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Molecules and Crystals

Problem 6.208

At very low temperatures the photoelectric threshold short wavelength in an impurity-free germanium is equal to \(\lambda_{t h}=1.7 \mu \mathrm{m}\) Find the temperature coefficient of resistance of this germanium sample at room temperature.

Reveal Answer
 6.208. α=1ρ∂ρ∂T=−πcℏkT2λr=−0.05 K−1,where ρ∼eΔE0/2kTΔE0 is the forbidden band width. \begin{aligned} &\text { 6.208. } \alpha=\frac{1}{\rho} \frac{\partial \rho}{\partial T}=-\frac{\pi c \hbar}{k T^{2} \lambda_{r}}=-0.05 \mathrm{~K}^{-1}, \text {where } \rho \sim \mathrm{e}^{\Delta E_{0} / 2 k T}\\ &\Delta E_{0} \text { is the forbidden band width. } \end{aligned}
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