Tuning biexciton binding and antibinding in core/shell quantum dots

We use a path integral quantum Monte Carlo method to simulate excitons and biexcitons in core/shell nanocrystals with Type-I, Type-II, and quasi-Type-II band alignments. Quantum Monte Carlo techniques allow for all quantum correlations to be included when determining the thermal ground state, thus producing accurate predictions of biexciton binding. These subtle quantum correlations are found to cause the biexciton to be binding with Type-I carrier localization and strongly antibinding with Type-II carrier localization, in agreement with experiment for both core/shell nanocrystals and dot in rod nanocrystal structures. Simple treatments based on perturbative approaches are shown to miss this important transition in the biexciton binding. Understanding these correlations offers prospects to engineer strong biexciton antibinding, which is crucial to the design of nanocrystals for single-exciton lasing applications.

Figure 1

CdTe/CdSe Type-II core/shell nanocrystal schematic and band edges, with electron and hole probability densities within a biexciton. (a) 1.95 nm core radius and 0.25 nm shell thickness, (b) 1.95 nm core radius and 2.5 nm shell thickness.

Figure 2

Exciton-exciton interaction energy ${\Delta }_{XX}$ versus CdSe shell thickness for a CdTe core diameter of 3.9 nm. Experimental data from Oron et al.[4] are black crosses, with experimental uncertainty approximately given by the symbol size. Blue diamonds show the PI-QMC results, and the line is a guide to the eye. The dashed blue line shows perturbation theory results. Inset shows the radial form of the confinement potential.

Figure 3

Exciton-exciton interaction energy (${\Delta }_{XX}$) versus CdSe shell thickness for various different CdTe core diameters, as indicated. Lines are a guide to the eye. Inset shows the radial form of the confinement potential.

Figure 4

Exciton interaction energies ${\Delta }_X$ as a function of CdSe shell thickness for various CdTe core diameters, as indicated. Perturbation theory result for 3.9 nm core are shown as a dashed blue line. Lines are a guide to the eye. Inset shows the radial form of the confinement potential.

Figure 5

Conditional probability densities are shown for a 6 nm CdTe core diameter and 2.5 nm CdSe shell thickness in row A, for a 6 nm CdTe core diameter and 0.25 nm CdSe shell thickness in row B, and for a 2 nm CdTe core diameter and 2.5 nm CdSe shell thickness in row C. The radial form of the confinement potential for each is illustrated. Shown in column 1 is $g_{ee}$, a conditional electron (falling within the blue rectangle) and the resulting electron distribution. Column 2 shows $g_{eh}$, a conditional electron and resulting hole distribution. Column 3 shows $g_{he}$, a conditional hole (falling within the red rectangle) and resulting electron distribution. Column 4 shows $g_{hh}$, a conditional hole and resulting hole distribution.

Figure 6

Calculated exciton-exciton interaction energy ${\Delta }_{XX}$ against shell thickness for CdS/ZnSe Type-II colloidal nanocrystal, with the radial form of the confinement potential shown in upper inset. Core diameter of 3.1 nm, with dielectric constant of ${\epsilon }_r=8$ (squares with solid line) and for a weaker dielectric constant of ${\epsilon }_r=5.4$ (diamonds and dashed line). Lower inset shows ${\Delta }_{XX}$ against ${\epsilon }_r$, for a fixed shell thickness of 2.5 nm.

Figure 7

Exciton-exciton interaction energy ${\Delta }_{XX}$ plotted against increasing shell thickness for ZnSe/CdSe inverted Type-I colloidal nanocystal with 3.0 nm (circles with solid line) and 3.9 nm (stars with dashed line) core diameters. The inset shows the radial form of the confinement potential and lines are a guide for the eye. Simulations are performed at 300 K.

Figure 8

Conditional probability densities are shown for a 3.9 nm ZnSe core diameter and 0.25 nm CdSe shell thickness in row A. For a 3.9 nm CdTe core diameter and 1.3 nm CdSe shell thickness in row B, and for a 3.9 nm ZnSe core diameter and 3 nm CdSe shell thickness in row C. The radial form of the confinement potential for each is illustrated. Shown in column 1 is $g_{ee}$, a conditional electron (falling within the blue rectangle) and the resulting electron distribution. Column 2 shows $g_{eh}$, a conditional electron and resulting hole distribution. Column 3 shows $g_{he}$, a conditional hole (falling within the red rectangle) and resulting electron distribution. Column 4 shows $g_{hh}$, a conditional hole and resulting hole distribution.

Figure 9

The effect of various parameters on the binding to antibinding regime transition for CdS/CdSe rod/core nanocrystal. Red circles with error bars are experimental data taken from Sitt et al.,[8] along with polynomial fit to experimental data (red dashed line). Electron masses used for each dataset are indicated, solid lines indicate a 0 eV conduction band offset. Dashed lines indicated a conduction band offset of 0.3 eV. All simulations are with ${\epsilon }_r=8$. Inset shows form of confinement potential, black solid line indicates potential with 0 eV conduction band offset, red dashed line shows potential with 0.3 eV conduction band offset. Lines are a guide to the eye.

Figure 10

Exciton-exciton interaction energy ${\Delta }_{XX}$ against core diameter, for a nanocrystal with a CdS rod and CdSe core. Closest fit of PI-QMC simulation (black diamonds) to experimental data from Sitt et al.[8] (red circles, dashed red line is polynomial fit to experimental data points) is with 0 eV conduction band offset and 0.2 $m_e$ electron mass, with ${\epsilon }_r=5.785$. Inset shows example confinement potential with 0 eV conduction band offset and position of core in rod.

Figure 11

Probability densities showing the role of correlation due to the Coulombic interaction in CdS/CdSe rod/core structure, here with a core diameter of 4 nm. The single-particle electron is highly delocalized along rod, the attractive Coulomb potential then strongly localizes the electron to the hole, as seen in the exciton and biexciton densities. Black lines show the width of the rod (5 nm), with the central 12.8 nm of the rod shown out of the total 40 nm length.