N anoporous atomically thin membranes offer trans- formative potential across a broad spectrum of applications including ionic/molecular separations, small molecule separation, dialysis, gas separation, proton exchange membranes, isotope separations, among others. [1][2][3][4][5][6][7] Among the different atomically thin 2D materials, monolayer hexagonal boron nitride (h-BN) offers a unique combination of atomic thinness, exceptional chemical resistance, remarkable thermal stability, and most importantly, its capacity to support lattice defects that manifest as nanopores in an atomically thin membrane. [8][9][10][11][12] These properties make monolayer h-BN ideally suited for fabricating atomically thin ceramic membranes with both high permeance (due to atomic thinness) and selectivity (via molecular sieving). 1,6 h-BN membranes have been explored for applications including DNA translocation, proton exchange 4,[13][14][15][16] and isotope separation 3,17 as well as ionic 18,19 and molecular separations.

However, introducing precise nanopores into monolayer h-BN presents significant challenges. Unlike graphene, where top-down etching techniques such as oxygen plasma and/or chemical etching readily introduce pores via a scalable process over large areas, the chemical inertness of h-BN limits pore formation to e-beam 20,21 and ion irradiation 22 that are often limited to small areas and low throughput or reactive ion etching techniques 23,24 or XeF 2 etching, 25 necessitating multiple process steps. Another challenge is the absence of a rapid and reliable method for characterizing defects in h-BN, preventing an effective feedback loop. For example, while graphene benefits from Raman spectroscopy as a reliable tool for defect analysis, equivalent techniques for h-BN currently remain elusive. 26,27 Current methods for nanoscale h-BN defect characterization such as scanning tunnelling microscopy/spectroscopy (STM/S) and scanning transmission electron microscopy (STEM) are expensive, have low throughput, and are impractical for large-scale characterization limiting progress of nanoporous atomically thin h-BN membranes. 8,21,28,29 We note that the ability to probe defects in the subnanometer to nanoscale range over large areas in monolayer h-BN is highly relevant to applications beyond atomically thin membranes, [15][16][17]21,[30][31][32][33][34][35] e.g., nanoelectronics, [36][37][38][39][40][41][42][43][44][45][46] neutron detectors, [47][48][49][50][51][52][53] photonics, 41,[54][55][56][57][58] oxidation protection, 59 semiconductor processing, 60,61 and others.

Here, we introduce a novel, scalable bottom-up approach to directly incorporate subnanometer-scale and nanoscale pores into monolayer h-BN during CVD by precisely tuning the synthesis temperature. While bottom-up synthesis of nanoporous monolayer graphene to fabricate atomically thin membranes exists, 7,62-72 they remain elusive for h-BN.

Additionally, we leverage a manufacturing-compatible process that integrates CVD-grown h-BN with poly ether sulfone (PES) through phase inversion, resulting in centimeter-scale h-BN+PES composite membranes. 63,73 Further, we use diffusionbased transport experiments, 63,74,75 including size-selective Ficoll sieving, [76][77][78] to characterize nanopore size distribution over large membrane areas. Our results indicate that CVD growth conditions play a critical role; i.e., subnanometer pores are maximized at intermediate temperatures (∼975 °C). This controlled bottom-up nanopore formation, governed by the kinetics of the growth and etching processes, offers a pathway to enable atomically thin h-BN membranes. Finally, the h-BN Figure 1. Bottom-up synthesis of monolayer h-BN. A) Hot-wall chemical vapor deposition (CVD) reactor setup using ammonia-borane as precursor for h-BN synthesis on polycrystalline Cu foil (also see Figure S6). B) Schematic of reactor and precursor chamber temperature profiles during CVD process. C) Exemplar optical image of unmerged monolayer triangular domains of h-BN on Cu foil after oxidization of the Cu foil by heating on a hot plate at ∼200 °C. D) SEM image of complete h-BN film on Cu, identified via wrinkles in h-BN formed due to difference in thermal expansion between h-BN and the underlying Cu catalyst. Inset: STEM image of h-BN lattice (also see Figure S8). E) XPS spectra of h-BN on Cu with characteristic N 1s and B 1s spectra. F) AFM micrograph and line profile of edge of h-BN film transferred to 300 nm SiO 2 /Si wafer. The thickness of the film is observed to be ∼0.56 nm, consistent with monolayer h-BN. G) Raman spectrum of continuous h-BN film transferred to 300 nm SiO 2 /Si wafer shows the characteristic E 2g peak. H) UV-vis absorption spectra and the computed Tauc plot and calculated optical bandgap of ∼5.9 eV. 97,104 All characterizations presented in Figure 1 are performed on h-BN grown for 90 min (for continous films and ∼22-25 min for unmerged domains) at 1025 °C with 3.5 mg precursor at 85 °C (see Supporting Information). membranes demonstrate separation factors as high as ∼97 for KCl (∼0.66 nm) versus lysozyme (∼3.8-4 nm) and ∼43 for Ltryptophan (∼0.7-0.9 nm) versus lysozyme, alongside high permeance values (KCl ∼(2.1-7.4) × 10 -6 m s -1 , L-Tr ∼(0.7-3.3) × 10 -6 m s -1 , Lz ∼(3.6-20.9) × 10 -8 m s -1 ) for model nanoscale separations. 79 ■ BOTTOM-UP SYNTHESIS OF MONOLAYER H-BN

Atomically thin membrane applications necessitate large-area synthesis of 2D materials, and chemical vapor deposition (CVD) has emerged as the preferred route for scalable and cost-effective high-quality 2D material synthesis, 8,80 including proof-of-concept demonstrations of manufacturing compatible roll-to-roll approaches. [81][82][83][84] However, 2D materials synthesized via CVD contain intrinsic lattice defects viewed as detrimental to electronic applications. 1,4,6,85 For membrane applications, defects in the 2D lattice manifest as pores in an atomically thin membrane. Here, we demonstrate direct incorporation of nanopores into the atomically thin h-BN lattice during CVD via facile tuning of CVD growth temperature and enable the creation of nanoporous atomically thin ceramic membranes with size-selective transport without the need for postsynthesis top-down pore creation approaches that are challenging for ceramics/h-BN. Unlike graphene where Raman spectroscopy offers a measure of defects in the 2D lattice, 26 no equivalent technique currently exists for probing defects in h-BN. Here, we use size-selective transport as a measure of defect sizes in monolayer h-BN over centimeter-scale areas by fabricating atomically thin membranes. 86 We use a custom-built hot-wall reactor (Figure 1A and Figure S6) with ammonia-borane precursor and H 2 gas to synthesize monolayer h-BN via CVD (Figure 1B) on polycrystalline copper (Cu) foil catalysts (see methods). 8,80 Ammonia-borane (precursor for B and N atoms 87,88 ) is heated in a side chamber and the products are introduced into the reactor with H 2 as the carrier gas to the Cu foil catalyst. 87,88 The Cu foil catalyzes monolayer h-BN via precursor dissociation, nucleation of h-BN domains (Figure 1C), and subsequent growth of the domains to merge forming a polycrystalline film with increasing CVD growth time (Figure 1D, Figure 2A). The triangular shape of the nuclei is attributed to the higher stability of N terminated edges. 86,87 The side chamber temperature (∼70-90 °C) allows for control over precursor delivery to the CVD reactor 87,88 (Figure 2) and the CVD reactor temperature (∼875-1025 °C) allows for control over film morphology (see Figure S1) and quality (Figures 3-5) as discussed further below. We only use h-BN grown at >925 °C for membrane fabrication (Figure 3), since growth at 875 °C results in an incomplete film (Figure S1).

h-BN nuclei on Cu foil appear as individual unmerged triangular domains that are readily visible via optical microscopy (Figure 1C) after selective oxidization of the uncovered Cu foil surface by heating it on a hot plate in ambient environment. [89][90][91][92] SEM images further confirm the triangular h-BN nuclei (Figure 2A images on the left column) on Cu foil as well as continuous h-BN films formed with increasing growth time (Figure 1D, Figure 2A images on the right column) and identified via with characteristic features such as wrinkles formed due to the difference in thermal expansion between h-BN and the underlying Cu catalyst upon cooling to ambient temperature. 93 Additionally, secondary and ad-layers are also seen as smaller triangles along with wrinkles in the continuous h-BN films (Figures 1D and 2A, Figure S1).

SEM images (Figure 2A) show h-BN surface coverage (Figure 2B) increases with time for all side chamber temperatures (∼70-90 °C) indicating precursor delivery throughout the growth period. 87,88 The side chamber temperature also influences the rate of h-BN growth on Cu (Figure 2C); i.e., complete surface coverage (continuous film) is achieved within 30 min for side chamber temperatures ∼90 °C, while temperature ∼70 °C yields incomplete films even after 45 min (Figure 2A). 87,88 These observations indicate that the CVD process is in a kinetic regime limited by precursor supply. 80,[94][95][96][97][98] Finally, h-BN domain sizes (triangular edge length) measured just before full film coalescence (Figure 2D) decrease from ∼17 to ∼13 μm upon increasing side chamber temperature from 80 to 90 °C (Figure 2D), indicating higher nucleation density with increased precursor delivery at 90 °C. 98 X-ray photoelectron spectroscopy of the h-BN films on Cu shows characteristic peaks in the core level N 1s (∼398.3 eV) and B 1s (∼190.7 eV) spectra (Figure 1E) with a B:N ratio ∼1 (Figure S2), confirming the elemental composition and stoichiometric balance of B and N atoms, respectively. 80,99 Atomic force microscopy of an h-BN unmerged film transferred to 300 nm SiO 2 /Si wafer shows film thickness ∼0.56 nm, consistent with monolayer h-BN 93,100 (Figure 1F), and Raman spectra show the characteristic E 2g peak ∼1372 cm -1 for h-BN (Figure 1G). 27,101 Finally, the UV-vis absorption spectrum (Figure 1H) shows a strong absorbance peak at ∼202 nm and the corresponding Tauc plot indicates an optical bandgap of ∼5.9 eV, also consistent with monolayer h-BN. 54,93,97,[102][103][104][105] Finally, atomic resolution scanning tunneling microscopy (STM) and scanning transmission electron microscopy images (STEM) images show a hexagonal honeycomb mesh and further confirm the high crystallinity of the h-BN films (Figure 4E and inset of Figure 1D).

Having confirmed atomically thin h-BN films have been synthesized via CVD on Cu, we proceed to fabricate centimeter-scale nanoporous atomically thin ceramic membranes via facile and scalable polymer casting (Figure 3A). 79,84 A thin layer of polyether sulfone (PES) solution is cast onto h-BN on Cu and the resulting stack (PES|h-BN|Cu foil) is immersed immediately in a water bath to induce phase inversion of PES (Figure 3A) converting it into porous supports for h-BN. 79,84 Subsequent removal of the Cu foil via etching results in large-area h-BN transferred to porous PES supports, forming atomically thin ceramic membranes (see the optical image in Figure 3B). SEM images (Figure 3C�top view, Figure 3D�cross section, and Figure S3) show 300-500 nm pores in the PES in the vicinity of h-BN effectively supporting the atomically thin monolayer and branch out to more finger-like structures further below, forming a hierarchical network of interconnected channels (Figure 3C,D, Figure S3) within the ∼50 μm thick PES supports (Figure S3A). 79,84 The insulating nature of h-BN and PES presents challenges with SEM imaging due to charging, but adlayers are visible upon careful observation (Figure S3C,D), indicating the presence of the h-BN film on the PES supports (PES surface porosity ∼50%, Imagej analysis of SEM images).

Pressure driven transport of ethanol confirms h-BN is successfully transferred to PES supports and relatively free of large tears. 75,85 Notably, compared to the control membrane, i.e., PES support (see methods), h-BN+PES effectively blocks >99% of pressure-driven ethanol flow (Figure 3E). Next, we proceed to measure and compare molecular diffusion through nanopores in h-BN to i) demonstrate molecular sieving though nanopores in h-BN membranes and ii) use diffusive transport to characterize nanopore sizes in h-BN as a function of synthesis temperature (Figure 3F-I, Figure 5).

Initially, we probe diffusive transport of single species using model analytes from subnanometer to nanometer length scales, i.e., KCl (hydrated diameter K + ∼0.66 nm, Cl -∼0.66 nm), NaCl (hydrated diameter Na + ∼0.72 nm, Cl -∼0.66 nm), Ltryptophan (L-Tr ∼0.7-0.9 nm), vitamin B12 (B12 ∼1-1.5 nm), and lysozyme (Lz ∼3.8-4 nm). 74,75,79,84 Notably, the addition of h-BN significantly reduces the diffusive permeance of all species compared to PES controls without h-BN (Figure 3F), indicating the observed transport resistance originates for monolayer h-BN. Further, the diffusive permeances though h-BN+PES and PES control membranes show a decreasing trend with increasing analyte size consistent with lower diffusivity for larger species (Figure 3G). The effectiveness of the PES control membranes is observed via the selectivity (ratio of permeance) of the probed analytes being similar to i) polycarbonate track etched membranes with straight channel ∼200 nm pores that do not overlap and ii) ratio of diffusivity of analytes in free solution (Figure S4). [106][107][108][109][110] To deconvolute transport from solution diffusivity, we use the permeance ratio of the h-BN+PES membrane to the PES control membranes, i.e., normalized flux (Figure 3H). We observe a reduction in normalized flux with increasing analyte size for the h-BN membranes, indicating the presence of nanopores in the ∼0.66-4 nm size range (Figure 3I); e.g., h-BN synthesized at 1025 °C exhibits normalized flux of KCl ∼23.8%, NaCl ∼20.6%, L-Tr ∼18.2%, B12 ∼11.1% and Lz ∼4.3%. Interestingly, a reduction in CVD temperatures results in significantly higher normalized flux; e.g., h-BN synthesized at 975 °C shows normalized flux of KCl ∼82.6%, NaCl ∼82.4%, L-Tr ∼81.1%, B12 ∼58.7% and Lz ∼9.1% (Figure 3I), indicating facile incorporation of nanopores into the h-BN lattice via a reduction in CVD temperature. Further, the normalized flux of Lz consistently increases as the h-BN growth temperature decreases, i.e. Lz ∼4.3% (∼1025 °C), ∼7.9% (∼1000 °C), ∼9.1% (∼975 °C), ∼11% (∼950 °C), ∼25% (∼925 °C), respectively, indicating an increase in defects >3.8-4 nm with lower h-BN growth temperatures. However, the permeance of smaller species do not particularly Nano Letters pubs.acs.org/NanoLett Letter follow this trend; e.g., h-BN grown at 975 °C shows the highest normalized flux for KCl, NaCl, L-Tr, and B12 with higher and lower growth temperature decreasing the normalized flux. Finally, we note that the entire process from h-BN synthesis to membrane fabrication is reproducible across multiple samples (Figure S7). The difference in normalized flux of the different analytes can be used to aid visualization of the distribution of nanopore sizes in the atomically thin h-BN membrane (Figure 3I). For example, the normalized flux associated with defect in the ∼0.66-1.5 nm size range can be obtained by subtracting the normalized flux of B12 (∼1-1.5 nm) from the flux of KCl (∼0.66 nm). Similarly, the difference between normalized flux of Lz (∼3.8-4 nm) and B12 represents defects in the ∼1.5-4 nm size range (Figure 3I). Hence, diffusive transport indicates the highest fraction of defects in the subnanometer size range for h-BN grown at ≥1000 °C, the ∼1.5-4 nm range for h-BN grown at intermediate temperatures of ∼950 °C and ∼975 °C, and ≥3.8-4 nm for h-BN grown at ∼925 °C. 79,80,111 These observations of diffusive transport are further supported by atomic resolution STM and SEM images of the as-synthesized h-BN directly on Cu for different synthesis temperatures (Figure 4, Figure S1) avoiding convolution from transfers processes that leave residues necessitating subsequent aggressive cleaning processes. 7,75,111 Representative STM images of films grown at 1025 °C shows the hexagonal h-BN lattice and a low density of subnanometer defects (Figure 4). A significant increase in number and size of defects is observed upon reducing growth temperature to ∼975 °C in agreement with transport measurements (Figure 3). An analysis of the representative STM images (while acknowledging limitations of STM to small scan areas) indicates defect density ∼6.8 × 10 12 cm -2 for 975 °C and ∼2.4 × 10 12 cm -2 for 1025 °C, respectively.

For temperatures ≤925 °C a distinct change in film morphology is seen (Figure 4 and Figure S1) compared to higher growth temperatures and STM imaging was nontrivial with an extremely rough surface. However, XPS indicates stochiometric balance of B:N ∼ 1 is maintained for all synthesis temperatures ∼875-1025 °C (Figure S2). While the exact mechanisms of nanopores formation remain an active area of research, we hypothesize it results from the complex interplay of several synergistic as well as competing h-BN growth steps including precursor dissociation on the Cu surface to form active species, diffusion of active species on the Cu surface, reaction rate to form the h-BN film, incorporation of elemental species into the Cu bulk and solubility, desorption from the Cu surface, and H 2 etching during growth that can all change with CVD temperature. 80,87,97,[112][113][114] Notably, a reduction in CVD temperature could potentially change the rate-determining step in the h-BN growth process (due to differences in activation energies and frequency factors for each of the different reaction rates involved) allowing for formation of defects that manifest as nanopores. Taken together, a reduction in CVD growth temperature enables straightforward synthesis of nanoporous atomically thin h-BN. Remarkably, the h-BN + PES membranes fabricated using h-BN synthesized ∼975 °C shows selectivity (ratio of permeance) for KCl/Lz ∼97 and L-Tr/Lz ∼43 (Figure S5). To the best of our knowledge, our experiments represent the first demonstration of fully functional centimeter-scale nanoporous atomically thin h-BN membranes for nanoscale separations.

While the single-analyte diffusion measurements allowed probing of defects in ∼0.66-4 nm size rage in centimeter-scale atomically thin h-BN membranes (Figure 3), characterizing size distribution of defects over a wider size range and with a continuum of analyte sizes could enable advances in h-BN Nano Letters pubs.acs.org/NanoLett Letter https://doi.org/10.1021/acs.nanolett.4c05939 Nano Lett. XXXX, XXX, XXX-XXX F defect characterization for membrane as well as other applications.

Using diffusive transport of FITC-labeled Ficoll (branched polymer of sucrose and epichlorohydrin) as feed, we probe defects in the ∼2-24 nm size range (1-12 nm radius) via sizeexclusion chromatography of the permeate diffusing through the h-BN + PES membranes (Figure 5A) fabricated using h-BN synthesized at different growth temperatures. [76][77][78] Figure 5B shows an increasing concentration of Ficoll over time from 1 to 7 days in the permeate with h-BN grown at high temperatures allowing for the least Ficoll transport throughout the size range, while decreasing the h-BN growth temperature results in more Ficoll transport (Figure 5B-D), consistent with diffusive transport experiments (Figure 3I). Notably, the size cutoff of 925 °C h-BN+PES membranes is ∼7 nm analyte radius, whereas h-BN grown at 975 and 925 °C exhbits a size cutoff ∼5 nm analyte radius (Figure 5C,D). Finally, a comparison of Ficoll transport of similar size to Lz (∼2 nm radius) with diffusive transport measurements of Lz (Figure 3) shows good agreement. Taken together, our Ficoll experiments successfully characterize size distribution (ranges ∼2-24 nm) of nanopores/defects in centimeter-scale atomically thin h-BN membranes in a resource efficient manner that has previously remained elusive.

In summary, we demonstrate a facile and scalable method for fabricating centimeter-scale atomically thin ceramic membranes via bottom-up synthesis and polymer casting. A reduction in CVD temperature allows for direct incorporation of subnanometer-scale and nanoscale pores into the h-BN lattice during growth, alleviating the need for postsynthesis top-down pore creation approaches that remain challenging and increase costs and process complexity. Using a manufacturing compatible polymer casting and phase inversion approach to form porous PES supports for the nanoporous h-BN, we demonstrate centimeter-scale atomically thin ceramic membranes. We characterize the nanopores over large areas in atomically thin h-BN via diffusive-transport of analytes and size-selective Ficoll sieving to measure size distributions. The resulting h-BN membranes show selectivity of ∼97 for KCl/Lz and ∼43 for L-Tr/Lz, alongside significantly high permeance, and present potential for applications including protein desalting, dialysis, and small-molecule separations. Our work provides foundational approaches to enable atomically thin ceramic membranes, unlocking the potential of materials like h-BN for nanoscale separations including in potentially harsh