4.7 Assume the Boltzmann approximation in a semiconductor is valid. Determine the ratio of \( n(E)=g_{C}(E) f_{F}(E) \) at \( E=E_{c}+4 k T \) to that at \( E=E_{c}+k T / 2 \).
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The density of states in the conduction band, \( g_C(E) \), is typically proportional to \( \sqrt{E - E_c} \). The Fermi-Dirac distribution under the Boltzmann approximation is \( f_F(E) \approx e^{-(E - E_F) / kT} \). Show more…
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Assume the Boltzmann approximation in a semiconductor is valid. Determine the ratio of $n(E)=g c(E) f_{F}(E)$ at $E=E_{c}+4 k T$ to that at $E=E_{c}+k T / 2$.
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