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The band gap in germanium is (Delta E=0....

The band gap in germanium is `(Delta E=0.68eV.)`.Assuming that the number of hole-electron pairs is proportional to `e^(-Delta E//2kT),find the percentage increase in the number of charge carries in pure germanium as the temperature is increased form 300K to 320K.

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The number of charge carries in an intrinsic semiconductor is double the number of hole-electron pairs if `N_(1)` be the number of charge carries at temperature `T_(1)` and `N_(2)` at `T_(2)`, we have
`N_(1)=N_(0)e^(-DeltaE//2kT_(1))`
and `N_(2)=N_(0)e^(-DeltaE//2kT_(2))`
The percentage increase as the temperature is raised from `T_(1)` to `T_(2)` is
`f=(N_(2)-N_(1))/(N_(1))xx100=((N_(2))/(N_(1))-1)xx100=100[e^((DeltaE)/(2k)((1)/(T_(1))-(1)/(T_(2)))),-1]`
Now `(DeltaE)/(2k)((1)/(T_(1))-(1)/(T_(2)))=(0.68eV)/(2xx8.62xx10^(-5)eV//K)((1)/(300K)-(1)/(320K))=0.82`
Thus, the number of charge carries increase by about `127%`
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RESONANCE ENGLISH-SEMICONDUCTORS-Exercise 3
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