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

The influence of self-heating by power dissipation on the operation of semiconductor devices proves to be important not only in the area of power electronics, but also for VLSI devices. Hence, besides the carrier densities (or quasi-Fermi potentials, alternatively), temperature has to be included as additional dynamic state variable in the simulation of the electric and thermal behavior of such devices. However, up to now only heuristically introduced heat generation terms have been proposed as source in the heat conduction equation. It is the scope of this paper to present a physically rigorous extension of the 'classical' (= isothermal) device equations to the case of variable (= spaceand time-dependent) temperature which is based on the principles of irreversible thermodynamics (e.g., Onsager's relations and conservation of total energy) and, moreover, which is consistent with the models usually considered within the framework of the widely accepted isothermal drift-diffusion approximation. It turns out in the present theory that the heat sources can intuitively be interpreted as sum of the Joule heat and Thomson heat of both the electrons and the holes plus a term accounting for carrier recombination. A critical comparison with previous work is made; it shows that, in the steady-state, some of the heuristic models for heat generation, thermal conductivity and heat capacity could indeed approximate the correct results within an error bound of 1...10Z. In the transient regime, however, none of the models used hitherto proves to be applicable, in particular, if short pulse rise times of (< 10 ns) are attained.