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The conductivity of a pure semiconductor...

The conductivity of a pure semiconductor is roughly proportional to `T^3/2 e^(-Delta E//2kT)where `(Delta)E`is the band gap.The band gap for germanium is 0.74eV at 4K and 0.67eV at 300K.By what factor does the conductivity of pure germanium increase as the temperature is raised form 4K to 300K?

Text Solution

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Here `delta = T(3//2) e^(-DeltaE//2KT)`
`:. (sigma_2)/(sigma_1) = (T_2/T_1)^(3//2) (e^(-DeltaE_(2)//2KT_(2))/(e^(-DeltaE_(1)//2KT_1))`
`= (300/4)^(3//2) (e^(-0.67//(2 xx 8.62 xx 10^(-5) xx 300))/(e^(-0.74//(2 xx 8.62 xx 10^(-5) xx 4)`
`= 10^(463)`
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