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 $
$σ = e^{4.55} = 94.63 (Ω-m)^{-1}$