The computed of a hypothetical cubic semiconductor shows two features
PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Dielectric and optical properties of solids · Dielectric and optical properties of solids
Solid State Physics, Ch Optical properties: interband absorption, excitons and luminescence
Problem
The computed ε2(ℏω) of a hypothetical cubic semiconductor shows two features, labelled E1 at 2.1eV and E2 at 4.4eV. Its band structure shows the following: along the Λ line from Γ to L, the top valence band and the lowest conduction band run almost exactly parallel over an extended stretch of that line, with a separation there of about 2.1eV; at one isolated point of the zone, a valence and a conduction band are separated by about 4.4eV, with the separation changing quickly in every direction away from that point.
((a)) Which peak, E1 or E2, arises from a one-parameter family of critical points (bands parallel along a line) rather than from an isolated point of the zone?
((b)) Explain in one or two sentences why bands running parallel along an extended line give a larger joint density of states than an isolated critical point at a single k.