SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION Anomalous Ion Transport in 2-nm Hydrophilic Nanochannels Chuanhua Duan and Arun Majumdar 1. Nanochannel Fabrication Figure S1 Nanochannel Fabrication Scheme Nanochannel width and length are defined by standard photolithography. Lam 4, a RIE (Reactive Ion Etching) instrument from Lam Inc was used for nanochannel etching. Two reactive gases were used during this step. SF 6 plasma RIE was used to remove native oxide layer on top of the silicon wafer and Cl 2 plasma was used to etch silicon. In our nature nanotechnology 1

2 supplementary information process, SF 6 etching was carried out at 50 W for 7 seconds and Cl 2 etching was carried out at 50 W for 13 seconds. The short etching duration and small power ensures shallow channel as well as small surface roughness. Following the nanochannel etching step, microchannels around 1 cm long and 500 μm wide were defined and etched. A standard deep reactive ion etching (DRIE) recipe was run for 20 minutes to etch 60-μm-deep microchannels. The top surface was then coated with a 1-m-thick oxide layer using PECVD (plasma enhanced chemical vapor deposition) at 350 C. This layer serves as a protection layer for both micro- and nanochannels during the subsequent reservoir etching step. Reservoirs were pattered from the back side and DRIE was again used to form straight etch-through holes. The 1-μm-thick oxide layer was removed by 5:1 HF solution after this step. The wafer was then sent into a furnace to grow a thermal oxide film at 1000 C. A 200 nm-thick dry oxide and a 300 nm-thick wet oxide was grown uniformly on the whole wafer surface. The total 500-nm-thick thermal oxide not only provides a good insulation layer for later electrical measurements but also avoids channel collapsing during anodic bonding. Afterwards, the silicon wafer was cut into dies and checked by AFM before final bonding. Channel width and height were confirmed from AFM images using the cross section analysis. In the meantime, a Pyrex wafer was also cut into dies with identical sizes. All dies were cleaned in hot piranha solution and blowdried by nitrogen. A glass die and a silicon die were brought into contact before putting them into the hotplate. Another silicon die with the similar size was placed on top of the glass die. This small piece was used to stabilize the temperature and uniformly distribute 2 nature nanotechnology

3 supplementary information the electrostatic field. Addition of this die also changed the traditional point contact during anodic bonding into plane contact, resulting in fast bonding and better quality. The hotplate was then heated and kept at 400 C for at least one hour. Bonding took one minute under 600 V (Fig. S2a). Since there are etch-through reservoirs in the silicon wafer, bubbles were not trapped during this process. After bonding, the chip was maintained on the hotplate for one night. This step is like an additional fusion bonding step, which increases the bonding quality but does not significantly change the channel height 1,2. Thereafter, the bonded chip was placed in a PECVD chamber with reservoir side up to grow a 3-μm-thick PECVD oxide on all exposed surface. This additional oxide layer prevents electrical leakage from any sharp corner. Finally, a 1-μm-thick PDMS was coated on top of the oxide layer using a stamp-stick technique 3. This PDMS layer is hydrophobic and thus prevents solution cross-contamination among reservoirs. nature nanotechnology 3

4 supplementary information 2. Nanochannel Stability a Silicon/Metal Glass 600V b C gap Silicon Hotplate 400 degree C c C gap C oxide Figure S2 Schematics of die-die anodic bonding and the equivalent electronic circuits. a, Schematics of die-die anodic bonding process. b, Normal anodic bonding with its equivalent electronic circuit. c, Anodic bonding with thick oxide layer and its equivalent electronic circuit. The thick oxide adds a serial capacitor during anodic bonding, which reduces the electrostatic pressure and avoids channel collapsing. 4 nature nanotechnology

5 supplementary information Figure S3 Schematic of gap of length w and height h at interface between glass and silicon subjected to externally imposed electrostatic pressure P. In the present work, anodic bonding with a thick oxide layer was used instead of the normal anodic bonding. Mao and Han used this approach to fabricate nanochannels down to 10 nm and found that the maximum channel width before channels collapse is a linear function of channel height 1. This observation is different from that of traditional anodic bonding, where the maximum channel width is a cubic function of channel height 4. We explored the underlying reason and found that this new trend could help us push the fabrication limit further. During a normal anodic bonding process, a glass wafer contacts a silicon wafer directly; while in the current case there is an additional thick oxide layer on top of the silicon wafer, which is originally designed to provide electrical isolation between silicon substrate and fluid solution. This oxide layer adds a capacitor in series, nature nanotechnology 5

6 supplementary information which shares a large fraction of the applied voltage drop and thus reduces the electrostatic attractive force between channel surfaces. Figure S2 shows the schematics of the bonding process and the equivalent electronic circuits. The stability of shallow channel fabricated on silicon wafer by anodic bonding with glass substrate has been considered by Shih et al 4. The same analysis was used here to determine the maximum channel width for a given channel height. Consider the geometry shown in Fig. S3, in which plane strain conditions and elastic deformation are assumed. The upward displacement of the silicon wall u Si and the downward displacement of the glass wall u g, as a function of horizontal distance x away from the centre of the channel are expressed as /2 Si ESi P w w usi 2(1 v ) ( x ), x (S1) 4 2 and /2 g Eg P w w ug 2(1 v ) ( x ), x (S2) 4 2 where P is the electrostatic pressure in the cavity, Si and g are the Poisson s ratio for silicon and glass, and Si and g are the Young s modulus for silicon and glass at the bonding temperature respectively. P could be further expressed as 2 1 Vgap P 0 (S3) 2 2 h where is the permittivity of vacuum, V gap is the voltage drop across the gap and h is the 6 nature nanotechnology

7 supplementary information channel height. The maximum displacement, u max, of the two walls occurring when x 0 is given by P P P u (1 v ) w(1 v ) w w (S4) 2 2 max Si Si ESi ESi Eeff defining the effective Young s modulus, E eff, through the equation (1 v (1 Si ) vg ) (S5) E E E eff Si g If umax h, the depth of the channel, channel will collapse during the anodic bonding process. Therefore, the largest channel width w max, able to survive collapse for a given height h satisfies the equality w E h (S6) 3 eff max 2 0Vgap For normal anodic bonding (Fig. S2B), V gap can be assumed to be equal to the applied voltage, resulting in w E h (S7) 3 eff max 2 0Vapplied Therefore, w max is proportional to h 3 for collapse to be avoided. For anodic bonding with a thick oxide layer, the layer serves as a series capacitor (Fig. S2C). The accumulated charge Q thus could be given as Q CgapVgap CoxideVoxide (S8) where C gap and C oxide are the capacitor of the gap and oxide layer, V gap and V oxide are the voltage drop across the gap and oxide layer, respectively. The sum of V gap and V oxide is nature nanotechnology 7

8 supplementary information equal to the applied voltage V applied. C gap and C oxide can be further expressed as C and C wl (S9) h gap 0 wl (S10) d oxide 0 oxide oxide where l is the channel length, oxide is the relative dielectric constant of silicon dioxide, and d oxide is the thickness of the oxide layer. V gap is then related to V applied through the equation Vgap V V oxide gap Voxide V applied h d h d h d oxide oxide oxide 0 0 oxide 0 0 oxide 0 0 oxide (S11) which can be rewritten as V gap h Vapplied 0 h d oxide 0 0 oxide (S12) In the case of h d oxide, equation (S12) can be further simplified as V gap V applied oxide (S13) d oxide h Substituting equation (S13) to equation (S6), w max for anodic bonding with thick oxide layer satisfied the equality w 2 eff oxide max 2 2 0Vappliedoxide E d h (S14) Therefore, w max is linearly proportional to the product of h and 2 d oxide. 8 nature nanotechnology

9 supplementary information Equations (S7) and (S14) relate the maximum channel width with channel height for normal anodic bonding and anodic bonding with thick oxide layer, respectively. It is clear that the addition of oxide layer will significantly increase the channel survivability as long as the oxide thickness is much larger than the designed channel height. Our tests proved that a 500-nm thermal oxide is thick enough to fabricate 2-nm-deep, 2-μm-wide nanochannels without channel collapsing. nature nanotechnology 9

10 supplementary information 3. Capability to detect fluorescent signal from 2-nm nanochannels Intensities of these two epifluorescence images were measured in Wasabi (Hamamatsu) using its area intensity analysis tool. The intensity of the dark background in both images is 205±1.6. The signal from 30-nm nanochannels is around 380±7. The net signal from fluorescent R6G molecules in 30 nm nanochannel is thus 175±7. Using a linear extrapolation based on the channel height, the net signal from fluorescent R6G molecules in 2 nm nanochannels should be 175, which is 12. The corresponding noise from the nm nanochannels is equal to 7, which is 1.8 as the shot noise is proportional to the 15 square root of the photon number. Consequently, the signal that we expect to measure in 2nm nanochannels should be 2 2 (205 12) , which is 217±2.4. Since the background is only 205±1.6, such signal is definitely detectable. We could also evaluate the expected fluorescent signal in 2 nm nanochannels based on the size of R6G. Since its diameter is around 1.2 ~1.4 nm, there are at most 25 layers of R6G molecules in 30 nm channels while only one layer in 2 nm channels. The net signal from fluorescent molecules in 2-nm nanochannels thus should be 175 7, which is ±1.4. The signal we expect to measure thus is 2 2 (205 7) , which is 212±2.1. This signal is again detectable, compared to the background intensity 205± nature nanotechnology

11 supplementary information 4. Ionic Conductance Measurement A Keithley 6430 sourcemeter (Keithley Instruments Inc.) controlled by a Matlab program was used for the conductance measurements. Ag/AgCl electrodes were used to make contact with the solutions. A home-built Faraday cage was used to isolate the measurements from electromagnetic waves and electric fields. Measurements were carried out at low voltage bias (±50 mv) using a single spiral out sweep sequence 0, +10, , -50 mv. For each measurement, we measured the conductance from reservoir 1 and 2 (total conductance) as well as reservoir 1 and 3 (microchannel conductance). The conductance from the nanochannels was then extracted from these two measurements. The ionic solution was introduced from top reservoir of the microchannel. Vacuum was applied to the other side of the channel to drive the solution flowing through the microchannel. This rinsing process was kept running for 5 minutes when a new ionic concentration was introduced. Conductance measurements were then immediately carried out three times. Between any two measurements, rinsing was also done twice using the same solution. This rinsing avoids concentration polarization during the measurement. The average conductance of these three measurements is referred as initial conductance at this concentration. The above steps of rinsing and measuring were repeated from low concentration to high concentration till all initial conductances were obtained. To investigate the time dependence of ionic conductance, measurements were taken after the chip was immersed into the solution for a period of time. Final conductance nature nanotechnology 11

12 supplementary information measurements at steady-state were done when the chip was immersed into the solution for at least 12 hrs. 12 nature nanotechnology

13 supplementary information 5. Solution ph measurement The adsorption of carbon dioxide can change ph of aqueous solutions. Carbon dioxide dissolves slightly in water to form a weak acid called carbonic acid, H 2 CO 3, according to the following reaction CO HOHCO Carbonic acid dissociates in water to form carbonate and bicarbonate. H CO HCO H CO H Protons are produced during this dissociation process. As a result, the ph of water exposed to air is around 5 instead of 7. All solutions used in this work were measured by a ph meter (PHB-600R from OMEGA). Figure S4 presents ph of KCl, NaCl and HCl solution. nature nanotechnology 13

14 supplementary information Figure S4 ph measurement at various concentrations. 14 nature nanotechnology

15 supplementary information 6. Slow Proton-Cation Exchange Process In the present investigation, we studied ion transport by experimentally measuring ionic conductance along nanochannels. We explored time and concentration dependence on ionic conductance. Figure S5 shows the time dependence of KCl conductance at 10 M, 1 mm and 1 M. Since the nanochannel is 140 μm long, K + and Cl - should diffuse from the microchannels and fill the nanochannels in a relatively short time (within 5s based on bulk diffusivity). It was not expected to see any conductance change with time after we completely rinsed the microchannels for 5 minutes. However, ionic conductance indeed changed with time. At 10 μm and 1 mm, it takes about 10 hours to reach a saturation point. Although 1M concentration takes less time, the duration is still much longer than the bulk diffusion time. There are several possible reasons. One is that the ion diffusivity decreases significantly in such small channels. Since diffusivity is directly proportional to ionic mobility, any change in diffusivity should reflect on the channel conductance. However, it is found that the mobility remains at least within the same order of magnitude according to the calculation based on the final conductance of 1 M KCl, which signifies that diffusivity does not significantly decrease. Hence, there must be some other reason. nature nanotechnology 15

16 supplementary information Figure S5 Time-resolved conductance of KCl solutions. Conductance reaches saturation within about 10 hours at concentrations of 10μM and 1 mm, while it reaches saturation within about 1 hour at 1 M. It is well known that silicon dioxide surfaces are negatively charged when it is brought into contact with aqueous solutions. It has been reported that kinetics of cationic adsorption on silicon dioxide surface is a slow process 5. The rate of cation adsorption depends on proton concentration and temperature. For a neutral solution, this process could take several hours while it could further extend to several days for a strong acidic solution. Raider et al. propose that protons occupy all available cation sites first due to its 16 nature nanotechnology

17 supplementary information higher diffusivity 5 than other ions. It is the competition between protons and other cations that causes the slow adsorption. Since we performed all the measurement at atmosphere, the ph in DI water and all other ion solutions was not 7 but around 5 due to CO 2 adsorption. Although the proton concentration was still low in the bulk solution, it could be relatively high inside 2-nm nanochannels due to electrostatic attraction of the negative surface charge. For example, given a surface charge density = 1 mc/m 2, the proton concentration could be as high as 10 mm ( n H + 2 / eh ) in a unipolar solution 6, where h is the channel height and e is the electron charge. These protons could significantly delay the cation adsorption kinetics. To prove this argument, the time dependence of HCl conductance at various concentrations was also investigated. The results are plotted in Fig. S6. In contrast with the behavior of KCl solutions, the conductance of HCl did not change with time at concentration 10 M and 1 mm. These results add strong evidence for the hypothesis of protons-cations competition. It is worth noting that at 1 M HCl concentration, the duration for equilibration is the same as that for 1 M KCl solutions. It is unclear at this point what causes this long saturation time at high HCl concentration. nature nanotechnology 17

18 supplementary information Figure S6 Time-resolved conductance of HCl solutions. The conductance of 10μM and 1 mm doesn t change during the measurements, while the conductance of 1M HCl saturates after half an hour. Error bars based on least count error analysis are not shown in the plot since they are smaller than the size of the symbol. 18 nature nanotechnology

19 supplementary information 7. Theoretical Model A one-dimensional analytical model considering quasi-electroneutrality condition and surface charge change was developed to quantitatively estimate channel concentration and surface charge density in 2-nm nanochannels. Consider an electrolyte solution that only includes KCl, HCl and water, and denote the ionic concentration by n H, n +, K n and n -, respectively. - OH Cl For a given surface charge density, the quasi-electroneutrality condition requires 2 /eh n n n n (S15) OH Cl H Na The surface charge is considered only from dissociation of surface silane group, which is changed with ph 7,8 as 0 0 K d K d n H + (S16) is the maximum possible charge density, is the fraction of sites actually dissociated and K d is the equilibrium dissociation constant. We use the Donnan equilibrium condition 9 to relate electric potentials and concentrations inside the nanochannel (nc) and the reservoir (bulk). n n nc bulk n n nc bulk e exp ( nc bulk ) kt e exp ( nc bulk ) kt (S17) Equations (S15-S17) yielded a set of nonlinear equations that was solved using Matlab. We assume ph in all KCl/NaCl solution is 5. The total charge density is assumed to be nature nanotechnology 19

20 supplementary information C/m 2, which corresponds to 8 charges/nm 2 and K d is set to be equal to 10-6 M 10. Both and K d chosen here are based on maximum reported values 11. This 1-D model is valid for all HCl solutions (from 10 μm to 1 M) and KCl/NaCl solutions below 10 mm where ionic concentration along the channel height direction can be assumed to be uniform. For higher concentration KCl/NaCl solution, this model will significantly overestimate the surface charge. In such case, we ran a 2-D simulation similar to ref. 12 to calculate surface charge density and nanochannel ionic concentration. The governing equations are Poisson-Nernst-Planck (PNP) equations, which are shown as below. 1 2 zaen a 0 a (S18) ( J ) 0 (S19) a zaena Ja Da( na ) kt (S20) Here is the permittivity of vacuum, is the dielectric constant of solution. Z a, J a and D a are the charge, flux and diffusivity of ions of species respectively. 1 μm 20 nature nanotechnology

21 supplementary information Figure S7 2-D domain for PNP simulation. Fig.S7 shows the 2-D domain for the simulation, where the total length of the channel is 1m and the height is 2 nm. Reservoirs 1 m x 1m in size are considered on both sides of the channel. We used the same boundary conditions as in ref. 12 for this 2-D simulation. The channel surface charge density was defined by equation (S16) instead of using a constant value. Equations (S18-S20) and (S16) were solved simultaneously. Afterwards, integration was carried out in the whole channel area to calculate the average ionic concentration. Table S1 lists the surface charge density and nanochannel ionic concentration estimated by these two models for KCl /NaCl solutions. The difference between these two models is less than 10% below concentration 10 mm. Table S1 Comparison between 1-D analytical Model and 2-D PNP simulation for KCl solutions in 2-nm nanochannels. 1D Analytical Model 2-D PNP Simulation n (M) mc/m 2 ) K + (mm) Cl - (mm) H + (mm) mc/m 2 ) K + (mm) Cl - (mm) H + (mm) 8.01E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-03 nature nanotechnology 21

22 supplementary information We also used this 2-D model to estimate surface charge density and ionic concentration for larger nanochannels (20-nm above). Figure S8 charts the measured KCl conductance and the corresponding 2-D theoretical prediction for 25-nm and 54-nm nanochannels. Combining with the concern of ionic mobility change, we can predict the ionic conductance in larger channels within 20%. Figure S8 KCl Conductance in 25-nm and 54-nm Nanochannels. 22 nature nanotechnology

23 supplementary information The above model (equations (S15-S17) for 1D and equations (S16) and (S18-29) for 2D) is very similar to the well-known site-dissociation and buffer-capacity model 10,13, which has been used to predict streaming current 11 in large nanochannels and ionic conductance in 10-nm nanopores 8. In that model, zeta potential is connected to the surface charge density through the following equation, kt B kt n B H, bulk ( ) ln ln e e K C 0 d (S21) where nh, bulk is the bulk proton concentration and C is the Stern layer s phenomenological capacity (2.9 C/m 2 for silica surface). To find the self-consistent solution in the surface charge governed regime, the site-dissociation and buffer-capacity model model runs a set of 2-D simulations that use different values of as boundary conditions to plot zeta potential as a function of. Intersection of this function with equation (S21) gives the final and. The final is then used as the boundary condition for another simulation to find the final concentrations n inside the nanochannel. Similar to that model, the model used in this paper also considers the surface-site- dissociation (see equation (S16)). The surface potential can be derived as a function of the surface charge density from equations (S16-S17) kt B kt n B H, bulk ( ) ln ln e e K 0 d The only difference between equation (S21) and (S22) is the third term (S22) in equation C (S22), which describes the potential drop through the Stern layer. In this paper, we nature nanotechnology 23

24 supplementary information intentionally ignore this term in our model. Such simplification does not affect the final simulation results a lot since this term is negligible compared with the other two terms in equation (S21). Furthermore, such simplification shortens calculation time significantly since we only need to run one 2-D simulation to get the final solution by using equation (S16) directly as the boundary condition. Table S2 and S3 show the simulation results of these two models for 2-nm and 25-nm nanochannels. In the surface charge governed regime, the difference in terms of surface charge density is less than 4%. In the bulkbehavior regime, such difference become bigger due to the increasing surface charge density, however the difference in terms of concentration is still low (below 10%). Table S2 Comparison between the current model and the sitedissociation and buffer-capacity model in 2-nm nanochannels. Current Model Site-dissociation and Buffer-capacity Model n (M) mc/m 2 ) K + (mm) Cl - (mm) H + (mm) mc/m 2 ) K + (mm) Cl - (mm) H + (mm) 4.97E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E nature nanotechnology

25 supplementary information Table S3 Comparison between the current model and the sitedissociation and buffer-capacity model in 25-nm nanochannels. Current Model Site-dissociation and Buffer-capacity Model n (M) mc/m 2 ) K + (mm) Cl - (mm) H + (mm) mc/m 2 ) K + (mm) Cl - (mm) H + (mm) 5.22E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 nature nanotechnology 25

26 supplementary information 8. Surface Charge as a Function of Channel Height Surface charge density in a nanochannel decreases with the decreasing channel height (Fig. S9). This can be explained as follows. Consider a channel where a surface reaction is in equilibrium. A reduction of channel height will result in an increase of all cation concentration. The consequent increase of nh will shift the surface reaction towards the formation of silanol groups. As a result, less silanol groups will be dissociated and hence the surface charge will be less than before. Figure S9 Surface charge as a function of channel height. 26 nature nanotechnology

27 supplementary information 9. Bulk Ionic Mobility Estimation It is well known that ionic mobility will decrease with the increasing concentration. For KCl/NaCl solutions, the ionic mobility at 1M is around 75% of that at infinite-dilution. This trend can be predicted by a modified Debye-Hückel theory 14. For full dissociated ions such as K+, Na+, Cl-, ionic mobility in a bulk solution can be expressed as bulk 1 cz 1 Iz 1 1 ca I 2 z (S23) where ( ) 3/2 c T and ( ) 1/2 c T depend on the absolute temperature and the dielectric constant of the solvent (For water at 25, 1 1/2 c ), nm M I 1/2 2 z j j j c M 1/2 and zn is the ionic strength, and a is an adjustable parameter related to the ion size (for K + /Cl -, a 0.3 nm, for Na +, a 0.4 nm ) 15. Mobilities of K +, Cl -, and Na + in infinite-dilution are m V s , m V s and m V s , respectively. Since proton transport is based on a totally different mechanism, we assume proton bulk mobility does not change, which is always equal to the proton mobility ( m V s,, H bulk H ) in infinite-diluted solutions. nature nanotechnology 27

28 supplementary information 10. Mobility Error Analysis Cation mobility in surface-charge-governed regime is expressed as nc Gl /2w (S24) Accordingly, the uncertainty of nc / bulk can be estimated as ( nc / bulk ) G l w bulk (S25) / G l w nc bulk bulk The major uncertainty of the mobility ratio comes from the determination of nanochannel height and width by AFM. The uncertainty of channel height is around 10% as the channel surface roughness is 0.2 nm. Although channel height is not an explicit factor for the uncertainty, the surface charge and nanochannel concentration indeed changes with the channel height. In fact, for a given channel height and a certain bulk concentration, the corresponding surface charge density and ion concentrations inside the nanochannel can be calculated from equation (S15-S17) (1-D model for small channel and low concentrations) or from Eq. (S16) and (S18-S20) (2-D simulation). Figure S9 has shown the dependence of the surface charge density on the channel height. From this model, the 10% uncertainty in channel height will translate into a 5% uncertainty in and nsince the bulk mobility is a function of n, such variance in n will also yield a 1% uncertainty in bulk. The uncertainty of channel width estimated from AFM scanning image is less than 5%. Other uncertainties are from the conductance measurement and channel length estimation. G G / is around 15%. nc bulk l is within 3% while l is less than 1%. The total uncertainty of 28 nature nanotechnology

29 supplementary information 11. Device to Device variation The whole final conductance measurements have been carried out in two different 2-nm nanochannel devices. Fig. S10 shows measured steady-state conductances from these two devices. All data shown in this paper is from Device 1. Regarding the device to device variation, conductances from two devices are really close in the surface-charge-governed regime, with a variation less than 10 %. The conductance difference in the bulk behavior regime is approximately 20%). Figure S10 Measured stead-state conductances from two different 2-nm nanochannel devices. nature nanotechnology 29

30 supplementary information 12. Mobility as a Function of Channel Height Figure S11 shows the dependence of cation mobilities on the channel height. Mobilities of K + and Na + ions were calculated based on conductances of 1 mm electrolyte solutions, while proton mobility was obtained from conductance of DI water. There is a clear trend that cation mobilities increase as the channel height decreases from 25 nm to 2 nm. Figure S11 Cation Mobility as a function of channel height 30 nature nanotechnology

31 supplementary information 13. References 1 Mao, P. & Han, J.Y. Fabrication and characterization of 20 nm planar nanofluidic channels by glass-glass and glass-silicon bonding. Lab Chip 5, (2005). 2 Haneveld, J., Tas, N.R., Brunets, N., Jansen, H.V. & Elwenspoek, M. Capillary filling of sub-10 nm nanochannels. J. Appl. Phys. 104, (2008). 3 Satyanarayana, S., Karnik, R.N. & Majumdar, A. Stamp-and-stick roomtemperature bonding technique for microdevices. J. Microelectromech. Syst. 14, (2005). 4 Shih, W.P., Hui, C.Y. & Tien, N.C. Collapse of microchannels during anodic bonding: Theory and experiments. J. Appl. Phys. 95, (2004). 5 Raider, S.I., Gregor, L.V. & Flitsch, R. Transfer of mobile ions from aqueoussolutions to silicon dioxide surface. J. Electrochem. Soc. 120, (1973). 6 Karnik, R. et al. Electrostatic control of ions and molecules in nanofluidic transistors. Nano Lett. 5, (2005). 7 Israelachvili, J.N. Intermolecular and surface forces. 2nd edn, (Academic Press, 1992). 8 Smeets, R.M.M. et al. Salt dependence of ion transport and DNA translocation through solid-state nanopores. Nano Lett. 6, (2006). 9 Bassignana, I.C. & Reiss, H. Ion-transport and water dissociation in bipolar ionexchange membranes. J. Membr Sci. 15, (1983). 10 vanhal, R.E.G., Eijkel, J.C.T. & Bergveld, P. A general model to describe the electrostatic potential at electrolyte oxide interfaces. Adv. Colloid Interface Sci. 69, (1996). 11 van der Heyden, F.H.J., Stein, D. & Dekker, C. Streaming currents in a single nanofluidic channel. Phys. Rev. Lett. 95, (2005). 12 Daiguji, H., Yang, P.D. & Majumdar, A. Ion transport in nanofluidic channels. Nano Lett. 4, (2004). 13 Behrens, S.H. & Grier, D.G. The charge of glass and silica surfaces. J. Chem. Phys. 115, (2001). 14 Baldessari, F. Electrokinetics in nanochannels - Part I. Electric double layer overlap and channel-to-well equilibrium. J. Colloid Interface Sci. 325, (2008). 15 Skoog, D.A. & Skoog, D.A. Fundamentals of analytical chemistry. 8th edn, (Thomson-Brooks/Cole, 2004). nature nanotechnology 31