Wavefunction delocalization in quantum dot arrays: an asymptotic analysis

Intermediate-band solar cells using quantum dot arrays (QDAs) are theoretically predicted to significantly increase the efficiency with which solar energy can be harvested. In the limit of identical quantum dots, the wavefunction for electrons in a QDA will be fully delocalized. Fully delocalized wavefunctions have been theoretically shown to reduce thermal losses and consequently increase photovoltaic device efficiency. However, even small nonuniformities can cause electrons to localize in a single quantum dot, negating any advantages from delocalized states. In this work a modified Schrödinger equation is used to model a two-dot array with nonuniform quantum dots and solved using perturbation methods. This result is extended to N -dot arrays, and several metrics are constructed to characterize the degree of delocalization. Our results, which compare favorably with numerical simulations, show explicitly how the amount of delocalization depends on key design parameters.