How a free electron is generated in a semiconductor Why the

How a free electron is generated in a semiconductor? Why the number of free electrons and holes are not always the same?

Solution

At low temperatures the electrons are bound in their respective positions in the crystal; consequently, they are not available for electrical conduction. At higher temperatures thermal vibration may break some of the covalent bonds. The breaking of a bond yields a free electron that can participate in current conduction. Once an electron moves away from a covalent bond, there is an electron deficiency in that bond. This deficiency may be filled by one of the neighbouring electrons, which results in a shift of the deficiency location from one site to another. This deficiency may thus be regarded as a particle similar to an electron. This fictitious particle, dubbed a hole, carries a positive charge and moves, under the influence of an applied electric field, in a direction opposite to that of an electron.

  

In a semiconductor the mobility of electrons (referring to ‘conduction electrons’ or ‘free-electrons’) is greater than that of a holes (indirectly referring to ‘valence electrons’) because of different band structure and scattering mechanisms of these two carrier types.

Conduction electrons (free-electrons) travel in the conduction band and valence electrons (holes) travel in the valence band. In an applied electric field, valence electrons cannot move as freely as the free electrons because their movement is restricted. The mobility of a particle in a semiconductor is larger if its effective mass is smaller and the time between scattering events is larger.

Holes are created by the elevation of electrons from innermost shells to higher shells or shells with higher energy levels. Since holes are subjected to the stronger atomic force pulled by the nucleus than the electrons residing in the higher shells or farther shells, holes have a lower mobility.