Which graph shows correctly the temperature (T) dependence of resistivity ( ) of a semiconductor?

Step-by-step solution

The resistivity of a semiconductor varies with temperature according to the relation = ₀ e^ E_g / (2k_B T) , where ₀ is a constant, E_g is the band gap energy, k_B is Boltzmann’s constant, and T is the absolute temperature. As T increases, the exponential term e^ E_g / (2k_B T) decreases, leading to a reduction in . This follows from increased thermal excitation of charge carriers across the band gap, enhancing conductivity. Since resistivity is the reciprocal of conductivity, it declines with rising temperature. G