Rigorous Thermodynamic Treatment of Heat Generation and Conduction in Semiconductor Device Modeling

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Not only in power electronics but in particular in the field of VLSI and ULSI, the influence of self-heating on the performance of a semiconductor device proves to be more and more crucial as the power density dissipated within the device increases in consequence of enhanced functional integration. Device modeling allows for such self-heating effects by the coupled simulation of both the electrical and thermal device behavior (i.e., besides the carrier densities, temperature has to be included as additional position- and time-dependent state variable). However, up to now only heuristically motivated models of heat flow and generation have been proposed. In this paper, a physically rigorous treatment of the problem is presented. It is based on the laws of phenomenological irreversible thermodynamics (e.g., Onsager's relations and conservation of total energy) and, moreover, it 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 (radiative and nonradiative) recombination 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. Furthermore, 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; it shows 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, in particular, if short switching times (< 10 ns) are attained and high current densities and steep temperature gradients are found.

Original languageEnglish
Pages (from-to)1141-1149
Number of pages9
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number11
StatePublished - Nov 1990
Externally publishedYes


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