Low Noise Ultrathin Freestanding Membranes Composed of Atomically-Thin 2D Materials

Abstract

The invention provides methods for direct growth of low noise, atomically thin freestanding membranes of two-dimensional monocrystalline or polycrystalline materials, such as transition metal chalcogenides including molybdenum disulfide. The freestanding membranes are directly grown over an aperture by reacting two precursors in a chemical vapor deposition process carried out at atmospheric pressure. Membrane growth is preferentially over apertures in a thin sheet of solid state material. The resulting membranes are one or a few atomic layers thick and essentially free of defects. The membranes are useful for sequencing of biopolymers through nanopores.

Claims

1. A device comprising (i) an ultrathin membrane comprising a two-dimensional transition metal dichalcognide material containing a nanopore, and (ii) a sheet of solid state material having an aperture, wherein the membrane spans the aperture and is attached to a surface of the sheet in an area surrounding the aperture, and wherein each nanopore has a diameter in the range from about 0.3 nm to about 50 nm.

2. The device of claim 1, wherein the two-dimensional transition metal dichalcogenide material is selected from the group consisting of GaS, GaSe, InS, InSe, HfS.sub.2, HfSe.sub.2, HfTe.sub.2, MoS.sub.2, MoSe.sub.2, MoTe.sub.2, NbS.sub.2, NbSe.sub.2, NbTe.sub.2, NiS.sub.2, NiSe.sub.2, NiTe.sub.2, PdS.sub.2, PdSe.sub.2, PdTe.sub.2, PtS.sub.2, PtSe.sub.2, PtTe.sub.2, ReS.sub.2, ReSe.sub.2, ReTe.sub.2, TaS.sub.2, TaSe.sub.2, TaTe.sub.2, TiS.sub.2, TiSe.sub.2, TiTe.sub.2, WS.sub.2, WSe.sub.2, WTe.sub.2, ZrS.sub.2, ZrSe.sub.2, and ZrTe.sub.2.

3. The device of claim 1, wherein the ultrathin membrane consists essentially of from one to several atomically thin sheets of the two-dimensional material.

4. The device of claim 3, wherein the thickness of the ultrathin membrane is 1-2 atomic layers.

5. The device of claim 1, wherein the ultrathin membrane has a density of holes and atomic vacancies in the range from 0 to about 10 per nm.sup.2.

6. The device of claim 1, wherein the ultrathin membrane has a background specific conductance, absent nanopores, of less than about 0.2 nS/m.sup.2.

7. The device of claim 1, wherein the ultrathin membrane spans a plurality of apertures in the solid state material.

8. The device of claim 7, wherein the plurality of apertures is arranged in a two-dimensional array.

9. The device of claim 7, wherein the ultrathin membrane comprises one or more nanopores within each aperture, and wherein each of said one or more nanopores has a diameter in the range from about 0.3 nm to about 50 nm.

10. The device of claim 1, wherein the solid state material comprises a material selected from the group consisting of silicon nitride, silicon dioxide, hafnium oxide, titanium oxide, and aluminum oxide and has a thickness in the range from about 5 nm to about 10 m.

11. The device of claim 1, wherein the nanopore has an ion current noise level of less than 400 pA at 200 kHz bandwidth.

12. A method of detecting a molecule, the method comprising the steps of: (a) providing the device of claim 1 comprising electrolyte solution on both sides of the ultrathin membrane, an electrode in each electrolyte solution, and a device for measuring ionic currents through the nanopore, wherein the electrolyte solution on one side of the ultrathin membrane comprises said molecule for detection; (b) measuring a baseline ionic current through said nanopore; and (c) observing blockage of the baseline ionic current by said molecule.

13. The method of claim 12, wherein the molecule is a nucleic acid or a protein.

14. The method of claim 12, wherein the molecule is detected as it moves through the nanopore of said ultrathin membrane.

15. The method of claim 12, wherein a nucleotide sequence or an amino acid sequence of the molecule is determined.

16. The method of claim 12, wherein a protein is detected, and the protein reduces the ionic current through the nanopore for about 2 msec to about 5 msec.

17. The method of claim 12, wherein the ultrathin membrane is functionalized in a region surrounding the nanopore with a functionalization moiety having a binding affinity for said molecule.

18. The method of claim 17, wherein the functionalization moiety is an enzyme or an antibody.

19. The method of claim 12, wherein at least one of said electrolyte solutions comprises an ionic species, the other of said electrolyte solutions comprises a fluorescent indicator that binds said ionic species and changes its fluorescence in response thereto, and a current through the nanopore carried by said ion is detected via the fluorescence of the indicator.

20. The method of claim 19, wherein the ion is Ca.sup.2+.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIG. 1A shows a schematic illustration of an aperture-limited freestanding ultrathin membrane fabrication process. A sheet of solid state material that contains a micron-scale hole (or array of holes) is placed over a boat containing a first membrane precursor in a quartz furnace. After an initial sublimation of the first membrane precursor material, temperature and carrier gas flow are adjusted such that a sublimated second membrane precursor material flows over the aperture. FIG. 1B shows a schematic illustration of a proposed mechanism by which aperture-limited growth of membrane occurs. Elements in the figure are not to scale. FIG. 1C shows further detail of the proposed mechanism. FIG. 1D shows a schematic illustration of a portion of a filter device of the invention.

[0018] FIGS. 2A-2C show characterization by electron microscopy of MoS.sub.2 membranes. FIG. 2A shows bright-field (BF) transmission electron microscopy (TEM) images of the CVD-assisted fabricated freestanding MoS.sub.2 membranes over micron-scale holes fabricated in silicon nitride (SiN) sheets. Panels (i)-(iv) show BF-TEM images of four different MoS.sub.2 membranes grown across micron-scale holes. The inset of a (i) shows the lithography assisted pattern written in the SiN sheet before MoS.sub.2 growth by CVD. FIG. 2B shows high-resolution TEM (HRTEM) images of the freestanding MoS.sub.2 membrane collected from the highlighted region in panel (i) shown with a dashed box. Panel (ii) shows single-layer and bilayer domains of MoS.sub.2 in the SiN sheet across an approximately 66 nm.sup.2 area. Panel (iii) shows an HRTEM image of a single-layer MoS.sub.2 membrane corresponding to the domain highlighted in the dashed box in panel (ii). The upper inset shows the corresponding diffractogram of the monolayer. The bottom portion shows a line-profile scanned across 10 lattice points. The lattice constant of the (100) plane was 0.27 nm. Panel (iv) shows an HRTEM image of a bilayer MoS.sub.2 domain from the area highlighted in the dashed box in panel (ii). The inset shows the corresponding diffractogram of bilayer MoS.sub.2. FIG. 2C shows BF-TEM images of a different device with a five submicron hole pattern after MoS.sub.2 growth, where four holes are completely covered with MoS.sub.2 sheets. Panels (ii)-(iv) show BF-TEM images at different magnifications of one of the three holes as highlighted in the dashed box, which is completely covered with freestanding MoS.sub.2 membrane. The different contrasts are due to the thickness variation of the MoS.sub.2 membrane. The ripples in the MoS.sub.2 membranes, which are due to strain applied on the SiN sheets, can clearly be seen in FIG. 2C (iii).

[0019] FIGS. 3A-3C show scanning transmission electron microscopy (STEM) images and secondary electron (SE) images of the device shown in FIG. 2A. FIG. 3A shows a STEM image of the same device shown in FIG. 2a, which confirms that MoS.sub.2 grows on the trans side of the membrane (i.e., side that faces away from the MoO.sub.3 boat). FIG. 3B shows a backscattering mode image of the same device, which further verifies that MoS.sub.2 grows on the trans side of the membrane. FIG. 3C shows a high-resolution STEM image of a MoS.sub.2 membrane collected in the highlighted region (dashed box) in FIG. 3A. The inset shows a diffraction pattern computed from the right side of the membrane, which corresponds to MoS.sub.2 bilayer structure.

[0020] FIG. 4A shows Raman characterization of MoS.sub.2 membranes. The Raman spectra were collected in the vicinity of the center hole in the device shown in FIG. 2A, which corresponds to MoS.sub.2 sheets that are 2-3 layers thick. FIG. 4B shows a Raman spectrum of a molybdenum diselenide (MoSe.sub.2) membrane grown on the aperture shown inside the dashed line box of the inset. The Raman spectrum was collected in from the area inside the box. The inset shows an optical image of the MoSe.sub.2 membrane deposited on an aperture-containing freestanding SiN sheet.

[0021] FIG. 5 shows an atomic resolution image of a freestanding 10 nm20 nm region of a MoS.sub.2 membrane. The inset shows the FFT spectrum of the image.

[0022] FIGS. 6A-6C show ion transport measurements through nanopores in MoS.sub.2 membrane devices. FIG. 6A shows a schematic representation of the device used for ion current measurements. FIG. 6B shows current-voltage curves of several nanopores (0.40 M KCl, pH 8, T=21 C., pore diameter d and conductance G indicated in legend). The current-voltage curve for d=0 is the horizontal line, and for d=16.3 nm is the line with greatest slope; the other lines have intermediate slopes proportional to the area of the nanopore. The inset shows a TEM image of several pores drilled adjacent to each other (scale bar=5 nm). FIG. 6C shows a comparison of experimental G and d values with theoretical curves computed for 1 to 4 MoS.sub.2 layers.

[0023] FIG. 7A shows ion current noise power spectral densities (PSD) for a MoS.sub.2 membrane containing a 2.8 nm diameter pore at different applied voltages (the applied voltages range from 0 (bottom) to 200 mV (top) at the left side of the figure). The solution was 0.40M KCl, pH 8, T=21 C. FIG. 7B shows PSD plots for an ultrathin graphene membrane containing a 7.5 nm diameter pore at 0 mV (bottom curve at left side) and 200 mV (top curve at left side) applied voltages. The graphene 1/f noise at 200 mV exceeded the MoS.sub.2 noise by an order of magnitude (compare noise values at 100 Hz in FIGS. 6A and 6B).

[0024] FIGS. 8A and 8B show detection of the transport of single-stranded DNA molecules through a 2.3 nm diameter MoS.sub.2 nanopore. FIG. 8A shows a three-second continuous current trace for a 2.3 nm diameter pore after the addition of 20 nM of 153-mer ssDNA to the cis chamber ([KCl]=0.40 M, V.sub.trans=200 mV, sampling rate=4.17 MHz, data low-pass filtered to 200 kHz). Concatenated sets of events at different magnifications are shown below the trace. FIG. 8B shows a scatter plot of fractional current blockade vs. dwell time td, as well as histograms of each parameter shown on each corresponding axis (n=number of molecules detected).

[0025] FIG. 9A shows calmodulin transport through a nanopore (22 nm diameter) in an ultra-thin MoS.sub.2 membrane. A continuous 1.5 s long current trace is shown. Calmodulin was present at 100 nM in the solution, and transport of calmodulin through the nanopore can be seen as downward spikes. Bias voltage was 100 mV. Inset shows an expanded view of representative calmodulin translocation events. FIG. 9B shows a histogram of time intervals between events. The capture rate (Rc) of calmodulin translocations is shown in the legend, which is the inverse of the time constant of the time interval distribution (solid diagonal line). FIG. 9C shows a scatter plot of the magnitude of current blockades vs. dwell time for 165 calmodulin translocation events (sampling rate=4.2 MHz, low-pass filtered at 50 kHz, T=25 C., 0.4 M KCl, pH 7.8).

DETAILED DESCRIPTION OF THE INVENTION

[0026] The invention provides freestanding ultrathin membranes of two-dimensional (2D) materials having unique properties including a pristine, monocrystalline or polycrystalline morphology that is robust and essentially free of defects, and provides exceptionally low electrical noise when measuring ionic currents through nanopores for biomolecule sequencing applications. The membranes are fabricated by a novel chemical vapor deposition process that produces aperture-dependent growth of a variety of 2D materials and avoids the need to transfer flakes of such materials to an aperture for various applications, with consequent introduction of structural defects and contamination. The fabrication process can provide membranes of large surface area, rendering them useful for water filtration applications. The membranes of the present invention also can be used as components of electronic devices, such as FETs or components of MEMS or NEMS devices.

[0027] An exemplary fabrication method is summarized by the fabrication scheme shown in FIGS. 1A and 1B. First, substrate or support structure 10 (e.g., silicon chips, optionally coated with a layer of silicon oxide 20) having window 33, over which is deposited a thin freestanding sheet 30 of a solid state material (e.g., 30-50 m.sup.2 of SiN of 100 nm thickness), is hot piranha cleaned and dried with a gentle flow of nitrogen (N.sub.2) gas, followed by warm deionized (DI) water rinsing. Next, positive electron beam resist is spun onto the cleaned and dried chip, and then one or more micron-scale apertures (optionally an array of such apertures) are written on the freestanding SiN membrane using e-beam lithography and subsequently developed.

[0028] Then, SiN is controllably etched through the apertures in SiN membrane using an SF.sub.6 reactive ion etch (RIE) plasma to produce one or more corresponding apertures 32 in the SiN sheet. Subsequently, the resist is stripped off using an acetone bath and hot piranha treatment. A freestanding membrane of 2D material, such as MoS.sub.2, then can be grown directly onto the aperture or pre-patterned array of apertures in the SiN sheet to form membrane device 100. For example, the membrane can be grown using molybdenum trioxide (MoO.sub.3) and sulfur (S) as precursors in a chemical vapor deposition (CVD) process carried out at 750-800 C. and atmospheric pressure. In such a CVD process, first membrane precursor 4 (e.g., MoO.sub.3 powder) is placed into boat 4-1 or other container in the CVD furnace, and second membrane precursor 2 (e.g., sulfur powder) is placed into boat 2-1 or other container in the CVD furnace.

[0029] The placement of the membrane precursor materials in the furnace is important. The prepared freestanding solid state sheet with its supporting substrate is placed above the first membrane precursor container such that sublimating first membrane precursor can rise up and contact the aperture in the solid state sheet where membrane fabrication is desired. The second membrane precursor container is placed upstream of the first membrane precursor container with respect to the flow of inert carrier gas 5, such that sublimating second membrane precursor rises up and is carried toward the aperture for membrane formation by the carrier gas. The flow of carrier gas is arranged so that the second membrane precursor is delivered by the carrier gas to the opposite side of the aperture from the side contacted by sublimating first membrane precursor. The membrane is formed on the side of the aperture to which the second membrane precursor is delivered; that side is referred to as the trans side of the device, the other side being the cis side.

[0030] FIG. 1C presents a model of the mechanism of membrane formation. Transition metal atoms 1 from the first membrane precursor accumulate on the underside (i.e., the cis side) of the sheet of solid state material 30 and inside of aperture 32. Atoms 3 of second membrane precursor accumulate on the upper side (i.e., the trans side) of the sheet. Both sets of atoms react and build membrane 40 at the trans side. The membrane structures depicted in FIG. 1C are nucleation structures which grow from the perimeter inwards toward the center to complete the membrane. While membrane formation is aperture limited, i.e., it occurs preferentially at apertures in the solid state sheet material, the finished membrane not only covers the aperture completely but also covers the trans side solid state sheet in a region surrounding the aperture, forming a leak-proof seal. If membrane growth is allowed to continue, membrane formation can continue at the trans side of the sheet and fuse to form a continuous sheet of membrane covering the sheet.

[0031] When the membrane fabrication process is allowed to form a continuous sheet of membrane, e.g., covering a plurality of apertures or an array of apertures, the resulting structure can form a filter device, a portion of which is depicted in FIG. 1D. In such a device, solid state sheet 30 containing apertures 32 is covered by a continuous sheet of 2D membrane 40, which provides a sieving effect, for example, allowing water molecules to penetrate but holding back dissolved solutes. Optionally, one or more nanopores can be introduced into the membrane at each aperture to provide pathways for desired solutes to pass through the filter, depending on their size or other molecular properties. In addition, the membrane and/or nanopores can be functionalized or chemically modified in order to confer selectivity to the molecular sieving effect of the filter.

[0032] The membrane can have a polycrystalline or monocrystalline structure and is preferably atomically thin, i.e., containing 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 layers of 2D material. Preferably, the membrane has a thickness in the range from about 0.7 nm to about 10 nm. For example, the membrane thickness can be less than 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 nm. In preferred embodiments, the membrane has 1 or 2 layers (i.e., 1-2 atomic layers) of 2D material, or a mixture of regions having 1 and regions having 2 layers. For example, a MoS.sub.2 membrane having 1 atomic layer refers to a 2D monocrystalline or polycrystalline arrangement having a single layer of MoS.sub.2 molecules, and it is understood that such a single layer may have sublayers of Mo and S atoms as dictated by the crystal structure. In certain preferred embodiments, the membrane is free of holes, atomic vacancies, or other structural defects over the entire area of membrane covering the aperture. In other preferred embodiments, the membrane contains 10 or fewer, 9 or fewer, 8 or fewer, 7 or fewer, 6 or fewer, 5 or fewer, 4 or fewer, 3 or fewer, 2 or fewer, or 1 or fewer holes or atomic vacancies per nm.sup.2 of membrane area covering the aperture. The density of holes or atomic vacancies can be controlled during fabrication in order to produce desired properties, such as desired molecular size cutoff in filtration.

[0033] A variety of 2D materials, i.e., materials that form atomically thin monocrystalline or polycrystalline two dimensional sheets, can be used to form the membrane. Such materials include GaS, GaSe, InS, InSe, HfS.sub.2, HfSe.sub.2, HfTe.sub.2, MoS.sub.2, MoSe.sub.2, MoTe.sub.2, NbS.sub.2, NbSe.sub.2, NbTe.sub.2, NiS.sub.2, NiSe.sub.2, NiTe.sub.2, PdS.sub.2, PdSe.sub.2, PdTe.sub.2, PtS.sub.2, PtSe.sub.2, PtTe.sub.2, ReS.sub.2, ReSe.sub.2, ReTe.sub.2, TaS.sub.2, TaSe.sub.2, TaTe.sub.2, TiS.sub.2, TiSe.sub.2, TiTe.sub.2, WS.sub.2, WSe.sub.2, WTe.sub.2, ZrS.sub.2, ZrSe.sub.2, and ZrTe.sub.2. The 2D materials can be, for example, transition metal chalcogenides or semimetal chalcogenides. Preferred 2D materials for the membrane are MoS.sub.2 and MoSe.sub.2. Suitable membrane materials can be fabricated in an aperture-limited fashion by CVD from two or more membrane precursor materials. The membrane precursor materials can be any chemical precursor of the membrane material compatible with the conditions required for CVD, and which react under the conditions of CVD to produce the membrane material in an aperture-limited fashion. Required properties of the precursor materials include thermal stability to several hundred degrees C. and ability to sublimate at such temperatures and bind the solid state sheet at the aperture.

[0034] In some embodiments, the device contains a substrate or support structure attached to the sheet of solid state material that carries the membrane. The support structure contains a window that provides access of fluid to the membrane. In some embodiments, the device contains an insulating layer disposed between the support structure and the sheet of solid state material. The supporting structure can comprise or consist of silicon, silicon dioxide, glass, quartz, or mica. In preferred embodiments, the support structure is silicon. The insulating layer can comprise or consist of silicon dioxide, glass, quartz, or mica. In preferred embodiments, the support structure is silicon, coated in whole or in part by an insulating layer of silicon dioxide. In some embodiments, the support structure and the insulating layer, if present, contain a plurality of windows, each window providing access to at least one well. In some embodiments the support structures contain one or more scored lines between two or more windows, the scored lines enabling the division of the device into two or more pieces, each piece containing one or more windows. In some embodiments, the device has at least 5, at least 10, at least 20, at least 50, at least 100, at least 150, or at least 200 windows.

[0035] The sheet of solid state material comprises or consists of silicon nitride, silicon dioxide, aluminum oxide, titanium oxide, or hafnium oxide. The sheet has a thickness in the range from about 5 nm to about 10 m. In preferred embodiments, the substrate is about 100 nm thick. The sheet of solid state material contains one or more apertures covered by membrane of 2D material. The apertures are generally circular, but could have another shape. The apertures have a diameter, or largest dimension across, in the range from about 0.02 m to about 2 m. In some embodiments, each aperture has a diameter of less than 2 m, less than 1.5 m, less than 1.2 m, less than 1 m, less than 750 nm, less than 500 nm, less than 400 nm, less than 300 nm, less than 200 nm, or less than 100 nm.

[0036] The invention includes an apparatus for the study of polymers, such as biopolymers, including polynucleotides, polypeptides, peptides, proteins, oligosaccharides, and polysaccharides, as they are transported through nanopores in a 2D material membrane. An embodiment of such an apparatus is depicted in FIG. 6A. Apparatus 110 includes nanopore membrane device 100, wherein membrane 40, containing nanopore 50, is positioned between first fluid reservoir 301 and second fluid reservoir 302; an electrode pair having first electrode 401 disposed in the first fluid reservoir and second electrode 402 disposed in the second fluid reservoir; voltage source 403 for establishing a voltage between the electrodes; and circuit 404 capable of detecting an electrical signal (e.g., ionic current through the nanopore) that correlates with the sequence of the polymer, or another aspect of the polymer molecule. The membrane device can be attached via adhesive layers 300 and 310 to first and second chambers (200 and 210 respectively), which can be constructed, for example, of a chemically inert polymer material such as PTFE, or of silicon, silicon dioxide, or quartz.

[0037] The membranes of the present invention are essentially free of structural defects. Defects such as cracks, holes, and atomic vacancies may allow ions or other solutes to pass through the membrane, thereby interfering with uses of the membrane including measuring ionic current to characterize polymers, and filtration. The presence of an intact membrane can be inferred from low specific conductance of the membrane. For example, while testing using a 1M or 0.4M solution of KCl at room temperature, the specific conductance may be less than 0.1 nS/m.sup.2, less than 0.2 nS/m.sup.2, less than 0.3 nS/m.sup.2, less than 0.5 nS/m.sup.2, less than 0.7 nS/m.sup.2, less than 1 nS/m.sup.2, less than 1.5 nS/m.sup.2, less than 2 nS/m.sup.2, less than 5 nS/m.sup.2, less than 10 nS/m.sup.2, or less than 20 nS/m.sup.2. Higher values of conductance can be useful in certain applications, such as selective filtration designed to trap only specific solutes or classes of solutes. Generally, the specific conductance is in the range from about 0.2 nS/m.sup.2 to about 1000 nS/m.sup.2. In a preferred embodiment, the specific conductance is less than 0.2 nS/m.sup.2 when measured using 0.4M KCl. With membranes of the present invention, the background electrical noise from the membrane itself, e.g., when measuring ionic currents through a nanopore in the membrane, is preferably less than 400 pA at 200 kHz bandwidth (i.e., low-pass filtered at 200 kHz).

[0038] Because the fabrication method of the present invention avoids transfer of the membrane after fabrication, the method reliably produces intact membranes that are free of cracks. For example, the percentage of intact membranes produced by the method may be greater than 60%, greater than 70%, greater than 80%, greater than 85%, greater than 90%, greater than 95%, greater than 98%, or greater than 99%. Whether a membrane is intact may be determined, for example, from its ionic conductance. Thus, a membrane may considered intact if the ionic conductance across the membrane is less than 0.1 nS/m.sup.2, less than 0.3 nS/m.sup.2, less than 0.5 nS/m.sup.2, less than 0.7 nS/m.sup.2, less than 1 nS/m.sup.2, less than 1.5 nS/m.sup.2, less than 2 nS/m.sup.2, less than 5 nS/m.sup.2, less than 10 nS/m.sup.2, or less than 20 nS/m.sup.2. The percentage of intact membranes also can be determined by inspection using electron microscopy.

[0039] For certain uses, one or more nanopores may be created in the membrane. As used herein, a nanopore is a pore having a diameter from about 0.3 nm to about 999 nm. However, in preferred embodiments, nanopores from about 0.3 to about 50 nm are used. The number of nanopores created per membrane may vary depending on the intended application of the membrane. For example, membranes designed for use in determining the sequence of bases in a polynucleotide may have only a single nanopore per membrane. Alternatively, membranes designed for use in deionization of aqueous solutions may have a plurality of nanopores per membrane.

EXAMPLES

Example 1. Fabrication of Freestanding Ultrathin MoS.SUB.2 .Membranes

[0040] Substrates for nanopore fabrication were 5 mm5 mm square Si chips with a 100-nm-thick SiN film deposited on a 2.5 m thick thermal SiO.sub.2 layer. The oxide layer helps to reduce electrical noise. The SiN film was protected with a 950 PMMA etch mask, and a small (2 m2 m) region with a pattern of four 600 nm-diameter holes and a central 1.5 m diameter hole was exposed using Nabity NPGS e-beam writing software on a Hitachi S-4800 scanning electron microscope. Exposed PMMA was developed with 3:1 isopropyl alcohol and methyl isobutylketone. The SiN film was etched to AFM- and ellipsometry-calibrated thickness in a Technics Micro-RIE Series 800 etcher using sulfur hexafluoride (SF.sub.6) at 300 mTorr and 150 W. PMMA was removed using acetone, and chips were cleaned with hot piranha solution followed by warm water to remove residual PMMA.

[0041] MoS.sub.2 membranes were synthesized using an atmospheric-pressure CVD process in a split tube furnace with a 35 mm O.D. quartz tube as follows. The chips were placed in the center of the furnace, suspended about 3 mm above MoO.sub.3 powder, and sulfur powder was placed in the upstream region of the furnace chamber.

[0042] Ar gas was flowed at 200 sccm through the chamber throughout the growth process as well as during the cooling process. First the temperature of the furnace was ramped from room temperature up to 300 C. at a rate of 30 C./min and held at the target temperature (300 C.) for 15 min to allow for sufficient MoO.sub.3 sublimation. Next, the temperature of the furnace was raised to 750 C. at a rate of 3 C./min, and sulfurization was allowed to proceed for 90 minutes. After that, the furnace was cooled down to room temperature under the continued flow of Ar gas, through the complete opening of the hood of the furnace.

Example 2. Structural Characterization of MoS.SUB.2 .Membranes

[0043] FIG. 2A shows bright-field (BF) TEM images of freestanding MoS.sub.2 membranes synthesized, without a substrate, onto micron-scale holes prefabricated in a thin sheet of SiN. Panels (i)-(iv) of FIG. 2A show high magnification TEM images of four different MoS.sub.2 membrane devices. Some holes are partially covered with multiple layers of MoS.sub.2, which possibly could be due to the insufficient nucleation time during CVD. It is noteworthy that unintentional wrinkles could be seen in some MoS.sub.2 membranes grown across holes, which may be due to stress exerted on the membranes as they freely suspend over the free aperture (see, e.g., FIG. 2A(iii)). Different domains of monolayer and multilayer MoS.sub.2 were observed in membranes grown across submicron aperture regions.

[0044] FIG. 2B shows high resolution TEM (HRTEM) images of the MoS.sub.2 membrane analyzed in the highlighted region as depicted in FIG. 2A(i) with a dashed box. In FIG. 2B it is clear that there were still some incompletely nucleated sites, as highlighted in FIG. 2B(iii) with a dashed box. In FIG. 2B(ii), monolayer and bilayer domains of MoS.sub.2 can clearly be seen in the freestanding membrane across an area of approximately 6 nm6 nm. Partially nucleated or incompletely nucleated sites can also be observed in FIG. 2B(ii). FIG. 2B(iii) shows an HRTEM image of single layer MoS.sub.2 membrane corresponding to the domain highlighted in the dashed box in panel (ii). The upper inset shows the corresponding diffractogram of the image, which further verifies the existence of monolayer MoS.sub.2 in the region highlighted with the dashed box in FIG. 2B(ii). The line-profile was manipulated by scanning across 10 lattice points (as depicted in FIG. 2B(iii)), which gave a lattice constant of MoS.sub.2 in the (100) plane of 0.27 nm (bottom inset). FIG. 2B(iv) shows an HRTEM image of a bilayer MoS.sub.2 domain corresponding to the area highlighted in the dashed box in FIG. 2B(ii). The two hexagonal lattice structures next to each other corresponding to two layers of MoS.sub.2 can be seen vividly in FIG. 2B(iv). The inset illustrates the corresponding diffractogram of bilayer MoS.sub.2 membrane.

[0045] FIG. 2C shows BF-TEM images of a device with a five submicron hole pattern after MoS.sub.2 growth, where four holes are completely covered with MoS.sub.2 membranes. The inset of FIG. 2C(i) shows the perforated substrate with an e-beam written five-hole pattern before MoS.sub.2 growth. Panels (ii)-(iv) of FIG. 2C show BF-TEM images of one of the membranes highlighted in FIG. 2C(i) with a dashed box. These CVD-grown freestanding MoS.sub.2 membranes contain different numbers of layers localized on the membrane as seen in FIG. 2C(ii). Unintentionally generated wrinkles in the MoS.sub.2 membranes can be seen in FIG. 2C(iii), which is likely due to strain applied to the freestanding MoS.sub.2 membranes across the free aperture. It is noteworthy that there was a preference of growing MoS.sub.2 membranes across cracks that were generated during the e-beam writing process and subsequently developed in CVD temperature ramping (not shown).

[0046] FIG. 3A shows an STEM image of the same sample shown in FIG. 2A(i). According to FIG. 3A, MoS.sub.2 membrane was grown 100% of the time in the crater side of the membrane. FIG. 3B illustrates the same membrane imaged in the backscattering mode (SE mode) from the crater side, which further verifies that MoS.sub.2 membrane was completely been grown on the crater side, and that the top of the sample is the membrane side on which there is no MoS.sub.2. This is an interesting observation, because the chip was placed facing membrane side down during CVD operation, whereby the chip was suspended about 3 mm above the MoO.sub.3 powder. Therefore having MoS.sub.2 completely grown on the crater side (and not on the membrane or top side) explains the growth mechanism of MoS.sub.2 across a perforated substrate. One possible explanation is that sublimated MoO.sub.3 leaks through the apertures in the SiN membrane and precipitates onto the crater side of the membrane due to the temperature gradient between top and bottom sides of the chip. Sulfurization takes place with the flow of sublimated S placed in the upstream portion of the chamber, which results in fabricating MoS.sub.2 sheets across the apertures in the substrate. This proposed mechanism is further verified from FIG. 2D, panels (i)-(iv), where there is a higher affinity in growing MoS.sub.2 sheets across sub micrometer slits in SiN freestanding window. FIG. 3C shows a high-resolution STEM image of one of the freestanding MoS.sub.2 membranes highlighted in FIG. 3A with a dashed box, which clearly demonstrates some Moir patterns. The FFT collected in the vicinity of the Moir patterns (inset, FIG. 3C) confirms that it is bilayer MoS.sub.2, where two sheets are slightly rotated on top of each other.

[0047] Raman spectroscopy measurements were carried out in the vicinity of the middle hole in the five-hole pattern (highlighted with dashed box in FIG. 2A) to probe the thickness as well as the crystal quality of the as-grown freestanding MoS.sub.2 membranes (FIG. 4). Raman spectroscopy was carried out using a Jobin Yvon LabRam HR800 spectrometer attached to an Olympus BH2 microscope. MoS.sub.2 AND MoSe.sub.2 membranes were imaged using a JEOL 2010FEG transmission electron microscope operating in bright-field mode at 200 kV, and STEM images were collected using a Hitachi HD 2700 at 200 kV, Cs-corrected. Two major Raman features are prominent in the resulting Raman spectrum in FIG. 3A: E2g1 (383 cm.sup.1), which corresponds to an in-plane mode resulting from the opposite vibration of two S atoms with respect to the Mo between them, and A1g (406 cm.sup.1), which is attributed to the out-of-plane vibration of only S atoms in opposite directions. [55-57] The frequency-shift difference between E2g1 and A1g modes is correlated to the number of layers in the multilayer MoS.sub.2 membranes. [58] According to the frequency-shift difference (about 23 cm-1) between the two modes, the center hole (about 2 m) was mostly covered with the 2-3 layer thick MoS.sub.2 membranes.

Example 3. Electrical Characterization of MoS.SUB.2 .Membranes Containing Nanopores

[0048] Following optimization of hole-free membrane growth, complete MoS.sub.2 membranes were grown on several devices, and a TEM beam was used to fabricate nanopores in these membranes in order to study ion transport through the pores. Because of the extremely thin membrane structure, only brief (about 1-2 sec) exposure times using a focused beam were sufficient to produce nanopores; great care was taken to avoid large pore formation, e.g., by reduction of spot size and beam current.

[0049] Following the fabrication of several pores of different diameters, the chips were assembled into a custom-made PTFE cell as shown in FIG. 6A. Prior to obtaining measurements, a chip was glued onto the top PTFE portion of the cell using a quick-curing elastomer, and a second layer of glue was applied to the membrane such that only about 1 mm.sup.2 was exposed, in order to minimize capacitance-mediated noise. After elastomer curing, the cell was assembled, the cis and trans compartments were filled with 0.40 M KCl electrolyte buffered to pH 8.0 using 10 mM Tris (G.sub.bulk=50 mS/cm), and a pair of Ag/AgCl wire electrodes was immersed in the chambers. The electrodes were connected to a Chimera Instruments high-bandwidth amplifier. FIG. 6B shows the current-voltage response of the MoS.sub.2 membranes with pores of various diameters. While no appreciable current was measured for the membrane without pores linear current/voltage responses were observed for the three nanopores tested. The responses were characteristic of ion-conducting nanopores. Linear fitting of the slopes of the curves yielded the membrane conductance (G) values which are reported in the legend of FIG. 6B. The inset TEM image (JEOL 2010FEG operating in bright-field mode at 200 kV) shows several nanopores fabricated adjacent to one another using an electron beam, ranging in diameter from 1 to 5 nm.

[0050] To rationalize the observed conductance levels to these pore diameters, the theoretically expected conductance values for circular nanopores of ideal diameter d are plotted in FIG. 6C. The values for MoS.sub.2 membranes of quantized thicknesses in the range of 1-4 layers (where each layer is 0.8 nm thick), are also shown in FIG. 6C. To obtain these curves, the access resistance in ultrathin membranes was taken into account, yielding the conductivity G for a MoS.sub.2 membrane containing a pore of diameter d as described in Equation (1)

G(d)=(4nh/d.sup.2+1/d).sup.1(1)

where is the bulk electrolyte conductivity, n is the number of MoS.sub.2 layers, and h is the thickness of a monolayer (0.8 nm). In FIG. 6C the conductance for three MoS.sub.2 membranes that contained no fabricated nanopores are also plotted, in which the mean conductance was 0.43 nS, a factor of 35 smaller than the conductance of the 2.8 nm pore. Overall, the experimental data indicated pores that of 1-2 layers thickness, apart from a small negative deviation for the larger pore, which most likely stems from about 10% error in pore diameter.

[0051] Next, the ion-current noise exhibited by nanopores in MoS.sub.2 membranes was determined and compared to that of nanopores in transfer-free graphene membrane (produced as described in WO 2015/077751, which is incorporated herein by reference). DC current values were very stable, with peak-to-peak noise values of about 400 pA at 200 kHz low pass filter setting. Power spectral density plots are shown in FIG. 7A for different applied voltages in range 0-200 mV. The pores exhibited typical 1/f noise regions that decrease with frequency until overwhelmed by capacitive noise at f>10.sup.4 Hz, which is dampened using the 200 kHz digital low-pass filter (shoulders on right). The 1/f noise in the MoS.sub.2 membranes was atypical of 2D pores. In comparison, graphene pores (see FIG. 7B), due to their more hydrophobic nature and charge fluctuations in the material, displayed larger 1/f current noise values than MoS.sub.2.

[0052] Table 1 displays noise values for pores in membranes made of 2D materials. Heerema and co-workers, as well as Merchant and co-workers, reported for a transferred graphene pore noise density of about 10.sup.4 nA.sup.2/Hz at a frequency of 100 Hz, whereas Waduge found for a transfer-free graphene pore a noise value of about 10.sup.5 nA.sup.2/Hz at 200 mV. In contrast, for MoS.sub.2 and SiN pores of similar conductance values and voltages, the present inventors observed noise densities at 100 Hz below 10.sup.6 and about 10.sup.7 nA.sup.2/Hz, respectively. This value for the present MoS.sub.2 membranes is lower than the noise reported by Feng and co-workers for a transferred MoS.sub.2 pore. Recently, 1/f noise in graphene has been attributed to mechanical fluctuations in the thin material. Since lower noise levels also have been observed in transfer-free graphene than in transferred graphene, it is apparent that the even lower noise exhibited by the present polycrystalline MoS.sub.2 membrane grown directly on apertures is likely a combination of superior mechanical stability afforded by the direct growth and a material-specific low noise of MoS.sub.2.

TABLE-US-00001 TABLE 1 1/f Ionic Noise Properties For Transferred And Direct-Growth 2D Pores Reference 2D Nanopore Noise at 100 Hz, 200 mV Hereema et al. (1) 10.sup.4 nA.sup.2/Hz, transferred graphene Merchant et al. (2) 10.sup.4 nA.sup.2/Hz, transferred graphene Waduge et al., 2014 (3) 10.sup.5 nA.sup.2/Hz, transfer-free graphene Waduge et al., 2015 (4) 10.sup.6 nA.sup.2/Hz, transfer-free MoS.sub.2 Feng et al. (5) 10.sup.4 nA.sup.2/Hz, transferred MoS.sub.2 (1) Heerema, S. J.; Schneider, G. F.; Rozemuller, M.; Vicarelli, L.; Zandbergen, H. W.; Dekker, C. 1/f Noise in Graphene Nanopores. Nanotechnology 2015, 26, 074001. (2) Merchant, C. A., et al. DNA Translocation through Graphene Nanopores. Nano Lett 2010, 10, 2915-21. (3) Waduge, P.; Larkin, J.; Upmanyu, M.; Kar, S.; Wanunu, M. Programmed Synthesis of Freestanding Graphene Nanomembrane Arrays. Small 2014, 11, 597-603. (4) Waduge, P.; Bilgin, I.; Larkin, J.; Henley, R. Y.; Goodfellow, K.; Graham, A. C.; Bell, D. C.; Vamivakas, N.; Kar, S.; Wanunu, M. Direct and Scalable Deposition of Atomically Thin Low-Noise MoS.sub.2 Membranes on Apertures. ACS Nano 2015, 9, 7352-9. (5) Feng, J., et al. Electrochemical Reaction in Single Layer MoS.sub.2: Nanopores Opened Atom by Atom. Nano Lett 2015, 15, 3431-8.

Example 4. Detection of Transport of DNA Molecules Through Nanopores in MoS.SUB.2 .Membranes

[0053] The utility of the present MoS.sub.2 containing nanopores in DNA transport experiments was tested by studying the transport of single-stranded DNA (ssDNA) through a MoS.sub.2 pore. Rather than using TEM fabrication, for this study the recently described electrochemical reaction (ECR) process was used. [59] Briefly, a voltage of 1 V was applied for 10-15 s, after which a jump in the membrane conductance was observed, and the voltage was turned off.

[0054] After measuring a pore conductance of about 5 nS, a sample of 153-mer ssDNA was added to a total concentration of 20 nM, a 200 mV voltage was applied, and current traces were recorded. A sample 3-s current trace is shown in FIG. 9A, which displays a stochastic set of downward current pulses, each indicating the transport of an individual DNA molecule through the pore. Below the continuous current trace in FIG. 8A are shown concatenated sets of events that were analyzed using Pythion software. In FIG. 8B is shown a scatter plot of the fractional current blockade (defined as the ratio of the spike mean amplitude to the open pore current) vs. dwell time for the 744 events in the experiment. Because of the 200 kHz bandwidth, events below 3 s are significantly distorted and therefore were discarded from the analysis. Histograms of both parameters are also shown above and to the right of the scatter plots, from which mean dwell time was determined as 16 s and mean fractional current blockade as 26%. On the basis of the values of the open pore current (1.32 nA at 200 mV) and the mean blockade values, the effective pore diameter and thickness were estimated as 2.3 nm and two MoS.sub.2 layers (1.6 nm), respectively. Given the relatively large pore size as compared with the nominal diameter of ssDNA (about 1.3 nm), the mean transport velocity of 0.1 s/bp is reasonable and in accordance with a prior study. [60]

[0055] Finally, the data in FIG. 8B shows many events with dwell times (td) below 10 s, which makes their detection challenging. However, because the mean capture rate was 0.95 s.sup.1 nM.sup.1 in the present experiment, and a mean capture rate of 0.02 s.sup.1 nM.sup.1 was obtained for a 1.7 nm diameter HfO.sub.2 pore under similar conditions, [61] it is concluded that DNA capture is efficient in a MoS.sub.2 pore.

Example 5. Detection of Transport of Protein Molecules Through Nanopores in MoS.SUB.2 .Membranes

[0056] Calmodulin transport was measured through an ultrathin MoS.sub.2 membrane containing a nanopore. The methodology was similar to that used in Example 4 to observe ssDNA transport, except that a larger pore diameter of 22 nm was used. FIG. 9A shows a continuous 1.5 s long current vs. time trace for the transport of 100 nM calmodulin through the 22 nm-diameter MoS.sub.2 nanopore at 100 mV bias voltage applied at the trans side. Downward spikes correspond to the translocation or interaction of calmodulin with the pore. The inset shows an expanded view of representative events. FIG. 9B shows a histogram of time intervals between events. The capture rate (R.sub.c) of calmodulin translocations is shown in the legend, which is the inverse of the time constant of the time interval distribution (solid line). FIG. 9C shows a scatter plot of current blockades vs. dwell times for 165 calmodulin translocation events (sampling rate=4.2 MHz, low-pass filtered at 50 kHz, T=25 C., 0.4 M KCl, pH 7.8).

Example 6. Fabrication of MoSe.SUB.2 .Membrane

[0057] 6 mg of Se powder was added to one of the quartz boats and 2 mg of MoO.sub.2 powder to the other boat. The Se boat was placed in the upstream region of the furnace while the MoO.sub.2 boat was kept in the center of the furnace. The furnace was purged with 10 sccm H.sub.2 for 30 min and then the temperature of the furnace was raised to 300 C. at a rate of 15 C./min under flow of 125 sccm Ar. The furnace was held at 300 C. for 10 min and then raised to 650 C. at a rate of 5 C./min. The furnace was held at 650 C. for 30 min, and then the hood of the furnace was opened and and the system allowed to cool to room temperature after 30 min under the flow of 10 sccm H.sub.2 and 125 sccm Ar. FIG. 4B shows Raman characterization of the MoSe.sub.2 membrane.

[0058] As used herein, consisting essentially of does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim. Any recitation herein of the term comprising, particularly in a description of components of a composition or in a description of elements of a device, can be exchanged with consisting essentially of or consisting of.

[0059] While the present invention has been described in conjunction with certain preferred embodiments, one of ordinary skill, after reading the foregoing specification, will be able to effect various changes, substitutions of equivalents, and other alterations to the compositions and methods set forth herein.

[0060] This application claims the priority of U.S. Provisional Application Nos. 62/118,795 filed 20 Feb. 2015 and entitled Aperture-Limited Fabrication of Freestanding MoS.sub.2 Membranes and 62/119,675 filed 23 Feb. 2015 and entitled Aperture-Limited Fabrication of Freestanding MoS.sub.2 Membranes. Both provisional applications are hereby incorporated by reference in their entirety.

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