The conductivity of an intrinsic semiconductor depends on temperature as`(sigma)=(sigma_0)e^(-Delta E//2kT),`where `(sigma_0)`is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T=300 K .Assume that the gap for germanium is 0.650 eV and remains constant as the temperature is increased.

Explanation

Since `sigma = sigma_(0e)^((-DeltaE)/(2KT))`
Given `Delta E = 0.650eV,T = 300K`
`K = 8.62xx10^(-5)eV
according to question ,
sigma_0 sigma_(0e)^((-DeltaE)/(2KT)) = 2xxsigma_(0)e^((-DeltaE)/(2 xx K xx 300)`
`(0.650)/(2xx8.62xx10^(-5)xxT) = (-0.650)/(2xx8.62xx10^(-5)xx300)`
`(-0.650)/(2xx8.62xx10^(-5)xxT) = 6.96561xx10^(-6)`
Toking 'in'on both sides.
`We get, `(-0.650)/(2xx8.62xx10^(-5)xxT`) = -11.874525`
`rArr (1)/(T`) = (11.874525xx2xx8.62xx10^(-5))/(0.65)`
`rArr T = 317.51178 = 318K`