Principles of Electronic Nanobiosensors
Unit 3: Sensitivity
Lecture 3.3: Potentiometric Sensors:
Charge Screening for Cylindrical Sensors
By Muhammad A. Alam
Professor of Electrical and Computer Engineering Purdue University
alam@purdue.edu
1
Outline
•Recall: Salt and screening
•Theory of screening for a Cylindrical NW sensor
•Comparison with experiments
•Special issues of small sensors
•Conclusions
|
Alam, Principles of Nanobiosensors, 2013 |
2 |
|
Recall: Salt screening for Planar Sensor
Salt
DNA
|
|
|
|
|
|
|
|
|
|
|
3 |
Alam, Principles of Nanobiosensors, 2013 |
|||
Screening different for 1D sensors?
aM |
fM |
pM |
|
|
|
|
|
|
|
|
|
|
nM |
µM |
|
|
|
|
|
|
|
mM |
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Geometry of diffusion was different, what about screening?
Alam, Principles of Nanobiosensors, 2013 |
4 |
Cylindrical NW sensor
LD + a +tox
|
|
QNW |
|
Qbio |
Q |
|
|
+ |
|
||
|
|
|
+ |
DL |
|
+ |
|
+ |
|||
+ |
|
Ψ |
+ |
||
|
|
||||
a |
|
|
|
0 |
|
|
Si |
|
Ox Electrolyte |
||
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
2πκsiε0 |
|
|
|
|
|
|
Cox |
|
|
|
Cox = |
|
|
||||
QNW = |
|
Qbio |
ln 1+(tox |
a) |
|||||||||
Cox |
+CDL |
|
|||||||||||
|
|
|
|
|
|
|
|
|
|
||||
L2D = |
|
κwε0kBTL |
|
|
CDL = |
|
|
2πκwε0 |
|||||
|
|
|
|
ln 1 |
+(LD |
a +tox ) |
|||||||
|
|
2 |
|
|
|||||||||
|
|
2z |
2 |
I0 Nav q |
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|||
Does offer some advantage !
5