Research ArticlePHYSICS

Two-dimensional limit of crystalline order in perovskite membrane films

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Science Advances  17 Nov 2017:
Vol. 3, no. 11, eaao5173
DOI: 10.1126/sciadv.aao5173
  • Fig. 1 Freestanding SrTiO3 membranes of a few unit cell thicknesses.

    (A) A schematic SrTiO3/Sr3Al2O6 film heterostructure grown on a SrTiO3 (001) substrate. The Sr3Al2O6 layer is dissolved in room temperature water to release the top SrTiO3 layer. (B) Optical image of a suspended SrTiO3 membrane [6 unit cells (u.c.) in thickness] on a silicon nitride transmission electron microscopy (TEM) grid with 2-μm diameter holes. Scale bar, 50 μm. (C) High-resolution TEM (HR-TEM) images of SrTiO3 membranes of different thicknesses. Scale bars, 10 nm.

  • Fig. 2 Crystalline domain imaging using DF-TEM.

    (A) Diffraction patterns from suspended SrTiO3 membranes (signals from the entire suspended area of 2-μm diameter), from 6- (left), 4- (center), and 2-u.c.thick (right) membranes. The exposure time varies from 1 (6 u.c.) to 10 s (2 u.c.). The red circle indicates the size of the aperture for DF-TEM to selectively collect signals from crystalline domains. (B) DF-TEM images from membranes of different thicknesses, for which crystalline domains are of white color. Scale bars, 10 nm. (C) Thickness-dependent (d) crystalline coherence length (L) calculated from the spatial correlation function 〈G〉 deduced from DF-TEM images. Inset: The raw data of the correlation function from a 6-u.c. thick membrane.

  • Fig. 3 RHEED patterns of SrTiO3 films before and after solvent exposure and transfer.

    Top: RHEED patterns of SrTiO3 films of different thicknesses grown on a Sr3Al2O6 20-nm film on a SrTiO3 (001) substrate. Middle: RHEED patterns of SrTiO3 films of different thicknesses grown on a Sr3Al2O6 5-nm film on a SrTiO3 (001) substrate after exposure to all solvents and polymer coatings used in the actual transfer process. The sacrificial layer (Sr3Al2O6) was too thin to be dissolved despite the long immersion in water; therefore, the SrTiO3 films are still epitaxially integrated to the 3D bulk crystalline heterostructure. Bottom: RHEED patterns of transferred SrTiO3 membranes (on Si/SiO2 substrates) of different thicknesses. The RHEED intensity of the 4-u.c. membrane diminished drastically and showed little signature of the crystalline phase. By contrast, the 8-u.c. membrane showed a similar RHEED pattern as the original film. No RHEED pattern was detected from the transferred 2-u.c. membrane.

  • Fig. 4 2D crystalline phase transition in SrTiO3 membranes.

    (A) Phase diagram of crystalline order in 2D membranes. The phase boundary is set by the BKT transition energy (1/2 E2D) proportional to the 2D modulus, thus the membrane thickness (see the Supplementary Materials) (5, 6). Thermal fluctuations at room temperature (kBT) are far below the BKT transition scale. However, fluctuation energy from interface bond breaking exceeds kBTBKT in the thin limit, collapsing the crystalline quasi-order for membranes thinner than the critical thickness (dBKT) during release from the bulk substrate. (B) Thickness-dependent dislocation area radius rd = (area)1/2 from DF-TEM images. Inset: An HR-TEM image of a dislocation for an 8-u.c. membrane. The green line encompassing the dislocation is closed, implying zero Burgers vector dislocation configuration. (C) A logarithmic plot of crystalline coherence length (L) versus (dBKT/d − 1)−ν for the membrane thicknesses below dBKT (2 to 5 u.c.). The gray line represents the least-square fitting of four data points assuming an exponential relation. Inset: critical exponent fitting from the crystalline coherence length, resulting in ν = −0.39.

  • Fig. 5 Phase diagram of 2D crystalline order limited by interface bond breaking.

    Crystalline correlation length (ξ) as a function of the membrane thickness (d) and bonding anisotropy (E/E) based on continuum elastic theory. Ionic bonding (Born-Lande model) lattice of α = 8 (corresponding to SrTiO3) and the numerical coefficients from Fig. 4C are assumed.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/11/eaao5173/DC1

    fig. S1. Growth of SrTiO3/Sr3Al2O6 films.

    fig. S2. Transfer of SrTiO3 membranes.

    fig. S3. Chemical stability of SrTiO3 films.

    fig. S4. Strain test using AFM force spectroscopy.

    fig. S5. In situ heating experiment in TEM.

    Control experiments

    Continuum elastic theory and atomic potential model

    References (34, 35)

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Growth of SrTiO3/Sr3Al2O6 films.
    • fig. S2. Transfer of SrTiO3 membranes.
    • fig. S3. Chemical stability of SrTiO3 films.
    • fig. S4. Strain test using AFM force spectroscopy.
    • fig. S5. In situ heating experiment in TEM.
    • Control experiments
    • Continuum elastic theory and atomic potential model
    • References (34, 35)

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