This paper aim in design and analysis of MEMS Pressure Sensor by using ANSYS software. A diaphragm based MEMS sensor in the range of 25MPa by measured center deflection of the circular pressure-sensitive and using the strain gauge for measurement.

1. ‫ﻣﻴﻜﺮوﻣﺎﺷﻨﻴﻜﺎري‬ ‫و‬ ‫رﻳﺰﻓﻨﺎوري‬ ‫اﻟﻤﻠﻠﻲ‬ ‫ﺑﻴﻦ‬ ‫ﻛﻨﻔﺮاﻧﺲ‬ ‫اوﻟﻴﻦ‬ICMEMS2014
‫ﻓﻨﺎوري‬ ‫ﭘﮋوﻫﺸﻜﺪه‬،‫اﻣﻴﺮﻛﺒﻴﺮ‬ ‫ﺻﻨﻌﺘﻲ‬ ‫داﻧﺸﮕﺎه‬ ‫ﻧﻮ‬ ‫ﻫﺎي‬29‫و‬30‫ﺑﻬﻤﻦ‬1392
Key words Pressure sensor, Circular diaphragm,
MEMS, Terms pressure, Small deflection, Finite
element, ANSYS,
Abstract: This paper aim in design and analysis
of MEMS Pressure Sensor by using ANSYS
software. A diaphragm based MEMS sensor in
the range of 25MPa by measured center
deflection of the circular pressure-sensitive and
using the strain gauge for measurement. First
this paper created the mathematical calculation
and then models the finite element analysis of
the diaphragm using ANSYS and determined the
pressure sensor in the range of 25MPa with
circular diaphragm is designed, which also
reflects the choice of correct design after
analyzing the effect of diaphragm thickness,
location and shapes of piezoresistor. Circular
diaphragm of different thickness and diameters
are simulated to meet the requirement of 25MPa
pressure. The whole fabrication process is
inexpensive and compatible with standard
MEMS process. Measurements show good
results such as high sensitivity 0~25MPa,
linearity 0~11.209MPa and upper pressure we
have 1.25% standard division. The work
indicates pressure sensor with circular
diaphragm could be fabricated for applications
of high range pressure measurement with high
precision.
1. Introduction
Pressure sensors have been developing rapidly
in the last decades with the development of
Micro Electro Mechanical System (MEMS)
technique and high demand of market. Recently,
with the rapid expansion of consumption of
pressure sensors of high range in petroleum
industry and daily applications, great efforts
have been directed towards high pressure
sensors in high temperature environment [1].
These devices can replace bulky actuators and
sensors with micro scale devices that can be
produced in integrated circuit photolithography
[2]. Capacitive sensor and resonator sensor have
been widely used. However, some defects of
them are difficult to overcome. The linear
outputs of capacitive sensor depend on complex
signal processing integrated circuit. The
resonator sensor has limitation to materials of
high quality and frequency. Besides, the cost is
too high. To overcome such disadvantages,
piezoresistive sensor has simple process circuit
Wheatstone bridge and cheap material silicon to
achieve high precision linear output. Many
piezoresistive sensors are fabricated with square
diaphragm of different thickness [3]. Compared
to the square diaphragm, circular diaphragm has
advantage in high pressure range. It has better
high frequency response in high range, although
the sensitivity is lower. The square diaphragm’s
nonlinearity in high range is harmful for the
sensor’s performance. Besides, its frequency
response is much lower than circular diaphragm
of same size. Thus, circular diaphragm with
meander-shaped piezoresistors is utilized for
sensors in high pressure measurement. Circular
diaphragm packaged with glass ring is simulated
by ANSYS software to determine optimal place
for piezoresistors distributed on the surface [4].
2. Structure and working principle
The conventional structure of piezoresistive
pressure sensor includes a square diaphragm as
shown in Fig 1. Piezoresistors are located at the
edge of diaphragm to transform pressure to
electrical signal. Stress distribution of one type
Modeling, Simulation and Design of a Circular
Diaphragm Pressure Sensor
ICMEMS2014-2026

2. ‫ﻣﻴﻜﺮوﻣﺎﺷﻨﻴﻜﺎري‬ ‫و‬ ‫رﻳﺰﻓﻨﺎوري‬ ‫اﻟﻤﻠﻠﻲ‬ ‫ﺑﻴﻦ‬ ‫ﻛﻨﻔﺮاﻧﺲ‬ ‫اوﻟﻴﻦ‬ICMEMS2014
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of square diaphragm C type is shown in
Fig 2. It can be observed that the stress
concentration region on the edge is long and
narrow. Thus, it’s possible that the piezoresistors
distributed on the edge may not cause changes
equally under corresponding pressure which is
harmful to the sensor’s linearity and life time of
sensor. Meanwhile, Comparing to square
diaphragm, the circular diaphragm has higher
natural frequency which is of great benefit to
dynamic applications. For example, the natural
frequency of circular diaphragm demonstrated in
this paper is 1.4MHZ which is much higher than
that of square diaphragm of similar size. So if
the sensors are used in dynamic measurement,
especially for high frequency applications, the
circular diaphragm should be unutilized.
The design model of circular diaphragm is
shown in Fig 3 and it’s bonded with borosilicate
glass ring to form inverted cup structure as
sensing unit of the sensor. The key parameters
are the diameter of effective area d=2a and the
thickness of piezoresistive element ph . The
theoretical model of effective area is shown in
Fig 4 from which displacement can be observed
and the following theoretical calculation and
analysis are based on the model. The pressure P
is equally distributed and it should satisfy the
following equations with the circular diaphragm
[4].
The behavior of a diaphragm will depend upon
many factors, such as the edge conditions and
the deflection range compared to diaphragm
bornosilicatepiezoresistive
r
Z0
hp
a
z
p
neutral axis
Fig 1: conventional structure of piezoresistive pressure
Fig 2: square diaphragm C type
Fig 3: effective area for sensing pressure
d
Effective area
Fig 4-1: rigidly clamped diaphragm and Fig 4-2: its
associated displacement under uniform pressure.
(1)
(2)
1
2
((1 )(3 ))a ν ν+ +

3. ‫ﻣﻴﻜﺮوﻣﺎﺷﻨﻴﻜﺎري‬ ‫و‬ ‫رﻳﺰﻓﻨﺎوري‬ ‫اﻟﻤﻠﻠﻲ‬ ‫ﺑﻴﻦ‬ ‫ﻛﻨﻔﺮاﻧﺲ‬ ‫اوﻟﻴﻦ‬ICMEMS2014
‫ﻓﻨﺎوري‬ ‫ﭘﮋوﻫﺸﻜﺪه‬،‫اﻣﻴﺮﻛﺒﻴﺮ‬ ‫ﺻﻨﻌﺘﻲ‬ ‫داﻧﺸﮕﺎه‬ ‫ﻧﻮ‬ ‫ﻫﺎي‬29‫و‬30‫ﺑﻬﻤﻦ‬1392
thickness. The edge conditions of a diaphragm
will depend upon the method of manufacture
and the geometry of the surrounding structure. It
will vary between a simply supported or rigidly
clamped structure, as shown in Fig 4-1 and
Fig 4-2. Simply supported diaphragms will not
occur in practice, but the analytical results for
such a structure may more accurately reflect the
behavior of a poorly clamped diaphragm than
the rigidly clamped analysis. At small
deflections (≤10% diaphragm thickness) the
pressure-deflection relationship will be linear.
As the pressure increases, the rate of deflection
decreases and the pressure-deflection
relationship will become nonlinear. The
deflection Z at radial distance r of a round
diaphragm under a uniform pressure P, rigidly
clamped as shown in Fig 4-2, is given by:
2
2 2 23(1 )
( )
16 p
P
z a r
h
ν−
= −
Ε
(1)
Where ph is the diaphragm thickness, Ε and ν
are the Young’s modulus and Poisson’s ratio of
the diaphragm material, respectively, and a is
the radius of the diaphragm. The maximum
deflection 0z will occur at the diaphragm center
where 0r = . Assuming a common value for
metals of 0.22ν = , the maximum deflection is
given by:
4
0 3
0.1784
p
Pa
z
h
=
Ε
(2)
The stress distribution will vary both across the
radius and through the thickness of the
diaphragm. For example, the neutral axis [shown
in Fig 4-1] experiences zero stress while the
maximum stress occurs at the outer faces. At any
given distance r from the center of the
diaphragm, one face will experience tensile
stress while the other experiences compressive
stress. There are two stress components
associated with a circular diaphragm: radial and
tangential. The radial stress, σr at distance r from
the center of the diaphragm is given by (3). The
maximum radial stress that occurs at the
diaphragm edge (r = a) is given by (4).
( ) ( )
2 2
2 2
3
3 1
8
r
Pa r
h a
σ ν ν
 
= ± + − − 
 
(3)
( )max
2
2
3
1
4
r
Pa
h
σ ν= ± + (4)
Radial stress is equal to zero at a value of r given
by ( )( )( )
1
2
1 3a ν ν+ + (shown in Fig 4-2). The
tangential stress, σt, at distance r from the
center of the diaphragm is given by (5). The
maximum tangential stress that occurs at the
diaphragm center (r = 0) is given by (6).
( ) ( )
2 2
2 2
3
3 1 1
8
t
Pa r
h a
σ ν ν
 
= ± + − + 
 
(5)
( )max
2
2
3
1
4
t
Pa
h
σ ν= ± + (6)
The diaphragm with embedded piezoresistors is
made by using silicon bulk micromachining
steps. Piezoresistors are made by selectively
doping the silicon diaphragm. The piezoresistors
are connected in the form of Wheatstone bridge
to output electric signal caused by pressure in
Fig 5. They should be located on the maximum
stress area in order to obtain high sensitivity.
The power supply is constant current.
1R R− ∆
4R R− ∆ 3R R− ∆
2R R− ∆
outV
Constant
Current
Fig 5: Wheatstone bridge

4. ‫ﻣﻴﻜﺮوﻣﺎﺷﻨﻴﻜﺎري‬ ‫و‬ ‫رﻳﺰﻓﻨﺎوري‬ ‫اﻟﻤﻠﻠﻲ‬ ‫ﺑﻴﻦ‬ ‫ﻛﻨﻔﺮاﻧﺲ‬ ‫اوﻟﻴﻦ‬ICMEMS2014
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Therefore, the functional relationship between
the fractional change in electrical resistance
( )R
R
∆ of the piezoresistor and the transversal
and longitudinal stress components is given by
for tangential resistors:
t t r r
t
R
R
π σ π σ
∆ 
= + 
 
(7)
For radial resistors:
t r r t
r
R
R
π σ π σ
∆ 
= + 
 
(8)
Where tπ and rπ are longitudinal and
transversal direction coefficients, respectively.
The power supply is constant current. Therefore,
the changes of resistance in an unbalanced
bridge caused by piezoresistance effect with the
load of pressure can directly transform into
voltage with equation (9).
1 3 2 4
1 2 3 4
o in
R R R R
V I
R R R R
−
= ⋅
+ + +
(9)
Where inI is bridge-input current, and oV is the
differential output voltage. When the pressure is
loaded, 1R and 3R have positive increment, on
the other side, 2R and 4R have negative
increment [6].
3. Analysis and simulation
The diameter and thickness of the diaphragm
and the distribution of piezoresistors affects the
sensor’s range, frequency response, sensitivity
and linearity. The distribution of piezoresistors
is mainly determined by the stress distribution
on the diaphragm and the glass ring packaged
with. Simulations used ANSYS of diaphragm
packaged with different boron glass ring under
the pressure 25MPa are shown in Fig 6. The
outside of the model is restricted by ring and the
pressure is loaded on the opposite of the model.
The stress along x direction is shown in Fig 4.
The sensitivity is mainly determined by the
difference of x stress and y stress at the point
where the resistor is placed. The curve in
Fig 7 and Fig 8 shows the x-y stress of
2 4a mm= and 2 2a mm= along the path of x
direction with the same thickness 0.4h mm= .
It can be seen that the x-y stress of 2 4a mm=
is much higher than that of 2 2a mm= . Thus,
the piezoresistors in Fig 7 will output higher
voltage and show better sensitivity under the
same load. But the piezoresistors in Fig 9 shows
better linearity. Besides, it is in accord with the
theoretical analysis that the deflection and stress
will increase with the increase of radius a within
the allowable pressure load P. Therefore, the
dimensions are determined to meet the
requirement of 25MPa with the consideration of
glass ring as follows: 2 4a mm= , 0.4h mm= .
The deformation on Z direction just the
deflection when P=25MPa is shown in Fig 6,
and the center deflection of the diaphragm is the
maximum shown in Fig 10: Z0 =9.5 µm. Fig 8
show the radial strain on the diameter path of
diaphragm when P=25MPa. Seen from Fig 7 and
Fig 11, the radial stresses and strains at the
a=0.0012mm and a=0.0048mm are much bigger,
where the piezoresistors must be embedded.

5. ‫ﻣﻴﻜﺮوﻣﺎﺷﻨﻴﻜﺎري‬ ‫و‬ ‫رﻳﺰﻓﻨﺎوري‬ ‫اﻟﻤﻠﻠﻲ‬ ‫ﺑﻴﻦ‬ ‫ﻛﻨﻔﺮاﻧﺲ‬ ‫اوﻟﻴﻦ‬ICMEMS2014
‫ﻓﻨﺎوري‬ ‫ﭘﮋوﻫﺸﻜﺪه‬،‫اﻣﻴﺮﻛﺒﻴﺮ‬ ‫ﺻﻨﻌﺘﻲ‬ ‫داﻧﺸﮕﺎه‬ ‫ﻧﻮ‬ ‫ﻫﺎي‬29‫و‬30‫ﺑﻬﻤﻦ‬1392
Fig 6: Finite element model of diaphragm Fig 7: Deformation on Z direction when P=25MPa
Fig 8: Stress on X direction when P=25MPa Fig 9: Von Mises stress when P=25MPa
1
X
Y
Z
FEB 8 2013
09:21:13
ELEMENTS
1
MNMX
X
Y
Z
-.134E+09
-.104E+09
-.735E+08
-.434E+08
-.132E+08
.170E+08
.472E+08
.774E+08
.108E+09
.138E+09
FEB 8 2013
09:32:58
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SX (AVG)
RSYS=0
DMX =.410E-06
SMN =-.134E+09
SMX =.138E+09
1
MN
MX
X
Y
Z
1.163
.173E+08
.345E+08
.518E+08
.691E+08
.863E+08
.104E+09
.121E+09
.138E+09
.155E+09
FEB 8 2013
09:32:17
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
SEQV (AVG)
DMX =.410E-06
SMN =1.163
SMX =.155E+09
1
MN
MX X
Y
Z
0
.455E-07
.910E-07
.137E-06
.182E-06
.228E-06
.273E-06
.319E-06
.364E-06
.410E-06
FEB 8 2013
09:36:46
NODAL SOLUTION
STEP=1
SUB =1
TIME=1
USUM (AVG)
RSYS=0
DMX =.410E-06
SMX =.410E-06

6. ‫ﻣﻴﻜﺮوﻣﺎﺷﻨﻴﻜﺎري‬ ‫و‬ ‫رﻳﺰﻓﻨﺎوري‬ ‫اﻟﻤﻠﻠﻲ‬ ‫ﺑﻴﻦ‬ ‫ﻛﻨﻔﺮاﻧﺲ‬ ‫اوﻟﻴﻦ‬ICMEMS2014
‫ﻓﻨﺎوري‬ ‫ﭘﮋوﻫﺸﻜﺪه‬،‫اﻣﻴﺮﻛﺒﻴﺮ‬ ‫ﺻﻨﻌﺘﻲ‬ ‫داﻧﺸﮕﺎه‬ ‫ﻧﻮ‬ ‫ﻫﺎي‬29‫و‬30‫ﺑﻬﻤﻦ‬1392
Fig 7: X-Y Stress distribution the path of X direction
2a=4mm , h=0.4mm
Fig 10: Z deflection with 2a=2mm, h=0.4mm
Fig 8: X-Y Stress distribution the path of X direction
2a=2mm , h=0.4mm
Fig 11: X-Y Strain distribution the path of X direction
2a=2mm , h=0.4mm
Structure size
2RP=2mm
hP=0.4mm
2RP=2mm
hP=0.2mm
2RP=4mm
hP=0.5mm
2RP=4mm
hP=0.3mm
Theoretical maximum deflection /µm 0.412 1.132 1.329 2.216
Maximum deflection by ANSYS/µm 0.565 1.130 1.326 2.211
Maximum stress by ANSYS /MPa 113.82 118.56 83.508 83.558
[1] J. von Berg, C. Sonderegger, S. Bollhalder, C. Cavalloni,
Piezoresistive SOI-Pressure Sensor for High Pressure and High
Temperature Applications, Sensor 2005, Volume (I), pp. 33-38.
[2] Zhong Z et al,” Calibration of a piezoresistive stress sensor in
(1 00) silicon test chips “in Proc. Elect. Packag. Tech Conf. 2002
pp 323-326.
[3].Yan-Hong Zhang, Chen Yang, A Novel Pressure Microsensor
With 30-um-Thick Diaphragm and Meander-Shaped Piezoresistors
Partially Distributed on High-Stress Bulk Silicon Region, IEEE
Sensors J.,vol.7,no.12, Dec.2007, pp.1742-1748.
[4] Xudong Fang, Libo Zhao, Yulong Zhao, Zhuangde Jiang, “A
high pressure sensor with circular diaphragm based on MEMS
technology” , The 2st International Conference of CSMNT, State
Key Laboratory for Mechanical Manufacturing System
Engineering, Xi’an, China
[5] MEMS Mechanical Sensors, Stephen Beeby, Graham Ensell,
Michael Kraft, Neil White, Chapter 6, Pressure Sensors, 2004
British Library Cataloguing in Publication Data
[6] MEMS, Design and Fabrication, edited by Mohamed Gad-el-
Hak., Chapter 7, Fabrication, Characterization, and Reliability
design and fabrication, © 2006 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group