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In the original transport energy model [10], the
downward hopping transport and the effect of degenerate statistics were
neglected. An electron with energy
, can
only hop to a free localized state. In variable range hopping (VRH)
theory, the numbers of empty sites enclosed by the contour
can be
determined by the following equation [19].
Here
is the Fermi-Dirac distribution function, and
is the probability that the finial site is empty. The Gaussian DOS is rewritten as
![$\displaystyle g\left(\epsilon\right)=\frac{N_t}{\sqrt{2\pi}\cdot{a}}\exp\left[-\left(\frac{\epsilon-\epsilon_0}{\sqrt{2}\cdot{a}}\right)^2\right],$](img326.png) |
(3.5) |
where
is the normalized energy
,
is the Gaussian
center,
is the effective DOS and
is defined as
,
where
is the standard deviation of the Gaussian distribution. If we let
be the
normalized Fermi-Dirac distribution function, then the carrier concentration can
be written as
 |
(3.6) |
Considering the distribution function,
will be
calculated as
![$\displaystyle R\left(E_t\right)=\left[\frac{4\pi}{3}\int_{-\infty}^{\epsilon_t} g\left(E\right)\left(1-f\left(\epsilon,\xi\right)\right)d\epsilon\right]^{-1/3}.$](img333.png) |
(3.7) |
Substituting (3.7) into (3.3), we obtain
 |
(3.8) |
where
![$\displaystyle \eta=\left[\int_{-\infty}^{\epsilon_{t}}\frac{\exp\left(-\frac{1}...
...\right)d\epsilon} {1+\exp\left(-\left(\epsilon+\xi\right)\right)}\right]^{4/3}.$](img335.png) |
(3.9) |
is the new transport energy and can be calculated by solving (3.9) numerically.
Next: 3.3 Results and Discussion
Up: 3. The Effect of
Previous: 3.1 Introduction
Ling Li: Charge Transport in Organic Semiconductor Materials and Devices