Study of local indium concentration in Ga_(1-x)In_xN quantum wells using quantitative scanning transmission electron microscopy

Abstract text (incl. figure legends and references)

Multiple quantum wells (MQW) and single quantum wells (SQW) of Ga_(1-x)In_xN on GaN are promising candidates for nanooptical light emitters due to high quantum efficiency. The band gap of Ga_(1-x)In_xN can be controlled over a wide wavelength range by tailoring the variation of the indium concentration [1]. In addition, the epitaxially grown quantum well structures can be easily modified using chemical etching for the formation of a pyramid containing quasi quantum dot structure. As the dimension of the quantum structure shrinks, the variation of the local indium concentration becomes detrimental to the optical properties. Therefore, a robust characterization technique is required to understand and optimize such complex structures on the atomic scale.

In this study, a single quantum well of Ga_(1-x)In_xN between GaN layers on an Al₂O₃ substrate was grown using metal organic vapor phase epitaxy. The cross-sectional specimen was prepared using focused ion beam (FIB), including the final low kV milling step. The prepared specimen was characterized using a double-aberration corrected JEOL NeoARM 200F equipped with a cold field emission gun. We directly measured local lattice parameters based on the analysis of individual atomic column positions obtained from the high-angle annular dark-field (HAADF) image in real space. For a precise local lattice parameter analysis, drift-corrected HAADF imaging was utilized based on a sequential imaging technique with reasonably short acquisition time (1 sec/frame) accompanied by post rigid registration technique for drift correction between acquired images (Fig. 1). Then, the local indium concentration was derived using a modified Vegard's law including biaxial elastic strain effects. Fig. 2(a) shows the HAADF image of the epitaxially grown GaN/Ga_(1-x)In_xN/GaN structure and the individual indium contents derived using the modified Vegard's law is shown at the unit cell level in Fig. 2(b). The mean indium concentration inside the single quantum well from this analysis was 15.7 at. %, showing a very good agreement with the X-ray diffraction (XRD) analysis result. This result was compared with the local composition information obtained from a quantitative intensity analysis of the HAADF image. Absolute quantification of scanning transmission electron microscopy (STEM) - HAADF intensity (normalized intensity by the incident electron beam) was applied based on frozen phonon multislice calculation results [2]. The local thickness information obtained using position averaged convergent beam electron diffraction (PACBED) supported the quantitative intensity analysis [3]. In addition, the local composition information obtained from the intensity analysis was compared with the results from the quantitative STEM – electron energy-loss (EEL) spectroscopy analysis on the unit cell level.

The combination of STEM imaging, PACBED and spatially resolved EEL spectroscopy techniques shows the validation of Vegard"s law for the Ga_(1-x)In_xN quantum well, providing more detailed information at the interfaces. The relationship between atomic structure and composition could be thoroughly studied. This robust combined STEM techniques will be ultimately applied to understand the effect of the changes in indium concentration on complex quantum dot structures.

[1] U. Rossow et. al., Phys. Status Solidi B, 258, (2021)

[2] J. LeBeau et. al., Physical review Letters, 100, (2008)

[3] J. LeBeau et. al., Ultramicroscopy, 110(2), (2010)