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An intrinsic semiconductor with mass of a hole mh, and mass of an electron me is at a finite temperature T. If the top of the valence band energy is Ev and the bottom of the conduction band energy is Ec, the Fermi energy of the semiconductor is

An intrinsic semiconductor with mass of a hole mh, and mass of an electron me is at a finite temperature T. If the top of the valence band energy is Ev and the bottom of the conduction band energy is Ec, the Fermi energy of the semiconductor is Correct Answer $${E_F} = \left( {\frac{{{E_v} + {E_c}}}{2}} \right) + \frac{3}{4}{k_B}T\ln \left( {\frac{{{m_h}}}{{{m_e}}}} \right)$$

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