a–d, The growth and surface morphology of ultrathin STO films of thickness four unit cells (a), three unit cells (b), two unit cells (c) and one unit cell (u.c.) (d) on six-unit-cell-thick SAO-buffered STO substrates. The RHEED intensity oscillations (red curves) exhibit four intensity oscillation periods in the growth of one-unit-cell-thick SAO (especially near the SAO surface). Insets, the RHEED diffraction patterns show clear fourfold reconstructed diffraction patterns. The atomic force microscopy (AFM) images (right panels) show clear steps and terraces, indicating the smooth film surfaces. e, High-resolution XRD 2θ–ω scans of a three-layered heterostructure consisting of an STO film (60 unit cells thick) on an SAO (four unit cells thick) on an STO substrate heterostructure and the corresponding freestanding STO film and STO substrate after releasing the sample. The asterisk denotes the background diffraction peak from the PDMS tape. f, Optical image of the freestanding 60-unit-cell-thick STO transferred onto PDMS with the support of a glass slide. g, Magnification of the 2θ–ω scans around the STO(002) substrate peak show clear thickness fringes, indicating the smooth surfaces of both the as-grown and freestanding films.