Now consider the electronic structure of this material. Suppose that the large atom 1 contributes two electrons and the smaller atoms 2 and 3 each contribute one electron to a nearly free electron gas. e) Show that this material will be a semiconductor. f) Show that the Fermi wavevector will be equal to the reciprocal unit cell parameter, KF = a*. g) Calculate the density of states g(E) of a one-dimensional free electron gas as a function of energy. Hence sketch g(E) for this material, shading the occupied energy levels and labelling the valence and conduction bands.

Now consider the electronic structure of this material. Suppose that the large atom 1 contributes two electrons and the smaller atoms 2 and 3 each contribute one electron to a nearly free electron gas. e) Show that this material will be a semiconductor. f) Show that the Fermi wavevector will be equal to the reciprocal unit cell parameter, KF = a*. g) Calculate the density of states g(E) of a one-dimensional free electron gas as a function of energy. Hence sketch g(E) for this material, shading the occupied energy levels and labelling the valence and conduction bands.