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Supporting Information
1. Device Fabrication
Inorganic nanotube nanofluidic transistors were fabricated by two separate steps --chemical synthesis of silica nanotubes for nanofluidic channels and integration with
lithographically defined microfluidic channels. Silicon nanowires were synthesized
and oxidized in dry O2 at 850 oC for 1 hour to form 35 nm silica sheath. To avoid
photoresist filling into the nanotubes, the as-made Si/SiO2 core-sheath nanowires were
left sealed instead of etching through the Si cores to form SiO2 nanotubes until all the
surface device structures had been fabricated. After dispersion of Si/SiO2 nanowires
onto quartz substrates, 100 nm Cr metal layer was sputtered on the substrates, and
subsequently etched with photolithography defined photoresist etching mask to form
Cr lines above the Si/SiO2 nanowire serving as gate electrodes. Then 2 m thick low
temperature oxide was deposited on the entire substrate using low-pressure chemical
vapor deposition (LPCVD) with SiH4 chemistry and then densified by annealing in
inert gas ambient. Two microfluidic channels are patterned and etched to connect the
both ends of Si/SiO2 nanowires. Two metal lines (Pt or Ag) were pattern on both sides
of the nanowire as source and drain electrodes. Practically, it is also very convenient
and reliable to simply insert two Ag/AgCl electrodes into liquid injection holes to
serve as source/drain electrodes. Finally the silicon core of the nanowire was etched
away using XeF2 to form the silica nanotube. The resulting devices were bonded with
a PDMS cover in which access holes had already been drilled. Before bonding, device
chips were cleaned with oxygen plasma at 200W for 1min and immersed in DI water
to form hydrophilic surfaces in microfluidic channels which facilitate the aqueous
solution injection during experiment. The device chips were taken out and dried by
nitrogen gun. A piece of fresh PDMS cover with access holes was cleaned in
isopropanol (IPA) for 3min assisted by ultrasonic treatment. Finally, the PDMS cover
was aligned and pressed onto the device chip to complete bonding process.
Measurements were conducted typically 1-3 days after bonding. Device cross-section
is schematically shown below.
the
access
holes
microfluidic channels
Source/drain
electrodes (Ag/Pt)
to
PDMS
CVD SiO2
Microfluidic channels
Quartz
Single silica nanotube
Cr gate electrodeQuart
z
2. Electrical measurements
All the electric measurements were conducted in a Faraday cage having a common
ground with all the measurement equipment. Current-voltage (I-V) characterization
was carried out with Keithley 236 source measure unit. Gate voltage was supplied
with Keithley 230 voltage source up to 100 V. The measurement system was
controlled with labview software and data was collected through an IEEE 4888
interface. A rise time of 33 sec was set for all the experiments. Data collection was
carried out with National Instrument DAQ 6052E PCI card (maximum sampling rate
100,000) controlled by Labview program. Ag/AgCl electrodes were used as source
and drain electrodes for all the experiment except for the DI water conductance
measurements in Figures 2a, b, for which inert Pt electrodes were used to avoid
contamination. All the electric measurements were conducted in a clean room to avoid
dust contamination.
3. Surface functionalization with APTES
APTES solution was prepared by adding 2% (vol) APTES liquid (Aldrich) to acetone,
which was pre-dried overnight using 4 –8 mesh (4A pore size) molecular sieves. The
as-fabricated device chips prior to PDMA cover bonding was cleaned with oxygen
plasma and dried at 100 oC in a convection oven for ~20min. Then the chips were
immersed in APTES acetone solution for desired time with the reaction container
capped to prevent moisture. After functionalization, the device chips were rinsed with
dry acetone a couple of times and then left in acetone overnight. Finally, PDMS cover
bonding was conducted in a similar way as described previously, but it took only 30
sec of oxygen plasma clean at 100W.
4. Scanning electron micrographs of devices
(A)
(B)
Field emission scanning electron microscopy (FESEM) characterization of asfabricated nanofluidic transistor before PDMS cover bonding. (A) and (B) show the
structure of microfluidic channels at both sides bridged by a single silica nanotube
which is embedded underneath LPCVD SiO2 layer. Metal gate electrode also
embedded in SiO2 layer is visible topographical in FESEM images. The inset of (B)
exhibits sidewall cross-sectional view of the nanotube which is buried underneath
LPCVD SiO2 layer and the bottom quartz substrate. Scale bar 100nm.
5. Unipolar ionic distribution and transport in silica nanotubes
(A)
- - - - - - - - - - - - - -
+
-
-
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-
-
-
-
-
-
-
-
-
+
+
+
- - - - - - - - - - - - - - - - - - - - - - - - - - -
>> Bipolar
Potential
+
+
+
+
-
+
+
+
+
+
-
+
-
+
+
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+
+
+
+
+
+
+
- - - - - - - - - - - - - -
(B)
Ion Concentration
+
+
+
+
+
+
+
+
+
Nanofluidic
channels
Ion Concentration
+
+
+
-
-
-
+
+
+ +
+
+
+
+
+ +
+
+
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+
+
+
+
+ +
+
+
+
+
Microfluidic
channels
-
Potential
>> Unipolar
(C)
(A) Schematic of the ion distribution and electric potential diagram for silica
microfluidic channels and nanofluidic channels. It qualitatively describes the
difference between microsized and nanosized fluidic systems and the formation of
unipolar ionic environment when shrinking channels size to approaching Debye
screening length. (B) Theoretical calculation of the total ionic density (cation and
anion) vs. the nanotube size based on the simple principle of charge neutrality.
(surface charge density was assumed to be 0.01 C/m2). Simulation clearly shows two
profound trends: first, decreasing nanotube diameter leads to more enhanced total
ionic density inside nanotubes, which is essentially the cations which are required to
balance the negative surface charge at the silica nanotube surface. Smaller nanotubes
squeeze the cations and increase the real ionic density to form unipolar carrier (ion)
profile inside nanotubes; second, low concentration ionic (<0.01M) solution tends to
form unipolar environment inside nanotube easily, while the high concentration
solution (>0.1M) only shows slight enhancement in very small nanotubes. This is due
to low ionic strength solutions have larger Debye screening length which allows
significant extension of surface charge effect across entire nanotubes. (C) is the
experimental data of KCl salt concentration dependence of the ionic conductance in a
single silica nanotube nanofluidic transistor which clearly shows deviation from
microfluidic system prediction (0 C/m2 line) and confirms the formation of unipolar
ionic conduction at low concentration (<1mM). High concentration solution in the
nanotube essentially behaves like bulk salt solution in microfluidic systems due to
very short Debye screening length (<3nm for [KCl]>0.01M).
6. Calculation of  potential and surfaces charge density using PossionBoltzmann equations
The ionic concentration is given by the Boltzmann distribution
  e 

n(  )  n0 exp 
 k BT 
(1)
where n  ( ) denotes the real cation and anion density, respectively, inside a nanotube
where electrical potential is  . n 0 denotes the cation or anion density at  = 0,
which equals the bulk KCl concentration, kB is Boltzmann constant, T is absolute
temperature, e is the charge of electron.
Total ionic density n (both cations and anions) is
 e 
  e 
 e 

  n0 exp 
  2n0 cosh 
n  n0 exp 
 k BT 
 k BT 
 k BT 
The net charge density  is
  e 
 e 
 e 
  n0 exp 
  2n0 sinh 

 k BT 
 k BT 
 k BT 
  n0 exp 
(2)
(3)
The Poisson equation for the electric potential is
 2 
 e
w

2n 0 e
w
 e 

sinh 
k
T
 B 
(4)
where  w is electrical permissivity of aqueous solutions.
In a symmetric system (cylindrical nanotubes), the boundary condition in the center is
d
dx
 0 which gives
x 0
 d ( x) 
2

  4 S n cosh  ( x)   cosh  (0) 
dx


2
(5)
Herein, x is the coordinate across the center of nanotube which is the origin. x is
normalized with the radius of nanotube R, such that 0≤x≤1. For simplicity, (x) is
also nondimenized by  (x)= e(x)/kBT .
(0) is calculated by integration of x from  to (0) and x from 1 to 0 in (5). Then
x can be numerically solved by integration from (0) to (x) while x from 0 to x.
/ ion density
0
R
x
Once the potential diagram (x) is solved for various zeta potentials (), then
Boltzmann distribution can be further utilized to calculate ionic concentration for both
cations and anions. The relation between surface charge density and zeta potential ()
is calculated based on the total charge neutrality.

1
1
1 1
2

xL

(
x
)
dx


2 xn0 sinh ( x) dx
2RL 0
R 0
(6)
Assuming the mobilities for K+ and Cl- are equal for simplicity, the enhance factor is
defined as the measured conductance in the nanotube over the ideal conductance in
bulk solution if it is confined in the same volume (S/S0). Then
S / S 0   2x(n   n  ) /( 2n0 )dx   2x cosh ( x)dx
1
1
0
0
(7)
For various zeta potential (), one can numerically compute a set of S/S0 according to
(5) and (7). Then based on the experimentally measured enhancement factor (S/S 0),
zeta potentials were back-extracted.
(6) gives the correlation between surface charge density ( and . So surface charge
density ( can be calculated from once it is known.