R659
Philips Res. Repts 23, 142-150, 1968
SPACE-CHARGE-LIMITED PHOTOCURRENT
IN VAPOUR-DEPOSITED LAYERS
OF RED LEAD MONOXIDE
by F. J. du CHATENIER
Abstract
A simple model is presented to describe the photoconduction in vapourdeposited layers of red lead monoxide when these layers are illuminated
with strongly absorbed light. The model is based on the mechanism of
space-charge-Iimited current from a finite reservoir of charge carriers.
The photocurrent-voltage
relation is obtained togetherwith the dependence on light intensity. At low voltages the presence of a large number
of traps appears to limit the sensitivity of radiation detectors for strongly
absorbed light. Some of the consequences of this model are discussed.
1. Introduetion
The mechanism of space-charge-limited current (SCLC) was first proposed
by' Mott and Gurney 1)., Lampert 2) included the effect of trapping of charge
carriers and obtained a rigorous solution of the problem for the case of injecting
contacts at which an infinite reservoir of charge carriers is present. In photoconductors it is possible, however, to bring about a finite reservoir of carriers
at a blocking electrode by optical injection if light of a suitable wavelength is
used and a transparent electrode is employed. This situation occurs in radiation
detectors illuminated with strongly absorbed light. It is the purpo~e of the
present paper to show that space charge may limit the photoconductivity to
very low values particularly when a large number of traps is present.
The theoretical approach follows in broad outlines the work of Lampert.
However, a different boundary condition is proposed here which generalizes
his approach and makes it applicable to the practical case of vapour-deposited
layers of red PbO illuminated with strongly absorbed light.
2. Theoretical approach
To solve the problem of space-charge-limited conduction we assume that the
contacts on the photoconductive layer prevent the injection of charge carriers
from the electrodes. We ignore edge effects and thus consider in effect a onedimensional problem. We will assume that the dark concentration of charge
carriers is zero. This is not a serious restrietion in the case of the PbO layers
used, for which "quasi-intrinsic" conditions exist 3) with a low dark concentration of charge carriers of approximately 103 crrr ". In fact, therefore, we
assume an insulator model with flat bands.
.'
We now illuminate the transparent anode of the layer with monochromatic
PHOTOCURRENT
IN VAPOUR-DEPOSITED
LAYERS OF RED PbO
143
light of a wavelength short compared with the threshold wavelength of the
photoconductivity. The absorption coefficient for this light has a high value,
therefore the light will be absorbed in a distance which is short compared with
the layer thickness d and will generate a' charge-carrier reservoir in a thin
region À, where it is assumed that À « d. This reservoir plays the role of a
virtual electrode which, under an applied positive voltage, injects holes into
the bulk (see fig. I).
-
À
~
hv
~
~
~
§L.
~
e
e
0
Fig. 1. Picture of the photoconductive
d
~
1+
layer, illustrating the symbols used in the calculation.
Let j be the current density, F(x) the local field intensity, p(x) the density
of holes in the valence band and p,ptheir mobility, e the static dielectric constant
of the insulator, pr(x) the number of trapped holes and Y the applied voltage.
For x > 0 the problem is controlled by the following set of equations:
j = ep,pp(x)F(x) = independent of x,
dF(x)
e8p(x) .
--=---
(2)
dx
8
(1)
e
Pt(x)
+ p(x)
(3)
p(x)
d
v= J F(x)
dx.
(4)
0
The first equation is the transport equation for holes in which the diffusion
term is neglected. This is not a serious omission as diffusion is usually only
important near the injecting electrode where the field strength is almost zero.
In the "finite-reservoir" case, where F(x) at the boundary is not zero, it is
estimated that the influence of diffusion is relatively small. In Poisson's equation (2) the ratio 8 of the concentration of the total number of holes to the
concentration of free holes is included. If the depth of the traps is Et, N, the
144
F. J. du CHATENIER
density of traps and N, the effective density of states in the valence band, then
the occupation of this trapping level is given by
p(X) exp (Et/kT)
Pt(x)
N;
Nt-pt(x)
so
fJ =
Pt(x)
+p(x)
= 1
p(x)
{Nt - Pt(x)} exp (Et/kT)
+ ---.
----N;
(5)
If we restrict ourselves to shallow traps, so that the quasi-Fermi level for
holes is always at least several kT above the trap level, fJ may be written as
fJ = (Nt/Nv) exp (Et/kT). These traps have the property of leaving free a fixed
proportion l/fJ of the space charge injected into the layer. As the holes cannot
recombine in the bulk in the absence of electrons, the continuity equation for
holes needs not be considered here.
The solution of this set of equations (1)-(4) is
3fJjV/8p,p
=
{2jdfJ /8p,p
+ F(O)2 }3/2 -
F(0)3,
(6)
where F(O) is the electric field at the boundary x = 0 (the anode).
Now a reasonable boundary condition has to be chosen. Assume that all
the light is homogeneously absorbed in a layer with a thickness A.(A. « d). The
continuity equation for holes in this layer is
dp
G
P
div j
-c
e
-=------
dt
A.
(7)
where G is the number of incident photons per second and per cm", j is the
current density of holes and -c is the lifetime of a hole before recombination,
which is possible as electrons are also generated in the region A.. Putting
divj = j/A. and dp/dt = 0 in the stationary state we obtainp(O) = (G - j/e)-c/A.
for the average concentration of holes in the reservoir at x = o. We have thus
divided the photoconductor into two parts. One part is a very thin region, with
a thickness A. comparable with the penetration depth of the light, in which
generation and recombination together with the divergence of the current control the concentration of charge carriers. The layer A. may be somewhat smoothed out because of the diffusion length of the carriers which, for red PbO, is
approximately 1 prn, This length is small compared with the thickness 20 (J.m
of the PbO layer. The other part of the layer carries a current subject to spacecharge limitation. At the interface x = 0 the condition for p(O) gives the
required boundary condition for the field strength through eq. (1):
.A.
F(O)= __ J __
-cep,p(G - j/e)
(8)
PHOTOCURRENT
3. General characteristics
IN VAPOUR-DEPOSITED
LAYERS OF RED PbO
145
of the model
The current-voltage relation may be distinguished in three characteristic
regions. In the región of low voltages the terms with F(O) in eq. (6) can be
neglected and the result is
(9)
which is the well-known formula for one-carrier SCLC in a solid with one injecting contact. The current does not depend on light intensity. In the vicinity
of the anode the space-charge density of holes is high and is very little affected
by the occurrence of current. With higher voltages and decreasing light intensity
the illuminated anode reservoir can no longer supply the full current value
prescribed by SCLC and the photocurrent approaches the value corresponding
to space-charge-free flow. The electric field will become nearly uniform and
equal to V/d. The terms with F(O) = Vld in eq. (6) are no longer negligible
and the current is given by
(10)
At intermediate voltages the current will be
!Lp-cGeV
j=----
u
(11)
which is the ohmic-current region. At still higher voltages the current saturates:
j
=
Ge. I
(12)
In the last two voltage regions the photocurrent is proportional to light intensity.
In fig. 2 the results of this model are presented for a special choice of the
parameters. The current density, calculated from eqs (6) and (8), has been
plotted as.a function of the applied voltage. At low voltages, where the current
varies with VZ, the current value is determined by !Lp/6. In the ohmic- and
saturated-current region the light intensity controls the current density. Whether
there is an ohmic region depends on the values of the parameters !Lp/6, f-lp-C/J..
and the light intensity. At relatively small values of f-lp/6 there is no ohmic
region at all. The saturation voltage usually occurs when the transit time TIr
equals the lifetime of the carriers. In the present model it is the transit time
in the illuminated region J.. that has to be considered, TIr = J..f f-lpF ~ J..d/ fl·p V.
Saturation sets in when TIr = -c thus Vsa, R:! J..d/!Lp-C. This value is meaningful
only in the case where an ohmic region is present.
The sensitivity for light intensity 1is usually expressed by j cc P. The value
of y is unity. in the saturated- and ohmic-current region, y = 0 in the pure
I
146
F. J. du CHATENIER
.~--------------------------------------~--------------------10-6,--
---,.-,--
..--
--,
j
(A)
r
1O-7f-----+---_-b---="---7'---I
10
102
-V(V)
103
Fig. 2. Calculated photocurrenl-voltage
characteristics for A = 10-4 cm, f.1.p = 2·5 cm2/Vs,
.=10-9 s, d = 2.10-3 cm and Ei = 2.10-12 F/cm.
Curves a and b represent the ohmic and saturated current given by eq. (10) for light intensities
of 1011and 1012 photons/cm" s, respectively.
Curves c and d represent the space-charge-Iimited current given by eq. (9) for IJ = 107 and
109, respectively. The smooth transitions from SCLC to space-charge-free flow for both light
intensities were calculated from eqs (6) and (8).
SCLC region. In the transition region y mayadopt
unity and is a function of light intensity.
values between zero and
4. SCLC in red lead monoxide
Measurements have been performed on layers of vapour-deposited red lead
monoxide. The conditions under which the PbO layers are deposited are similar
to those used in the manufacture of the "Plumbicon " television pick-up tube.
One of the contacts to the layer is a transparent Sn02 layer, the other one a
vapour-deposited Ag layer. Monochromatic light at 3700, 3950 and 4200 Á was
obtained with interference filters. A Jena BG 12 or UG 1 filter was used to
cut away unwanted light.
In fig. 3 results are given of measurements of photocurrent vs voltage at two
light intensities at a wavelength of 4200 Á. The absorption constant for this
light 4) is approximately 104 cm-I, therefore À will be about 1 [Lm. The dark
current, which is ohmic up to 30 V, is negligibly small compared to the photocurrent.
The experiments presented were performed on two different layers, one of
which (layer no. 2) was deliberately chosen with a worse sensitivity to blue light
than the other one. In fig. 3 the drawn curves represent the current-voltage
'
PHOTOCURRENT
IN VAPOUR-DEPOSITED
1O-6rj
(A)
I
-.-~
__
LAYERS OF RED PbO
147
_,_---__,
o
Fig. 3. Measured photocurrent vs voltage for light of 4200 A.
and 0 PbO layer no. 1 for light intensities of 1'5.1011 and 1'5.1012 photons/cmê s,
PbO layer no, 2 for 1'5.1011 photons/cmê s.
Drawn curves represent the photocurrent calculated from eqs (6) and (8) with the parameter
values mentioned in the text.
/j.
o
dependence as calculated from eqs (6) and (8). The parameters f.lp/8 and ftp.
were chosen so as to obtain a reasonable fit between theory and experiment at
the lowest light intensity. The f.lp. product is 1.3.10-7 cm2/V, the f.lp8 values
are 2.7.10-5 and 1.3.10-8 cm2/Vs, the lowest value corresponding to the worst
layer. The present model is seen to describe very well the observed photocurrentvoltage relation. A pronounced ohmic-current region is not observed for the
layers used. It can be noticed clearly that the decreased sensitivity to blue light
for layer no. 2 might be due to a relatively high density of traps.
The SCLC appears to be influenced by the illumination. This is also observed
at still lower light intensity and for light with shorter wavelength. This is not
predicted by the theory. However, as far as the real situation in the layer is
concerned some complications arise. First of all a small photo-voltaic effect
was observed, which was slightly dependent on light intensity, indicating either
a Dember effect or a small band curvature at the contact. Secondly the illumination is not homogeneous. Consequently the injecting reservoir may be expected
to expand into the layer as the light intensity increases resulting in an effectively
smaller value of the layer thickness d which enters into the current equation
to the third power. The latter supposition seems to be confirmed by the obser-:
vation that the effect of illumination intensity is less at smaller wavelengths as
the penetration depth of the light is smaller. However, a rough calculation
148
F. J. du CHATENIER
showed that the effect of reservoir expansion is not sufficient to explain fully
the discrepancy. Finally it might be that only quasi-equilibrium was reached
during the measurements, although each point in the lowest current region was
observed during at least 15 minutes. A redistribution of trapped carriers over
more types of trapping levels, with a decay time exceeding the time of observation, might be possible.
5. Supplementary measurements
Some measurements were performed in which layer no. 2 was illuminated
simultaneously with blue light and with light of energies below the band gap.
The sensitivity for short wavelengths appeared to rise to the space-charge-free
value, depending on the relative light intensities, when additional light was used.
Figure 4 shows the results of measurements in the case of simultaneous iIlumina1O-7,------,
r--
-,
j
(A)
r
a
1O- t------:;r"-:l7oL?J"'--..r<'-1-
.--T-.1---j
10
100
-V(V)
Fig. 4. Measured photocurrent vs voltage when PbO layer no. 2 was illuminated with light
of 3700 A at an intensity of 2·1.1011 photons/crnê s and various intensities of stimulating light
of 6900 A. The intensities of this 6900-A light are 10-2, 5.10-2, 10-1, 5.10-1, 2 and 4 in
arbitrary units, the highest incident-light intensity corresponding to 101S photons/cm- s
approximately. The photoresponse for 6900 A has been subtracted from the measured photocurrent. The dashed curve represents the calculated photocurrent for the trap-free case.
tion with a fixed intensity of light at 3700 Á and a variable intensity of light at
6900 Á. The band gap corresponds to 6400 Á. From the total current the
response for 6900-Á illumination has been subtracted. A plausible interpretation
of these results is that eléctrons which are optically generated from the metal
electrode by the red light 5) tend to neutralize the space charge due to the holes
PHOTOCURRENT
IN VAPOUR-DEPOSITED
LAYERS OF RED PbO
149
injected from the anode. The wavelength dependence of the stimulating light
has not yet been studied thoroughly. Experiments with a PbO layer without a
metal electrode, where the layer was scanned with an electron beam, suggested
that bulk generation of carriers played a minor role in this stimulating process.
In order to determine the energy position of the traps in the band gap, the .
temperature dependence of the space-charge-limited
photocurrent
was determined. The temperature dependence of the SCLC is governed by the depth Et
of the traps which enters the expression (9) for the current by means of the
factor (J. No discrete energy levels could be determined. The activation energies
involved in these experiments lie between 0·1 and 0·3 eV. Electrical-glow measurements were performed by standard techniques 6) illuminating the layer with
light of 3700 A under applied voltage at liquid-nitrogen temperature. The results
revealed traps at 0,34, 0,38, 0,45, 0·50 and 0·60 eV from the band. Shallower
traps could not be detected with the techniques used; possible glow peaks due
to deeper traps merged into the dark current. From the glow peaks we estimate
the capture cross-section S of the dominating traps, at 0,45, 0·50 and 0·60 eV,
to be of the order of 10-16.10-17 cm". A rough estimate of the trap densities
from the area under the glow curves gives trapped charge densities of the order
of 1014 cm- 3. From the relation io -1 = NtSVlh' where VIlt is the average thermal
velocity of the charge carriers, the time constant io at room temperature will
be ofthe order of 10-5 s for the three relevant traps. This value is much smaller
, than the time required to reach equilibrium during the measurements
of the
photocurrent. It is therefore reasonable to suppose that the observed large time
constants are due to redistribution
effects or to even deeper traps.
3
From eq. (5) it can be calculated that traps with densities between 1014 cmat 0·6 eV and 1017 cm? at 0·3 eV are sufficient to account for the (J value of
105• The dominating traps derived from the glow experiments fall within these
limits.
6. Conclusion
The model presentèd in this paper accounts very well for the photoconductive
properties of vapour-deposited
layers of red lead monoxide when illuminated
by strongly absorbed light. Whether these layers will be useful as photodetectors
for blue light depends on the transition voltage between the SCLC and the
ohmic. or saturated-current
region at the highest light intensity normally used.
This voltage depends on the value of the trapping parameter (J. If this voltage
is to have a reasonable value, then the number of traps must be limited. The
model improves upon most other models by giving a very simple quantitative
description of the photocurrent-voltage
relation both in the SCLC region and
in the saturated-current
region. The existence of the traps required in this model
is demonstrated by the electrical-glow measurements and the experiments on
the temperature
dependence of the space-charge-limited
photocurrent.
The
150
F. J. du CHATENIER
experiments in which the layers were simultaneously illuminated with blue light
and light with energy below the band gap confirm the physical foundation of
the model.
Acknowledgement
The author is indebted to Mr J. F. Wagendrever who carried out most ofthe
experimental work and to several colleagues for many useful discussions.
Eindhoven,
November 1967
REFERENCES
1) N. F. Mott and R. W. Gurney,
Electronic processes in ionic crystals, Oxford University
Press, London, 1940.
M. A. Lampert, Phys, Rev. 103, 1648, 1956.
J. van den Broek, Philips Res. Repts 22, 367, 1967.
J. van den Broek, Philips Res. Repts 22, 36, 1967.
C. R. Crowell, W. G. Spitzer, L. E. Howard and E. E. Labate,
1962.
6) L. Heijne, Philips Res. Repts Suppl. 1961, No. 4.
2).
3)
4)
S)
,
Phys. Rev.127, 2006,