Materials Science and Engineering: An Introduction

Published by Wiley
ISBN 10: 1118324579
ISBN 13: 978-1-11832-457-8

Chapter 18 - Electrical Properties - Questions and Problems - Page 781: 18.33

Answer

$σ = 94.63 (Ω-m)^{-1}$

Work Step by Step

Given: At temperatures near room temperature, the temperature dependence of the conductivity for intrinsic germanium is found to be given by $σ = CT^{-3/2} e^{(-\frac{E_{g}}{2kT})}$, where C is a temperature-independent constant and T is in Kelvins. Required: Using Equation 18.36, calculate the intrinsic electrical conductivity of germanium at 175°C Solution: Using Equation 18.36 and values from Table 18.3 as well as room temperature (298 K), conductivity ($2.2 (Ω-m)^{-1}$, and $E_{g} = 0.67 eV$, we compute the value of $C$: $ln σ = ln C (-3/2) ln T (-\frac{E_{g}}{2kT})$ $ln C = ln σ + (3/2)ln T + \frac{E_{g}}{2kT} = ln (2.2) + (3/2)ln (298) + \frac{0.67 eV}{2(8.62 \times 10^{-5} eV/K)(298 K)} = 22.38 $ Computing the conductivity at 175°C (448 K): $ln σ = ln C (-3/2) ln T (-\frac{E_{g}}{2kT}) = (22.38) -(3/2) ln (448 K) -(\frac{0.67 eV}{2(8.62 \times 10^{-5} eV/K)(448 K)}) = 4.55 $ $σ = e^{4.55} = 94.63 (Ω-m)^{-1}$
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