Generalized transport-band field-effect mobility in disordered organic and inorganic
semiconductors
P. Servati,
1
A. Nathan,
2
and G. A. J. Amaratunga
1
1
Electrical Engineering Division, University of Cambridge, 9 JJ Thomson Avenue, Cambridge CB3 0FA, United Kingdom
2
London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
Received 25 April 2006; revised manuscript received 30 June 2006; published 15 December 2006
Field-effect mobility
FE
and its activation energy in disordered inorganic and organic semiconductor thin-
film transistors is strongly dependent on bias conditions. This implies a nonlinear dependence of conductivity
on carrier concentration, which stems from the high density of trapped carriers while only a few contribute to
conduction. When
FE
is extracted from measurement data, the nonlinear conductivity-concentration depen-
dence is averaged over the semiconducting film. Consequently,
FE
becomes mingled with device attributes
such as gate capacitance in addition to terminal bias, which undermines the physical interpretation of
FE
and
subsequent comparison of measured values for different devices and different semiconductors. This paper
presents an effective mobility
eff
description at a reference carrier concentration, which separates the physical
conductivity-concentration dependence from the device and bias attributes, enabling comparison of carrier
transport in disordered semiconductors. In particular, by using the generalized concept of mobility edge and
exponential band tails we show that
eff
can be applied to a wide range of inorganic and organic semiconduc-
tors. Indeed, three parameters, viz.,
eff
, exponential band tail slope T
t
, and bias-independent activation energy
E
a0
of
eff
, can describe carrier transport in the transistor together with its bias and temperature dependence.
DOI: 10.1103/PhysRevB.74.245210 PACS numbers: 73.50.-h, 72.20.Ee, 73.61.Jc, 73.61.Ph
I. INTRODUCTION
Thin-film transistors TFTs using disordered inorganic
and organic semiconductors have become attractive for
emerging flexible electronics and active matrix organic light-
emitting diode AMOLED displays.
1–7
For these transistors,
parameters such as field-effect mobility
FE
are primarily
determined by disorder and grain size of the semiconductor,
which in turn are strongly influenced by fabrication tech-
niques e.g., vacuum deposition, ink-jet printing, or spin
coating and the associated process conditions. In hydrogen-
ated amorphous silicon a-Si:H, the disorder in the bond
lengths and angles leads to a high density of localized states.
These states trap most of the electrons and the observed low
conductivity can be attributed to the small fraction of carriers
excited to the extended states.
8,9
In amorphous organic semi-
conductors, disorder in the molecular arrangement and the
presence of grain boundaries lead to a high density of local-
ized states.
1–3,10,11
Hopping of carriers between these states
constitutes the means for conduction.
Despite differences in processes and presumed transport
mechanisms in this family of materials, unique similarities
are observed in the current-voltage I-V characteristics of
the TFTs. The I-V characteristics generally follow a power-
law dependence and the
FE
is systematically bias depen-
dent. For example, in a-Si:H TFTs,
FE
gradually increases
with increasing positive gate bias, which can be attributed to
the increased number of electrons excited to extended states
as the total density of accumulated electrons increases.
12–23
The same is observed for microcrystalline and nanocrystal-
line silicon TFTs.
24–27
Similarly, for a wide range of conju-
gated organic semiconductors,
FE
increases with increasing
negative gate bias and hole accumulation.
10,11,28,29
The dependence of
FE
on carrier concentration is also
reflected in the Arrhenius behavior of mobility in the tem-
perature dependence measurements of a-Si:H and organic
TFTs. Figure 1 illustrates temperature dependence of
FE
for
a-Si:H our own, pentacene,
10
polythienylene vinylene
PTV,
10
and poly5,5'-bis3-alkyl-2-thienyl-2,2'-
bithiophene PQT-12
30,31
TFTs at different gate biases. In-
deed the results for poly3-hexylthiopheneP3HT TFTs,
reported in Ref. 32, also falls close to PQT-12, which has
been omitted for readability reasons. As seen, the mobility
FE
generally shows Arrhenius behavior with an activation
energy E
a
, which decreases with increasing gate bias, as re-
ported in literature.
10,18,20,21,30
The dependence of E
a
on gate
FIG. 1. Temperature dependence of reported values of
FE
for
a-Si:H, PQT-12 Ref. 30, pentacene Ref. 10, and PTV Ref. 10
TFTs at different gate biases. The inset shows the bias dependence
of activation energy E
a
of
FE
for these materials.
PHYSICAL REVIEW B 74, 245210 2006
1098-0121/2006/7424/2452107 ©2006 The American Physical Society 245210-1