Photoinduced discharge characteristics of xerographic photoreceptors: Theory and experiment

] O U R N A L OF

Journal of Non-Crystalline Solids 137&138 (1991) 1329-1332 North-Holland

NON-CRYSTALLINE SOLIDS

Section 2Z Application of chalcogenides

PHOTOINDUCED DISCHARGE THEORY AND EXPERIMENT

CHARACTERISTICS

OF XEROGRAPHIC

PHOTORECEPTORS:

S.O. KASAP, V. AIYAH, B. POLISCHUK, Z. LIANG and A. BEKIROV Department of Electrical Engineering, University of Saskatchewan, Saskatoon, S7N 0W0, Canada The well-known deep trapping kinetics model of Kanazawa and Batra for photoinduced discharge which relates the residual potential, V r, to the range of the charge carriers (p.'~) has been reformulated by specifically including the effect of rate of trapping as being proportional to the instantaneous unoccupied density of traps. A partial differential equation is derived that describes the space and time evolution of the electric field within the material. By numerically solving this differential equation and integrating the electric field, the residual potential, V r, has been related to the charge carrier range and the deep trap capture coefficient. The theory is compared with experimental results from xerographic residual potential measurements to show that trap saturation effects can play an important role in the interpretation of V r.

1. INTRODUCTION

(a) The conduction equation is

Two important xerographic properties of a photoreceptor are the photoinduced discharge

Jc(x',t')= epp'(x',t')E'(x',t')

(1)

characteristic (PIDC) and the residual potential (Vr). The latter properties directly determine the sensitivity of

where Jc(x',t') is the conduction current density, E'(x',t')

the photoreceptor and the overall resolution 1. The

is the electric field, p'(x',t') is the instantaneous free

present paper addresses the key issue of relating the

hole concentration and ~ is the mobility.

PIDC and V r to the semiconductor properties, viz.

(b) Maxwell's equation for the total current in the

mobility, g, lifetime, "d, and the capture coefficient, Ct.

present open circuit (xerographic) configuration is

The well-known deep trapping model of Kanazawa and Batra 2"3 (KB) which relates the residual potential,

J(t') = Jc(x',t') + ~cqE'(x',t')/c3t' = 0

(2)

V r, to the p'~' product is reformulated by specifically including the effect of rate of trapping as being

where ~ is the permittivity of the medium.

proportional to the instantaneous unoccupied density

(c) Gauss' equation in point form is

of traps. The latter description had been neglected in the previous models of PID in the presence of deep trapping 2-4.

0E'(x',t')/0x' = (e/s)[p'(x',t') + pt'(x',t')]

(3)

where pt'(x',t') is the concentration of holes trapped at 2. PID AND TRAPPING KINETICS We consider a photoreceptor of thickness L which

position x' at time t'. (d) The continuity equation is

has its substrate grounded and its surface corona charged to a positive voltage V o so that the initial field,

0p'(x',t')/c3t' = -(1/e)c~Jc(x',t')/c3x' -- c3pt'(x,,t')/c3t' (4)

Eo, is Vo/L. We assume that the absorption depth is much less than the thickness so that PID is by hole

(e) The rate equation without detrapping is

conduction and that the photogenerated hole concentration far exceeds the thermal equilibrium concentration. The following equations then hold at

0pt'(x',t')/c3t' = p'(x',t')Ct[N t - pt'(x',t')]

point x' at time t' in the sample:

where Nt is the deep trap concentration and C t is the

0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.

(5)

1330

S.O. Kasap et aL / Photoinduced discharge characteristics of xerographic photoreceptors

capture coefficient. The quantity 1/NtC t is the

choice, we take K=10 -6 so that when m=1/2,

unsaturated deep trapping time denoted by "d.

t 1'=(2xl 06)to . If the transit time is typically 0.5#s, the residual voltage is then measured at about 1 second

The equations (1) to (5) have to be solved for E'(x',t') and this has to be integrated across the sample to find

after the illumination. As long as t1>>1, or K<
the surface potential V(t). By taking various partial

results, however, will always be consistent. Equation

derivatives of equations (1) to (5) we can eliminate

(6) can now be solved subject to eqn.(7) with K=10 .6

p'(x',t'), pt'(x',t') to obtain a single general expression

and m=1/2. The latter choice is appropriate for strong

for the electric field. If t o is the transit time of holes given

absorption and for PID 1 . The results, however, have

by to=L2/pV o, then in normalized space and time

been found to be independent of m.

coordinates, x=x'/L and t=t'/t o, the general PIDC 3. EXPERIMENTAL PROCEDURE

equation is

Xerographic measurements were basically carried E(c]2E/oqt2) + E2(c]2E/cqxSt)- (1 +c)(SE/~t) 2

out as described previously 5 but using a transparent probe (Trek Model 3629) and a Trek electrostatic

-- cE(SE/oqx)(cqE/~t) + (1/'c)E(SE/c)t) = 0

(6)

voltmeter (Model 362A) interfaced to a microcomputer. The sample was corona charged to a voltage V o by a

where E(x,t)=E'(x',t')/E o is the normalized field which is

scorotron and then step illuminated by strongly

unity at t=0 and the trapping parameters x and c are

absorbed blue light through the transparent probe.

defined by "~=~'/to=l/(toCtNt) and c=sCt/elJ.=d(epl;'Nt). Thus "~ is the normalized lifetime and c is a trapping

carried out using both conventional and interrupted

coefficient related parameter discussed below. For c=0

field time-of-flight (IFTOF) experiments as described

(e.g. large Nt), eqn.(6) is equivalent to that derived by KB 2.

300ps light pulse output at 460nm was used for

Mobility (~) and lifetime (':') measurements were

previously 5. Nitrogen laser pumped dye laser with a

Equation (6) can only be solved by numerical

photoexcitation. From IFTOF measurements, both I-L

techniques subject to initial conditions for PID. We

and "d could be independently obtained. Single shot

choose the KB initial conditions so that our results are

mode of excitation was used to avoid space charge

directly comparable with those obtained in references

accumulation. Furthermore, the lifetime determination

2 and 4 when c=0. It is assumed that discharge occurs

involved interrupting the photocurrent at various

over many transit times so that t>>l in eqn.(6). If the

locations in the photoreceptor to ensure that it

electric field at the surface vanishes at time t=t 1, due to

represented a meaningful parameter for the whole

the depletion of all the surface charges by

sample.

photoinjection, then by choice t1>>1 so that the

The samples were prepared by conventional

discharge process is not mobility limited but emission

vacuum evaporation techniques. Various 50p.m-200~m

and trapping limited. In the absence of trapping, PID

thick films of a-Se with 0-0.4%As content and doped with small amounts of CI (<10ppm), were deposited on

would be emission limited. Taking the quantum efficiency as proportional to E(O,t)m where m
(7)

where K is a constant which depends on the illumination intensity and the photogeneration process. To have E(0,t) vanish at t'=t l'>>t o, we need K<
to heated AI substrates (60-70°C) as described previously 5. 4. RESULTS AND DISCUSSION Figure 1 shows a typical PiDC of a positively charged a-Se:0.2%As film under various levels of light illumination. It can be seen that although the rate of discharge is affected by the light intensity, the final

S.O. Kasap et aL / Photoinduced discharge characteristics of xerographicphotoreceptors 1200

I

10 0

I

__ ~

O

1331

electrons

1000 >

~> 10 -1 800

o

o"~

600

Io

400

0 I°

m

o >

~

200 0

C=4

_I°

0.5

c=O

\

!

0.0

fo-

[

I

'1

1.0

1.5

-

\\

~ - -

"

2.0

Time,

Z

10-4 . . . . . . . . . . . . . . . . . . 10 -1 10 0

, ........ , . 101 10 2

Normollzed FIGURE 1 PID of positively charged a-Se:0.2%As (2ppmCI) film at three levels of light intensity (Io, 101o and 461o).

residual potential, Vr, is independent of the illumination

10 3

Lifetime

FIGURE 3 Dependence of v r on z. Solid curves are calculated from the present model for various c. Open (negative charging) and filled-in (positive charging) points are experimental. The dashed line is the Warter expression.

intensity. Figure 2 shows a typical PID for a negatively charged a-Se:0.2%As film. For large negative charging

to the depletion discharge process in the dark 6. To

voltages, the dark discharge rate was appreciable due

obtain the residual potential arising from trapped electrons alone, the measured residual potential, V r'

I

must be corrected by subtracting that arising from bulk

I

positive space charge built-up during dark discharge,

. . . . . . . . .

Vdd, SO that Vr=Vr'-Vdd. The build-up of opposite space charge during dark decay was negligible for

-50 >

positive charging.

C n_lO 0 (3

residual voltage (Vr) and the charge carrier range (Wd),

To obtain the relationship between the measured we plot the measured normalized residual voltage v r

o >

LIGHT ON

(=Vr/Vo) against the normalized lifetime -c. For the latter, the IFTOF measurements of p. and I:' were used since

-150

"c='d/to=Vol~'/L 2 for which we need both p. and "d. The plot of the experimental results are shown in Fig. 3 for -200

'

0.0

both holes and electrons. It can be seen that, as

'

0.5

Time,

1.0

1.5

s

expected, v r decreases with longer "c. It is interesting that both holes and electrons show a similar functional dependence on the charge carrier range p'c' and,

FIGURE 2 PID of negatively charged a-Se:0.2%As (2ppmCl). Vdd is the dark decay and V r' is the measured residual potential.

further, the measured v r vs z behavior follows quite closely the intuitive expression of Warter7; v r = 1/2"c for "c>>1, which is shown as a dashed line in Figure 3.

1332

S.O. Kasap et al. / Photoinduced discharge characteristics of xerographic photoreceptors

The numerical solution of equation (6) gives the

derived for the instantaneous electric field in the

instantaneous normalized electric field profile E(x,t) vs

photoreceptor during photoinduced discharge. The

x from which both the normalized surface potential,

solution of this equation for the residual potential at the

v(t), and the normalized bulk space charge density,

end of photoinduced discharge of a photoreceptor

dE/dx, can be calculated by integration and

under weak step illumination conditions (discharge

differentiation. We have calculated the residual

time much longer than the transit time) has been

potential, v r, by first calculating E(x,t) at time t=t 1 (at the

presented. Both xerographic residual potential and

end of PID) and then integrating E(x, tl) across the

interrupted field time-of-flight experiments have been

sample for various values of z and c. The results of the

carried out to relate the observed residual potential, V r,

numerical calculations are shown in Fig. 3 as solid

to the charge carrier range, #~'. Although the original

curves.

Kanazawa and Batra model was found to be

It can be seen from Fig. 3 that the experimental

inadequate, the model presented here with an

points lie around the c=1 theoretical curve. The

appropriate choice for ~Ct/e ~ (=1) and the intuitive

trapping process in a-Se:As photoreceptors must

Warter expression (Vr=L2/2Wc') were found to describe

therefore be described by c=1 or sCt/e#=d(ep.z'Nt)=l. It

the data reasonably well. The model however needs

is interesting to note that, for diffusion controlled

further refinements such as the inclusion of detrapping.

capture by an oppositely charged center, the Langevin equation gives "c'=s/(ep.Nt) which means that c must be unity. However, in amorphous semiconductors, the

ACKNOWLEDGEMENTS Financial support was obtained from the Natural

Langevin capture radius is expected to be cut-off early

Sciences and Engineering Research Council of

by the potential fluctuations due to the amorphous

Canada and the Selenium-Tellurium Development

structure so that c should be less than unity. If one

Association, Inc.

considers hole trapping into D- traps in a-Si:H, according to Street 8, who has measured p.z'Nt for holes in a-Si:H, one finds c=0.44 which is about the same order of magnitude. It is clear from Fig. 3 that the normal KB model (c=0 case) for the residual potential is completely inadequate whereas the model developed herein can account for the observed experimental results with a reasonable order of magnitude value for c. The model, however, neglects the possibility of release from the traps. The effect of detrapping during the PID process will be a reduction in v r so that the required value of c

REFERENCES 1. M.E. Scharfe, Electrophotography Principles and Optimization (John Wiley, New York, 1984). 2. K.K. Kanazawa and I.P. Batra, J. Appl. Phys., 43 (1972), 1845. 3. K.K. Kanazawa and I.P. Batra, J. Non-Cryst. Solids, 8-10 (1972), 768. 4. M. Okuda, K. Motomura, H. Naito, T. Matsushita and T. Nakau, Jap. J. Appl. Phys., 21 (1982), 1127. 5. S.O. Kasap, V. Aiyah, B. Polischuk, and M.A. Abkowitz, Philos. Mag. Lett., 62 (1991 ), 377.

for the best fit will be smaller than unity and quite consistent with trapping in amorphous semiconductors.

6. S.O. Kasap, J. Electrostatics, 22 (1989), 1406.

5. CQNCLUSIONS A general partial differential equation has been

8. R.A. Street, Philos. Mag.B, 49 (1984), L15.

7. P.J. Warter, Applied Optics (1969): Supplement 3, on Electrophotography, p.65.