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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 600K and that at 300K? Assume that the temperature dependence of intrinsic carrier concentration n_{i}is given by

`"n"_"i" = "n"_0 exp(- "E"_"g"/(2"k"_"BT"))`

where n_{0 }is a constant.

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#### Solution

Energy gap of the given intrinsic semiconductor, E_{g} = 1.2 eV

The temperature dependence of the intrinsic carrier-concentration is written as:

`"n"_"i" = "n"_0 exp [- "E"/(2"k"_"BT")]`

Where,

k_{B} = Boltzmann constant = 8.62 × 10^{−5} eV/K

T = Temperature

n_{0} = Constant

Initial temperature, T_{1} = 300 K

The intrinsic carrier-concentration at this temperature can be written as:

`"n"_("i"1) = "n"_0 exp[- "E"_"g"/(2"k"_"B" xx 300)]` ....(1)

Final temperature, T_{2} = 600 K

The intrinsic carrier-concentration at this temperature can be written as:

`"n"_("i"2) = "n"_0 exp[- "E"_"g"/(2"k"_"B" xx 600)]` ....(2)

The ratio between the conductivities at 600 K and at 300 K is equal to the ratio between the respective intrinsic carrier-concentrations at these temperatures.

`"n"_("i"2)/"n"_("i"1) = ("n"_0 exp [- "E"_"g"/(2"k"_"B" 600)])/["n"_0 exp ["E"_"g"/(2"k"_"B" 300)]]`

`= exp "E"_"g"/(2"k"_"B") [1/300 - 1/600] = exp [1.2/(2xx 8.62 xx 20^(-5)) xx (2-1)/600]`

`= exp[11.6] = 1.09 xx 10^5`

Therefore, the ratio between the conductivities is 1.09 × 10^{5}.

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