A Theoretical Estimate of the Temperature Dependence of Electron Concentration and Lorenz Number in the Spherically Symmetric Zone of Semiconductors

An accurate approach is proposed for the temperature dependence of electron concentration and Lorenz number in the spherically symmetric zone of semiconductors. The evaluation includes more accurate analytical calculations over the study for two parameters of Fermi functions. Recently, a new analytical approach for the calculation of the two parameters of Fermi functions has been reported in terms of summations of binomial coefficients and incomplete gamma functions. The method is applied to the case of the Ge and GaAs semiconductors, which can determine the electron concentration and Lorenz number as a function of temperature variation. The results obtained by the suggested and numerical methods are satisfactory for a wide range of temperatures. The method descriptions are very well for the investigation of other thermoelectric effects over the whole temperature ranges.