CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application claims the benefit of U.S. Provisional Application No. 63/042637, filed on June 23, 2020. The entire disclosure of the above application is incorporated herein by reference.

FIELD

[0002] The present disclosure relates to mechanisms by which to control the solid- state nanopore enlargement process under electrical stress.

BACKGROUND

[0003] Nanopores - nanometer scale holes that can be used to detect and interrogate single biomolecules one at a time - are poised to deliver on decades of promise in diverse fields, ranging from disease diagnostics and DNA sequencing to next- generation methods of archival information storage. Until recently, however, the high cost of the equipment needed to fabricate and subsequently control the size of solid-state nanopores was prohibitive, as was the low yield of useful nanopores, preventing this promising technology from making it out of a few well-equipped research labs.

[0004] Recent advances in solid-state nanopore fabrication by controlled breakdown (CBD) have made nanopores more accessible by eliminating the need for complex and expensive equipment, enabling both new labs and industrial players looking for scalable method of nanopore fabrication for commercial applications to enter the field. Nevertheless, irrespective of the fabrication method employed to make a solid-state nanopore, there will most certainly remain the need to precisely enlarge the pore using electrical stress to the required size so that it is optimized for the particular single molecule sensing application. However, there remain issues with pore enlargement using moderate voltage after fabrication. In particular, it has been noted that using too large a voltage bias for pore growth can lead to the formation of multiple nanopores instead of simply enlarging an existing pore, and as a consequence the time required to condition a pore to a large size (>20 nm) can be unreasonably long (>1 h) since low voltages must be employed during the growth process to avoid this possibility. While the mechanism of nanopore fabrication undera high electric field is well characterized, the factors that affect enlargement speed and how they in turn affect the probability of the formation of additional nanopores are still unclear.

[0005] Some preliminary work has attempted to elucidate the mechanism of pore growth under moderate electrical stress, suggesting Joule heating as a possible driver of growth. It was also recently shown that fixing the current through an existing nanopore and allowing the voltage to vary as the pore grew resulted in a final pore size that depended on the value of the current, but neither work is sufficient to positively determine the mechanism(s) that drive pore growth.

[0006] In addition to understanding the mechanism of pore growth, there is significant value in finding practical methods by which to speed up the production of nanopores without compromising quality (i.e. size precision, geometric stability, and low-frequency ionic current noise level) or opening unwanted additional nanopores. In this disclosure, a thorough study is presented of the means by which nanopore growth can be controlled.

[0007] The above section provides background information related to the present disclosure which is not necessarily prior art.

SUMMARY

[0008] This section provides a general summary of the disclosure and is not a comprehensive disclosure of its full scope or all of its features.

[0009] In one aspect, a method is provided for enlarging the size of a nanopore formed in a membrane. The method includes: disposing a membrane in a conductive liquid, where the membrane has a nanopore formed therein; selecting a value for an electric potential that induces an electric field in the nanopore cooperatively with setting conductivity of the conductive liquid, such that current through the nanopore is maximized at the chosen potential and the electric field in the nanopore is less than a maximum electric field threshold; and applying the electrical potential across the nanopore at the selected value, thereby enlarging the size of the nanopore.

[0010] The method may further include increasing the conductivity of the conductive liquid while applying the electrical potential at the selected value across the nanopore.

[0011] In one example, the value of the electric potential is set to induce an electric field that is one third the nominal dielectric strength of the membrane. In another example, the value of the electric potential is set to induce an electric field that is one half the nominal dielectric strength of the membrane.

[0012] In another aspect, the method for enlarging the nanopore can be combined with techniques for creating the nanopore in the membrane. In this method, a membrane without a nanopore is disposed in a conductive liquid. The method includes: applying an electric potential across the membrane, thereby creating a nanopore in the membrane; and enlarging size of the nanopore while the membrane remains in the conductive liquid.

[0013] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

DRAWINGS

[0014] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations and are not intended to limit the scope of the present disclosure.

[0015] Figures 1 A and 1 B are diagrams depicting an example apparatus for fabricating and conditioning nanopores in a membrane.

[0016] Figure 2 is a flowchart presenting an overview of the method for enlarging the size of a nanopore.

[0017] Figure 3 is a flowchart showing the method of enlarging the size of a nanopore combined with the controlled breakdown technique for forming the nanopore.

[0018] Figure 4A is a graph comparing pore growth rates when high and low conductivity electrolyte solutions are alternatively used to enlarge a nanopore.

[0019] Figures 4B and 4C are graphs comparing pore growth rates when similar conductivity solutions with different total electrolyte concentrations and cations are alternately used to enlarge nanopores.

[0020] Figure 5 is a graph showing the enlargement time required to reach certain nanopore sizes for two pores in 3.6 M LiCI pH 8 versus nine pores in 4 M KCI pH 8 demonstrating that pores grown in higher conductivity solutions reach the same target pore size faster than those grown in lower conductivity solutions.

[0021] Figure 6 is a graph showing typical results from a nanopore enlarged under conditions of alternating acidic and alkaline electrolyte with equal conductivities. [0022] Figures 7 A and 7 B are plots generated from DNA translocation data of pores enlarged using high conductivity solutions, comparing maximum current blockage caused by a DNA molecule partially obstructing the pore versus dwell time of the molecule in the pore, where an example of a membrane with a single pore is shown in Fig 7A and an example of a different membrane containing two pores in shown in Fig. 7B.

[0023] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.

DETAILED DESCRIPTION

[0024] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0025] Figures 1A and 1 B depict an example apparatus for fabricating one or more nanopores in a membrane. The apparatus is comprised generally of a fluidic cell 22; a pair of electrodes 24 electrically coupled to a voltage source; and a controller 26 interfaced with the current amplifier circuit 25. The voltage source is not shown but can be integrated on the circuit board with the current amplifier circuit 25. The fluidic cell 22 is further defined by two reservoirs 33 fluidly coupled to each other via a passageway 34 as best seen in Figure 1 B. A current amplifier circuit 25 is used to measure the current flow between the two reservoirs 33. In one embodiment, the controller 26 may be implemented by a data acquisition circuit 28 coupled to a personal computer 27 or another type of computing device. The fluidic cell 22 and/or the entire system can be disposed in a grounded faraday cage 23 to isolate electric noise. Thus, the setup is like that which is commonly used for biomolecular detection in the field of nanopore sensing. Other setups for fabricating a nanopore are also contemplated by this disclosure.

[0026] In the example setup, a silicon chip 31 is used to support a membrane 30. The silicon chip 31 is sandwiched between two silicone gaskets 32 and then positioned between the two reservoirs 33 of the fluidic cell 22. In some embodiments, the fluidic cell 22 is comprised of polytetrafluoroethylene (PTFE) although other materials are contemplated. A small pressure is applied to the two gaskets 32 by the fluidic cell 22 to seal the contact tightly. The two reservoirs 33 are filled with a conductive liquid, and the two electrodes 24 are inserted into the respective reservoirs of the fluidic cell 22.

[0027] In some implementations, the membrane 30 is comprised of a dielectric material, such as silicon nitride (SiN _x ). Membranes are preferably thin, with a thickness on the order of 10 nm, although membranes having different thicknesses are contemplated by this disclosure. Membranes comprised of other dielectric materials, such as other oxides and nitrides, which are commonly used as gate materials for transistors, also fall within the scope of this disclosure. Likewise, atomically thin membranes may be comprised of other materials such as graphene, molybdenum disulfide and the like. It is also contemplated that the membranes may be comprised of multiple layers of materials, including dielectric materials and/or conductive materials.

[0028] In the example setup, the current amplifier circuit 25 is a simple operational- amplifier circuit to read and control voltage and current. Operational-amplifiers are powered by a ±20 volt voltage source. In operation, the circuit takes in a command voltage (Vcommand) between ±10 volts from a computer-controlled data acquisition card, which is amplified to ±20 volts, and sets the potential across the membrane. Current flow between the two electrodes is measured at one or both electrodes with pA sensitivity. More specifically, current is measured with a transimpedance amplifier topology. The measured current signal (lout), converted to a voltage signal by the current amplifier circuit, is digitized by the data acquisition circuit and fed continuously into the controller. In this way, the current is monitored in real time by the controller, for example at a frequency of 10 Hz, though faster sampling rate can be used for faster response time. Other circuit arrangements for applying a potential and measuring a current fall within the scope of this disclosure. Conversely, circuit arrangements that apply a current to the electrodes and measure a potential are also envisioned.

[0029] Unlike nanopore formation by controlled breakdown, nanopore growth is primarily driven by the level of ionic current passing through the nanopore, rather than the strength of the electric field generating the current. Additionally, enlargement has a much weaker pH dependence than does nanopore formation. Results presented below indicate that the probability of forming additional (unwanted) pores during nanopore growth can be decoupled from the rate of growth of the nanopore, allowing for fast pore enlargement to any size without risking further nanopore formation.

[0030] Figure 2 provides an overview of the method for enlarging the size of an existing nanopore formed in a membrane. As a starting point, the membrane is disposed between two reservoirs containing conductive liquid in a setup, for example as described above in relation to Figures 1A and 1 B. In the example implementation, the conductive liquid is an aqueous salt solution. Aside from aqueous salt solutions, one can envision other types of conductive liquids. For example, one could use ionic liquids or salts dissolved in non-aqueous media, such as organic solvents. Other types of conductive liquids include but are not limited to aqueous monovalent salt solutions; aqueous salt solutions of valence of one or more; as well as salts of various valence dissolved in organic solvents such as ethanol, DMSO, isopropanol, chloroform, etc.

[0031] An electric potential (i.e., voltage) that induces an electric field across the nanopore is applied at a selected value as indicated at 41. Of note, the magnitude of the electric potential is selected cooperatively with setting conductivity of the conductive liquid, such that the current through the nanopore is maximized at the selected value and the electric field in the nanopore is less than a maximum electric field threshold. The value of the electric potential is preferably set to induce an electric field that is less than (or equal to) one half the nominal dielectric strength of the membrane. In one example, the value of the electric potential is set to induce an electric field that is one third of the nominal dielectric strength of the membrane. In other example, the value of the electric potential is based on the voltage at which the nanopore was formed as is further described below.

[0032] Subject to the constraint that the induced electric field is less than a maximum electric field threshold (e.g., the dielectric strength of the membrane), the conductivity of the conductive liquid is set so that the current through the nanopore is maximized at the selected electric potential. Current through the nanopore, to first order, is given by where s is the solution conductivity, determined by the salt concentration and identity, V is the voltage applied, L is the membrane thickness, and d is the pore diameter. Since L and d are changing during the process due to the conditioning, conductivity of the liquid is the remaining controllable variable. Because the objective is to maximize current, this means the method should maximize the conductivity of the liquid. For most salt types, this means using a saturated solution of the given salt for the solvent, and to choose a salt that is maximally conductive from among the available options.

[0033] To monitor the size of the nanopore, current flow through the membrane is monitored at 42 while an electric potential is being applied across the nanopore. In one embodiment, the electric potential applied across the nanopore for enlargement remains unchanged (e.g., 3-4 volts) while the size of the nanopore is determined. In other embodiments, the higher electric potential applied across the nanopore for enlargement is lowered to determine the size of the nanopore. The electric potential is preferably lowered to a value where the pore is guaranteed to be ohmic (e.g., 200mV). For example, an electric potential on the order of 3-4 volts may be applied during a first period of time and then lowered for a subsequent period of time which allows for measurement. The enlargement and measurement periods can be alternated until the nanopore reaches the desired size. In either case, the magnitude of the current passing through the nanopore is compared at 43 to a predetermined threshold, where the threshold corresponds to the desired size for the nanopore. When the monitored current reaches (or exceeds) the threshold, the applied voltage is terminated at 44. Other conditions for stopping the pore growth, such as choosing a maximally acceptable value for the low-frequency noise of the nanopores, are also contemplated by this disclosure.

[0034] While applying an electric potential to enlarge the nanopore, the conditioning speed can be increased by increasing the conductivity of the conductive liquid. That is, the conductivity of the conductive liquid can be increased in situ during the enlargement process. In one embodiment, the conductivity is increased by increasing the temperature of the liquid. This can be accomplished in different ways, including using a resistive heating element placed in the conductive liquid or through the use of a light source (e.g., laser). In some embodiments, an array of nanopores may be formed on a membrane. In this case, one or more of the nanopores can be selectively enlarged by directing a laser beam onto the nanopores of interest, thereby enlarging only these selected pores in the array of nanopores. Although the conductivity of the liquid is dependent on temperature, it is not necessarily monotonical and does not necessarily increase with increased temperature. In some instances, it is envisioned that conductivity may be increased with decreasing temperature. It is also envisioned that at lower temperatures it is possible that the redox reactions that enable current to pass though the membrane will happen more slowly, effectively increasing the dielectric strength of the membrane and allowing higher voltages, and therefore higher ionic currents, to be used during the enlargement process without risking additional nanopores opening.

[0035] Fabricating nanopores using controlled breakdown is one known technique for creating a nanopore in a membrane. The technique described above for enlarging the size of a nanopore can be combined with the controlled breakdown technique as shown in Figure 3. It is readily understood that the enlarging technique can also be combined with any other methods for creating nanopores as well.

[0036] As a starting point, a membrane is disposed in a conductive liquid of a setup, for example as described above in relation to Figures 1A and 1 B. An electric potential (i.e. , voltage) that induces an electric field across the nanopore is applied as indicated at 51. In one embodiment, a constant voltage is applied to the membrane. In other embodiments, the applied voltage is ramped up over time until the breakdown occurs and the nanopore is formed. For pore creation, the electric potential applied to the membrane preferably has a magnitude that induces an electric field having a value greater than 0.1 volt per nanometer across the membrane. Further details regarding the controlled breakdown technique can be found in U.S. Patent Publication No. 2014/0108008 which is entitled “Fabrication of Nanopores using High Electric Fields” and is incorporated by reference herein in its entirety.

[0037] After creating the nanopore in the membrane but before enlarging the size of the nanopore, the size of the nanopore is preferably determined at 52. To do so, another voltage is applied across the nanopore, thereby generating a current that flow through the nanopore. The magnitude of the voltage is selected to ensure that the size of the nanopore remains unchanged, is smaller than the voltage used to create the nanopore, and is such that the nanopore has an Ohmic current response to the chosen voltage value. Current flow through the nanopore is measured and then used to determine the size of the nanopore. Nanopore size can be inferred from the following equation, using the same variable definitions as defined above:

Typically, one assumes that L is equal to the nominal membrane thickness, but other methods of measuring L are also possible.

[0038] Next, the size of the nanopore can be enlarged. In one embodiment, the membrane remains in the same conductive liquid in which the nanopore was formed. In other embodiments, the conductive liquid encompassing the membrane may be different from the conductive liquid in which the nanopore was formed. That is, the conductive solution in the setup is changed.

[0039] To enlarge the size of the nanopore, an electric potential is reapplied at 53 across the membrane. As discussed above, the value of the electric potential is selected cooperatively with setting the conductivity of the liquid, such that the current through the nanopore is maximized at the selected value and the electric field in the nanopore is less than a maximum electric field threshold. In the case where the pore was formed by a voltage that ramped up over time, the value of the electric potential is determined by the voltage at which the breakdown occurred. The value of the electric potential is set at less than one half the voltage at which the breakdown occurred and preferably at one third the voltage at which the breakdown occurred. In other embodiments, the value of the electric potential is correlated to the nominal dielectric strength of the membrane, such as one third or one half of the nominal dielectric strength of the membrane.

[0040] To monitor the size of the nanopore, current flow through the membrane is monitored at 54 while the electric potential is being applied across the nanopore. Again, in some instances, the applied voltage can be lowered to a value where the pore is in ohmic regime for measurement purposes. The magnitude of the current is compared at 55 to a predetermined threshold, where the threshold corresponds to the desired size for the nanopore. When the monitored current reaches (or exceeds) the threshold, the applied voltage is terminated at 56. Other conditions for stopping the pore growth, such as choosing a maximally acceptable value for the low-frequency noise of the nanopores, are also contemplated by this disclosure.

[0041] Experimental results are presented in support of this disclosure. A determination was first made as to which aspect of the electrical stress experienced by a nanopore (current, voltage, electric field, etc.) determines the growth rate. To do so, nanopores were grown in alternating solutions of differing conductivities. Because the level of current passing through the pore at a given applied voltage is directly related to the conductivity of the solution at a given pore size, this comparison allows a sensitive measurement of the influence of ionic current on the pore growth profile while holding voltage and electric field constant.

[0042] An example growth profile of a pore enlarged in two different solutions is shown in Figure 4A. The electrolyte solutions used were 3.6 M LiCI (a = 16.95 S nr ¹ ) and 10 mM LiCI (s = 0.203 S nr ¹ ), both buffered at pH 8.0 with 10 mM HEPES. The voltage was pulsed between ±4.5 V with a 4 seconds hold time in each voltage polarity, with a measurement of the pore size occurring every 5 cycles totaling 40 seconds of electrical stress. The electrolyte was then swapped, and the measurements repeated for a total of ten solution changes. To measure the pore size after every cycle in the high conductivity condition, a +200 mV bias was applied for 7 seconds, where the first 5 seconds allowed the capacitive current to decay and the faradaic current to stabilize, followed by a current measurement averaged over the last 2 seconds. This depends on the chip capacitance (exposed area to liquid and dielectric properties) and can be shorter with low cap chips. The same procedure was then repeated using a -200 mV bias. Using these measurements of ionic current through the nanopore, the pore conductance G was calculated and used to determine nanopore diameter d using standard methods: where the effective length of the pore L is assumed to be the membrane thickness and the solution conductivity s is known. Note that pore size is not measured in the low conductivity condition directly since the size model used performs poorly in low salt concentrations.

[0043] As is clearly shown in Figure 4A, the growth rates of the pores are strongly determined by the conductivity of the solution and therefore the current passing through the pore. The nanopore consistently grew faster in the 3.6 M LiCI solution, at an average rate of about 0.11 nm cycle ¹ , whereas growth was near negligible using the 10 mM LiCI, at about 0.02 nm cycle ¹ .

[0044] In order to confirm that the pore growth rate was dependent on the conductivity of the electrolytic solution rather than the concentration or the identity of the ions, two different solutions of 1 .56 M KCI and 3.6 M LiCI each buffered at pH 8.0 with 10 mM HEPES were prepared with similar conductivities of s= 17.24 S rrv ¹ and s= 17.04 S nr ¹ respectively. Using these solutions, the same experiment was conducted, with results being shown in Figure 4B. The pores were subjected to the same voltage conditions as noted previously, but solution were swapped after every 20 cycles to ensure that the growth sustained in each condition was small enough that our growth rate comparisons between adjacent growth segments in different conditions are not significantly biased by the absolute value of the pore size. The results show that the growth rates in both electrolyte solutions are very similar, indicating that the identity of the cation and the concentration of the electrolyte (in this range) are likely both unimportant contributors to pore growth.

[0045] In order to quantify the reduction in time required to reach a target pore size for solutions of high conductivity, nine pores were grown in 4 M KCI pH 8 (o = 36.3 S nv ¹ ) compared to two pores grown in 3.6 M LiCI pH 8 (o = 17.04 S rrr ¹ ). Figure 5 plots the elapsed enlargement times for the pores to reach specific target sizes. After initial pore fabrication, each pore was flushed with the appropriate electrolyte solution and subjected to the same voltage stress during enlargement, resulting in different levels of ionic current through the pore. The pores grown in the 4 M KCI solution consistently reached the specified pore size faster than the pores grown in the 3.6 M LiCI solution, where the conductivity of the 4 M KCI was approximately two times higher than the 3.6 M LiCI. Note however that the growth rate difference exceeds this factor. Increasing the solution conductivity was shown to be a practical method of reducing pore enlargement time and can reduce the time required to make a usable nanopore by an order of magnitude.

[0046] Fabrication in high conductivity solutions of 4 M KCI was also attempted to differentiate between the mechanisms controlling pore creation versus pore enlargement. Breakdown (BD) times occurred on the same timescale as pores fabricated in 3.6 M LiCI for a given voltage profile, indicating that the driving force behind controlled breakdown (CBD) is fundamentally different from that behind subsequent pore enlargement, consistent with our previous work that showed that BD times were primarily determined by the current density in the membrane itself, mediated by the electric field, rather than being dependent on the conductivity of the solution. The fact that pore fabrication and growth are driven by different aspects of the electrical stress is of particular practical interest, since it allows for independent optimization of electrolyte solutions for one process over the other. In particular, we found in previous work that under high electric field stress it is possible to make multiple nanopores. This imposes strict limits on the voltage that can be used to enlarge an existing nanopore, since one risks opening a second nanopore if using a voltage that is so large as to make the mean breakdown time comparable to the required enlargement time, which in turn limits the speed at which the pore can be enlarged. By decoupling the breakdown and enlargement mechanisms, as shown in figure 5, it is possible to rapidly enlarge a pore at low voltage relative to that which was required to open the pore initially, simply by using a high-conductivity electrolyte to maximize the level of ionic current passing the pore at low voltage, without risking the opening of a second nanopore due to further dielectric breakdown events in other parts of the membrane.

[0047] Experiments were performed in which a nanopore was enlarged under conditions of alternating pH, using conductivity-matched electrolyte solutions in order to control for the effects of the value of the ionic current. In these experiments, 1.56 M KCI pH 4 (o = 17.90 S m- ¹ ) and pH 10 (o = 18.01 S m ¹ ), buffered with 17 mM CH ₃ COOH / 3 mM CHsCOONa and 10 mM NaHCOs _, respectively, were used. Pores were enlarged using ±3.5 V or ±4 V, switching between pH 4 and pH 10 periodically. Pore conductance was measured in both solutions to ensure agreement and the beginning and end of each cycle and were always within acceptable error. Whereas one would expect a 100-fold reduction in fabrication time using pH 4 versus 10, interestingly, growth rate shows instead a ~2-fold increase in growth rate as shown in Figure 6. While the difference in enlargement rate is small, it is statistically significant at the p<0.05 level, with pH 10 promoting faster pore growth than pH 4. The ratio of growth rates in pH 10 to pH 4 for adjacent conditioning cycles at ±3.5 V being 1.8 ± 0.3, and 1.6 ± 0.2 at ±4 V (error bars given 95% confidence interval). Note that this is opposite to the trend for fabrication times, in which more acidic pH values tend to result in much shorter fabrication times. This pH dependency cannot be explained by a Joule heating mechanism for pore growth, since the level of current passing through the pore in both cases is the same. It is known that alkaline solutions slowly dissolve SiNx chemically, which could potentially explain some of the observed difference, though the growth rates observed here are higher than would be expected for passive dissolution alone. Indeed, no growth at all is observed over the course of an hour spent passively in 1.56M KCI pH 10 for membranes from the batch used to generate figure 6.

[0048] DNA translocation experiments were conducted on pores enlarged using high conductivity solutions to assess the presence of a single nanopore in the membrane. Following pore enlargement to a target size, nanopores are electrically characterized to obtain more accurate size measurements and information about their ionic current noise profiles. Typically, a 30 seconds current trace is recorded using an applied bias of ±200 mV, and the corresponding power spectral density (PSD) plots are generated from this data. Pore size is also calculated as in the equation given in [0029] from an l-V curve swept from -200 mV to +200 mV. Pore size measured from conductance works well for a membrane containing a single nanopore, but the method cannot infer the presence of multiple pores. Using this geometrical conductance model, the calculated pore size in a membrane containing potentially two or more pores is measured as a single pore with an equivalent conductance to the multiple existing pores. Currently it is not practical to assess the geometry of multiple nanopores simultaneously using open-pore conductance alone, though in principle one can achieve this by measuring the change in conductance over time as a nanopore(s) are enlarged at a known rate, as the time- derivative of growth rate depends on the number of pores in the membrane.

[0049] Instead, the number of pores on a membrane was assessed by translocating DNA through it and plotting the maximum current blockage against the dwell time of the molecule in the pore. Because blockage depths and passage times of DNA is dependent on pore diameter, it is often possible to discern two distinct populations of translocation events when a second pore, >2 nm, is present. This method is expected to be reliable only in the case where both pores are large enough to allow DNA translocation, though smaller pores may be able to sense collisions. [0050] To demonstrate the conditions in which multiple pores can sometimes be formed when enlarging pores, two pores were fabricated and enlarged in 4M KCI pH 8. Figure 7 A show a low Mf noise pore of 20 nm diameter immersed in 3.6 M LiCI, at 200 mV, with 2.56 nM 4 kbp dsDNA on the one side of the membrane. As expected for a single nanopore inside the membrane, two levels of current blockage are observed: one for translocation events where the DNA polymer passes through the pore unfolded, and the other where it passes through partially folded. Figure 7B demonstrates the case of two pores existing in a membrane. This pore was fabricated and enlarged under identical conditions to the single pore previously discussed. Four blockage levels are observed, due to the presence of multiple pores of various sizes, where each pore was represented by one folded and one unfolded blockage level.

[0051] In both DNA translocation examples, the pores were grown using a square pulse alternating from +4.5 V to -4.5 V 4M KCI pH8, but the fabrication voltage for the single pore on the membrane was at -9.21 V versus -8.10 V for the membrane with multiple pores. The use of an excessively large pore enlargement voltage relative to the fabrication voltage resulted in the creation of an additional pore via CBD in figure 7B, though it is clear from figure 7a that both enlargement and formation of additional pores are stochastic processes and the presence of additional pores at the end of the enlargement process depends on the relative timescales for each. For this reason, increasing the pace of pore enlargement by increasing the voltage is not recommended, as we have noted in previous work, as the probability of forming additional pores increases exponentially with the conditioning voltage.

[0052] Note that pores enlarged in high conductivity solutions are not exempt from the possibility of creating multiple pores, but the speed of pore enlargement is instead decoupled from the mechanism by which additional pores are formed, allowing faster growth at lower voltage and consequently reduced probability of multiple pore formation before the desired pore size is reached. A general rule of thumb for preventing the formation of multiple pores is to limit the pore enlargement voltage to no more than half of the fabrication voltage, though it is possible to effectively enlarge a pore with significantly less voltage even than this if a high-conductivity electrolyte is used to mediate the process. Best practice for reliably enlarging a nanopore without risking fabrication of additional pores during the enlargement step is to use a high-conductivity solution combined with a pulsed voltage of approximately one third of the voltage at which the pore was formed during the fabrication step. [0053] From the above discussion it is clear that the primary driver of pore growth is the ionic current which passes the nanopore, but it is not the whole story, indicating that Joule heating alone is not the mechanism for pore growth. While certainly consistent with a current-driven mechanism, it is not consistent with the observed pH dependence. Given the high efficiency of heat dissipation in nanoscale geometries, it is also unlikely that Joule heating through ionic current could raise the temperature of the pore to a level that could cause material damage. Even assuming that it could, the previously suggested link between growth rate and resistive power dissipation in the pore does not address the mediating variable of local temperature, on which the growth rate dependence is unclear. A possible explanation is a chemical or electrochemical reaction between electrolyte and the walls of the pore which is activated by either slightly elevated temperatures or the interface potential, though the evidence available is insufficient to provide a conclusive answer. The role of pH in the process is likely mediated through the level of surface current. Pore walls will be more charged at pH 10 (strongly negative surface charge expected) than at pH 4 (weakly positive surface charge expected), which will lead to more surface currents, electroosmoticflow, and a general increase in the availability of reagents for the etching reactions responsible for pore growth.

[0054] In these experiments, nanopores were individually fabricated in 40 mih ^c 40 mhi, 12 ± 1 nm thick silicon nitride membranes. Each membrane was supported on a 200 mhi thick silicon frame with overall dimensions of 5 mm ^c 5 mm. All membranes were purchased from Norcada lnc (NBPX5004Z-HR).

[0055] Prior to nanopore fabrication, the membranes were piranha cleaned in a 3: 1 solution of H ₂ S0 ₄ :H ₂ 0 ₂ at approximately 90° C for one hour. After cleaning, these chips were immediately rinsed free of the acid using ultrapure water and then mounted into sealed, 3D printed flow cells filled with the appropriate filtered and degassed electrolyte solution. Electrolyte solutions used in this work include: 3.6 M LiCI pH 8.0 buffered with 10 mM HEPES (s = 16.95 S m ¹ to 17.04 S m ¹ ), 10 mM LiCI pH 8.0 buffered with 5 mM HEPES (s= 0.203 S m ¹ ), 4 M KCI pH 8.0 buffered with 10 mM HEPES (s= 36.3 S nr ¹ ), 1.56 M KCI pH 8.0 buffered with 5 mM HEPES (a = 17.24 S m ¹ ). 1.56 M KCI pH 4 buffered with 17 mM CH ₃ COOH / 3 mM CH ₃ COONa (s = 17.90 S m- ¹ ), and 1.56 M KCI pH 10 buffered with 10 mM NaHC0 ₃ (a = 18.01 S nr ¹ ). pH was adjusted using KOH/LiOH and HCI as appropriate. All chemicals were purchased from Fischer Scientific. The flow cells were fitted with Ag/AgCI electrodes in contact with the electrolyte solution on either side of the pore and used to apply voltage and measure current across the pore. Ag/AgCI electrodes were made by immersing 99.9% silver wire segments in Clorox bleach for 30 minutes. The connected flow cell was placed in a custom Faraday cage to shield it from external electromagnetic interference.

[0056] Pore fabrication, enlargement, and data acquisition during translocation experiments were carried out using custom LabVIEW software interfaced with a National Instruments DAQ card. An Axopatch 200B (Molecular Devices) patch-clamp amplifier was used to record current for noise analysis and DNA translocation data. Current traces from DNA translocation experiments were analyzed using a custom implementation of the CUSUM+ algorithm.

[0057] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

[0058] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms "a,” "an," and "the" may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed.

[0059] When an element or layer is referred to as being "on," “engaged to,” "connected to," or "coupled to" another element or layer, it may be directly on, engaged, connected or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being "directly on," “directly engaged to,” "directly connected to," or "directly coupled to" another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

[0060] Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.

[0061] Spatially relative terms, such as “inner,” “outer,” "beneath," "below," "lower," "above," "upper," and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "below" or "beneath" other elements or features would then be oriented "above" the other elements or features. Thus, the example term "below" can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.