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Semiconductors and Semiconductor Devices — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsSemiconductors and Semiconductor Devices5 Marks
Question
The conductivity of an intrinsic samiconductor depends on temperature as $\sigma=\sigma_0\text{ e}^{\frac{-\Delta\text{E}}{2\text{kT}}}$ where $\sigma_0$ is a constant. Find the temperature at which the conductivity pf an intrinsic germanium semiconductor will be double of its value at T = 300K. Assume that the gap for germanium is 0.650eV and remains constant as the temperature is increased.
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Answer

$\sigma=\sigma_0\text{e}^{\frac{-\Delta\text{E}}{2\text{KT}}}$
$\Delta\text{E}=0.650\text{eV},\text{T}=300\text{K}$
According to question, $\text{K}=8.62\times10^{-5}\text{eV}$
$\sigma_0\text{e}^{\frac{-\Delta\text{E}}{2\text{KT}}}=2\times\sigma_0\text{e}^{\frac{-\Delta\text{E}}{2\times\text{K}\times300}}$
$\Rightarrow\text{e}^{\frac{-0.65}{2\times8.62\times10^{-5}\times\text{T}}}=6.96561\times10^{-5}$
Taking in on both sides,
We get, $\frac{-0.65}{2\times8.62\times10^{-5}\times\text{T}'}=-11.874525$
$\rightarrow\frac{1}{\text{T}'}=\frac{11.574525\times2\times8.62\times10^{-5}}{0.65}$
$\Rightarrow\text{T}'=317.51178=318\text{K}.$

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