Intrinsic electric field effects on few-particle interactions in coupled GaN quantum dots

We study the multiexciton optical spectrum of vertically coupled $\text{GaN}∕\text{AlN}$ quantum dots with a realistic three-dimensional direct-diagonalization approach for the description of few-particle Coulomb-correlated states. We present a detailed analysis of the fundamental properties of few-$\text{particle}∕\text{exciton}$ interactions peculiar of nitride materials. The giant intrinsic electric fields and the high $\text{electron}∕\text{hole}$ effective masses give rise to different effects compared to GaAs-based quantum dots: intrinsic exciton-exciton coupling, nonmolecular character of coupled dot exciton wave function, strong dependence of the oscillator strength on the dot height, large ground-state energy shift for dots separated by different barriers. Some of these effects make $\text{GaN}∕\text{AlN}$ quantum dots interesting candidates in quantum information processing.

Figure 1

Electron (upper panel) and hole (lower panel) particle distribution (dotted line), conduction (upper panel) and valence (lower panel) band structure (solid line) along the growth direction for two coupled GaN dots of, respectively, $2.5\text{nm}$ and $2.7\text{nm}$ of height, separated by a $2\text{nm}$ AlN barrier.

Figure 2

Excitonic (solid line) and biexcitonic (dashed line) absorption spectrum of the GaN coupled dots of Fig. 1.

Figure 3

Biexcitonic shift of the ground-state transition in dot b for two coupled GaN dots as a function of dot height and base diameter. In curve $\left(A\right)$ only the base diameter of the dots is changed $\left(D=10\text{nm}\right)$; in curve $\left(B\right)$ only the height of the dots is changed $\left(L_d=2.5\text{nm}\right)$, while in curve $\left(C\right)$ $D$ is varied proportionally to $L_d$. The parameters for the parabolic potential is varied in the range: $\hslash {\omega }_e=74–290\text{meV}$, $\hslash {\omega }_h=33–130\text{meV}$. In particular, the values analyzed in the figures are $D=10\text{nm}$ $\left(\hslash {\omega }_e=290\text{meV},\hslash {\omega }_h=130\text{meV}\right)$, $D=11.75\text{nm}\left(\hslash {\omega }_e=170\text{meV},\hslash {\omega }_h=76\text{meV}\right)$, $D=13.5\text{nm}\left(\hslash {\omega }_e=131\text{meV},\hslash {\omega }_h=59\text{meV}\right)$, $D=15.25\text{nm}\left(\hslash {\omega }_e=97\text{meV},\hslash {\omega }_h=43\text{meV}\right)$, $D=17\text{nm}\left(\hslash {\omega }_e=74\text{meV},\hslash {\omega }_h=33\text{meV}\right)$.

Figure 4

Oscillator strength of the ground-state transition in dot $b$ for the same parameters of Fig. 3; labeling as in Fig. 3.

Figure 5

Upper panel: curve $\left(A\right)$ shows the biexcitonic shift of the ground state transition in dot $b$ for two coupled GaN dots of 2.5 and $2.7\text{nm}$ of height vs barrier width between the dots. Curve $\left(B\right)$ shows the corresponding biexcitonic shift in the pointlike charge approximation. Inset: as in main panel, but for large barrier widths. Lower panel: oscillator strength for the same parameters described above. Inset: internal electric field in dot b vs barrier width.

Figure 6

Excitonic distribution in a $2.5\text{nm}$ dot of a coupled dot nanostructure when the barrier width is $2\text{nm}$ (solid line) and $10\text{nm}$ (dotted line).

Figure 7

Exciton ground-state energy (upper panel) and oscillator strength (lower panel) in the dot b of two identical coupled GaN dots of $2.5\text{nm}$ of height vs barrier between the dots.

Figure 8

Electron and hole particle distribution along the growth direction for two coupled dots of, respectively, $2.5\text{nm}$ and $2.7\text{nm}$ of height, separated by a $2.5\text{nm}$ AlN barrier. The dot parameter sets corresponds to: (a) GaN, except $\text{valence}∕\text{conduction}$ band offset (GaAs one); (b) GaAs; (c) GaN, except $\text{electron}∕\text{hole}$ masses (GaAs ones); (d) GaN, except that the electric field is set to zero.