Page 43 - Organic Electronics in Sensors and Biotechnology

20 Chapter One

transistors was drawn, which was consistent over a range of scaled
channel lengths. In these partially ordered systems, experimental
data suggest that the charge transport mechanism is thermally acti-
vated and field-assisted hopping transport, and the hopping trans-
port between disorder-induced localized states dominates over the
intrinsic polaronic hopping transport seen in organic single crystals.
Figure 1.12 shows that the field-dependent mobility in the hopping
regime predicted by the polaron model 67

μ = μ 2kT sin h ⎛ eEa ⎞ ⎟ (1.4)
⎜
0 ⎠
eEa ⎝2kT
deviates significantly from the experimental data of field-dependent
mobility in polycrystalline pentacene thin-film transistors, whereas
the hopping transport between disorder-induced localized states
with Frenkel-Poole type field dependence fits the data quite well. The
low-field activation energy for the localized states induced by disor-
der is 130 meV in polycrystalline pentacene thin-flim field-effect
transistors, which is much larger than the intrinsic polaron binding
68
energy (21 to 35 meV) in polyacenes. Therefore charges are more
69
appropriately thought of as being trapped in localized states than
being dressed by intrinsic lattice distortions, which leads to the pref-
erence of the transport model in polycrystalline organic transistors as
demonstrated in Fig. 1.12.

10 –1 10 –1

–2
–2
10
10
Mobility [cm 2 /(V·s)] 10 –3 5 μm Mobility [cm 2 /(V·s)] 10 –3 5 μm
2 μm
2 μm
–4
–4
10
1 μm
1 μm
10
270 nm
270 nm
10 –5 500 nm 10 –5 500 nm
Frenkel fit Frenkel fit
Polaron fit Polaron fit
10 –6 10 –6
0 200 400 600 800 0 200 400 600 800
290 K 1/2 92 K 1/2
ds
ds
V g = –40 V sqrt (V /L) (V/cm) V g = –40 V sqrt (V /L) (V/cm)
(a) (b)
FIGURE 1.12 Comparison of Frenkel-Poole’s model vs. polaronic model. Shown are
representative plots at two temperatures to fi t the experimental data with Frenkel-
Poole’s model (gray dashed line) and polaronic model. Frenkel-Poole’s model and
the polaronic model follow different laws
⎛ ⎞ 2kT ⎛ eEa ⎞
μ = μ exp ⎜ β E ⎟ and μ = μ sin h ⎜ ⎟
0 0 eEa ⎝ 2kT ⎠
⎝ kT ⎠
respectively. Frenkel-Poole’s model fi ts the data quite well whereas the polaronic
model deviates obviously. (Reprinted with permission from Ref. 60. Copyright 2007,
American Institute of Physics.)