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