Potential discharge kinetics of double-layer polymeric photoreceptors

Journal of Non-Crystalline Solids 28 (1978) 305-317 © North-Holland Publishing Company

POTENTIAL DISCHARGE KINETICS OF DOUBLE-LAYER POLYMERIC PHOTORECEPTORS P.M. BORSENBERGER and W. MEY Research Laboratories, Eastman Kodak Company, Rochester, New York 14650, USA

Received 20 June 1')77 Revised manuscript received 10 November 1977

The photoinduced potential discharge kinetics of double-layer photoreceptors containing a polymeric charge-transport layer and a charge-generating layer of amorphous selenium have been investigated as a function of the electric field and the photoinjected charge density. Under space-charge-limited conditions, the discharge kinetics agree with existing theories and can be explained on the basis of a field-dependent drift mobility. For partial injection, the discharge is characteristic of dispersive transport and cannot be described by conventional discharge theory. Under these conditions, transit times of the trailing edge of the photoinjected charge cannot be detected and the rate of potential discharge is determined by the field dependence of the drift mobility. The effects of the electric field and variations of the field dependence of the drift mobility are presented and discussed.

1. Introduction Several theoretical papers have recently appeared in the literature concerned with the photoinduced discharge of corona-charged photoreceptors [ 1 - 7 ] . In this configuration, one surface of a photoinsulator is charged by a corona to some initial potential while the other is grounded. The photoreceptor is usually assumed to be exposed with a pulse of strongly absorbed radiation which creates a sheet of free carriers adjacent to the surface. Depending on the polarity of the illuminated surface, one type of carder remains in the absorption region to neutralize the surface charge and the other is injected into the bulk o f the photoreceptor. As the injected carriers drift through the sample, the surface potential decreases. For these exposure conditions, the discharge kinetics are determined by the photoreceptor thickness, the injected charge density and the drift mobility of the injected carders. As a result, potential discharge measurements provide a technique for studying charge transport in high-resistivity materials. Furthermore, this configuration is identical to that employed in electrophotographic recording and is of considerable technological interest. In a previous paper, an investigation of hole transport in binary solid solutions of 305

306

P.M. Borsenberger, I¢. Mey / Potential discharge kinetics of polymeric photoreeeptors

triphenylamine and bisphenol-A-polycarbonate by potential discharge techniques was described [8]. The results of that study indicated that for space-charge-limited conditions, the discharge kinetics were in good agreement with existing theories and could be explained on the basis of a drift mobility that was dependent only on the electric field and temperature. Under conditions of partial injection, where the injected charge density was less than the electrostatic surface charge, the time dependence of the potential discharge could not be explained by conventional discharge theories. These observations illustrate the importance of the injected charge density in the interpretation of potential discharge and charge-transport measurements. In this paper, we present the results of an investigation of the photoinduced discharge kinetics of selenium/poly(N-vinylcarbazole) (PVK) photoreceptors. This configuration comprises a thin charge-generating layer of amorphous selenium in contact with a transport layer of PVK. For comparison, the results of a series of measurements made with transport layers containing solid solutions of triphenylamine and bisphenol-A-polycarbonate are also presented. The emphasis of this study is directed to the effects of the electric field and the injected charge density. These materials were selected for two reasons: first, there is essentially no energy barrier for hole emission into PVK [9] or solid solutions containing triphenylamine, thereby eliminating uncertainties arising from the field dependence of the injection process; and second, since the field dependence of the hole mobility in PVK [10-12] is significantly different from solid solutions of triphenylamine and bisphenol-A-polycarbonate [8], a comparison of measurements performed on these materials provides an experimental basis for determining the effects of the field dependence of the drift mobility on the potential discharge kinetics. The purpose of this study was to investigate the time dependence of the photoinduced potential discharge in PVK and to compare the results with those observed in solid solutions containing triphenylamine.

2. Experimental The PVK was obtained under the trade name Luvican from Badische Anilin and Soda-Fabriken, Ludwigshafen, Germany. Prior to the preparation of the f'flm sampies, the PVK was purified by multiple recrystallization from solutions of benzene and methanol [13]. PVK f'dms were prepared from solutions of the polymer in dichloromethane. Solutions were coated on to semitransparent nickel-coated Estar substrates at room temperature, then heated to 100°C for 36 h under a nitrogen atmosphere to reduce the residual solvent concentration. From capacitance measurements and cross-section photomicrographs, the film thicknesses were determined as between 3.1 and 10.0/am. The selenium f'flms were prepared by thermal evaporation from a resistance-heated tungsten crucible at a pressure of 2 X 10 -s Torr. The selenium was deposited directly upon the PVK surface with thicknesses

P.M. Borsenberger, W. Mey / Potential discharge kinetics of polymeric photoreceptors

307

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Fig. 1. A schematic diagram of the experimental arrangement. of approximately 0.02/am. After the selenium deposition, the films were heated to 55°C in air for approximately 30 min. Throughout the film preparation, special precautions were taken to eliminate the exposure of the film samples to ultraviolet radiation. The techniques used for the preparation of the transport layers containing triphenylamine have been given elsewhere [8]. The potential discharge was measured by techniques which involve pulse exposures. The selenium-coated surface was charged to an initial potential Vo by passing it under a positive corona discharge. The surface potential V(t) was measured by placing the sample under the transparent electrode of a MOSFET electrometer-follower (Monroe model 145). The sample was then illuminated through the transparent electrode by a high-intensity, xenon-tidied lamp with a pulse duration of 1.2 /as. Nearly monochromatic radiation was obtained by means of a 400 nm bandpass filter. Since PVK [14] and solid solutions of triphenylamine show negligible absorption for wavelengths greater than approximately 370 nm, the absorption was restricted to the selenium emitter. In all cases, the selenium was positively charged. As a result, the photoinduced discharge is due to the injection and displacement of the positive carrier. No discharge is observed if the selenium is negatively charged. The exposure intensity and time were measured by a spectroradiometer (E.G. and G. model 585). The time derivative of the surface potential, I?(t), was obtained by passing the output of the electrometer through a differentiating amplifier (Tektronix model 501). The surface potential and the time derivative of the surface potential were then simultaneously recorded by a camera-equipped oscilloscope. All measurements were made at room temperature. A schematic diagram of the experimental apparatus is included in fig. 1.

3. Analysis Consider a perfect insulator in a planar configuration with a grounded electrode on one surface while the free surface is charged to some initial potential Vo. At t = 0, the sample is exposed to strongly absorbed radiation of arbitrary intensity. The absorption generates electron-hole pairs which are separated by the electric field. Depending upon the polarity of the surface charge, either electrons or holes are

308

P.M. Borsenberger, W. Mey / Potential discharge kinetics o f polymeric photoreceptors

injected into the transport layer while the other remains in the absorption region to neutralize the corona-induced surface charge. As the injected carriers drift through the transport layer, the surface potential decreases. For the analysis employed in this study, it is assumed that the exposure duration is short compared to the transit time of the injected carrier and that the absorption is restricted to a region which is thin compared to the photoreceptor thickness. Neglecting diffusion and trapping, the factors that determine the potential discharge for these conditions are the initial potential Vo, the thickness L, the injected charge density Po and the drift mobility #. It is assumed that the mobility is field dependent and of the form /~(E) = btoE"J ,

(1)

where/go is the mobility per unit field to the co power. Solutions for the rate of potential discharge for these conditions have been given previously [4-7]. The solutions are divided into two time zones: t ~ tx, where tT represents the transit time of the leading edge of the injected charge. For zone 1, which corresponds to t < tw,

co+2

[1-(1-P°)~°+21

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(2)

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(3)

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(4)

Po = eQo/CVo .

(5)

and

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~(t)For t > tT, (

L

rl L

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(6)

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(7)

P.M. Borsenberger, W. Mey / Potential discharge kinetics of potymeric photoreceptors

309

4. Results

4.1. Complete injection (Po = 1) An analysis of the experimental results is usually made from plots of the logarithm of the rate of potential discharge versus the logarithm of time. For exposures such that Po is unity, the rate of discharge should be independent of time for t < t T, whereas for t > t T the results should give a straight line with a slope of -(co + 2)/ (co + 1). For t < t T, the rate of discharge is proportional to V(0~+2), whereas for t > t T, the rate is independent of Vo. Figure 2 shows the time dependence of l?(t) for a 3.1/lm PVK film measured under conditions of complete injection *. As predicted from eqs. (6) and (7), the time dependence shows two distinct regions. For a short period following the exposure, the rate of discharge is independent of time and determined only by the initial voltage. At longer times, the rate is time dependent but constant for all values of Vo. The intersection of the two time zones represents the transit time of the leading edge of the injected charge for a given value of Vo/L. The solid line in fig. 2 corresponds to ~ = 2.0. Figure 3 illustrates the time dependence of l~'(t) for a serie~ of samples with PVK thicknesses between 3.1 and 9.0/zrn. The electric field was 4.8 × 10 s V/cm. The intersections of zones 1 and 2, which represent the transit times, are directly proportional to the sample thickness. An increase in dispersion of the transit times with increasing thickness is also observed. For t < tT, the rate of discharge is independent of thickness, where for t > tT, the slope is independent of thickness. For t < t T, the rate of potential discharge should be proportional to (Vo/L) w+2. Fig. 4 shows the dependence of I?(t < tT) on Vo/L for a series of PVK f'llms with thicknesses between 3.1 and 9.0/am. The solid line corresponds to ~ = 2.0, in agreement with the results illustrated in figs. 2 and3. From the time dependence of the photoinduced discharge and the variation of the rate of discharge with initial potential, it can be concluded that for spacecharge-limited conditions, the discharge kinetics are in good agreement with existhag theories and can be explained on the basis of a drift mobility that is dependent only on the electric field. The drift mobility can be expressed as /a(E) = 8.7 X 10-18E 2"° cmZ/V-s .

(8)

For the same approximate range of fields, values have been reported as 5.0 X 10 -18 E 2 cm2/V-s by Regensburger [10] and 3.7 X 10 -18 E 2 by Mort et al. [11]. At 5 × l0 s V/cm, Gill [12] reported approximately 1.5 × 10-6cm2/V-s, compared to * Since the field at the trailing edge of the injected charge goes to zero under complete injection, the photoreceptor cannot be completely discharged. In practice, the maximum values of 00 were approximately 0.95. From eqs. (2) and (3), it can be shown that the differences between these values and unity have a negligible effect on the measured values of the drift mobility.

310

P.M. Borsenberger, W. Mey / Potential discharge kinetics o f polymeric photoreceptors I

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2.2 X 10 -6 cm2/V-s found in this study. A comparison of these results leads to the conclusion that mobility values determined from space-charge-limited discharge measurements agree with published values.

4.2. Partial injection (Po < 1) For partial injection Po is less than unity, and the time dependence of the rate of potential discharge is given by eqs. (2) and (3). Since the trailing edge of the injected charge is subject to the field (1 - p o ) V o [ L , the transit time of the trailing

312

P.M. Borsenberger, 1t/. Mey / Potential discharge kinetics of polyrneric photoreceptors

edge is (1 - po)-(c°+i)tT . For partial injection, zone 2 is then bounded by t T and (1 - po)-(~+l)tT . For times greater than the transit time of the trailing edge, all charge has left the photoconductor, and the rate of change of the surface potential is zero. Figure 5 shows the time dependence of l/(t) for a 3.1/am PVK film for different values of Po. The intersection of zones 1 and 2, which indicates the transit time of the leading edge of the injected charge, is independent of the injected charge density. Contrary to the analysis, however, the time dependence of l/(t) in zone 2 is also independent of Po. For injected charge densities between 0.14 an;l 0.95, the calculated values of t F range between 5.0X 10 -4 and 2.5 s. From fig. 5, there are no indications of a transit time of the trailing edge in this time interval. Fig. 6 shows the time dependence of l?(t), expressed in multiples of the transit time, for Po = 0.07 and 0.95. As is iUustrated in fig. 5, the time dependence of l/(t) in zones 1 and 2 is independent of Po. The results also show that the dispersion in transit times of the leading edge of the injected charge increases as the photoinjected charge density increases: The dependence of V(t < tT) on Po for a field of 4.8 X 105 V/cm is illustrated in fig. 7. The solid line is calculated from eq. (2), with co --- 2.0 and/ao = 8.7 X 10 -18 cm4/V3-s. For partial injection, the rate of potential discharge in zone 1 is clearly less than that predicted from eq. (2).

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P.M. Borsenberger, W. Mey / Potential discharge kinetics of polyrneric photoreceptors

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314

P.M. Borsenberger, IV. May / Potential discharge kinetics of polymeric photoreceptors

Discharge measurements using ultraviolet PVK absorption were made at fields of 4.8 X 105 V/cm with 320 nm radiation. The injected charge density was 0.50. Transit times determined in this way were identical with those observed for selenium photoexcitation. Furthermore, the temporal behavior in zone 2 was the same for a charge generated in the PVK or in the selenium layer. These results indicate that the discharge kinetics are determined by transport within the PVK layer and are not affected by the selenium charge-generating layer. In a previous study of hole transport in solid solutions of triphenylamine and bisphenol-A-polycarbonate [8], it was shown that for space-charge-limited conditions the discharge kinetics could be described by a drift mobility given as /a(E) = 2.0 X 10 - 1 1 E cm2/V-s .

(9)

In these materials, the hole mobility is proportional to E, whereas in PVK the mobility is proportional to E 2. An extension of these measurements to partial injection is illustrated in fig. 8 which shows a plot of the time dependence of V(t) for a 40 wt% triphenylamine transport layer for different values of the injected charge dens!ty. The thickness was 4.1/am. For all exposures, the same temporal behavior of V(t) in zone 2 was observed. As in PVK, no indications of a transit time for the trailing edge of the injected charge were observed. Values of the transit time of the leading edge were also found to be independent of the injected charge. A compari-

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P.M. Borsenberger, I¢. Mey / Potential discharge kinetics of polymeric photoreceptors

315

son of the data in figs. 5 and 8 indicates that the dispersion in transit times of the leading edge of the injected charge is less in samples containing triphenylamine. In this material, transit times can be determined directly from oscillographs, in PVK, transit times can be determined only from the intersections of zones 1 and 2 from logarithmic plots of I?(t) versus time.

5. Discussion The basic observations of this study can be briefly summarized as follows: (1) For PVK, the time dependence of the rate of potential discharge and the variation of the discharge rate with initial potential agree with space-charge-limited discharge theory. Under these conditions, the discharge kinetics can be described by a mobility which is a function only of the electric field. (2) For partial injection, there is no indication of a transit time for the trailing edge of the injected charge in PVK or solid solutions of triphenylamine and the polycarbonate. For times greater than the transit time of the leading edge, the time dependence of the surface potential is independent of the injected charge and determined only by the field dependence of the drift mobility. For times less than the transit time, the rate of discharge is independent of time and determined by the electric field and the field dependence of the drift mobility. (3) The transit time of the leading edge of the injected charge is independent of the injected charge density. The dispersion in transit times increases as the field dependence of the drift mobility increases and as the injected charge density increases. For the discharge analysis employed in this study, the charge is assumed to be injected in the form of a thin sheet at x = 0 which then spreads as it propagates through the sample. The spread is determined by the difference in field at the leading and trailing edges, Vo/L and (1 - po)Vo/L, respectively. The intersection of zones 1 and 2 denotes the arrival of the leading edge of the injected charge at the substrate electrode. In zone 1 all of the charge is assumed to be mobile, with a drift velocity given as the product of the drift mobility and the electric field. Zone 2 describes the time interval between the arrival of the leading and trailing edges of the injected charge. During this period, charge is continuously leaving the sample at the substrate electrode. For partial injection, the rate of potential discharge in zone 1 is less than that predicted from the discharge analysis. This suggests that not all of the charge is moving with a velocity given by the drift mobility and the electric field. The fact that the rate of discharge is constant during this period indicates that the total mobile charge density is constant and not affected by deep trapping. Zone 2 is bounded by the arrival of the leading and trailing edges of the injected charge. For partial injection, there is no indication of a transit time for the trailing edge in either PVK or solid solutions of triphenylamine and the polycarbonate. It is our speculation that this is a consequence of the same phenomenon observed in zone 1,

316

P.M. Borsenberger, I¢. Mey / Potential discharge kinetics of polymeric photoreceptors

namely that all of the charge is not moving with a velocity given by the mobility and the electric field *. As a result, there is a wide dispersion of transit times for the trailing edge. In zone 2 the time dependence of the rate of discharge is independent of the injected charge density and is equal to that observed for space-charge-limited discharge where the field at the injecting electrode goes to zero, consequently the spread of charge extends for the width of the sample. Since the same temporal dependence is observed for partial injection, the results suggest that the dispersion in charge extends for the thickness of the sample, irrespective of the injected charge density. Dispersive transport has been observed in a number of disordered insulators [15-17] and explained on the basis of either multiple trapping [18,19] or the continuous-time-random-walk theory proposed by Scher and Montroll [20]. While we have not been able to formulate a quantitative discharge analysis based on either theory, there are several qualitative observations which can be made. The major predictions of the continuous-time-random-walk theory are universality and a thickness dependence of the apparent mobility. In PVK and solid solutions containing triphenylamine, mobility values determined from transit times do not show a thickness dependence. However, if the dispersion in transit times is neglected, logarithmic plots of the rate of potential discharge versus time do show universality with the electric field and the injected charge density. These results are qualitatively consistent with predictions of the continuous-time-random-walk analysis. If the dispersion were due to multiple trapping, it would appear that the trapping process would have to be very strongly field dependent to be consistent with the expermental results. RegarSess of the interpretation, there are two basic experimental observations which must be explained: first, the dependences of the dispersion of transit times on the injected charge density and the field dependence of the mobility; second, the dependence of the rate of potential discharge on the field dependence of the mobility in zone 2. At present, a more detailed analysis concerning the discharge kinetics in these materials cannot be presented.

Acknowledgements The assistance of Mr. E.H. Magin, who performed many of the electrical measurements, and Mr. L.E. Contois, who provided the photoconductive materials, is gratefully acknowledged. * An alternative explanation is that of sustained injection. If the holes were immobilized in surface traps, then released into the PVK by thermal processes, the injection would not be instantaneous. We have discounted this possibility for two reasons. First, the time dependence is the same for charge generated by the selenium emitter or for ultraviolet PVK absorption. In the latter ease, there is no selenium/PVKjunction. Second, for PVK absorption, the discharge kinetics axe the same for holes generated at the corona-chaxgedor substrate surfaces.

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References [1] I.P. Batra, K.K. Kanazawa and H. Seki, J. Appl. Phys. 41 (1970) 3416. [2] I.P. Batra, K.K. Kanazawa, B.H. Schechtman and H. Seki, J. Appl. Phys. 42 (1971) 1124. [3] H. Seki and I.P. Batra, J. Appl. Phys. 42 (1971) 2407. [4] I. Chen, J. Appl. Phys. 43 (1972) 1137. [5] H.J. Wintle, J. Appl. Phys. 43 (1972) 2927. [6] S.J. Fox, J. Appl. Phys. 45 (1974) 610. [7] T.J. Sonnonstine and M.M. Perlman, J. Appl. Phys. 46 (1975) 3975. [8] P.M. Borsenberger, W. Mey and A. Chowdry, J. Appl. Phys. 49 (1978) 273. [9] J. Mort, Phys. Rev. B5 (1972) 3329. [10] P.J. Regensburger, Photochem. and Photobiol. 8 (1968) 429. [ 11 ] J. Mort, I. Chen, R.L. Emerald and J.H. Sharp, J. Appl. Phys. 43 (1972) 2285. [12] W.D. Gill, J. Appl. Phys. 43 (1972) 5033. [13] W. K16pffer, J. Chem. Phys. 50 (1969) 2337. [14] G. Pfister and D.J. Williams, J. Chem. Phys. 61 (1974) 2416. [15] J. Mort, G. Pfister and S. Grammatica, Solid State Commun. 18 (1976) 693. [16] G. Pfister and H. Scher, Phys. Rev. B15 (1977) 2062. [17] R.C. Hughes, Phys. Rev. B15 (1977) 2012. [18] W.D. Lakin, L. Marks and J..Noolandi, Phys. Rev. B15 (1977) 5834. [19] F.W. Schmidlin, Solid State Commun. 22 (1977) 451. [20] H. Scher and E.W. Montroll, Phys. Rev. B12 (1975) 2455.