Centimeter-Scale Nanoporous 2D Membranes and Ion Transport: Porous MoS2 Monolayers in a Few-Layer Matrix.

Two-dimensional nanoporous membranes have received attention as catalysts for energy generation and membranes for liquid and gas purification but controlling their porosity and facilitating large-scale production is challenging. We show the growth and fabrication of centimeter-scale molybdenum disulfide (MoS2) membranes with tunable porous areas up to ∼ 10% of the membrane and average nanopore diameters as large as ∼ 30 nm, controlled by the etch time. We also measure ionic conductance between 0.1 and 16 µS per µm2 through variably etched nanoporous membranes. Ensuring the mechanical robustness and large-area of the membrane, bilayer and few-layer regions form a strong supporting matrix around monolayer regions, observed by aberration-corrected scanning transmission electron microscopy. During etching, nanopores form in thin, primarily monolayer areas whereas thicker multilayer regions remain essentially intact. Atomic-resolution imaging reveals that after exposure to the etchant, the number of V1Mo vacancies increases and nanopores form along grain boundaries in monolayers, suggesting that etching starts at intrinsic defect sites. This work provides an avenue for the scalable production of nanoporous atomically thin membranes.

Atomic-scale patterning in two-dimensional van der Waals superlattices.

Two-dimensional (2D) van der Waals superlattices comprised of two stacked monolayer materials have attracted significant interest as platforms for novel optoelectronic and structural behavior. Although studies are focused on superlattice fabrication, less effort has been given to the nanoscale patterning and structural modification of these systems. In this report, we demonstrate the localized layer-by-layer thinning and formation of nanopores/defects in 2D superlattices, such as stacked MoS2-WS2 van der Waals heterostructures and chemical vapor deposited bilayer WSe2, using aberration-corrected scanning transmission electron microscopy (STEM). Controlled electron beam irradiation is used to locally thin superlattices by removing the bottom layer of atoms, followed by defect formation through ablation of the second layer of atoms. The resulting defects exhibit atomically-sharp pore edges with tunable diameters down to 0.6 nm. Structural periodicities and focused STEM irradiation are also utilized to form close-packed nanopore arrays in superlattices with varying twist angles and commensurability. Applying these methods and mechanisms provides a forward approach in the atomic-scale patterning of stacked 2D nanodevices.

Angstrom-Size Defect Creation and Ionic Transport through Pores in Single-Layer MoS2.

Atomic-defect engineering in thin membranes provides opportunities for ionic and molecular filtration and analysis. While molecular-dynamics (MD) calculations have been used to model conductance through atomic vacancies, corresponding experiments are lacking. We create sub-nanometer vacancies in suspended single-layer molybdenum disulfide (MoS2) via Ga+ ion irradiation, producing membranes containing ∼300 to 1200 pores with average and maximum diameters of ∼0.5 and ∼1 nm, respectively. Vacancies exhibit missing Mo and S atoms, as shown by aberration-corrected scanning transmission electron microscopy (AC-STEM). The longitudinal acoustic band and defect-related photoluminescence were observed in Raman and photoluminescence spectroscopy, respectively. As the irradiation dose is increased, the median vacancy area remains roughly constant, while the number of vacancies (pores) increases. Ionic current versus voltage is nonlinear and conductance is comparable to that of ∼1 nm diameter single MoS2 pores, proving that the smaller pores in the distribution display negligible conductance. Consistently, MD simulations show that pores with diameters <0.6 nm are almost impermeable to ionic flow. Atomic pore structure and geometry, studied by AC-STEM, are critical in the sub-nanometer regime in which the pores are not circular and the diameter is not well-defined. This study lays the foundation for future experiments to probe transport in large distributions of angstrom-size pores.

Computer vision AC-STEM automated image analysis for 2D nanopore applications.

Transmission electron microscopy (TEM) has led to important discoveries in atomic imaging and as an atom-by-atom fabrication tool. Using electron beams, atomic structures can be patterned, annealed and crystallized, and nanopores can be drilled in thin membranes. We review current progress in TEM analysis and implement a computer vision nanopore-detection algorithm that achieves a 96% pixelwise precision in TEM images of nanopores in 2D membranes (WS2), and discuss parameter optimization including a variation on the traditional grid search and gradient ascent. Such nanopores have applications in ion detection, water filtration, and DNA sequencing, where ionic conductance through the pore should be concordant with its TEM-measured size. Standard computer vision methods have their advantages as they are intuitive and do not require extensive training data. For completeness, we briefly comment on related machine learning for 2D materials analysis and discuss relevant progress in these fields. Image analysis alongside TEM allows correlated fabrication and analysis done simultaneously in situ to engineer devices at the atomic scale.

Stochastic Ionic Transport in Single Atomic Zero-Dimensional Pores.

We report on single atomic zero-dimensional (0D) pores fabricated using aberration-corrected scanning transmission electron microscopy (AC-STEM) in monolayer MoS2. Pores are comprised of a few atoms missing in the two-dimensional (2D) lattice (1-5 Mo atoms) of characteristic sizes from ∼0.5 to 1.2 nm, and pore edges directly probed by AC-STEM to map the atomic structure. We categorize them into ∼30 geometrically possible zigzag, armchair, and mixed configurations. While theoretical studies predict that transport properties of 2D pores in this size range depend strongly on pore size and their atomic configuration, 0D pores show an average conductance in the range from ∼0.6-1 nS (bias up to 0.1 V), similar to biological pores. In some devices, the current was immeasurably small and/or pores could not be wet. Furthermore, current-voltage (I-V) characteristics are largely independent of bulk molarity (10 mM to 3 M KCl) and the type of cation (K+, Li+, Mg2+). This work lays the experimental foundation for understanding of the confinement effects possible in atomic-scale 2D material pores and the realization of solid-state analogues of ion channels in biology.

Ions and Water Dancing through Atom-Scale Holes: A Perspective toward "Size Zero".

We provide an overview of atom-scale apertures in solid-state membranes, from "pores" and "tubes" to "channels", with characteristic sizes comparable to the sizes of ions and water molecules. In this regime of ∼1 nm diameter pores, water molecules and ions are strongly geometrically confined: the size of water molecules (∼0.3 nm) and the size of "hydrated" ions in water (∼0.7-1 nm) are similar to the pore diameters, physically limiting the ion flow through the hole. The pore sizes are comparable to the classical Debye screening length governing the spatial range of electrostatic interaction, ∼0.3 to 1 nm for 1 to 0.1 M KCl. In such small structures, charges can be unscreened, leading to new effects. We discuss experiments on ∼1 nm diameter nanopores, with a focus on carbon nanotube pores and ion transport studies. Finally, we present an outlook for artificial "size zero" pores in the regime of small diameters and small thicknesses. Beyond mimicking protein channels in nature, solid-state pores may offer additional possibilities where sensing and control are performed at the pore, such as in electrically and optically addressable solid-state materials.

Gas flow through atomic-scale apertures.

Gas flows are often analyzed with the theoretical descriptions formulated over a century ago and constantly challenged by the emerging architectures of narrow channels, slits, and apertures. Here, we report atomic-scale defects in two-dimensional (2D) materials as apertures for gas flows at the ultimate quasi-0D atomic limit. We establish that pristine monolayer tungsten disulfide (WS2) membranes act as atomically thin barriers to gas transport. Atomic vacancies from missing tungsten (W) sites are made in freestanding (WS2) monolayers by focused ion beam irradiation and characterized using aberration-corrected transmission electron microscopy. WS2 monolayers with atomic apertures are mechanically sturdy and showed fast helium flow. We propose a simple yet robust method for confirming the formation of atomic apertures over large areas using gas flows, an essential step for pursuing their prospective applications in various domains including molecular separation, single quantum emitters, sensing and monitoring of gases at ultralow concentrations.