Electrical Polarization in AlN/GaN Nanodisks Measured by Momentum-Resolved 4D Scanning Transmission Electron Microscopy

We report the mapping of polarization-induced internal electric fields in AlN/GaN nanowire heterostructures at unit cell resolution as a key for the correlation of optical and structural phenomena in semiconductor optoelectronics. Momentum-resolved aberration-corrected scanning transmission electron microscopy is employed as a new imaging mode that simultaneously provides four-dimensional data in real and reciprocal space. We demonstrate how internal mesoscale and atomic electric fields can be separated in an experiment, which is verified by comprehensive dynamical simulations of multiple electron scattering. A mean difference of $5.3\pm 1.5\mathrm{MV}/\mathrm{cm}$ is found for the polarization-induced electric fields in AlN and GaN, being in accordance with dedicated simulations and photoluminescence measurements in previous publications.

Figure 1

(a) Schematic of the AlN/GaN wires with 4 nm layer periodicity and AlN shell. (b) Energy-dispersive x-ray (EDX) spectroscopy and $Z$-contrast scanning transmission electron microscopy (STEM) image, showing the sequence of pure AlN/GaN layers. (c) Momentum-resolved STEM principle. A probe is multiply scattered in the specimen (top). An array of diffraction patterns is recorded sequentially during rastering (center). For each scan position, the momentum transfer can be determined from the first moment of the diffraction pattern (bottom). (d) Map of the bright field (BF; left) intensity (int.) in numbers of electrons (el.) and the momentum transfers (right, color coded) as determined from the four-dimensional (4D) STEM data acquired within the yellow region in Fig. 1.

Figure 2

(a) A high-angle annular dark field (HAADF) STEM image acquired simultaneously with the 4D STEM data is used to calculate the Voronoi diagram. (b) Momentum transfers averaged over the colors separated into the $[1\overline{1}00]$ and the $[000\overline{1}]$ components. (c) Voronoi-cell-averaged electric field projection calculated directly from Fig. 2. (d) Line profile along growth direction $[000\overline{1}]$ after subtraction of a linear slope (black) fitted to the GaN regions. Arrows indicate the electric field differences between AlN and GaN.

Figure 3

Modeling the electric field in growth direction. (a) HAADF STEM profile for the region in Fig. 2, considered as being proportional to the chemical composition $c(x)$. (b) Negative gradient of Fig. 3. (c) Linear combination of Figs. 3 and 3 according to Eq. (3), determined by fitting the experimental (Exp.) profile to Fig. (d).

Figure 4

(a) Thickness-dependent simulation of the systematic error $\delta$ in Eq. (2), arising from the lack of inversion symmetry in wurtzite GaN/AlN. It amounts to $1\mathrm{MV}/\mathrm{cm}$ for the present wire. (b) ${\mathrm{NEXTNANO}}^3$ simulation of the electric field ($[000\overline{1}]$ component) assuming the actual three-dimensional (3D) wire geometry and fully strained (red) or fully relaxed (black) layers. (c) ${\mathrm{NEXTNANO}}^3$ simulation of the electric field ($[000\overline{1}]$ component) across a cross-sectional slice centered in a GaN segment.