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In an intrinsic semiconductor, the energ...

In an intrinsic semiconductor, the energy gap `E_(g)` of an intrinsic semiconductor is 1.2 eV. Its hole mobility is very much smaller than electron mobility and is indepndent of temperature. What is the ratio between conductivity at 600K and at 300K? Assume that the temperature dependence of intrinsic concentraction `n_(i)` is expressed as,
`n_(i)=n_(o)e^(-E_(g)^(')//k_B)T`, where `n_(o)` is constant and `E_(g)^(')` is an energy equal to `E_(g)//2`,
`k_(B)=8.62xx10^(-6)eVK^(-1)`.

Text Solution

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Here, `E_(g)/(2k)[1/T_(1)-1/T_(2)]=1.2/(2xx8.62xx10^(-5))[1/300-1/600]=11.6`
`n_(600)/n_(300)=e^(E_(g)/(2k)[1/T_(1)-1/T_(2)])=e^(11.6)=(2.718)^(11.6)=1.089xx10^(5)=1.1xx10^(5)`
`sigma_(600)/sigma_(300)=n_(600)/n_(300)=1.1xx10^(5)`
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