Work function

An electron is held by the forces of electrostatic attraction in a solid body. That is why a certain amount of work must be done to overcome these forces and thus remove the electron from the material.

Let W_a be the minimum energy required to remove an electron from a solid body and place it at rest some distance away from its surface. The work done on the electron to transfer it from the Fermi level to the level W_a is called work function (Fig. 2.5).

Fig.2.5. Work function for: a – intrinsic, d – electronic, c - hole semiconductors

Fig. 2.5. illustrates the work function for intrinsic, electronic, and hole semiconductors. It is obvious that the work function of an acceptor-impurity semiconductor is higher than that for a donor- impurity semiconductor.

The Fermi level is taken as the reference level on purpose. If, for instance, metal electrons that lie on the levels below the Fermi level are cut away then electrons having higher energy will move to take on the vacant lower levels, with the result that the metal will warm up at the expense of the released energy, i.e. part of work will be done on the metal. If electrons whose energy levels lie above the Fermi level are forced to leave the metal, the electrons equilibrium will be upset all the same, in this case electrons that have lower energy will fill a portion of free levels. The metal will grow cool, since a part of work required to transfer electrons into a field –free space will be done at the expense of the internal energy of the metal. The same happens in semiconductors.