Correlation functions of hot electrons in semiconductors

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Abstract
We present a general theory of the correlation functions for a steady state which is valid for arbitrary strengths of an applied electric field, as obtained in high-field transport in semiconductors. When limiting to the first two moments of the distribution function, we find a closed set of equations coupling energy and velocity which are amenable to an analytical solution. Thus, the theory provides an interpolation formula which gives smooth, analytical expressions for the correlation functions. These expressions can be made to fit the computer simulation by using these simulations to estimate the various parameters. The theory is found to be in excellent agreement with numerical calculations for a simple model semiconductor performed with an ensemble Monte Carlo technique.