The Bridge - Issue 2, 2021 - 17

Feature
Modeling of organic semiconductor conduction parameters
with reference to inorganic semiconductors
Organic semiconductor materials have relatively
higher energy gaps compared to the most common
semiconductor metallic material, e.g. silicon (Si). The
effective density of states according to the data in
the literature are not much different from those of
silicon, therefore, the intrinsic concentration of the
organic materials is very small. Accordingly, organic
materials approach the insulators rather than the
semiconductors. In this sense, practically in their
intrinsic state they behave as an insulator.
Regarding the purity of the materials, metallic
semiconductor is produced with high purity but the
organic semiconductors are produced with less purity
and they contain impurities leading to make them
either p-type or n-type conducting.
Once doped either intentionally or unintentionally one
can define for them a Fermi level as in the metallic
material. Otherwise, one describes them as insulators,
in the sense that their energy levels are aligned to the
vacuum level. If the material is doped, the energy levels
through a system of materials are aligned to Fermi level
at thermal equilibrium.
The doping of the organic semiconductors
The doping of the metallic semiconductors is by
atomic substitution while in the organic material it is
by adding doping atoms or doping molecules. The
doping by atoms is inferior than doping by molecules
as the doping by atoms results in unstable materials
[6]. The organic materials can then be doped by
adding molecules where one gets n-type and p-type
conduction. In case of doped organic semiconductor
one can define a Fermi level for the material Ef
such
that one can express the electron concentration by a
relation similar to that of the inorganic materials such
that the electron concentration n can be expressed as
in (1)a :
The same holds for the p-type organic semiconductor
such that the hole concentration p can be written as:
In case of n-type the donor molecule gives an electron
to the host molecules and it becomes a positive ion
which is considered immobile similar to the doping in
the metallic semiconductor. There is also an ionization
potential of the doping molecules where the doping
level is lying under the LUMO level by ionization energy
Eid
=EL
-ED
.
In a doped material, to determine the Fermi level one
uses the mass action law and the neutrality equation as
in the metallic semiconductors such that the following
relations hold:
The neutrality equation n= Nd
+ + p, Where Nd
distribution function Nd
Where;
+ = Nd f(Ed
, the Fermi Dirac
),
+ is
concentration of the ionized donor molecules.
The mass action law np= ni2
Similar equations hold for the acceptor molecules.
Current conduction in organic semiconductors
The current conduction mechanisms in metallic
semiconductors are also applicable in the organic
semiconductors. The common current mechanisms
in both types of semiconductors are the drift and the
diffusion currents. The mobile charge carriers can drift
under the influence of the applied electric field and can
also diffuse under the concentration gradients. The drift
current Jdrift
can be expressed by the known relation as
in (3):
Where E is the intensity of the electric field, q is
the electronic charge, μn
and μp
are the mobility of
electrons and holes, respectively and n and p are the
electron concentration and the hole concentration,
respectively.
The mobility μ is different from that of the metallic
semiconductors because of the nature of the organic
semiconductors. Here the electrons hop across
potential barriers from a molecule to its neighboring
one. The depth of the potential barriers is randomly
distributed around certain average value. It results
that the mobility will be dependent on the applied
electric field and the temperature in an activated
transport process. Specifically, the mobility increases by
increasing the electric field and temperature [7].
HKN.ORG
17
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The Bridge - Issue 2, 2021

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