Minority-carrier effects in chemically deposited PbS photoconductive films

Solid-State Electronics

Pergamon Press 1960. Vol. 1, pp. 148-156.

Printed in Great Britain

M I N O R I T Y - C A R R I E R EFFECTS IN CHEMICALLY D E P O S I T E D PbS P H O T O C O N D U C T I V E FILMS R. L. WILLIAMS* Canadian Armament Research and Development Establishment (Received 14 December 1959) Abstract--Using the PEM and Hall effect it has been established that the minority-carrier diffusion length in chemically deposited PbS cells is at least as large as the film thickness. The relative magnitude of the PEM voltage when cells are illuminated from the front and back surfaces indicates that the recombination process between 300°K and 200°K is governed by surface phenomena. The cell time constant, however, is determined by trapping processes. R 6 s u m 6 - - O n montre par des mesures d'effet P.M.E. et d'effet Hall que la longueur de diffusion des porteurs minoritaires dans les cellules de PbS d6posdes chimiquement est au moins aussi grande que l'~paisseur des couches. La valeur relative de la tension P.M.E. lorsque les cellules sont illumin6es sur les surfaces de face ou de l'envers indique que les processus de recombinaison h 300°K et 200°K sont r~gis par des ph~nom~nes de surface. La constante de temps est cependant d~terminde par le processus de pi~geage. Z u s a m m e n f a s s u n g - - U n t e r Benutzung des PEM- und des ttall-Effektes wurde festgestellt, dass die Diffusionslfinge der Minorit~itstr~iger in chemisch niedergeschlagenen PbS-Zellen mindestens so gross ist wie die Dicke des Films. Das Verh~iltnis der PEM-Spannungen im Fatle einer Bestrahlung der Zellen von vorne bzw. yon der Riickseite zeigt, dass der Rekombinationsprozess swischen 300°K und 200°K von Oberfl~ichen-Ph~inomenen abh~ingt. Die Zeitkonstante der Zellen wird jedoch von Trap-Prozessen bestimmt. INTRODUCTION A GREAT deal of w o r k has b e e n u n d e r t a k e n to determ i n e the factors controlling the sensitivity of P b S films. F o r m a n y years m u c h effort was used in a t t e m p t i n g to establish the role, if any, of barriers. W o r k by GIBSON, (1) I~,'~AHLMAN(2) and SLATER(3) indicated that barrier m o d u l a t i o n could be responsible for the p h o t o c o n d u c t i v e response. H o w e v e r , t h e o r y by PETRITZ (4) and the e x p e r i m e n t a l work of WOODS(5) gave strong evidence that the P C (photoc o n d u c t i v i t y ) effect was p r i m a r i l y a carrier-density phenomena. I n all m o d e l s it was necessary to have a rec o m b i n a t i o n process and only recent papers h a v e d e v o t e d any effort to this p r o b l e m . T h e w o r k of KLASSEN and BLOK(6) suggested the need of two levels to account for the r e c o m b i n a t i o n process. A * Now with RCA Victor Company Ltd. Research Laboratories, Montreal, Quebec, Canada.

single r e c o m b i n a t i o n level was suggested by PETRITZ et a/.(7) b u t one w h i c h was different f r o m t h e level controlling the resistance. I n the latter paper, it was suggested that in the sensitization process the m i n o r i t y - c a r r i e r lifetime b e c a m e v e r y small t h r o u g h the i n t r o d u c t i o n of sites into w h i c h the carriers were readily trapped. T h e s e centers had, it was suggested, small cross sections of r e c o m b i n a tion for holes, and thus one o b t a i n e d long lifetimes. PHOTOELECTROMAGNETIC EFFECT (PEM) GARTNER (8) has d e v e l o p e d expressions for t h e optically p r o d u c e d change in c o n d u c t a n c e and the PEM s h o r t - c i r c u i t current and o p e n - c i r c u i t voltage. T h e restriction of a v e r y large absorption coefficient has been relaxed in GARTNER'S d e v e l o p m e n t . T h e P E M open-circuit voltage, Vs, for a crystal with a diffusion length m u c h greater than the sample thickness and w i t h surfaces controlling 148

MINORITY-CARRIER

EFFECTS

I N PbS P H O T O C O N D U C T I V E

qOIl aK

×

[ KS2(I+S1/S2e-'O+S1S2(1-e-K) ] × . ~ +l-e-~ $1 + $2 + $1 $2

(1)

In this expression q is electronic charge, 0 the Hall angle, a the conductivity of the sample, I the number of photons incident per sec per cm 2, K the product of the absorption coefficient • and the sample thickness d, $1 = sld/D and $2 = s2d/D; in which sl and s2 are, respectively, the surface recombination velocities of the front and back surface of a sample whose ambipolar diffusion coefficient is D. This expression reduces to a simple form if K is much greater than one, and recombination at the back surface dominates, $2 >~ $1, viz.

vs -

-

(2)

(Y

If the surface recombination velocity of the front surface is greatest, $1 > $2 and

Vs

-q0ii[

s2

1 ]

L&(l + &)

K(1 + &id

(3)

It is seen that for dominant front-surface recombination the sign of the P E M voltage depends on the relative magnitudes of the two terms of expression (3). If the second term is dominant then the ratio of the open-circuit P E M voltage when the photons are incident on the front surface, Vsf, to that obtained by illuminating the same sample from the back, under identical conditions, Vsb, ($1 becomes Sz and $2 becomes S~) is

gsf Vso

1 --

K

1 =

149

GARTNER'S theory should then be applicable to direct-current P E M measurements, even in the presence of trapping.

the combination, is given by

Vs=

FILMS

- - - -

kd

(4)

It is seen that the ratio of the P E M voltages gives immediately a value of the absorption coefficient if the sample thickness is known, or it could give relative values for different wavelengths if d is unknown. The effect of trapping on diffusion has been considered by JONSCHER(9) and his conclusions are that, if steady-state or low frequencies are considered, diffusion distances are very little altered.

EXPERIMENTAL

PROCEDURE

Hall measurements The applicability of the theory of the Hall effect to PbS Ektron detectors has been considered by LUMMIS and PETRITZ(10) and WOODS.(5) Their model of the film structure is accepted and the expressions they quote are used to calculate mobilities and the product pd, the hole-carrier density times the thickness of the film. An Applied Physics Corporation vibrating-reed electrometer was used to measure Hall voltages. Its input impedance, being greater than 1015 ~, was sufficiently high to insure effective open-circuit measurements for all cell resistances encountered. The instrument sensitivity of 1 mV full scale was more than adequate for the measurement of the Hall voltages encountered. The resistance of the film was measured directly, the contacts being assumed to give no errors in this measurement.

The P E M effect for polycrystalline films For the P E M measurement the cell equivalent circuit was taken to be composed of two parts; a current generator described by P E M theory in parallel with the resistance the cell would have if barriers were absent, and the junction resistance in series with this combination. As the junction resistance is dominant, it is the value obtained when the cell resistance Rc is measured. With this equivalent circuit the P E M voltage Vpem measured by an instrument having an input resistance Rm would be VpemRm/(Rm + Re). This was verified experimentally. In general, open-circuit voltages were measured so that the effect of the junction resistance was nullified. The physical picture envisaged is that each crystallite can be treated as a separate P E M generator and the cell P E M voltage is the sum of a large number of such generators. As the barrier resistance is large compared to that of the crystallites, the P E M voltage is not laterally shorted out. The P E M voltages were measured with a HewlettPackard 425A direct-current microvolt-meter. T h e instrument, used with its input resistance of 1 M ~ removed, had a measured input resistance of 350 M(2. For cells with high resistances the

150

R. L. W I L L I A M S

vibrating-reed electrometer was used to measure the P E M voltages. A gain of 100 in sensitivity was obtained by applying the full meter-output voltage across a 25 mV full-scale Minneapolis-Honeywell recorder with suitable attenuating resistances. Used in this fashion 20 or 30 txV could be readily detected. For measurements of both P E M and Hall voltages the signals were recorded with a M i n neapolis-Honeywell instrument. T h e cells were shaped by placing a mask, having the desired configuration, over the cell and sandblasting away the unwanted cell areas. T h e procedure found most satisfactory for making electrical contact to the side arms was as follows. Gold was evaporated across approximately one half of the side arm, the plastic coating first being removed. T h e gold area was sufficiently large that a fine wire could be conveniently glued to the area with silver paint. These contacts proved to have photovoltages not appreciably greater than the proper cell contacts and showed little rectifying characteristics. As Hall voltages were measured under conditions of high illumination large photovoltages made measurements difficult. Most of the cells used were from a batch of 10x 1 0 r a m units which were shaped to give a central portion 5 x 10 m m with 1 m m side arms. T w o 4 x 4 m m cells were used but approximately the same proportions were maintained. Hall and P E M effects were performed using four wavelength regions: Bausch and L o m b filters were employed for 1 "25 and 2"1 t~ with a band pass of approximately one-fifth the center wavelength. A sodium lamp with a heat filter to isolate the lines at 0"5/x was used in limited cases; its intensity being rather small restricted the range of usefulness. As a general short-wavelength source, limited to wavelengths less than 0"8/x, a tungsten lamp and a heat filter were employed. I n all cases no focusing was used, to insure as uniform an illumination as possible. For absolute magnitude measurements, the light output of a Westinghouse 75 W projector lamp and the appropriate filter was compared to a calibrated bolometer. T h e Hall measurements under illumination were taken using a small mirror mounted just before the cryostat window to deflect the light beam 90=', i.e. the light beam was incident between the magnet poles.

T h e cryostat used for the measurements consisted of a liquid-air chamber from which the sample mount was suspended by copper-nickel tubing. T h e thermal conductance of the tubing was such that temperatures near that of liquid air could be reached and a heater wound on the sample mount could readily raise the temperature to 300°K. A thermocouple was employed to measure temperatures. T h e light beam used in the experiments was incident through a glass window of the vacuum jacket. EXPERIMENTAL RESULTS

(i) General As PbS photoconductive films are polycrystalline, a check was made to see how well the P E M voltage obeyed theory. T h e effect was linear with magnetic field between 0.8 and 9"6 kG, the latter field being used in practically all the measurements. T h e saturation of the P E M voltage with H, as predicted by KURNICK and ZITTER,(lI) of t~B(I + +/~2B2)-1/2 is not expected with the 10 k G field employed and a carrier mobility of 5-600 cin'Z/V sec. T h e P E M voltage was found to be linear with light flux for the range of photon signals from 1"1 x 1014 to 1 "6 × 1015 photons per sec. As the results to be quoted range over light-flux intensities of the order of 50 the generally consistent pattern of results obtained is good evidence of the general validity of the theory. T h e interpretation of parameters calculated and the effect of the fihn structure will be discussed further subsequently. (ii) The nature of the P E M effect One of the best indications that surfaces are controlling the recombination is through the use of formulae (2) and (3) and by illuminating the cell from the front and back. If one surface recombination is dominant the ratio of the front to the back open-circuit P E M voltages is kd and the signal changes sign on rotation. T h e P E M voltage was measured, then the cells rotated 1 8 0 , and the voltage measured again. T h e light intensity and magnetic field were not changed in the two experiments. A polarity reversal was found on rotation for all cells and all wavelengths tested: 0.5, 0-8, 1"25 and 2"25/~. Table 1 lists the results of such measurements. T h e loss of transmission due to the presence of the glass mounting for one side and the plastic film for the other was considered equal. T h e

MINORITY-CARRIER

EFFECTS

IN

PbS

PHOTOCONDUCTIVE

FILMS

151

Table 1. Evaluation of the absorption coefficient by illuminating a cell from the front and the back ( T = 295°K) A (/~) 1 "25 1 "25 1 '25 1 "25

Average k = 0"5 I 0"5 ]l Average k =

~bX 10 -14 (photons/sec)

kd

1'4 2.7 1"3 2.2 1-5 2.5 1-5 2.5 2"5 x 104, SCANLONk = 3"OxlO 4 (A = 1.25~) -! 3"8 I 6.7 -] 6"0 j 10.o 8"3 X 104, SeANLON k = 5"0 ×104 (~ = 0"5/~) 1 "3 2"8 6 "3 14

a g r e e m e n t b e t w e e n the average of the calculated values of the K's and those of SCANLON(1~) is quite good. T h e validity of GARTNER'S t h e o r y has been checked by BRAND et al.(la) but as details of their results have not b e e n p u b l i s h e d a s i m p l e experim e n t was p e r f o r m e d on a sample of G e to check the validity of e q u a t i o n s (3) and (4). T h e sample thickness was r e d u c e d to 9 " 6 × 10 -3 cm or about 1/10th of the s a m p l e ' s m e a s u r e d diffusion length. W i t h one surface etched and the other ground, the e x p e r i m e n t m e n t i o n e d above for P b S was perf o r m e d to d e t e r m i n e k. A value of 5"2 x 10 a c m 1 was obtained w h i c h is 26 per cent lower t h a n the value d e t e r m i n e d by DASH and NEWMAN(14). As a rather broad w a v e l e n g t h region was used a smaller value of k is e x p e c t e d f r o m the P E M m e a s u r e m e n t . T h i s result and the fact that the signal reversed sign w h e n the sample was rotated 180 ° are taken as good confirmation of the theoretical expressions. 1VIEASUREMENT O F Lx

M o s t of the P E M m e a s u r e m e n t s w e r e p e r f o r m e d b y i l l u m i n a t i n g the cell f r o m the front surface and calculating an "effective diffusion l e n g t h " Lz defined by the e q u a t i o n :

Vs-

k X 104 cm -1 ( d = 6 x 1 0 -5cm)

2¢BLx x 10 -s

pdW

T h e factor Lx/d is e q u a l to t h e bracketed Vterms of e q u a t i o n s (1-3). I n this expression ¢ is the n u m ber of p h o t o n s incident on the cell p e r second, W is the w i d t h of the cell and pd the p r o d u c t of the hole density times the thickness of the film. T h e

ec

(M) 2"50 2"45 2"33 2"14 2"45 2"51

factor 2 arises as the electron and hole mobilities have been assumed equal as suggested by the w o r k of ALLCAIER and SCANLON(15). T h e p r o d u c t pd was evaluated f r o m H a l l m e a s u r e m e n t s m a d e u n d e r identical conditions of i l l u m i n a t i o n to those of the P E M m e a s u r e m e n t . T h e m o s t extensive set of m e a s u r e m e n t s of Lz was p e r f o r m e d w i t h cell No. 3 which was a 10 x 10 m m cell. T h e results are listed in T a b l e 2. It is i m m e d i a t e l y a p p a r e n t that Lx is essentially i n d e p e n d e n t of t e m p e r a t u r e and light intensity.

Table 2. Diffusion length Lx for various light-flux levels and temperatures (sample P b S No. 3; h = 1"25 ~) T (°K)

(photons/sec)

~ X 10 -14

Lz × 106 (cm)

187 192 193 193 193 193 225 225 225 225 297 297 297 297 297 298 314 314 314

8.5 8.5 8.5 14-5 5.25 4.0 11 "5 7-0 3.2 1.9 7.75 3 -50 2-15 1-0 0.35 2.2 13 8.0 3.5

4.2 6-0 4.0 5"5 7-5 4.0 2.2 1.9 4.0 5-5 2.5 4-0 4.2 4-5 4.2 6.0 3.2 4.2 4-5

152

R. L. W I L L I A M S

A simple check of the wavelength-dependence of Lz was carried out using cell No. 2. Table 3 lists comparisons of Lx for 2"1 and 1 "25/x at room temperature and approximately 195°K. T h e values

Table 3. Wavelength variation of the diffusion length Lx (sample No. 2; H = 9.8 kg) T (°K)

¢ X 10-14 (photons/sec)

LxXlO 5 (cm)

3, (p.)

293 293

11 2.0

2'6 2'3

2"1 2'1

295 295

9"5

0"67 0"76

1 "25 1 '25

196 196

11 2"0

2"91 2.8

2'1 2.1

194 194

3.5 1.1

0'50 0"50

1.25 1.25

195 195

4-7 3.0

0-55 0.55

1.25 1.25

1-25

for k given by SCANLON (12) are: A = 1.25/z, k = 3-0x104 cm-1; A = 2-1 /x, k = 1-4x104 cm -1. Although the change of Lx with wavelength is not large, it is to be noted that it is always larger for the longer wavelength. Lx being proportional to the bracketed terms of equations (1-3), the behaviour is consistent with equation (3) if the second term in the bracket is dominant. Some variation of Lx with temperature is apparent for this cell but it is not large. As has been generally found, cells of a particular order have similar characteristics. T h i s was found for cells 1-6 which were the 10 x 10 m m cells. T w o 4 x 4 m m cells, 7 and 8, from a different purchase lot, were measured to see if the results were comparable to the 10 x 10 m m cells. Results of measurements on cell 7 can be summarized as follows: (1) At room temperature the average value of Lx for 1-25/x radiation was 2"7 x 10 5 cm (two readings). (2) T h e corresponding value at 194°K was 9"1 x 10 -5 cm (nine readings). (3) T h e ratio of Lx for 2-1/z to that at 1"25/x was 1.3 (293°K). (4) A sign reversal in the P E M voltage was found

at room temperature when the cell was rotated 180 ° . (5) T h e mobility was essentially independent of light flux and wavelength. (This information to be used later.) HALL MEASUREMENTS

T o evaluate L , of the P E M effect it was necessary to determine pd. This was obtained from Hall measurements. I n the course of these measurements it was noted that the mobility was a function of light level. Assuming that a unique relationship exists between the carrier density and the carrier mobility, some crude limits might be put on the value of the diffusion length by measuring the carrier mobility when the carriers are excited by differentwavelengths of light. I f the diffusion length of the minority carriers is much less than the reciprocal of the absorption coefficient, the optically excited carriers remain essentially where created, i.e. in a layer about k -1 cm thick. By contrast, if the diffusion length L9 is long compared to k -1 and the thickness of the film, the position of excitation by the use of different wavelengths of light would have little or no effect on the density distribution, the carriers quickly diffusing across the fihn. Diffusion times will be discussed in a following section. I f the carriers are confined to a layer about h 1 cm thick the value pd determined from Hall measurements would be in fact ph 1. As the mobility was known to vary with p, a result to be presented, the pd values obtained for each wavelength of light would have to be multiplied by a factor (dh) 1 to compare mobilities for the same carrier density. Or conversely, i f / z is plotted against pd, and LD is much shorter than h 1, the mobility curves would not be expected to coincide, as p would not be simply proportional to the calculated ~'~alue of pd b u t in error by different factors proportional to h -1. This assumes, as mentioned above, that/x and p are uniquely related. T h e results of the wavelength-mobility measurements are given in Fig. 1. I t is immediately apparent that the mobility is a function ofp. T h e r e is no appreciable difference in the value of/z for a given value of pd indicating that the diffusion length is not less than k 1. F o r cell No. 7, as previously mentioned, no variation of mobility with the density of optically excited carrier was found.

MINORITY-CARRIER

EFFECTS

I N PbS P H O T O C O N D U C T I V E

FILMS

153

30-

i I I

20-

i i

v

No. 2

Pbs

t ic

I

I

iO '0

I T IIII

1

1

LOu

pd,

nurnber/cm

I I I lll|

t012

I

2

FIG. 1. Mobility of optically excited carriers for three wavelength regions. (D T = 195°K, A =2.12t, [] T = 192°K, A < 0'8~* A T = 195°K, A = 1"25~

T h e experimental work of WOODS(5) dealt with the change of carrier mobility with light injection. His work established that in the range AR/R <~ 1 the photo-effects were primarily carrier-density effects. From the results just quoted the mobility changes are quite secondary for AR/R values up to approximately 100. RECOMBINATION

PROCESS--RESPONSE

TIME

T h e results of the P E M measurements indicate that recombination is taking place at the surfaces of the cell. T h e films are of the order of 0.6/, thick(16,17) and the time constant should then be controlled by recombination at the surfaces. For a semiconductor which has identical minority- and majority-carrier lifetimes SHOCKLEY(18) and McKELvEY and LONGINZC19) have developed expressions for the response time. For a thin layer with surface recombination dominant the lifetime becomes d/2s. T h e measured cell time constant is of the order of 3 x 104 so that for a film 6 x 10.5 in. thick s is 0.1 cm/sec. This is a low value of s. A second case is possible, namely that s is large but that diffusion is limiting the rate of recombination. T h e response time is then 4d2/rrD. The diffusion coefficient D can be estimated from ALLAGAIERand SCANLON'S(15) value for the single-

crystal electron mobility. As diffusion is across the film, barriers should not appreciably affect the value of D and it is calculated to be 14 cm2/sec at room temperature. The cell response time would then be 3 × 10-lo see, a value 10 -6 times smaller than observed. The above points indicate that processes other than simple recombination at the surface are taking place. Further evidence has been provided for this by the work of WOODS(5). From his analysis of Hall and conductivity data on PbS films it is apparent that minority-carrier lifetimes must be small compared to that of the majority carriers. This leads to two possible schemes. The minority carriers are trapped temporarily in the bulk of the crystallites and, after being thermally ejected from the centers, retrapped, probably many times, the carriers pairs eventually recombining at the surface. As an alternative to this process, minority carriers could be trapped at the surface and remain there until the eventual recombination with free holes, the majority carriers. If the latter process is the correct one, minority-carrier effects would be essentially complete when the electrons are trapped at the surface. By contrast to this behaviour, if trapping takes place in bulk with eventual recom-

154

R. L. W I L L I A M S

bination at the surface, minority-carrier effects would exist for a time comparable to the majoritycarrier lifetime. HAYNES and HORNBECK(20) derive the following expression for the response time in the presence of minority-carrier trapping:

I 10 3

",1

i

~- = Tg + ~'r + "rg~-r/'rt

where ~-g is the average time spent in traps, ~'r is the lifetime (time in the appropriate band) and may be the sum of a number of smaller intervals, and rt is the time before trapping. T h e expression used for m is related to the number of trapping centers per cm 3, N , the thermal velocity v, and the capture cross section Q, by the expression ~-t = (NQv) -1. The expression for the time constant is then -r = -rg +'rr + ' r g ' r r N Q v

For silicon, HAYNES and HORNBECK'Sresults suggested that for moderate light pulses all the traps are saturated when the light is on, i.e. N approaches zero and the time constant is for the first part of the decay ~- = 7g +'rr. As time progresses some of the traps are emptied and N, the number available for trapping, increases until the time constant becomes r a r r N Q v . If N is larger than normal carrier concentrations encountered, and the trapping process is dominant, a light pulse will decay with a time constant "rr'raNQv and be unaffected by the light-pulse amplitude. The time constant of the device is then determined by minority-carriers effects. FREQUENCY

RESPONSE

T o aid in determining the physical picture of the time history of the excited carriers, the frequency response of cell No. 2 was measured for the photoconductive, photovoltaic and photoelectromagnetic effects. The results of these measurements are shown in Fig. 2. The amplitudes of the P E M and PC signals have been arbitrarily made equal for easy comparison of the frequency response. T h e P - F curve was placed at a convenient amplitude for comparison with the other two curves. The drop in the photoconductive response curve near 3.5 kc/'s indicates a cell time constant of 46/~sec. The photovoltaic response shows no time constant effects out to 12 kc/s, but by contrast the

> ~" ~~ ~°~

Celt No.2::>'<:>''~'''"

x

×

Dpv, oPC. xREM

a:

× ×

x

! ix

i0L IOz

!

I I I lil!"

103 Frequency, C/S

I T i I

IO4

FIG. 2. Frequency response for the photoconductive, photovoltaic and photoelectromagnetic effects. P E M signal shows an even stronger frequency response than the photoconductivity. The significant feature of these curves is that the P E M has a timeconstant effect similar to that of the photoconductivity. The measurement of the P E M signal is difficult; even at low frequencies the magnitude of the PV and P E M signals are comparable, while at 10 kc/s the P E M voltage represents only a few per cent modulation of the photovoltage. The scatter in points near 10 kc/s is a consequence of this. Light intensities which changed the cell resistance by a factor of nearly 3 were used to measure the response curves of Fig. 2. This is not considered to reduce the validity of the results for the following reasons. Trapping effects such as described by HAYNES and HOm~BECK(20) tend if anything to be removed if high light levels are employed. P E M experiments performed with comparable light intensities gave no indication of any changed behaviour. DISCUSSION

(a) G e n e r a l The concept of trapping as outlined by HAYNES and HORNBECK,(20) coupled with surface domin-

MINORITY-CARRIER

EFFECTS

I N PbS P H O T O C O N D U C T I V E

ance of recombination, explains quite satisfactorily the results of the present experiments. The sensitivity of the cells arises from the presence of traps in which the minority carriers spend most of their time, and this delays the eventual recombination at the surface. During the periods that the minority carriers are trapped the majority carriers remain free to provide photoconduction. The significance of the lack of any evidence for a photovoltaic time constant comparable to the PC value is hard to evaluate. The photovoltaic voltage is the sum of many separate photovoltages at each of the inter-crystalline junctions. For crystallites whose dimensions are of the order of 10 -4 cm there are approximately 10 s junctions in a 10 x 10 m m cell. The problem of amplitude and time constant can be very complex. The junction mobility has been shown to be modified in a secondary manner by optically induced carrier-density changes. (b) Polycrystalline films The application of single-crystal theory to polycrystalline films is not without question of validity. T h e argument presented of each crystallite being a small P E M generator is felt to be valid but correction factors need to be applied to the magnitude of Vs obtained from such crystallites. T h e agreement between the value of k determined from the ratio of front to back P E M voltages and that determined by SCANLON(12) is felt to be partly fortuitous, but, taking the ratio of front to back P E M signals, common correction factors cancel out. On the whole, sufficient agreement with theory is found to justify the conclusions drawn but the calculated values of Lz should be treated as orderof-magnitude values. The present experiments indicate that most of the recombination is taking place at the front surface of the cells. This, combined with the sign reversal found when the cell was rotated 180 °, suggests that Lx should be equal to k -1, the second term of the bracket in equation (3). For the 10 × 10 m m cells the value of Lx is about one order of magnitude smaller than k -1. That Lz is smaller is not unexpected, as any correction for the polycrystalline nature of the film would tend to increase the calculated value of Lz. For the 4 × 4 m m cells Lx was comparable to k -1 but this result is not necessarily to be taken as better agreement with theory.

FILMS

155

(c) Low-frequency noise The present experiments were undertaken in an effort to find some substance for the arguments used by the author(el) to explain the origin of 1If noise in cells irradiated with short-wavelength radiation. The principle of short diffusion lengths rather than the concept of trapping was used to explain the results. The present experiments suggest that regardless of the position of excitation the surfaces control the recombination. The lack of 1If noise with long-wavelength background radiation cannot then be based on the explanation that recombination is in the bulk when long-wavelength radiation excites carriers there. ROBERTS(22) has suggested, and WILLIAMS(21) noted, that the energy difference of the different wavelengths might be the significant feature. ROBERTS points to the presence of the peak in sensitivity near 1/~ which he observed in PbSe and which also has been found in PbS.(1) He suggests that excitation of this level is the source of 1If noise. Two things are unsatisfactory with the explanation: first the l / f noise could, in certain cases, be produced with radiation of wavelengths longer than 1.8/~(23) and secondly that Eastman Kodak chemically deposited PbS ceils do not in general show this 1 rt peak. (17"24) Although the trapping effects believed to be present are somewhat akin to the small-diffusionlength arguments used previously,(21) the results reported, unfortunately, do little to clarify the earlier experimental results on the productions of 1.f noise by radiation. An explanation is more likely to be found if the source and mechanism of the 1If noise can be determined.

Acknowledgements--The author wishes to acknowledge many helpful discussions with G. Gmoux, and the assistance of M. SHEREBRINwho performed many of the measurements.

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