For a certain semiconductor, the densities of states in the conduction and valence bands . are: D(E)= A (E-E) · u(E - Ec) and Dv(E) = B · (E-E) · u(E-E), respectively. u(x), the unit step function, is defined as u(x) = 0 if x < 0 and u(x) = 1 if x > 0. Assume nondegeneracy, i.e. not too highly doped. You may find this fact useful: √xe* dx = 1 (a) Derive expressions for electron and hole concentrations as functions of the Fermi energy, EF. (b) If A = 2B, compute the intrinsic Fermi energy at 300 K.

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For a certain semiconductor, the densities of states in the conduction and valence bands
are: D(E)= A· (E – E) · u(E – E) and D₂(E) = B · (Ev - E) · u(E-E), respectively.
u(x), the unit step function, is defined as u(x) = 0 if x < 0 and u(x) = 1 if x > 0. Assume
nondegeneracy, i.e. not too highly doped. You may find this fact useful:
√xe* dx
=
1
(a) Derive expressions for electron and hole concentrations as functions of the Fermi
energy, EF.
(b) If A = 2B, compute the intrinsic Fermi energy at 300 K.
Transcribed Image Text:For a certain semiconductor, the densities of states in the conduction and valence bands are: D(E)= A· (E – E) · u(E – E) and D₂(E) = B · (Ev - E) · u(E-E), respectively. u(x), the unit step function, is defined as u(x) = 0 if x < 0 and u(x) = 1 if x > 0. Assume nondegeneracy, i.e. not too highly doped. You may find this fact useful: √xe* dx = 1 (a) Derive expressions for electron and hole concentrations as functions of the Fermi energy, EF. (b) If A = 2B, compute the intrinsic Fermi energy at 300 K.
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