Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots

A theoretical model for the electron-hole exchange interaction in three-dimensionally (3D) confining semiconductor nanostructures is presented to explain the observed decreasing tendency of the fine-structure splittings (FSSs) of small InGaAs/GaAs self-assembled quantum dots (QDs) with increasing the emission energies. The experimentally revealed FSS reduction is shown to be highly associated with the significant 3D spreading of electronic orbitals and reduced overlap of electron and hole wave functions in small and/or Ga-diffused QDs. The combination of quantum size and Ga-diffusion effects substantially reduces the averaged $e\text{−}h$ exchange interaction and leads to the reduced FSSs in the regime of high emission energy.

Figure 1

(Color online) (a) and (b) Polarized PL spectra taken from two single QDs at $T=5\text{K}$ with polarization directions along [110] and $\left[1\overline{1}0\right]$. Peaks corresponding to X and XX recombination are identified according to the power dependences of their intensities. (c) The measured FSSs as a function of X emission energy for 14 quantum dots (the horizontal line with double arrows lying below the horizontal axis highlights the spectral range of the measured emission energies), and (d) schematic diagrams of XX-X cascade decay in the absence and presence of the $e\text{−}h$ exchange interaction, respectively.

Figure 2

(Color online) (a) Lateral $e$ (blue squares) and $h$ (red circles) wave-function extent $\left(l_y^{e/h}\right)$. (b) Vertical $e$ (blue squares) and $h$ (red circles) wave-function extent $\left(l_z^{e/h}\right)$. (c) Emission energies as functions of the lateral size for different diffusion lengths. The vertical cyan solid line with double arrows indicates the observed spectral range of light emission from the dots. Accordingly, the lateral sizes of the measured dots are speculated to distribute in the hatched region. (d) Schematic depiction of a truncated-pyramid-shaped QD considered in simulation and the relevant defined parameters.

Figure 3

(Color online) (a) Parameters of $e\text{−}h$ wave-function overlap $\beta$ (blue squares), and lateral elongation of wave function normalized by dot shape elongation $\frac{\xi \left(1-\xi \right)}{\Xi \left(1-\Xi \right)}$ (red circles), as functions of the emission energy. (b) Inverse cubic power of the average in-plane interaction distance ${\left(l_y^{eh}\right)}^{-3}$ (dashed line with squares), and damped inverse cubic power of the in-plane interaction distance $\left[\gamma \left(l_z^{eh}\right){\left(l_y^{eh}\right)}^{-3}\right]$ (solid line with circles). A diffusion length $l_D=0.5\text{nm}$ is considered here.

Figure 4

(Color online) Calculated FSSs $\left(\equiv \left|2\delta \right|\right)$ as a function of the X emission energy obtained by using the full 3D formulation of Eq. (2) (red squares), the 3D formulation but with ${\beta }_z=1$ set artificially (blue circles), and the 3D formulation but with $\beta =1$ (identical 3D wave functions of electron and hole are assumed and the $e\text{−}h$ wave-function overlap is 100%) (green diamonds). The result obtained using the 2D model (black triangles) in Ref. 28 is also shown for comparison. A diffusion length $l_D=0.5\text{nm}$ is considered here.

Figure 5

(Color online) Measured and calculated FSSs of diffused QDs as functions of the X emission energy. Experimental data are shown by green filled squares. Theoretical results are calculated for different dot sizes and diffusion lengths, and are indicated by various kinds of different colored symbols. Solid (Dashed) lines: data for the QDs with the lateral shape elongation, $\Xi =95\mathrm{\%}\left(\Xi =98\mathrm{\%}\right)$.