processes i n Ionic C r y s t a l s , " (Oxford University Press, New York, 1940) (14) F. S e i t z , Revs. Modern Phys. 18, 384 (1946) (15) R. Hofstadter, Nucleonics 4, 2 (1949) (16) F.C. Champion, Proc. Phys. Soc. B, 65, 465 (1952) (17) International C r i t i c a l Tables, 1, 344 (18) J.C. WilLmot, Nature, Lond. 162, 996 (1948) (19) International C r i t i c a l Tables, I I I , 50 (20) H. Friedman, L.S. Birks, H.P. Cauvin, Phys. Rev. 73, 186 (1948) 49 (SI) A.J. Ahearn, Phys. Rev. 73, 524 (1948) (22) R. Hofstadter, Phys. Rev. 73, 631 (1948) (23) H.G. Moseley, C.G. Darwin, P h i l . Mag. 26, 210 (1913) (24) H. Mark, Naturwissenschaften 13, 1042 (1925) (25) J . Bardeen, W.H. Brattain, Phys. Rev. 74, 231 (1948) (26) K.G. McKay, Phys. Rev. 84, 829 (1951) (27) K.G. McKay, Phys. Rev. 76, 1537 (1949) (28) G. Benzer, Jour. Appl. Phys. 20, 1804 (1949) (29) W. Shockley, "Electrons and Holes i n Semiconductors," page 216, D. Van Nostrand Co. Inc., N.Y. (30) G.L. Pearson, J . Bardeen, Phys. Rev. 75, 865 (1949) (31) A. Smith, Phys. Rev. 35, 81 (1912) (32) G. Busch, H. Labhart, Helv. Phys. Acta. 19, 463 (1946) (33) W.F. Leverton, A.J. Dekker, Phys. Rev. 80, 732 (1950) 

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