The role of effective mass on semiconductor charge carrier localization as revealed by the split operator method

Charge carriers in a solid-state material are modeled as free particles with a variable “effective” mass that is derived from the curvature of the conduction/valence band. These effective masses of electrons and holes are unique to each material and are dependent on the internal band structure (e.g., heavy vs light holes). Quantum mechanical characterizations of nanomaterials employ effective mass theory using particle-in-a-box paradigms to calculate quantum confinement (i.e., localization) energies. However, semiconductor heterostructures, such as core/shell quantum dots, have spatially variant masses, and as a result, the Schrodinger equation must be solved via a numerical approach incorporating the Hermitian kinetic energy operator T̂∼∇m−1x∇. To this end, the split operator “spectral” method was modified with the variable mass kinetic energy operator to study a variety of core/shell quantum dots. The results reveal a preferential localization of charge carriers into regions of high effective mass, which has a non-negligible effect on structure/property relationships that are increasingly being used to guide the synthesis of semiconductor heterostructures, such as “giant” type II quantum dots.