Some evidence for the validity of the noise-temperature inequalityθ ≥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 temperatureθ. In equilibrium the external fieldF=0, and the fluctuation-dissipation theorem gives θ= T, the temperature. In a strong fieldF the Boltzmann equation in the constant relaxation approximation is used to calculate the driftu(F, T) the diffusion constantD(F, T), and the noise temperatureθ(F, T) for piecewise linear one-dimensional band structuresE(k). The validity of the noise inequalityθ ≥T has been shown for a large variety of band parameters and for all fields and temperatures.