Step 1: Recall the formula for intrinsic carrier concentration ( ).
The intrinsic carrier concentration in a semiconductor is a function of temperature and the energy bandgap . The standard formula is:
where is a material-specific constant and is the Boltzmann constant.
Step 2: Analyze the temperature dependence.
The formula shows that depends on temperature in two ways: through the term and the exponential term . The exponential term describes the dominant temperature dependence, but the question asks how the concentration *varies with* T, and the pre-exponential factor is a key part of this variation.
Step 3: Compare with the given options.
The options provided are power-law dependencies on . The pre-exponential factor in the expression for is , which matches option (3).