Electronic structure of $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{S}$ core-shell quantum dots

The electronic structure of $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{S}$ core-shell quantum dots (QDs) is calculated within a four-band envelope function formalism. The effective mass approximation used successfully to model PbS and PbSe core QDs is extended to include discontinuities in material parameters. The model shows that even though $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{S}$ is a type-II heterostructure, for typical quantum dot sizes type-II properties will not be observed. Instead, the wave functions are predicted to extend throughout both materials. Experimental results confirm the unique properties of these nanostructures.

Figure 1

Energy gaps in $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{S}$ core-shell QDs.

Figure 2

(Color online) LUMO and HOMO energy levels of $\mathrm{Pb}\mathrm{Se}∕\mathrm{Pb}\mathrm{S}$ QDs with (a) fixed shell thickness and (b) fixed outer diameter.

Figure 3

(Color online) Wave functions for a constant $3\mathrm{nm}$ diameter core and variable shell thickness of (a) $0.0\mathrm{nm}$, (b) $0.83\mathrm{nm}$, (c) $1.67\mathrm{nm}$, (d) $2.5\mathrm{nm}$.

Figure 4

(Color online) Wave functions for a constant $6\mathrm{nm}$ diameter core and variable shell thickness of (a) $0.0\mathrm{nm}$, (b) $1.67\mathrm{nm}$, (c) $3.33\mathrm{nm}$, (d) $5.0\mathrm{nm}$.

Figure 5

(Color online) Experimental transition energies inferred from absorption (a) and (b), and predicted values (c) and (d). Shell thicknesses from 0 to 3 monolayers (ML) with various core sizes are shown.