Question

Explain carefully what is meant by effective mass in the context of semiconductor physics. The energy band dispersion relation (E vs. k) for a simple one-dimensional monatomic semiconductor of lattice constant a can be written-

? = ?₀ [1 − cos(??)]

Derive an expression for the effective mass (m*) of an electron in the semiconductor, and sketch how m* varies as a function of k.

Answer 1

The effective mass of a semiconductor is obtained by fitting the actual E-k diagram around the conduction band minimum or the valence band maximum by a parabola. While this concept is simple enough the issue turns out to be substancially more complex due to the multitude and the occasional anisotropy of the minima and maxima. In this section we first describe the different relevant band minima and maxima, present the numeric values for germanium, silicon and gallium arsenide and introduce the effective mass for density of states calculations and the effective mass for conductivity calculations.

The electrons in a crystal are not free, but instead interact with the periodic potential of the lattice. In applying the usual equations of electrodynamics to charge carriers in a solid, we must use altered values of particle mass. We named it Effective Mass.