Book ChapterDOI
Theory of Hopping Conductivity in Disordered Semiconductors
P. N. Butcher
- pp 341-381
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The relationship between hopping conductivity and random walks in random systems is described in this article, where the randomness of the system is shown to play a major role in determining the frequency dependence of the ac conductivity.Abstract:
The semiclassical theory of hopping conductivity in disordered semiconductors is reviewed The relationship between hopping conductivity and random walks in random systems is described The randomness of the system is shown to play a major role in determining the frequency dependence of the ac conductivity The dc conductivity is controlled by the electron diffusivity which involves the product of the mean hopping frequency and the mean square distance moved per hop The mean hopping frequency is calculated for simple models and shown to contain no exponential factors The mean square distance moved per hop is exponentially smaller than the mean square nearest neighbour intersite spacing It is calculated for simple models by using an approach derived from percolation theoryread more
Citations
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Impurity Conduction at Low Concentrations.
TL;DR: In this article, the conductivity of an n-type semiconductor has been calculated in the region of low-temperature $T$ and low impurity concentration ${n}_{D}$.
Journal ArticleDOI
Theory of AC and DC Conductivity in Disordered Hopping Systems
TL;DR: In this paper, a self-consistent theory of ac and dc transport in disordered hopping systems is given, which is an extension of an effective medium approximation and a Cayley tree formalism, and calculated dc and ac conductivity are compared with the results of computer simulations of R-hopping networks and data of amorphous germanium.
Journal ArticleDOI
The Hall mobility of carriers hopping in an impurity band
P. N. Butcher,A. A. Kumar +1 more
TL;DR: In this article, a simple general formula for the Hall mobility was derived, which involves the contribution to the equilibrium hopping rates from Holstein's three-site process and the product of potential differences in the Miller-Abrahams network in zero magnetic field calculated with an electric field oriented in two orthogonal directions.
Journal ArticleDOI
Analysis of hopping conduction in impurity bands in inversion layers
K. J. Hayden,P. N. Butcher +1 more
TL;DR: In this paper, Percolation arguments are used to develop formulae for hopping conductivity involving localized states distributed over a bandwidth of energies, where all possible locations of the Fermi level are treated.
References
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Journal ArticleDOI
Impurity Conduction at Low Concentrations
A. J. Miller,Elihu Abrahams +1 more
TL;DR: In this paper, the conductivity of an n-type semiconductor has been calculated in the region of low-temperature $T$ and low impurity concentration ${n}_{D}$.
Journal ArticleDOI
Hopping Conductivity in Disordered Systems
TL;DR: In this paper, the authors considered a model in which charge is transported via phonon-induced tunneling of electrons between localized states which are randomly distributed in energy and position, and obtained an electrical conductivity of the form
Journal ArticleDOI
An introduction to percolation theory
TL;DR: Percolation theory, the theory of the properties of classical particles interacting with a random medium, is of wide applicability and provides a simple picture exhibiting critical behaviour, the features of which are well understood and amenable to detailed calculation.
Journal ArticleDOI
Low-Frequency Conductivity Due to Hopping Processes in Silicon
TL;DR: In this paper, a simple theory based on the currently accepted model of impurity conduction is given for the higher temperature range, which accounts well for the observed frequency and concentration dependences, but only order-of-magnitude absolute agreement is obtained.
Related Papers (5)
Equilibrium carrier mobility in disordered hopping systems
Numerical studies of the AC conductivity of hopping systems. I. Effects of space and energy disorder
Stochastic treatment of AC hopping conduction in disordered systems
Narendra Kumar,Jean Heinrichs +1 more