Fermi Dirac distribution: an effective alternative approach

The problem of analytical integration involving powers and derivatives of the Fermi function is frequently encountered in many theoretical analyses. To tide over this difficulty, an alternative model for the F.D. distribution function has been proposed. The model is apparently more convenient, because using this model one can now analytically evaluate the integrals much easily, and that too without incurring significant errors in the subsequent results. To assess the extent of validity of the assumed distribution function, the proposed model has been compared with the exact F.D function. The result seems to be satisfactory and motivate us for further analysis of low temperature electron transport in semiconductors using the proposed distribution function. The energy domain is divided into three regions, demarcated on both the sides of the Fermi energy, and the Fermi function is approximated for each regime. (author)