Explain the variation of carrier concentration with temperature in an extrinsic semiconductor

In an extrinsic semiconductor, the carrier concentration varies with temperature in a specific way. Here's a step-by-step explanation:

1. Low Temperature Regime: At very low temperatures, the thermal energy is not sufficient to excite the electrons from the donor or acceptor levels to the conduction band. Therefore, the number of free carriers is very low, and the semiconductor behaves like an insulator.

2. Intermediate Temperature Regime: As the temperature increases, thermal energy becomes sufficient to excite the electrons from the donor levels to the conduction band (in n-type) or from the valence band to the acceptor levels (in p-type). This leads to an increase in the number of free carriers, and the semiconductor starts to conduct. The carrier concentration increases with temperature in this regime.

3. High Temperature Regime: At even higher temperatures, the intrinsic carrier concentration (i.e., the number of electron-hole pairs generated by thermal excitation across the band gap) starts to become significant. This intrinsic carrier concentration increases exponentially with temperature. Therefore, at high temperatures, the carrier concentration in an extrinsic semiconductor is dominated by the intrinsic carriers, and it increases rapidly with temperature.

4. Very High Temperature Regime: At very high temperatures, the semiconductor becomes intrinsic, as the number of thermally generated electron-hole pairs far exceeds the number of doped impurity atoms. The carrier concentration is now independent of the doping level and depends only on the temperature.

In summary, the carrier concentration in an extrinsic semiconductor initially increases with temperature, then increases rapidly, and finally becomes independent of the doping level at very high temperatures.