Modeling the band gap of CdS quantum well structures

• A model of a quantum well’s energy is presented.
• A comprehensive plot of a CdS quantum well’s bangap is presented.
• Non-linear optical properties of CdS quantum well is discussed.
• DFT is used to calculate electron density of states for small CdS crystallites.
• Experimental data from literature is compared to our model and correlation is found.

Within the framework of the effective mass approximation, an excited electron is studied in a cadmium sulfide (CdS) quantum well with varying well widths. The envelope function approximation is employed involving a three parameter variational calculation wherein one of these parameters is the distance between the electron and the hole. The relative change in the electron's energy (relative to its energy when it is in the valence band; in the hole) is investigated as a function of the electron–hole distance. Results from numerical calculations are presented and the non-linear behavior of different sized CdS quantum wells are discussed. Comparisons between experimentally measured CdS band gap energies (as a function of well-width) and the simulation data are made. A good agreement between the current model and experimental data exists. Density functional theory (DFT) calculations are done on crystallites of extremely small sizes to compare the current model's bandgap energies to DFT-predicted bandgap values at these extremes.