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# Precise capture and dynamic relocation of nanoparticulate biomolecules through dielectrophoretic enhancement by vertical nanogap architectures

## Abstract

Toward the development of surface-sensitive analytical techniques for biosensors and diagnostic biochip assays, a local integration of low-concentration target materials into the sensing region of interest is essential to improve the sensitivity and reliability of the devices. As a result, the dynamic process of sorting and accurate positioning the nanoparticulate biomolecules within pre-defined micro/nanostructures is critical, however, it remains a huge hurdle for the realization of practical surface-sensitive biosensors and biochips. A scalable, massive, and non-destructive trapping methodology based on dielectrophoretic forces is highly demanded for assembling nanoparticles and biosensing tools. Herein, we propose a vertical nanogap architecture with an electrode-insulator-electrode stack structure, facilitating the generation of strong dielectrophoretic forces at low voltages, to precisely capture and spatiotemporally manipulate nanoparticles and molecular assemblies, including lipid vesicles and amyloid-beta protofibrils/oligomers. Our vertical nanogap platform, allowing low-voltage nanoparticle captures on optical metasurface designs, provides new opportunities for constructing advanced surface-sensitive optoelectronic sensors.

## Introduction

Bridging the gap between bulky materials and atomic/molecular structures sub-100-nm nanoparticles (NPs) are of great scientific interest owing to their extraordinary physical properties, for instance, significant enhancement of reactivity1, collective oscillation of electrons on localized surfaces2, and quantum confinement3. In particular, owing to the potential role of nanoparticulate biomaterials in unveiling sub-cellular biological mechanisms4, the capturing and trapping techniques of the bio-NPs in specific positions have been intensively studied not only to identify biological phenomena5,6 but also for next generation applications as drug delivery carriers7, imaging agents8, bioelectronic devices9, analytic lab-on-a-chip systems10, and biosensors11. Despite their increasing demand, manipulation of NPs is extremely challenging owing to the enhanced disruptive Brownian noise with reduction in NP sizes12. A variety of techniques have been developed to manipulate the spatiotemporal positions of NPs using external stimuli, including optical13,14, fluidic15,16,17, mechanical18,19, magnetic20,21, and electrical biases22,23,24,25. Among them, the usefulness of electrical techniques has been amply proven by easy actuation as well as uniform stimulation over large areas in a label-free manner. However, for conventional architectures with microgap electrodes, high voltage application is indispensable for trapping the suspended NPs in an aqueous environment, which inevitably accompanies the undesirable formation of electrolytic bubbles and the denaturation of biomaterials by Joule heating26.

As a promising alternative for microgap architecture, nanogap electrodes were previously utilized for NP capturing in low-voltage schemes27,28,29. Although NPs were well captured, sub-10-nm nanogap electrodes suffer from electron tunneling through a thin insulator30. Thus, a new strategy other than the reduction of insulator thickness is required to enhance the capacity for NP trapping. Conventionally, nanogap electrodes were prepared using expensive and sophisticated manufacturing methods that limited their shape and area. Small-area applicability and low-degrees-of-freedom in electrode designs have prohibited high-throughput molecular detection with nanogap structures as well as possible application on surface-sensitive optoelectronic sensors with various spectral ranges and enhanced sensitivities. Therefore, a platform that enables the implantation of optical metasurfaces along with dynamic manipulations of the bio-NPs on their sensing areas will offer opportunities to develop advanced surface-sensitive biosensors that are yet to be realized.

Herein, we report unique and versatile vertical nanogap electrode (VNE) that enables capturing and relocating bio-NPs, with large-area applicability and high degrees-of-freedom in electrode design flexibility (Fig. 1a). The VNE array, which is designed to generate well-controlled flow dynamics accompanied with improved particle capture, consists of a patterned insulator layer sandwiched between two electrode layers (one plane and one patterned; Fig. 1b). Enhanced performance was experimentally demonstrated by capturing sub-100-nm NPs in a sub-volt application to confirm NP capturing in a size-selective manner and relocate the bio-NPs, including nanometer-scale lipid vesicles and peptide assemblies, along with a theoretical analysis of electrokinetic behavior.

## Results

### Forces acting on suspended particles and resultant particle dynamics

Suspended particles under an AC electric field (E-field) experience dielectrophoresis (DEP)31, AC electro-osmosis (ACEO)32, and other various external forces. The ACEO flow is caused by the movement of surface-attracted ions, which results from a thin layer of induced charge on the solid–liquid interface called the electrical double layer (EDL). Although the ACEO can be applied to sort, transport, and position the suspended particles33, it can barely manipulate the particles in a material- or size-selective manner. Unlike the ACEO, the DEP force can selectively trap and expel suspended particles from the electrodes where the maximum E-field gradient is generated34. For a spherical dielectric particle of radius R suspended in a medium of permittivity εm, the time-averaged FDEP under an AC voltage frequency of f can be expressed as35

$${\mathbf{F}}_{{\mathrm{DEP}}} = \pi \varepsilon _{\mathrm{m}}R^3{\mathrm{Re}} \left[ {f_{{\mathrm{CM}}}(\omega )} \right] \cdot \nabla {\mathbf{E}}_{{\mathrm{rms}}}^2,$$
(1)

where Erms and ω are the root mean-squared E-field and angular frequency (ω = 2πf), respectively. The term Re[fCM(ω)] denotes the real part of the Clausius–Mossotti (CM) factor, which represents the effective polarizability of the particle in a medium. The CM factor is given by

$$f_{{\mathrm{CM}}}(\omega ) = \frac{{\varepsilon _{\mathrm{p}} \ast (\omega ) - \varepsilon _{\mathrm{m}} \ast (\omega )}}{{\varepsilon _{\mathrm{p}} \ast (\omega ) + 2\varepsilon _{\mathrm{m}} \ast (\omega )}},$$
(2)

in which $$\varepsilon _{\mathrm{p}} \ast$$ and $$\varepsilon _{\mathrm{m}} \ast$$ are the complex permittivities of the particle and medium, respectively, and are expressed by their respective permittivities (εp, εm) and conductivities (σp, σm); ε* = ε – i · (σ/ω), where $$i = \sqrt { - 1}$$. According to Eqs. (1) and (2), controlling the frequency and voltage amplitude serve to selectively capture the NPs according to material and size, respectively. To evaluate the competitive forces and resultant dynamics of a spherical particle (with its mass of mp) in an aqueous environment, the Langevin equation of particle velocity (up) was employed35:

$$m_{\mathrm{p}}\frac{{{\mathrm{d}}{\mathbf{u}}_{\mathrm{p}}}}{{{\mathrm{d}}t}} = {\mathbf{F}}_{{\mathrm{DEP}}} + {\mathbf{F}}_{{\mathrm{ACEO}}} + {\mathbf{F}}_{{\mathrm{ETF}}} + {\mathbf{F}}_{{\mathrm{grav}}} + {\mathbf{F}}_{{\mathrm{buoy}}} + {\mathbf{F}}_{{\mathrm{int}}} + \xi (t),$$
(3)

considering DEP force (FDEP), Stokes drag force induced by ACEO flow (FACEO) and electrothermal flow (FETF), gravitational force (Fgrav), buoyant force (Fbuoy), interparticle force from Coulomb interaction (Fint), and random Brownian force (ξ(t)). Because Stokes drag forces are defined as F = −6πηR(up − um), where up and um are the velocities of particles and fluidic flows, respectively, FACEO and FETF exerting on a single particle can be evaluated by inserting uACEO and uETF into um, respectively36. Considering the simulations (FETF, FDEP, and FACEO), calculations (Fgrav, Fbuoy, and ξ(t)), and low-concentration (10 ppm) condition (Fint) on the VNE having pattern size (L) and periodicity (P) of L = 10 μm and P = 30 μm (Fig. 1b), FDEP and FACEO dominantly determine the movement of 1-μm-diameter polystyrene (PS) particles, while the others are negligible (Supplementary Notes 15, Supplementary Table 1, and Supplementary Figs. 14). As the relaxation time (τ) of the particle (τ = m/6πηR ≈ 6 × 10−8 s) is much smaller than the typical experimental observation time (t), transient ballistic regime of short time scales (t τ) quickly reaches viscous regime of a time scale longer than τ (t τ). Thus, Eq. (3) can be approximated into terminal up of viscous regime as ref. 36

$${\mathbf{u}}_{\mathrm{p}} = \left( {{\mathbf{u}}_{{\mathrm{ACEO}}} + \frac{{{\mathbf{F}}_{{\mathrm{DEP}}}}}{{6\pi \eta R}}} \right)\left( {1 - e^{ - t/\tau }} \right) \approx {\mathbf{u}}_{{\mathrm{ACEO}}} + \frac{{{\mathbf{F}}_{{\mathrm{DEP}}}}}{{6\pi \eta R}}$$
(4)

with the assumption that the initial velocity of the particle is 0. From a dimensionless analysis of particles that exhibit small Stokes numbers (Supplementary Note 6), the viscous fluidic effect is expected to dominate over the negligible inertial effect and the motions of particles will be coupled with flow. Therefore, the movements and positions of the suspended particles under various AC conditions can be anticipated by calculating two dominant electrokinetics of DEP and ACEO.

### Dielectrophoretic- and AC electro-osmotic characterization and fabrication of VNE

According to Eqs. (1) and (2), FDEP is determined by physical factors such as particle size, πR3, frequency-dependent electrical properties of the particles and media, εmRe[fCM(ω)], and a gradient of the E-field squared, i.e., E2. Unlike other operating factors, E2 is determined by the structural characteristics of the electrodes. For the capture of smaller particles, the generation of higher values of E2 is advantageous for dielectrophoretic performance in particle capture. From this perspective, we evaluated E2 of VNE under various peak-to-peak voltages (Vpp) and compared the dielectrophoretic performance to E2 of conventional horizontal nanogap electrode (HNE) (Fig. 1c), with an identical gap distance of d = 100 nm using COMSOL Multiphysics software. According to the simulation results, E2 is found to be strongest at the nanogap and weakens farther away from the edges (Fig. 1d, e). By extracting and plotting the maximum value of E2 (E2|max) as a function of V2pp (Fig. 1f), the linear relation between these two parameters can be expressed as E2|max = αV2pp, where the slope of the plot (α) quantitatively represents the dielectrophoretic performance. Based on this analysis, it was found that VNE generated stronger E2 with more dramatic proportionality to the voltage than the HNE. For example, in the case of d = 100 nm, the simulated value of α from the VNE (αVNE) was αVNE = 2.4 × 1023 V2 m−3, whereas that from the HNE (αHNE) was αHNE = 3.7 × 1022 V2 m−3. This indicates that VNE generates 6.5 times stronger FDEP under identical voltage application and that HNE requires a 2.6 times larger voltage amplitude to generate identical trapping performance. This is attributed to the asymmetric structure of the VNE electrodes, i.e., the bottom electrode is a plane whereas the top one is patterned, inducing higher non-uniformity of the E-field than symmetrically arranged HNEs. Furthermore, to test whether FDEP of VNEs are enhanced at various gap distances, we conducted similar processes for d = 10 to 1000 nm (Fig. 1g). The calculated results clearly show that values of αVNE are 3.4 (d = 10 nm) to 16.5 (d = 1000 nm) times higher than αHNE. This demonstrates the improved DEP performance of VNE in particle capturing irrespective of the gap distance, although its enhancement decreases as d becomes narrower. From this simulation result, it is presumed that the VNE with d = 100 nm achieves an equivalent DEP performance to that of HNE with d = 20 nm. After establishing the superiority of VNEs in terms of DEP performance, the thermal Joule heating effect was investigated to confirm the viability of a biomaterial in the presence of E-fields. According to the simulated results for both VNE and HNE under various Vpp, a negligible temperature increment (ΔT) of <0.04 K was expected in the presence of Vpp = 10 V (Supplementary Note 7 and Supplementary Fig. 5).

Together with DEP performance, ACEO-driven local slip velocities at the boundary of two electrodes and resultant bulk fluidic flow across the insulator of both VNE and HNE were explored. The simulations of hydrodynamic bulky flow over the each electrode revealed that VNE generates a pair of micro-vortices rotating in opposite directions with distinct magnitudes (Fig. 1h), in contrast to symmetric HNEs, which yield bulky flows of equivalent magnitude in an outward direction from the nanogap (Fig. 1i). As is well known, the slip velocity, uslip, arising at the electrode surface from the interaction of the E-field and EDL, drives the bulky fluidic motions. We analyzed uslip to characterize ACEO behavior as a function of both frequency and position on the VNE surface (Fig. 1j–l). On the boundary of the VNE surface, uslip reached a maximum at the edge and became decreased away from the nanogap irrespective of the applied frequency (Fig. 1j). Although the simulation results show good correspondence with those of previous studies examining ACEO-assisted slip velocity above horizontally aligned electrodes32,37,38,39, the VNE offers unique hydrodynamic flows resulting in asymmetry in magnitudes of uslip at each micro-vortex (Fig. 1k, l). This imbalance of a faster uslip on the top electrode than that on bottom electrode arises from the structural configuration of VNE, as previously demonstrated by the use of asymmetric horizontal electrode arrays40,41,42 or non-planar ones43,44,45. Owing to this faster uslip on the top electrode, the micro-vortex on the top electrode induces larger flow streamlines than those on the bottom electrode (Fig. 1h). Moreover, this imbalance is intensified when the disparity of each flow across the vertical nanogap increases under different frequency conditions, and this hints at the frequency-dependent distinct dynamics of particles in combination with DEP (Supplementary Note 8, Supplementary Figs. 6 and 7).

Based on the theoretical results, VNE arrays with d = 100 nm were fabricated over a large area to demonstrate their structural fidelity and excellent production yields (Fig. 2, Supplementary Note 9, and Supplementary Fig. 8). On a glass substrate, a 40-nm-thick indium tin oxide bottom electrode was patterned and spin-coated with a 100-nm-thick insulating layer of poly(4-vinyl phenol) (PVP) and thermal crosslinking agent. Subsequently, a 40-nm-thick Au electrode was thermally deposited through a shadow mask. Next, the Au and insulating layers were patterned into 10-μm-hole arrays via photolithography and sequential etching processes (Fig. 2a). The photograph (Fig. 2b), micrographs (Fig. 2c), and scanning electron microscope (SEM) images (Fig. 2d, e) clearly demonstrate that uniform device architectures of well-controlled 100-nm-thick nanogap electrodes were achieved over a large area.

### Simulated particle dynamics under AC frequency

After designing the VNE arrays, we evaluated how AC frequencies affect the movement of suspended particles through two dominant forces of FACEO and FDEP (Ftotal = FACEO + FDEP, Fig. 3). We classify the frequency ranges into 3 regimes: low-frequency (1–10 kHz; regime I), mid-frequency (0.1–1 MHz; regime II), and high frequency (> 10 MHz; regime III), where each regime is expected to be dominantly influenced by ACEO, positive DEP (pDEP), and negative DEP (nDEP), respectively. The frequency-dependent dynamics of suspended particles on a single unit of VNE were simulated using a combination of ACEO and DEP (Fig. 3a–e) and experimentally monitored for cross-validation (Fig. 3f–j). Note that the electrohydrodynamic drag forces acting on the particle by ACEO were calculated using FACEO = −6πηR(up − uACEO), with assumptions that E-field had just been applied and that the particle was at rest prior to the AC application (up = 0)46. The DEP-induced velocity of particles (uDEP) was also calculated and simultaneously expressed in the form of uDEP = FDEP/6πηR for direct comparison with uACEO. To observe the real-time particle movement through bright-field (BF) microscopy, we used 1-μm-diameter PS particles with a concentration of 1.8 × 108 particles ml−1 and simulated the phenomena using physical values of Vpp = 2.5 V, εm = 80·ε0, σm = 1 μS cm−1, εp = 2.55·ε0, σp = 114 μS cm−1, and R = 500 nm. In regime I, pairs of asymmetric ACEO flows circulating above each surface of VNE were simulated both in 1 and 10 kHz. Because ACEO is predominant in the low-frequency range of regime I, the movements of particles are dominantly determined by ACEO rather than DEP. Within regime I, distinct particle dynamics are also expected with respect to the applied frequencies owing to the varying dominant forces; ACEO is dominant over DEP at 1 kHz (Fig. 3a), whereas they are comparable at 10 kHz (Fig. 3b), as shown through simulations (Supplementary Fig. 4). In contrast, the formation of the EDL layer is weakened at high frequency as the alternation of electrical signals is too rapid for ions to follow; thus, particles are majorly governed by FDEP (Fig. 3c–e).

The direction of FDEP can also be controlled by changing the frequency because FDEP highly depends on the polarizing behavior of particles. For example, particles move along the increasing field gradient at the condition of pDEP where Re[fCM(ω)] > 0, whereas repulsion of particles from the region of the highest field gradient is referred to as nDEP where Re[fCM(ω)] < 034. In particular, for charged particles with sizes comparable to their EDL thickness, ionic currents and their convection within the EDL play an important role in polarization and formation of induced dipole47. To evaluate the dielectric response of a suspended particle in the presence of an applied E-field, the Maxwell–Wagner–O’Konski (MWO) model was adopted to consider both local surface charges and the resultant surrounding EDL. In this model of MWO dielectric dispersion, the effective conductivity of particles (σp) with a radius of R can be described as σp = σbulk + 2Ksurf/R, which is a combination of the bulk conductivity (σbulk) and surface conductance (Ksurf) of particles48. This implies that NPs with high surface area to volume ratio experience higher Ksurf; thus, surface conductance become dominant in the case of smaller NPs. Because MWO theory works at low conductive environments49,50, the effective dielectrophoretic properties of PS NPs, including CM factor, were represented using the MWO model (Supplementary Note 10, Supplementary Table 2, and Supplementary Fig. 9). The crossover from positive to negative values of Re[fCM(ω)] occurs at a specific crossover frequency (fχ), which is 1.8 MHz in this case. Because Re[fCM(ω)] value decreases as the frequency approaches fχ, the pDEP force at 100 kHz (Fig. 3c) is found to be stronger than that at 1 MHz (Fig. 3d). Above 1.8 MHz, the directions of FDEP become reversed; thus, repulsion of particles from the nanogap is expected in regime III at 10 MHz (Fig. 3e).

### Experiments of particle capture and relocation

Based on the simulation analysis of the particle trajectories on VNEs, corresponding experiments were conducted using AC voltages of Vpp = 2.5 V (Fig. 3f–j and Methods). At 1 kHz (Fig. 3f), the particles were swirling over the single unit of VNE because they are significantly influenced by ACEO flows rather than the considerably weaker DEP force. However, at 10 kHz, suspended particles are migrated to the center of the unit cell, where flows are converged to form a point of stagnation (Fig. 3g and Supplementary Fig. 4). Unlike at 1 kHz, an application at 10 kHz generates both ACEO and DEP with comparable magnitudes. With an aid of attracting FDEP, particles are brought into proximity with the VNE electrode surface against upward ACEO flow. Then, because the ACEO-induced slip velocity (pushing toward center) is found to be stronger than the DEP force (attracting toward edges) at the collecting surface of the VNE, effective surface streams push particles toward the stagnation point where the pseudo-potential energy is the lowest (Supplementary Note 11 and Supplementary Fig. 10)51. In contrast, at 100 kHz (Fig. 3h) and 1 MHz (Fig. 3i) in regime II, the ring-shaped particle assembly was observed at the edge of nanogap, where the value of E2 is the largest and the pseudo-potential energy is the lowest (Supplementary Note 11 and Supplementary Fig. 10). Although ACEO flows still exist at 100 kHz, trapping at the stagnation deteriorates as a pair of asymmetric micro-vortices vanish into a single large flow and FDEP becomes stronger than FACEO (Supplementary Fig. 4). Instead, a long-range ACEO flow constantly conveys distant particles to the VNE, and the dominant FDEP successfully snatches the moving NPs from the flow and accumulate them to the edge of VNEs at 100 kHz. Note that the interparticle force component (Fint) is negligible when suspended particles are distant from each other. However, when they are trapped and come together (Fig. 3g, h), particle–particle interactions improve the trapping efficiency of the dielectrophoresis devices by the induced dipole moments of particles35,52,53. As predicted above, a small amount of particles trapped (Fig. 3i) at 1  MHz indicates a weaker FDEP (Fig. 3d) generated by a smaller Re[fCM(ω)] value compared to that at 100 kHz (Fig. 3c). Lastly, the particles are dislodged from the edge of the pattern by the nDEP force at 10 MHz in regime III (Fig. 3j). Although the particles can be collected at much lower voltage amplitudes, a significantly strong voltage of 2.5 V was applied to clarify the recognizable particle relocation by the frequency changes (Supplementary Movie 1). Furthermore, to investigate the minimum voltage and effective trapping volume, corresponding simulations and experiments were conducted by varying the voltage amplitudes at a fixed frequency of 100 kHz. When Vpp = 0.1 V, particles started to get captured and gradually populated the nanogap regions, and more particles were collected by increasing the voltage amplitude (Supplementary Note 12, Supplementary Figs. 11 and 12). Note that 0.1 V may not be the minimum trapping threshold, as our waveform generator was not able to supply a lower voltage. As an example of micron-scale bioparticles, the possible capturing ranges of yeast cells and Bacillus subtilis spores were theoretically evaluated using spherical- and elongated multi-shell dielectric models using MWO theory, and the trapping behaviors were experimentally confirmed under low-voltage amplitudes of Vpp = 0.5 and 0.8 V, respectively (Supplementary Notes 13 and 14, Supplementary Tables 3 and 4, and Supplementary Figs. 1316).

### Size-selective dielectrophoretic capture of NPs

After establishing the general principles of particle movement under the influence of two dominant electrokinetic forces in each frequency regime, the size-selective trapping and relocation of submicron particles in the vicinity of the nanogap were investigated further in the VNE (Fig. 4). Because FDEP is proportional to the volume of particle, πR3, (Eq. (1)), particles of different sizes could be selectively captured when they reached their respective threshold voltages for trapping. To examine the relationship between NP’s size and minimum voltages, we prepared a mixture solution of PS particles with diameters of 200, 100, and 50 nm tagged in different fluorescent (FL) dyes of blue (DAPI), green (FITC), and red (Texas Red), respectively. According to the calculation of the CM factor based on the MWO model, the values of fχ for each NP were calculated as 12, 18, and 37 MHz, respectively (Supplementary Note 10 and Supplementary Fig. 9). From this analysis, a frequency of 10 kHz was selected to achieve ACEO dominance, and 100 kHz guaranteed DEP dominance. For the real-time monitoring of NP capture and relocation, confocal FL microscopy was used to compare size-by-size capture for different AC voltage amplitudes (Fig. 4). At Vpp = 2 V and f = 10 kHz, all NPs were collected at the center of the circular pattern owing to the combination of FACEO and FDEP, and at the same time, the FL intensity, which indicates the population of NPs, were proportional to their size (Fig. 4a). Because the magnitude of FDEP is greater for larger particles, 200 nm particles tend to be more populated than smaller ones. This explains the role of FDEP on size-selective concentration at 10 kHz. In contrast, at 100 kHz, only 200 nm PS particles started to be captured at the nanogap from the averaged trapping threshold (Vth) of Vth = 0.33 V (Fig. 4b, e). As the AC voltage increased, the 100 nm particles began to be captured at Vth = 0.72 V while no 50 nm particles were monitored (Fig. 4c, e). Finally, the trapping of the 50 nm particles was observed for Vth = 1.24 V (Fig. 4d, e) while other larger particles became highly packed (Supplementary Note 15 and Supplementary Fig. 17). In this process, the time-lapse normalized FL intensities were analyzed and averaged for a VNE unit cell number (n) of n = 49, and each standard deviation (s.d.) of Vth was calculated to be 0.11, 0.12, and 0.22 V for PS NPs of 200, 100, and 50 nm, respectively (indicated as error bars in inset of Fig. 4e). Note that a glitch occurred at the moment when electrical signals changed owing to equipment limitations. The results clearly confirm that the VNE can also spatially relocate the NPs in a size-selective manner by controlling the frequency and magnitude of AC bias. That is, the frequency determines the local position of NPs whereas the control of voltage magnitude enables their selective capture according to size.

### Low-voltage trapping of nano-vesicles in pre-defined VNE geometry

Beyond the artificially synthetized NPs, the trapping behavior of nanoparticulate biomaterial was investigated using 50-nm-diameter small unilamellar vesicles (SUVs). SUVs, which are spherical vesicles bounded by a lipid bilayer, are widely used to study biological phenomena by mimicking extracellular vesicles (EVs), which are important mediators of intercellular communications in biological activities54. The SUVs were composed of 1,2-Dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) and 3 mol% of FL dyed lipid 1-oleoyl-2-{6-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]hexanoyl}-sn-glycero-3-phosphocholine (NBD-PC). To predict the frequency-dependent dielectric behavior of SUVs, the CM factor was calculated by utilizing the walled cell model designed by Jones (Supplementary Note 16, Supplementary Table 5, and Supplementary Fig. 18), followed by experimental corroborations. As the applied Vpp increased by 0.1 V every 10 s at a fixed frequency of 100 kHz, the SUVs began to be captured from Vth = 1.76 V (n = 81) with standard deviation of 0.23 V (indicated as an error bar in inset of Fig. 5a), and the amount captured increased accordingly with time and voltage amplitude (Fig. 5a). This low-voltage operation is one of the key prerequisites for the practical application of EVs on electric-biochips as it eliminates any possible scenarios of undesirable molecular phase transitions or thermal denaturation. Moreover, ACEO- and DEP-induced trapping of 50 nm SUVs to the center and edge of the VNEs were achieved at 10 kHz and 100 kHz, respectively, under a low voltage of 2 V over the millimeter-scale large area (Fig. 5b, c). From an analysis of the FL intensities on 400 unit cells, the variations of normalized FL intensities on each cell demonstrated uniformity and device robustness over a large area (Supplementary Note 17 and Supplementary Fig. 19). Additionally, the VNE patterns exhibited a high degree of design flexibility (emblems of ‘KIST’ and ‘SNU’; Fig. 5d), demonstrating the applicability of various pattern designs over large areas (Fig. 5e and Supplementary Movie 2). This demonstrates the potential applications of our VNEs for various optical and electrical structures as well as high-throughput analysis, which has remained challenging on conventional HNE configurations.

### Trapping of Aβ42 assemblies on VNE

Finally, the device performance was demonstrated at the molecular level by using real biomolecules of amyloid‐beta 1–42 (Aβ42) peptides, which are the predominant Aβ species and the major cause of Alzheimer’s disease (AD)55. Through self-assembly, Aβ42 peptide monomers are aggregated and form ordered structures of oligomers, protofibrils, and fibrils56. Among them, the Aβ42 oligomeric structure is more toxic than others because it binds to the neuronal synaptic membrane and causes a disruption of calcium homeostasis by forming Amyloid channels57. Despite the huge interest for its high association with the pathology of AD, studying the oligomeric Aβ42 is challenging owing to its extremely small size, ultra-low concentration, structural instability, and heterogeneity58. Therefore, new methods to collect and dynamically relocate the Aβ42 assemblies from low-concentrated solutions are highly desirable. To this end, a solution of 100 μM Aβ42 peptides was incubated separately with different durations (4 h vs 24 h) in deionized water at 37 °C and stained with thioflavin-T for visualization, and the Aβ42 solution was diluted into 1 nM to emulate the actual ultra-low concentration of Aβ42 peptide. Prior to the experiments, the CM factors of Aβ42 peptides were calculated by using dielectric models depending on molecular shapes and sizes (Supplementary Note 18, Supplementary Table 6, and Supplementary Fig. 20). For the 24 h-incubated samples without the delusion process, the FL micrographs clearly exhibit fibrous Aβ42 peptides confined at the edge of the VNE patterns under an AC bias of 3 V at 100 kHz (Supplementary Fig. 21). However, in the case of ultra-low concentration, additional FL photobleaching prohibited the reliable monitoring of captured Aβ42 through FL microscopy. Thus, SEM observation was performed for cross-validation. The fibrous Aβ42 peptides were observed at the center of the pattern at 10 kHz (Fig. 5f), while they were concentrated on the nanogap at 100 kHz (Fig. 5g). In contrast, spherical Aβ42 peptides were found at the center (Fig. 5h; 10 kHz) and edge of the pattern (Fig. 5i; 100 kHz) when exposing the 4 h-incubated Aβ42 solution to a higher AC bias of 5 V. To characterize the secondary structures of the 4 h-incubated Aβ42, a circular dichroism spectrometer was used. The results revealed 13.4% helix, 30.1% β-strand, 8.6% turns, and 47.8% other structures (Supplementary Note 19 and Supplementary Fig. 22), indicating that 4 h-incubated Aβ42 peptides are mostly in the form of oligomers and protofibrils59. Additional size validation and analysis were conducted using dynamic light scattering measurements and SEM spectroscopy, which represent the diameter variation of particulate Aβ42 from 10 to 60 nm, with the majority found to be 20 and 40 nm (well-matched with the reported size of oligomeric and protofibrous Aβ42)60. Because the 5 V application on VNE is regarded to generate ΔT < 0.01 K (Supplementary Note 7 and Supplementary Fig. 5), any possible damage of the captured Aβ42 by Joule heating was ruled out. The results clearly demonstrate that our VNE can capture and relocate the Aβ42 aggregates down to the oligomeric and protofibrous levels without damage.

## Discussion

Although low-voltage NP trapping on HNE was intensively exploited through atomic layer lithography27,28,61, the intrinsic nature of the horizontal configuration of its electrodes limited its practical application for wide spectral ranges of surface-sensitive optical sensors possessing maximized sensitivities. In comparison, three major advantages can be observed using the vertical configuration for NP manipulation. First, the VNE generates stronger DEP forces than HNE. The dielectrophoretic ability of the proposed VNE was investigated for the trapping of 200 nm PS beads with insulating thickness of 100 nm and minimum voltage of 0.33 V (Fig. 4). To the best of our knowledge, the performance observed is comparable to that of ‘the world’s sharpest DEP tweezer’ for capturing 190 nm PS beads in the presence of 0.5 V, as reported by Barik et al.27,62. This evidently implies that the reduction of insulating thickness in the VNE platform will be significantly advantageous for realizing high-production yields as well as for trapping extremely small NPs, which have yet to be captured by conventional HNEs (Fig. 1). Second, based on the understanding of frequency dependency of electrokinetics, the proposed VNE helps control the local position of NPs. Although most of HNEs have focused on capturing target NPs along the restricted nanogap regions, the proposed VNEs not only capture NPs along the nanogap regions in various shapes but dynamically control movements and local the position of NPs depending on the applied frequency (Fig. 3). Third, the VNE is advantageous for ease of fabrication, thereby achieving large-area scalability as well as reliability for massive sensor applications. Conventionally, HNEs have been developed through high-cost fabrication techniques such as e-beam lithography and focused ion beam. Although alternative methods were recently introduced, they still suffer from reliability issues and complicated nanofabrication processes63. Finally, owing to the high degree of design flexibility as well as the massive and simple fabrication, the proposed VNE could offer opportunities to develop an advanced optoelectronic sensor system by converging with various optical metasurface designs. Because the proposed VNE guarantees a high degree of design flexibility, the adoption of various optical nanostructures and sequential concentration of target NPs into the area of sensing hotspot will create tremendous opportunities to realize practical analytic methods, including surface-enhanced Raman spectroscopy (SERS)64, surface-enhanced infrared absorption (SEIRA)65, surface plasmon resonance66, and terahertz sensing based on metasurfaces67,68.

## Methods

### Voltage applications and data analysis

After mixing a poly(dimethylsiloxane) (PDMS) elastomer and a curing agent (Sylgard 184, Dow Corning) at a ratio of 10:1 with a total weight of 3 g, the mixture was poured and evenly spread on a petri dish (size of 120 mm × 120 mm) and cured on a hotplate (80 °C for 3 h) to achieve a 200-μm-thick PDMS film. Then, the PDMS film was punched using a 4-mm-diameter biopsy punch (MIL3334HH, Miltex) and placed on the periphery of the VNE patterns. A solution volume of 10 µL was dropped on the VNE array and covered with a glass slip to prevent water evaporation during voltage application. The customized software was designed using LabVIEW 2018 (National Instruments) to provide systematically controlled AC signals from a waveform generator (SDG2122X, SIGLENT). In this process, the FL and BF images of particulate materials were monitored using a FL microscopic system (LV100ND, Nikon) and a confocal microscopic system (Eclipse Ni-E, Nikon) and then analyzed using image processing software (ImageJ, National Institutes of Health, USA).

### SEM observation

Deposition of 2-nm-thick platinum on the samples was carried out using an ion sputter coater (E-1045, Hitachi) prior to observation with a SEM (Nova NanoSEM 200, FEI). An accelerating voltage of 10 kV and current of 140 μA was applied. For high-resolution SEM operation, a through-the-lens detector was used.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

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

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## Acknowledgements

This work was supported in part by KIST intramural grants (Nos. 2E30506, 2V07880 and 2E30140). Y.-S.R. acknowledges the support from Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-TE19303-01; S.-D.L., Brain Korea 21 Project funded by Ministry of Education of Korea; M.S., National Research Foundation of Korea (NRF) Global Frontier Program (No. CAMM-2019M3A6B3030638); Y.T.B., National Research Council of Science & Technology (NST) funded by the Korea government Ministry of Science and ICT (No. QLT-CRC-18-02-KICT); and S.-Y.L., the National Research Foundation of Korea (NRF) grant funded by the Korea government Ministry of Science and ICT (No. 2017R1C1B2003585).

## Author information

Authors

### Contributions

E.-S.Y. and Y.-S.R. designed and performed all the experiments, analyzed the data, and wrote the initial draft of the manuscript. E.-S.Y. and J.L. fabricated the devices. E.-S.Y., C.K., M.S., J.H.K., Y.T.B., S.-C.P., and S.-Y.L. performed the simulations and contributed to the data analysis. H.L. prepared the Aβ42 sample and performed the CD and DLS measurements. S.-M.L. and J.K. prepared yeast cells and Bacillus subtilis spores. T.K. performed the SEM measurements. S.-D.L. and Y.-S.R. provided scientific and technical guidance, performed the interpretation of the data, and finalized the manuscript. All authors agreed on its final content.

### Corresponding authors

Correspondence to Sin-Doo Lee or Yong-Sang Ryu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Yu, ES., Lee, H., Lee, SM. et al. Precise capture and dynamic relocation of nanoparticulate biomolecules through dielectrophoretic enhancement by vertical nanogap architectures. Nat Commun 11, 2804 (2020). https://doi.org/10.1038/s41467-020-16630-w

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