Electrostatic Control of Ions and
Molecules in Nanofluidic Transistors
Rohit Karnik,
†,
|
Rong Fan,
‡,
|
Min Yue,
†
Deyu Li,
†
Peidong Yang,*
,‡,§
and
Arun Majumdar*
,†,§
Department of Mechanical Engineering and Department of Chemistry,
UniVersity of California, Berkeley, California 94720, and Materials Sciences DiVision,
Lawrence Berkeley National Laboratory, Berkeley, California 94720
Received March 14, 2005
ABSTRACT
We report a nanofluidic transistor based on a metal-oxide-solution (MOSol) system that is similar to a metal-oxide-semiconductor field-effect
transistor (MOSFET). Using a combination of fluorescence and electrical measurements, we demonstrate that gate voltage modulates the
concentration of ions and molecules in the channel and controls the ionic conductance. Our results illustrate the efficacy of field-effect
control in nanofluidics, which could have broad implications on integrated nanofluidic circuits for manipulation of ions and biomolecules in
sub-femtoliter volumes.
Nanofluidic devices, such as protein ion channels and
inorganic pores and channels, have been used for highly
sensitive biomolecular sensing down to the single-molecule
level,
1-4
separation of DNA,
5,6
and as microfluidic intercon-
nects.
7
Charge-related effects such as concentration enhance-
ment
8
and effect of surface charge on ionic conductance
9
have also been reported. All these single nanofluidic channel/
pore devices transport ionic or molecular species passively
through the nanochannel, simply like electron transport
through a two-terminal device such as a resistor. Analogous
to metal-oxide-semiconductor field-effect transistors
10
(MOS-
FETs), introducing field effect modulation of ionic or
molecular species in micro/nanofludic systems would pro-
mote them to a higher level of controllability and even logic
operation. This level of control is highly desired and could
advance the development of large-scale nanofluidic circuits.
In an electrolyte solution, counterions accumulate near a
charged surface and co-ions are electrostatically repelled.
11
Due to this counterion shield, the electric potential decays
to its bulk value over a characteristic length known as the
Debye length. The Debye length, l
D
, decreases as the ion
concentration, n, increases, l
D
∝ n
-1/2
, and is typically 1-100
nm for aqueous solutions. In microchannels, the Debye length
is usually much smaller than the channel dimensions, and
the bulk of the solution is shielded from the surface charge
(Figure 1a). Therefore, although interfacial effects such as
electroosmotic flow can be controlled using field-effect and
surface modification in microchannels,
12
direct electrostatic
manipulation of ions across the microchannel is not possible.
However, in nanochannels with at least one dimension
* Corresponding authors: p_yang@uclink.berkeley.edu; majumdar@
me.berkeley.edu.
†
Department of Mechanical Engineering, UC, Berkeley.
‡
Department of Chemistry, UC, Berkeley.
§
Lawrence Berkeley National Laboratory.
|
These authors contributed equally to this paper.
Figure 1. Surface charge effects in microchannels and nanochan-
nels. (a) In a microchannel, the Debye length is typically much
smaller than the channel dimensions and most of the solution in
the channel is neutral. (b) In a nanochannel, the solution is charged
when the Debye length is larger than the channel dimensions. (c)
The electric potential in the microchannel decays rapidly to its bulk
value in a distance of the order of the Debye length. (d) The electric
potential even at the center of the nanochannel is influenced by
the surface charge and is not equal to the bulk potential. (e) The
concentration of cations (orange) and anions (blue) in the micro-
channel is equal to the bulk concentration. (f) In a nanochannel,
the counterion concentration (orange) is much higher than the co-
ion concentration (blue).
NANO
LETTERS
2005
Vol. 5, No. 5
943-948
10.1021/nl050493b CCC: $30.25 © 2005 American Chemical Society
Published on Web 03/31/2005
comparable to or smaller than the Debye length, electrostatic
fields can penetrate throughout the channel (Figure 1b),
enabling direct ionic/molecular manipulation using surface
charge or field-effect in such nanochannels. Martin et al.
employed nanotubule membranes, which are essentially an
array of nanochannels, for ion separation,
13
detection,
14
and
sizing.
15
They have demonstrated ion transport selectivity
depending on the charge effect in metal nanotubule mem-
branes,
13,16
which suggests the feasibility of developing an
ionic field effect transistor in nanofluidic systems similar to
MOSFETs. Modeling of metal-oxide solution systems in
silica nanotubes also shows a change in conductance on the
application of a gate voltage.
17
In addition, on-chip integra-
tion of single nanochannels is advantageous for constructing
networks that combine in-situ optical probing of analytes.
An early work over a decade ago investigated the change of
electrical conductance of glycerol-filled channels,
18
but their
device had an extremely long relaxation time and did not
allow for optical investigation. Here we demonstrate rapid
field-effect control of ionic concentrations and conductance
in nanofluidic transistors (nanochannels with gate electrodes)
in sub-femtoliter volumes and provide direct evidence using
fluorescence techniques.
Figure 2 shows nanofluidic transistors illustrating two
types of fluidic confinement used in this study: (i) two-
dimensional silicon dioxide nanochannels that are 30-40 nm
in height and 1 µm wide (Figure 2b); (ii) one-dimensional
silicon dioxide nanotubes that have internal diameters 10-
100 nm (Figure 2c). The former devices are made completely
by optical lithography, while the latter devices rely on
separate synthesis of nanotubes
19
and their subsequent
integration with microfabricated channels and gate electrodes
(see Supporting Information). Ag/AgCl electrodes were used
in the microfluidic channels/chambers on either side of the
nanofluidic channels for applying electrical bias and generat-
ing ionic current.
For a two-dimensional nanochannel, the ionic current
under source-to-drain electrical bias can be calculated as a
superposition of conductive and convective contributions
20
where the integration is across the channel cross-section (x-
direction), w is the width of the nanochannel, 2h is the height
and µ is the ionic mobility. The ionic concentrations [n
+
(x,z),
n
-
(x,z)] and the potential [φ(x,z)] distribution can be
obtained by solving the coupled Poisson-Boltzmann equa-
tions,
11,20
and the fluid velocity u can be obtained by solving
the Navier-Stokes equation.
20
At low bulk ionic concentra-
tions (n), when n,σ/eh, where σ is surface charge, coun-
terions accumulate in the nanochannel to neutralize surface
charge such that n
-
≈σeh, and conductance is governed by
surface charge.
9
Figures 3a,b show the measured ionic
conductance of the nanochannel and nanotube devices along
with theoretical predictions, which confirm surface-charge-
governed transport in our devices. The experiments tend to
agree with conductance measurements reported recently,
9
although with some deviations, presumably due to variation
of surface charge density.
21-23
For the two-dimensional
nanochannel, the results indicate that the surface charge
density ranges between 0.002 and 0.1 C/m
2
, while it is about
0.01 to 0.02 C/m
2
for the one-dimensional nanotubes. The
results are consistent with reported values of the surface
charge density.
9,24,25
It is worth noting that the data also
suggest that the surface charge increases with increasing KCl
concentration, which may be due to ionic adsorption
22
or
surface charge regulation
25
due to proximity of the nanochan-
nel surfaces. This effect seems to be absent in the conduc-
tance measurements reported for larger nanochannels and
microchannels.
9
I )
∫
-h
h
we[(n
+
+ n
-
)µE + (n
+
- n
-
)u]dx (1)
Figure 2. Nanofluidic transistor devices. (a) Schematic of a
nanofluidic transistor. (b) Micrograph of the two-dimensional
nanochannel transistor. Thirty nanochannels, 120 µm long, run left
to right and are connected by two microchannels. Three gate
electrodes run vertically across the nanochannels. Nanochannels
are made by etching a 35 nm thick and patterned poly-silicon layer
(inset). (c) Scanning electron micrograph (SEM) of a one-
dimensional single nanotube transistor before bonding with the
PDMS cover. The device contains a metallic gate electrode covered
by a silicon dioxide patterned film. The tube is connected on both
ends to microfluidic channels. Scale bar 10 µm. Upper right inset
is a transmission electron micrograph (TEM) of silica nanotubes
made by partial oxidation of silicon nanowires followed by etching
the remaining silicon core. Scale bar 200 nm.
944
Nano Lett.,
Vol. 5, No. 5, 2005
To further probe the electric potential in the nanochannels,
a negatively charged dye (Alexa Fluor 488 cadaverine,
monosodium salt) was introduced into the nanochannels. The
bulk dye concentration was kept constant at 100 µM while
the KCl concentration was varied (Figure 3c,d). The chosen
dye is insensitive to pH
26
and, hence, the observed fluores-
cence intensity may be assumed to represent the actual
amount of dye in the nanochannels. Strikingly, for low salt
concentrations, the fluorescence intensity is one-tenth of that
at high salt concentrations, in accordance with the theoreti-
cally predicted amounts of dye in the nanochannel (see
Supporting Information). As the ionic strength decreases from
0.9 to 100 µM, the Debye length increases to about 30 nm
and the effect of surface charge extends throughout the
nanochannel. These results suggest that the magnitude of
electric potential in the nanochannels is several times larger
than kT/e (26 mV) for low bulk concentrations. It implies
that the concentration of cations is much larger than that of
anions in the nanochannels.
A comparison with typical unipolar electronic devices, e.g.,
metal-oxide-semiconductor (MOS) systems,
10
leads to the
concept that a gate voltage may be employed to modulate
the ionic concentration in nanochannels. This effect is similar
to the field-effect modulation of carrier density in MOS
systems via capacitive coupling between the gate electrode
and the semiconductor. For low salt concentrations, external
charges (including surface charge), such as those generated
by an applied gate voltage, can affect the electric potential
throughout the nanochannel when the Debye length is
comparable to the channel size (Figure 4a). To examine the
gating effect without any source-to-drain voltage bias, the
negatively charged dye (Alexa Fluor 488) was introduced
into the channels at a concentration of 100 µM and the
fluorescence intensity below the gate electrode was measured
as a function of the gate voltage (Figure 4b). When a negative
gate voltage was applied, the dye below the gate was
repelled. On the other hand, the dye concentration was
enhanced by a factor of 2 when a positive gate voltage of
50 V was applied. Since the oxide capacitance is small,
assuming that the entire voltage drop occurs across the oxide,
it results in a change in surface charge of roughly 3 mC/m
2
for a gate voltage of 50 V. The dye concentration estimated
from the fluorescence intensity (Figure 4b) may be compared
with the theoretically calculated dye concentrations of 75,
30, 18, and 9 µM at surface charge densities of 0.1, 0.5, 1,
and 2 mC/m
2
respectively, suggesting that the observed
change in intensity is in the expected order of magnitude.
Moreover, theory predicts a highly nonlinear effect of surface
charge density on the co-ion concentration, which is evident
in the observed variation of intensity with gating voltage.
For better control over ionic concentrations, a low surface
charge, which determines the inherent ionic concentration
Figure 3. Electrostatic effects in nanochannels. The electrical conductance of the (a) nanochannel and the (b) nanotube devices deviates
from that expected from bulk calculations (0 C/m
2
) by several orders of magnitude for low concentrations. Different symbols represent
different devices in (a). Deionized water conductance in the nanochannels was also measured to give the data point at 10
-7
M. This result
is consistent with the theoretically calculated conductance with surface charge density as the parameter (solid lines indicated with respective
surface charge densities). (c) Fluorescence images of a negatively charged dye (Alexa Fluor 488, monosodium salt) at 100 µM concentration
in deionized water and in 0.9 M KCl. In deionized water, most of the dye molecules are excluded, while in 0.9 M KCl, the dye molecules
can enter the nanochannel because the surface charge is shielded. The dots outline three nanochannels, each 1 µm wide. The images are
enhanced and false-colored. Quantitative fluorescence intensity of the dye as a function of the ionic strength (d) shows a consistent decrease
with decreasing ionic strength and is compared with theoretical predictions for a monovalent anion in a 35 nm channel, assuming a surface
charge of 0.002 C/m
2
and 0.1 C/m
2
. Assuming that the dye concentration in 0.9 M KCl represents the bulk value, the average dye concentration
can be estimated for lower ionic strengths (right axis). The units of intensity are arbitrary. Intensity was measured over three 10 µm × 20
µm areas with ∼10 channels below the gates. Error bars are 1σ.
Nano Lett.,
Vol. 5, No. 5, 2005 945
in the nanochannels, is desirable. It is worth noting that it is
difficult to modulate carrier density in a MOS structure made
of a degenerately doped semiconductor. Similarly, an inher-
ent surface charge in nanochannels behaves like the high
doping level in a semiconductor, making gating control of
ionic concentration much more difficult.
To examine field-effect control of ionic conductance, the
fluorescence intensity distribution of the negatively charged
dye (Alexa Fluor 488) was imaged while a gate voltage was
applied simultaneously with a source-to-drain voltage bias
in the 2-dimensional nanochannel transistors. Controllable
concentration gradients were observed below the gate
electrodes; the direction of the concentration gradients could
be switched by changing the gate voltage polarity (Figure
5a). This effect is analogous to the drain-induced barrier
lowering (DIBL)
10
in a MOSFET, which creates an asym-
metric conduction channel and electric field distribution. The
gate bias and the source-drain bias control the magnitude of
the concentration enhancement: A gate bias of 50 V and a
source-drain bias of 5 V led to a 10-fold concentration
enhancement. This phenomenon, which is electrokinetic in
Figure 4. Field-effect modulation of ionic concentration in
nanochannels. (a) Schematic illustration showing how the applica-
tion of a gate voltage can control the ionic concentration. It is
analogous to the carrier density modulation with the application of
a gate voltage in a metal-oxide-semiconductor (MOS) structure.
(b) The fluorescence intensity of a negatively charged dye (Alexa
Fluor 488) can be controlled by the application of a gating voltage,
thus demonstrating field-effect control in nanochannels. The average
concentration of the dye in the nanochannel can be estimated
assuming that the intensity at 0.9 M KCl represents the bulk dye
concentration (right axis). Fluorescence intensity was measured over
four 6 µm × 10 µm areas below the gate electrode. Error bars are
1σ.
Figure 5. Field-effect control in nanofluidic transistors, which
mimic the modulation of channel conductance in the metal-oxide-
semiconductor field effect transistor (MOSFET). (a) Under a
source-drain bias of 5 V, gate voltage induces concentration
gradients that switch directions with gate voltage polarity. Green
arrows denote the concentration gradients; vertical arrows denote
edges of the gate electrodes while the dots outline three nanochan-
nels, each 1 µm wide. Differential ionic conductance (slope of I/V
curves) of the nanochannels (b) and the nanotubes (c) can be
modulated by a gate voltage. 100 µM KCl solution was used in
this experiment. The insets schematically illustrate the electric
potential from the gate electrode and across the nanotube when
applying negative, zero, and positive gate voltages, which accord-
ingly modulates ionic density and conductivity. The fluorescence
intensity of fluorescein-labeled 30mer single-stranded DNA (ss-
DNA) molecules can be modulated by a factor of 6 by the
application of a gate voltage (b), suggesting that flow control of
charged biomolecules is feasible. The 30-base ssDNA concentration
was 13.5 µM in 1 mM KCl. For the DNA experiment, fluorescence
intensity was measured over four 6 µm × 10 µm areas below the
gate electrode. Units of intensity are arbitrary. Images are enhanced
and false-colored. Error bars are 1σ.
946
Nano Lett.,
Vol. 5, No. 5, 2005
origin, reflects a balance between drift due to electrostatic
and electroosmotic effects and diffusion due to concentration
gradients. Similar phenomena have been theoretically de-
scribed for current-carrying ion-selective membranes.
27-29
The crucial difference here is that the ionic concentrations
are both spatially and temporally controllable by electrostatic
fields due to the microfabricated gate electrodes. This
phenomenon could potentially be harnessed for applications
such as isoelectric focusing of proteins
30
and analyte stack-
ing,
31
while retaining the design flexibility of microfabrica-
tion and the controllability of gating voltage. As the gate
voltage was changed from -75 V to 75 V, the ionic
conductance of the nanochannels monotonically decreased
(Figure 5b). Due to the inherent negative surface charge in
the nanochannel, most of the current is carried by the cations.
Hence, a negative gate voltage increases the cation concen-
tration, thus increasing the conductance, whereas a positive
gate voltage depletes the cations, resulting in a decrease in
conductance.
Unlike the MOSFET, where the only function is to control
electrical conductance, the nanofluidic transistor could be
used to tune the ionic environment as well as to control the
transport and concentrations of ions or particular charged
biomolecular species. Since biomolecules are typically
multivalent, gating control may be expected to be more
effective for controlling biomolecules than for monovalent
ions. We observed that the fluorescence intensity of 30-base
fluorescently labeled single-stranded DNA (ssDNA) in a 1
mM KCL solution could be controlled by a factor of 6 in
the nanochannels by the application of a gating voltage
(Figure 5b). In deionized water, no fluorescence was
observed, indicating that the DNA molecules were excluded
due to their negative charge. However, in 1 mM KCl, the
surface charge was partially shielded, enabling gating control.
Though the fluorescence intensity of fluorescein-labeled
DNA is pH dependent,
32
the 6-fold change in intensity cannot
be accounted for by the approximately 2-fold change in
intensity due to pH variations. This result demonstrates the
feasibility of electrostatic biomolecular control in nanoflu-
idics.
Single inorganic nanotube nanofluidic transistors based on
silica nanotubes were characterized for field-effect modula-
tion of ion transport. The microchannels were bridged by a
silica nanotube (nanotube wall thickness ∼35 nm) which was
covered by metallic surround gate electrodes. The KCl
solution with low concentration (e1 mM) was used, which
had a Debye length larger than 10 nm. Nanotube nanofluidic
transistors have two metallic surround gate electrodes. As
shown in Figure 5c, gate voltage shifts the potential diagram
across oxide, Stern layer and changes the effective surface
charge density and ζ potential on the inner wall surface.
When the nanotube size is comparable to Debye length, the
ionic conductance depends only on ζ potential and effective
surface charge, which enables gate control of ionic conduc-
tance. In the experiment, ionic conductance was calculated
from the slope of current-voltage (I/V) curves by linear
regression. Figure 5c shows the conductance at various gate
voltages. For a gate voltage varying from -20Vto+20 V,
the ionic conductance decreases monotonically from 105 pS
down to 45 pS, due to depletion of cations under applied
electric field, which shows a p-type transistor behavior.
In conclusion, we have clearly demonstrated that it is
possible to electrostatically control ion transport in both
2-dimensional nanochannel transistors and single 1-dimen-
sional nanotube transistors. If high dielectric constant materi-
als are employed to fabricate the nanochannel wall, an
enhanced field effect due to stronger capacitive coupling is
expected. Moreover, when multivalent species such as
biomolecules are present, the gating control over these
molecules will be enhanced by the Boltzmann factor exp((z
- 1)eφ/kT), where z is the number of charges on the species.
Modifying the channel surface to obtain a low surface charge
will further enhance the gating effect. The ability to spatially
and temporally tune the ionic and electrostatic environment
makes nanofluidic transistors a unique tool for biological
and chemical analyses in sub-femtoliter volumes. The single
nanotube transistors have the ability to manipulate and sense
extremely small amounts of charged species, or even single
biomolecules. Similar to metal-oxide semiconductor field
effect transistors (MOSFETs), the nanofluidic transistor has
the potential to form the building block of integrated
nanofluidic circuits for manipulating biomolecules with
single-molecule precision and control.
Acknowledgment. This work was supported by the
IMAT program, National Cancer Institute, and the Office
of Basic Energy Sciences, Department of Energy. We also
thank Richard Cote, Ram Datar, Hirofumi Daiguji, and
Andrew Szeri for their collaboration. A.M. would like to
thank the Miller Institute for a Professorship. P.Y. is an A.
P. Sloan Fellow. We thank the Microfabrication Laboratory
(UC Berkeley) and the National Center for Electron Micro-
scopy for the use of their facilities.
Supporting Information Available: Theoretical Analysis
and Materials and Methods. This material is available free
of charge via the Internet at http://pubs.acs.org.
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