give the equation for current density in form of fermi dirac distribution function and graph it

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Physics

give the equation for current density in form of fermi diracdistribution function and graph it

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To evaluate the current density we must specify how thescattering solutions are statistically weighted Let usfollow through the derivation of the electron density in aspatially uniform threedimensional semiconductor in equilibrium tocalculate the current density We approximate the conduction bandstructure by a simple parabolic dispersion relationwhere is the wavevector The probability that each state will be occupied by an electron is given by the FermiDiracdistribution functionwhere is the Fermi level or chemical potential and T being the absolute temperature To avoid confusion with thetransmission probability which is also denoted by T the absolutetemperature will always be shown multiplied by Boltzmanns constant Let us now make anassumption that the semiconductor crystal is acube with each side of length L and apply periodic boundaryconditions Then the stationary quantum states are plane wavesnormalized to unit amplitude of the formDue to the periodic boundary conditions must assume discrete valueswhere and are integers The total number See Answer

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