Page 39 - Organic Electronics in Sensors and Biotechnology

16 Chapter One

temperatures when the bandwidth is large compared to kT and the
mean free path is large compared to intermolecular spacing. As the
temperature is increased, both band and hopping contributions to
transport can exist, leading eventually to hopping-dominated trans-
63
port at high temperatures. At the other extreme, in highly disor-
dered semiconductors such as glasses and molecular doped polymers,
transport has been explained in terms of the correlated disorder
model which is characterized by a Frenkel-Poole type variation of
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mobility with electric field. The nature of charge transport in an
intermediate class (polycrystalline form) of semiconductors, which
contains ordered crystallites separated by disordered regions (grain
boundaries), can be expected to possess features of both crystalline
organic semiconductors as well as disordered ones. For a polycrystal-
line thin-film layer of an organic semiconductor such as pentacene
thermally sublimed in vacuum, most of the disorder is located at grain
boundaries. Therefore, when the channel length scales down to 500 nm
and smaller, which is comparable to the grain sizes of the organic
semiconductor layer, the average number of grains within one chan-
nel reduces as shown in Fig. 1.7, so that the dominant electrical trans-
port mechanism becomes different from that of large-scale devices
where channel lengths are much larger than the grain sizes. For poly-
crystalline organic thin-film transistors, field-dependent mobility and
limited injection through Schottky barrier at metal-organic semicon-
ductor contacts play important roles as the device geometry scales
down to these dimensions. To address this scaling behavior, the mobi-
lity vs. longitudinal field (nominally taken as V /L) was plotted in
ds
logarithmic vs. square root scales, respectively, for a series of channel
lengths at different temperatures, as shown by the scattered data in
Fig. 1.10. The mobility turns out to be a function of the longitudinal
field (increasing with the field) consistently throughout a wide range
of scaled channel lengths for the same morphology of organic semi-
conductor layer deposited at a given fabrication batch.
It is very important that the contacts do not influence the measured
mobility. For each channel length, as the source-drain voltage magni-
tude is increased from zero, the devices are initially injection-limited.
In this regime, the drain current increases exponentially with voltage,
as is expected when charge is injected over a Schottky barrier. In Fig. 1.6
it can be clearly seen that at small V , there is an exponential depen-
ds
dence of I on V (injection-limited regime). As the source-drain voltage
d ds
is increased, the devices are operated away from the injection-limited
regime. For this reason, in Fig. 1.10 we consider data only at high V for
ds
each channel length when the device operation has moved away from
the injection-limited regime to a regime where I increases slightly
d
superlinearly with V as is expected in the linear regime of operation
ds
of an organic transistor with some field-dependent mobility. For each
scattered curve in Fig. 1.10 measured at a certain channel length, the
“bottom part” of the curve (at relatively lower longitudinal fields,