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Lifetime of photogenerated carriers on surface of iodine single crystals
J. Phys.
Chem. Solids
Pergamon
Press 1965. Vol. 26, pp. 1133-1137.
Printed in Great Britain.
LIFETIME OF PHOTOGENERATED
CARRIERS ON
SURFACE OF IODINE SINGLE CRYSTALS M. SIMHONY Department
and J. GORELIK
of Physics, The Hebrew University, (Receiwed
16 Nooembe~
Jerusalem,
Israel
1964)
Abstract-The lifetime of carriers, generated at the surface layer of a crystal by a short flash of strongly absorbed light, can be obtained from oscillograms of transient space-charge-limited currents. The lifetimes in iodine crystals studied range from 1 to 3 psec at surface layers parallel to the (IC crystallographic plane.
1. INTRODUCTION
3. OSCILLOGRAMS
STRONGLY absorbed light generates a large reservoir of current carriers in a thin surface layer of the iodine crystals. By applying a suitable electric field, free holes are injected into the bulk of the crystal, giving rise to a space-charge-limited current (SCLC). Oscillograms of transient SCLC have been proved useful for a direct determination of the carrier mobility.(r-4) A method is now presented whereby the lifetime of carriers generated in the surface layer of the crystal can be obtained from these oscillograms.
2. EXPERIMENTAL
OF TRANSIENT
SCLC
Typical curves of transient SCLC in iodine crystals are shown by the solid lines in Fig. 1. Curve 1 is for intense steady illumination (infinite carrier reservoir). It shows that at the onset of the pulse (t = 0) the current density rises abruptly to an initial value js. As more and more holes are injected, the current increases gradually, until the first front of carriers reaches the cathode. This occurs at t = tl, the transit time of the leading carriers. Thereafter the current decays slowly to its steady-state value.@) With intense flash illumination (curve 2) the same initial current values
TECHNIQUE
The crystals are vapor-grown from purified iodine.(s) They are 0.8-l -7 mm thick and have large surfaces (up to O-5 ems) parallel to the UC crystallographic planes. One such surface is provided with a transparent conducting glass electrode (the anode). The opposite electrode is a platinum disc (area 0.1 or 0.05 ems); this is surrounded by a guard-ring which prevents surface leakage. The experimental arrangement has been described elsewhere.(lls) The voltage pulse applied to the crystal triggers a short (O*Zpsec), intense light-flash; light in the spectral region of the fundamental filters
absorption
and is focused
transient
CRO.
_ _
SCLC
_.
._.
of iodine(s)
on the sample
passes through surface.
The
is amplified and displayed on a
FIG. 1. Schematic diagram of transient space-chargelimited currents. The dashed curve is for the trap-free, infinite reservoir case. Curves 1 and 2 are for steady and for flash illumination, respectively.
1133
M.
1134
SIMHONY
are obtained, but at times approaching tr the current is markedly smaller than in the foregoing case. This results from the emptying of the carrier reservoir during a time te which is smaller than tl. We conclude, therefore, that as long as t is smaller than te the reservoir contains many more carriers than are being instantly injected into the bulk (see Discussion), and the depletion of the reservoir does not affect the current. At t = te the last carriers are injected; from then on the current is due to the propagation of a space-charge (SC) layer along the crystal, and is smaller than the SCLC because the number of moving carriers is smaller. The transit times tl, obtained from the current curves for both steady and flash illumination, are the same within experimental error. This shows that the speeding-up action of the SC layer(s) on the leading carriers is not appreciably weakened by the absence of excess charge behind it, possibly because the thickness of the layer is large. The nearly linear current decay for t > tl (see oscillogram, Fig. 2) results from the uniform outflow of carriers from the sample. By extrapolating the decay-line to the time-axis [the dark current line) we obtain the time tl+ tf, at which the last injected carriers reach the cathode. (The small current at t > tl+ tf is due to thermal release of carriers from traps). The measurement of tf is used for the calculation of the emptying time of the reservoir (see Section V). Finally, the oscillograms permit the approximation of the total number Nt of carriers injected per unit area, tl+tf Ni =
(l/q)
j-
jack
0
by simply measuring the area between the traces and the dark current line (4 is the electronic charge). 4. LIFETIME
CALCULATION
The depletion of the carrier reservoir following the cessation of the light-flash results mainly from two processes, recombination at the surface layer and injection into the bulk. We assume these processes to be independent of one another; the recombination rate is N/r, where N is the carrier
and J.
GORELIK
density at the surface and 7 is an average lifetime (see Discussion). The continuity equation can be expressed as dN/dt = -N/r--J,
(1)
where J is the injection rate. We consider injection taking place during a time te which is smaller than tl. The slight increase of the current which occurs then is due to the increase in the number of moving carriers, and excludes any significant variation of the injection rate. To a good approximation we may therefore take the injection rate as a constant given by
J = Nilte,
(2)
where Ni is the total number of carriers injected per unit area. From equation (1) we then obtain N = NO exp(-t/T)-JT[l-exp(-t/T)]
(3)
where No is the value of N at t = 0. Assuming N z 0 at t = te, we obtain the solution T[exp(t&)-
l] = No/J.
lf te is three or more times larger than (4) may be simplified to give 7 ‘2X&?/T)
=
(4) 7,
No/J.
equation
(5)
The oscillograms yield the time tl+ tf, at which the last injected holes reach the cathode. This time is also equal to te+ tz, where t2 is the transit time of the last carriers. We may represent t2 by ktl, k being a numerical factor. The emptying time of the reservoir is then
t&j= tf-(k-l)t~.
(6)
Due to the repulsion of charge in the SC layer, tz is larger than the transit time to for a spacecharge-free flow, to = Lz/pV = 1*25tl; (L is the thickness of the crystal, p is the mobility of carriers, and V is the applied voltage). We conclude therefore that K is larger than 1.25. On the other hand, according to the theoretical calculations,@) K is smaller than 2. As we show in the Discussion the value of K may be fixed as 1.5. 5. RESULTS
AND
DISCUSSION
The results obtained from a group of crystals are presented in Table 1. The designation of the crystals, their thickness, and the applied voltages
FIG. 2. Oscillogram of transient SCLC obtained by flash illumination. (The initial, rapid decay of the trace is a disturbance due to the capacitative surge.)
[facing
page1134
LIFETIME
OF PHOTOGENERATED
CARRIERS
ON SURFACE
OF IODINE
SINGLE
CRYSTALS1135
Table 1 Total number of injected holes
Transit time
W
w
Crystal
Thickness
Voltage
No.
(L)
(v)
cm
V
107/cm2
2
3
4
5
50 100 200 300 400 600
22 77 190 300 450 810
155 76 38 26 19 13
77 250 580
1
Ip-2
0.082
Time of outflow (Q)
Reservoir emptying time (te)
Empt. time by injection only
Lifetime
(No/J)
+z-
p set 6
7
8
9
95 53 32 24 20 14
18 15 13 11 10 8
8000 2000 680 370 220 100
2.2 2.2 2.3 2.2 2.2 2-l
62 31 16
40 22 12
9 7 5
1200 280 86
I.3 I.3 I.2
l-3
99 56 41
19 16 14
3900 620 330
2.9 3.0 3.0
3.0
2.2
Ip-23
0~110
200 400 800
Ip-53
0.164
200 400 600
420
160 80 53
0.120
200 400 600 800 1000
56 190 360 500 690
82 40 28 21 16
49 27 20 16 13
8 7 6 5.5 5
1400 370 170 110 72
I.1 I.2 1.2 I.2 1.2
I.2
0.065
100 200 300 400 500
100 260 490 640 900
44 22 15 11 9
30 18 14 11 9.5
8 7 6.5 5.5 5
800 270 130 86 56
1.3 I.3 I.4 I.3 1.3
1.3
Ip-56
60
are listed in the Columns 1, 2 and 3, respectively. Columns 4, 5 and 6 show values obtained from oscillograms taken at each voltage: the total number Nf of injected carriers, the transit time 11, and the time tf during which the injected holes flow out of the crystal. These values can be obtained with sufficient accuracy (k 5 per cent) if trapping is slow; otherwise the release of carriers from traps strongly deforms the current curve, making the inflection at t = tl obtuse and shortening the linear section of the decay at t > tl. In crystals grown from purified iodine,@) the trapping times (400 to 1000 psec) greatly exceed the duration of the transient process at all voltages applied (except the lowest ones, where they are only a few times larger) and the accuracy is quite high. Thin
crystals carefully selected from commercial iodine of ACS specification, e.g. crystal No. 60 (see Table l), may also yield sufficient accuracy. The values of te (Column 7) are derived from equation (6) with K = 1.5. Column 8 indicates the values of No/J = N&/Nt, which is the time it would take to empty the reservoir by injection only; these values are calculated with Ns = lOll/cms (see below). Finally, Column 9 shows the lifetime values, as derived from equation (5) (te is larger than T). They are seen to range between 1 and 3 psec for the different crystals. For each crystal the lifetimes calculated from data obtained at the different applied voltages are very close to the average value (also shown in Column 9) and independent of the voltage.
M.
1136
and J.
SIMHONY
The requirement that the carrier lifetime be independent of applied voltage allows us to fix the values of K and NO within narrow limits. This is illustrated by Fig. 3. The circles here show the lifetime values (crystal Ip-2), as listed in the Table 1. Figure 3(a) shows that even small (5 per cent) variations of k from the value 1.5 makes the
_
No=d/c":
2.0 -
0
0
N,=5x10”/cm2 ”
1.5 -
(b “$0
60
so
100
200
200 Voltage,
600
V
FIG. 3. Choice of the parameters k and No. Circles show the lifetime at different voltages, calculated with k = 1.5 and No = 1011/cm2. The triangles show lifetime values calculated with other pairs of k, No, as indicated on the curves.
dependent on the voltage; for 7 decreases, and for k = 1.55 it increases with l’. Figure 3(b) shows that the variation of iVs also made the lifetime a function of the applied voltage; for NO = 5.1011/ems, 7 decreases with P’, and for NO = 2~101s/cms it increases. That this choice is unique within fairly narrow lifetimes
k = 1.4,
(triangles)
GORELIK
limits is shown by a detailed calculation [using equation (4)], based on other pairs of k, NO values. Thus, k = 1.55, with NO = 2.1011, 50 1011 or even lOls/cms, and also k = 1.4, with any one of these three values of NO, yield a voltage-dependent lifetime. We thus conclude that k is 1.5 in a range 14-l-55, and NO is lOrr/cms in a range between 20 101s and 5.1011/ems. Because the measured photon flux is lOls/cms, we obtain the most probable value of the quantum efficiency as 0.1. We shall now justify the assumption that the reservoir is large during most of the emptying time, te, and that therefore equation (3) is applicable during most of the emptying time. We shall do this by using Fig. 4. The solid curves here represent the decay of the carrier density in the reservoir (crystal Ip-56), according to equation (4), at two applied voltages (200 and 1000 V); the dashed line shows a decay which would be due to recombination only. It is seen that the number of carriers instantly injected into the bulk does not appreciably lower the curves, and they closely follow the dashed line. At t = te - 7 In 2, i.e. near to t = te, the recombination rate becomes equal to the injection rate and the curves fall off rapidly. Until this time the reservoir is seen to contain many more carriers than are injected instantly, and the carrier flow is analogous to that in the case of an infinite reservoir. The rapid fall off of the curves justifies the use of the boundary condition iV M 0 at t = te. The obtained lifetime values are hundreds of times smaller than the hole trapping time in the bulk of the iodine crystals. This can be explained by a very fast trapping of photogenerated electrons at the surface layer. The photogenerated holes recombine, therefore, with the electrons inside the layer. Holes injected into the bulk do not have partners to recombine with, and their lifetime is large. The fast trapping of electrons can be also derived from the fact that currents obtained with the illuminated electrode negative are negligibly small. It is quite likely that 7 is not constant but depends on the instantaneous density of carriers in the reservoir. Analysis under these conditions would be, however, nigh impossible. The experimental values quoted should, therefore, be regarded as averages over the entire decay range.
LIFETIME
OF PHOTOGENERATED
CARRIERS
ON SURFACE
OF IODINE
SINGLE
CRYSTALS
1137
lO”T
Iodine lp-56 N,e+-Jr(I-e+)
r = I.2pse.c
\ IO”Ni
109-
-
\ IOOOV
1
108-
Time,
psec
FIG. 4. Decay of the carrier density in the photogenerated reservoir at the crystal surface. The decays at 200 and 1,000 V are shown by the solid curves. The dotted line corresponds to a decay due to recombination only. Acknowledgement-The gratitude to Professor stimulation.
authors wish to express their A. MANY for his help and
REFERENCES 1. MANY A., SIMHONY M., WEISZ S. Z. and LEVINKIN J., J. Phys. Ckem. Solids 22, 285 (1961). 2. MANY A. and RAKAVY G., Phvs. Rev. 126. 1980
3. MIWY A., WEISZ S. Z. and SIMHONY M., Phys. Rev. 126, 1989 (1962). 4. MANY A., SIMHONY M., WEISZ S. Z. and TEUCHER Y., J. Phys. Chem. Sol& 25, 721 (1964). 5. SIMHONY M. and GORELIK J., to be published. 6. Moss T. S., Photoconductim’ty in the Elements, p. 232. Butterworths, London (1952); BRANERA. A. and CHEN R., J. Phys. Ckem. Solids 24, 135 (1963).
Chem. Solids
Pergamon
Press 1965. Vol. 26, pp. 1133-1137.
Printed in Great Britain.
LIFETIME OF PHOTOGENERATED
CARRIERS ON
SURFACE OF IODINE SINGLE CRYSTALS M. SIMHONY Department
and J. GORELIK
of Physics, The Hebrew University, (Receiwed
16 Nooembe~
Jerusalem,
Israel
1964)
Abstract-The lifetime of carriers, generated at the surface layer of a crystal by a short flash of strongly absorbed light, can be obtained from oscillograms of transient space-charge-limited currents. The lifetimes in iodine crystals studied range from 1 to 3 psec at surface layers parallel to the (IC crystallographic plane.
1. INTRODUCTION
3. OSCILLOGRAMS
STRONGLY absorbed light generates a large reservoir of current carriers in a thin surface layer of the iodine crystals. By applying a suitable electric field, free holes are injected into the bulk of the crystal, giving rise to a space-charge-limited current (SCLC). Oscillograms of transient SCLC have been proved useful for a direct determination of the carrier mobility.(r-4) A method is now presented whereby the lifetime of carriers generated in the surface layer of the crystal can be obtained from these oscillograms.
2. EXPERIMENTAL
OF TRANSIENT
SCLC
Typical curves of transient SCLC in iodine crystals are shown by the solid lines in Fig. 1. Curve 1 is for intense steady illumination (infinite carrier reservoir). It shows that at the onset of the pulse (t = 0) the current density rises abruptly to an initial value js. As more and more holes are injected, the current increases gradually, until the first front of carriers reaches the cathode. This occurs at t = tl, the transit time of the leading carriers. Thereafter the current decays slowly to its steady-state value.@) With intense flash illumination (curve 2) the same initial current values
TECHNIQUE
The crystals are vapor-grown from purified iodine.(s) They are 0.8-l -7 mm thick and have large surfaces (up to O-5 ems) parallel to the UC crystallographic planes. One such surface is provided with a transparent conducting glass electrode (the anode). The opposite electrode is a platinum disc (area 0.1 or 0.05 ems); this is surrounded by a guard-ring which prevents surface leakage. The experimental arrangement has been described elsewhere.(lls) The voltage pulse applied to the crystal triggers a short (O*Zpsec), intense light-flash; light in the spectral region of the fundamental filters
absorption
and is focused
transient
CRO.
_ _
SCLC
_.
._.
of iodine(s)
on the sample
passes through surface.
The
is amplified and displayed on a
FIG. 1. Schematic diagram of transient space-chargelimited currents. The dashed curve is for the trap-free, infinite reservoir case. Curves 1 and 2 are for steady and for flash illumination, respectively.
1133
M.
1134
SIMHONY
are obtained, but at times approaching tr the current is markedly smaller than in the foregoing case. This results from the emptying of the carrier reservoir during a time te which is smaller than tl. We conclude, therefore, that as long as t is smaller than te the reservoir contains many more carriers than are being instantly injected into the bulk (see Discussion), and the depletion of the reservoir does not affect the current. At t = te the last carriers are injected; from then on the current is due to the propagation of a space-charge (SC) layer along the crystal, and is smaller than the SCLC because the number of moving carriers is smaller. The transit times tl, obtained from the current curves for both steady and flash illumination, are the same within experimental error. This shows that the speeding-up action of the SC layer(s) on the leading carriers is not appreciably weakened by the absence of excess charge behind it, possibly because the thickness of the layer is large. The nearly linear current decay for t > tl (see oscillogram, Fig. 2) results from the uniform outflow of carriers from the sample. By extrapolating the decay-line to the time-axis [the dark current line) we obtain the time tl+ tf, at which the last injected carriers reach the cathode. (The small current at t > tl+ tf is due to thermal release of carriers from traps). The measurement of tf is used for the calculation of the emptying time of the reservoir (see Section V). Finally, the oscillograms permit the approximation of the total number Nt of carriers injected per unit area, tl+tf Ni =
(l/q)
j-
jack
0
by simply measuring the area between the traces and the dark current line (4 is the electronic charge). 4. LIFETIME
CALCULATION
The depletion of the carrier reservoir following the cessation of the light-flash results mainly from two processes, recombination at the surface layer and injection into the bulk. We assume these processes to be independent of one another; the recombination rate is N/r, where N is the carrier
and J.
GORELIK
density at the surface and 7 is an average lifetime (see Discussion). The continuity equation can be expressed as dN/dt = -N/r--J,
(1)
where J is the injection rate. We consider injection taking place during a time te which is smaller than tl. The slight increase of the current which occurs then is due to the increase in the number of moving carriers, and excludes any significant variation of the injection rate. To a good approximation we may therefore take the injection rate as a constant given by
J = Nilte,
(2)
where Ni is the total number of carriers injected per unit area. From equation (1) we then obtain N = NO exp(-t/T)-JT[l-exp(-t/T)]
(3)
where No is the value of N at t = 0. Assuming N z 0 at t = te, we obtain the solution T[exp(t&)-
l] = No/J.
lf te is three or more times larger than (4) may be simplified to give 7 ‘2X&?/T)
=
(4) 7,
No/J.
equation
(5)
The oscillograms yield the time tl+ tf, at which the last injected holes reach the cathode. This time is also equal to te+ tz, where t2 is the transit time of the last carriers. We may represent t2 by ktl, k being a numerical factor. The emptying time of the reservoir is then
t&j= tf-(k-l)t~.
(6)
Due to the repulsion of charge in the SC layer, tz is larger than the transit time to for a spacecharge-free flow, to = Lz/pV = 1*25tl; (L is the thickness of the crystal, p is the mobility of carriers, and V is the applied voltage). We conclude therefore that K is larger than 1.25. On the other hand, according to the theoretical calculations,@) K is smaller than 2. As we show in the Discussion the value of K may be fixed as 1.5. 5. RESULTS
AND
DISCUSSION
The results obtained from a group of crystals are presented in Table 1. The designation of the crystals, their thickness, and the applied voltages
FIG. 2. Oscillogram of transient SCLC obtained by flash illumination. (The initial, rapid decay of the trace is a disturbance due to the capacitative surge.)
[facing
page1134
LIFETIME
OF PHOTOGENERATED
CARRIERS
ON SURFACE
OF IODINE
SINGLE
CRYSTALS1135
Table 1 Total number of injected holes
Transit time
W
w
Crystal
Thickness
Voltage
No.
(L)
(v)
cm
V
107/cm2
2
3
4
5
50 100 200 300 400 600
22 77 190 300 450 810
155 76 38 26 19 13
77 250 580
1
Ip-2
0.082
Time of outflow (Q)
Reservoir emptying time (te)
Empt. time by injection only
Lifetime
(No/J)
+z-
p set 6
7
8
9
95 53 32 24 20 14
18 15 13 11 10 8
8000 2000 680 370 220 100
2.2 2.2 2.3 2.2 2.2 2-l
62 31 16
40 22 12
9 7 5
1200 280 86
I.3 I.3 I.2
l-3
99 56 41
19 16 14
3900 620 330
2.9 3.0 3.0
3.0
2.2
Ip-23
0~110
200 400 800
Ip-53
0.164
200 400 600
420
160 80 53
0.120
200 400 600 800 1000
56 190 360 500 690
82 40 28 21 16
49 27 20 16 13
8 7 6 5.5 5
1400 370 170 110 72
I.1 I.2 1.2 I.2 1.2
I.2
0.065
100 200 300 400 500
100 260 490 640 900
44 22 15 11 9
30 18 14 11 9.5
8 7 6.5 5.5 5
800 270 130 86 56
1.3 I.3 I.4 I.3 1.3
1.3
Ip-56
60
are listed in the Columns 1, 2 and 3, respectively. Columns 4, 5 and 6 show values obtained from oscillograms taken at each voltage: the total number Nf of injected carriers, the transit time 11, and the time tf during which the injected holes flow out of the crystal. These values can be obtained with sufficient accuracy (k 5 per cent) if trapping is slow; otherwise the release of carriers from traps strongly deforms the current curve, making the inflection at t = tl obtuse and shortening the linear section of the decay at t > tl. In crystals grown from purified iodine,@) the trapping times (400 to 1000 psec) greatly exceed the duration of the transient process at all voltages applied (except the lowest ones, where they are only a few times larger) and the accuracy is quite high. Thin
crystals carefully selected from commercial iodine of ACS specification, e.g. crystal No. 60 (see Table l), may also yield sufficient accuracy. The values of te (Column 7) are derived from equation (6) with K = 1.5. Column 8 indicates the values of No/J = N&/Nt, which is the time it would take to empty the reservoir by injection only; these values are calculated with Ns = lOll/cms (see below). Finally, Column 9 shows the lifetime values, as derived from equation (5) (te is larger than T). They are seen to range between 1 and 3 psec for the different crystals. For each crystal the lifetimes calculated from data obtained at the different applied voltages are very close to the average value (also shown in Column 9) and independent of the voltage.
M.
1136
and J.
SIMHONY
The requirement that the carrier lifetime be independent of applied voltage allows us to fix the values of K and NO within narrow limits. This is illustrated by Fig. 3. The circles here show the lifetime values (crystal Ip-2), as listed in the Table 1. Figure 3(a) shows that even small (5 per cent) variations of k from the value 1.5 makes the
_
No=d/c":
2.0 -
0
0
N,=5x10”/cm2 ”
1.5 -
(b “$0
60
so
100
200
200 Voltage,
600
V
FIG. 3. Choice of the parameters k and No. Circles show the lifetime at different voltages, calculated with k = 1.5 and No = 1011/cm2. The triangles show lifetime values calculated with other pairs of k, No, as indicated on the curves.
dependent on the voltage; for 7 decreases, and for k = 1.55 it increases with l’. Figure 3(b) shows that the variation of iVs also made the lifetime a function of the applied voltage; for NO = 5.1011/ems, 7 decreases with P’, and for NO = 2~101s/cms it increases. That this choice is unique within fairly narrow lifetimes
k = 1.4,
(triangles)
GORELIK
limits is shown by a detailed calculation [using equation (4)], based on other pairs of k, NO values. Thus, k = 1.55, with NO = 2.1011, 50 1011 or even lOls/cms, and also k = 1.4, with any one of these three values of NO, yield a voltage-dependent lifetime. We thus conclude that k is 1.5 in a range 14-l-55, and NO is lOrr/cms in a range between 20 101s and 5.1011/ems. Because the measured photon flux is lOls/cms, we obtain the most probable value of the quantum efficiency as 0.1. We shall now justify the assumption that the reservoir is large during most of the emptying time, te, and that therefore equation (3) is applicable during most of the emptying time. We shall do this by using Fig. 4. The solid curves here represent the decay of the carrier density in the reservoir (crystal Ip-56), according to equation (4), at two applied voltages (200 and 1000 V); the dashed line shows a decay which would be due to recombination only. It is seen that the number of carriers instantly injected into the bulk does not appreciably lower the curves, and they closely follow the dashed line. At t = te - 7 In 2, i.e. near to t = te, the recombination rate becomes equal to the injection rate and the curves fall off rapidly. Until this time the reservoir is seen to contain many more carriers than are injected instantly, and the carrier flow is analogous to that in the case of an infinite reservoir. The rapid fall off of the curves justifies the use of the boundary condition iV M 0 at t = te. The obtained lifetime values are hundreds of times smaller than the hole trapping time in the bulk of the iodine crystals. This can be explained by a very fast trapping of photogenerated electrons at the surface layer. The photogenerated holes recombine, therefore, with the electrons inside the layer. Holes injected into the bulk do not have partners to recombine with, and their lifetime is large. The fast trapping of electrons can be also derived from the fact that currents obtained with the illuminated electrode negative are negligibly small. It is quite likely that 7 is not constant but depends on the instantaneous density of carriers in the reservoir. Analysis under these conditions would be, however, nigh impossible. The experimental values quoted should, therefore, be regarded as averages over the entire decay range.
LIFETIME
OF PHOTOGENERATED
CARRIERS
ON SURFACE
OF IODINE
SINGLE
CRYSTALS
1137
lO”T
Iodine lp-56 N,e+-Jr(I-e+)
r = I.2pse.c
\ IO”Ni
109-
-
\ IOOOV
1
108-
Time,
psec
FIG. 4. Decay of the carrier density in the photogenerated reservoir at the crystal surface. The decays at 200 and 1,000 V are shown by the solid curves. The dotted line corresponds to a decay due to recombination only. Acknowledgement-The gratitude to Professor stimulation.
authors wish to express their A. MANY for his help and
REFERENCES 1. MANY A., SIMHONY M., WEISZ S. Z. and LEVINKIN J., J. Phys. Ckem. Solids 22, 285 (1961). 2. MANY A. and RAKAVY G., Phvs. Rev. 126. 1980
3. MIWY A., WEISZ S. Z. and SIMHONY M., Phys. Rev. 126, 1989 (1962). 4. MANY A., SIMHONY M., WEISZ S. Z. and TEUCHER Y., J. Phys. Chem. Sol& 25, 721 (1964). 5. SIMHONY M. and GORELIK J., to be published. 6. Moss T. S., Photoconductim’ty in the Elements, p. 232. Butterworths, London (1952); BRANERA. A. and CHEN R., J. Phys. Ckem. Solids 24, 135 (1963).