Energy loss from hot electrons in a metal film

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Abstract
In this paper we discuss the energy-loss rate from electrons in a metal film heated by an applied electric field. The acoustic-phonon spectrum in the film has been described by a confined three-dimensional phonon density of states that takes into account the finite thickness of the film. The relationships between the energy-loss rate, the electric field, and the electron temperature are shown to depend on the acoustic coupling strength between the film and the underlying substrate. In agreement with previous analysis, with perfect acoustic coupling the electron temperature and electric field are related by a power law that depends on the phonon dimensionality. However, when the acoustic coupling is less than perfect significant departures from the power-law relationship are found.