Fig. 3: Band profiles and depletion layer modulation via photodoping.

a Simulated conduction band profiles of core–shell nanocrystals with increasing shell thickness before (black curve) and after (blue curve) the injection of photoelectrons. The light-induced bending of the bands close to the surface of the nanocrystal is the main mechanism responsible for the storage of extra electrons. b Calculated electron density profiles of the same nanocrystals. The depletion region \({{{W}}}\) is shaded in orange. The active region (\({{{{R}}}}_{{{{active}}}}\)) of the NC is observed as the region of the NC volume not affected by \({{{W}}}\). A discrepancy between \({{{{R}}}}_{{{{active}}}}\) and the structural core (\({{{{R}}}}_{{{{core}}}}\)) and shell (\({{{{t}}}}_{{{{s}}}}\)) dimensions (given in white and light blue in the background) is observed. The largest variations in \({{{{n}}}}_{{{{e}}}}\) after photodoping occur towards the edge region of the nanocrystal with a significant rise of carrier density in the shell region (blue shaded regions). Due to photodoping, the active region expands (\({{{{\Delta }}}{{{R}}}}_{{{{active}}}}{{{ > }}}{{{0}}}\)). Consequently, the depletion layer is progressively suppressed (\({{{\Delta }}}{{{W}}}{{{ < }}}{{{0}}}\)) during the storage of electrons with photodoping (from light orange to dark orange). c Carrier density profiles obtained from the fitting of the experimental data using the multi-layer optical model. The expansion of the active region (\({{{{R}}}}_{{{{active}}}}\)) and \({{{W}}}\) modulations of core–shell NCs of increasing \({{{{t}}}}_{{{{s}}}}\) upon photodoping are observed similar to from the results from the numerical simulations. The filling of the depleted regions with extra electrons is highlighted in blue in panels b and c. The pale blue circle represents the NC shell.