Mapping twist and strain evolution during thermal relaxation of twisted hexagonal boron nitride interfaces

Precise control over both twist angle and strain is necessary to design novel properties originating from moiré superlattices in van der Waals heterostructures. However, the heterostructure assembly process typically imparts twist angle inhomogeneity and strain, and the origin of these unintentional distortions is often not explicitly known. Post-stacking thermal annealing has been shown to reduce the twist angle due to gradual relaxation and rotation of the moiré interface and might also reduce spatial inhomogeneity. Here, we apply scanning probe microscopy to elucidate the thermal relaxation of twist angle and strain within ferroelectric hexagonal boron nitride structures. We develop and compare real-space and FFT-based twist/strain extraction algorithms for hBN interfaces with nominal twist angles ranging from 0.08º to 0.28º. Applying successive annealing steps under ambient and UHV conditions, at temperatures up to 400 ºC, reveal spatially-dependent evolution of twist and strain, and suggest potential sources of strain generation and pinning within fabricated stacks.