In an intrinsic semiconductor the energy gap Eg is 1.2eV. Its holemobility is much smaller than electron mobility and independent oftemperature. What is the ratio between conductivity at 600K andthat at 300K? Assume that the temperature dependence of intrinsiccarrier concentration ni is given byni=n0exp(-Eg/2kBT) where n0is a constant.

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Solution

The given temperature dependence of the intrinsic carrier concentration is,

n i = n 0 exp[ − E g 2 K B T ]
Where, K B is the Boltzmann constant and its value is 8.62× 10 −5 eV/K, Tis the temperature and n 0 is constant.

The intrinsic carrier concentration at initial temperature of 300 K is,

n i1 = n 0 exp[ − E g 2 K B 300 ](1)

The intrinsic carrier-concentration at final temperature of 600 K is,

n i2 = n 0 exp[ − E g 2 K B 600 ](1)

The ratio between the conductivities is the ratio of the intrinsic carrier concentrations.

Divide equation (2) by equation to get the ratio of conductivities.

n i2 n i1 = 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 2×8.62× 10 −5 ( 1 600 ) ] =exp[ 1.2× 10 5 10344 ]
Further, solve the above equation.

n i2 n i1 =exp[ 11.6 ] =1.09× 10 5
Thus, the ratio of the conductivities of the semiconductors is 1.09× 10 5 .

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