Theoretical Bounds on Electron Energy Filtering in Disordered Nanomaterials

Electron energy filters have recently been proposed as a method of reducing the effects of thermal broadening in device and sensing applications, enabling substantial improvements in their room temperature performance. Nanostructured materials can act as electron energy filters by funneling thermally broadened electrons through discrete energy levels. In this study, we develop a theoretical model of the electron filtering properties of nanostructured materials that explicitly includes the effects of thermal broadening and size heterogeneity on the heterogeneity of nanostructure energy levels. We find that under certain conditions quantum dot solids can perform as effective electronic energy filters. We identify a material-specific length scale parameter, L_crit, that specifies the maximum mean quantum dot size that can yield effective energy filtering. Moreover, we show that energy filtering materials composed of quantum dots with size near L_crit are maximally robust to heterogeneity in quantum dot size, tolerating variations ∼10% of the mean size. The length scale L_crit can be estimated directly from the widely tabulated density of states effective mass and shows that semiconductors with light conduction band electrons, such as III-V type materials InSb and GaAs, are the most forgiving for energy filtering applications. Taken together, these results provide a practical set of quantitative design principles for semiconductor electron filters.