# Charge Carrier Mobility

Transport in organic semiconductors refers to how charges move through a material with the application of an electric field. Transport can refer to the migration of excitons along chains or between chains. It involves the process of energy transfer from one chain to another. In this section we will be concerned with charge carriers, electrons and holes.

### Charge carrier mobility

The performance of any organic device depends on the mobility of the charge carriers. For example, if the charge applied to an OLED remains stuck next to the electrodes for a long time this will not lead a internal current that is transformed into the emission of photons. Similarly after absorbing energy and attaining the excited state an organic photovoltaic must separate the charge and transport it to the electrodes. Charge carrier mobility in transistors determines how fast the device can be turned on and off.

Charge carrier mobility is the speed (cm/s) at which the charge carriers move in the material in a given direction, in the presence of an applied electric field (V/cm):

$\mu = \frac {cm^2} {Vs}\,\!$

For amorphous silicon μ ~ 5 x 10-1 – 10-3 cm2/Vs

For organic semiconductors to be competitive with amorphous silicon they must approach μ of 1 cm2/Vs. 1 cm2/Vs is also a borderline value between the transport band regime and the hopping regime. These are the two modes of charge transfer. If the mobility is significantly lower than one it is in the hopping regime, if it is significantly higher it is the band regime.

### Electronic Coupling

In both the band regime and the hopping regime it is necessary to maximize the electronic coupling between adjacent units, molecules or polymer segments, in order to maximize the charge mobility. Electronic coupling is the mobility defining factor in band regimes, and one of several defining factors in the hopping regime. Geometry relaxation in molecules or chain segments takes over as dominant charge transfer process as they enter the hopping regime. Marcus theory is able to begin to explain transport properties but one must go beyond that for a full explanation of transport.

Transport depends on the structure or morphology of your system. The size of grains in a crystalline material has a direct impact on mobility. If there are very small grains, there are lots of grain boundaries to overcome and therefore lower mobility. When one speaks of the mobility of a material it refers to the measurement of a specific sample. For example, the way you prepare a thin film of pentacene can affect the mobility. Often samples will be affected by defects and traps that prevent measuring the ideal “intrinsic mobility”.

For a theoretical exploration of mobility we will assume that we are dealing with a single perfect crystalline such as rubrene. But also recognize that many crystalline materials include areas that more amorphous, may have variations in grain sizes, impurities etc. Amorphous materials are easier to process for example by inkjet printing or spin coating. These disordered systems are much harder to describe.

A polyphenylvinylene (PPV) that has been oxidized because of the presence of water or oxygen will cause electrons to be trapped in carbonene functionalities, so mobility will be impaired because of defects and impurities. Its difficulty to characterize impurities, sometimes referred to traps; shallow traps occur if the energy that is needed to detrap the carrier is smaller than kT, or deep traps occur if the energy required to detrap the carrier is significantly larger than kT. Purification is essential to improve performance of devices based on organic semiconductors.

For more information of the transport properties of disorder materials see Bässler et al. ,Conwell et al., Epstein et al.

Flash Simulation

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