Joint density of states in low dimensional semiconductors

• Quantum well DOS is not a sharp steplike function.
• An accurately JDOS expression for direct transitions is proposed.
• Direct optical transitions are described by considering three spatial dimensions.
• In low dimensional semiconductors, DOS is calculated by convolution operation.
• Quantum well and superlattice absorption coefficients are accurately calculated.

We present a different approach to evaluate density of states for quasi-bidimensional systems, which bonds density of states in the confinement direction with in-plane 2D density of states. Applying the convolution operation, we propose an accurately mathematical expression that combines directly the valence band and conduction band density of states functions to generate a joint density of states for direct transitions. When considering low dimensional semiconductors, another expression is found which shows that the density of states for electrons (holes) can be calculated by convolution operations between the confinement direction and in-plane electron (hole) density of states. Using both expressions, we have calculated the quantum well and superlattice absorption coefficient, resulting in positive alignment with experimental data. A more complete description of physical absorption is achieved with this new approach.