Profiling and Modification of Silicon Nitride Based Planar Substrates and Nanopores

................................................................................................................. ii ACKNOWLEDGEMENTS ......................................................................................... v PREFACE .................................................................................................................. viii TABLE OF CONTENTS ............................................................................................ ix LIST OF FIGURES .................................................................................................. xiii LIST OF TABLES .................................................................................................. xxvi CHAPTER 1: BACKGROUND ................................................................................. 1 NANOPORE FABRICATION AND CONDUCTANCE MODEL .......................... 1 NANOPORE CHARACTERIZATION ..................................................................... 2 i) TOTAL NANOPORE LENGTH .................................................................... 2 ii) NANOPORE SHAPE ...................................................................................... 3 iii) NUMBER OF NANOPORES ..................................................................... 4 NANOPORE SURFACE MODIFICATIONS ........................................................... 5 ELECTROLESS GOLD PLATING, SPATIAL PATTERNING AND SERS .......... 6 POLYSACCHARIDE PROFILING .......................................................................... 7 REFERENCES ........................................................................................................... 9 CHAPTER 2: PREFACE .......................................................................................... 12 CHAPTER 2: NANOPORE SURFACE COATING DELIVERS NANOPORE SIZE AND SHAPE THROUGH CONDUCTANCE-BASED SIZING ................ 13 ABSTRACT ............................................................................................................. 13 INTRODUCTION .................................................................................................... 13 THEORY .................................................................................................................. 16 METHODS ............................................................................................................... 19 RESULTS AND DISCUSSION .............................................................................. 22 CONCLUSIONS ...................................................................................................... 33 REFERENCES ......................................................................................................... 38 CHAPTER 3: PREFACE .......................................................................................... 40 CHAPTER 3: REAL-TIME PROFILING OF SOLID-STATE NANOPORES DURING SOLUTION-PHASE NANOFABRICATION ....................................... 41 ABSTRACT ............................................................................................................. 41


NANOPORE FABRICATION AND CONDUCTANCE MODEL
(This sub-section is explored in detail in chapters 2, 3 and 4).
Fabricating nanopores was historically both time-and cost-strained as it required either charged-particle microscopes, for example, transmission electron microscopes (TEM) 19,20 , scanning electron microscopes 21 (SEM) and helium ion microscopes 22 (HIM), or an accelerator facility, before the emergence of techniques such as dielectric breakdown 23 . Microscopic inspection, for example, TEM, can determine the nanopore dimensions. However, from a practical standpoint, scanning every nanopore is not feasible and is expensive as well. Other disadvantages such as deposition of contaminants in vacuum chambers and fracture of nanopores during handling also exist.
In the case of dielectric breakdown, fabrication takes place in the native sensing environment of a nanopore, mounted separating two electrolyte reservoirs. Such solution-based methods are well-complemented by using conductance based models to estimate size parameters of a nanopore 24,25 , These terms can be formulated by using Ohm's law for a conductor, resistance=resistivity · length/area. The first term, bulk = • (∫  , uses the surface charge density, , and the counterion mobility, , to determine the passage of ions along the surface of the nanopore. This model has the potential to allow for the real-time monitoring of the nanopore growth so that by setting a predetermined current threshold during the voltage-controlled dielectric breakdown, a nanopore with the size of interest could be fabricated 23 .

NANOPORE CHARACTERIZATION i) TOTAL NANOPORE LENGTH
(This sub-section is explored in detail in chapters 3 and 4).
In integral solved form of equation 1 25 . One approach to gain additional conductance data points to solve for the true { 0 , } combination would be to surface-modify the nanopore, for example by electroless plating, hydrosilylation or silane chemistry-so that a minimum of two conductance data points can be generated 24 . Another possible method would be to monitor pore formation with time-an array of real-time pore data would be generated.
Since real-time/step-wise conductance data acquisition is experimentally possible, a framework that would simulate a set of conductance data to deduce the initial geometric parameters, { 0 , } was developed. This framework holds promise to be extended to experimentally observed conductance data.

ii) NANOPORE SHAPE
(This sub-section is explored in detail in chapters 3 and 4).
The values of the two integrals of equation 1, A (volume integral) and B (surface integral), are shape-dependent. It has also become a standard practice to assume the shape of the nanopore to be cylindrical ( = 0 2 , = 2 0 ) unless the shape is clearly known, and even then the cylindrical approximation remains popular. Other nanopore shapes exist-double-conical, conical-cylindrical and hyperbolic are a few examples [25][26][27][28][29] -which are both material and fabrication method dependent. For example, anisotropic etching of track-damaged silicon nitride produces conical or double-conical pores depending on whether the etching is done from a single side (conical) or from both the sides (double-conical) of the damaged track 26 . In some instances, the possibility for conversion of one shape to another exists, if fabrication conditions are not controlled properly 29 . If the initial conductance is assumed to be 200 nS ( = 10 nm,1M KCl electrolyte at pH 7) for a silicon nitride nanopore, the calculated 0 for cylindrical, double-conical, conical-cylindrical (assuming the inner cylindrical length to be 0.6 ) and hyperbolic shapes would be ~6.4, 3.1, 5.5, and 4.0 nm respectively. There is, for example, an error greater than 50% in calculated 0 , if a double-conical nanopore is wrongly assumed as a cylindrical nanopore or visa-versa. A need to deduce the shape of a nanopore therefore exists. Shape introduces another variable in addition to the two free geometric parameters, { 0 , }. The same framework that was developed to solve for { 0 , } was used with critical modifications in the form of having additional simulated data points for robustness of the method and to solve the additional unknown, nanopore shape.

iii) NUMBER OF NANOPORES
(This sub-section is explored in detail in chapters 3 and 4).
As an added complexity to nanopore characterization, it is assumed that only one nanopore is formed when one was intended. However, recent work showed that this is not always the case: an unoptimized multilevel pulse voltage injection (MPVI) method yielded multiple pores when one was intended 30  otherwise. Hence, there exists a need to differentiate between a double pore and a single pore case before precious analyte is spent/wasted in an incorrectly configured nanopore device. One of the methods to distinguish a single pore from its double pore counterpart is to use λ-DNA as a gauging molecule. That is to use, 〈 〉 and λ-DNA the time-averaged conductances of open, and analyte-filled, nanopore and radius of λ-DNA respectively 23 .

NANOPORE SURFACE MODIFICATIONS
(This sub-section is not explored in detail due to intellectual property filing).
In addition to analyte sticking, the charge of the pore sometimes decreases the translocation frequency by opposing the translocation by having electro-osmotic movement (in addition to electrostatic repulsion 31 ) opposite to the direction in which the analyte is moving. This would require the experiment to be done over an extended period to collect an appreciable amount of data, or done at higher voltages risking voltage-driven electrode reactions. Switching the charge of the pore is possible through pH tuning if the surface contains an isoelectric point, which is the case for silicon nitride rich in hydroxy, amine and other nitrogen-based moieties 32 . However, the pH at which this switching occurs would sometimes be at a regime which can cause degradation of the analyte. A gentler approach would be to modify the nanopore surface with a surface terminal group that would produce the nanopore surface charge of interest at the desired experimental pH. Such changes would lead to changes in the direction of electroosmotic flow. Careful attention, however, must be paid to the translocation velocity as it must be within the bandwidth limitation of the data acquisition electronics. Some of the recent surface modification efforts involve silane chemistry where an organosilane 6 molecule is initially reacted with a pristine silicon nitride nanopore surface 33 . This requires the nanopore to be treated with piranha solution so that the nanopore surface would be clean and rich in hydroxyl groups. We carried out hydrosilylation on freshly fabricated nanopores to avoid such harsh surface treatments (e.g. piranha). Once the initial monolayer of molecules is photochemically laid, subsequent reactions, for example, condensation and even click, were carried out to further modify the nanopore surface. Such modification steps also provide the ability to tune the size of a nanoporefabricating nanopores with diameters <5 nm is a challenging task and these modifications can allow one to shrink a pore that is initially made larger than expected back to the challenging <5 nm size regime.

ELECTROLESS GOLD PLATING, SPATIAL PATTERNING AND SERS
(This sub-section is explored in detail in chapters 5, 6 and 7 for single-molecule sensing and manipulation [1][2][3][4][5][6][7][8][9] . A nanopore, at its most basic level, is a nanometer-diameter through-hole in an insulating membrane. When such a membrane is used to divide an electrolyte-filled cell, and a transmembrane potential is applied, the flow of electrolyte ions through the nanopore can be readily measured. The presence of a single molecule in the nanopore can then be detected and identified if it perturbs the electrolyte-only, open pore current in a characteristic way. Experimental measurements of nanopore conductance in the absence of analyte show a rich behavior dependent upon the intricate interplay between nanopore geometry, nanopore surface chemistry, electrolyte composition and potential drop across the nanopore. This behavior is captured by theoretical treatments and simulations employing varying levels of sophistication 10-16 . There are three broad classes of nanopores in routine use: proteinaceous pores such as -hemolysin and MSPA, solid-state pores such as those fabricated in silicon nitride and silicon oxide using direct electron-and ion-beam milling, and solid-state pores formed by solution processing of ion-tracked polymer and silicon nitride films 1-4, 7, 17 . These pore classes and fabrication conditions present quite different geometries and surface chemistries, and quite different challenges and opportunities. Protein pores offer self-assembly of reproducible pore structures with rich surface chemistries determined by the functional groups-amino acids in native pore structures, modifiable through complex formation and biochemical manipulation-lining the nanopore interior. Solidstate nanopores crafted in micro-and nanofabrication-compatible materials such as silicon nitride and silicon dioxide offer the prospect of streamlined fabrication of robust, complex nanopore devices for single molecule measurement and manipulation. The ability to create solid-state nanopores with a variety of sizes and shapes to accommodate a wide range of target applications is also driving their increasing popularity. The surface chemistry of native solid-state nanopores is relatively simple, with silicon oxide nanopore surface chemistry, for instance, typically treated as being governed by the single chemical equilibrium [10][11] SiOH ⇌ SiO -+ H + Advances in the surface chemical modification of nanopores, however, are dramatically blurring the boundaries between the rich surface chemistry of protein pores and the relatively straightforward chemistry of native solid-state pores. A variety of methods exists to tune nanopore surface chemistry, from direct covalent attachment to the use of physi-and chemisorbed layers [18][19][20][21][22] . Such surface modifications can be used to alter the nanopore surface chemistry and they can also be used to appreciably change the physical dimensions of the nanopore. Thus, what emerges is a design framework in which physical and molecular approaches can be used to tune the solid-state nanopore size and properties to suit applications as diverse as the fundamental investigation of receptor-ligand interactions 23 and rapid, low-cost DNA sequencing 24 . The consequent challenge is the characterization of the resulting nanopore on a length scale that is challenging to access experimentally. Characterization approaches that rely on charged particle imaging place substantial demands on the user, and require access to facilities and expertise in methods beyond those required for nanopore use 10,[25][26] . The development of characterization methods requiring routine nanopore operation, alone, thus continues, with the improved accessibility and efficiency of nanopore methods an attractive target 10,27 . Such methods would additionally promise benefits for advancing the foundations of nanopore technology by permitting, for example, nanopore size and shape to be monitored and used for feedback during solution-based nanopore fabrication approaches 19,[28][29][30] .
Given the central role of the nanopore ionic conductance in many nanopore experiments, and given that the conductance is determined by factors including the nanopore size and surface chemistry, it is common to use the ionic conductance to characterize the nanopore. Using a simple but experimentally supported model for nanopore conductance [10][11]19 , we have previously shown that the electrolytedependence of the conductance offers, in general, only a limited view of nanopore structure 27 . In particular, the ability to determine at most two nanopore geometry parameters does not necessarily permit unambiguous identification, by conductance, of nanopore shape. Independent knowledge of some elements of the size or shape, though, can be used within that framework to allow the evaluation of conductance-derived parameters, or to impose constraints that allow the partial recovery of more geometric information from nanopores described by more than two geometric parameters 27 . In this work, we show that by using the electrolyte-dependence of nanopore conductance before and after surface coating, we can more completely characterize nanopore size and shape without the need for independent geometry inputs. In particular, for experimentally realistic three-parameter pores, the augmented approach allows nanopore size and shape to be completely recovered from the conductance.

THEORY
We adopt a widely-used theoretical model for the nanopore conductance that has been successfully used to model experimental results [10][11]19 . We focus on nanopores less than 20nm in diameter, for which the access resistance is a negligible contribution 31 , leaving two contributions to the nanopore conductance, 10, 27 The bulk term, bulk arises from the flow of ions through the pore, treated here as a uniform flow 32 where K is the solution conductivity and r(z) is the radius of the pore as a function of the distance into the pore, in a cylindrical coordinate system. The surface term, surface , accounts for the flow of counterions along the charged surface of the pore, which is especially significant in low bulk ionic strength solutions 10-11 where σ is the surface charge concentration, and μ is the mobility of the counter ions proximal to the surface. This surface term thus augments the conductance with additional information involving the geometry and the surface chemistry. For a nanopore with surface chemistry governed by the chemical equilibrium in equation 1, the surface charge will arise from the charged SiOgroups on the surface, and the mobile counterions will be cations.
where 0 is the permittivity of the solution and к -1 is the Debye screening length, where nKCl is the numerical concentration of the potassium chloride electrolyte, allows one to find a solution for the surface charge concentration of the pore [10][11]33 .
The nanopore conductance in equation 2 can be expressed in a form that clarifies its geometrical and surface chemical underpinnings 27 where A and B are the volume and surface integrals, respectively, in equations 3 and 4.
When a continuous coating of thickness is applied to the nanopore surface, the new conductance of the nanopore can be expressed as ′ total ( ) = ′ ( ) + ′ ( ) ′| ′| (9) where the prime denotes the parameter value after surface coating. Measurement of the nanopore conductance at a minimum of two electrolyte concentrations, each, before and after changing the surface coating (a dimension change, ≠ 0, is required, and a surface charge density change from to ′ is likely), formally allows for the unique determination of the geometry parameters , ′ ( ), and ′ ( ). These parameters can then be used to determine the values of the underlying geometric parameters such as the nanopore limiting radius.
The implementation of this approach is not restricted to experiments in which only changes in the solution electrolyte concentration are used to predictably change the solution conductivity, , and the surface conductivities | | and ′| ′|. Chemical and physical parameters both implicit and explicit in Equations (6) and (7) can be used instead, including: a direct change of solution pH, a change of solvent to drive changes in ion mobility or surface acid dissociation constants, or a change in temperature to affect the surface acid dissociations and ion mobilities. The method is quite general and relies only upon the explicit functional dependence of the conductance shown in Equations (8) and (9). It does not rely upon the particular chemical or physical parameter used experimentally to deliver the underlying functional dependence of , | | and ′| ′|.

METHODS
In all calculations where the parameters appear, the bulk solution pH was fixed at 7.5 and the nanopore membrane thickness, L, was held fixed at 30nm. The aqueous electrolyte solution was composed of potassium chloride, so that the solution conductivity was calculated from where K = 7.6 × 10 −8 m 2 /(V • s) and Cl = 7.9 × 10 −8 m 2 /(V • s) are the mobilities of the potassium and chloride ions, respectively 11 . The solution permittivity was approximated as 0 = 77.75 0 throughout. Native, uncoated nanopores had their surface chemistry described by the equilibrium in Equation 1, with a constant pKa=7.9 34 .
The surface charge density, , of the uncoated nanopores was calculated as the simultaneous solution to equations 6 and 7, where Γ and C were held constant at 8 × 10 18 m −2 , and 0.3 F • m −2 , respectively, and were not changed after surface coating [33][34] .
We selected a number of common nanopore radial profiles, listed in Table 1.1, to describe the shape of the nanopores. We chose to model an amine-terminated, covalently modified nanopore surface to give a surface coating involving the acid-base equilibrium −NH 2 H + ⇌ − NH 2 + H + (11) and described by pK a = 10.8. The 1.7nm-thick coating was assumed to smoothly and uniformly coat the surface without changing the nanopore shape and with the monolayer chains orthogonal to the surface at the point of attachment. The surface coating did, however, change the sign of the charge on the nanopore surface and the identity of the mobile surface counterions, from cations in the native pore to anions in the coated pore.
To investigate the ability of the proposed method to recover the nanopore size and shape for nanopores with limiting radii, 0 , between 2.5 and 10nm, we computed the integrals , ′ ( ), and ′ ( ), using = 1.7nm to account for the length of the silane-coupled monolayer, for each nanopore radial profile listed in conical-cylindrical and exponential-cylindrical profiles, and an 0,ref = 7 cylindrical nanopore was used to geometry-optimize cylindrical, conical, hyperbolic, conicalcylindrical and exponential-cylindrical profiles. All native geometry parameters, except for L, were varied during the geometry optimizations. The geometry optimizations were first performed with fixed monolayer thickness, = 1.7nm, and then repeated in a separate trial with as a free parameter, in an attempt to recover the layer thickness.
The optimization used the Nelder-Mead minimization algorithm, and involved varying the underlying geometry parameters (e.g. 0 , , etc.) of the radial profiles to minimize where the subscript "ref" denotes the known, reference, parameter value, and the subscript "fit" denotes the corresponding value calculated using the trial values. Given the form of the conductance (equations 8 and 9), minimization of RMSE AB delivers a weighted conductance-based geometry optimization. An error threshold of 10 -12 was used in the optimization runs, and the optimized structure was the result of the trial with the lowest RMSEAB. A similar metric expressed directly in terms of conductance requires an average across N potassium chloride concentrations ) + ( The potassium chloride concentrations used here ranged from 0.01M to 1M, with the ith concentration calculated from 10 −2+( −1)0.01 M.

RESULTS AND DISCUSSION
In the most common implementation of conductance-based nanopore sizing, the nanopore conductance at a single electrolyte concentration is used to extract a radius, and nanopore surface charges may be either included or neglected in the calculation.
We explore this canonical single-point approach as a prelude to the consideration of the  To generate Figure 2.1, the conductance of the uncoated reference nanopore was calculated using a realistic radial profile with three tunable geometric parameters (exponential-cylindrical, see Supplemental Table S1) 10 and accounting for the surface charge established by the equilibrium described in Equation 1. At each electrolyte concentration considered, the single conductance value was used to determine the radius of a particular single-free-parameter nanopore profile-here, either the original reference profile with fixed l=11nm, and b=0.19nm -1 , or a cylindrical profile-by including or neglecting the surface charge. In solutions with high bulk conductivity and high ionic strength, omission of the surface charge had little effect on the best-fit nanopore radii. There was, however, a clear difference in the nanopore radii determined via assumption of the nanopore shape-a difference that persisted across solution electrolyte concentrations. At lower electrolyte concentrations, the profile-specific errors in best-fit radii were dramatically superseded by the errors arising from the neglect of surface charges in the geometry optimization. This tremendous sensitivity to the surface chemistry points both to the potential to profile the surface chemistry via conductance and to the necessity to consider it 10-11, 14, 35 . It is moreover essential to emphasize that in addition to the visible differences in cylindrical and exponentialcylindrical best-fit radii shown in Figure 2.1, the two optimized versions of the same nanopore have dramatically different shapes-one has a cylindrical restriction of 11nm in length that then opens towards the membrane surfaces, the other a cylindrical restriction that spans the entire 30nm membrane thickness. These observations underscore the importance-and difficulty-of using conductance to determine nanopore shape and surface chemistry, together: a single conductance value can be exactly satisfied by nanopores of a host of different sizes and shapes. Extension of this basic, single-point optimization to use the electrolyte-dependence of the conductanceat minimum a two-point optimization, but more practically requiring more than two data points to improve the fit statistics-offers the possibility of determining the bulk and surface contributions. In addition, the extension delivers an additional degree of freedom for nanopore geometry optimizations: it permits the optimization of radial profiles with up to two free geometry parameters 27 . Given that transmission electron microscope (TEM)-fabricated nanopore profiles can require description by no less than three free parameters, such a geometry optimization requires parameter constraints or reductions. This has the consequence of compromising the nanopore size determination and moreover prevents even the shape of pores from being determined without additional information 27 . One of the substantial and myriad benefits conferred by coating nanopores with overlayers, then, is the additional degrees of freedom provided for conductance-based geometry optimizations.
Nanopores and nanopore surface functionalization are frequently characterized using a conductance-based method that does not involve variation of the electrolyte concentration, however. The approach is analogous to the single-point optimization of Figure 2.1 and uses the nanopore conductance at a single electrolyte concentration, before and after surface coating. The use of two conductance values provides a much-needed additional degree of freedom compared to the single-point measurement, but the available information is still limited. In particular, one would perform a single measurement of the conductance before and after (′) coating, 1 = 1 + 1 | 1 | and ′ 1 ( ) = A( ) 1 + B( ) 1 ′| 1 ′|, respectively, where the subscript "1" denotes the particular value of the parameter. Rewriting A( ) = α(δ) and B( ) = β(δ) (with different values of α(δ) and β(δ) for each nanopore size and shape), and defining effective (eff) values α( ) 1 = K 1,eff and β( ) 1 ′| 1 ′| = ( 1 ′| 1 ′|) eff yields two equations 1 = 1 + 1 | 1 | and ′ 1 ( ) = A K 1,eff + B ( 1 ′| 1 ′|) eff that makes this approach formally equivalent to the two-point nanopore geometry optimization that had previously been explored in detail 27 . While delivering generally superior performance to a single-point optimization, it nevertheless has well-characterized performance limitations in comparison to the optimization method introduced here. For example, such a two-point approach cannot be used to uniquely geometry optimize nanopores requiring more than two free geometry parameters 27 .
We now consider the nanopore optimization method outlined in the Theory and Methods sections, a method that requires knowledge of the nanopore conductance at a minimum of two electrolyte concentrations, before and after surface coating. The method therefore requires a minimum of four conductance values (a four-point optimization), but in practice more than these four conductance values would be used in order to improve the fit statistics, at least the first time that a pore was to be characterized. Equation (13) could be used to guide the geometry optimization using the conductance directly. In the conductance equations, Equations (8) and (9), however, the physical pore dimensions and the surface chemical properties are separable contributions to the conductance. To highlight the performance of the optimization method in recovering nanopore size and shape, we used Equation (12) to perform the The optimization results presented here using Equation (12) deal with geometry only, and are completely independent of the surface chemistry, which need not be specified.
Experimentally, this geometry-based approach would have great utility if a two-step optimization were adopted. In the first step, the conductance versus electrolyte concentration curves (Equations 8 and 9) would be fit to extract best-fit values for , ′ ( ), and ′ ( )-parameters that would be, at this stage, devoid of physical meaning because the core geometry parameters underlying their values would not yet be considered. Within the framework of the conductance model described by Equations (8) and (9), this first step would thus require no knowledge of nanopore geometry, but would require only knowledge of its surface chemistry. Minimization of RMSEG to achievable ~10 -12 levels (cf. Figure 2.2) may require slight fine-tuning of surface parameters to optimize the fit to the conductance. The best-fit , ′ ( ), and ′ ( ) would then serve as the reference values to govern the subsequent determination of nanopore size and shape using Equation (12)-a geometry-only optimization.  Table 1 were performed, without constraints on the values of the geometry parameters (other than L=30nm and = 1.7nm, as outlined in Methods). The lowest values of the optimization metric RMSEAB were for the exponential-cylindrical profile-the shape matching the reference nanopore shapeand were orders of magnitude lower, for all nanopore sizes considered, than the RMSEAB for all of the other candidate nanopore shapes. The RMSEAB metric was therefore clearly able to correctly identify the nanopore shape. The errors in conductance, RMSEG, corresponding to all of the RMSEAB-best-fit geometries, were also calculated, although they were not used for the optimization. While the RMSEG are scaled by the solution and surface physicochemical parameters, they still showed the same relative trends and magnitudes as the RSMEAB and the same performance in correctly identifying the nanopore shape from amongst the candidates. An examination of the best-fit limiting radii, , for each trial shape further emphasizes the merits of this conductance-based characterization approach. The cylindrical, conical and hyperbolic profiles rejected by the RMSEAB metric yielded radii whose deviations from the reference radii were significant on the length scale of nanopore-based single-molecule sensing and manipulation. In spite of broad structural similarities (inner cylinders that widen towards the membrane surfaces) and limiting radii in very close agreement, the RMSEAB metric was able to clearly differentiate between conical-cylindrical and exponential-cylindrical pore shapes. This inability of the conical-cylindrical pore to match the exponential-cylindrical nanopore conductance occurred in spite of the variation of − 0 from ~3.5nm to ~7nm with increasing 0,ref , and varying from 9.8 to 11nm versus the constant 11nm in the reference nanopores (not shown). This ability to distinguish between even structurally similar three-parameter (or fewer) nanopore shapes using the present four-point method is in marked contrast to earlier reports using two-point conductance optimizations 27 . The inability of the conical-cylindrical trial profile to match the conical reference conductances arises from its limiting behavior as → 0: the uncoated pore profile reduces to a conical profile, but the coated profile remains conical-cylindrical.
Nevertheless, the optimized values of the conical-cylindrical profiles indicated strong conical character: limiting radii essentially matching conical reference limiting radii, and values of nearing zero (not shown).
Four-point optimizations of hyperbolic and conical-cylindrical reference nanopores similarly allowed the correct determination of the reference nanopore shapes and their geometry parameters. A particularly interesting case of the ability of the fourpoint optimization to correctly determine the shape of reference nanopores with three free parameters or less occurred when using a cylindrical reference nanopore. All of the trial profiles listed in Table 1 and Supplemental Table S1 will reduce to a cylinder as a limiting case. It is therefore possible to fit a cylindrical reference pore with a conical-30 cylindrical profile, for example, by satisfying either = , and = . It is necessary, therefore, to examine not only the RMSEAB or RMSEG for a particular trial profile, but also the resulting best-fit geometry parameters that could indicate a cylindrical reference nanopore even when using a conical-cylindrical trial, for example. The trial nanopore profiles span a range of experimentally representative nanopore shapes and, with a maximum of only three free geometry parameters, can nevertheless reproduce experimental conductance measurements 10,27 . The ease with which RMSEAB and RMSEG, when coupled with examination of the resulting best-fit parameters, determined the optimal radial profiles with fixed-hinged on the number of free parameters in the trial shapes compared to the degrees of freedom delivered by the functional form of the conductance. The four-point method should also be able to uniquely geometry-optimize four-parameter models, thereby allowing the nanopore surface coating thickness, , to be an additional free parameter of the optimization.

CONCLUSIONS
Surface-coated nanopores are receiving increasing attention for the ability of surface coatings to tune nanopore dimensions and surface chemistry, and to confer powerful performance capabilities on a host of nanopore single molecule sensing and manipulation schemes. Knowledge of a nanopore's size, shape and surface chemistry thus bears on nanopore creation, modification and application. While nanopore conductance is governed by the nanopore geometry and surface chemistry in concert with experimental parameters such as electrolyte composition and temperature, careful design is necessary if the measured conductance is to be used to reveal the underlying nanopore properties. The use of experimentally realistic trial nanopore profiles, coupled with consideration of the resulting best-fit parameters in the context of nanopore fabrication and surface functionalization details, is naturally essential to the success of this method. This is especially true when optimizing models with the full four degrees of freedom permitted by the method. The geometry optimization results were achieved using an experimentally-supported nanopore conductance model [10][11] that allows the effects of nanopore geometry on the conductance to be clearly separated from the effects of surface chemistry. In this context, the conclusions drawn regarding the quality of the geometry optimization results presented here are general and, so long as the surface modification changes the nanopore dimensions, are not restricted to a particular choice of surface chemical modification.
The four-point conductance framework introduced here was able to correctly identify nanopore shapes and to determine the correct magnitudes of all key geometry descriptors of realistic nanopores with greater structural complexity than had previously been possible by conductance, alone. This capability included the complete characterization of an elegant, experimentally-determined nanopore profile representative of TEM-manufactured nanopores 10 without requiring constraint of its parameters 27 . The performance capabilities thus dramatically exceed those of the more usual single-point conductance approach based on a cylindrical nanopore approximation, and of the more sophisticated two-point conductance approaches.
Beyond recovering the native nanopore structure, the four-point method was able to also probe the thickness of the surface coating, . With the use of approaches that yield well-defined surface coatings, the best-fit values for the coating thickness emerge as an additional metric for evaluating the conductance-based nanopore characterization.
Straightforward measurements of the electrolyte-concentration-dependent conductance of nanopores can thus serve as a simple yet powerful foothold for peering into these bioinspired nanoscale environments.   KEYWORDS: Nanopore; dielectric breakdown; electroless plating; nanopore conductance; silicon nitride nanopore; nanopore size; nanopore radius.

ABSTRACT
We describe a method for simply characterizing the size and shape of a nanopore during solution-based fabrication and surface modification, using only lowoverhead approaches native to conventional nanopore measurements. Solution-based nanopore fabrication methods are democratizing nanopore science by supplanting the traditional use of charged-particle microscopes for fabrication, but nanopore profiling has customarily depended on microscopic examination. Our approach exploits the dependence of nanopore conductance in solution on nanopore size, shape, and surface chemistry in order to characterize nanopores. Measurements of the changing nanopore conductance during formation by etching or deposition can be analyzed using our method to characterize the nascent nanopore size and shape-beyond the typical cylindrical approximation-in real-time. Our approach thus accords with ongoing efforts to broaden the accessibility of nanopore science from fabrication through use: it is compatible with conventional instrumentation and offers straightforward nanoscale characterization of the core tool of the field.

INTRODUCTION
A nanopore is a nanofluidic channel, with dimensions in all directions generally less than 100 nm, that can be used to deliver a host of capabilities for single-molecule sensing. 1-10 High-profile nanopore sensing efforts have targeted sequencing single strands of DNA and RNA; protein conformational analysis; and characterization of other biomolecules, molecular complexes, and nanoparticles. In the most straightforward implementation of nanopore sensing, the nanopore is the sole path connecting two reservoirs containing electrolyte solutions. Electrodes in each reservoir establish a potential difference across the nanopore that drives ions through the nanopore: passage of a target molecule, nanoparticle, or complex through the nanopore perturbs that ionic current and provides molecular-level information. That information naturally depends on the target's dimensions and physicochemical properties and the ionic solution composition, but it is also profoundly affected by the size, shape, and surface chemistry of the nanopore. In the case of a (cylinder-like) double-stranded DNA polymer that fills the entire length of a cylindrical nanopore as it transits through, a simple geometric treatment considering only the displacement of bulk ions by the polymer gives a straightforward expression for the macromolecule-induced conductance change 11 with 〈 〉 and 〈 〉 the time-averaged conductance through an unobstructed and DNAcontaining nanopore, respectively, and DNA and the cross-sectional radii of the molecule and nanopore. The expression does not capture the panoply of complex phenomena giving rise to conductance perturbations in nanopore sensing, 12-13 but does, in convenient closed form, appropriately underscore the importance of nanopore dimension. This geometric basis of the conductance change has been used to infer biopolymer conformation, for example: a folded-over polymer presents a larger effective cross-section than a linear one. 14 The more elusive dependence of current change on single-stranded DNA base sequence, for example, underpins efforts to sequence single strands of DNA using nanopores. 2,8 In a powerful implementation of nanopore force spectroscopy, details of interaction energetics can be revealed if, and only if, a nanopore size is properly engineered to sterically force the linearization of a folded moiety during passage, or rupture of an intermolecular complex by barring passage of one of the partners. [15][16][17] The ionic conductance ( ), alone, of a nanopore with a charged surface can be expressed as the sum of a bulk and surface conductance term 18-21 when access resistance is negligible. 22 Overlapping Debye layers require a more sophisticated treatment, but need not be considered over a broad useful range of nanopore sizes and solution ionic strengths. [23][24] This simple formulation for has been supported by experimental measurements in which nanopore conductance was measured for nanopores that had size and shape interrogated by combinations of transmission electron microscopy and electron energy loss spectroscopy. 13,18 The bulk conductance is determined by the solution conductivity, K, and a volume integral, , over the unique nanopore shape: bulk = (∫ reported parameter values, which may be only a subset of those needed to fully characterize a given nanopore profile, include the limiting radius (the minimum radius along the profile), 0 , and total nanopore length, , that can in some cases be equated with the supporting membrane thickness. The experimentally-supported 13, 18 treatment of the nanopore conductance here assumes axially and cylindrically symmetric nanopores in a size regime where access resistance is negligible, 22 and that any surface charge emerges from a singly ionizable surface species described by a characteristic pKa Native or engineered nanopore surface chemistry is an important element in nanopore performance, and contributor to nanopore conductance. The conductance can be naturally exploited for nanopore characterizations in conjunction with solution-based nanopore fabrication methods, and is especially useful when more complex methods present barriers to use. Charged-particle milling is an established, but challenging and burdensome, approach for formation of the smallest, <10 nm nanopores in thin developed for polymer membrane nanopores have been extended to silicon nitride membranes which offer benefits such as the fabrication of smooth nanopores with lengths <100 nm. 32,35 More recently, dielectric breakdown (followed by voltageassisted etching) of an impervious, insulating membrane, has emerged as a powerful new technique for nanopore fabrication. 36 It is an entirely solution-based approach, using essentially the same equipment required for conductance-based nanopore measurements, and quite readily produces nanopores in a wide range of sizes, including in the coveted <5 nm diameter range. The nanopore conductance can be measured during fabrication, providing an indication of the nanopore size at a given point in time.
The dielectric breakdown approach allows nanopores to be fabricated in their native environment, in the same holder where they will be used for experiments, and without the contamination and damage risks associated with charged particle techniques. A conductance-based characterization will not damage a molecular surface coating suitable for conductance-based sensing, and can harness the natural and direct connection to the nanopore surface chemistry that makes it a valuable method for characterizing chemically-tailored nanopores. 9,23,34,37 The conductance model is equally useful when a pore is formed and enlarged, and when an initially large pore is resized by solution-based deposition, including film growth. 9,19,35,38 Etching and deposition may be used in concert, with a pore being initially etched larger than desired to accommodate an electroless gold film, for example, that may ease nanopore surface chemical modification. In this work we wanted to understand how the measured conductance during nanopore fabrication-by deliberate expansion, closure, or both in consort-could be used to profile the nascent nanochannel. Simulations will focus, for expediency, on nanopores fabricated via deposition of surface coatings: the principles, however, are general.

THEORY
The algebraic structure of = • + | | • , and its underlying dependencies, means that a single-point conductance measurement can provide enough information to size a nanopore only when the shape is known and the fitting involves only a single geometric degree of freedom. Measurement of versus -by changing the electrolyte solution conductivity-for a given nanopore can provide greater insight into the nanopore size, shape, and surface chemistry. 18,[21][22][23] The conductance change after adding a monolayer of known thickness, for example, can provide similar information to what is provided after a solution conductivity change, and measuring versus for the nanopore before and after monolayer formation provides the richest description of the nanopore within this framework. 23 Changes of electrolyte solution are tedious, however, and disruptive to a solution-based nanopore fabrication approach. A simple ongoing measurement of the nanopore conductance during nanopore formation, however, can be done as part of the fabrication process, and is in fact performed routinely on a single-point measurement basis. Each fixed-time conductance is of course connected through Equation (2) to the instantaneous nanopore size and shape, where the applicability of the conductance model has been independently verified by electronbased imaging and spectroscopy. 13,18 A single conductance value, however, offers a limited ability to characterize a nanopore described by more than one free geometric parameter. Measurement and use of a series of conductance values at times : We make the reasonable assumption that material transfer will be uniform across the surface, so that the nanopore shape will remain unchanged. Silicon nitride, the most common membrane material in which to form nanopores, is amorphous, and so will not inherently be prone to anisotropic etching. 39 Electroless plating, a surface deposition method that has been used with great success in resizing nanopores, 9 conformally coats even rough surfaces, 40 and film growth by polymer chain extension, for example, should be another effective route to reliably tune nanopore size. 41 We can then write  Tables S-1 and S-2 for notation and equations). Independent experimental studies of nanopore profiles 18,22 were used to guide the constraints and to make reasonable parameter value assignments to allow for numerical examples; the nanopore characterization method is general, however, and does not depend upon these particular numerical values. 21,23 We restricted the initial outer radius to be 10 nm greater than the initial limiting radius (not applicable to the cylindrical profile), [21][22] and fixed the initial cylinder length of the conical-cylindrical pore to be 0.6 times its initial total length. The deposited coating was piecewise curved to maintain a uniform coating thickness across the entire nanopore surface (Figure 3.1 and Table S-2). Equation (4) then becomes Parameter values used in calculations were typical of experiments and consistent with those in prior work with silicon nitride nanopores: 21 for example, 1 M potassium chloride electrolyte solution in water, K=14.95 S·m -1 (calculated using ion mobilities), pH=7.0, and surface pKa=7.9. The material transfer rate was kept constant, = 0 ⁄ = 0.6 nm/h. More important than the particular parameter values, though, it is the form of equation (2) and its functional dependencies that are significant in this work.

RESULTS AND DISCUSSION
The ability to characterize a nanopore in real-time, during its formation, using only its conductance, is an incredibly compelling goal. Its pursuit relies on the connection between the conductance of a nanopore and its size, shape, and surface chemistry, and its attainment hinges on properly exploiting the functional form of that connection. We will focus on nanopores fabricated by deposition of a coating onto the outer membrane surface and inner surface of an existing, larger pore, but similar arguments hold for a nanopore formed by etching of a smaller pore to create a larger pore. there is not a unique solution. To use a single-point conductance value to characterize a nanopore by more than a broad range of possible shapes and sizes, or to provide better than an approximate size given an assumed profile, additional information is required. 21,23 Most commonly, knowledge of the particular fabrication method and conditions is used to choose an expected nanopore profile, and can often be used to constrain the nanopore length to an experimental parameter such as the thickness of the membrane in which it is formed. Measurement of the conductance of a nanopore in time, in an essentially single-point sense, has demonstrated utility as a monitor of nanopore evolution even if it cannot provide an unambiguous characterization. Yet the timedependence provides a set of experimental data points that we seek to mine to more fully characterize the nanopore than is possible using a single-point measurement of the conductance Figure 3. 2. The plotted lines denote the pairings of limiting nanopore radius, , and nanopore length, , for each nanopore profile, that will produce a 200 nS conductance.
The most immediately striking consequence of a real-time measurement of the conductance is that, as shown in Figure 3.3, it reveals a clear distinction between different nanopore profiles. When different candidate profiles are used to fit experimental nanopore conductance data, the conductance versus time provides a means to determine nanopore shape and size. To produce the data plotted in Figure 3.3, we used the four representative nanopore profiles all with an initial 200 nS conductance and 10 nm total nanopore length. The initial nanopore limiting radii were ~6.4, 3.1, 5.5, and 4.0 nm, respectively, for the cylindrical, double-conical, conical-cylindrical, and hyperbolic nanopore profiles. We calculated the conductance for each profile as the radii were reduced at the same rate, = . nm/h, during a simulated, deposition-based fabrication process. As shown below, the radius change after a given time must be known, but the method does not require a constant material transfer rate. We chose a constant rate, commonly observed in micromachining processing, 39 however, because it affords straightforward insights into the functional dependencies beyond what is revealed by the numerical results. Given the form of equation (5), it is perhaps unsurprising that even with constant (and therefore identical absolute rates of change of the radii across profile type), is not linear and depends on profile type (inset of Figure 3.3). The quantitative details of this behavior provide a means of extracting nanopore size and shape information from the measured conductance changes. Figure     We chose to simulate the deposition-based fabrication of nanopores with an initial conductance, shape expt ( 0 ) = 200 , and initial radius, 0,shape expt ( 0 ) = 3.5 nm (both values the same for all simulated experimental shapes); Figure 3.2 gives the corresponding initial nanopore lengths, shape expt ( 0 ), for each nanopore profile. For each nanopore profile, we set the initial nanopore size, ( 0,shape expt ( 0 ), shape expt ( 0 )), and used the progression of dimensions, ( 0,shape expt ( 0 ) − Δ ( 0 , ), shape expt ( 0 ) + 2Δr i ( 0 , )), to simulate the post-deposition conductances shape expt ( 1 ) and shape expt ( 2 ). For a constant material transfer rate, , Δ = ( − 0 ) . While more generally Δ = Δ ( , 0 , ( )), the procedure implemented here relies on knowledge of this radius change only, not whether the material transfer rate is constant in time or not. We outline the conceptual framework for the characterization and provide a detailed step-by-step tutorial in the SI. The initial conductance, shape expt ( 0 ), was used in conjunction with Figure 3.2 to establish the set of candidate {( 0,shape ( 0 ), shape ( 0 ))}, for each nanopore profile, whose members all have the initial conductance ℎ ( 0 ) = shape expt ( 0 ). The range of candidate sizes, for each candidate shape, is represented by the dotted lines in Figure 3.4a-d. Given shape expt ( 0 ), alone, neither size nor shape can yet be determined. Each of these possible candidate geometries (size and shape) was then modified by the deposition of material to provide sets of nanopore dimensions given by {( 0,shape ( 0 ) − Δ , shape ( 0 ) + 2Δ )} for times 1 , 2 , and 3 , with corresponding sets of conductances { shape ( 1 )}, { shape ( 2 )}, and { shape ( 1 )} (solid curves in Figure 3.4ad). We then used the post-deposition shape expt ( i ) to determine the nanopore size and shape. We found the initial limiting radius, 0,shape ( 0 ), for each nanopore shape, that gave a conductance ℎ ( 1 ) = shape expt ( 1 ). That is, when the experimental nanopore was cylindrical, we found the 0,shape ( 0 ) for cylindrical, double-conical, conicalcylindrical, and hyperbolic profiles that allowed the candidate pore conductance to match the experimental value, and plotted the radii in Figure 3.4e. Figure 3.4f-h are plots of the 0,shape ( 0 ) when the conductances of double-conical, conical-cylindrical, and hyperbolic experimental nanopores were equated to the conductances of the same four candidate shapes. No matter the experimental profile, after two conductance values, all four candidate shapes-with different sizes-were equally viable conductance-based matches. By repeating this process by finding 0,shape ( 0 ) to satisfy shape ( 2 ) = shape expt ( 2 ), the experimental nanopore size and shape both emerge. When the candidate nanopore profile matches the simulated experimental profile, all extracted 0,shape ( 0 ) have the same value for all , which essentially delivers a simultaneous solution of for all time-points. The curves in Figure 3.4eh illustrate this successful characterization; the agreement is shown in terms of 0,shape ( 0 ), but shape ( 0 ) has the same behavior. Measurement of more conductance points does not provide more information, given the framework presented here, but can add numerical robustness to this approach.
Alternatively, the formal need for only three conductance values allows one to piecewise repeat the shape-and size-profiling on independent sets of three conductance values throughout the duration of the fabrication, allowing for the possibility to extend this method to anisotropically-etching or -depositing materials. An extreme departure from the usual progression of conductance in time may signal the need for a more involved steady-state solution-based characterization of a pore after fabrication, 21 although even in this case the present time-dependent method should provide bounds on the evolving nanopore size. We note again, for generality, that while we used a constant , the plating rate must be known, but need not be constant. Fitting conductance values in time leverages the form of equation (2) to reveal the nanopore shape and extract dimensions from a solution-based nanopore fabrication method.

CONCLUSIONS
The charged-particle, complex instrumentation approaches that dominated early nanopore fabrication methods allowed, in principle, for high-resolution nanopore characterizations, although such capability was rarely employed beyond determining a limiting radius. These instrumental approaches face limitations such as high likelihood of surface contamination and inability to probe soft (e.g. organic) nanopore coatings, and they add workflow steps that could be costly in time and instrumentation. Even so, since the nanopores were formed in these instruments, it was expedient to follow fabrication with the chosen degree of characterization in the same instrument. The ongoing development of completely solution-based methods-including the advent of new techniques-to fabricate nanopores has ushered in an exciting new area for nanofluidics, generally, and nanopore science in particular. Nanopores can now be formed in their native liquid environment, and without the instrument and workflow cost of charged-particle methods. We have modelled the nanopore conductance with a simple framework that nevertheless includes an explicit surface chemistry term and has demonstrated concordance with independent experimental characterizations of nanopore sizes and shapes of most importance for routine use in single molecule science. 13,18 We have presented theoretical examples that describe the creation of small nanopores by coating larger nanopores, so that fabrication involves a decrease in the nanopore radius and conductance. The results, however, are equally applicable to nanopore fabrication methods such as dielectric breakdown followed by voltageassisted etching, or the chemical etching of ion-tracked membranes. The nanopore conductance is routinely measured during dielectric breakdown as a diagnostic, and such a measurement can be readily implemented during nanopore fabrication by material deposition. We have shown here that by analyzing a series of conductance measurements in time, rather than only an instantaneous measurement, we are able to extract information on nanopore size and shape, and thereby enrich the execution and interpretation of nanopore experiments without increasing the experimental burden.  formalism supports the detection and characterization of defects, as well as the determination of pore number, but with implementation performance depending on the measurement context and results. In some cases, the ability to discriminate numerically between the correct and incorrect nanopore profiles was slight, but with accompanying differences in candidate nanopore dimensions that could yield to post-fabrication conductance profiling, or be used as convenient uncertainty bounds. Time-dependent nanopore conductance thus offers insight into nanopore structure and function, even in the presence of fabrication defects.

INTRODUCTION
Nanopores are a rising tool for single-molecule science, featuring prominently in DNA sequencing efforts, but with broader reach into biophysics, and bioanalytical and materials chemistry. [1][2][3][4][5][6][7][8][9][10][11][12] The nanopore heart of these techniques is a nanofluidic channel generally less than 100 nm in all dimensions, formed through a membrane or support, with the particular dimensions dictated by the analyte and method. The essential determinants of nanopore performance include the elements of three general nanopore-specific parameter groupings: nanopore size, shape, and surface chemistry. [13][14][15][16][17][18][19] Even the most basic nanopore operating configuration illustrates the importance of these parameters, and also provides a means for assaying them. A nanopore is positioned as the sole fluid path between two wells of electrolyte solution.
Application of suitable voltages, typically ≤200 mV, across the impermeable support where is the nanopore surface charge density that attract counterions of mobility, .
The pore has a radius, r(z) , that can vary along length, L, of the pore (aligned with the z-axis as shown in Figure S4 been to assume formation of a single nanopore when one is intended, and to overlook possible structural defects. Inaccurate nanopore models will affect the quality of conductance characterizations, and other work has shown (and taken advantage of) the influence of internal nanopore structural irregularities on analyte current blockages. [32] While it is essential to control the size of isolated nanopores for single-molecule characterization and sensing applications; the use of arrays of nanopores as filters for physical and chemical separations multiplies the challenges and underscores the need to detail the formation of even single nanochannels. [11] The extreme, ~10 nm feature size has historically been challenging to nanopore fabrication (and characterization) efforts. Methods have tended to be instrumentationintensive, using charged-particle microscopes such as scanning and (scanning) transmission electron microscopes (SEM and (S)TEM), and helium ion microscopes, or ion accelerator facilities to prepare membranes for subsequent chemical etching steps. [33][34][35][36][37] More recently, ~20 V potentials applied across thin membranes immersed in electrolytes conventionally used for nanopore experiments resulted in (controlled) dielectric breakdown of the films, and could produce size-tuned nanopores following voltage-assisted etching. [38] This truly low-overhead approach can yield <10 nm diameter nanopores, and produces them reliably wetted for use, without the risks of drying and surface contamination from steps such as TEM-based fabrication (or examination). A similarly all-solution-based approach uses deposition of largely conformal films to shrink suitable pores to the desired final dimension. [9,39] By deliberately and beneficially removing high-magnification charged-particle microscopes from the fabrication workflow, however, the opportunity to immediately image the fabricated pores is lost. We therefore explored existing nanopore conductance formalisms [13,18] and developed a framework to use conductance to characterize nanopore size, shape, and surface chemistry. [14][15][16] We most recently showed that the method could yield real-time insight into these nanopore properties during solutionphase fabrication processes such as those outlined above. [14] In all instances, however, the simulations assumed perfectly formed single nanopores. Here we (1) deliberately introduce defects into the pore models, and we moreover (2) allow for the possibility that a measured conductance arises from two separate nanopores forming in the same membrane (denoted a double pore). The latter allowance arises from TEM observations, post-pore fabrication, showing that dielectric breakdown formation of nanopores using unoptimized multilevel pulse-voltage injection could yield more than one pore. [40] Conductance-based measurements should allow for these realities, at least through the setting of reasonable uncertainty levels. We focus here on nanopores formed in thin, free-standing silicon nitride membranes, so that our numerical simulations use parameter values from the most commonly used nanopore material platform. The films are amorphous and thus not inherently prone to anisotropic etching, [41] and silicon nitride is notably resistant to structural and chemical modification absent deliberate action.

METHODS
The form of Equation 1 means that a single measured conductance does not yield a single unique solution for the nanopore size and shape. [14][15][16] One can gain more degrees of freedom by measuring the conductances at two different solution conductivities, , [15,16] or after (or during) controlled structural modifications. [14,15] A time-dependent framework was developed and examined conventionally in earlier work-without considering either defects or multiple pores. [14] During nanopore formation-by dissolution or deposition of material-the nanopore conductance is a function of time because the dimensions of the nanopore, { ( , )}, are changing in time, t: This particular implementation can determine geometries with two free parameters, and we chose the limiting (minimum) radius, 0 ( , ), and the total nanopore length, ( ). [14] The presence of a defect disrupts the usual cylindrical symmetry. For a membrane with more than one nanopore, the nanopores are conductors in parallel (with identical surface chemistries and electrolyte contents) so that their conductances would be added directly, = ∑ . Using a single measurement of the conductance at a single time , it is not possible to distinguish between a single large pore and two smaller pores, or between a pore with or without a defect, when The size-and geometry-dependence of the conductance change in time, however, and then fit the data using candidate nanopore profiles. [16,18] The focus was whether including either defects or double pores would negatively affect the feasibility of the approach augured by the formalism. To allow this emphasis, the effect of measurement noise on the conductance was neglected. The change in nanopore radius in time, = mt , occupies a privileged role as the material transfer rate (with opposite signs for etching and deposition). We used a constant | mt | = 0.6 nm/h to highlight the nonlinear dependence of conductance on geometry in Equations 1, 3, and 4, and in keeping with the linear etch rates common to micromachining, but the method does not depend on that particular magnitude or time-dependence. [14,41] We chose four nanopore profiles finding widespread use: cylindrical, double-conical, conical-cylindrical, and hyperbolic (Figure S4.1), but the method does not hinge on these particular choices. [13,16,18,37,42] The label 0 is used here to denote the radius of the cylindrical pores, and the minimum radius (at any given time) of the pores with radii varying with ; "pinch" and "outline" labels will be introduced for the 0 of cylindrical nanopores with defects. All profiles were conventionally restricted to two free parameters, each, ( 0 and ) with the outer radius of the three tapered profiles fixed to be 10 nm greater than their corresponding 0 , and the initial length of the inner cylinder of the conical-cylindrical pore restricted to 0.6 times its overall length, ( 0 ), where 0 is the starting time. To model the double pore case, the two pores were set to be identical. Parameter values and calculations were consistent with previous work: [14][15][16]22] 1 M potassium chloride electrolyte solution in water, K=14.95 S·m -1 , pH 7.0, and silicon nitride surface pKa=7.9, with calculated in the usual way. [16,22] The influence of solution pH is outlined in Figure S4.3 and the discussion immediately preceding it. For the defect-free pores, surface-deposited films were treated in a piecewise curved manner to maintain a uniform surface coating thickness (Figure S4.1) across the entire nanopore surface. [14] For the case of the pores with defects (Figure 4.1a) the half-cylinder protrusions running along the full length of the pore interior were centered on the pore outline, opposite each other. Simulations of ( ) were performed using 0.01 nm step sizes in the nanopore radius (or 1 minute increments given mt ), and fits to 0 ( 0 ) versus t were plotted using 0.05 nm increments.

RESULTS AND DISCUSSION
Post-fabrication comparisons of electron microscopic and steady-state conductance measurements support the independent use of Equation 1 for nanopore characterization. [13,16,18,20,21,24] Conductance measurements recorded during a fabrication process such as dielectric breakdown, however, occur in a different context than post-fabrication measurements. [38,43] In  [43] measured and mean without biasing the fit with an explicit choice of nanopore shape, we modified the cylindrical model of Equation S1 by replacing bulk with bulk , and surface with surface . We optimized the parameters and using the fit to the experimental data (with known 0 , , and ) in  (Figure 4.2c). The experimental ( ) of Yanagi et al. [43] was fit best, using Equation 1, by a conical-cylindrical model with overall length equal to the nominal membrane thickness. The cylindrical model using Equation S1 and with an effective length equal to a fraction of the nominal membrane thickness [43] did not fit as well as the conical-cylindrical model, but outperformed the remaining candidates. Overall, Equations 1 and S1 produce reasonable nanopore sizes when applied to conductance data recorded during nanopore fabrication. As discussed in earlier work [14], a timedependent material-transfer rate, mt ( ), is no impediment to the time-dependent conductance profiling framework. [14] As the first application of Equation 1 to more complex nanopore configurations, we investigated the effect of defects on our ability to extract reasonable geometric descriptions of nanopore sizes. With larger initial defect size, the initial radius of the cylindrical outline of the nanopore (the "outline radius", 0 outline ( 0 )) must also be larger to compensate for the internal volume lost for ionic transport.
Defects distort the circular symmetry of the nanopore and introduce "pinch points" (as illustrated in Figure 4  ~4.1 and ~5.9 nm, respectively, dictated by the conductance and radii). We attempted to fit these data by using the (known) material transfer rate and varying the dimensions of three candidate nanopore profiles: a defect-free cylindrical nanopore, and profiles with 0.1 and 1.0 nm-radii defects. The question was whether fitting to the case sim ( ) would reveal the existence and size of defects. A step-by-step tutorial for this process is provided in earlier work, [14] which we abbreviate here to allow a suitable focus on fabrication irregularities. The initial conductance, case sim ( 0 ), was used to determine the (infinite) set of {( 0,candidate ( 0 ), candidate ( 0 ))} for which candidate ( 0 ) = case sim ( 0 ).
After the dimension changes from depositing material at the known rate (outline and pinch radii diminish at mt , whereas the cylinder length increases at 2 mt ), only one pairing ( 0,candidate ( 0 ), candidate ( 0 )) for each candidate also satisfied candidate ( 1 ) = case sim ( 1 ). This answer gave the unique initial nanopore size for each candidate with its specified defect size, but could not be used to identify the simulated defect size. That is, all three candidate profiles could exactly reproduce the two simulated conductances.
After propagating the deposition one more time from the three different ( 0,candidate ( 0 ), candidate ( 0 )), only one pair of initial nanopore dimensions gave When the candidate profile is incorrect, then the plotted data is no longer horizontal.
Thus, in Figure 4.3a, when the simulated data is generated using a cylindrical pore with a 0.1 nm-radius defect, only the fit data using the 0.1 nm-defect candidate pore is perfectly horizontal. The defect-free nanopore fit data is close to horizontal and overlaps substantially with the outline radius of the simulated pore, but the 1 nm-defect fit data has a larger nonzero slope and is therefore the incorrect candidate. While 0 outline ( 0 ) of the 1 nm-defect candidate was not substantially larger than the true 0 outline ( 0 ), its small 0 pinch ( ) would suggest an incorrect threshold for analyte size-exclusion. Figure 4.3b

77
shows that a 1 nm-defect simulated pore is successfully fit only with a 1 nm-defect candidate pore, and that radii for the remaining two candidates lie between limits set by the pore with the larger defect. In both fitting examples, the slopes of the fit data provide an indication of the correct defect magnitude, being positive when the candidate defect is too large, and negative when the candidate defect is too small. One might thus imagine a strategy in which a wider range of candidate defect sizes were used to more readily We extended this exploration of the effect of defects by considering the effect of candidate nanopore shape on the conductance-based geometry optimization. A second complication for nanopore formation is the formation of more than one pore when only one is intended. Microscopy can be used to directly enumerate the pore number, but at the cost of instrumentation and user burdens, and possible nanopore surface contamination, among other drawbacks. We wanted to determine if conductance could provide any insight into this possible problem of multipore formation. We explored the case of double pores of matching size and shape. Figure S4.4 illustrates that the conductance change in time provides the prospect of differentiating between single and double pore systems, just as it did for single pores of different shapes. [14] To explore whether the conductance time trace could reliably determine the size and number of the pores during their fabrication, we simulated conductances for single and double pore configurations of the four profiles in Figure S4

CONCLUDING REMARKS
The performance of a nanopore used for applications such as single-molecule sensing, separations, and manipulations is dictated in large part by its size, shape, and surface chemistry. These three parameter groupings underpin the nanopore conductance and allow a suitable analysis framework to use straightforward measurements of the conductance as a means to gain insight into these nanopore properties. Nanopore conductance is routinely used to coarsely gauge nanopore size during use, typically with at least the assumption of a cylindrical shape, and then often with deliberately incorrect parameter constraints to ensure that reasonable numerical estimates of the radius are       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 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.    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 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, lowamplitude 102.5eV Si2p peak that appeared after Scheme 5.1 tin-sensitization 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 5.1 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
Thin, silicon-rich silicon nitride films prepared by low pressure chemical vapor deposition (LPCVD SiNx) are a prevalent element of micro-and nanofabricated devices and they can be used to confer mechanical and chemical robustness, diffusion inhibition, and dielectric strength. [1][2][3] Devices and applications exploiting these beneficial native features can be augmented and improved using designer metal overlayers that fulfill structural roles, serve as electrodes, and provide alternative surface chemistry options, including as a platform for subsequent thiol monolayer self-assembly. The field of nanopore single-molecule sensing offers compelling examples of the prospects of merging SiNx thin films and designer metal layers into devices, and does this within a nanofluidic context where the need for versatile metallizing approaches is clear. [3][4][5][6][7] The most common solid-state nanopores are <100 nm-diameter nanofluidic channels formed through <100 nm-thick, free-standing SiNx films, and nanopore-integrated metal films can enhance sensing capabilities by serving as optical elements such as light shields and plasmonic films, as electrodes for tunneling and other molecular control and sensing functions, and as a means to tune nanopore size and surface chemistry. [3][4][5][6][7][8] The nanoscale dimensions of the SiNx film and pore can be significant barriers to efforts to incorporate such functional metal films, particularly when the interior of the pore must be metallized. Solution-based metallization routes offer an appealing route with natural compatibility with nanofluidic devices. Surface capture of nanoparticles-by specific and nonspecific attachment mechanisms-is a possible solution-based route to surface metallization. [9][10][11][12] Electroless plating is a compelling alternative: a solution-based process useful for metallizing a wide variety of materials, including nonconductive and irregularly shaped materials. 7, 13-14 Solution access, rather than line-of-sight as in physical vapor deposition, dictates where surface plating will occur, so that electroless plating is an appealing choice for fashioning nanofluidic devices where even irregular and concealed surfaces may require metallization. To fully exploit solution-based metallization as a tool for micro-and nanofabrication, however, requires control not just over the plated film composition, thickness, and grain size, but also over its spatial disposition, which must be at least partly independent of underlying substrate patterning. 15 We wanted a patterning approach that did not need mechanical access to target surfaces, both to improve the generality of the approach, and to minimize the risk of damage that can accompany repeated handling of thin films-especially of freestanding thin-films. We sought to develop a gentle, solution-based patterned metallization approach 16-17 capable of plating a range of even structured substrates, including inside existing (nano)fluidic channels. 3,7,[14][15]18 The horizons of singlemolecule science have recently been dramatically expanded by the development of simple methods for fabricating nanopores: entirely solution-based processes requiring only uncomplicated instrumentation are removing barriers to the widespread use of nanopore methods. 19 To conserve the benefits of simple pore formation methods, our focus also included developing similarly widely-accessible, straightfoward solutionbased approaches to patterned metallization. We therefore wanted to avoid the instrumentation and processing overhead associated with traditional photoresist-based approaches and more exotic analogues and alternatives. 11, 20-23 Instead, we chose to photo-pattern the covalent attachment of an organic monolayer to SiNx, 24 and to investigate its ability to then template the substrate metallization. By only attaching the protective layer where it was desired, rather than removing portions of a patterned photoresist film, for example, we sought to simplify the processing compared to conventional approaches. With the use of an initially liquid patterning precursor (here, 1-octene), we sought to gain greater tolerance to irregularities-including the presence of engineered structures such as nanofluidic channels-of the SiNx surface. For metallization, we initially adopted an electroless plating approach that had been specifically developed for gold-plating SiNx. 7,25 The approach is outlined in Scheme 6.1, and full details of materials, instrumentation, and safety precautions are provided in the Supporting Information (SI).
We had previously developed a gold electroless plating approach for SiNx that required a hydrofluoric acid (HF) etching step prior to surface metallization 7,25 . The HF etching step offered a natural point to incorporate patterned monolayer formation in an effort to guide the spatial extent of the substrate metallization. An alkane monolayer could be covalently linked to HF-etched SiNx through the photochemically-driven hydrosilylation of a 1-alkene. 24 Tremendous care must be exercised in the use of HF, and we detail the precautions-including additional protective equipment and monitored work-in the SI. The UV (254 nm) photoirradiation was through copper transmission electron microscopy (TEM) grid masks, with different bar sizes and spacings (see SI for specifications), that had been placed directly on the wafer (without securing them or preventing liquid access underneath), with both wafer and mask then immersed in the 1-alkene. Plating selectivity depended on rigid adherence to the rinsing steps detailed in the SI, and, as in prior work, we ensured compatibility of the process with free-standing ultrathin SiNx membranes by avoiding ultrasonic cleaning steps. 20 We proposed to spatially pattern LPCVD SiNx metallization by forming a physical barrier on the surface to control where the metal plating could take place. The first step of patterned plating thus involved the formation of this patterned protective layer. In our prior work to develop an electroless gold plating procedure for SiNx, we found it was essential to first etch the SiNx surface with dilute HF. 7 This same initial etching step forms the starting point for the covalent attachment of 1-alkenes (or 1-alkynes) by photochemical (or thermal) hydrosilylation on silicon-rich SiNx 2, 24 to form alkane monolayers that could potentially function as a barriers for electroless plating. Photoirradiation using a UV lamp (254 nm) proved convenient in transferring the spatial patterning offered by a selection of copper transmission electron microscopy (TEM) grids (Figure 6.1a) to the SiNx surface. Figure 6.1b is a photograph of a representative substrate after patterned irradiation through a thin (<2 mm) layer of neat 1-octene held under a quartz plate in a specially constructed holder. This optical micrograph taken during the evaporation of a dichloromethane drop placed on the surface reveals the transfer of the TEM grid pattern to the surface-functionalized substrate. Such patterned substrates were then electrolessly gold-plated, using the threesolution-Sn (II)/Ag (I)/Au (I)-process beginning with Sn (II) sensitization that had been proven successful for HF-etched SiNx (see SI for complete details of metallization solutions and process flow). 7,25 While gold replicas of the TEM grid masks can be seen in Figure 6.1c, it is also apparent that the plating spatial selectivity was quite poor compared to its Pd (II)-initiated counterpart, Pd (II)/Ag (I)/Au (I) (vide infra, and calculation details in SI). Substrate tolerance of electroless plating, via substrate tolerance of the Sn (II) sensitization step, is one of the benefits of electroless plating: 13,23 it is clearly-in this instance, at least-detrimental to patterned metallization. Figure   6.1d provides a magnified view, by field emission scanning electron microscopy (FE-SEM), of a Sn (II)/Ag (I)/Au (I)-metallized substrate. We did not explore using ultrasonic cleaning steps to improve the plating selectivity, 20, 26 because we wanted to remain compatible with plating free-standing SiNx films that are a compelling structural element, especially for nanofluidic devices. 3-7 We abandoned Sn (II)-sensitized electroless plating when efforts to improve the spatial selectivity by using different rinsing steps, for example, proved ineffective. We tested, instead, a palladium-based treatment 27  We focus in this work on characterizing the spatial selectivity and the physical structure of the gold layers resulting from this successful initial Pd (II) surface treatment. We present analyses of gold replicas produced after ~30 minute immersions in the Au (I) bath. This duration provides a balanced perspective of film nascence and degree of spatial selectivity. Examination of gold replicas using digital holographic microscopy (DHM; Figure 6.1g) allowed us to determine that the gold films were ~23±1.5 nm thick. Higher magnification scanning electron micrographs in Figure 6  To explore the spatial patterning in further detail, we focus on gold replicas of 100 mesh copper grids. The copper bars of these grid masks were 54.4±1.3 m wide (measured by FE-SEM with analysis details in the SI), and they were placed on the SiNx surfaces under 1-octene without securing them or attempting to prevent liquid access underneath. The spatial selectivity, defined in a classical signal-to-noise sense (details in the SI), was ~10.1 for the 1-octene-patterned Pd (II)/Ag (I)/Au (I) route that we focus on here, in contrast to ~2.7 for the 1-octene-patterned, Sn (II)-sensitized route, and ~3.2 for the former solution steps with air-patterning in place of 1-octene. In addition to FE-SEM micrographs, we collected elemental maps from representative gold replicas using energy-dispersive x-ray spectroscopy (EDS; also commonly abbreviated EDX). The maps and electron micrographs in Figure 6

INTRODUCTION
Surface-enhanced Raman spectroscopy (SERS) is a tool at the forefront of chemical analysis for analytes ranging from single molecules to bacterial cells. [1][2][3][4][5] Raman enhancement is engineered by tuning SERS substrate design parameters such as elemental composition; the size and shape of nanoscale elements; close-range interparticle spacing responsible for hot spots; and patterning of solid substrates that can include ordered and random hierarchies across short, long, and multiple length scales. 1, 3, 6-10 Physical structure of the SERS-active metal layer-either its inherent structure or the structure imposed upon it by an underlying support layer-is a critical and performance-determining factor. Considerable effort has been devoted to crafting a host of solid-supported SERS substrates, with results that inspire further efforts to improve and expand fabrication options, sensing capabilities, and sensing performance. 1,3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] Top-down nanofabrication using conventional and unorthodox approaches can produce exquisitely structured substrates, but can require substantial practitioner expertise along with expensive, specialized, and complicated instrumentation, and can moreover substantially limit the palette of fabrication materials. SERS substrates developed outside the material and processing constraints of conventional micro-and nanofabrication have been compelling. Both approaches and material sets hold promise.
We sought, therefore, to develop a general route for nanofabricating SERS substrates that would bridge both paradigms-to draw on the strengths of each, and to be useful for both. Conventional micro-and nanofabrication approaches offer well-established, highly optimized, large-scale manufacturing capabilities for reproducibly fabricating nanoscale structures. A less conventional fabrication material such as paper offers a myriad of advantages that have driven its adoption as a material of choice for low-cost diagnostics for use in resource-limited settings. 23,[27][28] The genesis for the present work was the discovery that gold films we had electrolessly plated onto silicon nitride as part of a nanofabrication effort were also capable, easily and without optimization, of generating reproducible SER spectra. 29 We wanted to take a variety of interesting and functional support materials and structures, and determine if a simple electroless plating process could make them SERS-active-thereby augmenting their core functions by creating multifunctional SERS substrates. This goal of multifunction does not exclude the conventional quest for maximum signal enhancement, but does require that SERS substrate evaluation be application-context dependent. Paper, for example, can support a SERS-active metal component, offers obvious advantages such as low-cost and ubiquity, and has a pore structure that could improve sensing selectivity through separations by chromatography or by physical filtering. 18-21, 23-26, 28, 30-42 Electroless plating is a robust technique for surface metallization, wellestablished in commercial manufacturing applications for forming decorative, electrical, and optical elements, and with excellent substrate tolerance. 17,24,29,33,41,[43][44][45][46][47][48][49][50][51][52] Objects are immersed in liquid baths, with solution access and homogeneity dictating the uniformity of the plating: rough and large-area surfaces can be coated without the geometric-including line-of-sight-constraints of physical vapor deposition.
Equipment overhead is minimal, the surface being plated need not be conductiveallowing for support material tolerance-and the plating occurs without the need for external electrical power. Electroless plating is inherently different than the capture, by nonspecific or specific attachment protocols, of pre-formed, frequently ligand-coated solution-phase nanoparticles onto a surface: 11-12, 15-16, 18, 30-32, 36-38, 40 the electrolessly plated metal film structure, properties, and composition can be controlled through surface pretreatment, plating bath formulation, and process conditions, and can occur on a timescale that can be measured in minutes. Vitally important for our pursuit of a library of multifunctional SERS substrates, electroless plating is, in principle, compatible with coating sophisticated top-down nanofabricated, and low-cost bottomup assembled structures and surfaces.
The term "electroless deposition" is used to describe a number of different plating mechanisms, including autocatalytic, substrate-catalyzed, and galvanicdisplacement processes. 50 We adopted a single electroless plating process that had been optimized for coating nonconductive porous plastic membranes. 49 In brief, a Sn (II) solution is used to sensitize the surface which, when treated with an ammoniacal silver nitrate solution, undergoes a redox reaction to produce a nanoscopic metallic silver layer. Gold plating is then accomplished by immersing this surface in a Au (I)containing plating bath: the aurous ions galvanically displace silver, giving gold particles that catalyze the reduction of aurous ions by formaldehyde also present in the bath. Tin-based sensitizers provide fairly indiscriminate surface sensitization, which is beneficial since tolerance to surface composition is a desired goal of our SERS substrate fabrication explorations. There is also much flexibility in plating chemistry after sensitization, allowing full access to the metals typically used for SERS. While silver coatings can be produced through electroless plating, the chemical stability of gold motivates our testing of gold-coated substrates for SERS activity. The use of a conventional electroless plating protocol, with only minor material-specific modifications in washing steps, allowed us to focus on support material composition and physical structure-and thereby, function-in our exploration of whether electroless plating could be a general tool for incorporating SERS sensing capabilities into already functional and structured materials and platforms.
We selected a range of support structures and material compositions to explore the generality of using electroless plating to form a library of SERS substrates. Siliconrich LPCVD silicon nitride (SiNx) films on silicon were chosen for their ability to support a variety of nanofabricated structures and roles. [53][54][55] Polished SiNx films ensured the nanoscale gold grain structure would be the dominant substrate structural feature. Silicon nitride films with nanoscale through-channels introduced key structural features (the individual nanochannels and the nanochannel array) underpinning designer filters and multifunctional chemical analysis platforms using plasmonic nanopores. [56][57] Surface-grafting of an acrylate-based polymer generated a more subtle structural modification of the planar SiNx thin film, and was intended to increase the number of possible sensitizer interaction sites on the film. Our next selection was standard filter paper, a frequent actor in paper-based low-cost diagnostics. 23,27 We explored the effect of fiber dimensions and spacing, by electrolessly plating and attempting to record SER spectra from standard filter paper and nanocellulose fiber paper-the fourth and fifth choices of material and structure. We characterized a commercial substrate (Silmeco) based on a gold-coated nanopillar array architecture 9 and etched away its gold coating to expose the sixth surface for examining electroless plating for SERS: a nanopillar array. Given the vastly different SERS substrate configurations, and the often severe approximations necessary to calculate enhancement factors, 46 we used a comparison framework designed to compare SERS performance across disparate substrates. The method yields a SERS enhancement value (SEV), which is defined as the ratio of the analyte concentrations that produce the same instrument response by normal Raman and SER measurements. 58 While spectral acquisition was formalized to allow comparisons between substrates, it nevertheless cannot account for the performance benefits of matching substrate function to a particular application.

EXPERIMENTAL
A detailed listing of materials and exposition of methods is provided in the Supporting Information. All substrates were electrolessly gold-plated by sequential immersion in the same series of tin (II) chloride-, ammoniacal silver nitrate-, and sodium gold sulfite-containing solutions (Scheme S7.1), with appropriate rinsing steps in between immersions. The solutions were prepared as previously reported. 29,59 Immediately prior to direct plating of bare silicon or silicon nitride surfaces, they were oxygen-plasma-treated and then etched with dilute hydrofluoric acid. The severe chemical hazards presented by hydrofluoric acid require special precautions such as those detailed in the Supporting Information. A subset of cleaned and etched planar silicon nitride supports was polymer-coated by formation of a covalently-linked sodium polyacrylate film before electroless plating, and once polymer-coated, was treated neither with plasma nor hydrofluoric acid. Silmeco gold-coated nanopillar SERS substrates were used, as-supplied, for comparison measurements. These silicon nanopillar substrates were also immersed in iodide-based gold etchant and then, after plasma treatment and HF etching, electrolessly gold-plated. Whatman 1 filter paper was plated without modification. Nanocellulose fibers were formed between two glass slides into a crude paper-like mat ~1 mm thick (referred to as "nanocellulose paper") before plating. Surface characterization of the plated metal films was performed by field emission scanning electron microscopy (FE-SEM), x-ray photoelectron spectroscopy (XPS), and surface enhanced Raman spectroscopy (SERS).
SER spectra were acquired at an excitation wavelength of 785 nm, with a ~100 µm diameter (full-width-half-maximum) beam, and at an excitation power of ∽57 mW for cellulose and as-provided Silmeco, and ∽250 mW for all other substrates.
Standard solutions of 4-nitrobenzenethiol (NBT) in ethanol were prepared, covering a concentration range from 5×10 -9 to 1×10 -4 M. All measurements (save for replated Silmeco) were performed with the substrates immersed in the standard solutions.
Substrates were immersed in standard NBT solutions and SERS spectra were recorded every 2 minutes until saturation of the signal level. Following piecewise linear background subtraction (details provided in the SI), the data was analyzed according to a framework using receiver operating characteristic (ROC) curves and kinetic analysis to calculate the SEV. 58 Figure 7.1a shows photographs of the complete set of materials before and after electroless gold plating: we use the term "support" to denote a material prior to gold plating, and the term "substrate" to denote a gold-plated support. All supports were successfully gold-plated by the series of baths of Scheme S7.1, as confirmed by visual inspection and XPS analysis ( Figure S7.1). All plated substrates could be used to record SER spectra of 4-nitrobenzenethiol (NBT). The support composition, however, placed restrictions on the experimental parameters. Lower excitation power was required to avoid signal saturation using the as-supplied Silmeco substrates, and substrate damage using the cellulose-based substrates. The higher excitation power left a through-hole in the paper substrate, as shown in Figure 7.1b, and a hollow in the thicker nanocellulose substrate after 10 exposures (~60 s each) when both were irradiated when dry; fume evolution was observed when immersed in ethanol. No damage was apparent when unplated paper that had been soaked in NBT was irradiated, so that the damage mechanism is reasonably ascribed to photothermal transduction by the gold film. This susceptibility of paper to burning is a noted benefit of using paper diagnostics in resource-limited settings where safe disposal options for biocontaminated devices may be limited. 23 For the Silmeco and polymer substrates, even the measurement at the lowest concentration demonstrated a better than 90% probability of detection for a 10%

RESULTS AND DISCUSSION
probability of false alarm and due to this, we can report only a minimum SEV. 58 These results emerged from proof-of-principle experiments of the general utility of electroless plating for SERS substrate creation rather than from longer-term substrate-specific optimizations. They are thus useful, when paired with the demands of a particular application, for indicating where efforts to gain additional enhancement might be warranted. The polymer-grafted silicon nitride is of note not simply for providing the largest SEV of our electrolessly plated substrates, but as an example of the benefits of nanoscale tailoring of SERS substrates, and for serving as a bridge between substrates based on traditional, silicon-containing nanofabrication materials, and those based on larger organic polymer fibers. More broadly, the design of a SERS substrate type should balance, in an application-specific way, the SEV and any special capabilities, such as filtering, offered by a given substrate. For example, gold films electrolessly plated onto and into these membrane filters can be used to physically optimize filter performance by tuning pore dimensions; to chemically optimize filter performance by serving as a first step in surface functionalization; and to augment filter performance by adding SERS-sensing capabilities in addition to separation. 29,61 Ultrathin, nanofabricated membrane filters, such as nanoporous silicon and silicon nitride, offer significant advantages over conventional polymer ultrafiltration membranes. 54 organisms such as bacteria, or even to separate macromolecules. Sensitivity might be enhanced by optimizing pore dimensions and distributions to form a nanoplasmonic array, 56 but at the cost of filtration performance (and selectivity). 57 A different example of the need to balance SEV and other application demands is illustrated in Figure S7.4: electrolessly gold-coated paper was used for the SERS readout of a crude paper-based assay that performed physical filtration and chromatographic separation. This multifunction capability augments the spectral selectivity of SERS for greater ease of analysis of multicomponent samples, but by no means circumscribes the utility of SERS-active paper. Indeed, the development of paper-based diagnostics has been characterized by the incorporation-by a variety of approaches, sophisticated and simple-of ever-greater function into paper-based supports. 23,[27][28]42 One means to create useful multifunctional SERS substrates-or even highly    [56][57] and the nanoporous membrane was moreover free-standing between support bars (not shown) so that it was electrolessly gold-plated within the pores and on both sides of the membrane. We avoided any ultrasonic cleaning steps that might cause rupture of this thin porous membrane, and we were consistent in this purposeful omission across all substrates. The three substrates were composed of nanostructured gold films with low-and high-aspect ratio grains, but the preponderance and character of the high-aspect ratio structures differed dramatically between the substrate types. The polymer-grafted silicon nitride gold film bore the greatest number of integral highaspect ratio features, and with a unique grain structure characterized by the prevalence of larger, sharper, and more finely substructured gold flakes that projected from the surface. These flakes provide an increase in surface area for chemisorption of the NBT, and more significantly, are nanostructured on a length scale favorable for the existence of hot spots, and with an aspect ratio amenable to signal enhancement by the lightning rod effect. 4 The nanoporous substrate imposed gaps between gold grains, although on length scales optimized, in this substrate, for filtering rather than hot spot formation. 57 The loss of planar substrate area might be compensated for by plating sufficiently long pores, but the nanochannel surface is normal to the conventional substrate surface, and longer pores would affect through-pore flow rates. Overall, detrimental decreases in sensitivity from surface area losses to pores may be quickly outpaced by beneficial gains to analytical performance through the selectivity and throughput that emerges from careful tuning of the pore geometry to support rapid and tuned sample filtering.  layers. The pore, or void space, size distribution in paper can be controlled during its manufacture, and is an important metric when selecting commercial filter paper, for example. The hand-fabricated nanocellulose substrate was highly textured and convoluted, without the fiber bundling, alignment, and low packing density that produced obvious microscale voids in the paper substrate. The ability of electroless plating to coat rough, nonplanar surfaces-beyond what was seen in the plating of the curved pore walls orthogonal to the planar upper surface of the porous silicon nitride film-is dramatically illustrated by the impressive surface coverage. Thick, porous supports such as the nanocellulose paper have a large surface area for platingdistributed throughout their interior-and require a greater minimum plating solution volume than a planar support. Similarly, most of the plated gold surfaces will be able to bind analyte but will be optically inaccessible, and must be considered when aliquoting samples. Even after addressing these issues, the available signal strength using the cellulose-supported substrates was limited by the lower allowable excitation intensity.
The fiber-based construction of the cellulose substrates, however, is an intriguing structural design feature that can provide additional analytical capabilities such as swab sampling and chromatographic separation. 35,44,71 The cellulose substrates are evocative of other fiber-mat platforms used for SERS, [11][12][14][15][16][17][18][19][20][21][22] with paper supports being available at scale and at low cost using well-established manufacturing methods. When the ability to filter or chromatographically separate a sample using a SERS-active porous substrate is desired in addition to SERS sensing, one must consider the effect of the pore size on each capability-and on the interplay between each capability. Pore size is tunable through support fabrication or through the plating time-dependent thickness-within the limits of cost and available gold in the plating bath-of the plated gold layer. The flexibility, simplicity, and ease-of-handling of these nanofiber-based substrates stand in stark contrast to the more delicately engineered Silmeco nanopillar arrays, particularly for applications in resource-challenged settings. The superb Raman enhancement that the nanopillar substrates provided when used as-supplied, without modification, reinforces the utility of rationally patterning traditional micro-and nanofabrication materials to create SERS substrates. One must, however, be careful during handling and solution processing to prevent unwanted damage or modification of such high-aspect ratio features: 9 the gold-etched surface shows some broken nanopillars. SEM images in Figure 7.5 show that our general process chemistry was able to successfully electrolessly gold-plate a nanopillar array.

CONCLUSIONS
Electroless plating is a robust method for fashioning a variety of materials, exhibiting a range of structural features and capabilities, into SERS-active substrates.
The general electroless plating procedure we employed was able to successfully plate gold onto planar, porous, nanopillar, and fibrous surfaces; into well-defined nanochannels and variably-sized void volumes; onto traditional nanofabricationcompatible materials; and onto less conventional device platform materials such as paper that are important in the domain of low-cost diagnostics. All resulting substrates in our library were capable of generating SER spectra. This electroless plating approach produced nanostructured films where the size, shape, and position of the gold grains could be tuned by the particular material and form factor of the support material being plated, and this tuneability was evident from both microscopic imaging and SERS intensities. The underlying support structure for the gold plating did more than imprint structure on the gold film, though. Electroless plating of already functional structured supports created multifunctional SERS substrates. The force of the work presented here is thus both foundational and prospective: there is much promise in exploring electroless plating-including extensions such as patterned electroless plating 51, 55 -as a straightforward, robust, and low-overhead method to create custom SERS-active substrates that augment the compelling material properties, structures, and capabilities of their supports. Multifunctional SERS substrates require a rich, and applicationspecific, context and framework for design and performance evaluation. The substrate must, of course, generate a useful Raman spectrum, but the particular implementationfrom design and fabrication to end-use-dictates the balance between Raman enhancement and other capabilities such as integral sample processing. This balance dictates how to tune the electroless plating process chemistry, and the support structure, to optimize the SERS substrate. We believe that electroless plating has great potential in the creation of multifunctional SERS substrates useful for answering a host of design and sensing challenges.
ASSOCIATED CONTENT

SUPPORTING INFORMATION
The following files are available free of charge. clinical consequences in the United States, including ~100 deaths-underscoring the need for more sensitive sensing methods for contaminant flagging. [14][15][16][17][18][19] Glycan samples can be challenged by heterogeneity and low abundance in addition to chemical and structural diversity, so while new analysis tools have been broadly called for, 12,13,20 single-molecule-sensitive methods are a particularly compelling goal for glycomicsmore so given the absence of sample amplification techniques analogous to PCR for DNA sequencing 21 .
Nanopore single-molecule methods have emerged as a powerful tool for characterizing DNA and proteins including aspects of sequence, structure, and interactions. [22][23][24][25][26][27][28] Monomer-resolved length determinations of more prosaic polyethylene glycol samples further buttress the potential of suitably configured nanopore assays for the analysis of polymers with biological utility. 29 The simplest implementation for nanopore measurements places the nanopore-a <100 nm-long nanofluidic channel through an insulating membrane-between two electrolyte solutions (Figure 8.1). Ion passage through the nanopore in response to a voltage applied across the pore gives the baseline "open pore" current, ; passage of a molecule into, across, or through the nanopore disrupts this ion flow to give a blocked-pore current, .
A discernible current perturbation reveals the presence of an analyte, and the sign, magnitude, and temporal structure of depend strongly on size and shape of the analyte-and of the nanopore-and on the applied voltage and bulk and interfacial charge distributions. It thus provides insight into analyte presence, identity, and properties, including interactions between the analyte and pore interior or surface. [29][30][31][32] Analysis of the resistive-pulse characteristics of a sample offers the potential to glean molecular-level insights, but the characteristics can also be used more simply as benchmarks in quality assurance assays where atypical signal sample impurities.
Much groundwork must be laid, including proof-of-principle experiments, if nanopore methods are to emerge as a tool for glycan profiling-and by extension as a tool for -omics writ-large (spanning genomics, proteomics, and glycomics). Protein nanopores, polymer, and glass-supported nanopores have been used to detect sugar-pore binding, polysaccharides, and enzyme-digested oligosaccharides. [33][34][35][36][37][38][39][40][41][42] While solid-state nanopores in thin (~10 nm) membranes have been often portrayed as the preeminent nanopore platform, their use to profile classes of molecules beyond DNA and proteins is in its infancy. These nanopores can be size-tuned 43 to match analyte dimensions (especially relevant for branched polysaccharides), and when fabricated from conventional nanofabrication materials such as silicon nitride (SiNx), 44, 45 offer resistance to chemical and mechanical insult alongside low barriers to large-scale manufacturing and device integration. The potential for integration of additional instrumentation components, such as control and readout electrodes, around the thinfilm nanopore core, is especially compelling. 28,44,45 Recent (nanopore-free) work on recognition electron tunneling measurements on polysaccharides, for example, has reaffirmed the importance of a nanopore development path that values augmented nanopore sensing capabilities. 46 A key question concerning the use of SiNx nanopores for polysaccharide sensing is whether this fabrication material is compatible with sensing glycans. The often challenging surface chemistry of SiNx (giving rise to a complex surface charge distribution) 44, 45, 47 may lead to analyte-pore interactions that hinder or prevent its use.
Variability in polysaccharide electrokinetic mobility arising from differences in molecular structures may exacerbate the effect of these interactions. These issues become particularly important when analyte translocation through a constricted pore is required, such as in transverse electron tunneling measurements. 28,46 The aims of the present work were threefold: (1) to introduce and test the feasibility of SiNx nanopores for sensing polysaccharides; (2) to explore the preliminary performance of this class of nanopores in this implementation; and (3) to gauge the prospects of a clinically relevant assay to detect a toxic impurity in the anticoagulant heparin. The broader implications of the successful use of SiNx-a readily nanofabrication-compatible material-to form the nanopores would be to conceivably smooth the path to large-scale production and to provide a platform amenable to modification for nanopore sensing configurations beyond resistive pulse sensing. We chose a set of polysaccharides with varied compositions to both gauge performance and challenge the SiNx nanopores. Naturally occurring sodium alginate, with applications in biomedical and food industries, presents an overall negative, but unexceptional, formal charge in neutral pH aqueous solutions. We used samples from two different suppliers-A1 (Alfa Aesar; ~74 kDa based on viscosity measurements) and A2 (FMC

Corporation;
~18 kDa based on viscosity measurements)-to explore the sourcing variability for a sample extracted from seaweed. 48 This variability can be as prosaic as molecular weight to more enticing changes in the relative abundances of alginate's constituent mannuronate (M) and guluronate (G) residues. 48 In contrast to alginate, heparin, the prevalent anticoagulant drug, is the most highly negative charge-dense biological molecule known. 49 This exceptional charge density couples with the demonstrated difficulty, by other methods, of detecting the negatively charged oversulfated chondroitin sulfate (OSCS; contaminant molecular weight ~17 kDa 50 ) in a heparin sample [14][15][16][17] to make the analysis of heparin (~16 kDa) and OSCS by nanopore a compelling experimental test with clinical relevance. ("cis-" side, according to nanopore convention) unless otherwise noted, and applied voltages were referenced to the ground electrode ("trans-" side) on the other side. The mechanism of A1-induced signal generation was investigated in a series of experiments. Using a setup ( Supplementary Figure 8.2) that physically separated electrodes and nanopore, events were only detected when A1 was injected into the well proximal to the nanopore, thus supporting a signal generation mechanism involving interaction with the nanopore and not with the electrodes. This result did not, however, distinguish between passage-free collision with the nanopore opening ("bumping" or "blocking") or translocation through the pore. 32 Either mechanism (including extending the idea of "bumping" or "blocking" to allow for transient interactions of the analyte with the pore mouth), though, has the potential to deliver analytically useful sensing performance.

Introduction
Low analyte concentrations challenge the direct investigation of polysaccharide translocation through small, single nanopores. In one experiment to investigate this, a solution of A1 was added to the headstage side of a ~22 nm-diameter nanopore and was left overnight with a +200 mV applied voltage. The initially analyte-free contents of the ground-stage side were then transferred to the headstage side of a fresh ~17 nmdiameter pore, and an appreciable number of A1-characteristic events (182 in 1 h) were detected again at +200 mV. Acid digestion was used as a signal generation and amplification technique (complete details in the Supplementary Information) to convert A1 polymers to many smaller fragment-derived species absorbing at ~270 nm. 51  , so that the overall charge density of this molecule was expected to be higher than A1. Further analysis was consistent with alginate A1 having a ratio of guluoronic (G) to mannuronic (M) residues exceeding that of A2, with values from IR spectroscopy of ~63%G/37%M and ~57%G/43%M, respectively. 48 Nanopore profiling of A2 showed differences compared to A1. Using the same electrolyte for A2 as for A1, measurements generated a ~7-fold lower event frequency with longer durations for A2 compared to A1, despite the 75fold higher A2 concentrations required for reasonable measurement times. Enzymatic digestion of A2 produced events at a higher frequency than for undigested A2, but still at lower frequency than for A1. The events for the digested sample of A2 were ten-fold shorter-lived than for the A2 polymer, but not appreciably different in terms of blockage depth (Figure 8.3).   Polysaccharide translocation was independently confirmed and signals were generated only when the analytes had access to the nanopores, so these events either arose from analyte interactions with the pore mouth rather than from complete translocation, or the blockage magnitude analysis must include additional factors such as charge density carried by the analyte, itself, and mobile charge at the analyte-solution and solutionnanopore interfaces. 55,56 The effects of these and more complex interfacial phenomena emerged in one of the more startling observations in this work: that the voltage polarity for signal generation with both alginate samples was opposite to that expected for electrophoretic motion of an anionic polymer, whereas for heparin the voltage polarity was consistent with electrophoresis.
In addition, when comparing the two alginates, the more charge-rich A2 was detected at a lower event frequency than A1. Nanopore-based studies with polyethylene glycol polymers point to a change of effective analyte charge by sorption of electrolyte ions (K + for those studies) with the resultant analyte motion then being electrophoretic for the voltage polarity and the sign of the sorbed charge. 29 The results of Supplementary the direction of signal generation is still consistent with electroosmosis. The lower event frequency compared to A1 can be understood as arising from opposing electrophoretic and electroosmotic driving forces, but with the electrophoretic force on A2 being greater than on A1. More detailed exploration of the differences between A1 and A2 must also contend with their different molecular weights and their different chain flexibilities arising from their different M/G ratios. In the case of heparin, the charge density is sufficiently high so that events are detected using a voltage polarity that would drive the anionic polymer towards the nanopore.
The experimental investigations including and beyond the ones presented here, exploring the underpinnings of the nanopore-generated signal using (polysaccharide) biopolymers with greater chemical and structural complexity than the canonical nanopore test molecule, DNA, or than homopolymers such as polyethylene glycol, should also provide fertile ground for high-level simulations. Interfacial effects will require additional study in the context of polysaccharides, but hold possibilities for tuning sensing selectivity and sensitivity. Indeed, explicit consideration of sensing conditions-including nanopore size, electrolyte composition, and voltage polarityalready augments the ability to compare nanopore molecular fingerprints as shown in

METHOD OF CALCULATING VOLUME (A) AND SURFACE (B) INTEGRALS
Integrals were calculated using Mathematica 10  This conductance could be generated equally well by any appropriate combination of nanopore shape and geometric parameters, ( 0,shape ( 0 ), shape ( 0 )), plotted in Figure   188 3.2. The dotted lines in Panels a-d below show the range of possible 0 shape ( 0 ) for each shape given the 200 nS initial conductance.
Step 1 in construction of  Step 4 in construction of  Reprinted with permission from [1]. Copyright 2016 American Chemical Society.
Nanopore Access Resistance. Departures from the cylindrical profile, or from bulk-only access resistance formulations, can make arriving at closed-form solutions for the access resistance of a nanopore difficult or intractable. [2][3][4][5][6] A conventional formulation for the access resistance of a cylindrical nanopore, here with a surface conductance term included in parallel with the bulk conductance, gives = ( where the second fraction arises from a common formulation of the nanopore access resistance, 2 access ⁄ (where there is a 1 access ⁄ contribution from each open side of the nanopore). [2][3][4][5][6] More complex treatments exist that also include a surface term in the access resistance, and others have noted the difficulty of treating the access resistance of other nanopore shapes. [2,3] To investigate the effect of including the access resistance into the conductance modelling, we used equation (S1) to calculate the conductances of nanopores with selected aspect ratios, ( 0 )/ 0 ( 0 ), and then fit the results to the cylindrical conductance model of equations (1) and (S1), where access resistance is neglected in equation (1). Simulation results are shown in Figure S4.2.
Constructing a more general analytic formulation of 2 access , beyond that shown in equation (S1) for a cylindrical nanopore, remains challenging, especially if nanopore surface contributions are to be included. [2,6] Scaling arguments and earlier work, [2] however, offer a possible approach in which setting access = 0 is followed by numerical calculations of , a parameter dependent on nanopore shape. The dependence of nanopore conductance show in Equation (1)  Thus, without change of either nanopore dimension or solution conductivity, a change of solution pH can change the nanopore conductance-especially at lower solution conductivities. [7,8] This behavior is shown in Figure S4.3, and can be expressed by rewriting Equation (1) as where the parameter (pH) is used to explicitly carry the pH-dependence of the nanopore conductance (calculated relative to a particular chosen reference pH). In this form, with | (pH ref )| and (pH) constant in time for a given fixed solution composition as for Equation (1), the consequence of solution pH is simply a reweighting of the surface contribution to the conductance, relative to the behavior at the reference pH. Figure S4.3 shows the time-dependence of the conductance of the nanopore conductance at several pH values, and their successful use to correctly recover the nanopore size.   Figure S4.4b shows that, as established for single pores, [1] the conductance change in time provides the prospect of differentiating between single and double pore systems. As an example of the complexity introduced by more than one nanopore, the double pore conductance of the cylindrical pore here lies close to the single pore conductance of the hyperbolic profile.
Such time traces thus reveal insights into the type and number of pores, but also suggest practical challenges.  preferably be deactivated by precipitation by the addition of dilute hydrochloric acid or sodium chloride prior to disposal 6 .

PREPARATION OF SODIUM GOLD SULFITE 4, 7
The synthesis of the gold plating solution was in accordance with the Abys et al. Line profiles at several points across the step edge were analyzed, using the planar silicon nitride surface as a reference for quadratic background subtractions. For each background-subtracted profile, the means of the coated and uncoated sides were calculated (omitting large particle outliers from the statistics), and averaged for each chip over several profiles. These mean step heights were then averaged over each deposition time and temperature point, propagating the standard deviation as an uncertainty to yield the final reported step heights (Figure 5.1).
Gold film morphology was examined 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). Custom code was written in Mathematica 9 (Wolfram Research, Champaign, IL) to yield gold film grain size estimates via watershed analysis. X-ray photoelectron spectroscopy was used for the majority of the elemental analysis. XPS spectra were acquired using a PHI 5500 system (Physical Electronics, Inc., Chanhassen, MN) using unmonochromatized Al Kα radiation (1486.6 eV) and an aperture size of 600 × 600μm 2 . Survey scans were performed with 0.8eV step sizes and 20ms per step, with a pass energy of 187.85eV and 10 scans per spectrum.
High resolution spectra were recorded with 50 scans per spectrum, 0.1eV step sizes, 40ms per step and a pass energy of 23.50eV. Spectra were analyzed initially with 205 Multipak 6.1 (Physical Electronics). All curve fitting was performed using XPSPeak 4.1 8 using linear baselines and the minimum meaningful number of fixed 90% Gaussian-10% Lorentzian peak profiles per peak, with all other peak parameters free.
To compensate for substrate charging, we aligned the N1s peak from silicon nitride substrates to 398.00eV, and the lower binding energy Si2p peak from silicon substrates to 99.25eV 9 , shifting spectra by up to 0.49eV. The particular choice of reference precludes analysis based on the binding energy, alone, of that component of the XPS spectrum. We chose these peaks, rather than the commonly used C1s peak 10 , because they had better signal-to-noise ratios; the peak fitting reliability would be less frequently compromised by the presence of multiple contributing features; and the C1s binding energy, itself, has been shown to be variable, notably in response to the particular surface treatment of silicon 9,11 . To gain a measure of the binding energy uncertainties useful for guiding the interpretation of binding energy shifts, and of the consistency of the reference alignment, we fit the main, shifted, C1s peak centers, yielding a range of values between 284.61 and 285.49eV that arises from a combination of the shortcomings of multicomponent peak fitting and any real shifts in binding energy. As an additional check on the silicon nitride alignment, we also aligned the spectra using Spectra were collected at three random locations for each substrate and averaged together after correcting to a zero baseline at ~494cm -1 .  UVP, LLC, Upland, CA, USA). The chips were rinsed with dichloromethane, allowed to dry, rinsed by isopropanol, and then processed in the metal-ion-containing solutions.

AG (I) / AU (I)
The patterned SiNx chips were immersed in 1 M hydrochloric acid for 5 minutes, washed with isopropanol, and then immersed for 5 minutes in 2 mL of ammoniacal silver nitrate solution followed by one rinse with methanol and three rinses with water.
The chips were then submerged in the Au (I) bath as described in the two previous sections.

GRID RECOGNITION
To distinguish between grid and grid-free zones of an FE-SEM or DHM contour image, each image was first filtered using a median filter with an appropriate pixel value threshold (usually 5), followed by image binarization (with automatic thresholding) and color-negation.

THICKNESS OF DEPOSITED GOLD
ImageJ 8 was used to extract raw gold film thickness data from a DHM image at 5× magnification, provided by Lyncée Tec, of a gold replica of a 100 mesh grid. The grid recognition algorithm was used to distinguish between grid and grid-free zones of a given contour plot. The mean film thickness with standard deviation (~23±1.5 nm) was calculated by averaging across 10 such grid images each with metal-plated grid lines containing at least 35,000 pixels.

WIDTH OF GOLD AND COPPER (TEM) GRID LINES
Regions of interest of grid-recognized FE-SEM micrographs were chosen so that the grid lines we analyzed were distant from the curved sections (from the as-supplied Cu mesh) at grid line intersections. At least 300 line profiles were sampled from each micrograph, and used to calculate a mean grid line width and standard deviation

SELECTIVITY
Pixel values corresponding to grid and grid-free regions of grid-recognized FE-SEM images were used to build histograms for each region. A single Gaussian fit was made to each of the histograms using the following equation, where 2 , , , and are the amplitude coefficient, mean, standard deviation, and pixel intensity, respectively. All parameters were left free during the fit to the histogram, using Mathematica's nonlinear-model-fit method with "Automatic" setting. The selectivity was then defined, in a classical signal-to-noise sense, as

ELECTROLESS PLATING
Electroless plating baths were prepared as previously reported 1 (note: a mass of 0.1500 g of barium hydroxide octahydrate was incorrectly reported previously 2 as 1.500 g). Material-specific preliminary processing steps preceding the electroless plating method are detailed below, before a more general discussion of the electroless plating steps outlined in Scheme S1. long gloves over extended-cuff nitrile gloves. We also used a "buddy system" so that one researcher supervised the other's work with HF. All labware, gloves, and working areas were thoroughly rinsed with water after use.

POLYMER-GRAFTED SILICON NITRIDE
A subset of purchased planar silicon nitride films (with films on silicon supports cut to 1 cm×1 cm) was polymer-grafted, as described briefly here, before electroless plating. The as-supplied silicon nitride-coated substrates were exposed first to 10 minutes of a nitrogen plasma, and then to 5 minutes of an oxygen plasma, using a Glow under argon for 10 minutes at 30°C, followed by filtering into a Schlenk flask containing four of the silicon nitride substrates that had been pretreated with allyl 2-bromo-2methylpropionate. The wafers were gently stirred (300 rpm) in this solution at 30°C, under argon, for 2 hours. 4 After this polymerization step, the substrates were alternately washed with water and ethanol at least three times, then dried under an argon stream.

SILICON NANOPILLAR ARRAY (GOLD-ETCHED SILMECO)
A number of the commercial gold-coated silicon nanopillar SERS substrates were immersed in gold etchant under vacuum (to remove any initial air layer and any generated bubbles preventing full etching solution access between the pillars) for 30 minutes and then washed with copious amounts of water. A gold coating was no longer visible, and while x-ray photoelectron spectroscopy (XPS) analysis showed low residual amounts of gold, there was no measurable SERS response from the gold-etched Silmeco substrates before they were electrolessly plated according to Scheme S1.

CELLULOSE
Whatman 1 filter paper substrates were used without modification.
Nanocellulose fibers were formed into a crude paper-like mat by filtering the assupplied slurry of nanocellulose in water with a polyethersulfone membrane with 0.1 μm pores. When most of the water had filtered through, the resulting paper-like mat (hereafter referred to as "nanocellulose paper") was compressed to ~1 mm thickness (thickness chosen for fabrication convenience) between two glass slides in a customdesigned, 3D printed holder and left to dry under vacuum in a desiccator for two days before plating.

SILICON-AND SILICON NITRIDE SURFACES
Prior to plating, the planar and nanoporous silicon nitride chips, and the goldetched silicon nanopillar array, were subjected to cleaning and etch steps. Nitrogen and oxygen plasma treatment were used to remove organic contaminants and hydrofluoric acid etching was used to remove surface oxide layers, as described above and also in 230 reference 1. Plasma-based surface pretreatments were not performed for the surfaces bearing organic moieties.

ELECTROLESS PLATING SCHEME
Scheme S1 illustrates the general electroless plating process which followed the previous material-specific surface preparation steps, and consisted of sequential plating bath immersions interleaved with rinsing steps. Electroless plating of planar and porous silicon nitride, polymer-grafted silicon nitride, and gold-etched Silmeco was carried out for 2 hours at ~3°C with gentle rocking of the plating baths. Whatman 1 filter paper substrates and nanocellulose paper were electrolessly plated at room temperature for 2 hours with gentle rocking using a BenchRocker 3D (Benchmark Scientific, Edison, NJ, USA), and then vacuum dried (~15 minutes) as the final step. Plating bath volumes were 2 mL, 2 mL, and 1.5 mL for tin-, silver-, and gold-containing solutions for all substrates except for nanocellulose paper for which the volumes were tripled. Solvent washes between metal ion baths were identical for all plated materials: after tin, rinsing and 5 minutes of soaking in methanol followed by drying; after silver, soaking in methanol for 5 minutes and in water for 5 minutes; and after gold, alternate rinses with methanol and then water at least three times.

231
Scheme S7. 1. Process flow for the electroless plating steps common to the plating of each support type.

SURFACE CHARACTERIZATION OF ELECTROLESSLY PLATED FILMS
Gold film morphology was examined using a Zeiss Sigma VP FE-SEM at an  substrates. The full-width-half-maximum excitation spot size was ~100 µm, measured at the substrate surface with the reader head placed at a slight stand-off of ~2.0 mm from the substrate. Each substrate was placed in a glass beaker and a spectrum was acquired at this point to ensure that the substrate was not contaminated. The substrate was then immersed in ethanol and spectra were collected every 2 minutes for about 20 minutes.
Once this ethanol-only blank experiment was done, the substrate was removed from solution and dried under nitrogen before being immersed in the standard NBT solution.
A spectrum was recorded every 2 minutes until equilibrium was reached, and then the rinsing, drying, immersion, and signal acquisition were repeated for all NBT standard solution from lowest to highest concentration. To provide (unenhanced) Raman spectra for the SEV analysis, 5 the same procedure was repeated using a gold-free silicon nitride substrate, using NBT concentrations in the range of 2 × 10 −4 M to 2.5 × 10 −3 M.

SPECTRAL ACQUISITION FOR DRIED SAMPLES
A 1.67×10 -5 M solution of NBT in acetonitrile was prepared and a 5 µL aliquot was pipetted onto the Silmeco substrate. The substrate was allowed to air-dry for about 5 minutes before spectral acquisition, and the Raman spectrometer read head was aligned with the center where the pipette tip had been for drop-casting. There was a slight ~1.2 mm stand-off between the SERS substrate and the pipette tip and read head to prevent mechanical damage to the SERS substrate (the nanopillar substrates were especially susceptible to scratches). Excitation power was 250 mW. This alignment of pipette tip and read head was repeated for the other drop-cast spectra in Figure S7.2a, and additional details specific to each substrate are provided in the figure caption.

SPECTRAL ANALYSIS
All spectra were analyzed by custom programs written in Mathematica 11.2 (Wolfram Research, Champaign, IL). Acquired spectra were background-subtracted using piecewise linear fitting between local minima that were selected using a relative thresholding approach to bracket known spectral peaks. To obtain the SEV for all substrates, the remainder of the analysis was performed according to Guicheteau et al. 5 For each spectrum we calculated the ratio of the area of the ~1330 cm -1 peak of NBT to the area of the ~880 cm -  Raman measurements, with solid lines to aid the eye. Spectra were acquired using 250 mW excitation, except as noted: for cellulose substrates and commercial substrate, excitation was limited to 57 mW. Limits of detection (LOD = 3 blank sensitivity ⁄ ) were estimated by fitting the first 3-4 data points of each response curve to a straight line.
The sensitivity was equated to the linear slope and the standard deviation of the blank, blank , was calculated from experimental measurements. The LOD, in matching order to the substrates, were 2.58×10 -10 , 2.7×10 -10 , 2.13×10 -10 , 1.08×10 -9 , 1.16×10 -8 and 3.62×10 -11 M, but these should be understood, along with the data below, as providing a benchmark for optimizing the application-specific substrate preparation.

GENERAL NANOPORE SENSING PROCEDURE
Nanopores in the ~10 nm-thick silicon nitride membranes were fabricated by controlled dielectric breakdown using 11-15.5 V DC applied potentials. 3 The nanopore formation was carried out in 1 M KCl electrolyte, HEPES-buffered to pH ~7, and the membranes and pores were secured in custom-machined PTFE holders with ~500 µL sample wells. Nanopore conductances, G, were the slope of the linear fit to the experimental Ohmic current-voltage data, measured in 1 M KCl electrolyte buffered with HEPES at pH ~7. The corresponding nominal nanopore diameters were calculated using a conductance model (including bulk, surface, and access resistance terms) and cylindrical nanopore shape suitable for this salt concentration and fabrication method, The respective molecular masses of the two alginate samples were determined by this method to be ~286 kDa and ~74 kDa for A1, and ~71 kDa and ~18 kDa for A2.
Using a polymer's molecular weight, , we can calculate the hydrodynamic radius ( A is Avogadro's number) 9 h = ( 3[ ] 10 A ) 1 3 ⁄ to be ~19 nm for A1 and ~8 nm for A2 (using n as the molecular weight). The corresponding root-mean-squared end-to-end distance, 〈 ̅̅̅ 〉 ⁄ for each sample is equal to . h . interact with the nanopore. When a 4 µL aliquot of the alginate was added to the head stage side of the lower cell, only 18 appreciable current transients were detected in a 1 hour measuring period, contrasted with 561 events in 1 hour when the alginate was directly injected adjacent to the head stage side of the nanopore. The additional electrolyte between electrodes and nanopore reduces the cross-pore applied potential compared to the usual single-cell sensing configuration.

ACID AND ENZYMATIC DIGESTION PROCEDURES ACID DIGESTION POST-NANOPORE MEASUREMENT
A ~9 nm nanopore was mounted in the PTFE sample holder. A 200 μL amount of 0.2% (w/v) A1 was added to the head stage side in 5 µL aliquots per hour throughout the work day during 4 days of application of a +200 mV cross-membrane voltage. For overnight voltage applications, the electrode polarity was maintained, but the electrodes were placed in the opposite wells. The head-stage and initially analyte-free ground side solutions were extracted, individually mixed with 1 mL of 75% sulphuric acid and heated overnight (16 h) at 80°C. Samples were diluted with 3 mL of water before spectral acquisition. For comparison, 500 µL aliquots of 0.2% (w/v) A1 and A2 were each subjected to the same acid digestion and dilution before spectral acquisition.

ENZYMATIC DIGESTION FOR SPECTROSCOPIC MEASUREMENTS
A 2250 µL aliquot of 0.2% (w/v) A1 was added to a 150 µL aliquot of 1 unit/mL alginate lyase and heated in a water bath at 37˚C for 30 minutes. The procedure was repeated for sample A2, but the sample was diluted with 10 mL H2O before spectral acquisition.

ENZYMATIC SAMPLE PREPARATION FOR NANOPORE SENSING
For enzymatic digestion, samples of 3% (w/v) A2 were mixed with alginate lyase (1:1 (v/v) mixture with 1 unit/mL enzyme) for 10 minutes at 37°C. 20 μL of this mixture was added to the headstage side and events were detected with the application of +200 mV on the head stage side. Measurements in the presence of 20 μL of 1 unit/mL of alginate lyase, alone, in the headstage side support that the detected events in the presence of analyte originated from enzymatic digestion products.  where the parameters had conventional meanings, and the event duration was expressed in µs. The event duration corresponding to the peak of the event count distribution, , was found by taking the first derivative of the curve.   absorption at ~1100 cm -1 allows calculation of the M/G ratio that varies with particular alginate source. 14 Using this approach, alginate A1 was determined to be ~63%G/37%M, and alginate A2 was ~57%G/43%M. These relative proportions were supported by additional analysis: in Supplementary Figure 8.3b, the particular alginate lyase was a mannuronic lyase, so that the greater absorption from the digestion of A2 than A1 was consistent with a greater proportion of M in A2. ii) OSCS and iii) heparin contaminated with OSCS through a ~14 nm diameter pore.

RECOGNITION FLAG GENERATION
Recognition flag generation was done using custom codes written in to the logarithm (log10) of the event duration ( ) using a bin width of 0.25 (here, determined using the USP OSCS data). (6) The same 0.5% filter was applied to these histograms, which then had their counts normalized. (7) The event duration threshold was taken to be the nearest bin at the distance of three standard deviations (after the 0.5% filter) from the bin with the maximum number of counts. (8) When events had been detected at log 10 above this threshold, the recognition flag was set to red to signal the presence of heparin; it was otherwise left white.