Premium
Integral evaluation in semiconductor device modelling using simulated annealing with Bose–Einstein statistics
Author(s) -
Cole E.A.B.
Publication year - 2007
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.649
Subject(s) - statistical physics , simulated annealing , fermi gamma ray space telescope , distribution function , fermi–dirac statistics , physics , mathematics , quantum mechanics , computer science , mathematical optimization , electron
Fermi 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.