Question

(iii) A consequence of the Free Electron approach is that the electron mass me effectively becomes a variable, the so-called effective mass, me * , which is governed by the curvature of the Ek vs. k function. Show that where the curvature of this function is large the effective mass is small. [4 marks]

(iv) It is often found that some ‘useful’ semiconductors such as silicon or gallium arsenide have bands which show a high degree of curvature, whereas many insulators do not. Discuss how this influences the properties of each type of material.

Answer 1

Effective mass expression can be derived by differentiating twice kinetic energy expression and further analysed as follows