Polarization properties of single zinc-blende GaN/AlN quantum dots

We study by microphotoluminescence the polarization properties of single zinc-blende GaN/AlN quantum dots fabricated by two growth processes: the droplet epitaxy technique and the Stranski-Krastanov growth mode. A statistical analysis of their polarization properties both at the mesoscopic and nanoscopic scales indicates that it is possible to modify the phase and amplitude of their valence band mixing by switching on and off the influence of AlN antiphase domains through the growth process. $k.p$ calculations show that the strain effects and quantum dot geometries resulting from the growth process play a major role in shaping their polarization properties.

Figure 1

Representation of the QD polarization properties: (a) without valence band mixing and (b) with valence band mixing as calculated for a lens-shape ZB GaN QD with height ${\delta }_{001}=2.5\mathrm{nm},\sigma =0$ and inplane aspect parameter $\alpha =({\delta }_{110}-{\delta }_{1–10})/10{\delta }_{001}=-0.75$ $({\delta }_{110}$ and ${\delta }_{1–10}$ are the dimensions of the QD along $\left[110\right]$ and $\left[1\overline{1}0\right])$. The resulting DLP is 69%. The blue and pink lines correspond, respectively, to eigenstates $\left|X\rangle \right.$ and $\left|Y\rangle \right.$ or $|\tilde{X}\rangle$ and $|\tilde{Y}\rangle$. The black line corresponds to the total QD polarization. (c) DLP of truncated-pyramid SK QDs for various α (closed squares) and σ (open squares). (d) Same as (c) for lens-shape DE QDs. Lines are guides for the eye. Arrows indicate the orientation of stress and shape anisotropy. The closed (open) triangles represent the DLP calculated for QDs with α = ± 0.5 and σ = 0.5 GPa applied along $\left[1\overline{1}0\right]$.

Figure 2

(a) 5×5-μm AFM scan of the top AlN surface evidencing the presence of two antiphase domains. The dashed line highlights the domain boundary. Orthogonal domains oriented along $\left[110\right]$ and $\left[1\overline{1}0\right]$ are labeled APD and $\overline{\mathrm{APD}}$, respectively. (b) 1×1-μm AFM scan of the top AlN surface for $\overline{\mathrm{APD}}$.

Figure 3

Two-dimensional map of the SK QD μPL integrated intensity in a given area of the sample for transmission angles of the polarization analyzer (a) θ = ${45}^{\circ }$ and (b) θ = $-{45}^{\circ }$ highlighting, respectively, APD and $\overline{\mathrm{APD}}$ domains. (c) Polar plot of the integrated intensity of QD ensembles as a function of θ for a DE QD ensemble (blue dots) and SK QD ensembles located in APD (pink dots) and $\overline{\mathrm{APD}}$ (black dots). The dashed lines are fitting curves of the form $I\left(\theta \right)=I_{\max }·\mathrm{co}{\mathrm{s}}^2(\theta -{\theta }_0)+I_{\min }·\mathrm{si}{\mathrm{n}}^2(\theta -{\theta }_0)$. For each sample the intensity is normalized to the maximum intensity.

Figure 4

(a) μPL spectrum of an APD SK QD mesa for various transmission angles θ of the polarization analyzer depicting the QD ensemble luminescence and one spectrally isolated single QD peak at 3.93 eV. (b) θ-dependent μPL spectra of a single SK QD emitting at 3.70 eV and emerging from a different mesa. (c) Polar plot of the integrated intensity of the single SK QD displayed in (b). The dashed line is a fitting curve of the form $I\left(\theta \right)=I_{\max }·\mathrm{co}{\mathrm{s}}^2(\theta -{\theta }_0)+I_{\min }·\mathrm{si}{\mathrm{n}}^2(\theta -{\theta }_0)$. The measured QD DLP is 98% and the polarization angle is ${\theta }_0=-{37}^{\circ }$. (d) Statistics of the polarization angle (bottom-left axes) and the degree of linear polarization (top-right axes) of 38 single SK QDs found in both APD (pink bars) and $\overline{\mathrm{APD}}$ (black bars) domains. For all SK QDs, the degree of linear polarization is larger than 95%.

Figure 5

(a) μPL spectrum of a DE QD mesa for various transmission angles θ of the polarization analyzer depicting spectrally isolated single QD peaks at 3.76, 3.78, and 3.82 eV. (b) θ-dependent μPL spectra of single DE QDs emitting at 3.71 and 3.77 eV and emerging from two different mesas. (c) Polar plot of the integrated intensity of the QDs displayed in (b) (respectively, closed and open circles). The dashed line is a fitting curve of the form $I\left(\theta \right)=I_{\max }·\mathrm{co}{\mathrm{s}}^2(\theta -{\theta }_0)+I_{\min }·\mathrm{si}{\mathrm{n}}^2(\theta -{\theta }_0)$. The QD DLP is, respectively, 28% and 91% and the polarization angle is, respectively, ${\theta }_0=3^{\circ }$ and ${\theta }_0={90}^{\circ }$. (d) Statistics of the polarization angle (bottom-left axes) and the degree of linear polarization (top-right axes) of 61 single DE QDs.

Figure 6

μPL spectra of a single DE QD for various transmission angles θ of the polarization analyzer at (a) 4 K with DLP = 12 ± 5%, and (b) 100 K with DLP = 11 ± 5%. (c) DLP of three different DE QDs as a function of temperature. The lowest DLP data correspond to the QD observed in Figs. 6 and 6. Lines are guides for the eye. Vertical bars represent the error on the $I\left(\theta \right)=I_{\max }·\mathrm{co}{\mathrm{s}}^2(\theta -{\theta }_0)+I_{\min }·\mathrm{si}{\mathrm{n}}^2(\theta -{\theta }_0)$ fitting.

Figure 7

Isosurfaces of the piezoelectric potential (a) $V_p=\pm 60\mathrm{mV}$ for truncated pyramid SK QDs and (b) $V_p=\pm 80\mathrm{mV}$ for lens-shape DE QDs. (c) Isosurfaces of probability density ${\left|\langle \psi |\psi \rangle \right|}^2$ for the first four electron and hole states as obtained from eight-band $k.p$ calculations of symmetric truncated pyramid SK QDs with σ = 0. The state energies are $E_{E0}=3.4621\mathrm{eV},E_{E1}=3.4771\mathrm{eV},E_{E2}=3.479\mathrm{eV},E_{E3}=3.4937\mathrm{eV},E_{H0}=-0.1847\mathrm{eV},E_{H1}=-0.1875\mathrm{eV},E_{H2}=-0.1889$, and $E_{H3}=-0.1895\mathrm{eV}$. (d) Same as (c) for lens-shape DE QDs. The state energies are $E_{E0}=2.9561\mathrm{eV},E_{E1}=2.9862\mathrm{eV},E_{E2}=2.9960\mathrm{eV},E_{E3}=3.0188\mathrm{eV},E_{H0}=-0.7329\mathrm{eV},E_{H1}=-0.7378\mathrm{eV},E_{H2}=-0.7392$, and $E_{H3}=-0.7394\mathrm{eV}$. (e) Contribution of HH, LH, and SO bands to the ground-hole state of lens-shape DE QDs for various σ applied along $\left[110\right]$.