Correlation functions and electronic noise in doped semiconductors

We present an original Monte Carlo study of correlation functions for the general case of a doped semiconductor under the influence of an electric field of arbitrary strength. Number, velocity, and energy of the carriers are taken as relevant variables. These lead to a set of 25 correlation functions that, for the case of a cubic semiconductor and an electric field in the 〈100〉 direction as investigated in this paper, reduce to 11 nonvanishing functions. By using an analytical model based on coupled Langevin equations together with the results of the Monte Carlo simulations, we have quantitatively analyzed the different coupling processes as functions of the electric field. The simulations are performed for lightly doped p-type Si at 77 K. We demonstrate that even at equilibrium the coupling between energy relaxation and generation-recombination processes can lead to a strongly nonexponential decay of the corresponding correlation functions. At higher fields, we find the interesting result of a transition from two real relaxation rates for energy and longitudinal velocity to a pair of complex-conjugate values, which indicates some kind of ordering in the system driven by the electric field. At the highest fields, this ordering disappears and the rates again become real. The theory so developed is shown to provide a rigorous scheme for a microscopic interpretation of noise-spectroscopy measurement.