Correct Answer - Option 2 : Increases exponentially with temperature
Analysis:
The formula for the conductivity (σ) of a pure semi-conductor is given by:
\(\sigma = {n_i}q\left( {{\mu _n} + {\mu _p}} \right)\) ---(1)
Where,
q is the charge on the moving particle
ni is intrinsic carrier density
μn is electron mobility
μp is hole mobility
The intrinsic carrier concentration is given by:
\( {n_i} = A{T^{3/2\;}}{e^{ - \left( {\frac{{{E_{Go}}}}{{2KT}}} \right)}}\)
EG0 = Energy Bandgap of the semiconductor.
Equation (1) can now be written as:
\( {\rm{\sigma }} = \left( {{{\rm{\mu }}_n} + {{\rm{\mu }}_p}} \right){{\rm{n}}_i}qA\;{T^{3/2\;}}{e^{ - \left( {\frac{{{E_{Go}}}}{{2KT}}} \right)}}\)
From the above, we observe that the conductivity is exponentially related to the temperature, and with an increase in temperature, the denominator of the exponential term will increase, resulting in increasing the negative exponential value. This will eventually increase the conductivity of the semiconductor.
