Nanopore design for exceptional rectification of DNA translocation


 Solid-state nanopores (SSNPs) of on-demand shape and size can facilitate desired sensor performance. However, reproducible production of arrayed nanopores of predefined geometry is yet to demonstrate despite of numerous methods explored. Here, bowl-shape SSNPs combining unique properties of ultrathin membrane and tapering geometry are demonstrated. The bowl-SSNP upper opening is 100-120 nm in diameter, with the bottom opening reaching sub-5 nm. Numerical simulation reveals the formation of multiple electroosmotic vortexes (EOVs) originating from distributed surface charge around the pore-bowl. The EOVs determine, collaboratively with electrophoretic force, how nanoscale objects translocate the bowl-SSNPs. Exceptional rectification with higher frequencies, longer duration and larger amplitude is found when DNA strands translocate downwards from the upper large opening than upwards from the bottom smallest restriction. The rectification is a manifestation of the interplay between electrophoresis and electroosmosis. The resourceful silicon nanofabrication technology is ingeniously shown to enable innovative nanopore designs targeting unprecedented sensor applications.

unique properties. The concept of BNPs is rst validated using numerical simulation, with reference to our previously studied TPPs 24 . Unlike the BNPs sculptured using focused ion beams 11,19 , our focus is to study the unique translocation characteristics of the BNPs based on standard silicon technology that supports reproducible and mass production. Both experimentally con rmed and theoretically supported, the bowl-look interior coupled with distributed surface charge on the ultrathin membrane around the smallest restriction of the BNPs give rise to an exceptionally high recti cation factor for translocation of heavily charged DNA.

Theory of BNPs
Numerical simulation results for a hemispherical BNP of d p =5 nm at the bottom (diameter of the smallest restriction), h=55 nm (thickness of the membrane), D p =~110 nm (diameter of the upper opening or the hemisphere) and natural surface charge density [28][29][30] of −0.02 C/m 2 for silicon dioxide (SiO 2 ) in Fig. 1a clearly show the formation of EOVs. The lower reservoir beneath the smallest restriction is grounded as the potential reference, while a bias voltage is set to the upper reservoir above the large opening. At positive bias V=+500 mV, a strong downward electroosmotic ow from the upper reservoir along the surface of the BNP sidewall is directed to a warm-coloured "pear" in the lower reservoir through a narrow channel (width<1 nm). This is complemented by a comparably strong upward ow immediately above the smallest restriction. In addition, a strong upward ow near the edge of the smallest restriction is observed in the lower reservoir. Hence, two vortexes, i.e., cyclic ows between the warm and cold colour regions, are formed, with the upper vortex being much stronger in ow rate than the lower one. At negative bias V=-500 mV, the position of and ow direction in the vortexes remain, although not only the size of the vortexes but also the EOF distribution greatly differ due to induced surface charge (ISC). This invariance in position and ow direction of the vortexes after reversing the polarity of external bias is of signi cant implications for DNA translocation shown below. The root cause for the intriguing vortex formation is the surface charge imparity primarily due to the effect of ISC 31 near the smallest restriction where the membrane remains ultrathin for an extended stretch (Fig. S1b, S2 in Supporting Information). Neglecting the ISC effect would lead to symmetric EOFs about the smallest restriction but with opposite directions at positive and negative biases, as expected (Fig. S1d, S2).
Ionisation of the hydrogen on their phosphate backbone makes DNA molecules heavily negatively charged 32 . Movement of DNA molecules in a BNP can, therefore, be controlled electrophoretically and signi cantly modulated electroosmotically 10,25 . At V=+500 mV (Fig. 1a), the electrophoretic force pulls a DNA molecule upwards from the lower reservoir. However, the electroosmotic force below the smallest restriction tends to drag the molecule downwards while that above pushes it upwards. Thus, the electroosmotic force tends to prevent the DNA molecule from entering the BNP from the lower reservoir but drive it out from the BNP (once it is inside) into the upper reservoir. At V=-500 mV, the direction of the electrophoretic force is reversed but those of the EOFs in the EOVs remain identical to those at V=+500 mV as seen in Fig. 1a. A DNA molecule driven by the electrophoretic force to enter the BNP from the upper reservoir becomes decelerated by the electroosmotic force when it gets close to the smallest restriction. A long transfer time for the DNA molecule in the BNP is, therefore, anticipated. Similarly, the DNA molecule is accelerated once it moves out into the lower reservoir. The maximum ratio of the electroosmotic force to the opposite electrophoretic force at the same position along the central axis is calculated in Fig. 1b for a simpli ed assessment using one DNA base pair (bp) segment as a nanoscale object being exerted by the different forces. A rapid growth of the importance of the electroosmotic force with decreasing d p is evident. The total force, i.e., the sum of electrophoretic and electroosmotic force, exerted on such a DNA segment is shown in Fig. 1c to peak sharply near the smallest restriction. In both cases of d p =5 and 10 nm, the peaks are strongly asymmetrical although the peak heights are largely insensitive to d p .
The ratio of the total force at V=-500 mV to that at V=+500 mV on the DNA segment is depicted in Fig. 1d for three BNPs of different d p . The c-axis, with the position of the smallest restriction as its origin, points to the direction of the electrophoretic force for both positive and negative biases. The total force at V=-500 mV is 4-5 times stronger than that at V=+500 mV for DNA approaching the smallest restriction of the d p =5 nm BNP, whereas it is about 30% stronger at V=+500 mV than that at V=-500 mV after it passes through the smallest restriction. Hence, the DNA segment is much more strongly attracted to the smallest restriction from the upper reservoir at negative bias, but it is more easily pulled out from the BNP to the upper reservoir at positive bias. Higher frequency and longer duration for DNA translocation are, then, predicted at negative bias than at positive bias. It is also found in Fig. 1d that the ratio decreases with increasing d p in the c<0 domain and that changing d p causes little difference in this ratio for driving the DNA segment out from the BNP in the c>0 domain.

Fabrication and characterisation of BNPs
Process details for the fabrication of BNPs are summarised graphically in Fig. 2a. The process module employed is local oxidation of silicon (LOCOS) established in standard silicon technology for device insulation 33 , i.e., Step 6 in 2a. This module leads to the formation of BNPs in a self-limiting manner in an originally amorphous silicon layer deposited on an oxidised silicon wafer. As the expensive and noncustomised SOI wafers are no longer a necessity for making SSNPs, the concept underlying this fabrication process is expected to stimulate design innovations implementable on other substrates than silicon thereby opening up opportunities much beyond today's practice.
The micrographs in Fig. 2b-e present typical data for the BNPs formed with slightly different processes, see Methods. While the bottom openings of the BNPs in 2b-c are irregular, those in 2d-e are, respectively, circular (d p =65 nm) and elliptic (d p1 =7 nm and d p2 =15 nm) resembling fairly well the shape of the top opening yet of much smaller dimensions. More details supported by experimental data are collected in Fig. S3 (Supporting Information). The irregular bottom openings (2b-c) can be a manifestation of pore formation at the junction of triple silicon crystal grains (Fig. S3). The irregularities can also result from crystal-plan-dependent oxidation and/or local thickness variation of the silicon layer upon crystallisation and grain growth during processing; the latter is evidenced by a roughened surface in Fig. 2f where the cross-section with a 15-degree tilt of a BNP array is shown. The BNP with a concavely curved sidewall is clearly visible as well.
Current-voltage (I-V) characteristic curves of a BNP, measured in electrolytes of different KCl concentration, are depicted in Fig. 2g. Details of the measurement implementation are provided in Methods. To extract d p from nanopore conductance values obtained from the I-V characteristics, a resistance model 34 (see detailed derivations in Supporting Note 1) was used to t the conductance vs. conductivity plot in Fig. 2h. The resultant d p for this BNP was 4.4 nm with an average surface charge density of σ=-0.017 C/m 2 . This σ value agrees with the typical charge density of SiO 2 surface [28][29][30] , as well as with that for the TPPs 24 . The slight non-linear I-V characteristics result from the asymmetric pore geometry and the inhomogeneous surface charge distribution. The latter is mainly generated by the ISC effect 31 , especially near the tip of the smallest restriction of the BNP.

Translocation of DNA in BNPs
Translocation experiments were rst carried out using the d p =4.4 nm BNP with λ-DNA, see Methods for more details. Typical translocation spikes in Fig. 3a could be observed only at negative biases, which can be accounted for by invoking the 4-fold difference in the ratio of total force at negative bias to that at positive bias in Fig. 1d. The observed bias-dependent frequency of translocation events (FTE) is a result of the competition between capture probability and temporary clogging 35 , compounded by the rapid increase in the ratio of electroosmotic force to electrophoretic force ( Fig. S7 in Supporting Information).
Frequently observed translocation waveforms displayed in Fig. 3b are characterised by a long low-level blockage followed by a short high-level one falling directly back to the baseline. The 16-μm-long λ-DNA with 48,502 base pairs soaked in electrolytes can convolute into a loose clump of 1.2 μm in gyration diameter 36 . With a persistence length of 35 nm typical for double-stranded DNA 37 , part of the λ-DNA can dwell in the bowl and occupies a considerable volume in the high-electric-eld region of the BNP. This behaviour can render a signi cant semi-blockade responsible for the long low-level blockage in Fig. 3b.
Although the 35-nm persistence length makes bending of the λ-DNA unlikely to t into the 4.4 nm pore, the λ-DNA can slightly move and rotate until eventually threading through the BNP and causing the short high-level blockage. Lacking such a dynamic mechanism in the absence of a similar bowl below the BNP can explain no observed translocation from the lower reservoir, at positive bais.
The λ-DNA translocation experiments were then implemented on a larger BNP of d p =8 nm. The pore size was similarly extracted from the conductance data. The amplitude, duration and FTE were extracted from the original records of ionic current traces. The average and spread of these three parameters are compared for different biases in Fig. 3c-e. The amplitude increases signi cantly with the absolute bias voltage, consistent with other reports [38][39][40] . The amplitude at negative biases is generally higher than that at positive biases. Although their dependency on bias voltage is weak, both duration and FTE are consistently higher at negative biases than at positive biases. The inset of Fig. 3d with typical examples of current traces at -500 mV (blue) and +500 mV (dark red) visualises the remarkable differences in amplitude, duration and FTE.
Fluctuations in current are contributed by translocation spikes, baseline tremble and drift and background noise. The standard deviation in current for the BNP of d p =8 nm is shown to grow with absolute voltage in Fig. 3f and is larger at negative biases than at positive biases. Thus, translocation of λ-DNA at negative biases is more likely to take place and the interaction between the λ-DNA and the nanopore is stronger, since the former leads to more spikes while the latter contributes to an unstable baseline. The outstanding DNA translocation phenomena are closely correlated to the unique structure of and the EOF distribution in the BNPs displayed in Fig. 1. Hence, it is theoretically predicted and experimentally veri ed that the DNA molecules have a higher probability to translocate at negative biases than at positive biases in the BNPs.

Methods
COMSOL simulation. Numerical simulations based on COMSOL Multiphysics of bowl-shape and truncated conical nanopores with similar dimensions of the experimental BNPs were carried out to gain insights into the nanopore physics. The simulation included the uid domain and the membrane domain whose relative permittivity was set to 80 and 11.7 for water and silicon, respectively. The ionic movement in an electrolyte was governed by the Nernst-Planck equation, while the electric potential distribution was described by the Poisson equation and the uid ow was determined by the Navier-Stokes equations. The "Transport of Diluted Species" module (Nernst-Planck equation), the "Electrostatics" module (Poisson equation) and the "Laminar Flow" module (Navier-Stokes equations) were incorporated and fully coupled in our two-dimensional axisymmetric simulation. The mobility of K + and Cl − was 7.0×10 −8 m 2 V -1 s -1 and 7.2×10 −8 m 2 V -1 s -1 , respectively. The respective diffusion coe cient was then determined through the Einstein relation. With a rotational symmetry along the central axis of the nanopore, the distributions of electric eld and electro-osmotic ow were plotted in cross-section along this axis. Nanopore fabrication. The BNPs were fabricated on ordinary (100) double-side polished silicon wafers 325 μm in thickness. After standard wafer cleaning, the fabrication started by thermal oxidation at 1000°C to grow a 150-nm-thick SiO 2 layer. A 55-nm-thick amorphous silicon (a-Si) membrane layer was subsequently deposited at 560 °C, followed by a 20-nm-thick stoichiometric silicon nitride (Si 3 N 4 ) layer at 775 °C, both by means of low-pressure chemical vapour deposition (LPCVD). Although crystallisation of the a-Si layer was inevitable during the Si 3 N 4 deposition, this silicon layer is still referred to as a-Si for convenience. The front side of a few selected wafers was subject to ion implantation of arsenic to a dose of 5×10 15 cm -2 at 20 keV in order to place the dopant peak at the interface between a-Si and Si 3 N 4 . Some of the implanted wafers were annealed in nitrogen atmosphere at 850 °C for 1 hour to electrically activate the dopants, i.e., letting the arsenic atoms replace silicon atoms in the silicon lattice, due to which grain growth in the a-Si layer was expected. After stripping the Si 3 N 4 layer in H 3 PO 4 solution followed by standard wafer cleaning, a fresh LPCVD-Si 3 N 4 layer was deposited again at 775 o C. Circular windows of 60 to 100 nm in diameter were then opened up in the Si 3 N 4 layer on the front side by combining electron beam lithography (EBL, Nanobeam Ltd.) with reactive ion etching (RIE). Local oxidation (LOCOS) of the a-Si exposed in the Si 3 N 4 windows was performed in dry oxygen at atmospheric pressure and 850 to 1100°C for different lengths of time to attain the target LOCOS outcome. It could be noted that LOCOS was developed for electrical insulation of devices in integrated circuits before transistors reached submicron dimensions 33 .
Square cavities of side length 150 µm were etched through the silicon substrate and stopped at the 150nm-thick SiO 2 layer from the rear side. This design was realised using photolithography in combination with deep RIE followed by 30% KOH wet etching at 80 °C. The SiO 2 could provide an excellent etch stop for the KOH etching, because the ratio of KOH etching rate of SiO 2 to that of Si is 1:200. Thus, the a-Si layer on the front side was protected during this step. The large cavities on the rear side were characterised by sloped, instead of vertical, sidewalls at a xed angle, due to the well-established silicon etch anisotropy in KOH-based solutions, i.e., the preferential chemical reaction of KOH with the (100) planes to the (111) planes of a silicon crystal. Finally, the LOCS SiO 2 grown in the Si 3 N 4 windows along with the SiO 2 layer in the large cavities were removed in a buffered hydro uoric acid. Free-standing silicon membranes with BNPs were obtained.
The formation of bowl-shape nanopores is a natural consequence of the LOCOS process. In the Si 3 N 4 windows, the mechanical stress generated during the LOCOS process can be engineered to lead to a selflimiting growth of oxide studs as the nanopore precursors. When the oxide studs are selectively stripped off, nanopores are left behind in the a-Si membrane. By virtue of the LOCOS process, the interior of the nanopores assumes a concave, bowl-look shape. Thus, the self-limiting oxide growth and the subsequent selective oxide removal are key to the formation of highly reproducible BNPs. Although an ordinary silicon wafer is the starting material in this work, other substrates such as quartz or sapphire that can withstand high temperature processing in a standard silicon process line can also be considered. This possibility makes the process extra robust and versatile.
The irregularities in Fig. 2b-c are attributed to the dependence of the oxidation rate on crystal orientation 33 of the crystallised a-Si with crystallites sizing tens of nanometres. It can also result from local thickness variation represented by the surface roughening in Fig. 2f. Rough surfaces can be planarised by means of chemical mechanical polishing, a standard process in modern integrated circuit fabrication. The satisfying result with an ideal circular pore in Fig. 2e points to the paramount importance of dopant activation prior to oxidation, because heavily doped silicon is known to oxidise faster and the rate of oxidation is less dependent on crystal orientation than undoped silicon 33 . Prolonging the oxidation time while exploiting the self-limiting nature of the process may also improve the uniformity (Supporting Note 1). The observed formation of nanopores at the triple junction of silicon crystal grains (Fig. S3) can be mitigated via induced grain growth at low temperatures 41 or mediated by metal or metal silicides 42,43 .
Use of tailor-made silicon-on-insulator wafers including lateral overgrowth epitaxy 44,45 can also be an alternative.
DNA sample preparation. λ-DNA was purchased from Merck KGaA, Darmstadt, Germany. The DNA was used without further puri cation and dispersed in a 500 mM KCl solution to the concentration of 78 pM (2.5 μg/ml).
Electrical characterisation and data processing. In all measurements, the bias voltage was set to the upper reservoir on the large opening side of the BNP, while the lower reservoir on the smallest restriction side was grounded, in agreement with the con guration in the COMSOL simulations.
Before measurement, the BNP chips were thoroughly cleaned in a piranha solution with H 2 SO 4 :H 2 O=3:1 (volume ratio) for 30 min and rinsed in deionized water. The chips were then sandwiched by two custommade polymethyl methacrylate lids with two polydimethylsiloxane O-rings (inner diameter 8 mm) on the two sides for seal. An inlet and an outlet were made in each lid and the KCl solution with certain concentration and λ-DNA dispersions could be injected to the two sides of the nanopore chip. The uids in the two sides were separated by the chip and the only path of ionic current was through the nanopore. The resistivity of the KCl solution was calibrated using a conductivity meter (Lab 945, Xylem Analytics Germany Sales GmbH & Co. KG). A pair of pseudo Ag/AgCl reference electrodes (2 mm in diameter (Warner Instruments LLC.)) was also mounted in the middle of the lids, which was used to apply a bias voltage and to measure the ionic current. The bias voltage was controlled and the ionic current was recorded using a patch clamp ampli er (Axopatch 200B, Molecular Device Inc.). The ionic current was digitalised by an Axon Digidata 1550A (Molecular Device LLC.) and recorded using the software Axon pCLAMP 10 (Molecular Device LLC.). DNA translocation was detected at a 10 kHz sampling frequency with a 1 kHz four-pole Bessel low-pass lter. The entire experimental set-up was placed inside a Faraday cage to shield against electromagnetic interference.
The translocation spikes on the current traces were extracted automatically by employing a MATLAB program using the function ndpeaks. The threshold for recognition of a possible spike in the program was set to be eight times the root-mean-squared value of the background noise. The amplitude and duration of each translocation spike were extracted and the translocation frequency was calculated as the reciprocal of the time interval between consecutive events. In addition, the general uctuation of the current traces was evaluated by their standard deviation. The components in high frequency range (1 kHz-10 Hz) and low frequency range (<10 Hz) were separated using a lter and the standard deviation was calculated separately.  Figure 1 COMSOL simulations for BNPs of dp=5 and 10 nm at the bottom (diameter of the smallest restriction that represents the narrowest physical passage of the nanopore), h=55 nm (thickness of the membrane) and Dp=~110 nm (diameter of the upper opening that is equal to the diameter of the hemisphere), in 500 mM KCl and with σ=−0.02 Cm-2 inherent surface charge density. a, Distribution of the EOF velocity at −500 mV (left half) and +500 mV (right half) of a BNP of dp=5 nm as the diameter of its smallest restriction. Warm colours (red and yellow) indicate downward ows, whereas cold colours (blue and green) present upward ows. The small black arrows indicate the direction of the EOF. b, Dependence on dp of the maximum ratio of the electroosmotic force to the opposite electrophoretic force at the same position. c, Total force on the DNA molecule along the central axis of BNPs of dp=5 and 10 nm. Inset: the coordinate with the origin lining up with the edge of the smallest constriction and pointing to the lower reservoir. d, Variation of the corresponding ratio of the total force at negative bias to that at positive bias along the c-axis de ned as the direction of DNA translocation, i.e., from the upper reservoir to the lower reservoir at negative bias (-500 mV) and from the lower reservoir to the upper reservoir at positive bias (+500 mV).

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. Nanoporedesignforexceptionalrefecti caitionofDNAtranslocationSI.docx