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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^(-Delta E//2kT_(1))`
`N_(2)=N_(0)e^(-Delta E//2kT_(2))
the percentage increase as the temperature is raised form `T_(1) to T_(2)`is
`f=(N_(2)-N_(1))/(N_(1))xx100=((N_(2))/(N_(1))-1)xx100`
`100[e^((Delta E)/(2k))((1)/(t_(1))-(1)/T_(2))-1].
Now, `(Delta E)/(2k)((1)/(t_(1))-(1)/T_(2))`
`(0.68eV)/(2xx8.62xx10^(-5)eVK_(-1))((1)/(300K)-(1)/320K))`
`=0.82.`
`Thus,f=100xx[e^(0.82-1]~~127.`
Thus ,the number of charge carries increases by about 127%.
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