A fundamental noise limit for biased resistors at low temperatures

Abstract

A biased resistor at low temperature T is modelled by a degenerate Fermi gas whose electrons scatter from phonons in thermal equilibrium and impurities while moving in the presence of a finite electric field E. A nonperturbative solution of the Boltzmann equation valid for thin films yields a Fermi-like steady state distribution characterized by an effective temperature T* (>T). For large fields the energy scale (T*) is set by the energy (eEl*) absorbed in an inelastic mean free path (l*∝T*−3/2). This yields T* proportional to E2/5. At low temperatures and frequencies the Johnson noise temperature is T*, independent of the bath temperature for large fields.