Accurate interlayer distance measurement in bilayer graphene on SiC by high-resolution electron microscopy data...

Fine-tuning the interlayer distance in bilayer graphene (BLG) is essential for advancing novel devices that utilize graphenes' exceptional properties. Thus, the precise measurement of interlayer distances with sub-angstrom accuracy in BLG is important. In this study, we develop an approach that focuses on local interlayer spacing measurements and employs further statistical analysis to achieve a sub-angstrom accuracy of the obtained mean distance value. The proposed approach utilizes high-resolution transmission electron microscopy (HRTEM) data combined with the exit wave reconstruction technique. As a result, it allows for the extraction of an exit wave phase map that is free from the delocalization effect and contains structural information at the atomic scale. The effectiveness of the developed approach was validated through testing on atomistic 6H-SiC/BLG structures, found via molecular dynamics simulations. The mean interlayer distance d measured using the phase map calculated for the test structure closely matched the interlayer distance obtained from direct atomic positions. The application of the distance measurement approach to the experimental exit wave phase map, yielded d=(0.351 ± 0.018) nm. The utilization of two slightly over-focused micrographs demonstrated d=(0.355 ± 0.027) nm and d=(0.359 ± 0.027) nm. Due to the delocalization effect, these values were somewhat larger than the value from the reconstructed exit wave phase map. If extremely high accuracy of the d measurement is not needed, it is sufficient to use a slightly over-focused image, leading to a mismatch value of ≈2%. Overall, the developed approach for measuring interlayer distances in BLG is essential for exploring the correlation between d in van der Waals 2D materials and their properties.