Nanoscale EELS analysis of $\mathrm{InGaN}∕\mathrm{GaN}$ heterostructures

Kramers-Kronig transformations have been used to analyze the low-loss EELS spectrum of $\mathrm{InGaN}∕\mathrm{GaN}$ MWQs from which the ${\epsilon }_2\left(E\right)$ spectrum was extracted. The ${\epsilon }_2\left(E\right)$ spectrum contains information about absorption from the $d$ levels to the conduction bands in $\mathrm{InGaN}∕\mathrm{GaN}$ heterostructures. We have constructed maps of $\mathrm{Ga}$ distributions from the $\mathrm{Ga}$ absorption peak at $\sim 23\mathrm{eV}$ instead of using the traditional edges in the energy core loss spectrum. The use of the ${\epsilon }_2\left(E\right)$ spectrum has shown an increased clarity in the information gained, and often the possibility of analyzing the strain within quantum wells that contain defects such as dislocations and $\mathrm{V}$-defects. It is demonstrated that the $\mathrm{Ga}$ inside the quantum wells has a nonhomogeneous distribution using this novel technique.

Figure 1

(a) SDD from $\mathrm{GaN}$ in the $15–35\mathrm{eV}$ energy range. The plasmon peak (A) and different $\mathrm{Ga}$ transitions (B–D) has been marked. (b) ${\epsilon }_2\left(E\right)$ deduced from Kramers-Kronig analysis. The main contribution to ${\epsilon }_2\left(E\right)$ in this range has been marked as $\mathrm{Ga}$ $3d$. Both (a) and (b) show the position of background and signal window.

Figure 2

STEM dark field image of five $\mathrm{InGaN}∕\mathrm{GaN}$ MQWs with white arrows indicating the $\mathrm{InGaN}$ QW positions. The analyzed area is marked as spectrum image. Spatial drift corrections were also considered and adjusted during the acquisition of the spectrum data.

Figure 3

Background subtracted spectrum images with a signal window of $3.4\mathrm{eV}$ placed in the (a) SSD spectrum and (b) ${\epsilon }_2\left(E\right)$ as shown in Fig. 1. The $\mathrm{InGaN}$ quantum well positions have been marked. Areas of high $\mathrm{Ga}$ distribution inside the quantum well are indicated with A in (b). The positions 1 and 2 indicate the $\mathrm{GaN}$ and $\mathrm{InGaN}$ ${\epsilon }_2$ spectra shown in Fig. 4.

Figure 4

Superposition of ${\epsilon }_2\left(E\right)$ spectra corresponding to $\mathrm{GaN}$ and $\mathrm{InGaN}$ quantum well areas. A shift and change in the shape is observed, which is related to the strain in the heterostructure.

Figure 5

Strain distribution by mapping the $\mathrm{Ga}$ $3d$ transition Gaussian center shift. A large shift is observed in areas corresponding with $\mathrm{InGaN}$ quantum wells.

Figure 6

STEM dark field image of V-shape defect attached to a threading dislocation in $\mathrm{InGaN}∕\mathrm{GaN}$ MQWs. $\mathrm{InGaN}$ quantum well positions are marked with black arrows The analyzed area is marked with spectrum image. “Hole” indicates the area where the electron beam was kept stationary while SI acquisition was set up. Spatial drift was corrected during the acquisition of the spectrum data.

Figure 7

Background subtracted spectrum image from $3.4\mathrm{eV}$ energy window placed at the $\mathrm{Ga}$ $3d$ transition in the ${\epsilon }_2\left(E\right)$ spectrum.

Figure 8

Strain distribution by mapping the $\mathrm{Ga}$ $3d$ transition Gaussian center. Unlike Fig. 7 all five QW can be seen including the strain associated with the hole (marked). This indicates that the shift is due to strain induced by either In, defects(hole) or the dislocation.