Fig. 1: Evolution of the space between Cu foil and the SiO₂ substrate with increasing temperature.

a Plot and fit of the van der Waals force as a function of the distance between hBN and SiO₂. The attractive force is negligible when the distance is larger than 0.9 nm and increases within the distance range of 0.33–0.8 nm. The orange squares represent the calculated data and the dark green line is the fitted curve. The light blue and light yellow shaded areas correspond to the repulsive and attractive force. Inset: schematic diagram of hBN on SiO₂. b Charge density difference diagram of hBN/SiO₂ with distances of 0.8 nm and 0.33 nm. The yellow and blue colours correspond to the charge accumulation and depletion, respectively. c Schematic diagrams of the evolution of the space between the Cu foil and SiO₂ substrate with increasing temperature. d, e Typical optical images of the cross section of the Cu/SiO₂ substrate annealed at room temperature (d) and 1080 °C (e). The cross-sectional optical images are obtained with a portable microscope at room temperature (see the setup in Supplementary Fig. 14). f Cross-sectional high resolution transmission electron microscopy image of the Cu/SiO₂ structure annealed at 1087 °C. The distance becomes smaller than 0.8 nm.