Effective mass approximation for two extreme semiconductors: Band gap of PbS and CuBr nanoparticles

Abstract

An effective mass approximation (EMA) with finite-depth square-well potential is used to investigate the size-dependent band gap (BG) of PbS and CuBr nanoparticles embedded in different matrices. These two materials are interesting from the theoretical point of view as PbS is a low-BG material with smaller effective masses and larger dielectric constants, whereas CuBr is a wide-BG material with larger effective masses and smaller dielectric constants. Comparing the experimental BGs with our theoretical calculations, it is shown that EMA provides a better description of the experimental data, especially for CuBr, when the Coulomb interaction having the size-dependent dielectric constant is included in the calculation. Further, comparing the change in the BG of spherical nanoparticle, nanowire and thin film, it is predicted that the effective dimensionality of semiconductor nanoparticles can be increased by embedding them in another semiconducting matrix.