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TUTORIAL REVIEW

Cite this: Lab Chip, 2016, 16, 3855

Received 26th May 2016,Accepted 16th August 2016

DOI: 10.1039/c6lc00688d

www.rsc.org/loc

Field effect nanofluidics

Shaurya Prakash* and A. T. Conlisk*

Nanoscale fluid transport through conduits in the 1–100 nm range is termed as nanofluidics. Over the past

decade or so, significant scientific and technological advances have occurred in the domain of nanofluidics

with a transverse external electrical signal through a dielectric layer permitting control over ionic and fluid

flows in these nanoscale conduits. Consequently, this special class of nanofluidic devices is commonly re-

ferred to as field effect devices, analogous to the solid-state field effect transistors that form the basis for

modern electronics. In this mini-review, we focus on summarizing the recent developments in field effect

nanofluidics as a discipline and evaluate both tutorially and critically the scientific and technological ad-

vances that have been reported, including a discussion on the future outlook and identifying broad open

questions which suggest that there are many breakthroughs still to come in field-effect nanofluidics.

Introduction

The ability to move ions, molecules, and water over nanoscaledimensions with exquisite spatial and temporal control imply-ing high precision and selectivity is fundamental to all lifeprocesses and several engineered systems. The growing em-phasis and interest in the transport and behaviour of bothsingle and small ensembles of ions and molecules in waterled to the emergence of nanofluidics as a multi-disciplinaryarea of study. Therefore, nanofluidics defines fluid-basedtransport processes within systems with critical dimensionson the order of 1–100 nm.1–3

The domain encompassed by nanofluidics is broad withmany different types of devices, systems, and consequentlyapplications impacted by nanofluidics. Among this variety,there is a class of devices, referred to as ‘field-effect’ nano-fluidic devices that borrow technological inspiration from thesolid-state electronic or semiconductor devices and form thebasis for this review article. Specifically, in the context of thisarticle, field effect follows the analogy to solid-state electron-ics, where an externally applied potential in a transverse di-rection to the flow generates an electric field within the work-ing fluid volume to affect ion and fluid transport. Notably,the electrode being used to apply the transverse potentialis fluidically isolated from the nanofluidic conduit by adielectric layer.

We begin by discussing many fundamental concepts thatgovern all of nanofluidics. We also note that over the years nu-merous advances have been made in many aspects of differentnanofluidics and related nanofabrication technologies withseveral excellent reviews and books available to the readers.1–12

The discipline most often associated with the detailedstudies on transport processes is fluid mechanics. The storyof the evolution of present-day nanofluidics can be related tothe first experiments in 1838 by Jean Louis Marie Poiseuillein identifying the relations governing motion of blood.1

Using pressure to drive flows, Poiseuille found that

(1:1)

where Q is the volumetric flow rate of a fluid driven by apressure drop Δp across a tube of length L and diameter d.Consequently, as the diameter of the tube approaches nano-fluidic length scales, driving pressures become enormous(e.g. for water the pressure drop across a 100 μm long chan-nel, 1 nm in diameter for only an attoliter (10−18 m3) per sec-ond incompressible laminar flow would be greater than3 GPa2). Therefore, pressure driven flows for nanofluidicsfind niche applications.13,14

One notable aspect of nanofluidics, and perhaps micro-fluidics, is the ability for these systems to be a ‘unifier’ ofphysical principles. In particular, fluid mechanics plays thedominant role in the successful operation of these devices.Moreover, because of the large surface area to volume (SA/V)ratio, surfaces may be tailored electrically to achieve the de-sired objective.15 For many lab-on-chip applications, masstransfer occurs for ions and solutes in aqueous solutionswhich can also be used to transport charged biomoleculesand is essential to understand. This means that the develop-ment of micro- and nanodevices considered here requiresknowledge of fluid flow and mass transfer, electrostatics,electrokinetics, electrochemistry, and possibly molecularbiology. All of the essential principles governing device phys-ics between these disciplines occur simultaneously in a givenapplication. Consequently, it may be said that micro- and

Lab Chip, 2016, 16, 3855–3865 | 3855This journal is © The Royal Society of Chemistry 2016

Department of Mechanical and Aerospace Engineering, The Ohio State University,

Columbus, OH 43210, USA. E-mail: [email protected], [email protected]

http://crossmark.crossref.org/dialog/?doi=10.1039/c6lc00688d&domain=pdf&date_stamp=2016-09-29

3856 | Lab Chip, 2016, 16, 3855–3865 This journal is © The Royal Society of Chemistry 2016

nanofluidics bring together or unify and integrate multiplescientific disciplines in a large number of applications.

In considering the equations of motion that describe theinteraction between forces and the subsequent motion offluids, there are two main classes of forces that drive flows.The first one is surface forces (e.g. pressure), and the secondone is body forces (e.g. gravity or forces arising from electricor magnetic fields). Since mechanically applied pressure-driven forces for nanofluidics are not practical, the use ofbody forces such as electric fields is common.3 However, it isalso worth noting that the use of capillary forces and osmoticgradients is also finding application for manipulation andtransport of fluids in these small conduits. Next, fundamen-tal concepts underlying nanofluidics are described.

Fundamental concepts, governingequations, and assumptions

Theoretical analysis for nanofluidic devices and componentsrelies on the choice of nanoscale conduit geometry. It is im-portant to briefly review the broad-ended terminology used bya variety of researchers. Initial investigations began in ‘ultra-fine’ capillaries16 or narrow cylindrical channels.17 With theadvent of advancing computing capability coupled with ad-vances in microfabrication and nanofabrication, a variety ofnanoscale conduits were developed.3 Notably, the cylindricalconfigurations were referred to as either nanocapillaries,nanotubes, or nanopores depending on the substrate mate-rials and aspect ratio. A different name was adopted for non-circular cross-sectional nanochannels referring to conduitswith width and height significantly greater than the depth asnon-circular, slit-like nanochannels. Essentially, many nano-scale conduits or nanoarchitectures exist and fall under thedomain of nanofluidics.

In order to better understand the underlying physics, webegin with the governing equations for steady, incompress-ible flow in a channel. The Navier–Stokes equations in vectorform are given by

(1:2)

where fB is the body force and u is the streamwise velocity inthe x direction.1 In many cases and most commonly for thetypes of flows discussed in this mini-review, the flow can be as-sumed to be fully developed and the equation of motion inthe streamwise direction is given in dimensionless form by

(1:3)

Note that in eqn (1.3) , with h being the height of the

channel and λD being the Debye length, as discussed below.The first term on the right hand side corresponds to thedimensionless body force in the presence of an electric field.1

Moreover, in most channels (Fig. 1), we start with the analy-sis of a simpler configuration. Consider long channels wherethe channel length is much larger than the width and height,and the aspect ratio A = h/W ≪ 1 and the flow is fully devel-oped and steady. It is also worth noting that the convectiveterms in the Navier–Stokes equations vanish identically dueto the fully developed and one-dimensional approximationthat is commonly invoked.

Since the use of the electric field is the most commonmethod of inducing the body force to generate transport, it iscommonly applied in nanofluidics (and also in microfluidics).3

Moreover, as described in the applications section, for field-effect nanofluidic devices, strong electrolytes such as KCl andNaCl form the basis for nearly all reported data. Therefore, un-der such conditions, the salt component is nearly entirely dis-sociated and so the electrolyte mixture to be analyzed nomi-nally comprises three components: undissociated water andcations and anions from the salt. In the presence of the elec-tric field, the molar flux, NA, for species A for a dilute solutionwill then be given by the Nernst–Planck equation:

(1:4)

Here, DAB is the binary diffusion coefficient, μA is the ionicmobility and can be related to the diffusion coefficient by

with F being the Faraday constant, R being the uni-

versal gas constant, T being the absolute temperature, being

the electric field, and zA being the ionic valence. The secondterm on the right hand side of eqn (1.4) is called electrical mi-gration. Now, the governing equation for the transport of spe-cies A in terms of concentration can also be written as

(1:5)

Fig. 1 Geometric layout of a nanochannel that allows analysis togetherwith the use of approximations to eliminate the use of 2D or 3D modellingand focus on 1D modelling since aspect ratios A = h/W ≪ 1. Theschematic shows channel length L, width W, and height h along with thex, y, and z components of velocity in u, v, and w if the modelling is donein Cartesian coordinates. The flow is streamwise along L. Figurereproduced with permission from A. T. Conlisk, Essentials of Micro- andNanofluidics, Cambridge University Press, New York, 2013.

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Here, Ex, Ey, and Ez are the scalar components of the electricfield in the x, y, and z directions, and the diffusion coefficientis assumed constant. Eqn (1.5) can be written in terms of molefraction, XA, if the total concentration remains constant, whichis the case in many practical devices, and is expressed as fol-lows for a rectangular cross-sectional channel:18

(1:6)

where, for electrolyte species i = 1, 2, …, N, Xi is the mole frac-tion of the ith electrolyte, zi is the valence of that electrolyte,and φ is the electrical potential. Here, y and z are the dimen-sionless coordinates normalized by the channel height h andwidth W, respectively. Notably, the non-linear terms vanishidentically. To complete the set of essential governing equations

under steady state conditions, , and the electric field

may be defined as with φ being the electric potential.

If the electrical permittivity εe is constant, then the Poissonequation is used to connect the potential to the mole fractionsand can be written as

(1:7)

Choosing φ0 = RT/F and U0 = εeE0φ0/μ as the characteristic po-tential and velocity scales or non-dimensionalization,1 respec-tively, the non-dimensional Poisson equation then becomes

(1:8)

where, E0 is the constant electric field in x-direction, μ is viscos-ity of the fluid.

The equations for momentum, Poisson, and species leadto a total of 2 + (N − 1) system of partial differential equa-tions where N is the number of distinct mixture species

expressed as mole fractions and also accounted for in calcu-lations for electrical potential and fluid velocity. The systemof equations must be solved subject to boundary conditions,which are, in general, the no-flux conditions on each ionicspecies at the (solid) wall, either specified potential or speci-fied surface charge density, and the no-slip conditions on theaxial velocity. It is worth noting that once gating electrodes(for field-effect flow control, see Fig. 2 for the schematic) areincorporated, the boundary conditions deviate from the stan-dard conditions discussed here. For example, the field effectarising from the externally imposed gate potential must beaccounted for by solving for the electric potential inside thegate dielectric simultaneously.19 Specific boundary conditionsfor gated systems may also change if more than one gateelectrode is active requiring consideration of possible slipconditions and/or accounting for fringing and inter-gateelectrode capacitance effects.1–3,9,20–24

The underlying theoretical development for electricallydriven flows or electrokinetic flows in microfluidics andnanofluidics has been discussed extensively in numerous re-views and books.1–3,9,15,25–30 Therefore, only essential con-cepts are discussed here. When an electrically conductingfluid flows in a channel or conduit where the walls of theconduit are charged,31 this phenomenon is calledelectromigration.1–3 The region near the walls of the channelis characterized by an excess in the number of counterions(ions having charge opposite to the walls); this excess chargemust be balanced by the surface charge density. The regionnear the walls characterized by counterions pinned (consid-ered to be immobile) to the walls next to mobile co-ions andcounterions is called the electrical double layer (EDL).

The representative thickness of the EDL, which is charac-terized by the Debye length λD, is given by

(1:9)

Fig. 2 The schematic shows the geometrically comparative layout of a solid-state field effect transistor (FET) with a p-channel comprising holesas primary charge carriers. The right panel shows a nanofluidic FET with the microchannels acting as fluidic reservoirs analogous to the solid-stateFET. The primary charge carriers in this example are the cations suggesting that the surface charge on the walls of the nanochannel is negative.Assistance from C. Boone is acknowledged in the preparation for this figure.

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Here, εe is the permittivity of the solution, T is the tempera-ture, F is the Faraday constant, and Is is the ionic strength of

the solution, , where zi and ci are the valence

and molar concentration of the ith electrolyte species,respectively.

Background on field effect flowcontrol

Field-effect fluidic devices32 are analogous geometrically tothe solid-state electronic transistors (Fig. 2). One of the firstdemonstrations of using an external field to manipulate thewall zeta potential, ζ, used two capillary tubes with the annu-lus between the tubes filled with a potassium phosphatebuffer at pH 6.33 The buffer in the annulus was held at a dif-ferent potential than the axial potential driving the flowthrough the inner capillary permitting independent controlover the ζ.33 Notably, the fluid between the two capillarieswas also pumped using a vacuum pump to allow enhancedconvection for minimizing joule heating.33 Essentially, theidea to actively manipulate the surface charge and the surfacepotential for flow control was initiated in the literature as op-posed to then commonly used methods for passive surfacecharge modification15 or control over working fluid (i.e.

buffer) properties such as pH.34 Consequently, the idea offield-effect fluidics, later named as ‘fluiditronics’ through theuse of ‘flowFETs’ was put forth.35–38

In these early devices with field effect control over flows,typically glass capillaries were used with extension to variousconfigurations of microchannels for control over both electro-osmosis and particle transport.39 The axial fields commonlywere in excess of 100 V cm−1, and the gate potentials reportedwere in the several kV range for most microfluidic devices.40

The gate potentials were applied by wrapping or painting aconducting material over a portion of the capillary tube togenerate a structure for applying a transverse or gate poten-tial (Fig. 2), with continued engineering advances enablingmore robust microfluidic devices41 and subsequent loweringof the gate potential from several kV to O (100 V) range42 forelectroosmotic flow control.

Notably, in many microfluidic devices, the electrolyte solu-tion was in direct contact with the electrode. In the case ofthe transverse electrode, two types of excitation signals at thegate are possible, direct current (DC) or alternating current(AC). The AC gated devices in cases with direct fluid contactoperate in a regime governed by alternating current or in-duced charge electroosmosis (ACEO or ICEO).43–46 On a morehistoric note, the development of ACEO47 can be traced backto the origins of manipulating particles for assembly of col-loidal aggregates48,49 with continuing development of other

Table 1 Summary of some recent examples from published reports for myriad nanofluidic conduits or nanoarchitectures demonstrating a variety offabrication methods, range of length scales explored, and different materials used

Nanoarchitecturetype

Nanoarchitecturedimensions,Dia × L or L × W × H

Main nanoarchitecturefabrication methods Gate material

Gatedielectric

Gate dielectricdeposition method Reference

Nanochannel 25 μm × 25 μm (W × Honly)

Si etch and anodicbonding

Si contact Si3N4 None Schasfoort et al.(1999)

Nanopore/nanotube 10–100 nm × 10 μm Sacrificial etch of Sinanowires

Cr SiO2 LPCVD Karnik et al.(2005)

Nanochannel 120 μm × 1 μm ×30–40 nm

Sacrificial etch of poly-Si Cr SiO2 LPCVD Karnik et al.(2005)

Nanopore/nanotube ≤7.9 nm × 400 μm Sol–gel dip coating andcalcination

Cr/Au SiO2 Dip coating Fan et al. (2008)

Nanochannel 16 mm × 400–500 nm× 100 nm

Interferometriclithography and RIE

Doped Si SiO2 Thermal oxidation Oh et al. (2008)

Nanopore/nanotube 5–12 nm × 12 μm Nuclear track and etch Au SiO2 PECVD Kalman et al.(2009)

Nanopore/nanotube ≤10 × 140 nm E-beam, RIE TiN TiO2 ALD Nam et al.(2009)

Nanopore/nanotube ∼25 nm × 20 μm Nanowire templating ITO SiO2 LPCVD Vermesh et al.(2009)

Nanochannel 12 mm × 5–100 μm ×860 nm

RIE Si Si3N4 LPCVD Veenhuis et al.(2009)

Nanopore/nanotube 30 nm × 100 nm FIB or TEM Various Al2O3 ALD Jiang et al.(2010)

Nanopore/nanotube 160–220 nm × 80–140nm

FIB Au Al2O3 ALD Paik et al.(2012)

Nanopore/nanotube 20 × 300 nm Porous aluminamembrane

Al Al2O3 Anodization Shin et al.(2012)

Nanopore/nanotube 7.5 nm × 20 μm E-beam, RIE, wet etch Aluminum-dopedzinc oxide

Al2O3 ALD Lee et al. (2015)

Nanochannel 5 mm × 30 μm ×16 nm

UV lithography, wet etch Cr/Au PDMS Spinning Fuest et al.(2015)



emerging microfluidic methods for particle manipulationand aggregation.50 The use of ACEO methods has also led todevelopment of microfluidic pumps operating in a variety ofconfigurations.51–54 However, the methods of ACEO with di-rect contact of electrolytes and fluids with electrodes havealso led to reports with contamination of electrodes.55

As continued advances occur in nanofabrication, gatednanofluidic devices were reported56–58 showing several noveltransport phenomena not previously observed with gatedmicrofluidic systems.59,60 Moreover, in the nanofluidic de-vices, the electrodes were isolated from the fluid by means ofa dielectric layer (e.g. SiO2 or PDMS) leading to ‘field-effect’control over transport.

Development and characterization offield effect nanofluidic devices

Over the years, numerical and theoretical investigations formass transport and fluid flow in nanofluidics have rapidlyoutpaced experimental observations. In part, the key chal-lenges are the difficulties in fabricating and fluidically sealingnanoarchitectures that act as reliable conduits for such experi-mental studies. Nanofabrication has seen significant advancesover the past decade,3,9,61,62 including building upon the ad-vances from fabrication in solid-state electronics and micro-electromechanical systems (MEMS) technologies.63–65

Table 1 presents a summary of device platforms developedfor gated transport through various nanoscale conduits overthe past few years. The table does not present a comprehen-sive compilation of the results but attempts to capture the va-riety of materials, critical dimensions, and methods usedboth in fabricating the nanoarchitectures and the use of gatedielectric materials.66–74 From Table 1, it is evident that alarge variety of materials have been used and there is as yetno consensus or optimal choice of materials for fabricatinggated devices. Moreover, it is worth noting that a variety offabrication methods have also been used, which also demon-strates the need for a broader discussion on the best pathforward for designing and fabricating optimal field effectnanofluidic devices.

Field effect nanofluidic or gated nanofluidic devices com-prise the main functional nanoscale conduit or nano-architecture (i.e. a nanopore, a nanotube, a nanocapillary, ora nanochannel) which connects two fluidic reservoirs (cf.Fig. 2, the fluidic reservoirs are analogous to the ‘source’ and‘drain’ in the solid state FET) with an axial potential dropalong the length of the nanoarchitecture driving electroki-netic flow in the streamwise direction. An independently con-trolled ‘gate’ electrode is located at some position along thelength and applies a transverse potential to the device wall,thereby allowing control over the excess surface charge andsurface potential locally.

Gated nanopore and nanotube devices feature similar ra-dial geometries as the original capillary electrophoresismicrofluidic systems. Typically, the nanopore or nanotubewill present a circular or elliptical cross-section75,76 with an

embedded electrode77 that acts as the gate electrode. Notably,the gate electrode sits as a band along the entire circumfer-ence of the nanopore or nanotube. Moreover, the position ofthe gate electrode with respect to the downstream (or up-stream) distance from the ‘source’ (or ‘drain’) reservoirs hasbeen shown to affect ionic flow in radial and non-radialgeometries.78,79

As discussed above, the geometric similarity with solid-state FETs leads to operational similarities as well. One ofthe key elements in determining nanofluidic FET operationis the role of leakage or gate current i.e. the measurable, fi-nite current that may be induced due to coupling betweenthe gate and the drain. Typically, in solid-state devices, theleakage current causes issues with parasitic energy loss, de-termination of an accurate ‘off’ state, and scaling ofMOSFETs to the deep sub-micron regime.80 Similarly, innanofluidic FET devices, the overlap between the gate anddrain regions in affecting gate induced leakage current hasalso been reported.81 In contrast to the solid-state devices,mechanistic understanding of the electrolyte type and com-position, nanochannel dimensions and designs, gate dielec-tric material and thickness, and applied potentials (both axialand gate) on leakage current (Ig) remains an open question.Moreover, the primary management of leakage current is bylimiting the range of gate potentials used with respect to theapplied axial potentials.20,79,81

The development of field effect nanofluidic devices(FENDs) has also been aided by significant theoretical andmodelling analysis to explain and validate observed experi-mental trends including extent of gate, dielectric thickness,ion compositions, and pH dependence.21,24,82–86 Interest-ingly, while the modelling investigations have matched manyexperimental results, these results have also shown differ-ences with a significant gap in theory and experiments andtherefore a continued need to not only refine but also de-velop new models that account for changes in local pH, pos-sible site binding and/or surface reactions with multiple spe-cies, and effects of leakage current.23,87–90

Fig. 3 shows a snapshot from the variety of configurationsthat have been reported for the FENDs with critical dimen-sions varying from sub-10 nm to 35 nm. It is important tonote that in slit-like nanochannels such as those shown inFig. 3A, B, and D and in yet another configuration in Fig. 4, itis essential to determine accurately the depth of the nano-channel since that is the governing length scale for the flow.Typically, before nanochannels are sealed, the depth is mea-sured by means of an AFM.91,92 Once the nanochannels aresealed or bonded, two commonly used methods for furtherverification of the nanochannel depth are typically deployed.One is direct cross-sectional SEM imaging as shown in Fig. 4.However, direct cross-sectional imaging is difficult due toseveral challenges, including the possibility of change inchannel dimensions during the process of cutting to obtainan open cross-section.91

The second method commonly used to determine thenanochannel depth is indirect and is based on a fit to the



measured nanochannel conductance. As an example, con-sider the nanochannel conductance G for KCl across a rangeof concentrations, given by93

(1:10)

Fig. 3 The images show examples of nanochannels or nanopores with embedded and isolated gate electrodes. (A) The schematic for a fieldeffect nanofluidic (FET) device geometrically analogous to a solid-state transistor57 and (B) the scanning electron microscopy (SEM) imagefrom Karnik et al. (2005), showing silica nanochannels with gate electrodes.57 Reprinted with permission from Karnik et al., Nano Lett., 2005,5, 943–948. Copyright (2005) American Chemical Society. (C) Another configuration shown as a schematic for the FET with the fluidic con-duit being a nanopore. In this configuration, a membrane with a TiN layer was sandwiched between silicon nitride films with nanopore for-mation following established MEMS processes.81 TiO2 atomic layer deposition (ALD) was used to yield the final nanopore with isolation asshown by the orange layer at a critical dimension of sub-10 nm.81 Reprinted with permission from Nam et al., Nano Lett., 2009, 9, 2044–2048. Copyright (2009) American Chemical Society. (D) A schematic showing yet another nanofluidic FET configuration for development ofreconfigurable diodes.19 Reprinted with permission from Guan et al., Nat. Commun., 2011, 2, 506.

Fig. 4 Sequence of images showing (A) the three material layers comprising a nanofluidic platform recently reported for a field-effectnanofluidic switch.79 Notably, in this work, the microfluidic knowledge base of working with glass–PDMS was exploited for an easier fabrica-tion system compared to many of the other systems reported and discussed in this review. (B) SEM image for the nanochannel cross-section showing a 16 nm deep nanochannel bonded and sealed with the PDMS–glass interface, (C) schematic showing the cross-sectionalgeometric layout, and (D) side-view schematic showing the position of the gate for controlling field-effect transport in the nanochannel.Reprinted with permission from Fuest et al., Nano Lett., 2015, 15, 2365–2371. Copyright (2015) American Chemical Society.



where μi is the ionic mobility for species i, NA is Avogadro'snumber, w is the width of the nanochannel, L is the length ofthe nanochannel, h is the nanochannel depth or height, c isthe bulk concentration, e is the elementary charge, and σs isthe surface charge density. The conductance (inverse of resis-tance and usually quantified as measured current divided byapplied stream-wise voltage) is classified over two distincttransport regimes as a function of bulk concentration. Thesecond term is referred to as the bulk transport governed re-gime (BTGR) and is used as a fitting equation to measuredconductance to estimate the nanochannel height with variousexamples from reported data shown in Fig. 5. The surfacecharge governed regime (SCGR) is also used to fit to the ‘pla-teau’ part of the measured data in Fig. 5A to estimate the sur-face charge density within the nanochannels. The concentra-tion at which the BTGR transitions to SCGR is called thetransition concentration, ct, and has recently been shown tobe a function of type of cations in the solution for negativelycharged surfaces.87 Notably, in ungated nanofluidic configu-rations with positively charged walls, the relative importanceof anions and their valence has also been shown.89

Therefore, the implication of many of these reports forvarious nanofluidic configurations is that as the EDLs be-come larger due to either dilute electrolyte solutions or re-

ducing nanoarchitecture critical dimensions deviations occurfrom the common thin EDL assumption in microfluidics,3

the counter-ions not only dominate transport16,17,94 but alsoinfluence nanochannel conductance, selectivity, and gatingcharacteristics.87 It is worth noting that the approachdiscussed here for KCl with respect to eqn (1.6) assumes thatKCl is fully dissociated in the BTGR. Moreover, ionic mo-bilities used for fitting experimental data are usually tabu-lated bulk values. Due to the importance of using conduc-tance as a metric for quantifying ionic transport throughboth gated and ungated nanochannels, and the use ofungated nanochannel conductance as a baseline to deter-mine the effect of gating or recording gated current mod-ulation, a new terminology for ungated conductancetermed as ‘intrinsic conductance’ for the nanochannelshas also been proposed.87

It can be seen from eqn (1.10) that the SCGR is indepen-dent of the nanochannel height and is a function of the sur-face charge density. Therefore, it would be expected that un-der dilute solution conditions when EDLs interact theconductance will change with changing surface charge aswas indeed confirmed,57 and a representative data set isshown in Fig. 5B with the height independence58 shown inFig. 5C.

Fig. 5 The images show representative data for ungated (intrinsic)79 nanochannel conductance which forms the baseline for comparison in gateddevices. (A) Representative data reported for a nanofluidic switch by Fuest et al. (2015)79 with broad regions for SCGR and BTGR marked as shownfor the discussion corresponding to eqn (1.6). The transition region is also shown which varies as a function of concentration and ion type.109

Reprinted with permission from Fuest et al., Nano Lett., 2015, 15, 2365–2371. Copyright (2015) American Chemical Society. (B) Data from Karniket al. (2005)57 showing changes in nanochannel conductance for various surface charge densities. Reprinted with permission from Karnik et al.,Nano Lett., 2005, 5, 943–948. Copyright (2005) American Chemical Society. (C) Data from Stein et al. (2004)58 showing that in the SCGRnanochannel conductance is independent of channel height. Reprinted with permission from D. Stein, M. Kruithof and C. Dekker, Phys. Rev. Lett.,2004, 93, 035901. Copyright (2004) by the American Physical Society.



As discussed briefly above, the role of leakage current inmost nanofluidic devices has been discussed peripherally bylimiting the applied gate potential and minimizing the con-tribution of leakage current to the total current as a generallyaccepted practice, although some researchers use a thresholdwith measured leakage current lower than the total axial orionic current.19 However, since most fabricated devices usethin films as isolating dielectric layers, some finite leakagecurrent is likely expected and evaluation of the presence ofleakage current on specific applications may require furthersystematic investigation.

Applications

The main promise of nanofluidics, including gated devices,is due to the fact that engineered systems can now approachlength scales similar to the critical inter- and intra-cellularlevel structures that permit essential transport in biology.Therefore, it is not surprising that the first applications fornanofluidics were in achieving selective transport10,95–100

mimicking biological ion channels that use a combination ofsurface charge and nanoscale dimensions to permit selectiveion transport along with explorations of these technologicalplatforms for biological and chemical species analysis.101,102

One of the methods to fabricate gated nanoarchitecturescomprises the use of an ion beam or electron beam to millthrough-holes in free-standing polymeric membranes76,77 (seeadditional examples in Table 1). Usually, the free-standingmembrane is first coated with a metallic layer (e.g. Au), and

then, the through-holes are drilled. Subsequently, conformaldeposition methods such as ALD are used to electrically iso-late the metal layers and form the gated structure. In a recentreport, ∼200 nm diameter electrically gated nanopores wereused as a biomolecular switch.71 It was shown that the gatednanopore structure demonstrated effective electrostatic con-trol of the nucleic acid transport with >1000-fold modulationusing sub-1 V gate biases. The authors showed that by usingexternally controlled parameters of surface charge and electro-lyte concentration, the relative contribution of electroosmoticflow and DNA electrophoresis could be manipulated permit-ting the reported levels of DNA capture.71

One of the main reasons to use gated nanofluidic devicesfor DNA analysis and related assays is because DNA translo-cates too quickly across a nanofluidic architecture, and there-fore, any analysis would command significantly higher tem-poral resolutions in imaging or DNA detection than currentlyavailable. Therefore, by gating, ionic and molecular flows canbe controlled to manipulate the translocation of DNA.71,78 Inanother recent example, it was shown that for a 50 nm criti-cal dimension on the nanofluidic architecture, translocationspeed of λ-DNA chains decreased from over 18 mm s−1 to1.33 mm s−1 by changing the gate potential from a floatingstate to 9 V.103 In other related experiments with dyes orusing fluorescence based measurements to evaluate the effectof the gate potential,70,104 it has been shown that the trans-port control is significantly enhanced at dilute concentrations(i.e. increasing Debye length) and therefore once againconfirming the important role of surface charge in

Fig. 6 The images show one example of manipulating large molecules such as proteins (A and B)20 in nanochannels with gate voltage. Reprintedwith permission from R. Karnik, K. Castelino and A. Majumdar, Appl. Phys. Lett., 2006, 88, 123114. Copyright (2006) by the American PhysicalSociety. And also switching ON/OFF states for ionic transport (C and D)79 in field effect nanofluidic devices. Reprinted with permission from Fuestet al., Nano Lett., 2015, 15, 2365–2371. Copyright (2015) American Chemical Society.



nanofluidics. It is expected that the next stage of many of thesetypes of biological analyses will be to perform logic operationswith the FENDs. In order to facilitate these envisioned logic op-erations, nanoscale fluidic switches have been reported (Fig. 6).

Most biological assays for gene sequencing, targeted drugdelivery,105,106 and eventual use in clinical diagnostics rely onspecific analysis of ionic and molecular components in bio-fluids. One of the challenging problems pertains to analysisof proteins. For example, in a recent review on the benefits ofmicrofluidics for biological applications,107 it was discussedthat conventional immunoassays are unable to determine ifthe observed covariance between proteins is connected to sin-gle cells or a by-product of interaction from a pooled sample.The use of small volume analysis enabled by microfluidicsand nanofluidics has assisted in profiling specific signallingproteins due to confinement of lysates from individualcells.107 In contrast to ions and DNA, proteins present signifi-cant analytical challenges due to the ability to change confor-mation or structural rearrangement in the presence ofcharged surfaces.108 By using a liquid volume of <1 pL, gatednanochannels were used to demonstrate direct flow controlover a model protein, avidin,20 presenting one of the early re-ports on the use of fluidic transistors for development of pro-posed integrated circuits for analysis of single cell contents.The performance of these gated devices was limited due toleakage current through the gate.20

The examples for various applications here show the po-tency of field-effect nanofluidics as a platform for potentiallyremarkable advances that go well beyond existing tools forchemical and biological species analysis and related trans-port phenomena.

Summary and conclusions

Nanofluidics in general and the sub-domain of gated nano-fluidics form a vibrant and exciting area of research. Many re-searchers have demonstrated numerous advances in fabrica-tion technologies, related theoretical and modellingdevelopments, and important applications. Despite this rapidprogress and growing body of knowledge over the past de-cade in gated nanofluidics, many questions remain open asdiscussed throughout this mini-review.

Acknowledgements

The authors express their gratitude toward the wonderfulcommunity of scientists and engineers that have madepioneering advances that permit this review. We also ac-knowledge funding from various US federal agencies that hascontributed to our work cited in this article, including the Na-tional Science Foundation (NSF), the US Army Research Office(ARO), and the Department of Energy (DoE).

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