Problem 4 (25 points) The band gap energy for silicon and germanium are: Silicon: E_g = 1.12 eV Germanium: E_g = 0.66 eV (a) Estimate the ratio of the number of electrons in the conduction bands of germanium and silicon at a temperature of 400 K. Assume the Fermi energy is at the center of the gap. (b) Electrons in the conduction band that fall back into the valence band will cause the semiconductor to emit light. For germanium and silicon, what is the wavelength of the light emitted? (c) In what region of the electromagnetic spectrum is the emitted light? (can we see it?)
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617 \times 10^{-5} \, \text{eV/K} \)), and \( T \) is the temperature in Kelvin. Show more…
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Estimate the ratio of the number of electrons in the conduction bands of germanium $\left(E_{g}=0.66 \mathrm{eV}\right)$ and silicon $\left(E_{g}=1.12 \mathrm{eV}\right)$ at a temperature of $400 \mathrm{K}$. Assume that the Fermi energy is at the center of the gap.
Estimate the ratio of the number of electrons in the conduction bands of germanium $\left(E_{\mathrm{g}}=0.66 \mathrm{eV}\right)$ and silicon $\left(E_{\mathrm{g}}=1.12 \mathrm{eV}\right)$ at a temperature of $400 \mathrm{~K}$. Assume the Fermi energy is at the center of the gap.
Pure germanium has a band gap of 0.67 ev. The Fermienergy is in the middle of the gap. (a) For temperatures of 250 $\mathrm{K}$ ,$300 \mathrm{K},$ and 350 $\mathrm{K}$ , calculate the probability $f(E)$ that a state at the bottom of the conduction band is occupied. (b) For each temperature in part (a), calculate the probability that a state at the top of the valence band is empty.
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