-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
1/32
Network f or Comput at ional Nanotechnology
Performance Limits of
Nanobiosensors
M. Alam and P. Nair
Purdue UniversityWest Lafayette, IN
[email protected]
mailto:[email protected]:[email protected]
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
2/32
Network f or Comput at ional Nanotechnology
A Simple Idea .
An array
Time
Conductan
ce(G)
G
tsresponse time
G0
Individual sensorCapture Probe
C
A
G
A
T
Q1
C
AG
A
T
T
T
A
C
G
Q2
Q1
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
3/32
Network f or Comput at ional Nanotechnology
with remarkable result s
aM fM pM nM M mM M
Historically
ChemFET/IsFET
In the future..
Nanodots ?
Recently
Si-NW/CNT
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
4/32Network f or Comput at ional Nanotechnology
Electrostatics ?
ISFETNanosensor
Electrostatics explains a factor of 2-5,not 2-5 orders of
magnitude change in sensitivity !
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
5/32Network f or Comput at ional Nanotechnology
Geometry of Diffusion
0~D
M
s Dt k
Ref. APL, 88, 233120, 2006
Program is in www.nanohub.org
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
6/32Network f or Comput at ional Nanotechnology
Diffusion-Capture Model
2dD
dt
=
0
0
( )F s R
F s
dNk N N k N
dtk N
=
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
7/32Network f or Comput at ional Nanotechnology
Diffusion Capacitance
s0
2 0D n =
( )0 0 sQ C =
( )0 0 sI C = ( )
( )
0
0 0
11
0 0
(Planar)
2= (NW)
log / 4
(ND)
DCW
D
W a a
D
a W a
=
+
= +
( )
( )
0
0 0
1
10 0
(Planar)
2= (Cylinder)log /
4(Sphere)
CW
W a a
a W a
=
+
=
+
s
0
2
0 =
W
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
8/32Network f or Comput at ional Nanotechnology
Cumulat ive Capture
s
0
( )0 o sI C =
( )
( )
0
0 0
11
0 0
2=
log / 4
DCW
D
W a a
D
a W a
=
+
= +
0F sdNI A Ak Ndt
= =
( )1
0
0 0
1
F
AN t t
C k N
= +
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
9/32Network f or Comput at ional Nanotechnology
Diffusion Distance
ISFET(n = 1)
Nanowire sensor(n = 2)
Nanosphere sensor(n = 3)
W=(2Dt)1/2 W=(4Dt)1/2 W=(6Dt)1/2
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
10/32
Network f or Comput at ional Nanotechnology
Time dependent capture
( )
( )
0 0
11
0 0
2
2=
log 4 /
4
6
t
D
C Dt
D
Dt a a
D
a Dt a
=
+
= +
( )1
2
0
1
t F
AN t t
C k N
= +
( )
( )
0
0 0
11
0 0
2=
log / 4
DC
W
D
W a aD
a W a
=
+
= +
2
1 ( ) 2W t nDT =
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
11/32
Network f or Comput at ional Nanotechnology
Pret ty good approximat ion .
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
12/32
Network f or Comput at ional Nanotechnology
Scaling Law
0~D
M
s Dt k
( )1
0
0
1
S
t F
N t N
At
C k N
=
= +
( )
( )
0 0
11
0 0
(Planar)2
2= (NW)
log 4 /
4 (ND)
6
t
D
C Dt
D
Dt a a
D
a Dt a
=
+
= +
Response is dictated by geometry of diffusion !
0.5
0~
2s S
t ND
00~
s
SN
ta
D
0
0~s
SN
ta
D
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
13/32
Network f or Comput at ional Nanotechnology
Limits of Sensor Response
(SiNW)00~
s
SN
ta
D
(Planar)0.5
0~
2s S
t ND
100s
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
14/32
Network f or Comput at ional Nanotechnology
Planar vs. NW Sensor
W= (4Dt)1/20
0W/a0
W= (2Dt)1/2
0
0~s
SN
ta
D0.5
0 ~
2s St N D
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
15/32
Network f or Comput at ional Nanotechnology
NW vs. Nanodot Sensors
0
0~s
SN
ta
D
0.5
0~
2s S
t ND
100s
0
0~s
SN
ta
D
(Nanodot)
(Planar)(SiNW)
Fi i Si Eff Di i ?
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
16/32
Network f or Comput at ional Nanotechnology
Finite Size Effects: 2.xDimension ?
Shorter cantilever should capture more protein ..
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
17/32
Network f or Comput at ional Nanotechnology
A Puzzle and its resolution
-40-20
020
-500
500
0.1
0.2
0.3
0.4
0.5
XY
We assumed .
-40-20
020
-500
500
0.1
0.2
0.3
0.4
XY
Actually
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
18/32
Network f or Comput at ional Nanotechnology
Simulation support s experiment
2dD
dt=
0
0
( )F s R
F s
dN k N N k N dt
k N
=
Gupta, Nair, et al. PNAS, 13, 13362, 2006
ith k bl lt
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
19/32
Network f or Comput at ional Nanotechnology
with remarkable results
aM fM pM nM M mM M
Historically
ChemFET/IsFET
In the future..
Nanodots
Recently
Si-NW/CNT
Composites more sensitive than planar, but less than NW(A. Star,
PNAS,103, 4,921, 2006)
0~ ?D
M
s Dt k
Composites of Si-NW & CNT
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
20/32
Network f or Comput at ional Nanotechnology
p(Diffusion in 1.x Dimensions)
Nanosys Inc.
Igal Schatz, PolymerPhysics Review, 2005
Si-NW
CNT
Grow on hightemp. substrate
Disperse in solventSpread on soft substrate
Transit ion among
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
21/32
Network f or Comput at ional Nanotechnology
0
2
log[sinh(2 P)/ P ]W
DC
a
=
P
ginteger dimensions
2D to 1D Transit ion
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
22/32
Network f or Comput at ional Nanotechnology
2D to 1D Transit ion
100s
Planar
NW
10-5
100
105
10-5
100
105
Time (s)
N(t)(#/m)
Numerical
Analytical
Dimensionality changes with time!
Initially 2D
Eventually 1D
1D
2D
Fractal Dimension of Composites
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
23/32
Network f or Comput at ional Nanotechnology
Fractal Dimension of Composites
100
102
10410
0
102
104
log(N)
log (1/h)
h=2
1 2 3 4 5 60
1
2
3
4
5
1 2 3 4 5 60
1
2
3
4
5
h=8
1 2 3 4 5 60
1
2
3
4
5
h=4
1 2 3 4 5 60
1
2
3
4
5
h=16
1 2 3 4 5 60
1
2
3
4
5
h=32
1 2 3 4 5 60
1
2
3
4
5
h=64
0 5 10 151
1.2
1.4
1.6
1.8
2
DF
S [1/m2]
C = 5.717
Slope=F.D.
Ninad Pimparkar byBox Couting Method
Fractional Diffusion
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
24/32
Network f or Comput at ional Nanotechnology
on Fractal Surface
100s
Planar
NW
Dimensionality changes with time!An example of Geometrical
Frustration.
1D
2D
1D
2D
time
N
0~D
M
s Dt k
1D/ D !
=
Cantor Sensor
A Femto-Molar Sensor ?
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
25/32
Network f or Comput at ional Nanotechnology
A Femto-Molar Sensor ?
00~
sSNt a
D
2-4 nm
C(T)/bp0.6-0.7
C
A
G
A
T
T
T
A
C
G
Smaller radius Shorter base-pair Higher temp
(diffusion/Conjugation)
LNA/PNA-DNA
On Growth and Form
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
26/32
Network f or Comput at ional Nanotechnology
On Growth and Form
Lifes Other Secretby Ian Stewart
Everywhere Nature works trueto scale, and everything has aproper
size accordingly," wroteThompson. "Cell and tissue,shell and bone,
leaf and flower
are so many portions of matter,and it is in obedience to thelaws
of physics that theirparticles have been moved,moulded and
conformed."
Biomimet ic design ?
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
27/32
Network f or Comput at ional Nanotechnology
Biomimet ic design ?
Hodgkin-Huxley, 1952
Efficiency of cells and sensitivity of biosensors .
Squid AxonRed Blood Cell
Summary
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
28/32
Network f or Comput at ional Nanotechnology
Summary
aM fM pM nM M M
Reaction-diffusion model Analogous systems Geometry of diffusion
Proteins on cantilevers
Fractal surface/fraction diffusion Geometrical frustration
Percolation vs. fractal dimension Bio-mimetic design
1/
0 ~
D
s Dt k
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
29/32
Network f or Comput at ional Nanotechnology
Questions & Answers
Fractional DiffusionF l S f
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
30/32
Network f or Comput at ional Nanotechnology
on Fractal Surface
100s
Planar
NW
Dimensionality changes with time!An example of Geometrical
Frustration.
1D
2D
1D
2D
time
N
Cantor Sensor
Ensemble Average and fM Detect ion
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
31/32
Network f or Comput at ional Nanotechnology
g
1000s
Pret ty good approximat ion
-
7/31/2019 Geometry of Diffusion and the Performance Limits of
Nano Bio Sensors
32/32
Network f or Comput at ional Nanotechnology
Pret ty good approximat ion .
