Exciton Ground State in Zincblende-Type Semiconductors

We are now interested in the following problem: Let us consider the ground state of an ideal direct gap semiconductor at low temperature, i.e. at T = 0 K, containing N electrons. As indicated in Fig. 2.2 the semiconductor is characterized by the presence of an energy gap between the lowest lying conduction band (noted “c”) and the uppermost valence band (noted “v”). In addition the semiconductor is supposed to possess only one conduction and one valence band and the states are defined by spin-orbitals. The N electrons occupy all electronic valence-band states and all conduction-band states are unoccupied. This system shows no electric conductivity (or it behaves as an insulator) since, when applying a small electric field to it, no electric current can flow. The sample can be polarized by the field but no free electric charges can move in the material. This situation characterizes the crystal-ground state whose energy and charge distribution is supposed to be known.