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 (= space-and 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.

No abstract

No abstract

A novel generalized Lagrange multiplier method for functional optimization with inclusion of subsidiary conditions is presented and applied to the optimization of material distributions in thermoelectric converters. Multistaged devices are considered within the same formalism by inclusion of position-dependent electric current in the legs leading to a modified thermoelectric equation. Previous analytical solutions for maximized efficiencies for generators and coolers obtained by Sherman [J. Appl. Phys. 31, 1 (1960)], Snyder [Phys. Rev. B 86, 045202 (2012)], and Seifert et al. [Phys. Status Solidi A 207, 760 (2010)] by a method of local optimization of reduced efficiencies are recovered by independent proof. The outstanding maximization problems for generated electric power and cooling power can be solved swiftly numerically by solution of a differential equation-system obtained within the new formalism. As far as suitable materials are available, the inhomogeneous TE converters can have increased performance by use of purely temperature-dependent material properties in the thermoelectric legs or by use of purely spatial variation of material properties or by a combination of both. It turns out that the optimization domain is larger for the second kind of device which can, thus, outperform the first kind of device.