Assessment of 1/f noise associated with nanopores fabricated through chemically tuned controlled dielectric breakdown

Abstract

Recently, we developed a fabrication method—chemically-tuned controlled dielectric breakdown (CT-CDB)—that produces nanopores (through thin silicon nitride membranes) surpassing legacy drawbacks associated with solid-state nanopores (SSNs). However, the noise characteristics of CT-CDB nanopores are largely unexplored. In this work, we investigated the 1/f noise of CT-CDB nanopores of varying solution pH, electrolyte type, electrolyte concentration, applied voltage, and pore diameter. Our findings indicate that the bulk Hooge parameter (α_s) is about an order of magnitude greater than SSNs fabricated by transmission electron microscopy (TEM) while the surface Hooge parameter (α_b) is ~3 order magnitude greater. Theα_s of CT-CDB nanopores was ~5 orders of magnitude greater than theirα_b, which suggests that the surface contribution plays a dominant role in 1/f noise. Experiments with DNA exhibited increasing capture rates with pH up to pH ~8 followed by a drop at pH ~9 perhaps due to the onset of electroosmotic force acting against the electrophoretic force. The1/f noise was also measured for several electrolytes and LiCl was found to outperform NaCl, KCl, RbCl, and CsCl. The 1/f noise was found to increase with the increasing electrolyte concentration and pore diameter. Taken together, the findings of this work suggest the pH approximate 7–8 range to be optimal for DNA sensing with CT-CDB nanopores.

1. Introduction

A nanopore sensing device, in its simplest definition, is a nanoscale aperture spanning an impervious biological or solid-state membrane. The analyte is added to one side (typically the cis side) and driven through the nanopore in response to a voltage bias applied to the other side (trans side). When the analyte translocates through the membrane, it causes a perturbation in the open-pore current (i.e., resistive pulses or events) stamping information characteristic of the analyte [1]. The reach of nanopore applications is extensive and has been utilized to analyze small molecules [2-6], bioparticles [7-11], nanoparticles [12], and polymers [13]. Biological nanopores, despite being available on a limited size range, offer better signal resolution because of their low-noise characteristics. High noise is an inherent problem that has hampered the progress of solid-state nanopores (SSNs) while its origin may partly arise from the fabrication and characterization conditions [14,15]. This (high noise) has restricted SSNs from competing with their biological counterparts especially in sequencing efforts for which the noise level should be 5 × smaller than 1% of the open-pore ionic current [16]. Specifically, the low noise associated with biological nanopores has paved the way to study ionic current modulations arising from molecular and ionic transport whereas such efforts are challenging with SSNs. Membrane type, operational chemistry (e.g., electrolyte type, concentration, and pH), instrumentation (e.g., low-pass filter setting), and temperature significantly govern the noise associated with SSNs. Chemical, physical, and electronic approaches have been proposed and adopted with varying degrees of success to counter the inherent noise of SSNs. For example, surface passivation by atomic layer deposition (ALD) of homogenously layered thin films of material [14], using ionic liquids to minimize fluctuations in the local electrolyte conductivity [17], polydimethylsiloxane (PDMS) coating to reduce the dielectric noise of nanopore chips [18], piranha treatment to reduce flicker noise [18], complementary metal-oxide semiconductor (CMOS) integrated nanopore platforms [19], and use of materials with lower loss factors [20] are among the key strategies explored to reduce noise in SSNs.

The noise associated with nanopores could be segmented into four frequency regions: (i) 1/ f type noise (S_f), (ii) white noise (S_w, shot and thermal noise which is also frequency-independent), (iii) dielectric noise (S_d), and (iv) amplifier noise (S_a) [21]. In the case of silicon nitride (Si_xN_y)—the ubiquitous choice of nanopore membrane material—the noise is dictated by dielectric and low-frequency noise (1/ f type) [18]. Although the exact origin of 1/ f noise is uncertain, several mechanisms have been proposed over the years [22-24]. More importantly, the 1/f noise captures the contributions from the bulk, surface, and access conductance which are inextricably linked with physical (e.g., shape and size) and chemical (e.g., pK) parameters of the nanopore [21,25-27]. The white noise is thought to be comprised of thermal and shot noise and can be expressed as, S_w = S_thermal + S_shot = 4KTG + 2Ie where K, T, G, I, and e are the Boltzmann constant, temperature, open-pore conductance, ionic current, and elementary charge, respectively [21]. Looking at the expression for S_w, it can be inferred that, for example, decreasing the pore diameter and increasing the pore length (both would decrease G) will reduce overall white noise. However, care should be taken as the former would encourage irreversible pore clogging from the analyte (or it could prevent the entry of the analyte if the pore size was too small). The dielectric noise could originate from the thermal fluctuation of the leakage current and can be expressed as, S_d = 8π KTDC_chipf, where D and C_chip are dielectric constant and membrane capacitance. It is clear that S_d can be reduced by manipulating C_chip and D. Coating the chip with an insulating material (e.g., PDMS) would reduce C_chip. Additionally, use of a material with a low loss factor, such as quartz [20], would reduce S_d as well—unlike Si_xN_y which suffers from high loss factor of Si leading to higher S_d.

A host of methods are available for SSN fabrication [28-32], and in this work, we used nanopores fabricated through chemically-tuned controlled dielectric breakdown (CT-CDB) and assessed their 1/ f noise for different electrolyte types (LiCl, NaCl, KCl, RbCl, and CsCl) in a range of electrolyte concentrations (0.5–4 M), pH values (2–12), applied voltages (25–200 mV), and pore diameters (~6–~32 nm). The CT-CDB nanopores have been shown to outperform their CDB counterpart in both sensitivity and stability aspects [33]. The noise characteristics of CT-CDB nanopores have not been investigated yet. Given the advantages that the CDB process carries (e.g., low-cost overhead, time efficiency, and solution-based fabrication), coupled with the improvements offered by CT-CDB (e.g., excellent baseline stability over several hours, less prone to analyte clogging, and higher responsiveness to negatively charged analytes such as DNA and proteins), it is imperative to assess the noise properties of CT-CDB nanopores to lay the groundwork for further improvement of their sensing capabilities.

2. Materials and methods

2.1. Nanopore fabrication

All nanopores were fabricated through nominally ~12 nm thick silicon nitride (Si_xN_y) purchased from Norcada Inc. (NBPX5001Z-HR). To minimize device-to-device variations that may arise because of the membrane fabrication process, we used devices from the same batch (lot number L04079-02) supplied from Norcada Inc. In brief, both cis and trans side reservoirs were filled with a blend of 2:9 sodium hypochlorite (425 044, Sigma–Aldrich): 1 M KCl (P9333, Sigma–Aldrich) buffered at pH ~7 using 10 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES, Sigma–Aldrich, H0527) [33]. An electric field <1 V/nm was applied until a rapid surge in the leakage current was observed, which indicated pore formation. Then controlled voltage pulses were applied until the pore size of interest was reached.

2.2. Nanopore size estimation

After the pore formation, the content in the flow cells was exchanged with the electrolyte of interest (e.g., 1 M KCl buffered at pH ~7). The diameter of the pore was estimated from the slope (i.e., open-pore conductance, G) of a current-voltage curve (I-V) using the following conductance model,

$$\begin{gathered} G={\left(\frac{1}{G_{\text{bulk}}+G_{\text{surface}}}+\frac{1}{G_{\text{access}}}\right)}^{-1} \\ =K{\left(\frac{1}{\frac{\pi r_0^2}{L}+\frac{\mu \mid \sigma \mid }{K}\cdot \frac{2\pi r_0}{L}}+\frac{2}{\alpha \cdot 2r_0+\beta \cdot \frac{\mu \mid \sigma \mid }{K}}\right)}^{-1}, \end{gathered}$$ (1)

where G, r₀, L, K, σ, μ, α, and β are the open pore conductance, nanopore radius, membrane thickness, electrolyte conductivity, nanopore surface charge density, mobility of counter-ions proximal to the surface, and model-dependent parameters (both parameters were set to 2), respectively [33,34]. Nanopores are available in a wide variety of shapes and a cylindrical geometry was assumed for Eq. (1) [35-37]. The σ of Eq. (1) can be approximated as,

$$\mid \sigma \mid \cong \frac{C_{\text{eff}}}{{\beta }_{T}e}W\left(\frac{{\beta }_{T}e}{C_{\text{eff}}}\text{exp}((pH-pK)\text{ln}(10)+\text{ln}(e\Gamma ))\right),$$ (2)

where e, Γ, β_T, C_eff, and W are the elementary charge, number of surface chargeable groups, the inverse of the thermal energy, effective Stern layer capacitance, and Lambert W function, respectively [38].

2.3. Electrolyte and DNA preparation

All electrolytes were prepared (purchased through Sigma–Aldrich) by dissolving the as-supplied salts LiCl (213 233), NaCl (S5886), KCl (P9333), RbCl (R2252), and CsCl (289 329)) in >18 MΩ cm resistivity ultra-pure water (ARS-102 Aries high purity water systems). All electrolytes were buffered using 10 mM Tris buffer (J61036, Fisher Scientific). Electrolytes were then filtered using 0.22 μm vacuum filter units (Millipore Sigma Stericup, S2GPU05RE) and the pH was adjusted by adding concentrated drops of HCl (H1758, Sigma–Aldrich) and/or KOH (306 568, Sigma–Aldrich). Both pH and conductivity were measured using an Orion Star pH meter.

Double-stranded DNA (dsDNA, 1kb) was purchased from Fisher Scientific (10787 018). The dsDNA was added to the cis side to a final concentration of ~17 ng/μL. All experiments were done using 4 M LiCl buffered using 10 mM tris buffer, +200 mV of applied voltage, 100 kHz low pass filtering, and 250 kHz sampling frequency.

2.4. Electrical measurements

All measurements were done using Ag/AgCl electrodes using the voltage-clamp mode of the Axopatch 200B low-noise amplifier (Molecular Devices LLC). Signals were acquired at 250 kHz and filtered at 10 kHz using the Bessel filter of the Axopatch system. The signal was digitized either using a PCIe-6321 connected to a BNC 2110 (National Instruments) for I-V measurements (Axopatch controlled through custom-coded Labview scripts), or Digidata 1440A (Molecular Devices LLC) for power spectral density (PSD) and DNA sensing experiments.

2.5. Power spectral density (PSD) measurements

Each nanopore was equilibrated in the experimental electrolyte solution for at least 15 min after which the open-pore current was acquired at 50 mV (unless otherwise mentioned) for at least ~60 s. Representative 2 s current traces (500 000 current points) were then fast-Fourier-transformed using the fft function of MATLAB (R2018a) to compute the PSD curve. On average, a minimum of three traces of the 60 s trace were used for statistical analysis. The fitting of the low-frequency range of the PSD is outlined in the Supporting Information Section 2 and Section 2.6 of the main text.

2.6. Fitting the low noise component of power spectral density (PSD)

Since the solution chemistry metrics used in this study (pH, electrolyte type, and concentration) are reflected through the low-frequency noise regime of the PSD spectra, high frequency S_d and S_a noise components were discounted from the analysis. The work of Fragasso et al. proposed a model comprising of S_w, S_f, and a Lorentzian shape noise component to fit the low-frequency noise range [25]. The latter (i.e., Lorentzian shape noise) was noted to be more conspicuous in smaller diameter nanopores while mainly serving as a fitting parameter and not being inherently present in all nanopores. The magnitude of the 1/ f component has been found to obey Hooge’s phenomenological relation and was quantified using,

$$S_f=\frac{\alpha }{N_c}\cdot \frac{I^2}{f},$$ (3)

where α, N_c, I, and f are the Hooge parameter, total charge carriers, averaged current, and frequency, respectively [26,27]. Having low 1/ f noise characteristics is essential to maintain a lower I_rms (root mean square current) at bandwidths where biomolecule translocation experiments operate [14,18]. Other formulations for S_f have been proposed which capture surface, access, and geometric contributions of the pore [25]. In this study, the low frequency noise was fitted using,

$$S_{low,f}=S_w+\frac{\mathrm{A}}{f},$$ (4)

where A is a constant that captures contributions from the bulk, surface, and access resistance components of the nanopore as outlined later in Eq. (5). Each PSD was fitted using Eq. (4) and the 1/ f noise at 1 Hz (S_{1/ f,1Hz}) was extracted for comparison purposes (see Supporting information Section 2 for fitting details). Since a fit is less susceptible to point variations, we resorted to the fit value rather than taking the raw PSD value corresponding to the frequency of interest. We used approximately ~11 nm diameter pores (unless otherwise mentioned) and measured the open-pore current at 10 kHz low-pass filtering with buffered electrolyte to construct PSDs.

Equation (1) can be segmented into three resistance regimes: cylindrical $\left(\frac{1}{K\frac{\pi r_0^2}{L}}\right)$, surface $\left(\frac{1}{\mu \mid \sigma \mid \cdot \frac{2\pi r_0}{L}}\right)$, and access $\left(\frac{2}{K\cdot \alpha \cdot 2r_0+\beta \cdot \mu \mid \sigma \mid }\right)$. Both cylindrical (R_cyl) and surface (R_surface) resistances are parallel to each other and the access (R_access) resistance is in series to the resultant of R_cyl and R_surface (R_pore = R_cyl //R_surface with “//” indicating the resistors are parallel to each other). Thus, the total ionic resistance (R_total) of the pore become R_pore+R_access. Using these definitions, the 1/ f noise can be expressed as,

$$S_{1∕f}=\frac{V^2}{f{R}_{total}^4}\left[\frac{{\alpha }_b{R}_{access}^2}{N_{access}}+\frac{{\alpha }_b{R}_{pore}^4}{R_{cyl}^2{N}_{cyl}}+\frac{{\alpha }_s{R}_{pore}^4}{R_{surface}^2{N}_{surface}}\right],$$ (5)

where V, N_x, α_b and α_s are applied voltage, number of charge carriers corresponding to each ionic resistor component, and Hooge parameter for the bulk and surface 1/ f noise, respectively [25]. The σ associated with R_surface and R_access can be calculated using Eq. (2). Alternatively, streaming potential [39] and surveying the open-pore conductance with electrolyte concentration [40] are also used in literature for the estimation of σ. Two different Hooge parameters are used because the noise arising from the bulk and surface resistors of the nanopore are different [25]. The definitions of N_x are provided in the Supporting information Section 1. Using the definitions provided in the Supporting information Section 1 and Eq. (2), a plot of S_{1/ f} with solution pH can be fitted with Eq. (5) (Fig. 1B) while having α_b, α_s, pK, and C_eff as free parameters. The L was set to the nominal membrane thickness (12 nm).

Figure 1.

(A) The power spectral density (PSD) curves corresponding to solution pH ~2, ~4, ~6, ~8, ~10, and ~12, (B) $\frac{1}{f}$ noise at 1 Hz (S_1/f,1Hz) as a function of solution pH with the solid line being a fit made using Eq. (5).(C) Open-pore conductance as a function of the solution pH with the solid line being a fit made using Eqs. (1) and (2). All experiments were conducted using 0.5 M LiCl at +50 mV applied voltage, 10 kHz low-pass filtering, and 250 kHz sampling rate. See Supporting information Fig. S1 for fit-lines corresponding to Eq. (4) which shows S_w and A/f components at each pH for PSD shown in Fig. 1A.

3. Results and discussion

3.1. Noise characteristics with pH

The proton exchange model is widely used as an explanation for the pH-dependent noise which can be expressed in a more general way as,

$${\chi }^{-}+H^{+}\rightleftharpoons \chi H,$$ (Equilibrium 1)

where χ⁻ and χ H are the deprotonated and protonated states of the surface head groups governed by an equilibrium constant pK (defined as the logarithmic ratio of the protonation (K_p) and deprotonation (K_D) rate constants). The pH-G surveying (of CT-CDB nanopores) contradicts the amphoteric Si_xN_y surface behavior and points to an acidic-head group rich surface chemistry. It is still unclear as to what chemical species play a vital role in the surface chemistry of CT-CDB nanopores. Thus, to account for this ambiguity, we used the symbol χ as a generalization method. The surface pK, which is consequently different from the bulk value due to steric effects [41], can be calculated by, for example, surveying the open-pore conductance (obtained from Eq. (1)), or noise (obtained from Eq. (5)) with pH [33,38,42]. The knowledge of pK is important for biomolecule translocation experiments as it would govern the surface-charge density (of the pore surface) at a given solution pH and thereby the electroosmotic force (EOF) acting on the molecule, which could be opposing or reinforcing the electrophoretic force (EPF). Additionally, the position of Equilibrium 1, which is inextricably linked with the pK (and solution chemistry), would influence the low-frequency noise level of the device (explained later in Section 3.3). Thus, the knowledge of pK allows one to strike a balance between the forces acting on the molecule (i.e., EOF and EPF) and the noise associated with the device which will be discussed subsequently.

To calculate the pK using noise characteristics, the 1/ f noise at 1 Hz (S_{1/ f,1Hz}) was plotted against solution pH as seen in Fig. 1B (see Fitting Low Noise Component of Power Spectral Density (PSD) under Materials and Methods for noise calculation details). For this, the PSD shown in figure 1A were fitted with Eq. (4) (see Supporting information Section 2 for fitting details) to extract S_{1/f, 1Hz} at each solution pH. The S_w did not show an appreciable change with pH as seen in Supporting information Fig. S2. The averaged value of S_w across the pH range (from 2 unique nanopores) was found to be 4.4 × 10⁻³ ± 1.7 × 10⁻³ pA²/Hz, which is comparable (in the same order of magnitude) with that reported for TEM-based nanopores [25]. The pH dependent_{1/f, 1Hz} data shown in Fig. 1B were then fitted with Eq. (5). From the fit of Fig. 1B (using three unique nanopores), the pK, α_b and α_s were found to be ~10.8 ± 0.1, ~3.4 × 10⁻⁵ ± 2.7 × 10⁻⁵ and, ~1.2 ± 0.2, respectively. The pK is about 1 unit greater than the pK obtained for CT-CDB previously [33]. The higher standard deviation associated with α_b is due to one of the pores having a considerably low value compared to the rest (i.e., α_b~0.3 × 10⁻⁶). If α_b from that pore is disregarded, the final α_b would become ~4.9 × 10⁻⁵ ± 1.1 × 10⁻⁵. The α_s is ~5 orders of magnitude greater than α_b, which suggests the 1/ f noise arising from the surface contributions is greater than that arising from the bulk contributions. The higher contribution of the surface Hooge parameter compared to its bulk counterpart has been reported before both in SSNs and semiconductor devices [25,43]. As seen in Fig. 1B, the noise is nearly plateaued up to pH ~8 and then starts to rise rapidly with increasing pH. This behavior is inextricably linked with the pH-G pattern shown in Fig. 1C where G starts to rise with pH at higher pH values. This can be attributed to the onset of the deprotonation of surface head groups as shown previously [33,38]. Thus, as the pH is increased, the surface contribution to the overall noise of the device increases. The α_b reported herein is about an order of magnitude greater than that reported for TEM-based SSNs while the α_s of CT-CDB nanopores is ~3 orders magnitude greater than the previously reported α_s for TEM-based SSNs [25,44]. Although CT-CDB nanopores offer capabilities that justify its adoption for measurements at physiological pH values (and below)—less prone to clogging, higher sensitivity to a negatively charged analyte, excellent temporal open-pore stability among others [33]—its noise performance starts to decay rapidly at higher pH values. Since most translocation experiments with nanopores are carried out at pH ≤8, we do not see this as a detrimental limitation hindering the advancement of CT-CDB nanopores. Looking at Eqs. (1), (2), and (5), when σ approaches zero (i.e., σ → 0), R_surface → ∞ and R_pore and R_access reduces to R_cyl and $\frac{1}{K\cdot \alpha \cdot r_0}$, respectively. Thus, Eq. 5 reduces to

$$S_{f,\sigma \to 0}=\frac{V^2}{f{R}_{total}^4}\left[\frac{{\alpha }_b{R}_{access}^2}{N_{access}}+\frac{{\alpha }_b{R}_{pore}^2}{R_{cyl}^2{N}_{cyl}}\right],$$ (6)

where R_total of Eq. (6) is the linear addition of R_cyl and R_access. Equation (6), unlike Eq. (5), is pH independent and solely depends on the geometric parameters of the nanopore. Thus, the condition outlined in Eq. (6) would be satisfied in the plateaued region of Fig. 1B (i.e., pH <~8). As an auxiliary method of estimating the pK, the open-pore conductance was plotted against the operational pH as shown in Fig. 1C. The open-pore conductance was then fitted using Eqs. (1) and (2), and the pK was found to be ~10.6 ± 0.3 (in close agreement with the pK obtained from the fit of Fig. 1B. While fitting, Γ, C_eff, pK, and r₀ were set as free parameters, whereas L was set to 12 nm, the nominal membrane thickness). This is about ~0.8 units (of pK) higher than previously reported values [33]. However, the upper error limit of the previously reported value and the lower error limit of the value reported herein are mere ~0.4 pK units apart. Although we used the same nanopore device product (from Norcada Inc.) in the two studies, they came from two different production batches. Thus, any surface composition difference that arises during the wafer fabrication process (or any other workflow step that influence the elemental/stoichiometric composition of the device) would be reflected in the pKwe obtained through the fit of Fig. 1C. However, for pore performance and size estimation, the useful pH is typically ≤8 where the surface parameters play a negligible contribution to the overall conductance (i.e., σ~0).

3.2. DNA Response with solution pH

Although the 1/ f noise did not appreciably change up to pH ~8, it is important to strike a balance between analyte responsiveness and solution pH. For example, the isoelectric point (pI) of DNA (although base-pair composition-dependent) is generally around ~5 [45]. Therefore, even though the 1/ f noise is low at pH ~5, the net charge of DNA would be close to zero, resulting into a small EPF imparted on it. Thus, the throughput at pH ~5 would be meagre as evident in Fig. 2A and 2F. For any translocation experiment, there is an onset time, which is defined as the time required to initiate the translocation process. At pH ~5, we did not observe appreciable events for the first approximately 60 min. Nanopore devices are expected to be high-throughput platforms and such a wait time defeats the motive for using SSNs for sensing. Although the event rate increased at pH ~6 (Fig. 2B and 2F), the device was more prone to transient clogging at these two pH values (~5 and ~6), likely due to the low EPF imparted on the DNA molecule. The event rates at pH ~7, ~8, and ~9 were at least 9.5× greater than that at pH ~6. We observed an increase in event rate up to pH ~8 and a drop at pH ~9. This drop in event rate could be due to the onset of the EOF of the CT-CDB. Given the surface charge density at pH ~7, ~8, and ~9 (−0.137, −1.37, and −13.7 mC/m², respectively; calculated from the fit of Fig. 1C and Eq. [2]), the EOF would be opposing the EPF. Experiments beyond pH ~9 were not carried out as hydrolysis and denaturing (of DNA) could happen, which would alter the structural properties of DNA. Statistically significant event counts (>1000) were obtainable only for pH ~7, ~8, and ~9. The conductance change due to DNA translocations was modeled as described previously (see Supporting information Section 3 for fitting details). The ratio of the folded over to linear translocations were found to be ~1.95 ± 0.06, 1.89 ± 0.02, and 2.05 ± 0.01 for pH ~7, pH ~8, and pH ~9, respectively, which is in close agreement with the ideal expected value (i.e., 2 [46]). Considering the noise behavior of CT-CDB nanopores and their DNA responsiveness with pH, a pH of ~7 or ~8 would be more conducive for sensing experiments with DNA. Thus, we chose pH ~7 (closer to the physiological pH of 7.4 ± 0.5) for further investigation of the noise characteristics associated with CT-CDB nanopores.

Figure 2.

Sixty second current traces at (A) pH ~5, (B) pH ~6, (C) pH ~7, (D) pH ~8, and (E) pH ~9 in response to +200 mV. (F) The capture rate corresponding to each of the dsDNA translocation experiments of (a)–(e) All experiments were done using ~10.5 ± 0.4 nm diameter pores, 100 kHz low pass filtering, and 250 kHz sampling frequency. Scatter Plots and histograms corresponding to change in conductance due to DNA translocation at pH ~7, pH ~8, and pH ~9 is shown in Supporting information Fig. S3.

3.3. Noise characteristics with electrolyte type

The equilibrium with surface chargeable head groups and metal ions are thought to play a vital role in the low-frequency noise characteristics and can be expressed as [47],

$$\chi H+M^{n+}\rightleftharpoons \chi M^{n-1}+H^{+},$$ (Equilibrium 2)

where Mⁿ⁺ is an n-valent cation. Higher noise can be expected if the exchange reaction occurs frequently, which is the case when the binding energies of χ H and χ Mⁿ⁻¹ are comparable. Thus, when Equilibrium 2 is favored to either side (i.e., the binding energies are far apart), a reduction in the 1/ f noise can be expected. This is because, when the equilibrium is favored to one side, the exchange rate between the metal ions(Mⁿ⁺) and the protons (H⁺) will be low, resulting in low ionic current fluctuations. The noise also depends on the adsorption affinities of the metal ions. Smaller radii ions are shown to have a higher affinity for silanol groups [47]. Although the exact surface chemistry of nanopores fabricated through Si_xN_y membranes by the CT-CDB method is not well understood, considering the membrane material, the surface could be thought to be rich in some silicon-based acidic head group. The 1/ f component of PSD spectra at 1 Hz shown in Fig. 3B for LiCl (black), NaCl (red), KCl (blue), RbCl (green), and CsCl (purple) indicates, S_{1/ f,1Hz} increases up to KCl and starts to decrease afterwards. The conductivities of the solutions were different as they had different ionic properties. The conductivities of 0.5 M solutions of LiCl, NaCl, KCl, RbCl, and CsCl were 4.07, 4.55, 5.78, 5.96, and, 6.08 S/m, respectively. Thus, to enable comparisons, we normalized S_{1/ f,1Hz} with the square of the open-pore current (S_{1/ f,1Hz}/I²) as shown in Fig. 3C. Interestingly, the noise level of 0.5 M LiCl was ~1 order magnitude less than the rest of the electrolytes and, unlike Fig. 3B, there was no appreciable difference in the noise level between the rest of the electrolytes. These findings partially contradict the results presented by Matsui et al. for CDB fabricated nanopores, where an increase in normalized noise with increasing cationic radius (i.e., increasing atomic number) was observed [47]. Figure 3B and 3C suggests that LiCl has lower 1/ f noise characteristics compared to the rest of electrolytes and may presumably be due to the suppression or favoring one side of Equilibrium 2. Since LiCl exhibits the lowest 1/ f noise characteristics and is able to shield the charge of biomolecules to slow their transit through the nanopore [48], it is evident, unless a detrimental structural change is caused as a result of the presence of Li⁺, that LiCl may be the better electrolyte to use for nanopore experiments with CT-CDB nanopores.

Figure 3.

(A) The power spectral density (PSD) curves corresponding to (0.5 M) LiCl, NaCl, KCl, RbCl, and CsCl at +50 mV applied voltage and 10 kHz low pass filtering. (B) S_1/f,1Hz (1/f noise at 1 Hz) and (C) negative log of S_1/f,1Hz/I² (noise at 1 Hz normalized by the square of open-pore current) of each electrolyte type. (D) S_1/f,1Hz and (E) Open-pore conductance with time corresponding to 0.5 M LiCl (black) and 0.5 M KCl (red). Extended current traces corresponding to (E) are shown in Supporting information Fig. S4. The solid lines in (E) are linear fits made to the raw data. The rate of growth (i.e., the slope of the linear fit) for 0.5 M LiCl and 0.5 M KCl were found to be ~0.012 and ~0.002 pA/s, respectively.

The total experimental time length associated with nanopore experiments can span from few minutes to few hours. During lengthy experiments, nanopore characteristics are assumed to stay appreciably constant. Such characteristics include open-pore current and noise features. To investigate the validity of these assumptions, from the electrolytes explored thus far, we chose to further examine with the two commonly used electrolytes in nanopore technology: LiCl and KCl. The open-pore current was measured continuously for ~2 h at +50 mV (0.5 M electrolyte concentration buffered at pH ~7). The PSD analysis was done every 10 min and S_{1/ f,1Hz} was then plotted as a function of time as seen in Fig. 3D. We did not see an appreciable change in the S_{1/ f,1Hz} with time for LiCl whereas KCl showed some variability with time. This further strengthens the notion of better performance associated with LiCl over KCl and its suitability for lengthy experiments while preserving pore properties. One of the promising qualities offered by CT-CDB nanopores is the exceptional open-pore current stability. In our previous work, we were able to perform experiments with DNA in 4 M LiCl buffered at pH ~6 as well as pH ~7 for an excess of 8 h while collecting >2 × 10⁵ events at both the pH values. [33]. We investigated the open pore stability of CT-CDB fabricated nanopores by calculating the open-pore current every 10 min using the mean current of a 2 s trace for both electrolytes as shown in Fig. 3E. We only observed a mere increase of ~1.6 nS (LiCl) and ~2.1 nS (KCl) in the open-pore conductance (over 2 h). Extended current traces (i.e., 1800 s) for both electrolytes are shown in Supporting information Fig. S4.

3.4. Noise characteristics with applied voltage and electrolyte concentration

To quantitatively understand the noise characteristics with electrolyte concentration and applied voltage at pH ~7 (where σ → 0), one has to look closely at Eq. (6) and the definitions associated with N_x corresponding to cylindrical and access resistances. Through the equations provided by Fragasso et al. [25] (see Supporting information Section 1), it is clear that N_x is proportional to the electrolyte concentration, pore diameter, and pore length. Equation (6) can be rearranged as,

$$S_{f,\sigma \to 0}=\frac{K^2\cdot V^2}{f\cdot C}{B}^{\prime },$$ (7)

where B′ is the geometric constant (see Supporting Information Section 1 for more details) and C is the ionic concentration. Since, as shown in Fig. 3E, CT-CDB pores in LiCl do not grow appreciably over 2 h, our assumption of constant pore diameter would hold (essential for the derivation of Eq. (7) from Eq. (6) as shown in the Supporting Information Section 1). We first investigated the impact that the applied voltage has on the 1/ f noise characteristics by ramping it up from +25 to +200 mV in +25 mV increments using CT-CDB nanopores submerged in 0.5 M LiCl and 4 M LiCl (Fig. 4A and 4B)—the two extreme concentrations used in this study. Although it is possible to go to lower concentrations, nanopore experiments are generally done in this concentration range [48,49]. The S_{1/ f,1Hz} with applied voltage was then fitted using Eq. (7) as seen in Fig. 4B. The α_b was found to be ~36.0 × 10⁻⁵ (4 M LiCl) and ~4.3 × 10⁻⁵ (0.5 M LiCl). The α_b for 0.5 M LiCl is within error from that obtained from Fig. 1B where experiments were conducted using 0.5 M LiCl at +50 mV. Although our results indicate α_b up to +200 mV to be less dependent on the applied voltage, there is no guarantee that it would be the same beyond this voltage. The voltage experiments were capped at +200 mV as this is the upper voltage limit of the front switch setting of the Axopatch 200B. For voltages >200 mV, the rear switch setting would have to be used which inherently has higher noise than the front switch setting. The α_b of 4 M LiCl, on the other hand, is ~8× greater than that of 0.5 M LiCl. These results indicate that the bulk contribution to the 1/ f noise increases with increasing electrolyte concentration. To further assess the effect of electrolyte concentration on 1/ f noise, PSD was collected for 0.5–4 M LiCl as shown in Fig. 4C. The 1/ f noise at each concentration was multiplied by its concentration and presented as a function of the electrolyte conductivity in Fig. 4D for ease of fitting with Eq. (7) (solid-red). Supporting information Fig. S5 presents the 1/ f noise with electrolyte concentration with a linear fit only as a guide to the eye. The raw data, however, does not fall well along the fit in Fig. 4D using Eq. (7), which is also apparent by the regression coefficient (R²) of the fit (~0.929). When we replaced the K² term of Eq. (7) with K^eff (analogous to effective conductivity), the R² increased to ~0.996, indicated by the dashed-red fit line in Fig. 4B. However, the reasoning behind this behavior is not clear yet. Using two unique nanopores (~11.6 ± 0.6 nm), the exponent e f f was found to be 4.3 ± 0.8.

Figure 4.

(A) The power spectral density (PSD) curves and (B) S_1/f,1Hzcorresponding to 0.5 M LiCl (top) and 4 M LiCl (bottom) with applied voltage (+25 mV to +200 mV, in +25 mV increments) using a ~11.2 nm diameter pore. Only +25, +50, +100, +150, and +200 mV are shown in (a) for clarity. (C) PSD curves and (D)S_1/f,1Hz (noise at 1 Hz) versus electrolyte conductivity corresponding to 0.5, 1, 1.5, 2, 2.5, 3, and 4 M LiCl at +50 mV of applied voltage using a ~12 nm diameter pore. Only 0.5, 1, 2, 3, and 4 M LiCl are shown in (C) for clarity. The fits in solid red in (B) and (D) are from Eq. (7). The fit in dashed red in (D) is by replacing K² of Eq. (7) with K^eff (see manuscript for more details). All experiments were conducted with buffered electrolytes (pH ~7), 10 kHz low-pass filtering and 250 kHz sampling frequency.

3.5. Noise characteristics with pore diameter

Lastly, we investigated the effect of pore diameter on the 1/ f noise characteristics of CT-CDB nanopores using 0.5 and 4 M LiCl. As seen in Fig. 5C, the S_{1/ f,1Hz} increases with increasing diameter for both electrolyte concentrations. This observation contradicts both what has been observed previously for SSNs [21, 25] and Eqs. (5 and 6) and Supporting information S11. The conventionally observed decrease in 1/ f noise with increasing pore diameter could be partly due to weakening of the surface effects. However, one must be mindful of the limitations associated with each fabrication method. For example, TEM is capable of fabricating pores in a wide range of diameters (from few nanometers to >100 nm in diameter). In contrast, the operational range of CDB is mostly limited to <40 nm, while laser-assisted CDB could reach diameters around ~50 nm [50]. Studies with larger diameter pores (in the ~40 nm range) are seldom reported [49,51] and are mostly done in the <30 nm diameter range [3,52]. To produce larger diameter pores through CDB, a higher voltage must be applied. This could also lead to the formation of multiple pores. Additionally, higher Joule energy will also be released during the breakdown, which could negatively impact the noise properties of CDB-based nanopores. CT-CDB is not immune to these effects either. Equation (5) and its derivatives do not capture such effects during pore fabrication using CDB. We humbly note that we were not able to develop an equation to model the behavior of S_{1/ f,1Hz} with pore diameter and thus present results on a very qualitative note. From Fig. 5C, it is clear that S_{1/ f,1Hz} associated with 4 M LiCl is higher (as expected) than that in 0.5 M LiCl. The slopes suggest that S_{1/ f,1Hz} noise deteriorates ~1 order magnitude faster in 4 M LiCl with increasing pore diameter compared to 0.5 M LiCl.

Figure 5.

(A) The power spectral density (PSD) curves with pore diameter in 0.5 M LiCl, (B) PSD curves with pore diameter in 4 M LiCl, (C) S_1/f,1Hz (noise at 1 Hz) versus pore diameter corresponding to 0.5 M LiCl (solid circles) and 4 M LiCl (solid squares). All experiments were conducted at +50 mV of applied voltage.

4. Concluding remarks

The low-frequency noise characteristics of nanopores fabricated through the CT-CDB process are investigated in this work as a function of solution pH, electrolyte type, electrolyte concentration, applied voltage, pore diameter, and pH. The low-frequency regime is dominated by 1/ f and white noise. The 1/ f region captures surface-chemical dependence of the noise and therefore is a suitable metric to gauge the noise performance of a device under different electrolyte chemistries. CT-CDB nanopores, unlike their CDB and TEM counterparts, exhibit a pH range where the conductance is relatively constant followed by an increase in the conductance with pH resembling a nanopore wall surface composed of acidic surface head group type. The 1/ f noise is initially characterized using Eq. (5). The 1/ f noise up to pH ~8 is thought to be largely independent of surface contributions. The Hooge’s parameters corresponding to the bulk and surface contributions (α_b and α_s, respectively) are found to be ~3.4 × 10⁻⁵ ± 2.7 × 10⁻⁵ and, ~1.2 ± 0.2, respectively by fitting the data corresponding to S_{1/ f,1Hz} (1 Hz noise of 1/ f noise component) with pH using Eq. (5). The α_s is ~3 orders of magnitude larger than the previously reported values in the literature for TEM-based nanopore while α_b is an order of magnitude greater. From the same fit, the pK of the surface is found to be ~10.8 ± 0.1, which is about 1 unit greater than the previously reported value. To strike a balance between 1/ f noise and sensing experiments, DNA translocations are tested in the pH 5–9 range in single pH increment steps. The event rate is found to be meagre (<1 events/s) for pH 5, whereas higher pH values produced event rates that are at least 9.5 × greater than that at pH 5 and 6. Although noise is low at pH and 6, it is not suitable for DNA sensing experiments with CT-CDB pores due to poor event rates. The event rate increases up to pH 8 and drops at pH ~9. This is thought to be due to the EOF opposing the EPF responsible for the transit of DNA across the pore. The 1/ f noise characteristics are investigated with LiCl, NaCl, KCl, RbCl, and CsCl (0.5 M concentration at pH ~7) and the current normalized noise indicated LiCl to have ~1 order of magnitude less noise compared to the rest. Interestingly, the noise does not fluctuate appreciably from NaCl to CsCl, which contradicts previous observations. This could be due to a surface chemistry that is sensitive to LiCl and less sensitive to other cations used herein. As expected from Supporting information Eq. (S11), the 1/ f noise increases with increasing electrolyte conductivity and applied voltage. In contrast to TEM-based SSNs, the S_{1/ f,1Hz} of CT-CDB nanopores increased with increasing pore diameter. We have observed through our use of CDB nanopores that the pore quality decreases with increasing diameter, which could be due to the release of Joule heat during the breakdown process. However, the reasons behind this phenomenon are not entirely clear and a new model is needed to explain these observations as Eq. (5) (or its derivatives) are unable to map these observations.

Abbreviations:

ALD

atomic layer deposition

CDB

controlled dielectric breakdown

CMOS

complementary metal oxide semiconductor

CT-CDB

chemically-tuned controlled dielectric breakdown

EOF

electroosmotic force

EPF

electrophoretic force

PSD

power spectral density

SSN

solid-state nanopore

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.