Abstract
AbstractFermi integrals arise in the mathematical and numerical modelling of microwave semiconductor devices. In particular, associated Fermi integrals involving two arguments arise in the modelling of HEMTs, in which quantum wells form at the material interfaces. The numerical evaluation of these associated integrals is time consuming. In this paper, these associated integrals are replaced by simpler functions which depend on a small number of optimal parameters. These parameters are found by optimizing a suitable cost function using a genetic algorithm with simulated annealing. A new method is introduced whereby the transition probabilities of the simulated annealing process are based on the Bose–Einstein distribution function, rather than on the more usual Maxwell–Boltzmann statistics or Tsallis statistics. Results are presented for the simulation of a four‐layer HEMT, and show the effect of the approximation for the associated Fermi integrals. A comparison is made of the convergence properties of the three different statistics used in the simulated annealing process. Copyright © 2007 John Wiley & Sons, Ltd.
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