### Abstract:

The effect created by the applied electric field and temperature gradient on the electrons in a
semiconductor is to change the distribution function of electrons from its equilibrium condition.
In the absence of external fields, the distribution of electrons in a semiconductor under equilibrium
conditions may described by the Fermi-Dirac distribution function. Thus, this effects created by
applied electric field as well as the temperature gradient on electron transport in a n-type Silicon
were discussed in this project. The Boltzmann transport equation was solved by applying the
relaxation time approximation method in the presence of electric field to obtain a general expression
for Fermi-Dirac distribution function for the degenerate electron gas in doped semiconductor
material. Employing the results of solved Boltzmann transport equation, the expression was derived
for electron mobility and electron conductivity. The results of the study were described in
numerically, graphically and qualitatively. In the integral equation of electron concentration n,
it is difficult to evaluate because the normalized Fermi energy EF is unknown. Thus, by using
iteration method for a given arbitrary value, the integral equation was evaluated mathematically
using a Mathematica 5.1 software program and the results we got were in agreement with those in
the literature. From the numerical computation we observed that; the Fermi energy increases exponentially
with increasing electron concentration, conductivity increases linearly with increasing
electron density and mobility decreases with the dopant density.