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.

Explanation

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%`