Modelling thermal effects in energy models of carrier transport in semiconductors

Energy transport models of carrier behaviour in semiconductors are based on equations of carrier momentum and carrier energy conservation. Some terms of the modelling equations describe momentum and energy transfers between carriers and the lattice during scattering. The authors demonstrate how empirical parameters can quantify the inter-band scattering components of energy transport models for the Shockley-Hall-Read, band-to-band, impact ionisation and optical recombination and generation mechanisms. An evaluation of the empirical parameters is presented for Shockley-Hall-Read recombination and generation. Further, energy transfer is considered from the point of view of the lattice, and it is shown that a lattice energy conservation equation, which describes thermal effects in semiconductors, can easily be appended to the energy transport modelling equations. The explicit consideration, in energy transport models, of carrier energy gain from the electric field and carrier energy loss due to scattering leads to a more accurate thermal model than is possible with drift-diffusion transport models appended with a lattice heat flow equation incorporating a Joule-type heating term.