Post on 05-Jan-2022
Modeling of Directional Dependence in Nanowire Flow Sensor A. Piyadasa1,3 , P. Gao1,2,3
1. Department of Physics, University of Connecticut, Storrs, CT, USA 2. Department of Materials Science & Engineering, University of Connecticut, Storrs, CT, USA
3. Institute of Materials Sciences, University of Connecticut, Storrs, CT, USA
Introduction: Developing a reliable and robust micro scale gas flow sensor has proven to be an important requirement for future micro- and nano-electromechanical devices. Current study is focused on modeling a novel form of multi-directional gas flow sensor which is designed by utilizing a Si nanowire array and its piezoresistive properties to change conductivity upon flow pressure on the sensor material. Finite element analysis (FEA) model constructed using COMSOL Multiphysicsยฎ software has been used for modeling piezoresistive phenomena in the nanowire array. Figure-1 shows the nanowire array gas flow sensor with gas flowing through the channel.
Conclusions: 3D model has been developed to test the directional dependence of nanowire gas flow sensor. Output of the nanowire flow sensor is directly proportional to the induced stress in the nanowire base. Average values of the stress components ๐๐ฅ๐ง and ๐๐ฆ๐ง varies with flow direction allowing the sensor to detect the gas flow direction inside the channel. Current results show that the anisotropic properties of the material can be successfully used in the gas flow sensor to differentiate flow components in different directions.
References: 1. Smith, C. S. Piezoresistance effect in germanium and silicon. Phys. Rev. 94,
42โ49 (1954). 2. A. Amin, โNumerical computation of the piezoresistivity matrix elements for
semiconducting perovskite ferroelectrics,โ Phys. Rev. B, vol. 40, 11603, 1989. 3. S.D. Senturia, โA Piezoresistive Pressure Sensor,โ Microsystem Design, chapter
18, Springer, 2000.
Figure 1. Nanowire flow sensor
Gas inlet
Gas outlet
Nanowire array
Computational Methods: Single nanowire model (Figure 2) has been constructed using COMSOL Multiphysicsยฎ to test the piezoresistive phenomena and its directional dependence in the nanowire array. Constructed model consists of three types of physics coupled together, fluid flow and structural mechanics (Fluid Structure interaction) and piezoresistivity (MEMS module). The fluid flow in the channel is described by the incompressible Navier-Stokes equations for the velocity field, u = (u, v), and the pressure, p
๐๐๐ข
๐๐กโ ๐ป โ โ๐๐ผ + ๐ ๐ป๐ข + ๐ป๐ข ๐ + ๐ ๐ข โ ๐ข๐ โ ๐ป ๐ข = ๐น
โ๐ป โ ๐ข = 0
The nanowire is fixed to the piezoresistive base (Figure 3) and all the other surfaces of the nanowire experience a load from the gas flow which is given by, (n is the normal vector to the boundary).
๐น๐ = โ๐ โ (โ๐๐ผ + ๐ ๐ป๐ข + ๐ป๐ข ๐ )
Acknowledgement: The authors are grateful for the partial funding support by the US National Science Foundation and the Department of Energy.
Figure 2. Single nanowire model and parameters
Symmetric boundary
No slip boundary
Slip boundary Parameter Value
NW Length 8um
NW radius 200nm
Base thickness 300nm
Base side 800nm
Channel length 1.2um
Inlet velocity 0.05m/s
Input voltage 1E-6V
Electric field, E, and the current density, J, within a piezoresistor is: ๐ธ = ๐ โ ๐ฝ + โ๐ โ ๐ฝ
where ฯ is the resistivity and ฮฯ is the induced change in the resistivity which is related to the stress, ฯ and piezoresistive tensor ฮ by the constitutive relationship:
โ๐ = ฮ โ ๐ For Silicon :
ฮ๐๐ฅ๐ฅ
ฮ๐๐ฆ๐ฆ
ฮ๐๐ง๐ง
ฮ๐๐ฆ๐ง
ฮ๐๐ฅ๐ง
ฮ๐๐ฅ๐ฆ
=
6.6 โ1.1 โ1.1 0 0 0โ1.1 6.6 โ1.1 0 0 0โ1.1 โ1.1 6.6 0 0 0
0 0 0 138.1 0 00 0 0 0 138.1 00 0 0 0 0 138.1
โ 10โ11 ร
๐๐ฅ๐ฅ
๐๐ฆ๐ฆ
๐๐ง๐ง
๐๐ฆ๐ง
๐๐ฅ๐ง
๐๐ฅ๐ฆ
Induced voltage in nanowire base due to stress :
๐๐ฅ
๐๐ฆ
๐๐ง
===
138.1 ร 10โ11 ร ๐๐ฅ๐ง
138.1 ร 10โ11 ร ๐๐ฆ๐ง
(1 + (โ1.1 โ ๐๐ฅ๐ฅ โ 1.1 โ ๐๐ฆ๐ฆ + 6.6 โ ๐๐ง๐ง) ร 10โ11)
ร ๐0 รร ๐0 รร ๐0 ร
๐ฝ๐ง
๐ฝ๐ง
๐ฝ๐ง
รรร
๐๐๐
Results: Average induced stress components ๐๐ฅ๐ง and ๐๐ฆ๐ง vs. flow direction is plotted in Figure 4 and change in resistivity components โ๐๐ง๐ฆ and โ๐๐ง๐ฅ vs. flow direction is plotted in Figure 5.
-400
-300
-200
-100
0
100
200
300
400
500
0 90 180 270 360
Ind
uce
d S
tres
s (N
/m^2
)
Angle (Degrees)
Stress component_zy
Stress component_zx-5.00E-11
-4.00E-11
-3.00E-11
-2.00E-11
-1.00E-11
0.00E+00
1.00E-11
2.00E-11
3.00E-11
4.00E-11
5.00E-11
0 90 180 270 360
Ch
ange
in r
esis
tivi
ty (
ฮฉm
)
Angle (Degrees)
change in resistivity โฯ_zy
change in resistivity โฯ_zx
Figure 4. Induced stress vs. flow direction Figure 5. Resistivity change vs. flow direction
From Figure 6 it shows the change in induced electric field in the nanowire base with the varying flow direction in the channel.
-2.00E-06
-1.50E-06
-1.00E-06
-5.00E-07
0.00E+00
5.00E-07
1.00E-06
1.50E-06
2.00E-06
0 90 180 270 360
Ind
uce
d E
lect
ric
fiel
d (
V/m
)
Angle (Degrees)
E_x
E_y
Figure 6. Induced electric field vs. Flow direction
Input Voltage
Induced Ex
Induced Ey
Figure 3. Single nanowire Input / Output
Flow sensor can be used in determining the flow direction by analyzing the two voltage outputs from the sensor. Flow in +y direction :- ๐ธ๐ฅ โ 0 , ๐ธ๐ฆ โ ๐๐๐๐๐ก๐๐ฃ๐ ๐๐๐ฅ๐๐๐ข๐ Flow in - y direction :- ๐ธ๐ฅ โ 0 , ๐ธ๐ฆ โ ๐๐๐ ๐๐ก๐๐ฃ๐ ๐๐๐ฅ๐๐๐ข๐ Flow in +x direction :- ๐ธ๐ฆ โ 0 , ๐ธ๐ฅ โ ๐๐๐๐๐ก๐๐ฃ๐ ๐๐๐ฅ๐๐๐ข๐ Flow in - x direction :- ๐ธ๐ฆ โ 0 , ๐ธ๐ฅ โ ๐๐๐ ๐๐ก๐๐ฃ๐ ๐๐๐ฅ๐๐๐ข๐
Fixed Boundary
Excerpt from the Proceedings of the 2014 COMSOL Conference in Boston