2. Band structure of GaAs Below is the band structure for GaAs. The lattice constant for GaAs is a = 5.65 Å. sa: VA T= 300K 0.40 ev Ec 1.90 ev 1.71 ev 1.42 ev Ey 0.34 ev - heavy hole - light hole - split off (1,1, 1) - (0,0,0) - (1,0,0) (a) Is GaAs a direct or indirect gap semiconductor? From the figure above, estimate the energy gap in GaAs. (b) Direct optical transitions in semiconductors correspond to electronic transitions in which there is no change in momentum. What are the energies of direction transitions in GaAs for k =(1,1,1), k = 0, and k = (1,0,0). What photon wavelengths are required for these optical transitions? (c) Consider the indirect transitions of an electron from k = 0 to k = "(1,0,0) and k = 0 to k =(1,1,1). Calculate the change in momentum for these transitions. What are the longest photon wavelengths required for these transitions? What are corresponding momenta for these photons and compare them with the change in momentum of the electron involved with their corresponding indirect transition? 2.

2. Band structure of GaAs Below is the band structure for GaAs. The lattice constant for GaAs is a = 5.65 Å. sa: VA T= 300K 0.40 ev Ec 1.90 ev 1.71 ev 1.42 ev Ey 0.34 ev - heavy hole - light hole - split off (1,1, 1) - (0,0,0) - (1,0,0) (a) Is GaAs a direct or indirect gap semiconductor? From the figure above, estimate the energy gap in GaAs. (b) Direct optical transitions in semiconductors correspond to electronic transitions in which there is no change in momentum. What are the energies of direction transitions in GaAs for k =(1,1,1), k = 0, and k = (1,0,0). What photon wavelengths are required for these optical transitions? (c) Consider the indirect transitions of an electron from k = 0 to k = "(1,0,0) and k = 0 to k =(1,1,1). Calculate the change in momentum for these transitions. What are the longest photon wavelengths required for these transitions? What are corresponding momenta for these photons and compare them with the change in momentum of the electron involved with their corresponding indirect transition? 2.