J. Phys. C: Solid State Phys., 18 (1985) L51-L54. Printed in Great Britain
LETTER TO THE EDITOR
Carrier trapping in one-dimensional systems: example
organic PDATS
K J Donovan and E G Wilson
Physics Department, Queen Mary College, London E l 4NS
Received 1 October 1984
Abstract. New data on the decay of photocurrent following a 10 ns laser pulse are presented
for the ideal one-dimensional semiconductor crystal PDATS. The first carrier trapping event
is identified and clearly distinguished from subsequent dispersive trapping and trap release
events. The trapping is of one-dimensional form. The characteristic trapping time is 500 ns.
For a camer velocity of 2.2 x l@ms-' the traps are 1.1 mm apart on a chain.
PDATS singlecrystal is an ideal one-dimensional semiconductor. The polymer backbones,
which are parallel and straight for macroscopic distances, are of covalently bonded
conjugated carbon atoms. The energy gap is 2.4 eV. The large sidegroups, which are
electronically inert up to about 5 eV, space the backbones apart by 0.7 nm. Thus each
chain functions as a one-dimensional molecular wire when excess electrons or holes are
introduced.
This letter presents new data on carrier trapping and trap release in PDATS. It allows
of a clear distinction between two unexpected phenomena, which are currently at risk
of being confused.
The first unexpected phenomenon is the saturation of the intrinsic drift velocity U of
a carrier, with electric field E , for motion on a perfect chain. The magnitude of U ,
2.2 X I d ms-', is close to the velocity of sound S, 3.6 X lo3m s-'; the magnitude of the
low-field mobility pisultra-high, p > 20 m2s-l V-' . These results (Donovan and Wilson
l979,1981a, b, Donovan et a1 1984a,b, c) find a natural explanation as being the motion
of a solitary wave acoustic polaron in one dimension (Wilson 1983).
The second unexpected phenomenon is the saturation of the trap limited velocity
( u ( t ) ) with E , which is characteristic of one dimension (Movaghar etal 1984). This is
expected whether or not the intrinsic velocity is saturated.
The risk of confusion is to suggest (Bassler 1984) that all experimentally observed
motion is saturated because it is trap limited. Those who find a saturated intrinsic drift
velocity unpalatable can then continue to believe that U is linear in E.
Consider carriers created at random positions, by a spatially uniform and short
duration light pulse, and drifting in one dimension to randomly positioned traps or
barriers of mean separation s. Then the current density J ( t ) due to such motion falls as
the carriers are trapped. If there were no succeeding trap release or barrier jump, then
it is easy to show (Wilson 1980) that
J(t)/Jo = E*(tu/s)
0022-3719/85/020051 + 04 $02.25@ 1985 The Institute of Physics
(1)
L5 1
L52
Letter to the Editor
where E2 is the exponential integral function. Thus the characteristic time to trap is
t = S/U. This is in contrast to three dimensions, where in the same circumstances
(2)
J(t)/Jo = exp(-&).
Here 1/23 is the probability per unit time of trapping, and is not directly related to U.
Figure 1 shows the fit of equation (1) to experimental data on the decay of the
photocurrent induced by a 10 ns duration N2 laser pulse. The experimental response
time does not limit the displayed data. For t C 1 ys the agreement is good.
-8
-7
-6
-5
log t Is)
Figure 1. Logarithm of the photocurrent in arbitrary units as a function of the logarithm of
the time t in seconds. The solid lines follow equation (1) with t = s/u = 500 ns: A 2 kV; 0
1 kV; 0 500V; V 2 0 0 V ; A 100V.
However, at longer times trap release or barrier jump causes the current to be greater
than suggested by equation (1). A model of the current as carriers undergo such trapping
and trap release events in one dimension has been given by Movaghar et al(1984). They
show good fits of photocurrent decays, over 5 time decades, in the domain 10 ps < t <
1s, to the theoretically derived equation
log(u(t)) = (1 - a)log( WOE) - a l o g t
+ constant.
(3)
Here a i s a parameter measuring the distribution of the trap release rates or barrier jump
probabilities. From the t dependence of (u(t)) then a w a s experimentally found to be
0.85. WOis a parameter modelling the intrinsic motion along the chain. For U linear in
E , WOis field-independent: then (u(t)) is expected to vary as E ' - & ,which is essentially
saturated. For U independent of E , WOvaries as E - * ;then (U(?))is also expected to be
independent of E. The experimental dependence of (v(t))on E was not able to distinguish
these two cases.
Letter to the Editor
L53
It is clear that the form equation (3) which so successfully describes (u(r))between
10 ps and 1s does not work in the domain 10 ns to 1 ps. Figure 1does, however, indicate
a transition from the asymptotic form of equation (1) to that of equation (3) between 1
and 10 ps; this is further displayed in figure 2.
Thus it is possible to distinguish clearly the short-time region, in which a diminishing
number of freely drifting carriers have not yet trapped or reached a barrier, from the
long time region in which dispersive trapping and release or barrier jump events are
occurring.
The experiments which lead to the conclusions about the intrinsic motion were
conducted in the short-time region, at a time of 5-10 ns, substantially less than t.Thus
the deduced intrinsic velocity U found in those experiments is indeed independent of
traps or barriers.
-1
m
d
-4
log tis1
Figure 2. Logarithm of the photocurrent in arbitrary units as a function of the logarithm of
the time tin seconds. The data is at V = 2 kV. The full curve of least curvature is equation
(l),the full curve of greatest curvature is equation (2) and the broken curve is equation (3)
with (Y = 0.85. The inset shows the logarithm of the initial photocurrent JO in arbitrary units
as a function of the logarithm of the applied voltage V.
Figure 2 compares the two decays of equations (1) and (2) with the experimental
data. The one-dimensional form is a better fit than the three-dimensional form. This is
evidence for the one-dimensional nature of the first trapping event.
Figure 1 shows that the characteristic time t = s/u is independent of field. This is
consistent with the fact that U is independent of field.
The characteristic time is 500 ns in this sample; it is found to vary from sample to
sample. From the known value of U , s in this sample is 1.1mm. Such large values for the
mean distance apart of traps on the chain have been reported before (Donovan and
Wilson 1981a); there the mean distance s/2 of a photocarrier to travel to a trap was
measured by a different technique requiring no knowledge of the drift velocity. On the
best sample they found s = 1.4 mm.
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Letter to the Editor
The current density JO depends on the quantum efficiency r] for the creation of
carriers, and on the probability q that the carriers escape geminate recombination and
contribute to the photocurrent, according to the equation
Jo
e(r]q)u.
(4)
Since v is independent of field, the E field dependence of 10,shown in figure 2, is due
solely to that of (qq).In a one-dimensional system the E field dependence of Q, is
expected to be linear at low fields and become weakly superlinear at the higher fields
used in this work (Blossey 1974, Haberkorn and Michel-Beyerle 1973, Wilson 1980).
This theoretical expectation is supported by computer simulation of Q, by Ries eta1
(1983). r] itself may have a weak E field dependence due to field induced exciton fission
(Seiferfeld et a1 1983). The field dependence of JO is in accord with these expectations.
It is also in accord with measurements of (qq)by different techniques by Donovan and
Wilson (1981b), by Seiferfeld et al(1983), and by Donovan et af (1984a, b, c).
References
Bassler H 1984 Polydiacetylenes Synthesis, Structure and Electronic Properties eds. D Bloor and R R Chance
to be published
Blossey D F 1974 Phys. Rev. B 9 5183
Donovan K J, Freeman P D and Wilson E G 1984a Mater. Sci. 10 61
- 1984b Molec. Cryst.-Liq. Cryst. in press
- 1984cJ . Phys. C: Solid State Phys. submitted
Donovan K J and Wilson E G 1979J . Phys. C: Solid State Phys. 12 4857
- 1981a Phil. Mag. B 44 9
- 1981b Phil. Mag. B 44 31
Haberkorn R and Michel-Beyerle M E 1973 Chem. Phys. Lett. 23 128
Movaghar B, Murray D W, Donovan K J and Wilson E G 1984J. Phys. C: Solid State Phys. 17 1247
R e s B, Schonherr G, Bassler H and Silver M 1983 Phil. Mag. B 48 87
Seiferfeld U, Ries B and Bassler H 1983J . Phys. C: Solid State Phys. 16 5189
Wilson E G 19801. Phys. C: Solid State Phys. 13 2885
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