Photoluminescence of Tetrahedral Quantum-Dot Quantum Wells

Taking into account the tetrahedral shape of a quantum-dot quantum well (QDQW) when describing excitonic states, phonon modes, and the exciton-phonon interaction in the structure, we obtain within a nonadiabatic approach a quantitative interpretation of the photoluminescence spectrum of a single CdS/HgS/CdS QDQW. We find that the exciton ground state in a tetrahedral QDQW is bright, in contrast to the dark ground state for a spherical QDQW. The position of the phonon peaks in the photoluminescence spectrum is attributed to interface optical phonons. We also show that the experimental value of the Huang-Rhys parameter can be obtained only within the nonadiabatic theory of phonon-assisted transitions.

Figure 1

The tetrahedral quantum-dot quantum well (a) and the average probability densities in the plane $x=y$ of an electron on the twofold degenerate ground state level $E_{e0}$ (b), and a hole on the fourfold degenerate ground state and first excited state levels $E_{h0}$ (c), and $E_{h1}$ (d). A quarter ($y<x<-y$) of the tetrahedron in (a) is removed to show the position of the HgS shell. The factor of $\sqrt{2}$ multiplying the $x$ and $y$ coordinates in (b)–(d) is used to keep the same scale with the $z$ coordinate.

Figure 2

Normalized intensities of the lowest exciton levels in the optical absorption spectrum of a tetrahedral QDQW (the inset gives the intensities for the spherical QDQW considered in Ref. 8). Spectral lines are broadened by a Gaussian to enhance visualization.

Figure 3

Amplitudes of several interface phonon modes averaged as $V_{Q,n}(\xi )={\Phi }_{Q,n}(\xi )\sqrt{{\int }_{S(\xi )}|{\phi }_Q{|}^{2}dS/{\int }_{S(\xi )}dS}$ (for denotations see text). Vertical dashed lines show the boundaries of the tetrahedral shells. Isosurfaces $V_{p_z,5}(\mathbf{r})=10\mathrm{meV}$ (red) and $V_{p_z,5}(\mathbf{r})=-10\mathrm{meV}$ (blue) in the HgS shell are shown. The amplitudes $V_{p,4}$ and $V_{p,5}$ give the highest one-phonon peaks in the PL spectrum in Fig. 4.

Figure 4

PL spectrum of a tetrahedral QDQW normalized to the zero-phonon line’s intensity. Calculated spectral lines (black curve) are broadened by a Gaussian to facilitate visualization. Experimental spectra are measured at $T=10\mathrm{K}$ with excitation wavelength 633 nm and intensity $15\mathrm{kW}/{\mathrm{cm}}^2$ (green curve) [6] and with excitation wavelength 442 nm and intensity $5\mathrm{kW}/{\mathrm{cm}}^2$ (red curve) [19]. The inset gives one- and two-phonon bands (magnified by factors of 40 and 4000, respectively) as calculated within the adiabatic approximation.