Nanometre-thick single-crystalline nanosheets grown at the water–air interface

To date, the preparation of free-standing 2D nanomaterials has been largely limited to the exfoliation of van der Waals solids. The lack of a robust mechanism for the bottom-up synthesis of 2D nanomaterials from non-layered materials has become an obstacle to further explore the physical properties and advanced applications of 2D nanomaterials. Here we demonstrate that surfactant monolayers can serve as soft templates guiding the nucleation and growth of 2D nanomaterials in large area beyond the limitation of van der Waals solids. One- to 2-nm-thick, single-crystalline free-standing ZnO nanosheets with sizes up to tens of micrometres are synthesized at the water–air interface. In this process, the packing density of surfactant monolayers adapts to the sub-phase metal ions and guides the epitaxial growth of nanosheets. It is thus named adaptive ionic layer epitaxy (AILE). The electronic properties of ZnO nanosheets and AILE of other materials are also investigated.


Supplementary Notes
Supplementary Note 1: X-ray photoelectron spectroscopy of ZnO nanosheets Supplementary Figure 2a

Supplementary Note 2: DFT simulation methods and results on the crystal structure and band structure of ZnO nanosheets
For the bare ZnO(0001) slab, we surprisingly find that the most stable atomic arrangement is the tetragonal structure. In contrast, the planar structure is 44 meV per Zn atom (44 meV/Zn) higher than the tetragonal one. Although a bilayer planar ZnO(0001) was experimentally obtained on Ag(111), 1 our calculations suggest that the planar slab is more stable than the tetragonal one only when the thickness is equal to or less than three ZnO layers (Supplementary Figure 8). The wurtzite structure is the least stable form and it dynamically evolves to the planar structure in a fully geometry relaxation, which may explain the previous theoretical findings of planar structures. 2 For a ZnO(0001) slab with surfactants closely packed on one surface, the tetragonal structure is still the most stable one. The wurtzite-like structure is less stable than the tetragonal structure by 10 meV/Zn, while the planar structure becomes dynamically unstable. The energetics of the three phases are summarized in Supplementary Table 2.

Supplementary Note 3: Control experiments using stearic acid as the surfactant monolayer.
To further prove the critical role of the interactions between oleylsulfate and Zn 2+ ions, we did the syntheses with the same experimental parameters except using stearic acid to replace oleylsulfate. As shown in Supplementary Figure 10, we could only obtain large area amorphous film with sporadic, small crystallites, without forming faceted triangular morphology, much like the amorphous film formed initially during the synthesis using oleylsurfate. Therefore, it is certain that the interactions between oleylsulfate and Zn 2+ ions are more than just electrostatic, and the specific bonding between the two parties is necessary to help the inter-distance between oleylsulfate molecules adapt to the Zn 2+ ions in order to foster the epitaxial growth of ZnO nanosheets. nm. Supplementary Figure 11a

Supplementary Discussions
We think the formation of the nanoparticles in the SEM images is likely due to the residue chloroform that was used to disperse the surfactant monolayer. The precursors might have gone into the organic phase where they nucleate and grow in a dissimilar way from the aqueous phase.
There are two experiment evidences to support this. First, if we waited 5 to 10 minutes for the chloroform to completely evaporate before moving the glass vial to the oven to initiate the reaction, the amount of unwanted particles on the nanosheets were significantly reduced. Second, instead of a water-air interface, we are able to grow ZnO nanosheets at water-cyclohexane interface (Supplementary Figure 1d). In this case, none of the nanoparticles appeared on the nanosheets.

X-ray photoelectron spectroscopy
XPS spectra of ZnO nanosheets were acquired by Thermo K-alpha X-ray photoelectron spectrometer with a focused, monochromatic X-ray source and monoatomic ion gun.

Calculation of electric potential profile and Zn 2+ concentration profile from the surfactantwater interface into the bulk solution.
A charged surface, such as the surfactant monolayer, will push and pull on charged species in Thus, the total of all ion concentrations at the closest approach to the 2D charged layer must be equal to or less than this atomic density.
∑ n i ≤ 6.54729 * 10 27 ions m 3 Supplementary Table 1 shows a clear violation of this condition.
Iterative numerical calculation was applied to find the limit of at which Supplementary Eq. 2 and Supplementary Eq. 3 obtained the condition required in Supplementary Eq. 5. This yielding the critical criteria for the surface potential: x=0 ≤ 0.090994 V. In order to achieve this potential, far less than the 0.23309 V previously determined to be present at the charged monolayer, a charged stern layer is assumed to form adjacent to the charged self-assembled surfactant monolayer. Using Supplementary Eq.
2 and Supplementary Eq. 3 again, except now fixing x=0 = 0.090994 V and solving for σ, it is found that a surface charge density of 0.0651358 2 is capable of maintaining a x=0 = 0.090994 V in the required aqueous conditions. Physically, this apparent surface charge density σ A is the 2D charge density necessary to create an electric field strong enough to condense the charged species in solution into a close packing structure. Because the superposition principle applies in electromagnetism, the 2D charge density (σ A ) that the solution experiences is a sum of the surfactant monolayer's charge density (σ M ) and the Stern layer's charge density (σ S ).
To gain insight into the nature of the charged Stern layer, and determine if it is physical reasonable, rearranging Supplementary Eq. 7 and solving for σ S yields: This value for σ S is well within the theoretical maximum 2D charge density (σ σ Max S is greater than the previously determined value of 0.735952 2 for σ S and thus σ S is deemed a physically reasonable value for the stern layer charge density.

ZnO-based FET and calcations on the carrier concentration and hole mobility
Supplementary Figure 6a shows a metal pad array with nanosheets on them and Supplementary   Figure 6b shows the single nanosheet-based FET from which the I-V characteristics in main text Figure 4 were obtained.
The hole concentration and hole mobility were calculated by following two equations, respectively.
and ds ox where V th is the threshold voltage. C ox is the capacitance of the dielectric oxide. Q is the charge of an electron. W, h, and L are the channel width, height, and length of the nanosheet, respectively. A channel is the channel area defined by the channel length times channel width. ε 0 and ε ox are the electrical permittivity of vacuum and Al 2 O 3 , respectively. The latter was assumed to be 10 based on literature value and the growth condition. 5,6 t ox is the thickness of Al 2 O 3 . g m is the transconductance at gate voltage V ds .
The Brillouin zone is sampled with a 5 × 5 × 1 Monkhorst-Pack grid. The atom positions and in-plane lattices are fully relaxed until the force on each is less than 10 -3 eV/Å. The surfactant molecules are packed closely on the slab surface, with a density of one surfactant molecule per four surface Zn atoms.
To reduce the computational cost, a 3-carbon chain is used to represent the 18-carbon chain in oleylsulfate. Tests show that this simplification has a minor influence to the properties we are interested in.

Simulated electron diffraction pattern of ZnO nanosheets
JEMS was used to simulate the electron diffraction patterns along the surface normal of the nanosheets for Wurtzite structure (0001) and the tetragonal structure (100), as shown in Supplementary Figure 9.

Synthesis of NiO nanosheets by ionic layer epitaxy
In a typical synthesis of NiO nanosheets, 0.0648g NiCl 2 was dissolved in 50 mL DI water. After complete dissolution, 130 µL hydrazine was added to the aqueous solution. Subsequently, 10 mM 1M NaOH solution was added, yielding a clear green solution. Depending on the opening size of the reactor, 0.02 mg/L chloroform solution of stearic acid was spread onto the surface of the growth solution. After 5 mins, the solution was placed in 70 °C oven and the reaction was conducted for 30 minutes.

Synthesis of Au nanosheets by ionic layer epitaxy
To synthesis Au nanosheets, in a 6-dram vial, 10μL of a 0.10 M NaOH solution was diluted with 5.790mL of water and 1.000mL of a 2.0 mM L-Arginine solution. To this, 0.200mL of 17.14mM HAuCl4 solution was added and gently swirled to combine. 10μL of stearic acid in chloroform (1mg/5mL) was gently dropped on top of the water and left to evaporate for 10 minutes. The vial was then capped tightly and placed in a 90°C convection oven for 2 to 7 hours. The vial was left to cool to room temperature and the surface of the water was then sampled with a SiO 2 -coated silicon wafer for SEM imaging.