How does the receptivity of (i) a conductor and (ii) a semiconductor vary with temperature? Give reason for each case.

It must be resistivity not receptivity.

1.

Resistivity of a conductor increases with increases in temperature.

Reason: Increase in temperature lets the kernels of the conductor vibrate and also there occurs thermal vibration in the molecules, these decreases the mean free path of the electrons inside the conductor. Increase in mean free path decreases the relaxation time for the electron. Now as because resistivity of a conductor is inversely proportional to the relaxation time (τ) the resistivity increases with temperature.

ρ = 2m_e/(ne²τ)

=> ρ α 1/τ

2.

Resistivity of a semiconductor decreases with temperature.

Conductivity of a material is determined by two factors: the concentration of free carriers available to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and carrier concentration are temperature dependent.

At absolute zero temperature any semiconductor (Si or Ge) behaves as an insulator. Some electron-hole pairs may get generated due to thermal energy at room temperature (300 K). At higher temperature, more electron-hole pairs are generated. The concentration of charge carriers will be higher at higher temperature. Thus, the conductivity of intrinsic semiconductor increases with increasing temperature and the resistivity decreases with increase in the temperature.