Electronic structure of InP/ZnSe quantum dots: effect of tetrahedral shape, valence band coupling and excitonic interactions

TL;DR

This work addresses how tetrahedral geometry and valence-band mixing influence the near-band-edge electronic and optical properties of InP/ZnSe quantum dots. It combines a multi-band $k\cdot p$ framework for electrons and holes with configuration-interaction to account for excitonic and carrier-carrier interactions, directly comparing tetrahedral and spherical shapes under the $\overline{T}_d$ symmetry and including dielectric confinement. The results show that tetrahedral QDs largely retain spherical-like degeneracies and spectral assignments, with important differences emerging for large QDs due to relaxed selection rules and significant valence-band mixing; excitonic and Coulomb effects are largely perturbative, producing a modest redshift and size-dependent trion/biexciton binding. These insights clarify spectral assignments for InP/ZnSe QDs and inform design strategies for low-toxicity, tunable optoelectronic devices in LEDs, bioimaging, and photovoltaics.

Abstract

The energy levels and optical transitions of tetrahedral core/shell InP/ZnSe quantum dots (QDs) are investigated by means of multi-band k$\cdot$p theory. Despite the $\overline{T}_d$ symmetry relaxing spherical selection rules, the near-band-edge excitonic spectrum is reminiscent of that obtained for spherical nanocrystals. Exceptions appear in large (red-emitting) QDs, where transitions violating the (quasi-)angular momentum selection rule ($ΔL=0,\pm 2$) are observed, and the ground state does not become dark ($P_{3/2}$-like). Valence band coupling is important in determining the symmetry, degeneracy and energy of hole states, with split-off holes playing a greater role than in CdSe QDs. The ($1S_e$-like) electron ground state exhibits moderate delocalization into the ZnSe shell. The confinement regime is then strong even for thick shells, which results in Coulomb interactions being mostly perturbative. Electrons remain largely localized in the InP core even in negative trions, despite electron-electron repulsions. At the same time, the asymmetry between Coulomb attractions and repulsions leads to negative (positive) trions being bound (antibound) by tens of meV. The biexciton binding energy switches from positive to negative, depending on the QD size.

Figures (6)

• Figure 1: Electronic structure of non-interacting electron and hole. (a) and (b): schematic of the spherical and tetrahedral core/shell QDs under study. (c) and (d): electron energy levels for varying $r_c$. (e) and (f): hole energy levels for varying $r_c$. (g) and (h): energy difference between $1P_{3/2}$ and $1S_{3/2}$ states. In spherical QDs, $r_s=5$ nm. In tetrahedral QDs, $r_s=8$ nm.
• Figure 2: Charge density of near band edge electrons (a) and holes (b) in a spherical QD with $(r_c,r_s)=(1.5,5)$ nm. (c) and (d): same but for a tetrahedral QD with $(r_c,r_s)=(3.0,8.0)$ nm. The isosurfaces contain 70% of the charge density.
• Figure 3: Spectral assignment of the lowest transitions in the absorption of InP/ZnSe QDs. (a) Spherical QD with $(r_c,r_s)=(1.5,5.0)$ nm. (b) Tetrahedral QD with $(r_c,r_s)=(3.0,8.0)$ nm. In each panel, the top spectrum gives the absorption of non-interacting electron-hole pairs, and the bottom one that of interacting excitons. The insets represent the geometry under study. In the calculation, $T=0$ K.
• Figure 4: Absorption spectrum of $X$ in (a) spherical and (b) tetrahedral QDs with different core size. The spectra are offset vertically for clarity. Dotted lines are guides to the eyes. Red lines and characters are used to highlight transitions forbidden in spherical QDs. The energy reference is that of the $1S_{3/2} 1S_e$ transition. (c) Wave function of the main HH and secondary LH components of $1P_{3/2}$ when $r_c=6$ nm. The numbers give the weight of the component within the state.
• Figure 5: Emission spectrum of $X$ in InP/ZnSe QDs with (a) spherical and (b) tetrahedral shape, as a function of the core size. The population of states is calculated at $T=300$ K. Shell sizes are the same as in Fig. \ref{['fig4']}.