Some evidence for the validity of the noise-temperature inequality θ ≥T in the relaxation approximation of the one-dimensional electron transport problem in high electric fields

The conjecture that "noise" is always smallest in an equilibrium system is made quantitative for a transport problem by identifying "noise" with the noise temperature θ. In equilibrium the external field F=0, and the fluctuation-dissipation theorem gives θ= T, the temperature. In a strong field F the Boltzmann equation in the constant relaxation approximation is used to calculate the drift u(F, T) the diffusion constant D(F, T), and the noise temperature θ(F, T) for piecewise linear one-dimensional band structures E(k). The validity of the noise inequality θ ≥T has been shown for a large variety of band parameters and for all fields and temperatures. © 1974 Plenum Publishing Corporation.