Contribution of strain and relaxation to dynamical diffraction in 4D-STEM signals

Abstract text (incl. figure legends and references)

Novel semiconductor devices have continuously been decreasing in size over the last few decades. With decreasing dimensions, a devices" electronical properties are mostly governed by effects from material interfaces, opening up a wide range of parameters used for modern semiconductor engineering. Strain engineering, for example, can lead to much desired quantities like high carrier mobilities in silicon transistors [1]. For the further advancement of semiconductor engineering and device growth, knowledge of strain fields is crucial feedback for the growth process.

Anyhow, gaining knowledge of growth-induced strain and strain relaxation effects on a nanometer scale can be challenging. One commonly used method for mapping strain is Nanobeam Electron Diffraction (NBED) [2] where one calculates the displacement from the variation of the recorded diffraction spots. In NBED measurements, however, the intensity in a diffraction spot can vary due to dynamical diffraction effects, posing a common problem for spot position detection [3]. To minimize these effects, one typically tries to use a collimated electron beam and focus solely on the relative distance of the diffraction spots. Nevertheless, by doing this, spatial resolution is limited by the beam diameter which typically is in the order of a few nanometers.

In this work, we have chosen an alternative way by investigating the patterns in diffraction discs. We acquired 4D-STEM signals of (Al,Ga)N quantum wells (QWs) in a GaN matrix using a convergent electron beam. This results in a much smaller beam diameter at the specimen surface. At every scan position, this yields a disc shaped diffraction spot mimicking the shape of the used condenser aperture where each disk contains features of dynamical diffraction. We evaluate these features for diffraction spots for a systematic row perpendicular to the QW layers. Figure 1 shows one measurement obtained this way, using a representation of the dataset reduced from four into two dimensions: This is achieved by spatially averaging the data along the y-axis and in reciprocal space along the axis perpendicular to the systematic row. The recorded pattern changes visibly in the region of the QW layer. However, these changes also extend further into the unstrained GaN. We compare the obtained results to beam-calculations solving Darwin-Howie-Whelan equation. The strain field was simulated using finite element calculations (Figure 2). As a result, we attribute long range changes in the recorded patterns to relaxation effects of specimen surfaces. For varying QW sizes and specimen thicknesses, we employ this method to investigate relaxation effects.

[1] Friedrich Schäffler 1997 Semicond. Sci. Technol. 12 1515
[2] V. B. Ozdol et al Appl. Phys. Lett. 106, 253107 (2015)
[3] T.C. Pekin et al., Ultramicroscopy 176 (2017) 170–176

Figure 1: 2D representation of 4D STEM data scanning across an AlGaN/GaN QW structure. In the highlighted region shifts of the diffraction disc and changes in patterns from dynamical diffraction become visible.

Figure 2: Calculated displacement relative to a GaN reference lattice showing the effects of relaxation. The simulated beam direction runs from bottom to top, meaning a positive displacement effectively points downwards.