Figure 2: Simulations for the methodical study of GaN.

(a) Ronchigrams of GaN simulated for 1.3 nm specimen thickness, arrayed with respect to the position of the STEM probe. The primary effect of the atomic electric field is a redistribution of intensity (Int., colour-coded) within the ronchigrams. The arrow denotes intensity transferred even to opposite direction. All data in this figure are based on these simulations. For better visibility, only subsets of the 80 × 80 raster are shown in a–d. (b) Vector field for the expectation value of the momentum transfer calculated from equation (1) and the ronchigrams in a. The momentum transfer correlates directly with the gradient of the Coulomb potential shown colour-coded and as white isolines (Volt units). Length of the black legend vector is 5h nm⁻¹. (c) Electric field derived from the momentum transfer in b via equation (2), showing the radial characteristic at both sites. The field strength decreases near nuclei because of the extension of the STEM probe. Length of the black legend vector is 3 V pm⁻¹. (d) Electric field used in the simulation (negative gradient of potential in b), convolved with the probe intensity according to equation (3). It agrees nearly perfectly with part c with a maximum error of 0.1 V pm⁻¹. Length of the black legend vector is 3 V pm⁻¹. (e) Divergence of the momentum transfer in b, being proportional to the charge density according to equation (4). The inset depicts the theoretical result obtained by DFT. (f) Electron density calculated from the divergence of the momentum transfer in b according to equation (4) with the proton density entering as prior knowledge. The inset shows the electron density obtained directly by DFT, convolved with the probe intensity. Scale bars top left in b–f are 50 pm.