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Question

In an intrinsic semiconductor the energy gap Eg 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 temperature dependence of intrinsic carrier concentration ni is given by
ni=noexp(Eg2kBT)
Where n0 is a constant.

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Solution

Given,
Energy gap in a semiconductor, Eg=1.2eV
For a temperature-dependent intrinsic semiconductor:

ni=n0exp(Eg2kBT)

Simplifying the equation:

Eg2k[1T11T2]

1.22×8.62×105[13001600]=11.59

Therefore,

ni1ni2=1.2eVe2×kB×6001.2eVe2×kB×300

=e1.2eV2×kB(13001600)

=e1.2×1.6×10192×1.381×1023×600

ni1ni2=e11.59=1.072×105

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