The discussion based on using Eqs. (3) and (4) as a model for the spatial resolution is misleading and incomplete. Equation (3) gives rc as 0.028 nm, so from Eq. (4), the distance where the intensity drops by a factor of 2 is 0.05 nm for the 0.7-eV excitation and 0.15 nm for the 0.3-eV excitation. Clearly this does not match the measured variation of the signal as the beam is moved into the AlN layer. The distance rc corresponds to the resolution of the microscope which is very small compared to the nanometer dimensions of the structures. From Fig. 1, the dark patches corresponding to regions with higher B content are about 2 nm across, and the interface has a roughness of about 1 nm. It would therefore be more appropriate to integrate Eq. (4) over one of these regions, or one could argue that it is similar to excitation of a dielectric slab with an aloof beam with impact parameter r. The solution is a Bessel function of the second kind K0(2?rv), which approximately matches the decrease in the signal shown as Supplemental Material Fig. 3.We are grateful to Professor R. Egerton for pointing this out.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics