Question

Discuss the main differences of direct gap and indirect gap semi-conductors.

Answer 1

A direct band gap occurs when the valence band maximum (VBM) and the conduction band minimum (CBM) are at the same k point., generally at the Gamma point.

We have an indirect band gap when the VBM and the CBM are at two different k points.

The above definitions are for the optical band gaps, They are sometimes called fundamental (smallest) gaps, even though there exists another definition of the "fundamental" gap that involves difference of energies for the system with (N-1), N, and (N+1) particle (electrons).

Generally, the VBM is at the Gamma point. Depending on the materials (i.e., crystal symmetry), the CBM can be found at the X, L or other high symmetry points.

As the lattice constant INCREASES (i.e., effect of increasing temperature), the direct band gaps of semiconductors generally DECREASES (at the gamma point).

However, as the lattice constant INCREASES, some indirect gaps are found to INCREASE (a bit) in many materials [even though the direct gap at Gamma, that is not the optical gap for indirect gap materials [as it is larger than the indirect gap] DECREASES as the lattice constant increases.