Solutions to the Fermi-Dirac Integrals in Semiconductor Physics Using Polylogarithms

The value of polylogarithms for calculating Fermi-Dirac integrals has been recognized in the field of statistical physics. However, its value has not become widely recognized in condensed matter physics or semiconductor device modeling. The utility of the polylogarithms is that they are built into standard computer mathematical packages so that neither approximations nor numerical integrations of Fermi-Dirac integrals are necessary. The direct relationship between Fermi-Dirac integrals and polylogarithms is reviewed and several examples of Fermi-Dirac integrals in semiconductor physics are discussed.