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
A. $${E_F} = \left( {\frac{{{E_v} + {E_c}}}{2}} \right) - \frac{3}{4}{k_B}T\ln \left( {\frac{{{m_h}}}{{{m_e}}}} \right)$$
B. $${E_F} = \left( {\frac{{{k_B}T}}{2}} \right) + \frac{3}{4}\left( {{E_v} + {E_c}} \right)\ln \left( {\frac{{{m_h}}}{{{m_e}}}} \right)$$
C. $${E_F} = \left( {\frac{{{E_v} + {E_c}}}{2}} \right) + \frac{3}{4}{k_B}T\ln \left( {\frac{{{m_h}}}{{{m_e}}}} \right)$$
D. $${E_F} = \left( {\frac{{{k_B}T}}{2}} \right) - \frac{3}{4}\left( {{E_v} + {E_c}} \right)\ln \left( {\frac{{{m_h}}}{{{m_e}}}} \right)$$
Answer: Option C
This Question Belongs to Engineering Physics >> Solid State Physics
The valence electrons do not directly determine the following property of a metal
A. electrical conductivity
B. thermal conductivity
C. shear modulus
D. metallic lustre
A. $${\left( {\frac{{2Q}}{P}} \right)^{ - 6}}$$
B. $${\left( {\frac{Q}{P}} \right)^{ - 6}}$$
C. $${\left( {\frac{P}{{2Q}}} \right)^{ - 6}}$$
D. $${\left( {\frac{P}{Q}} \right)^{ - 6}}$$
A. $$N\mu \coth \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$
B. $$N\mu \tanh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$
C. $$N\mu \sinh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$
D. $$N\mu \cosh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$
A. $$\sqrt {2C\left( {\frac{1}{{{M_1}}} + \frac{1}{{{M_2}}}} \right)} $$
B. $$\sqrt {C\left( {\frac{1}{{2{M_1}}} + \frac{1}{{{M_2}}}} \right)} $$
C. $$\sqrt {C\left( {\frac{1}{{{M_1}}} + \frac{1}{{2{M_2}}}} \right)} $$
D. zero
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