Energy Conservation in Collisional Broadening

Electron-phonon coupling is central to semiconductor transport simulation. It is often treated in the simple Fermi’s Golden Rule formulation, but even at modest fields, such as those commonly present in modern semiconductor devices, finite state lifetime effects become important. Such effects are treated formally by including self-energy in the scattering formulation [

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,

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]. In order to make the problem more tractable, especially for efficient Monte Carlo simulation, various simplifying assumptions are made. The most common form is to assume a Lorentzian distribution. This assumption is well justified by perturbation theory, and is simple to calculate and implement. In the limit of infinite state life-time, it collapses to the energy-conserving delta function of the Fermi’s Golden Rule. On the other hand, when non-zero broadening is present, energy is no longer conserved, and this has been noted in some cases to lead to accumulated broadening [

3

]. Such accumulation of energy can lead to non-physical results and push the electron energy distribution into the hot electron regime. Our goal is to explore the reasons for this accumulation of energy and propose remedies which can be implemented in standard simulation tools.