Boltzmann Transport Equation for Degenerate Electron Gas in Semiconductor in the Presence of Electric Field

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Date

2022-02-06

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Addis Ababa University

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.

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Keywords

Boltzmann Transport, Equation for Degenerate, Electron Gas, Semiconductor, Presence of Electric Field

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