The Bridge - Issue 2, 2021 - 18

Feature
Modeling of organic semiconductor conduction parameters
with reference to inorganic semiconductors
The other current that can exist in the organic material
is the diffusion current when concentration gradients
of electrons and holes can be formed. The diffusion
current Jdiff
has the well-known expression:
Where Dp
and Dn
are the diffusion constants of the
holes and electrons, respectively. The concentration
gradients dp/dx and dn/dx are of holes and
electrons, respectively.
The diffusion coefficient D is related to the mobility
μ by the Einstein relation:
Where Vt
is the thermal voltage.
There is also the space charge limited current SCLC
when the electric conduction is affected by single type
charges either electrons or holes.
The SCLC will be treated in detail when dealing with
the conduction in metal organic semiconductors
diodes. The space charge limited current prevails when
the conduction is unipolar in originally semi insulating
materials with very low mobility.
This state is presented in the intrinsic organic materials
injected by either electrons or holes from metallic
electrodes. It is observed many times in such
organic materials.
Recombination of mobile charge carriers
in organic semiconductors
Recombination is the disappearance of a mobile
electron in a hole. This process leads to the loss of
mobile charge carriers and thereby affects much the
electrical characteristics of the semiconductor devices
including solar cells and light emitting diodes.
The recombination mechanisms were studied
intensively in metallic semiconductors [5] and to less
extent in the organic semiconductors.
From the conceptual point of view, the recombination
mechanisms occurring in the metallic semiconductor
also occur in the organic semiconductors. These
mechanisms can be classified into radiative and
non-radiative types. Radiative recombination is a
consequence of the direct fall of electrons from the
conduction band to the valence band while the nonradiative
one when the fall of the electrons occurs
THE BRIDGE
through trap levels in the bandgap. These trap
levels are called recombination centers. The most
dominant non-radiative recombination mechanism
is that of the Shockley-Read-Hall. It exists in all
semiconductor materials.
Every recombination mechanism has its specific
dependence on the hole and electron concentrations
and its rate constants. For more details on such
recombination mechanisms, please refer to the ref. [5].
There is a specific recombination mechanism which
exists in the organic semiconductors. It is the Langevin
which occurs as direct consequence of an electron
and hole comes in the field of the other in a low field
mobility materials. They get this chance when they
meet while moving. Its recombination rate rlv
expressed by [8].
can be
Where, ε is the permittivity. It is found that this
mechanism is applicable in case of the organic LEDs,
while it must be reduced by an appreciable factor
when applied to organic solar cells. Generally, the
rate can be expressed by rlv
=kr pn , where kr
is the
recombination rate constant that can be determined
experimentally.
A quantity which can be used to characterize
semiconductor materials is the minority carrier lifetime
τ which is defined by: τ=dn⁄U n
[5], where Un
is the
excess recombination rate for the electrons and dn is
the excess electron concentration.
The semiconductor equations
The semiconductor equations [5] are also applicable
for the organic semiconductor as they are of general
formulation. These equations are the, the poison equation,
the current equation, and the continuity equations.
These equations can be formulated as:
With ρ is the charge density and D is the electric
displacement.
Where, Nd
+ and Na
- are the ionized donor and acceptor
molecules concentrations. The current equations can
be written in the form:
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The Bridge - Issue 2, 2021

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