In-Plane, In-Series Nanopores with Circular Cross Sections for Resistive-Pulse Sensing

Abstract

Resistive-pulse sensing with solid-state nanopores is a sensitive, label-free technique for analyzing single molecules in solution. To add functionality to resistive-pulse measurements, direct coupling of the nanopores to other pores and nanoscale fluidic elements, e.g., reactors, separators, and filters, in the same device is an important next step. One approach is monolithic fabrication of the fluidic elements in the plane of the substrate, but methods to generate pores with circular cross sections are needed to improve sensing performance with in-plane devices. Here, we report a fabrication method that directly patterns nanopores with circular cross sections in series and in plane with the substrate. A focused ion beam (FIB) instrument is used to mill a lamella in a nanochannel and, subsequently, bore a nanopore through the lamella. The diameter and geometry of the nanopore are controlled by the current and dose of the ion beam and by the tilt angle and thickness of the lamella. We fabricated devices with vertical and tilted lamellae and nanopores with diameters from 40 to 90 nm in cylindrical and conical geometries. To test device performance, we conducted resistive-pulse measurements of hepatitis B virus (HBV) capsids. Current pulses from T = 3 capsid (~31 nm diameter) and T = 4 capsid (~35 nm diameter) were well resolved and exhibited relative pulse amplitudes (Δi/i) up to 5 times higher than data obtained on nanopores with rectangular cross sections. For smaller pore diameters (≤ 45 nm), which approach the diameters of the capsids, a dramatic increase in the pulse amplitude was observed for both T = 3 and T = 4 capsids. Two and three pores fabricated in series further improved the resolution between the relative pulse amplitude distributions for the T = 3 and T = 4 capsids by up to 2-fold.

Graphical Abstract

Resistive-pulse sensing with solid-state nanopores provides direct, label-free, and real-time analysis of individual biomolecules.^1–4 Currently available nanofabrication techniques are able to easily tune the size, geometry, and surface properties of solid-state nanopores.^1,3,5–7 Methods to form nanopores in a range of substrate materials, e.g., Si, Si_xN_y, SiO₂, and polymers, include focused electron beam drilling,^8–10 focused ion beam (FIB) milling,^11–14 nanoimprint lithography,¹⁵ pipet pulling,^16–18 and controlled dielectric breakdown.^19–20 With the electron and ion beam and dielectric breakdown methods, nanopores are typically formed in a free-standing membrane and perpendicular to the substrate, i.e., out-of-plane. Considerable effort has been made to optimize these fabrication methods, which readily fabricate nanopores with diameters of single nanometers. However, in many cases, integration of these nanopores into a sensing platform with, for example, microfluidic chambers, requires precise alignment of the nanopores with other components.^14,21–24

An alternative approach is to design and pattern the micro- and nanofluidic channels in the plane of the substrate, which permits monolithic coupling of all fluidic components. These in-plane nanochannels and nanopores are usually a set of interconnected nanoscale trenches fabricated directly by FIB milling into glass substrates^25–27 or replication of nanoscale features into polymers.²⁸ With the in-plane architecture, multiple fluidic components, e.g., multiple pores in series,²⁹ can be easily combined in a single device without the need to align components after fabrication. In addition, these in-plane devices permit enhanced fluid control, lower sample consumption, coupling of multiple detection methods (e.g., electrical and optical), and improved mass transfer of analytes.^24,28,30 However, because in-plane nanopores are typically fabricated perpendicularly to the substrate surface, control over the pore size and geometry is limited, and the pores tend to have rectangular or U-shaped cross sections.^24,27,30

We report a method that combines the benefits of integration of in-plane features with geometric control of out-of-plane nanopores to fabricate in-plane, in-series nanopores with circular cross sections. To generate these circular nanopores, rectangular nanochannels were fabricated in segments with FIB milling into the glass substrate with standing vertical or tilted lamellae formed between each segment. The nanopores were then bored into the lamellae as a single spot. We explored the impact of the incidence angle and dose of the ion beam on the geometries of the lamellae and nanopores and of the thickness and angle of the lamella on the nanopore geometry. Pore diameter increased with ion beam dose, and pore diameter decreased with lamella thickness when milled at constant dose. Next, we tested the devices by conducting resistive-pulse measurements of hepatitis B virus (HBV) capsids that contained a fixed ratio of T = 3 capsids (~31 nm diameter) and T = 4 capsids (~35 nm diameter).^31–32 The resistive-pulse data exhibited up to a 5-fold improvement in relative pulse amplitudes (Δi/i where Δi is the pulse amplitude and i is the baseline current) when compared to nanopores with rectangular cross sections. We also observed up to a 2-fold improvement in measurement precision when three pores in series were used.

Results/Discussion

Fabrication of Nanopores in Vertical and Tilted Lamellae.

Fabrication of the nanofluidic devices (Figure 1) occurred in three steps: (1) wet chemical etching of microchannels into the glass substrate, (2) FIB milling of nanochannels with lamellae in the 10 μm gap between the microchannels, and (3) FIB milling of the nanopores into the lamellae. The glass substrates were coated with 30 nm Cr film to minimize charging during FIB milling and scanning electron microscope (SEM) imaging and to serve as an etch mask for wet-chemical etching. Figure 2a–b shows the fabrication schemes for forming nanopores with circular cross sections in vertical and tilted lamellae, respectively. For devices with vertical lamellae, the lamellae are milled with an incidence angle of the ion beam of 0° (∠beam = 0°), with the stage of the FIB instrument tilted at 54° (∠stage = 54°), and without rotation (∠rotate = 0°). (Note that the incidence angle of the focused ion beam is defined as the angle between the ion beam and surface normal.) After milling the lamellae, the nanopores are milled into the lamellae with an ion beam incidence angle of 36° from the same direction (∠beam = 36°, ∠stage = 0°, ∠rotate = 0°). For the devices with tilted lamellae, the lamellae are milled with an ion beam incidence angle of 26° (∠beam = 26°, ∠stage = 28°, ∠rotate = 0°). The substrate is then rotated 180°, and the nanopores are milled perpendicularly to the lamella surface (∠beam = 0°, ∠stage = −10°, ∠rotate = 180°).

Figure 1.

(a) Schematic of the glass nanofluidic device with two V-shaped microchannels connected by a nanochannel with multiple lamellae and nanopores in series. Hepatitis B virus (HBV) capsids in 1 M NaCl buffer solution are loaded into the sample reservoir and electrokinetically driven through the nanopore sensing region. (b)-(c) Schematics of the nanopores with circular cross sections milled in (b) vertical and (c) tilted lamellae. Nanopores are milled with an incidence angle of the ion beam of (b) 36° in the vertical lamellae and (c) 0° in the tilted lamellae.

Figure 2.

(a-b) Fabrication schemes of nanopore formation in (a) vertical and (b) tilted lamellae. The two types of the nanopores are fabricated by changing the tilt and rotation angles of the stage of the focused ion beam (FIB) instrument during lamella milling and nanopore drilling. (c)-(d) Scanning electron microscope (SEM) images of nanopores formed in (c) vertical and (d) tilted lamellae. Insets: enlarged images of the lamellae and nanopores. Scale bars are 1 μm. (e)-(f) SEM images of the entrance and exit of the nanopores in (e) vertical and (f) tilted lamellae. Nanopore diameters were measured at a 54° tilt angle. FIB sectioning permitted SEM imaging of the axial cross section of the nanopore axis in (e) vertical and (f) tilted lamellae. Scale bars are 200 nm. To minimize charging during FIB milling and SEM imaging, substrate surfaces are coated with a 30 nm Cr film (bright layer in panels (e) and (f). The nanochannels and nanopores are not coated with the Cr film.

SEM images of the nanochannels, lamellae, and nanopores fabricated in the nanofluidic devices are shown in Figure 2c–d. As discussed below, the nanopore diameter and geometry were dependent on incidence angle of the ion beam, lamella thickness, and ion beam dose. Any number of combinations of the tilt angles for the lamellae and nanopores can be used. However, the vertical and tilted lamellae described above represented the two basic configurations, in which the normal axis of the lamella was either parallel to the overall fluid flow (vertical lamella) or to the nanopore axis (tilted lamella).

To characterize the nanopores, we used SEM imaging to measure the entrance and exit pore diameters and visualize the axial cross section (Figure 2e–f). We used the conductive Cr film (30 nm, bright top layer) on the glass surface to minimize any issues with the substrate charging and lowered the e-beam energy to 10 keV to increase the contrast of the nanopore relative to the lamellae. As seen in the SEM images, the entrance and exit pores have circular cross sections for both the vertical and tilted lamellae. Although the pore diameters were measured at a 54° angle from the substrate surface, distortion of the measurement was minimized because the measurement was taken along the X-axis which ran parallel to the stage tilt axis (Figure S1). The SEM images of the pores were typically of higher resolution for the pore entrance than pore exit because the angle of the electron beam in the SEM is closer to the nanopore axis when imaged from the entrance pore side. We also used FIB sectioning to expose the axial cross section of the nanopores. As seen in Figure 2e–f, the pore geometry ranged from cylindrical to conical along their pore axes.

Dependence of Nanopore Geometry on Incidence Angle of the Ion Beam.

The SEM images in Figure 2e–f show that the nanopores fabricated in vertical and tilted lamellae have circular cross sections. However, if the lamella thickness was held constant at ~300 nm, nanopores milled into vertical lamella appeared more conical (Figure S2), whereas nanopores milled into tilted lamella are more cylindrical (Figure 2f). Because the two types of the pores differed by the incidence angle of the ion beam to the lamella surface (∠beam = 36° for vertical lamella and ∠beam = 0° for tilted lamella), we explored the angular dependence of the material sputtering and redeposition on the 3D morphology of the nanopore (Figure S3). On a planar glass substrate, a series of holes were milled with increasing incidence angle. As the incidence angle increased, the ion beam formed more elongated pores, and the pore geometry became more conical (Figure S3). For tilted lamella with the pore milled perpendicularly to the lamella surface, both side walls of the pore were nearly parallel to the incident ion beam (Figure 2f).

Dependence of Nanopore Geometry on Ion Beam Dose and Lamella Thickness.

To better control pore fabrication, we systematically studied the effects of lamella thickness (Figure 3a) and ion beam dose (Figure 3b) and compared the entrance pore diameter (Figure 4a) and exit-to-entrance diameter ratio (Figure 4b) in vertical and tilted lamellae. Figure 3a shows that at a constant ion beam dose (5 pC), the entrance pore diameter decreases with increasing lamella thickness, whereas Figure 3b shows that at a constant lamella thickness (70 nm), the entrance pore diameter increases with increasing ion beam dose. This trend of increasing pore diameter is also reflected in the decreasing electrical resistance of the pore (Figure 3). In Figure 4a, larger pore diameters at the entrance resulted at higher FIB dose and thinner lamellae. A two-stage pore growth process was observed in both lamellae where the nanopores expanded quickly at low FIB doses, then more slowly after a transition point, and gradually approached a linear growth rate.^33–34 We also found that this transition point occurred at a higher ion beam doses when the lamellae were thicker. In Figure 4b, smaller cone angles were observed at lower FIB doses in both lamellae, indicating pores with more significant conical shape. The exit-to-entrance ratio becomes relatively constant for different lamella thicknesses after the transition point.

Figure 3.

Variation of the entrance pore diameter and resistance of the nanopores with (a) lamella thickness and (b) ion beam dose for tilted lamellae. (a) With a constant ion beam dose of 5 pC, the nanopore diameter decreased with increasing lamella thickness. (b) For a constant lamella thickness of 70 nm, the nanopore diameter increased with increasing ion beam dose. Insets: SEM images of the nanopore entrance. Scale bars are 100 nm. To show general trends, data from fifteen two-pore devices with similar tilted lamella thicknesses and ion beam doses were grouped and averaged, and the error bars are the standard deviation for n ≥ 3 for lamella thicknesses, ion beam doses, nanopores, and resistance measurements.

Figure 4.

(a) Variation of the entrance diameter of the nanopores with ion beam dose (3 to 30 pC/point) and lamella thickness (230, 300, and 380 nm). (b) Variation of the exit-to-entrance diameter ratio of the nanopores under the same fabrication conditions as panel (a). Data were obtained from eleven test structures with the three lamella thicknesses and series of individual pores milled for each dose. To minimize distortion due to the tilt angle, the nanopore diameter was measured along the horizontal axis.

We observed a larger impact of the lamella thickness on nanopore size and shape for vertical lamellae. Figure 4a shows larger FIB doses were required to penetrate vertical lamellae (transition point: 8 to 20 pC/pt) with increasing thickness. The required dose for tilted lamella followed the same trend but to a much lesser extent. In Figure 4b, we observed the same delay of the transition point for vertical lamellae as thickness increased. Interestingly, we observed little dependence of lamella thickness on the cone angles of nanopores in tilted lamellae.

To explain pore expansion with FIB dose and lamella thickness, we start from the basic sputtering mechanism for sculpting pores. First, the general trend for pore diameters to increase with FIB dose in both types of lamellae is explained by the increasing sputtering yield.^35–36 The presence of the transition point can be explained by the two-stage pore expansion theory.³³ The nanopore diameter grows rapidly at lower doses due to the center of the ion beam interacting with the lamella. The pore diameter expands much more slowly after the nanopore reaches a diameter similar to the beam for which the wings of the Gaussian beam are responsible for most of the sputtering.

The thickness of the lamella determines the pore diameter and shape by affecting sputtering efficiency and redeposition yield. Thinner lamella can be approximated as a two-surface system during FIB sputtering where the material near both surfaces of the lamella are sputtered due to the collision cascade of the ion, thereby producing larger nanopores in thinner lamellae than in thicker lamellae at the same ion beam dose.³⁵ The enhanced sputtering in thinner lamellae was also observed by the more rapid pore expansion rate for nanopores on thinner lamellae.

The conical shape of the nanopores in vertical lamella resulted from the competition between angle dependent sputtering yield and redeposition rate.³⁶ Thinner lamellae have insignificant conical features because of the larger sputtering yield, which results from the larger incidence angle and two-surface system, which outcompetes the accumulation of the redeposited material. As the lamella thickness increases, the two-surface sputtering is no longer valid, and the shape of the pore is soon dominated by the significantly increasing redeposition flux. The total flux of the redeposition is a function of the emission angle of the sputtered material and its subsequent incidence angle for redeposition, which strongly depends on the nanopore geometry. For vertical lamellae, the accumulated redeposition from the previously sputtered material on the back of the pore wall, in turn, facilitates further redeposition due to the smaller incidence angle and short travel distance for the sputtered material to redeposit, therefore, enhancing the conical geometry of the nanopore. For tilted lamellae, the thickness dependence is much smaller because the angle of the incidence ion beam is less affected by redeposition inside the nanopore.

Resistive-Pulse Measurements.

Next, we demonstrated resistive-pulse sensing^37–40 with these in-plane circular nanopores. Figure 5 shows the current pulses from resistive-pulse measurements from five two-pore devices with tilted lamella and nanopore diameters of 40, 45, 55, 80, and 90 nm. We observed continuous passage of the T = 3 and T = 4 HBV capsids for all these pore diameters, and each capsid produced the expected pair of current pulses corresponding to the two pores in series. In Figure 5a, a direct comparison of the pulse amplitude is made which reveals the inverse relationship between the pore diameter and pulse amplitude, whereby the pulse amplitude increases with decreasing pore diameter. Current traces of raw data from devices with pore diameters of 40, 55, and 90 nm are enlarged in Figure 5b. For the two-pore devices with 55 and 90 nm pores, the two current pulses from pores 1 and 2 have very similar amplitudes. However, for two-pore devices with 40 nm pores, the current pulse at pore 1 was significantly larger than the current pulse at pore 2, which indicated that the T = 4 capsid fit more tightly in pore 1 than pore 2 although their nominal entrance pore diameters were similar. Histograms of the relative pulse amplitudes (Δi/i), where Δi is the pulse amplitude and i is the baseline current, are plotted for each pore diameter in Figure 5c. A 5-fold increase in the relative pulse amplitude was observed by decreasing the pore diameter from 90 nm to 45 nm. Even the largest diameter pore (90 nm) had sufficient sensitivity to resolve T = 3 and T = 4 capsids, which differ in diameter by only 4 nm.

Figure 5.

(a) Concatenated current pulses of T = 3 and T = 4 hepatitis B virus (HBV) capsids from two nanopores in series on tilted lamellae with entrance pore diameters of 40, 45, 55, 80, and 90 nm. Concatenation of the current pulses shows progressively increasing pulse amplitude (Δi) with decreasing pore diameter. (b) Current traces of raw data from three of these two-pore devices with large (90 nm), medium (55 nm), and small (40 nm) nanopore diameters. Pore 1 (p1), pore 2 (p2), pulse amplitude (Δi), and pore-to-pore time (t_pp) are indicated. (c) Histograms of the relative current pulse amplitude (Δi/i) for devices with entrance pore diameters of 40 , 45, 55, 80, and 90 nm. Relative pulse amplitude distributions are normalized to 1.0, and the color scheme of the distributions matches the pore diameters in panel (a). Data were obtained from five two-pore devices with tilted lamellae.

Because the T = 3 and T = 4 capsids are composed of the same dimer, their electrophoretic mobilities are very similar. Consequently, the two capsids are not easily resolved by their dwell times in the pores, i.e., the time that the capsid takes to pass through the pore. Figure 6 shows the average dwell time of the T = 3 and T = 4 capsids passing through pores with diameters of 40 and 45 nm. T = 4 capsids do exhibit some longer dwell times, due to the tighter fit of the capsid in the pore. However, the T = 3 and T = 4 capsids are not readily discriminated based solely on their dwell times.

Figure 6.

Variation of the relative pulse amplitude (Δi/i) with average dwell time for T = 3 and T = 4 HBV capsids passing through two nanopores in series on tilted lamellae. The two two-pore devices with tilted lamellae had average entrance pore diameters of 40 and 45 nm. The dwell time is the time a capsid takes to pass through the pore.

Figure 7 summarizes data taken from ten two-pore devices with tilted lamellae. Because the final lamella thickness varied from 110 nm to 160 nm from device to device due to minor variations in FIB milling conditions, we used the ion beam dose divided by lamella thickness to compare the data. The pore diameter increased with ion beam dose but decreased with lamella thickness when milled at a constant dose. After this normalization, the entrance pore diameter increased with dose/thickness (Figure 7a), and the measured pore resistance concurrently decreased with pore diameter. Figure 7d shows a series of SEM images of pores with entrance diameters of 40, 45, 55, 80, and 90 nm, which correspond to the range of pore diameters in Figure 7a. Also, the relative counts of the T = 3 and T = 4 capsids remained constant across all pore diameters (Figure 7c), which suggests that the larger T = 4 capsid was not entropically hindered from entering the pore compared to the T = 3 capsid.

Figure 7.

(a) Variation of entrance pore diameter (circles) and nanopore resistance (triangles) with ion beam dose/lamella thickness for two-pore devices with tilted lamella. Resistance was measured with 1 M NaCl. Ion beam dose divided by lamella thickness is used to normalize pore diameters across devices and lamella thicknesses. (b) Variation of the pulse amplitude ratio (Δi ratio) for T = 3 and T = 4 HBV capsids with ion beam dose/lamella thickness. (c) Variation of the fraction of T = 3 and T = 4 HBV capsids detected by resistive-pulse sensing with ion beam dose/lamella thickness. (d) SEM images of nanopores with entrance pore diameters of 40, 45, 55, 80, and 90 nm (left to right). Scale bar is 100 nm. Data were obtained from ten two-pore devices with tilted lamellae in panels (a) and (b) and nine two-pore devices with tilted lamellae in panel (c).

Figure 7b shows the Δi ratio for T = 3 to T = 4 capsids, which was ~0.7 for pore diameters ≥ 45 nm. In the simplest approximation, the Δi ratio of the T = 3 capsid (~31 nm in diameter) to T = 4 capsid (~35 nm in diameter) is proportional to the ratio of their volumes, which is 31³/35³ ≈ 0.7 based on the capsid diameters. For smaller pore diameters (< 45 nm), which approach the diameters of the capsids, a dramatic increase in the relative pulse amplitude (Δi/i, in Figure 5) was observed especially for the slightly larger T = 4 capsids, and the Δi ratio for T = 3 to T = 4 capsids decreased from ~0.7 to < 0.5. The marked increase in pulse amplitude for T = 4 capsids relative to T = 3 capsids resulted in the decrease in the Δi ratio. The same trends for the Δi ratio and signal-to-noise ratio are observed for two-pore devices with vertical lamella (Figure S4)

To better understand this transition in the Δi ratio, we compared the experimental results with the theoretical resistive-pulse values calculated with a semi-analytical model, which numerically solved the Laplace equation over the 3D geometry of the nanopore by simply considering the electric field change when non-conductive particles passed through cylindrical nanopores of different diameters (Figure S5). These models gave comparable resistive-pulse amplitudes to the experimental data for pore diameters ≥ 50 nm without taking into account either the surface charge or fluid flow within the pore.

The Δi ratio behavior in Figure 7b is similar to what was observed with single track-etched conical nanopores.⁴¹ For the track-etched nanopores, the pulse amplitude ratio for T = 3 and T = 4 capsids decreased from ~0.7 to 0.3 as the pore tip diameter of the conical pore decreased from 60 to 40 nm. The tighter fit of the larger T = 4 capsid resulted in a larger than expected relative pulse amplitude (Δi/i) for the T = 4 capsid compared to the Δi/i for the T = 3 capsid. For the circular nanopores reported here, a similar significant change in the Δi ratio occurred with pores having the smallest diameters (40 nm, Figure 7b), and a concurrent increase in the residence time of the T = 4 capsid in the pore was also observed for some of the measurements (Figure 6).

Figure 8 shows how the relative pulse amplitude (Δi/i) and signal-to-noise ratio increased with decreasing pore diameter, because the fraction of the capsid volume relative to the pore volume increased with decreasing pore diameter. For a given pore diameter, e.g., 40, 45, 55, 80 or 90 nm, the relative pulse amplitude does not change with the electric field strength because both the pulse amplitude and baseline current scale proportionally with the field strength. The signal-to-noise ratio, however, increases nonlinearly with an increasing field strength.

Figure 8.

Variation of the (a) relative pulse amplitude (Δi/i) and (b) signal-to-noise ratio for T = 3 and T = 4 HBV capsids (squares) with ion beam dose/lamella thickness for two-pore devices with tilted lamella. For reference, panel (a) includes the entrance pore diameter (circles). Ion beam dose divided by lamella thickness is used to normalize pore diameters across devices and lamella thicknesses. Data were obtained from nine two-pore devices with tilted lamellae.

From the compiled data in Figure 8a, we observed a systematically larger Δi/i for resistive-pulse measurements on nanopores with circular cross sections than on nanopores with rectangular cross sections with comparable lateral dimensions.²⁶ The increase in relative pulse amplitude for nanopores having similar critical dimensions, e.g., pore diameter or pore depth and width, can be attributed to minimizing the cross section of the pore that is inaccessible to the particle being measured. In the case of pores with rectangular or U-shaped cross sections, the corners of the pore are inaccessible to an HBV capsid with an icosahedral geometry, whereas for the pores with circular cross sections, the capsid can access the entire cross section. As an example, the Δi/i for a rectangular nanopore (45 nm wide x 45 nm deep) was 0.39% and 0.56% for T = 3 and T = 4 capsids, respectively.²⁶ For the 45 nm diameter pores reported here, the Δi/i was 1.9% and 2.7% for the T = 3 and T = 4 capsids, respectively, which is a 4.9-fold increase in Δi/i for both capsids compared to the rectangular pore. For the smaller pores with a 40 nm diameter, the increase in Δi/i is even greater. The Δi/i was 3.0% and 6.7% for T = 3 and T = 4 capsids, respectively, but a direct comparison with a rectangular nanopore (40 nm wide x 40 nm deep) is not possible, because those pores do not readily pass the T = 4 capsid, most likely because the cross section is more U-shaped from the top-down milling.

Increased Resolution with Multiple Nanopores in Series.

An advantage of the in-plane architecture is the ability to fabricate multiple pores in series to improve the precision of resistive-pulse measurements.^26,29 Here, we demonstrated a similar experiment with the circular nanopores by comparing the resolution (R_s) of relative pulse amplitude distributions for T = 3 and T = 4 capsids on devices with two and three pores in series.

$$R_s=\frac{{\overline{\mathrm{\Delta }i/i}}_{T=4}-{\overline{\mathrm{\Delta }i/i}}_{T=3}}{2({\sigma }_{T=4}+{\sigma }_{T=3})}$$

where $\overline{\mathrm{\Delta }i/i}$ is the peak center in the Δi/i distributions for T = 3 and T = 4 capsids, and σ is the corresponding standard deviation. Figure 9 shows the resolution increased with increasing relative pulse amplitude for both two- and three-pore devices. This relationship also held for devices with atypically large pulse amplitudes (i.e., measurements with pore diameters < 45 nm). For two-pore measurements, the resolution improved 1 to 1.5-fold, and for three-pore measurements, the resolution improved 1.5 to 2-fold, which is expected for three independent measurements, 3^0.5 ≈ 2.

Figure 9.

Variation of the resolution between the relative pulse amplitude distributions for T = 3 and T = 4 capsids with average pulse amplitude (Δi/i) for T = 3 and T = 4 capsids. Resistive-pulse measurements were made with (a) seven two-pore devices with tilted lamellae and (b) five three-pore devices with tilted lamellae.

Nanofluidic device designs with multiple pores in series have several benefits. With two or more pores in series, two or more independent measurements of each capsid are made and averaged, which improves the precision of the particle-size measurement compared to a single measurement.^26,29 Additional pores in series (e.g., up to eight pores in series²⁹) further narrows the particle-size distribution, but the overall resistance of the nanopore region increases and leads to lower pulse amplitudes (Δi) and poorer limits of detection. Multi-pulse sequences also provide a current pulse pattern during translocation for each particle that is easily recognized through data analysis and minimizes counting of non-resistive-pulse events. Measurement precision can be further improved by conducting multicycle measurements across multiple nanopores.⁴²

Conclusions

We have developed a method to fabricate nanopores with circular cross sections in series and with an in-plane format. Vertical and tilted lamellae were formed while milling the nanochannels, and circular nanopores were subsequently milled through the lamellae. The nanopore diameters increased with ion beam dose and decreased with increasing lamella thickness at constant dose. For the resistive-pulse measurements of the HBV capsids, we observed up to 5-fold increase in the relative pulse amplitude compared to measurements with pores with rectangular cross sections, because the icosahedral shape of the capsids matched closely the circular pore geometry. In addition to the increased sensitivity, having multiple pores in series increases measurement precision. We anticipate this fabrication method can be applied to a range of single molecule measurements that require a higher signal-to-noise ratio and increased resolution among sample components.

An additional benefit of the in-plane format is any arbitrary two-dimensional architecture can be designed and fabricated. Consequently, integrated fluidic channels, such as tee and cross intersections, can be easily coupled with the nanopores and make possible the manipulation of fluid volumes on scales compatible with the nanopores. Examples of coupled fluidic elements include filters to remove aggregates, reaction chambers to conduct single particle reactions, and channels to separate individual particles or precisely measure physical properties of particles, e.g., electrophoretic mobility and surface charge. Moreover, because these in-plane devices are fabricated on glass substrates, simultaneous electrical and optical measurements are able to probe, for example, virus inactivation with femtosecond laser radiation.⁴³

Methods/Experimental

Device Fabrication.

Fabrication of the nanofluidic devices occurred in three steps: (1) wet chemical etching of microchannels into the substrate, (2) FIB milling of the nanochannels with lamellae in the 10-μm gap between the microchannels, and (3) FIB milling of the nanopores into the lamellae. For the data reported, we fabricated fifteen substrates with various test structures to evaluate ion beam milling parameters of the lamella and nanopores and for cross section analysis of the nanopores. We report data collected from 25 two-pore devices with tilted lamellae, five three-pore devices with tilted lamella, and eight two-pore devices with vertical lamella. The success rates for these devices were >90% for milling the nanopores of the desired diameters, for successfully bonding cover plates to the devices, and for measuring current through the nanopores. Similarly, successful translocation of T = 3 and T = 4 capsids through the nanopores was > 90% for nanopores with diameters ≥ 45 nm but dropped to 30% for nanopores with diameters < 45 nm because the T = 4 capsid (35 nm diameter) fit more tightly in the pores and clogged them more easily. We estimate the error of the SEM measurements of the entrance pore diameters to be ± 2 nm. Therefore, we report the nanopore diameters as their nominal values of 40, 45, 55, 80, and 90 nm. For characterization of the devices, e.g., current measurements and resistive-pulse sensing, the data are measured independently of the pore diameters and are reported with higher precision.

Microchannel Fabrication.

In the first step, two V-shaped microchannels were patterned on D263 borosilicate glass substrates by standard photolithography and wet-chemical etching.²⁶ D263 substrates were coated with a 30 nm Cr film by thermal evaporation (BOC Edwards Auto 306), spin coated with photoresist (S1813 G2, Kayaku Advanced Materials, Inc.), and exposed through the photomask (HTA Photomask). After photoresist development (MF-319, Kayaku Advanced Materials, Inc.), the Cr film and glass substrate were sequentially etched in Cr etchant (8002-A, Transene Co., Inc.) and buffer oxide etchant (BOE, Transene Co., Inc.). After etching, the photoresist was stripped with acetone, but the remaining Cr film was left intact on the substrate for FIB milling and SEM imaging to reduce charging.

Nanochannel, Lamella, and Nanopore Fabrication.

Subsequently, the nanochannels, lamellae, and nanopores were milled into the 10-μm gap between the two microchannels with the FIB instrument (Auriga 60, Carl Zeiss, Inc.) through the Cr film (30 nm). The FIB milling parameters (e.g., pattern, ion beam dose, scanning strategy, stage tilt, and rotation angle) were controlled by the Nanopatterning and Visualization Engine (NPVE) software (FIBICS, Inc.). Specific parameters for fabricating the nanochannels, lamellae, and nanopores are detailed in the Results and Discussion. The vertical and tilted lamellae were formed while the nanochannels were being milled by the FIB instrument in the gap between the microchannels. To fabricate the tilted lamellae, a linear dose gradient was required to pattern the nanochannels to avoid formation of oblique bottoms resulting from accumulated redeposition of material opposite the incident beam. For the tilted lamellae, the 3D Profiler function in the NPVE software was used to apply about 65% of the maximum dose away from the lamella and to increase continuously the dose to 100% along the nanochannel to compensate for the reduced sputtering yield near the lamellae. Next, the tilt and rotation angle of the stage were adjusted to mill the nanopores into the lamellae with the ion beam. A 30 keV Ga⁺ beam with currents from 2 pA to 20 pA and doses from 2 pC/point to 30 pC/point was used to mill the nanochannels, lamellae, and nanopores.

Device Characterization.

After FIB milling, the nanopores were characterized with the SEM. The length of the nanopore was obtained from the thickness of lamella from the top-view of the device. Two methods were used to determine the 3D structure of the nanopore (Figure 2e–f): (1) direct measurement of the nanopore diameters corresponding to the entrance and exit of the ion beam from the two sides of the lamella and (2) exposing the axial cross section of the nanopore by sectioning with the FIB and imaging with the SEM. In the first method, SEM images of the nanopore were obtained at a tilt angle of 54°. To minimize the distortion errors, the diameter parallel to the tilt axis are reported (Figure S1). Rotation of the substrate by 180° allowed the same measurement for the exit pore diameter. The second method directly visualizes the axial geometry of the nanopore which is otherwise buried inside the glass substrate. Note that this method is destructive, and devices cannot be used after sectioning. If not indicated specifically, pore diameters are reported for the entrance pore by the first method.

Device Bonding.

To bond a cover plate to the substrate, the Cr film on the substrate was removed with a ceric ammonium nitrate/nitric acid etchant (1020, Transene Co., Inc.). The glass substrate and #1.5 cover glass were thoroughly cleaned and then hydrolyzed in 0.1 M of NaOH at room temperature with 10 min of sonication. Afterwards, the device and cover glass were sonicated in water to remove residual salt on the surface, dried with a stream of nitrogen, and brought into contact with each other. The initially bonded device was further dried at 90 °C overnight and permanently annealed in a furnace at 545 °C for 10 h.

Sample Preparation.

HBV capsids were assembled from the core protein dimers (Cp149, 34 kDa) expressed in E. coli and purified.⁴⁴ Dimer was assembled by addition of NaCl to 0.5 M and incubating overnight, and the resulting mixture of T = 3 and T = 4 capsids were purified on a 10% – 40% (w/v) continuous sucrose gradient in 50 mM HEPES (pH 7.5) with 0.3 M NaCl that was centrifuged at 150,000 g for 6 h. The upper particle band (T = 3 capsids) and the lower particle band (T = 4 capsids) were extracted and dialyzed into 50 mM HEPES (pH 7.5) with 1 M NaCl and concentrated to 0.2–0.3 mg/mL. The capsid solutions were diluted in 1 M NaCl to a final dimer concentration of ~0.1 μM prior to sample loading.

Resistive-Pulse Measurements.

After sample was loaded into the sample reservoir (Figure 1), an Axopatch 200B current amplifier (Molecular Devices, Inc.) was used to apply a potential with Ag/AgCl electrodes between the sample and waste reservoirs to drive the sample electrokinetically through the nanochannels and nanopores (Figure 1a). The amplifier also measured the current during the sample translocation with a sampling frequency of 40 kHz and low-pass filter frequency of 10 kHz. All electrical measurements were conducted inside a Faraday cage covered with acoustic wedge foam.

Current vs. time data were imported into MATLAB (Mathworks, Inc.) and analyzed for current pulses. A modified version of OpenNanopore program⁴⁵ was used to detect the pulses above the adaptive threshold (4.25σ) from the local average baseline current (i) and determine the pulse amplitude (Δi) and dwell time (w) for each event. Next, the time duration between each pulse pair was tabulated and plotted on a log scale from which the distributions of the pore-to-pore times (t_pp) from single capsids and uncorrelated events were differentiated. A Gaussian function was fitted to the log(t_pp) distribution, and a cutoff of ±2.5σ from the fit was used as a selection criterion to ensure pulse sequences were from the same capsid. This selection method, combined with the number of nanopores in the device, grouped the resistive pulses into separate events for further analysis. To assess each device, the Δi/i values for each capsid were averaged and compiled in a histogram. Gaussian functions were fitted to the Δi/i distributions to determine the mean, standard deviation, and relative amounts of T = 3 and T = 4 capsids.