The Bridge - Issue 2, 2021 - 21

Feature
Modeling organic semiconductor metallic contact and optoelectronic
parameters with reference to inorganic semiconductors
Conduction in Metal Organic Semiconductor
Metal MOSM Diodes
The first challenge for determining the current of
the MOSM Diode is the energy alignment at the
metal organic semiconductor interface. When the
semiconductor material is doped then one can define
for it a Fermi level and accordingly the Fermi level will be
constant at the interface similar to the metal- inorganic
semiconductor.
In case of intrinsic organic semiconductor, it behaves
as an insulator because of the relatively large bandgap
and the amorphous nature of the material. In this case,
the energy alignment will be according to the vacuum
energy level. That is at equilibrium the energy levels align
themselves to the vacuum level, Evac. Such simplifying
assumptions can facilitate the derivation of mathematical
expressions for the currents.
Inspecting the literature concerned with the currents
in the MOSM diodes with one charge type, it is found
that the current can be either injection limited from the
M-S contact or it can be space charge limited inside the
semiconductor itself. The space charge limited current
exists when it is much less than injection current. The
injection current is limited by the height of the injection
barrier at the contact which is more or less independent
of the applied voltage except the image force barrier
lowering and equal to the difference between the work
function of the metal and the electron affinity of the
organic semiconductor.
It is required to determine the factors limiting the current
in the MOSM diode under the assumption of single
charge type injection in the organic semiconductor.
That is the metal can inject either electrons or holes in
the organic semiconductor. Basically the current can be
injection limited or space charge limited. In each case the
I-V relationship of the diode is completely different.
Now let us describe the current of the MOSM diode
when it is limited by the potential barrier between the
metal and the organic semiconductor. Figure 1 shows the
energy band diagram before contacting the diode layers
and after contacting.
Assuming that the energy level alignment will be the
vacuum level, then at the metal semiconductor contact
of the cathode, a potential energy difference φb between
the metal and the organic semiconductor will be formed
that can be expressed by the difference between the
Figure 1: Energy level diagram a) before contacting MOSM diode and b)
at equilibrium; the dotted line refers to energy level diagram at applied
voltage Va
.
metal work function φk and the electron affinity χ , that is:
The current will be limited by the thermionic injection
from the metal that can be expressed by the well
known relation:
With A =
,where φ= φb, m is the effective mass
and h is the Planck constant.
The origin of the space charge limitation is very low
mobility of the organic semiconductors and the unipolar
behavior in addition to the relatively low electric field.
Accordingly, during their flow inside the material the
charge carriers accumulate in it and build space charge
that impedes the motion of the charges from the injector
to the injecting contact to the collecting contact.
The space charge limited current is well known from the
transport of electrons in vacuum and it is termed the
three halves power law where the current is proportional
to V3/2
, where V is the voltage across the diode. It also
exists in the conduction by insulators, but with
other forms.
For a 1D trap-free solid, the corresponding SCL current
density is known as the Mott-Gurney (MG) law [1],
given by:
Where εr is the relative permittivity of the solid. If the
solid has an exponentially distributed traps (in energy),
it is known as the Mark-Helfrich (MH) law, or the
trap-limited SCL current density JMH
;
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21
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The Bridge - Issue 2, 2021

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