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In an intrinsic semiconductor the energy...

In an intrinsic semiconductor the energy gap `E_(g)` is 1.2 eV. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at 600 K and that at 300 K? Assume that the temerature dependence of intrinsic carrier concentration `n_(i)` is given by
`n_(i)=n_(0)"exp"(-(E_(g))/(2k_(B)T))` where `n_(0)`is a constant.

Text Solution

Verified by Experts

Let `K_(1) "and" K_(2)` be the conductivity of the material at 600 K and 300 K respectively.
`K_(1)/(K_(2))=(n_(1))/n_(2)=(n_(0)e""^(-(E_(g))/(2k_(B)T_(1))))/(n_(0)e"^(-(E_(g))/(2k_(B)T_(2))))=e^((E_(g))/(2k_(B))((1)/(T_(2))-(1)/(T_(1))))`
`["Here",E_(g)/(2k_(B))((1)/T_(2)-(1)/(T_(1)))=(1.2)/(2xx8.6xx10^(-5))((1)/(300)-(1)/(600))]`
=11.6279
`:. (K_(1))/K_(2)=e^(11.6279)=1.12xx10^(5)`
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