Unconventional quantum-confined Stark effect in a single $\mathrm{GaN}$ quantum dot

We show that a peculiar excitonic effect and a confining potential in self-assembled hexagonal $\mathrm{GaN}∕\mathrm{AlN}$ quantum dots produce an unconventional quantum-confined Stark effect. In contrast to the conventional quantum-confined Stark shift, the emission line from a single $\mathrm{GaN}$ dot under the applied electric field perpendicular to the growth direction blueshifts nearly symmetrically with respect to the direction of the field. The field dependence of the emission lines is reproduced in a charge self-consistent effective mass calculation, taking into account strain, piezoelectric charge, and pyroelectric charge. The unconventional blueshift is attributed to a significant variation of the exciton binding energy, made obvious by a cancellation between the energy shifts of electron and hole confined states.

Figure 1

(a) Schematic of the sample structure used to apply the electric field. (b) Microphotoluminescence spectra for applied voltages between $-8$ and $8\mathrm{V}$. (c) Emission energy shift as a function of the applied bias voltage.

Figure 2

(a) Schematic of the $\mathrm{GaN}∕\mathrm{AlN}$ dot used for the calculation. (b) Calculated probability density distribution for the ground electron and hole states.

Figure 3

(Color online) (a) Calculated energy shifts of electron energy level $\left(\mathrm{\Delta }{E}_c\right)$, hole energy level $\left(\mathrm{\Delta }{E}_v\right)$, and transition energy without excitonic effect $[\mathrm{\Delta }{E}_{cv}=\mathrm{\Delta }(E_c-E_v\left)\right]$ as a function of the electric field. (b) Calculated variation of the binding energy $(-\mathrm{\Delta }{E}_{\mathrm{bind}})$ and the Stark shift of the excitonic state $[\mathrm{\Delta }{E}_{ex}=\mathrm{\Delta }(E_c-E_v-E_{\mathrm{bind}}\left)\right]$. The experimentally measured energy shift (squares) averaged for positive and negative fields is also shown. The dashed line represents the oscillator strength.

Figure 4

(Color online) Calculated energy shifts of the Stark shift of the excitonic state plotted for various spontaneous polarization differences $\mathrm{\Delta }p$.