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Organic semiconductors can be considered as hopping networks and are
characterized by strong disorder in both energy and space [8,9]. This makes
it very difficult to solve the problem analytically or simulate the
carrier transport and recombination in such a system by starting from a
oneparticle master equation. Consequently, an analytical approach to this
problem is normally based on a specific set of assumptions and
simplifications [20,68]. The concept of transport energy is a very
useful tool for the analysis of charge
hopping transport in organic semiconductors. The importance of the transport energy
stems from the fact that it maximizes the probability for a carrier to hop upward. It does not
depend on the initial energy of the carrier and serves as an analog of
the mobility edge [10].
The transport energy concept is based on the MillerAbrahams expression
[7,71]. This equation can be written as

(3.1) 
For a particular density of states
, the transport
energy can be obtained in the following way [10]. For an electron with
energy , the median rate of a upward hop to a
neighboring localized state with energy is

(3.2) 
where
The transport energy can be calculated by maximizing the rate (3.2) with
respect to the final energy

(3.3) 
After some calculation we obtain

(3.4) 
Here we can see that the transport energy does not depend on the
initial energy . The transport energy has been extended to an exponential
DOS in [10] and later to a Gaussian DOS in [77].
Next: 3.2 Theory
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Ling Li: Charge Transport in Organic Semiconductor Materials and Devices