Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling

A treatment of the self-heating problem is presented. It is based on the laws of phenomenological irreversible thermodynamics (e.g. Onsager´s relations and conservation of total energy) and is also consistent with the physical models usually considered in the isothermal drift diffusion approximation. The classical isothermal device equations are extended and completed by a generalized heat-conduction equation involving heat sources and sinks which, besides Joule and Thomson heat, reflect the energy exchanged through recombination (radiative and nonradiative) and optical generation. Thus the extended model also applies to direct semiconductors (e.g., optoelectronic devices) and accounts for effects caused by the ambient light intensity. It fully allows for low temperature since the case of incomplete ionization of donors and acceptors (impurity freeze-out) is properly incorporated in the theory. A critical comparison with previous work is made, showing that, in the steady state, some of the heuristic models of heat generation, thermal conductivity, and heat capacity could indeed approximate the correct results within an error bound of 1-10%. In the transient regime, however, none of the models used previously seems to be reliable, particularly, if short switching times (<10 ns) are attained and high current densities and steep temperature gradients are found