Size-dependent optical and electrical properties of PbS and ZnO nanostructures: a comparative theoretical study

Abstract

Size-dependent optical and electrical properties of semiconductor nanostructures are governed by quantum confinement and strongly influenced by intrinsic electronic structure. This work presents a systematic theoretical study of PbS and ZnO nanostructures with the objective of comparing narrow and wide band gap semiconductors in a single framework. The size dependence of band gap, refractive index, optical dielectric constant, carrier concentration, and electrical conductivity is assessed using three complementary theoretical models: the Brus model, the Hyperbolic model, and the Cohesive Energy model. The obtained results are critically compared with existing experimental and theoretical studies to determine the applicability of the models in various confinement regimes. The findings demonstrate that quantum confinement effects are more pronounced in PbS, resulting in strong band gap widening and high optical constants at small particle sizes, compared with ZnO, which shows weaker size dependence and a rapid approach to bulk behavior. Strong confinement in PbS is well described by the Brus model, whereas the Hyperbolic model better describes the bulk-convergence behavior of ZnO with general agreement in larger size regimes. Analysis of electrical transport indicates that carrier concentration and conductivity are strongly model-dependent. PbS shows strong confinement-induced suppression at very small sizes followed by rapid conductivity enhancement with increasing particle diameter, whereas ZnO exhibits smoother conductivity growth and saturation behavior associated with its intrinsic n-type character. In general, this paper establishes that no single model describes all size-dependent properties and highlights the significance of choosing theoretical approaches according to the type of material, size regime, and desired physical property.