Location of quantum dots identified by microscopic photoluminescence changes during nanoprobe indentation with a horizontal scan

The location of quantum dots (QDs) embedded in a GaAs matrix is successfully identified by microscopic photoluminescence (PL) measurement during nanoprobe indentation with a horizontal scan at low temperature $\left(10\mathrm{K}\right)$. By introducing a high-sensitive load cell and a focused ion beam-fabricated flat-apex nanoprobe, the indentation force and PL of QDs are measured simultaneously at each point in the direction of the nanoprobe horizontal scanning with a constant indentation force. The experimental results show that the emission energy from QDs has a strong dependence on the location of QDs relative to the nanoprobe-indented location. Consequently, the emission energy shifts with the nanoprobe scan, generating an emission trace with a constant indentation force. Based on the energy shift of the ground state of the QD simulated by the combination of three-dimensional finite element strain calculation and strain-dependent $\mathbf{k}\mathbf{\bullet }\mathbf{p}$ Hamiltonian, an estimation method is developed, which enables us to identify the location of the QD from its emission trace in the nanoprobe indentation experiment. Results indicate that all the emission traces clearly observed are emitted from the QDs around the edge of the nanoprobe-indented area. Further discussion reveals that the evolution of shear strain generates hole accumulation around the contact edge of the indented nanoprobe. Consequently, the high density of holes enhances the PL of the QDs in that region.

Figure 1

Sketch of the experimental setup.

Figure 2

(Color online) Dependence of the emission energy of QDs on the indented position of the nanoprobe $(F=1.3\mathrm{mN})$. (a) The whole experimental results. (b) Illustration of the typical emission traces from QDs [part of the total 42 traced streaks, refer to the abscissa for the relative position in (a)].

Figure 3

Illustration of the simulation model in the nanoprobe indentation (not to scale).

Figure 4

The FE model. (a) The mesh of the global model; (b) Submodel along $x$ axis (left side), half of the QD is modeled due to the symmetry. The small FE model (right side) which is the center part of the large submodel is used for lattice-mismatched strain calculation. The mesh of the QD is also shown in the insert.

Figure 5

Strain components along the $x$ axis due to indentation $\left(1.3\mathrm{mN}\right)$ calculated in the global model (GaAs matrix) at $z=46.5\mathrm{nm}$ in the $x\text{−}z$ plane.

Figure 6

The distribution of ${\epsilon }_{xz}$ in the GaAs matrix due to indentation $\left(1.3\mathrm{mN}\right)$.

Figure 7

Shift of CBM in the GaAs matrix due to indentation $\left(1.3\mathrm{mN}\right)$.

Figure 8

Shift of VBM in the GaAs matrix due to indentation $\left(1.3\mathrm{mN}\right)$.

Figure 9

Shift of VBM in the GaAs matrix due to indentation $\left(1.3\mathrm{mN}\right)$. The slice is plotted at $z=46.5\mathrm{nm}$ plane and the dashed line in the figure is the boundary of the contact area.

Figure 10

Indentation induced energy shift of individual QDs calculated in submodel $(F=1.3\mathrm{mN})$. The cross points of the dashed grid represent the individual InGaAs QDs.

Figure 11

Illustration of the coordinate used in the location identification of QD.

Figure 12

Illustration and definition of the emission traces obtained in scan experiment.

Figure 13

The identified locations of typical QDs by the horizontal scan experiment (part of the total 42 QDs). The QDs are represented by the rectangular symbols and the serial numbers correspond to the traced peak in Fig. 2.

Figure 14

Comparison between the experiment and simulation results for some emission traces. The abscissa is the difference in the $x$ coordinate between the nanoprobe and the QD. The ordinate is the energy shifts of $\Delta E^{\exp }+\Delta E_0$ (shown in open circles) and $\Delta E^{\mathit{sim}}$ (shown in solid lines).

Figure 15

Illustration of the relative locations of emission traces in experiment (Fig. 2) to the indented location. Each emission trace starts from right and ends at left side in this figure. Emission traces from QD9 and QD15 corresponds to the emission lines in Fig. 14.

Figure 16

Illustration of the holes concentration due to nanoprobe indentation in global model. The shifts of VBM are plotted according to the results of GaAs matrix at $z=46.5\mathrm{nm}$ in the $x\text{−}z$ plane.

Figure 17

Comparison of the indentation-induced energy shift of VBM in GaAs matrix with nanoprobes different in radius. The shifts of VBM are plotted according to the results of GaAS matrix along the $z$ axis under the contact edge (at top free surface, $z=0\mathrm{nm}$). The nominal indentation pressure is equivalent to the uniform pressure of $1.0\mathrm{mN}$ force on a nanoprobe with a radius of $425\mathrm{nm}$.