Explain temperature dependence of electrical resistivity and conductivity in semiconductors.
The electrical conductivity of the semiconductors changes considerably with temperature changes. At absolute zero, this behaves as an insulator. And at room temperature, due to thermal energy, several of the covalent bonds of the semiconductor break. The breaking of bonds sets those electrons free that are engaged in the formation of such bonds. It results in few free electrons. All these electrons constitute a small current if potential is applied across the semiconductor crystal. It demonstrates the conductivity for intrinsic semiconductor increases along with increase in temperature as specified by η=A exp(-Eg/2kT), here η is the carrier concentration, T is the temperature, Eg is the energy band gap and A is constant. If in extrinsic semiconductors, addition of small amount of impurities creates a large number of charge carriers. That number is so large that the conductivity of an extrinsic semiconductor is a lot of times more than an intrinsic semiconductor at the room temperature. In n-type semiconductor each donor has donated their free electrons at room temperature. The additional thermal energy only serves to raise the thermally generated carriers. It increases the minority carrier concentration. A temperature is reached while the number of covalent bonds which are broken is so large which the number of holes is almost equal to the number of electrons. After that the extrinsic semiconductor behaves as intrinsic semiconductor.