Charge transport mechanisms are theoretical models that aim to quantitatively describe the electric current flow through a given medium.
Starting with Ohm's law and using the definition of conductivity, it is possible to derive the following common expression for current as a function of carrier mobility μ and applied electric field E: The relationship
Charge transport in the same material may have to be described by different models, depending on the applied field and temperature.
[2] In the case of nearest-neighbour hopping, which is the limit of low concentrations, the following expression can be fitted to the experimental results:[3] where
[4] At high concentrations, a deviation from the nearest-neighbour model is observed, and variable-range hopping is used instead to describe transport.
[3] At low carrier densities, the Mott formula for temperature-dependent conductivity is used to describe hopping transport.
For low temperatures, assuming a parabolic shape of the density of states near the Fermi level, the conductivity is given by: At high carrier densities, an Arrhenius dependence is observed:[3] In fact, the electrical conductivity of disordered materials under DC bias has a similar form for a large temperature range, also known as activated conduction: High electric fields cause an increase in the observed mobility: It was shown that this relationship holds for a large range of field strengths.
[5] The real and imaginary parts of the AC conductivity for a large range of disordered semiconductors has the following form:[6][7] where C is a constant and s is usually smaller than unity.
The field dependence of the current density j through an ionic conductor, assuming a random walk model with independent ions under a periodic potential is given by:[8] where α is the inter-site separation.
Characterization of transport properties requires fabricating a device and measuring its current-voltage characteristics.
Devices for transport studies are typically fabricated by thin film deposition or break junctions.
The dominant transport mechanism in a measured device can be determined by differential conductance analysis.
In the differential form, the transport mechanism can be distinguished based on the voltage and temperature dependence of the current through the device.
For Poole–Frenkel hopping, for example, Tunneling and thermionic emission are typically observed when the barrier height is low.