Unified analytical treatments of the two-parameter Fermi functions using binomial expansion theorem and incomplete gamma functions

This work studies the current status of the theories of kinetic effects and electron transport phenomena in semiconductors and its application to the physics of semiconductors and numerical simulation studies. The studies of two-parameter Fermi functions have played a major role in the development of kinetic effects and electron transport phenomena in semiconductors. Also, this work introduces new approximations for analytical evaluation of the two-parameter Fermi functions. Efficient analytical calculation formulae of the two-parameter Fermi functions are possible for a wide range of its parameters. The accuracy of the obtained formulae have been confirmed by comparison with previously published results. The new approach is seen to be a significant improvement.