Download Ultrapure, high mobility organic photoconductors

'Appl. Phys. A 36, 163-170 (1985)
Applied .o,,..
Physics A Surfar
9 Springer-Verlag 1985
Ultrapure, High Mobility OrganicPhotoconductors*
W. Warta, R. Stehle, and N. Karl
Physikalisches Institut, Teilinstitut 3, Universit/it, Pfaffenwaldring 57, D-7000 Stuttgart 80,
Fed. Rep. Germany
Received 13 September1984/Accepted2 October 1984
Abstract. This contribution demonstrates that high charge carrier mobility (< 400 cm2/Vs)
is an inherent property of ultrapure organic molecular crystals at low temperatures. Small
concentrations of traps, however, can completely obscure these microscopic transport
properties on macroscopic scales. We describe extensive purification procedures with
naphthalene and perylene, which led to the observation of high mobilities. At the same time
we demonstrate that charge carrier transport measurements are a sensitive tool for the
analytical characterization of high purity organic molecular crystals.
PACS: 72.80L, 72.20H, 81.10
This report is concerned with ultrapurification, and
characterization by electrical transport measurements,
of two typical representatives of organic photoconductors, the aromatic hydrocarbons naphthalene, C~0H8
(I), and perylene (peri-dinaphthalene), C2oH12 (II).
(I) naphthalene
(i1) perylene
Both form molecular crystals of monoclinic symmetry,
space group P21/a, with Z = 2 and Z = 4 molecules in
the unit cell, respectively. The "dimeric" perylene
structure, projected along the molecular planes, is
shown in Fig. 1 F1].
Increasing interest in this class of organic molecular
crystals arose, on the one hand, from their potential
applicability as low-cost photoconductors: Due to the
extended re-electron systems of the constituent molecules 1, these crystals exhibit a separation between the
* This work has been presented in part at the VIIth Intern.
Conf. on Crystal Growth, Stuttgart (1983)
1 and in contrast to the purely or-bonded molecules such as,
e.g., polyethylene
ill/
Fig. 1. The e-perylene crystal structure projected along the
intersection line of the molecular planes of the two symmetryrelated molecular pairs [1]
valence and the conduction band of only a few eV;
consequently charge carriers can be excited by light in
the visible or near UV range. On the other hand, an
understanding of the basic physical processes which
can occur in these molecular crystals is interesting in
itself. For example, the question how their charge
carrier transport properties can be described theoretically is one of the major unresolved problems in
modern solid-state physics.
164
W. Warta et al.
The investigations presented here are part of a larger
program designed to obtain reliable experimental data
over wide temperature ranges on charge-cartier transport in organic photoconductors. Naphthalene and
perylene were selected, among others, to serve as model
substances. Naphthalene is one of the most simple
aromatic molecules; very extensive investigations are
available of both its molecular and its crystal properties. Its melting point, however, (m.p. = 80.5 ~ is
too low for any potential practical application. In
contrast, perylene, which melts at 278 ~ is an example
of a fairly stable, larger aromatic molecule. Both
materials can be zone-refined and obtained as fairly
perfect single crystals by the Bridgman method.
We have chosen not to measure the electrical conductivity as such, since it is in the most general case
composed of at least four independent material properties: the electron and hole concentrations, n- and
n +, and the electron and hole mobilities, # - and #+,
respectively
= e(n-#- + n+#+).
(1)
Instead, we decided to focus on the basic transport
quantities, # - and/~+. These mobilities can, in principle, be measured separately by the time-of-flight
technique, cf. [2], where the transit of electrons
or holes over macroscopic sample dimensions (of
typically 0.2-1 ram) is observed.
However, most chemical impurities can very efficiently
capture charge carriers during passage through the
crystal, because the wide band gaps which are typical
for this material class provide a wide energy range in
which impurity states can act as traps. It is therefore
crucial to study charge carrier transport properties at
extremely low impurity concentrations. In addition,
the concentration of physical (lattice) defects has to be
kept low by careful annealing and handling of the
crystals, since at the present level of chemical purity,
physical defects can no longer be considered to give rise
to only minor contributions for the total trapping
behaviour.
Traps which are energetically deep with respect to kT
can completely prohibit the observation of carrier
transits. Shallow traps can repeatedly hold charge
carriers for short time intervals, until they are
thermally released to the conduction states again. A
strongly reduced, thermally activated "effective" mobility is therefore commonly observed in such cases,
cf. [3]. The intrinsic transport properties, the "microscopic" mobilities (or "lattice mobilities") are obscured in such situations. Early mobility results have
often suffered from these different trapping influences.
(This is at least and definitely known to be so in
cases where more efficient purification later led to
higher, non-thermally activated mobility values.)
Historically, the measured microscopic mobilities were
often on the order of 1 cm2/Vs, cf. [4, 5] which is very
small in comparison with the mobilities in standard
inorganic semiconductors, such as silicon or germanium. An increase of the mobilities # with decreasing temperature T, # oc T", (n < 0), was found with some
of the purer samples: This increase was usually restricted to narrow temperature intervals near room
temperature (and therefore not very big). The reason is
that even very shallow trapping influences, not seriously disturbing room-temperature transport, can
limit the observability of transits at lower temperatures, since the time constants for thermal detrapping
increase exponentially on cooling. The reproducibility
of mobifity results was sometimes rather poor between
different laboratories, which may also have been due to
(unknown) impurities which were present in variable
amounts in the different samples.
There were only three cases reported in the literature
where crystal quality permitted reaching lower temperatures: The electron-mobility tensor component
#~;~, in anthracene was measured down to liq. N2
temperature [4, 6]; (surprisingly it exhibited the abnormality of remaining nearly temperatureindependent between 373 and 83 K, amounting to
0.4cmZ/Vs). In naphthalene the observation of a
transition from a nearly temperature-independent
electron-mobility tensor component #~;c.= 0.4 cm2/Vs
to one rising exponentially below 120 K was accomplished in a measurement down to 31 K, where #~c.
=2cmZ/Vs was reached [7]. Durene was the only
example for which fairly high low-temperature mobilities have been reported (#+ = 55 cmZ/Vs at 120 K)
[83.
The aim of the work presented here was to improve
purification procedures and to grow high-quality
single crystals of naphthalene and perylene in order to
find out if and to which maximum value intrinsic
charge carrier mobilities continue to increase with
decreasing temperature, and, if high charge carrier
mobilities might eventually constitute a common lowtemperature property of aromatic crystals.
On our way to gradually increased purities we found,
among other things, that temperature-dependent
charge carrier mobility measurements represent a very
sensitive analytical tool for the assessment of purity
of organic aromatic crystals and we wish to focus on
this aspect in this publication.
Purification Procedures
We started with the purest commercially available
material (naphthalene "for scintillation", Merck, perylene "purum", Fluka). Naphthalene was prepurified by
liquid chromatography. After vacuum sublimation,
Ultrapure, High Mobility Organic Photoconductors
165
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z
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1
,
i
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the major part of the impurities was removed by an
initial zone refining step, consisting of 100 zones passed
across the naphthalene and perylene tubes at a speed of
10 mm/h.
Two
impurities
in
naphthalene,
//-methylnaphthalene and thionaphthene, are hard to
deplete below 1 ppm by zone refining, because at lower
concentrations they exhibit distribution coefficients
close to one. In this ease (as in others, such as pyrene)
treatment with molten potassium [9] (of. [10]) was
applied in order to chemically modify the distribution
coefficients of these persistent impurities by transforming them to reaction products with a more favorable
distribution coefficient, or to non-volatile potassium
salts which remain in the residue in a subsequent
sublimation step. The principle of potassium fusion is
sketched in Fig. 2 [,10]. The material is sublimed
through a sequence of adsorbents (teflon wool, t,
charcoal, c, and 4 fi, molecular sieves, m) into a reaction
flask, 2, which had been coated with a potassium
mirror. The molten components are allowed to react
for about 12 hours. This step is repeated twice. Subsequently, the purified material is collected in zone
refining tubes, z, for the main zone refinement. Prezonerefined perylene was used without potassium
treatment. In three following zone refining steps a total
number of about 500 molten zones were passed in a
similar way across the naphthalene and the perylene
ingots.
The first step consisted in a normal vertical zone
refinement, using a multistage intermittent technique.
Then reverse horizontal zone refinement followed. For
this purpose, the material was transferred to a narrower zone refining tube after removal of the impure
ends (~ 15% at each side). Finally, another normal
vertical zone refining step was applied, using a zonerefining tube equipped with a break seal. This break
seal can be opened under vacuum conditions, allowing
transfer (under complete exclusion of air) of the purest
~00
'~ 300
/
Fig. 2. Schematic representation of
the assemblyused for
prepurification of naphthalene by
treatment with molten potassium
metal. For explanation, see text
and [9, 10]. After [-10]
5
I 200.
100
i
tO
i
i
i
i
20
30
/+0
50
i
60 [crn3
Fig. 3. Distribution of the lifetime of free triplet excitons zr
(monitored by delayedfluorescence)along a typicalnaphthalene
zone refining ingot (whichis schematicallyrepresented, with the
sequence of the molten zones indicated, below the figure).
Crystals were grown from the 400 ms lifetime fractions
fraction of the material to a separate ampoule for
Bridgman crystal growth. As another precaution,
yellow safety lights were used during the entire
material handling and purification procedures, in
order to avoid photochemical reactions of the
material. To exclude the possibility of thermal decomposition by overheating, material transfer from one
ampoule to another was always effected by sublimation in a stabilized temperature heat box, rather than
by melting by a flame. For more details of the
purification procedures and the apparatuses used, the
reader may consult [-10].
The progress o f purification was controlled by gas
chromatography, mass spectrometry, and (in the case
of napththalene) with extreme sensitivity by liquid He
fluorescence spectrometry, cf. [11] and references given
therein. Under favourable conditions impurities with
166
w. Warta et al.
concentrations down to ~ 10 -8 mol/mol can be detected with the latter method. A rather convenient, but
unspecific method for quick purity check is the measurement of triplet exciton lifetimes by exciton-exciton
annihilation and delayed fluorescence, cf. [11]. An
example of observed triplet exciton lifetimes along a
naphthalene zone refining ingot is given in Fig. 3. A
remarkably high triplet exciton lifetime was reached in
the purest fractions.
Sample Preparation
Bridgman crystals were grown by conventional techniques [10]. Thin slices of these crystals, necessary
for the mobility measurements, were prepared by dissolution sawing with a string saw, equipped with a
solvent-wetted cotton thread. (Solvents were xylene in
the case of perylene and a cyclohexane + 10% xylene
mixture in the case of naphthalene.) Extreme care
had to be taken especially for naphthalene, not to
exert mechanical or thermal stress to the crystals.
Otherwise structural defects are introduced which
were found to strongly influence the observed
mobilities.
Mobility Measurements
Mobilities were measured by the "time-of-flight" technique [2], (Fig.4), were charge carrier pairs are created
near one surface of a crystal slice of typical dimensions
50mmZ•
at time t=O by a pulse of
~, hv I- (+)~
I
j l
I
I
__l__
C
- -[~
-
I
.._1_
crystctt
amplifier
l
osciltoscope
Fig. 4. Schematic representation of the set-up used for measuring
electron and hole mobilities by the time-of-flight method; the
transit of charge carriers through the crystal (left)causes a pulse
j(t) whoserise and decaytime are dependent, among other things,
on the stray capacitance C. The signal is amplified by a
preamplifier (center) and then fed to an oscilloscope(right side).
The duration of the exciting laser flash, displayed on the upper
oscilloscopetrace, must be short compared with the transit time z
to be measured
strongly absorbed light (2<320nm in the case of
naphthalene and 2 < 450 nm in the case of perylene).
We used a commercial KrF excimer laser (Lambda
Physik, type E M G 102), emitting single 2 = 2 4 8 n m
pulses of 8 ns halfwidth, for naphthalene, and a homemade N2 laser, emitting 2 = 337 nm pulses of 0.8 ns
halfwidth, for perylene. For the measurements, individual crystal platelets were sandwiched between a
metal rear electrode and a semi-transparent front
electrode [a vapor-deposited silver film in the case of
perylene, or a conductive layer (Aurel A, Balzers) on
quarz glass in the case of naphthalene]. A potential
difference applied across the sample generates an
electric field parallel to the normal to the platelet.
Depending on its polarity, either holes or electrons are
drawn through the bulk of the crystal. While they are
moving with constant velocity, a constant current
flows in the low resistance external circuit (RC ~ z, see
below). As soon as the "carrier sheet" reaches the rear
electrode, the photocurrent pulse amplitude drops to
zero (under idea/conditions). The kink thus indicates
the arrival time t = z. With the crystal thickness L, the
drift velocity v = L/z can be determined, and from the
definition equation of the mobility v = #E the latter
material property can be derived. (To be more precise,
# is, in general, a symmetric tensor of the second rank,
and the quantity measured in a typical time-of-flight
experiment is the velocity component parallel to the
applied electric field E, v II- The quantity defined by the
ratio of cause (E) and response (v It), the "mobility in the
given direction" 1-12], #11, is in general a certain
linear combination of all 6 independent tensor
components.)
Time-of-flight pulses were picked up at a (selectable)
resistor R, preamplified (either by a Tektronix
P 170 CF cathode follower plus 1121 preamplifier, or
by a Tektronix P 6201 FET probe plus Avantek two
stage preamplifier, GPD461+462), displayed single
shot on a fast real time oscilloscope (Tektronix, type
7104 with 7A29 and 7B 15 plug in units), and photographed for evaluation. Temperature-dependent measurements were performed in a He gas-flow cryostate
(home-made) with the sample in vacuum (perylene), or
in another He gas flow cryostate (Oxford Instruments,
type CF 204), with the sample in He heat exchange gas
(a situation which reduces sublimation losses of the
volatile naphthalene crystals at the higher temperatures, but limits the useful upper electric fields by gas
discharge).
Experimental Results
We wish to demonstrate two examples of the exciting
low-temperature results which we were able to achieve
Ultrapure, High Mobility Organic Photoconductors
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167
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~176176176
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t
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E [kV/cm'l
Fig. 6. Electric field dependence of the hole drift velocities in
1
o E = 3kV/cm
a E= 5kV/cm
[] E = 10kV/crn
o E = 12kV/cm
10
~..~
" ~ ~.
f N'~
\
30
100
--mm,,=- T[K3
300
Fig. 5. Electron and hole mobilities in naphthalene for the electric
field E parallel to the crystallographic a axis, for different field
strengths (marked by differentsymbols)between 3 and 12kV/cm.
Crystal thickness was 1010(10)~tm.The + symbols in the lower
right comer represent previously available data 1-13]
with the ultrapurified crystal material. In Fig. 5 mobilities of holes and electrons in the crystallographic a
direction in naphthalene are plotted versus temperature in a log/log plot. In this type of plot a straight line
indicates a #oc T" temperature dependence of the
mobilities. It is seen that for the electron mobility we
could establish a T - 1.4 dependence down to 27 K. The
hole mobilities could be followed even down to 4.2 K.
In this temperature region high mobilities are reached.
The highest observed value is /~+=400 cmZ/Vs. To
demonstrate the progress which the described ultrapurification of the material has allowed us to achieve,
the best data o f # + available so far [13] are inserted as
crosses and connected by a dashed line. We can now
clearly attribute the decrease of the hole mobilities in
these earlier measurements [13] to impurity
trapping.
In the region of high mobilities at low temperatures a
remarkable new effect appears which has not been
reported for any organic material before [14]: the
mobilities become electric field-dependent, they decrease with rising field. We have represented in Fig. 5
mobilities for various electric field strengths. At each
temperature the different symbols refer to different
magnitudes of the electric field. To demonstrate this
extraordinary behaviour more clearly, we have also
naphthalene at three temperatures for Ella. The broken lines
were drawn to connect the experimentalpoints and extrapolated
to v~rlft~0 for E~0. They reflect a strongly sub-Ohmic
behaviour. Low fieldmobilitieswould be represented by the lowfieldslope of these curves (ifthere were experimentallyaccessible
points). Ohmic behaviour would be indicated by the tangential
(full) lines
plotted the original drift velocity data versus the
electric field (Fig. 6). There the strong deviation from
Ohmic behaviour is demonstrated most clearly. Already at 31 K the observed drift velocities fall well
below the straight line through the origin, representing
Ohm's law. Below about 10 K the drift velocities tend
to saturate with increasing field.
As a second example we will present similar observations which were made with the electron mobility in
perylene. For the a direction an exact /zocT -1'78
dependence is obeyed down to about 40 K for low
fields (Fig. 7). For very high fields a field dependence of
the mobility can be observed already at about 100 K.
The drift velocity versus field plot (Fig. 8) again
demonstrates strong non-Ohmic behaviour.
The strong non-Ohmic behaviour of the drift velocities
in these two substances closely resembles the observations which were reported before for conventional
inorganic semiconductors (such as silicon and germanium), and explained as hot carrier effects, cf.
[-15, 163.
Below 3 0 K the perylene electron mobilities of the
example described (Fig. 7) begin to become influenced
by residual shallow trap states (clearly visible in the
figure only for the low electric field points obtained at
E=6kV/cm). Such trap influence was found more
pronounced in another crystal which was made from
less purified perylene (for which the reverse horizontal
zone refining step was left out). The low temperature
behaviour in crystal samples of the two different
perylene batches differed in that the electron mobilities
in the less extensively purified material displayed a
168
W. Warta et al.
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kV/cm
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kV/cm
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20
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13kV/cm
+E=
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o E=
22kV/cm
o E=
27kV/cm
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+%
+++
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Fig. 9. Electron mobility as a function of temperature in perylene
in an oblique crystallographic direction [~ E, a =45(1) ~ g E, b
=66(1) ~ ~ E , c * = 5 5 ( 1 ) ~ sample thickness was 370(10)pm].
The broken line is a fit with the Hoesterey-Letson type shallow
trapping model [3] with the parameters trap depth, Etr
= 17.5 meV, and trap concentration, Ntr/Nb = 5 x 10 - 4 m o l / m o l
I
A
o~
n
o,
8 kV/cm
~---
o
1,5
p
10
TCK]
I
1 -
-t-tog
I
Fig. 7. Electron mobilities in perylene for the electric field E
parallel to the crystallographic a direction for different field
strengths (marked by different symbols) between 6 and 60 kV/cm.
The crystal slice had a thickness of 252(3)Ixm
>
I 'l'l
~
/~
Ella
'
n=-1,87
,
I
50
,
E [kV/cm]
Fig. 8. Electric field dependence of the electron drift velocities in
perylene at 5 temperatures for Ella
maximum at somewhat higher temperature and a
more pronounced relative decrease below the maximum. In a crystal slice of the less purified material (cut
in an oblique crystallographic orientation) shallow
trap-limited electron mobilities were followed down
to 14 K (Fig. 9) in order to be able to try a fit by the
Hoesterey-Letson multiple shallow trapping formula
[3] for obtaining the trap parameters. In this model the
carrier mobilities fall with decreasing temperature
because the carriers stay for increasingly longer time
intervals in the trap states before they are thermally
reactivated to move freely in the band for a short while.
These trap-influenced "effective mobilities" #elf are
governed by the underlying microscopic (lattice) mobility #o(T), the density of trap states Ntr, relative to
band states Nb, and a Boltzmann factor with the trap
depth Etr:
#af(T) = #o(T) [1 + (Nt~/Nb) exp (Et~/kT)] -1
(2)
Before we apply this formula to interpret the results of
Fig. 9, we wish to emphasize that between 40 and
300 K the perylene mobilites were reproducible within
experimental error between crystals fro m different
batches, which [besides the fact that the temperature
dependence was found to obey a #o oc T n (n < 0) law]
supports their interpretation as true lattice mobilities.
This good reproducibility is also demonstrated by the
fact that it was possible to closely fit the experimental
data of 15 series of measurements in 10 different
crystallographic directions by a (temperaturedependent) second rank tensor [17].
We find for the less purified crystal, by fitting [19] the
Hoesterey-Letson equation (2) to the experimental
points (Fig. 9) between 20 and 14 K, that there is only a
very shallow trap left with a trap activation energy of
Err = 17.5 meV
and
a
concentration
Ntr/N b
= 5 x 10-4 mol/mol. A trap with these parameters can
only exert notable influence on the (macroscopic)
Ultrapure, High Mobility Organic Photoconductors
I
I
I
earlier measurement in the higher temperature range
reported in the literature [18], which we have inserted
into Fig. 10 as circles. These previously reported
mobilities are very small and exhibit a thermally
activated behaviour, i.e. decreasing values with decreasing temperature, opposite to the microscopic
mobilities reported in this paper for the respective
temperature range. They can be quantitatively interpreted by fitting the shallow trapping equation (2) to
the experimental points (dashed line), with po(T) from
our trap-free microscopic mobility data, and the trap
parameters: N t r / N b = l . 7 x l O -3 mol/mol and Err
= 270 meV. The span of orders of magnitude in the
mobilities between impure and ultrapure crystal
material which we demonstrate here for naphthalene
and perylene, clearly indicates the high sensitivity of
charge carrier mobility data against impurities and
imperfections.
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Conclusion
4
In summary, we reported on extensive purification
procedures which allowed us to grow ultrapure
organic molecular crystals. A characteristic feature of
these ultrapure crystals are their relatively high,
electric-field-dependent microscopic (lattice) mobilites
at low temperatures. These experimental results not
only close, in a sense, the "mobility gap" which existed
so far between high-mobility inorganic and lowmobility organic semiconductors; they also demonstrate that charge carrier mobility measurements are a
useful and sensitive tool for the characterization of
high purity organic crystals. In this paper we have
emphasized the latter aspect. The other aspects will be
treated in more detail elsewhere.
o'f
o'I
0,01 ~ tog I
30
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100
3OO
~.,.-
169
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T rK]
Fig. 10. Electron mobilities in a 306(3)I~m thick perylene crystal
for the electric field E parallel to the crystallographic c* direction.
The open circles in the lower right comer represent previously
available mobility data [18]. The dashed line is a HoestereyLetson type shallow trapping model fit with the trap parameters
Etr=270meV and Nt~/Nb=1.7 x 10-3 mol/mol, revealing that
the purity of the crystals used in these older measurements was
insufficient for obtaining the true (microscopic) lattice mobilities
transport behaviour at the lowest temperatures
(T < 40 K). The origin of this trap is unknown, but it is
likely that it reflects residual chemical impurities,
which act either directly, or indirectly by X-trap
formation (perturbation of the energy levels of one or
more neighbouring molecules). But we cannot exclude
that the nominally less purified crystal contained
accidentally more physical imperfections (lattice defects, such as vacancies or dislocations) and that these
physical imperfections, and not residual chemical
defects dominated in influencing transport at the
lowest temperatures.
H o w sensitive mobilities are to deeper traps (most
probably caused by chemical impurities) can be demonstrated by comparing our results for the crystallographic c'-direction (i.e., perpendicular to the cleavage
plane) in perylene, plotted in Fig. 10, with results of an
Acknowledgements. We wish to express our gratitude to
M. Gerdon, Chr. Herb, W. Tuffentsammer and G. Pampel for
their great engagement in purification, crystal growth and purity
control. We are also grateful to our colleagues at the mechanical
workshop who, among other things, designed and built one of the
He gas flow cryostates. The excimer laser was kindly placed at
our disposal by Prof. M. Pilkuhn and his eoworkers. This work
was supported by the "Stiftung Volkswagenwerk" (ultrapurification and characterization) and by the "Deutsche Forschungsgemeinschaft" (charge carrier transport).
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170
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7. L.B. Schein, A.R. McGhie: Phys. Rev. B20, 1631 (1979)
8. Z. Burshtein, D.F. Williams: Phys. Rev. B 15, 5769 (1977)
9. W. Tuffentsammer: Stuttgarter Kristallabor (unpublished)
10. N. Karl: High purity organic molecular crystals, in Crystals 4
(Springer, Berlin, Heidelberg, New York 1980)
11. N. Karl: J. Crystal Growth 51, 509 (1981)
12. J.F. Nye: Physical Properties of Crystals, Their Representation by Tensors and Matrices (Clarendon Press,
Oxford 1972)
13. J. Berrthar, M. Schott: Mol. Cryst. Liq. Cryst. 46, 223 (1978)
14. Electric field-dependent electron mobilities #~. reported for
anthracene at 140K by S.Nakano, Y. Maruyarna: Solid
State Commun. 35, 671 (1980) could not be reproduced by
L.B. Schein, R.S. Narang, R.W. Anderson, K.E. Meyer, A.R.
McGhie: Chem. Phys. Lett. 100, 37 (1983) even not at still
higher electric fields
15. K. Seeger: Semiconductor Physics, Springer Ser. Solid-State
Phys. 40 (Springer, Berlin, Heidelberg 1982)
W. Warta et al.
16. E.M. Conwell: In Solid State Physics, Suppl. 9 (Academic,
New York 1967)
17. R. Stehle, N. Karl: To be published
18. Y. Maruyama, T. Kobayashi, H. Inokuchi, S. Iwashima: Mol.
Cryst. Liq. Cryst. 20, 373 (1973)
19. For the fit an underlying microscopic mobility #o(T) was
assumed which was obtained from an extrapolation of the
T > 4 5 K mobilities using the (E-~0) tangent, n = - 1 . 8 7 ,
drawn in Fig. 9. It turns out that the trap activation energy
obtained from the data between 14 and 20K is rather
insensitive to the exact go(T) dependence. Even assuming a
constant value, #o = 100 cm2/Vs, would cause only a minor
change of the resulting trap depth (to 16.1 meV). Between
these two extreme assumptions, the resulting trap concentration changes from 5 x 10 - 4 to 2 • 10- 4 mol/mol. - The
discrepancy between the calculated and the measured mobility curves in the range between 20 and 45 K results from
the fact that the measured mobifities in this high-mobility
region are strongly dependent on the applied electric field
strength. - For very shallow traps, as found here, the
possibility of field-activated detrapping (Pool-Frenkel effect)
can require a revision of the simple Hoesterey-Letson
description. However, this effect can be estimated to decrease
the thermal activation energy by only a few meV for the fields
used here