Molecular-Level Design of Nanoscale Environments for Enhanced Single-Molecule Sensing

Single molecule studies depend upon precise control over the chemical and physical structure of the nanoscale sensing instrumentation and environment, and this demand is particularly stringent in the case of nanopores, a unique tool for singlemolecule sensing and manipulation. The size and shape of the nanopores are critical to their function, and each facet, alone, presents experimental hurdles; this dissertation contains an approach to address both, simultaneously. A method for electroless deposition of gold onto solid-state silicon nitride nanopores has been developed to provide a foundation for precision tailoring of surface properties and nanopore size to study single analyte molecules and their interactions with other molecules of interest. This study was designed to develop a set of tools to directly modify the surface of silicon nitride, and through this approach, to customize the nanopore size and surface properties for various molecular systems under investigation. The techniques discussed in this dissertation were successfully used to electrolessly deposit gold into silicon nitride pores, to create customized nanopores. These nanopores were characterized via a non-imaging, conductance-based, technique developed in this research group, and subsequently used to study the translocation of DNA molecules through the pores.

We hypothesize that incomplete solution exchanges between steps left residual tin and silver on the surface of the membrane, which were later reduced by formaldehyde during the final 3-hour gold-plating step of the procedure. 89,90 Such crystals are not seen in the area around the nanopore arrays, themselves, where gold is found in the highest concentrations. The light dispersion of gold across the entire silicon nitride membrane attests to the mass transport of gold ions through the pore, and was most likely facilitated by the gentle rocking of the membrane during the plating process.
The sharp contrast between the dusting of gold coating the entire surface and the gold plated around the pore arrays provides evidence for supporting the mass-transport process of gold and formaldehyde through the nanopore array. Biologically-relevant molecular interactions occur in an incredibly welldefined environment that takes tremendous effort, special preparation, and special approaches to replicate, or approximate, using traditional chemical tools. Protein nanopores are widespread in nature and, as a biological structural element, offer highly reproducible nanoscale channels with rich internal surface chemistry. They are thus a compelling tool that could be used to better explore molecular interactions.
Early work focused on one nanopore , a naturally occurring When a molecular-scale hole is drilled through a thin, free-standing membrane, a solid-state nanopore is born. Such a membrane can be used to divide two halves of an electrochemical cell (Figure 1.2), and when an applied voltage drives charged molecules through the single opening between the two halves of the cell, a single molecule sensor is born. By monitoring the current passing through the pore, and the changes that occur as target molecules reside inside the nanopore, information about the size, shape, and charge of the analyte can be determined [22][23][24][25] , and more sophisticated experiments can elucidate diffusion and binding kinetics for various ligand-receptor interactions [26][27][28][29][30][31][32] .
Silicon nitride has emerged as a ubiquitous substrate material in the world of nanofabrication, including to fabricate solid-state nanopores, due to its accessibility and suite of favorable properties such as durability and electrical insulation [35][36][37][38][39] . Ag/AgCl electrodes in each well provide current measurements based on a voltage applied. A molecule electrophoretically driven, by the applied voltage, through the nanopore is said to translocate, and will result in a corresponding change 25,33,34 in current magnitude when the molecule is within the nanopore, disrupting the normal voltage-driven ionic flow.
Careful and creative design can leverage this constellation of beneficial properties to create versatile tools for chemical analysis. Nanopores with molecular-scale diameters can be fabricated by a number of methods, with varying degrees of difficulty 40-47 , but precision control over the sub-attoliter interior of the nanopore continues to remain extremely challenging. Such control, however, is imperative when a single analyte molecule is electrophoretically driven into a constrained channel 19,33,48  Surface-deposited thin gold films offer a way to exert control over the chemical environment of a nanopore 39,49-52 . By electroless deposition of gold onto all sensitized surfaces of a silicon nitride nanopore, a blank canvas for chemical modification is created 39 that is much less challenging than the native silicon nitride surface. Well established gold-thiol chemistry can then be employed to form selfassembling monolayers (SAM) on the gold-plated surface of the nanopore 53 . This offers a way to chemically define the physical size and volume of the nanopore, and results in total chemical control over the interior of the pore, as demonstrated in Figure   1 The process of metal plating the solid-state silicon nitride nanopore, itself, proves challenging. With nanopores in particular, traditional physical deposition methods, such as vapor deposition or sputtering, are not amenable to coating the entire nanoscale three-dimensional surface while keeping the pore unobstructed. Electroless  39,49,54 . Increased extension of longer chains into the pore interior should shrink the effective pore diameter. The SAM terminal group also provides control over the chemical environment within the nanopore.
deposition is an alternative, solution-based method for metallizing insulating substrates such as silicon nitride. Electroless deposition differs from the more familiar electrodeposition in that the surface onto which the metal is being plated does not have to be conductive, and no external or applied voltage is required to reduce the metal of choice onto the surface. The benefit of electroless plating, beyond the self-catalyzing series of redox reactions that allows for precise control over the metal deposition, is that it is totally solution-based and does not require any specialized equipment. By controlling various parameters of the plating procedure, such as pH and plating time, the thickness and nanostructure of the deposited gold coating can be modified. The complex and varied surface chemistry of silicon nitride -it is, in part, this complex silicon nitride surface chemistry that motivates use of gold as the surface functionalization base-does not lend itself to a straight-forward application of current electroless deposition techniques 38,55 . Thus, it is necessary to develop a new procedure to overcome the challenges of electroless deposition onto silicon nitride substrates.
The physical dimensions of the nanopore can then be tuned by the plated gold thickness. Fine-tuning of the sizes and chemistry of the nanopore can occur through the self-assembly of thiol-terminated molecules on the gold surface.
The ability to coat all surfaces of a solid-state silicon nitride nanopore opens up the possibility for innumerable studies on previously studied [22][23][24]30,31 , as well as new, analyte molecules. This ability provides a means to chemically control a surface to design a volume to exact physical and chemical specifications, for use as a tool with which to then explore the world on a single-molecule level. The project in this dissertation studies various facets of solid-state nanopore design and applications to single-molecule sensing. First, a method for the deposition of gold onto silicon nitride is explored. Then, self-assembled monolayers (SAM) will be studied in nanopores and the effect their terminal functional groups have on the nanopore function. Lastly, the gold-and SAM-coated nanopores provide a platform for studying individual receptorligand interactions by nanopore force spectroscopy (NFS 26,29,31,32,56

ABSTRACT.
A method to directly electrolessly plate silicon-rich silicon nitride with thin gold films was developed and characterized. Films with thicknesses less than 100nm were grown at 3 and 10°C between 0.5 and 3 hours, with mean grain sizes between ~20-30nm. The method is compatible with plating free-standing ultrathin silicon nitride membranes, and we successfully plated the interior walls of micropore arrays in 200nm-thick silicon nitride membranes. The method is thus amenable to coating planar, curved, and line-of-sight-obscured silicon nitride surfaces.

BACKGROUND.
Thin gold films have widespread technological utility, from forming conductive elements and overlayers, to serving as a platform for chemical surface modification by molecular self-assembly 1 . For gold films incorporated into conventional micro-and nanofabricated devices, silicon nitride is an appealing choice for a substrate. It is a standard nanofabrication material, offering, in addition, favorable inherent properties such as mechanical strength 2-3 , chemical resistance, and dielectric strength [4][5] . Silicon nitride is thus ubiquitous as a structural and functional element in nanofabricated devices where it plays a variety of roles 2, 5-8 . Its surface chemistry, however, presents especial challenges given the complex mixture of silicon-, oxygen-, and nitrogen-bearing surface species 5 . The nominal surface modification of silicon nitride is frequently carried out in practice using silane-based modification of a silica layer that may itself not be well-defined 9 . Thus, there remains both a need and opportunity to expand the suite of approaches useful for surface functionalizing silicon nitride directly. Electroless deposition is a particularly compelling approach to film formation: deposition proceeds from solution allowing the coating of three-dimensional surfaces, including surfaces hidden from line-of-sight deposition methods; no electrochemical instrumentation is required; no electrical power must be supplied nor must the substrate be conductive; there is no need for expensive vacuum deposition equipment; and a variety of classical physicochemical parameters such as reagent composition, solution properties such as pH and viscosity, and temperature, are available to tune the film properties [10][11] . There is a wealth of familiar approaches for the electroless plating of substrates such as polymers, for example, but no established prior art for the direct metal-cation-mediated electroless plating of gold onto silicon nitride [12][13] . A particularly compelling sequence exists for the electroless gold plating of poly(vinylpyrrolidone)-coated polycarbonate substrates (Au/PVP) 13 : direct sensitization of the PVP surface with Sn 2+ , activation by immersion in ammoniacal silver nitrate to oxidize the surface Sn 2+ to Sn 4+ by reducing Ag + to elemental silver (producing, also, a small amount of silver oxide), and finally gold plating by galvanic displacement of the silver with reduction of Au(I) to Au(0) accompanied by the oxidation of formaldehyde. Amine and carbonyl groups in the PVP layer were proposed to complex the tin cation during sensitization 13 . Extending this approach, Sn 2+ has been reported to complex effectively with oxygen-rich polymer surfaces 12 and with quartz and silica substrates 10, 14-16 . Tin(II) sensitization has also been reported on NaOH-roughened surfaces 17 , suggesting that a specific chemical interaction may not be essential 18 , and underscoring the utility of electroless plating for rough and high-surface-area surfaces where physical deposition is challenged 19 . In principle, though, a smooth silicon nitride substrate with a welldefined silica surface layer should be amenable to direct tin sensitization. Yet, electroless deposition of gold on planar silicon nitride has been limited to routes requiring the use of a silica layer with organic linkers and metal layers between the silicon nitride and gold overlayer 18 . In the first case, covalent attachment of an organic monolayer using silane chemistry can be beneficial for film adhesion, but adds operational complexity 18 and can constrain downstream processing conditions. In the second case, the intervening layers may lend beneficial properties, or may similarly introduce compositional constraints on applications, or morphological constraints on the final gold film nanostructure. Regardless of the ability to carry out a silica-based modification, it does not eliminate the benefits of a direct functionalization of silicon nitride. We present a dramatically simplified electroless gold deposition method in which we eliminate the initial covalent attachment of an organic monolayer to the substrate, and in which we do not need to initially mask the silicon nitride surface chemistry with a silica overlayer. Our method directly sensitizes the silicon nitride substrate with a Sn 2+ solution, followed by a series of metal ion treatments in which we exert control over the gold film thickness using process time and temperature. Film thicknesses ranged from 30 to 100nm for deposition times from 0.5-3h, and temperatures of 3 and 10°C.

MATERIALS AND METHODS.
Full details of materials and preparation are provided in the Supporting Information (Appendix 1 in this Thesis). In brief, polished silicon-rich low-pressure chemical vapor deposited (LPCVD) silicon nitride-coated silicon wafers were cleaved into ~1cm 2 chips. The chips were then electrolessly plated with gold deposited from solution as outlined in Scheme 1. Ultrasonic cleaning of the substrate 20 was strictly avoided so that straightforward extension of the scheme to ultrathin silicon nitride windows would not cause window fracture 2-3 . Each chip was plasma-cleaned and then briefly etched in a dilute hydrofluoric acid (HF) solution to remove unwanted native silicon oxide and expose the silicon nitride surface 4,20 . The prepared chips were immersed in a tin(II) chloride sensitizing solution, followed by a soak in ammoniacal silver nitrate solution 10,13 . The chips were carefully rinsed between each step of the process. Electroless gold plating was carried out by immersing chips in ~1.5-3mL (0.75mL for micropores) of sodium gold sulfite plating solution 21 , with gentle rocking, in a refrigerator (3°C plating) or thermoelectric cooler (10°C plating). After plating for the desired time at the desired temperature, the chips were carefully rinsed, dried and then characterized. Gold film thicknesses were obtained by atomic force microscopy (AFM) measurements across an edge from the film to the substrate. Film morphology was examined by field-emission scanning electron microscopy (FE-SEM) and analyzed using a watershed analysis. Elemental analysis of the gold film was carried out by energy-dispersive x-ray spectroscopy (EDS) and by x-ray photoelectron spectroscopy (XPS). Characterization details are provided in the Supporting Information (Appendix 1 in this Thesis, page 91). Scheme 1. Electroless plating of silicon nitride. The silicon nitride-coated substrates are plasma-cleaned of organics and HF-etched before the surface is exposed to Sn 2+ ions which are oxidized during the redox-driven deposition of an elemental silver layer. Gold plating begins with galvanic displacement of the elemental silver.

Figure 2.1 shows photographs of an array of silicon nitride-coated substrates
subjected either strictly to the steps in Scheme 1, or to control experiment variations.
Adherence to Scheme 1 produced gold films, evaluated by visual inspection, with good quality and excellent macroscopic surface coverage, and delivered these results reliably over many months of repeated trials. More detailed characterization of these films is provided below. Departures from the scheme, however, yielded generally poor or inconsistent results. We focused our attention on varying the surface preparation steps, specifically testing surface preparations that did not involve HF etching designed to remove the oxygen-containing overlayer. Tin(II) sensitization after sodium hydroxide surface roughening had been reported on silicon nitride powders of unknown stoichiometry 5,17 . Indeed, surface roughening to improve film adhesion is a familiar preliminary process in electroless plating 11 . Substituting 1, 4.5, or 9M NaOH treatments for the HF etching of Scheme 1, however, generated only gold smudges after 3 hours of plating at 3°C. The silicon-rich nature of our LPCVD films is a possible contributing factor to the poor plating quality after NaOH treatment in comparison to the published results 17 , given the general challenge that silicon nitride stoichiometry and available surface species-and thus functionalization opportunities 20 -depend on the details of the silicon nitride synthesis 5 . Our use of large-area, planar substrates introduces another likely explanation: it provides a stringent test of film deposition quality, and easily reveals defects that may be more difficult to discern on a film coating a powder. Traditional silicon nitride surface modification schemes rely frequently on modification of a silica layer on the silicon nitride surface 22-23 rather than of the silicon nitride, itself. Careful attention to the quality of the oxygen-containing surface layer can circumvent difficulties that stem from a lack of definition of this silica layer 22 . Holtzman and Richter used nitric acid to enrich the number of surface hydroxyl groups on silicon nitride so that they could use silane chemistry to provide an organic monolayer foundation for an overlying electrolessly deposited gold film 18 . While successful, the approach must contend with the acknowledged challenges of silane chemistry 18 and with the persistence of the organic linker layer. Given the affinity of Sn 2+ for such an oxygen-enriched silicon nitride surface, and given prior demonstrations of electroless gold plating on silica surfaces 10 , we replaced the HF etch in Scheme 1 with a 20 minute treatment in 10% (v/v) nitric acid at 80°C. The results, shown in Figure 2.1, were promising, with repeated, although not consistent, deposition of (visually inspected) high-quality gold films. It is likely feasible to optimize this route to routinely deposit high-quality, uniform gold films, but our goal was to develop a simple route to electrolessly plate gold directly onto silicon nitride. Treatment of silicon-rich LPCVD silicon nitride surfaces with dilute hydrofluoric acid eliminates the native oxide 4, 23 and leaves a Hterminated surface with Si-H, NH and NH2 moieties 22 . Given the appeal of this surface for surface functionalizations 20, 22 , we tested its compatibility with tin(II)-based sensitization. Scheme 1 thus follows the plasma-based cleaning steps with an HF etch step that removes oxide and H-terminates the surface 22 , and ends with the gold plating treatments 13 . We note that in the absence of the HF-etching step, chips would sporadically be coated with patchy gold layers, but no uniform high-quality gold films were observed on these chips even after 3 hours in the gold plating solution.  listed, and were in the range ~3-5x10 -6 Ω·cm; thin film resistivities higher than the known bulk gold resistivity (2.2x10 -6 Ω·cm) 11 are not surprising 18 . SEM micrographs EDS analysis of these larger features showed them to be gold (see Chapter 2 Supporting Information Figure S1). Many of these outcroppings had quite convoluted shapes; there is the potential for quite compelling applications arising from both the regular and irregular film grain structures [24][25] . Indeed, the films are useful as a platform for surface-enhanced Raman spectroscopy (SERS).  While the electroless gold plating was strongly sensitive to the surface preparation of the silicon nitride, we note, for completeness, that the exposed silicon at the edges of the chips was consistently gold-plated, regardless of whether the wafer was treated with HF, HNO3 or NaOH. Polished ~1cm 2 silicon chips treated according to Scheme 1 developed uniform, high-quality gold films across the surface. This result suggests that the silicon-rich nature of our silicon nitride films may contribute to the electroless plating process in Scheme 1. Candidate mechanisms for tin-sensitizing silicon nitride thus extend beyond those involving nitrogen-containing surface species 13 . The prospect of definitive elucidation of the mechanism, however, must be Nevertheless, the steps of various electroless plating approaches have a sound electrochemical basis and the method has a demonstrable outcome 11 . XPS spectra were recorded from silicon nitride chips after each major step of Scheme 1. Selected spectra and details of the analysis are provided in the Supporting Information (Chapter 2 Supporting Information Figure S2). XPS spectra were also recorded from silicon chips for use as a guide to unravelling the overlapping contributions to the Si2p region of the silicon nitride spectra, especially. HF treatment of the oxygen-plasma-cleaned silicon and silicon nitride caused a significant diminution of oxygen-related peaks at ~104eV (Si2p) and ~533eV (O1s), with the first component no longer evident. These spectral features-including the residual O1s peak that could indicate surface reoxidation generating a small number of surface hydroxyl groups, but has been principally attributed to presumably surface-inaccessible bulk oxygen-are consonant with those recorded from silicon nitride substrates prepared for direct covalent chemical modification 9,20,22 . The tin(II) treatment steps caused an appreciable widening of the residual, post-HF-etch O1s peaks of silicon and silicon nitride. We subjected silicon and silicon nitride substrates to two control treatments at this stage of Scheme 1: in the first, we omitted the hydrofluoric acid step prior to the introduction of the tin solution, and in the second, we prepared the tin sensitizing solution without adding tin.
In none of the cases was the appreciable widening of the O1s peak observed. The broad, low-amplitude 102.5eV Si2p peak that appeared after Scheme 1 tinsensitization of silicon also appeared after tin-free control processing, and it suggests submonolayer oxygen coverage that can arise from aqueous processing 23,26 . The analogous formation of silicon oxynitride 27-28 on the silicon nitride substrate would be more difficult to discern from the main Si2p peak due to spectral overlap. Tin oxidation states can be difficult to definitively identify by XPS measurement 16,29 , but the shifts of the best-fit ~487eV Sn3d5/2 peak to lower binding energy after the addition of silver(I) ions to both substrates (by ~0.5eV for SiNx and ~0.15eV for Si), would be consistent in direction with the oxidation of tin(II). The Sn3d5/2 peaks were affected by the substrate preparation, with ~0.2eV greater width on silicon and silicon nitride substrates that had not been treated with hydrofluoric acid, with an accompanying ~0.4eV shift to higher binding energy on the silicon substrate. Overall, the XPS spectra suggest complex roles for oxygen and tin in the surface sensitization steps and, while the detailed mechanism of sensitization remains unresolved, adherence to Scheme 1 exposed the silicon-rich LPCVD silicon nitride surface for direct surface modification and yielded high-quality gold films.
In fact, in spite of complex and challenging surface chemistry, the choice of silicon nitride as a substrate opens a panoply of possible applications for consideration, and the use of a solution-based gold plating method allows us to coat surfaces that are difficult or impossible to reach by line-of-sight metal coating methods. We paid special attention in our development to be able to coat free-standing thin silicon nitride membranes. As a final demonstration of the capabilities of this method, we electrolessly gold plated micropore arrays fabricated in thin (200nm) silicon nitride membranes.

INTRODUCTION.
When a molecular-scale hole is drilled through a thin, free-standing membrane, We have made progress in functionalizing silicon nitride, but the desired ~10 nm length-scale of our pores presents severe challenges, especially when imaging the pores to confirm that an electrolessly-plated gold film and subsequent SAM are present within their interior geometries. Moreover, charged particle microscopy is not ideally suited for imaging organic-coated nanopores, and it can lead to contamination and damage that would prevent the coating's subsequent characterization in actual use.
To overcome this obstacle, we take advantage of a much simpler method of studying the nanopore interior based on measuring the flow of small monovalent ions through the pore. This technique measures the nanopore conductance, which depends in a direct way, outlined below, upon the nanopore size and shape so that pore narrowing due to gold or monolayer coatings can be directly and nondestructively measured. 13,14,24 It has the particular advantages that it is strongly sensitive to the nanopore surface coating, and it is far less likely to cause damage than, for example, ~100 keV electrons in transmission electron microscopy. Equation (1) This term, Gbulk, is the bulk ionic conductance, which is treated as a uniform flow of ions through the pore, where Kelectrolyte is the conductivity of the electrolyte and r(z) is the radius of the circularly symmetric pore as a function of the distance into the pore 27 . For ease of calculations, and consistency with previous studies 18 , the pore will be treated as a cylinder, which makes the volume parameter in equation (1) equal to πr0 2 /L0, with r0 and L0 being the initial pore radius and the pore length, respectively. 13 For our calculations, the manufacturer-specified nominal SiNx membrane thickness will be used as the pore length, L0.
The bulk conductance model fits high ionic strength data (dotted fit in Figure   3.2), but as the electrolyte concentration in the pore drops, the interaction of the charged pore surface with the ions in solution is no longer negligible, and a second term is needed in the conductance equation, as seen in Equation 2. The second term 13,14 in Equation 2 incorporates the total surface charge density of the membrane substrate (σSiNx), the mobility of the counterions proximal to the surface, µK, (K + in the case of natively negative SiNx pores at our experimental pH of 7-7.5), and the surface-area parameter, which for a cylindrical pore is 2πr0/L0.

Equation (2)
The inclusion of the surface conductance of the pore (dashed fit in Figure 3.2) dramatically improves the overall fit of the conductance model to the IV curve data, but is not complete without the inclusion of the access resistance [28][29][30][31] , which stems from the ionic current flow converging to the restrictive pore mouth, as in Equation 3. Equation (3) The access resistance depends upon the bulk electrolyte conductivity, the pore radius, as well as the surface charge density and the layer of counterions that forms on the surface, and it adds in series with the bulk and surface resistances, which are, in turn, added in parallel with each other. [33][34][35][36] There are two adjustable parameters 33 , A and B, which we have found to be 1 and 3, respectively;

Figure 3.2 Three conductance models fit to the same data points. IV curves of a single
SiNx pore in a 13-nm-thick silicon nitride membrane were measured at 0.01, 0.1, and 1M, pH 7 HEPES-buffered potassium chloride electrolyte. The three conductance models shown are a bulk-only fit (dotted), which overestimates the pore radius and diverges from the data points at all but the highest ionic strengths; bulk and surface term fit (dashed), which underestimates the pore radius and diverges from the data at very low ionic strengths; and the combined bulk, surface, and access resistance terms (solid) that fits the data across all ionic strengths. The pore radii extracted with each parameter are indicated in the legend.
these values were mathematically optimized provide the best fit of Equation 3 to data collected on pores of varying initial radii, pore coatings, and manufacturer-declared nominal thicknesses. The access resistance as shown accounts for half of a sphere at one opening of the pore, and thus must be doubled to account for both ends of the pore. The inclusion of all three terms fits the experimental data (solid fit in Figure 3.

2)
across the range of electrolyte concentrations examined.
The conductance-based study of a SAM formed on the gold interior of a nanopore has the benefit of providing a clear, albeit indirect, indication that we have gold-plated and SAM-functionalized the inside of the pore when compared to measurements of the pre-coated pore We build on this established geometric framework while noting that it may require modification to reflect the use of an electrically floating, conducting, base layer to coat the nanopore membrane.
To fit a single pore pre-and post-modification, the bare IV curve data at 0.01, 0.1, and 1M KCl is fit to Equation 3, and the bare pore radius is extracted, along with the surface charge density of the SiNx pore, as shown in Table 1. The initial calculated pore radius (decreased by an unknown coating thickness) is then used as a starting point-along with the post-coating conductance values at 0.01, 0.1, and 1M KCl-to solve for the total thickness of the combined gold and SAM. To do this, we make the approximation that the change in measured conductance is solely due to the change in pore radius and effective pore length by the deposition of the coating. Simply put, the degree by which the conductance changes is directly proportional to the thickness of the deposited coating, and, if the bare pore radius is known, then the coating thickness can be calculated.
The overall approach draws heavily from a sophisticated treatment of analyteinduced nanopore blockage currents by Reiner and co-workers in which we realized that their treatment of a large surface-immobilized molecule within a nanopore could be extended, with some manipulation, to represent a molecular coating applied to a nanopore surface. 33 The method detailed by Reiner described discrete regions within the pore: the region of the pore without the molecule adsorbed to its side wall, and the region where the large molecule resided within the pore. The latter region was of a reduced cross-sectional area, due to the physical dimensions of the blockage molecule, and the conductance model for this region incorporated a term to describe affinity of the electrolyte ions for the blockage molecule, which differed from the ionic affinity for the pore walls. Our work was particularly inspired by the inclusion of the two different surface conductance terms, which allowed us to create our own model of a two-region pore: one with a molecular coating, and one that remained unmodified, where our partial coating was treated as an analog to Reiner's molecular blockage.
The extension of the two-region conductance model afforded the opportunity to study a real-world problem, that of incomplete monolayer coverage, within the nanopore environment with which we were familiar. In our calculations, we assumed that there is a not ideally packed SAM covering the gold-plated surface of the pore. This sparsely-arranged monolayer contained some number of molecules that, when spatially rearranged, could form a full, ideally-packed, monolayer that covered some fraction, ϕ, of the available pore surface area (Figure 3.3D). Additional modifications of the Reiner equations included the incorporation of surface conductance terms for both regions of the pore, as well the inclusion of an access resistance 28-30 .

Figure 3.3 Vertical cutaways through a bare silicon nitride nanopore (A), the same pore after electroless gold-plating (B), and the gold pore after functionalizion with an incomplete thiol-terminated SAM (C). To simplify calculations, the incomplete SAM is modelled as an ideally equivalent configuration of complete monolayer covering a fraction, ϕ, of the available surface area, (D). The total effective thickness of the gold coating plus the thickness of the monolayer, δ, defines the decrease in radius of the coated pore region, and the increase in pore length.
Here, using an electroless gold layer as a support substrate for a SAM, the fractional coverage is much more complicated than laid out within this paper, and the original silicon nitride surface will be covered with a fractional gold-plated layer, which is in turn functionalized with a fractional SAM. This would create three regions within the pore, but for simplicity, we have condensed this model to two regions: a bare silicon nitride region, and a region coated by gold and a SAM of total effective thickness, δ.
For the sake of simplicity, the coating of the pore is treated as an ideallypacked SAM that covers a fraction, ϕL0, of the length of the pore, where (surface area covered by gold+SAM)/(total surface area of pore) is ϕ.

Equation (4)
In the second region of the nanopore, the discontinuous gold+SAM covering the entire length of the pore is mathematically treated as a complete layer that only covers a fraction, ϕ, of the available pore surface area (Figure 3.3C). There is consequently a reduction in the total number of electrolyte ions that can physically fit within the pore volume, due to the gold+SAM occupying some of the internal volume of the pore; the local ionic concentration (molecules/unit volume) is thereby changed, and the equation for the bulk conductance proximal to the coated pore region must be Equation (6) Within the above equation, the contribution to the total conductivity by the chloride anion remains unchanged, because that species is not adsorbed onto either the bare SiNx surface or the gold+SAM-coated region. 33 However, the contribution of the cation is scaled by the fraction of cations that are bound to the SAM (mB Equation 7 33 ) compared to the total number of cations in the entire coated pore volume (mT, Equation 8, for a cylindrical pore) 33 . The potassium ions within our pore system have a different association constant for the bare SiNx, compared to that for the SAM. At high ionic strengths, there exists a complete electrical double layer on the coated region of the pore, and all of the potential K + adsorption sites are occupied, making the ratio (mB/mT) equal to 1, and KSAM=Kelectrolyte, but this is not the case for the lowest ionic strength solutions, and must be incorporated into our conductance model. Equation (8) In calculating the ratio, mB/mT, the number of bound cations, mB, is dependent upon a quadratic parameter, α, described by Equation 9. This parameter includes a term for the maximum number of cations that can be bound to the surface if the entire pore was coated by the monolayer (n), as well as the association constant of the potassium ions for our SAM, KA.
Equation (9) To calculate n, some physical properties of the SAM must be known. The radius of the headgroup of the monolayer, rSAM, is one factor in determining how many monomeric units can fit onto the pore surface, in an ideal packing conformation. This packing conformation must be modified to account for the curvature of the pore; this becomes exceptionally important with small pores with radii that are of similar length scales to the thickness of the SAM. Finally, with an optimally-packed monolayer on the curved interior surface of the cylindrical pore, the number of monomeric units required to bind a single cation, x, must also be known. These factors all combine in Equation 10, resulting in a value for n: the maximum number of potassium ions that could be adsorbed onto the surface of a pore of a given initial radius, r0, with a gold+SAM coating of total effective thickness δ.
, for PEG 81 : x=4, rSAM= 0.332nm Equation (10) The quadratic parameter ( , for PEG 81 : ΔGpore= -0.497 eV, s=0.21 Equation (11) In the calculations of pore radius for our experiments, V was held to 0.200V, the maximum voltage magnitude applied during an IV curve acquisition. The parameter, s, represents the ratio of electroosmotic viscous force to electrophoretic force on a cation as a function of its distance into the pore, and has been estimated at 0.21 for PEG residing exactly half-way into a SiNx pore 24 .
In addition to the bulk conductance, a surface conductance term ( , and access resistance ( ) also contribute to the total conductance of the coated region of the pore. The surface conductance and access resistance terms, Equation 12 of the coating, σSAM. We have assumed for the sake of simplicity that the overall charge density of our gold+SAM coating is not significantly different than that of the bare SiNx surface in our electrolyte solution, making σSAM= σSiNx; σSiNx is one of the two parameters (r0 being the other) that is determined by solving Equation 3 prior to plating and SAM-coating the nanopore.
Equation (12) Equation (13) The three conductance terms from Equations 5, 12, and 13, can be incorporated into one equation (Equation 14) to describe the total conductance through the coated pore region.
Equation (14) A comprehensive equation (Equation 15) incorporates all of the terms described above, for the coated and uncoated regions of the pore, and can be used to calculate the effective fractional coating of the surface (ϕ), as well as the effective thickness (δ) of that coating; here, the coating is the electroless gold layer, plus the SAM on top of it.
Equation (15) When applying the equations discussed above to real-life data, IV curves from a single nanopore are acquired at 0.01, 0.1, and 1M KCl concentrations prior to coating and again after the full gold+SAM coating has been applied. Equation 3 is used with the unmodified pore data to yield the initial pore radius (r0) and the surface charge density (σSiNx). These values are used with Equation 15 to fit the post-coating pore conductance data, resulting in a value for the effective coating thickness, δ, and the fraction of the pore surface covered by the applied coating, ϕ. One caveat to this conductance model is that it does not account for the complexities introduced by an electrically-conductive, ungrounded surface, and thus the results retain a degree of inherent inaccuracy. Moreover, the assumption we have made to treat a three-region system by a two-region scheme would introduce further inaccuracy. However, our final two-region approach could prove to be quite useful in a situation where a silicon nitride pore is directly and covalently functionalized by an organic monolayer 15 , this two-region model would provide a much more accurate representation of the monolayer thickness and surface coverage than it does for the gold-SAM system described herein.

Figure 3.4 Nanopore conductance fits before (blue, fit using Equation 3) and after (red, fit using Equation 15) electroless plating a single, nominally-10-nm-long, 9.2nm-radius SiNx nanopore with a film of electroless gold, followed by self-assembly of a methyl-(PEG)4-thiol monolayer, totaling 5.2 nm in effective thickness and 54%
in fractional coverage. There are two fit regions seen post-functionalization, which converge at 0.2M-the point of 90% K + saturation of the monolayer for this given pore, given its particular degree of coverage (inset). The maximum number of potassium ions that could be bound to the SAM within this pore (mB) was 282; below that number, at electrolyte concentrations less than 0.2M there is one fit region, and above the saturation point, the trace features a second region.

Imaging Nanoporous Substrates
The conductance-based techniques discussed above provided indirect evidence consistent with the formation of an electrolessly plated film and subsequent SAM attachment within the pore, but an effort was made to directly confirm the success of the coatings. Instead of immediately undertaking the challenge of imaging single nanopores, a micron-scale imaging step (described in Chapter 2 of this thesis) was undertaken using microporous arrays 16   (inset, Figure 3.5b). The images from the field-emission scanning electron microscope (FE-SEM) of the deliberately fractured membranes were facilitated by the number of nanopores in the membrane; no matter the fracture axis, minimal searching would yield at least one cross-sectional view of the interior of a representative pore. In contrast with the microporous substrates, the cross-sections of the nanopores did not appear to be continuously plated with a gold film along the length of the pores, as seen in Figure 3.5c of a deliberately fractured nanoporous membrane. The one hour plating time of the nanoporous membrane in Figure 3.5c has been shown to deposit essentially void-free films of approximately 42 nm in thickness on planar substrates, but the deposition process did not proceed in the same manner into the nanoporous substrate, nor as into the micropores 16 from earlier studies, which featured continuous gold films of ~10nm thickness, as determined by SEM, for the same hour plating duration. The discontinuity of the gold film on the nanoporous sample may be an artificial effect due to focal-depth limitations; the bright islands seen are those protruding from the plating surface.
It is important to note the length of these nanosieve nanopore arrays-650 nm-in comparison to the length of the micropore arrays-200 nm-and the single nanopores-10-30 nm-may contribute to the incomplete through-pore plating seen.
The micropores had the favorable combination of minimally restricted solution access, along with a shorter pore length, and thus were fully coated. It is possible that the nanopore channels were simply too long, and/or needed to be in the plating solution for longer than one hour, for there to be adequate deposition of a continuous gold film given the asymmetric plating conditions. The 10-30 nm thickness of most single nanopores should be thin enough to afford solution access throughout the pore channel, but that access will be more restricted due to the pore's limited diameter.
With the initial promising results from the nanoporous membranes, we proceeded with proof-of-principle experiments in our target of a <100 nm nanopore.
In an effort towards electroless deposition of gold into these smaller, and thinner, nanopores, the aforementioned gold deposition procedure was carried out asymmetrically (Figure 3.6) on a set of five-by-five helium-ion-drilled nanopore arrays 37,38 , in which the original nanopore diameters post-fabrication were less than 20 nm, as determined by calibrated He-ion beam dwell times, and the manufacturerspecified membrane thickness was 30 nm. This experiment also allowed us to examine the penetration of plating solution into the pore, and to ease into nanopore imaging for a pore size where many-pore arrays are not available. The images seen in Figure 3  This set of experiments demonstrates that gold plating can occur through the nanopores, where the diffusion of gold ions, and the conversely diffusing formaldehyde, move from one well through the corresponding nanopore to the other well, and that this process can clearly be imaged. The imaging of the ionic masstransport process here demonstrates plating results that add convincing direct evidence in support of the symmetric plating results characterized by conductance (Figure 3.5).
The asymmetric imaging shows that it is certainly possible for enough gold solution to diffuse through the pore so that it comes in contact with all internal pore surfaces, thereby suggesting that solution access should be sufficient to support gold-plating the interior of a nanopore.
The conductance-based measurements allow for testing of pores for coverage after gold-plating, as well as molecular-coating via thiol-attachment to the gold surfaces. Additionally, the molecular functionalization may be reversible [39][40][41] , which would allow the study of conductance changes in fixed spatial increments before and after molecular monolayer formation, rather than time-dependent ones. Non-imaging based techniques have been developed to indirectly size-profile single nanopores, including those coated with fragile organic monolayers that would be damaged upon exposure to a high-energy electron beam in an electron microscope. 14,23  13,14 The ultimate goal of this electroless plating procedure was to symmetrically coat single nanopores in free-standing silicon nitride membranes, followed by surface modification by attachment of thiol-terminated self-assembled monolayers.

Conductance-Based Characterization of Coating Steps
Measurements of through-pore currents as a function of applied voltage yielded conductance values for two individual helium-ion drilled nanopores fabricated in 30nm-thick silicon nitride membranes, as shown in Figure 3.8 as a function of surface modification step. Both pores had an initial radius greater than 75nm, and as expected, when the pore diameter was reduced by a film of gold or formation of a SAM on top of the gold layer, the conductance measurement dropped accordingly; conversely, the conductance increased after a plasma-cleaning step was introduced to remove the SAM.
Based on the gradual increase in overall conductance of the coated nanopores seen over a month of experimentation, it was hypothesized that a portion of the first deposition of gold onto the surface of the wafers, and into their corresponding nanopores, may have equilibrated into the electrolyte, to be washed away during solution exchanges; may have become damaged upon un-mounting and re-mounting for plasma-cleaning; or may have become annealed during exposure to the elevated temperatures of the plasma chamber. This prompted a second electroless deposition process to fill in any gaps, most likely catalyzed by the gold already on the surface, to ideally complete the continuity of the gold film. For one of the pores studied, there was a corresponding decrease in measured conductance after this second round of plating, while there was an unexpected increase in conductance for a second pore subjected to the same procedure. Both nanopores, though internally inconsistent with respect to the renewal of the gold film, did show a decrease in conductance after exposure to a fresh solution of the mPEG-SH molecules (see inset Figure 3.8 which compose the respective SAMs. This step, referenced as step number 6 of Figure 3.8, was done as a simple experiment to demonstrate that we can exert chemical control over the terminal surface functionalities within the nanopore. The mPEG-SH coating for one nanopore was carried out at 3°C for 12 hours to ensure a uniform coating 44 , with an expected decrease in conductance confirming its assembly on the thin gold film within the pore. The second nanopore was subjected to carboxy-PEG-SH soak, which also resulted in a corresponding decrease in conductance. The conductance decreases seen in both pores from step 5 to 6, and the corresponding decrease in pore diameter (consistent with a 2.1nm-thick mPEG SAM, as reported 44 from dry film XPS measurements), suggest that the SAM was indeed bound to the gold surfaces of the nanopores, thus demonstrating our ability to coat the interior of nanopores with a chemically functionalized layer of our choosing.   Equation (16) This is a not a significant difference from the 2.4-nm radius calculated for this pore by using the conductance (Equation 15), and the small discrepancy is most likely due to the differing surface conductance values; i.e. the differing interactions between the cations in solution and the gold and the SAM-functionalized surfaces, which are not accounted for in the bulk conductance model, 24,33,49 as well as the two-region model that was used in place of the actual (most-likely) three-region arrangement.
A heat map can be generated from the events in

CONCLUSIONS
The use of gold-plated and surface-modified nanopores provides new ways of precise control over internal nanopore dimensions and surface chemistry. This has a two-fold advantage for nanopore research; the size and shape of nanopores can be precisely tailored to specific analyte dimensions; and the control over the surface chemistry of the nanopore can be used to optimize the conditions for specific experiments. The functionalization procedure outlined within this paper has been applied to planar silicon nitride, and has been shown to plate three-dimensional surfaces such as micro-and nanoporous membranes. Conductance measurements on single nanopores exposed to the gold-plating procedure have supported the hypothesis that the internal dimensions of nanopores can be controlled by the thickness of gold deposited on their interiors. By choosing complementary pore dimensions, gold film thickness, and SAM functionalities, this electroless plating process might also be used to physically and chemically tune the pore dimensions. This method of nanopore customization has been shown to successfully deposit successive coatings into the pore, as confirmed by conductance measurements, and the pores have furthermore been used to detect translocation of single molecules of λ-DNA that are consistent with translocation shapes and blockage populations shown in unfunctionalized pores. nitrile gloves, respectively. Finally, we employed a "buddy system" so that one researcher monitored the other's work with HF. All labware and gloves were thoroughly rinsed with water after use.

Self-Assembled Monolayer Coating and Removal.
An aqueous solution of mPEG-SH 0.1mM in concentration was prepared and 9 mL was exchanged into each well of the Teflon pore holders. The pores were allowed to soak in the refrigerator for 12 -

Characterization.
Gold film depositions were carried out in triplicate at each temperature and time point, and the 3°C trial was repeated so that each film thickness was based on deposition and measurements from between 3-6 different silicon nitride chips (allowing for occasional chip breakage). A step edge from gold film to exposed silicon   Dielectric Breakdown Nanopore Fabrication.
Commercial transmission electron microscopy (TEM) substrates, fabricated from freestanding silicon nitride membranes (from 10 nm in thickness), and supported by silicon frames, were mounted in custom Teflon holders (Chapter 3 Supporting Information Figure S1), with silicone elastomer gaskets between each side of the membrane and the holder to ensure a water-tight seal for the plating solutions, which were contained in 0.5 mL wells. Each well contained solutions that touched one side of the silicon nitride chip via a channel cut into the Teflon. Each well of the Teflon holder was initially filled with ethanol and put into a small vacuum chamber to remove any air present between the silicon nitride membrane and gaskets, and from inside the pores of the membrane. Each side of the membrane was then exposed to solution by exchanging the ethanol within the solution wells for 1M KCl, pH 7.5 for breakdown. After being mounted in their holders, the membranes were subjected to an Chapter 3 Supporting Information Figure S1. Schematic of Teflon holder for asymmetric electroless plating of micro-and nanoporous substrates. The silicon support chip is mounted in between two silicone gaskets, which fit into a recessed area between the two halves of the Teflon holder. Small channels in the holder allow the solutions in each well to come into contact with one half of the chip, with the only mixing points of the two solutions being the pores in the silicon nitride membrane.
The porous membranes were then prepared for plating with a dilute HF etch.
For imaging purposes, this was done asymmetrically-there were different solutions in each well during the process. Plating solutions were exchanged on each side of the pore asymmetrically in volumes from 0.5-9 mL. One half of the membrane was immersed for 45 minutes in a 50/50 methanol/water solution that was 0.025M tin(II) chloride and 0.07M trifluoroacetic acid, while the other half was only exposed to water for the same duration of time; both exchanges were 5 mL in volume. Both sides were exposed to a 9-mL methanol exchange and 5-minute methanol soak, followed by was followed for the dielectrically-fabricated single nanopores in silicon nitride windows, as well as for a series of nanopores drilled by a helium ion microscope (HIM), (Zeiss), but both sides of the membrane were exposed to the same set of sensitization and plating solutions. See Scheme S2 for an outline of the plating steps and reactions occurring in each step.
It is important to be reminded that hydrofluoric acid, even at dilute concentrations, presents significant chemical hazards upon operator exposure, requiring special working precautions. All beakers for HF containment were polypropylene, instead of glass which can be etched and rendered permeable. Dilute (5%) stock solutions were purchased to avoid handling concentrated solutions and Calgonate (Port St. Lucie, FL) 2.5% calcium gluconate gel was kept at hand in case of accidental skin exposure. To minimize exposure risk, all personnel wore a full-face shield, a disposable polypropylene apron, and thick neoprene long-sleeved gloves over standard chemical safety glasses, laboratory coat, and long-sleeved nitrile gloves, respectively. Finally, we employed a "buddy system" so that one researcher monitored the other's work with HF. All labware and gloves were thoroughly rinsed with water after use.
S Scheme S2. Electroless plating of silicon nitride. The silicon nitride-coated substrates are HF-etched before the surface is exposed to Sn 2+ ions which are oxidized during the redox-driven deposition of an elemental silver layer (reaction a) Gold plating begins with galvanic displacement of the elemental silver (reaction b) and proceeds also by formaldehyde reduction (reaction c).
sodium tetrachloroaurate dihydrate was added to approximately 15 mL ultrapure water at 80°C with stirring. To this solution were added 0.1500g barium hydroxide octahydrate and 54μL of 50% w/w sodium hydroxide to yield an orange-yellow precipitate. The solution was boiled until all visible water had evaporated, and then allowed to cool to room temperature. The precipitate was slurried with approximately 10mL of ultrapure water and filtered through a medium porosity Buchner funnel. The precipitate was slurried with approximately 10mL of ultrapure water, heated to 60-65°C with stirring, cooled, and then filtered (bis). The precipitate was then slurried with approximately 20mL of ultrapure water, and 0.500g sodium sulfite was added to the solution. The solution was heated to 60-65°C with stirring until the precipitate turned blue-purple. This solution was filtered while still warm, and the resulting filtrate was diluted to a final volume of 25mL. The pH was adjusted with 1M sodium hydroxide to a final pH above 10.

Nanopore Imaging.
Gold-plated nanopores were imaged using field-emission scanning electron microscopy (FE-SEM) and elemental analysis of the gold film was carried out by energy-dispersive x-ray spectroscopy (EDS). This imaging was done using a Zeiss Sigma VP FE-SEM at an electron energy of 8keV (Oberkochen, Germany), and elemental analysis by EDS was performed on the same instrument equipped with an Oxford Instruments X-MaxN 50mm 2 silicon drift detector (Concord, MA). Single nanopore diameters were approximated based on conductance measurements.

Analysis of Plated Nanopores.
and +200 mV of applied potential. The resulting slope of the I-V relationship at 0.01, 0.1, and 1M electrolyte concentration were fit to the total conductance model for a cylindrical pore as shown in Equations 3 and 15 (for bare and coated pores, respectively) of the main manuscript [6][7][8][9][10][11][12][13] . Conductance fits for the pores used in this paper can be seen in Chapter 3 Supporting Information Figure S2 through Chapter 3 Supporting Information Figure S5. Events were extracted using a threshold of 0.93 I/I0 and the blockage magnitude was normalized to the initial open pore current. Events shorter than 1ms and longer than 10s in duration were not used.