A Deterministic approach to noise in a non-equilibrium electron–phonon system based on the Boltzmann equation

A deterministic model for electron velocity fluctuations in a non-equilibrium bulk electron–phonon system is presented. The model is based on the spherical harmonics expansion of the system of the two coupled Boltzmann equations for electrons and phonons. Bulk GaN at 300 K ambient temperature is selected as a model system. The Langevin approach is used for noise calculations, and expressions for the power spectral density of the electron velocity fluctuations are presented in the paper. Convergence behavior of the model is discussed in detail. Results of the developed noise model are verified against a consistent Monte Carlo model, and excellent agreement is obtained in the range of frequencies, where the Monte Carlo method yields reliable results. Introduction of nonequilibrium phonons substantially increases the electron noise temperature at frequencies below 100 GHz.