Piezoresistive Sensors Principles, Materials, Fabrication and Applications
Chang Liu
Micro Actuators, Sensors, Systems Group
University of Illinois at Urbana-Champaign
Chang Liu
MASS
UIUC
Definition of Piezoresistive Sensing
• Also called strain sensors or strain gauges.
• A strain gauge is a device used to measure how much a
component distorts under loading.
• The electrical resistance of a sensing material changes as a result
of applied strains.
• A strain gauge is a conductor or semiconductor material that can
be directly fabricated on the sensor itself or bonded with the
sensor.
• In macroscopic systems, such as strain sensors in machine tools,
aircraft, strain gauges are most likely bonded onto parts.
Chang Liu
MASS
UIUC
Stress-Strain Relation
Chang Liu
MASS
UIUC
Physical Causes of Piezoresistivity
• Change of relative dimensions, as the resistance is related to
length and cross-sectional area (local).
l

L
L
R
dR

dL

d


dA
A
A
A
A2
dR dL d dA



R
L

A
Chang Liu
MASS
UIUC
Why Electrical Conductivity Change With
Stress/Strain?
• Change of electrical conductivity and resistivity as a result of
crystal lattice deformation.
• Strain causes the shape of energy band curves to change,
therefore changing the effective mass, m*. Therefore electrical
conductivity s changes.
2
Chang Liu
Crystal bandgap structure
m* 
h
d 2 E / dk 2
s
qt
m*
MASS
UIUC
Basic Formula for Describing Piezoresistivity
• G is called Gauge Factor of a piezoresistor. It determines the
amplification factor between strain and resistance change.
R
L
G
R
L
stresss  E
R
R
G R 
l
R
l
Material
Chang Liu
Gauge factor
Metal foil
1-5
Semiconductor (crystal)
Diffused semiconductor
80-150
10-200
Why the big difference between materials?
MASS
UIUC
Applications at Macroscale
• Spot-weldable strain gauges are used with
strain gauge sensors and a vibrating wire
indicator or data logger to monitor strain in
steel members. Typical applications include:
• Monitoring structural members of buildings
and bridges during and after construction.
• Determining load changes on ground anchors
and other post-tensioned support systems.
• Monitoring load in strutting systems for deep
excavations.
• Measuring strain in tunnel linings and supports.
• Monitoring areas of concentrated stress in
pipelines.
• Monitoring distribution of load in pile tests.
Chang Liu
MASS
UIUC
Metal Strain Gauge
•
•
For metals, the resistivity is not
changed significantly by the stress. The
gauge factor is believed to be
contributed by the change of
dimensions. These may be made from
thin wires or metal films that may be
directly fabricated on top of micro
structures. Typical strain gauge pattern
is shown in the following figure. Thin
film strain gauges are typically
fabricated on top of flexible plastic
substrates and glued to surfaces.
etched foil gauges
–
Chang Liu
These strain gauges consist of a
conduction path etched onto metal clad
plastic film. The strain gauges are
designed to be glued, using very special
procedures onto the component to be
tested. When the component stretches,
the strain gauge will also stretch as will
the etched conduction path.
An interactive guide can be found at
http://www.measurementsgroup.com/guide/index.htm
MASS
UIUC
Strain gauge selection and use
Metal alloys
• Constantan, a Nickel-Cu alloy:
–
Of all modern strain gage alloys,
constantan is the oldest, and still the
most widely used.
–
constantan tends to exhibit a continuous
drift at temperatures above +150 deg F
(+65 deg C);
• Nickel-Chrominum alloy
Chang Liu
MASS
UIUC
Two Primary Classes of Piezo-resistor
Configuration
Chang Liu
MASS
UIUC
Semiconductor Strain Gauge
• The very first semiconductor strain gauge used a doped silicon
strip attached to a membrane of another material.
• In semiconductor strain gauges, the piezoresistive effect is very
large, leading to much higher G.
• P-type silicon has a G up to 200 and n-type has a negative G of
down to -140.
• Strain gauges can be locally fabricated in bulk silicon through
ion implantation or diffusion
Chang Liu
MASS
UIUC
Gauge factor of polysilicon with doping
• Gauge factor is a function of doping material or doping
concentration.
• Because grains are randomly oriented, gauge factor is not
sensitive to orientation.
N type
Phosphorous doped Si
30
28
26
24
22
20
18
16
14
12
10
8
-22
-20
-18
-16
-14
-12
-10
-8
-8
-6
-4
-2
1019
Chang Liu
P type
Boron doped Si
1020 1021
1019
1020 1021
MASS
UIUC
Chang Liu
MASS
UIUC
Why Use Semiconductor Strain Gauge
• Higher G than metal alloy strain gauges
• Easily fabricated with controlled performance specifications
using precise ion implantation and diffusion
• Easily integratable with silicon, a material used for sensors and
signal processing.
Chang Liu
MASS
UIUC
Merit of Piezoresistive Sensors Vs Capacitive
• Capacitive sensing is perhaps the most dominant positionsensing technique for microfabricated sensors. However, there
are a number of limitations imposed on capacitive sensors.
• The detection of position is constrained to small vertical movement
(parallel plate) and horizontal movement (transverse or lateral comb
drives).
• The area of overlapped electrodes must be reasonably large (as a rule
of thumb, tens of mm2). If the overlap area is small and the vertical
displacement is large, capacitive sensors are not suitable.
Chang Liu
MASS
UIUC
Single Crystal Silicon Vs. Polycrystal
• Single Crystal Silicon: Uniform crystal orientation throughout
the entire material.
– Method of growth: heat melt (bulk); epitaxy (thin film)
• Polycrystal silicon: crystal orientation exist with in individual
grains which are separated by grain boundaries.
– Methods of growth: low pressure chemical vapor deposition;
sputtering (like a metal).
Chang Liu
Single crystal
Polycrystal
MASS
UIUC
The piezoresistive coefficients
• Ohm’s law in matrix form
• The relation between changes of resistivity and the applied
stress and strain
Chang Liu
MASS
UIUC
Piezoresistivity Components
Chang Liu
MASS
UIUC
Example
Chang Liu
MASS
UIUC
Methods for Compensating Temperature Effect
• Doped silicon strain sensors are also sensitive to temperature.
In order to isolate the effect of temperature and strain, it is
important to compensate for the temperature effect.
• Common technique: Use a reference resistor which is subject to
the same temperature but not the strain. The difference of signal
between these two sensors give overall effect due to strain.
• Second technique: Wheatstone bridge
Chang Liu
MASS
UIUC
Wheatstone Bridge Circuit Transforming resistance change to voltage change
Common configuration.
Rs  R  R
 R2
R4 
Vin
Vout  

R

R
R

R
2
3
4 
 1

R
R 
Vin 
Vout  

R

(
R


R
)
2
R


R 

(R 
) 

R
1
R

2
Vin
 Vin  



R
 2 R   R 2( R 
 2 R  R 2 
) 

2 

Chang Liu
  R / 2 
Vout  
Vin
 2 R  R 
Temperature in-sensitive!!
MASS
UIUC
Strain Gauge Made of Single Crystal Silicon
- A Pressure Sensor
•
•
•
•
Process
Etch backside to form
diaphragm with controlled
thickness.
Silicon is selectively doped
in the region where stress is
greatest.
Difference of pressure
across the diaphragm will
cause stress concentration.
Chang Liu
MASS
UIUC
Stress Analysis and Sensor Placement
• Sensor placement in the highest stress region.
displacement
Stress
 4w
4w
4w p
2 2 2  4 
x 4
x y
y
D
Differential eq.
For displacement.
2mx 
2ny 

w   amn 1  cos
1  cos

a
b



m 1 n 1


4 2t E
s x ( x, y)   2
a 1 m 2
Chang Liu
2mx
2ny
2mx 2ny 
 2
2
2
2
a
m
cos(
)

m
n
cos(
)

(
m

m
n
)
cos(
)(

mn 
a
a
a
a 

m 1 n 1


MASS
UIUC
Pressure Sensor Based On Polysilicon
• Sensors placed on edges (highest tensile stress) and center
(highest compressive stress).
Chang Liu
MASS
UIUC
Fabrication Process
Chang Liu
MASS
UIUC
Fabrication Process (Continued)
Chang Liu
MASS
UIUC
Chang Liu
MASS
UIUC
Piezoresistive Accelerometer
Chang Liu
MASS
UIUC
Condition for Mechanical Equilibrium
• Total force on a given mechanical member is zero.
• Total moment on a given mechanical member is zero.
Tensile
Compressive
Chang Liu
MASS
UIUC
Chang Liu
MASS
UIUC
Chang Liu
MASS
UIUC
Chang Liu
MASS
UIUC
Relationship between maximum stress and applied
force
• The stress within the cross-section provide counter moment
(torque) to balance the torque created by the applied force.
• The magnitude of the torque is force times the length of arm, l.
• Therefore M=Fl.
s
du y y


 y/
dx ds 
1
M

 y" x
 EI
t
Mt
smax   ( y  ) 
2
2 EI
Chang Liu
MASS
UIUC
Example 6.2
Chang Liu
MASS
UIUC
Chang Liu
MASS
UIUC
Good vs. Bad Designs
Chang Liu
MASS
UIUC
• When one tried to bend a cantilever beam, the failure always
occurs at the anchored end and the surface of the beam. Why?
• Because the longitudinal stress is the greatest at that point.
Chang Liu
MASS
UIUC
Comments on Mechanical Failure
• Two failure modes
– Fracture
• if the strain in the material exceed the fracture strain, the material will
undergo catastrophic failure due to fracture.
• In design, it is important to not only design the mechanical structure
accurately but also to leave safety margins.
– Fatigue
• If repeated cycle of force is applied to a mechanical member, with the
induced strain much lower than that of the fracture strain, the member
may failure after repeated cycles.
• Mechanism: microscopic defects (bubbles, dislocations) amplifies
over time and causes stress concentration (re-distribution of stress).
The defects are often hidden underneath the surface of the material.
Chang Liu
MASS
UIUC
Stress-Strain Curve
• Silicon is a strong material, not a tough material.
Chang Liu
MASS
UIUC
Case 6.1: Analysis of Accelerometer
• Acceleration induced force F, F=ma.
• The force induces stress at the fixed end of the cantilever beam.
• The stress is detected by chance in resistance.
Assumptions
•
•
•
•
assume entire resistance is
concentrated at the
anchor;
for moment of inertia at
the end, ignore the
thickness of the resistor.
Assume the stress on the
resistor is the maximum
value.
The proof mass is rigid. It
does not bend because of
the significant thickness
and width.
Chang Liu
MASS
UIUC
Analysis of Sensitivity
• Under a given a, the force has a magnitude F  m  a
L
• The moment applied at the fixed end of the beam is M  F (l  )
2
• Therefore the maximum strain, which is the strain experienced
by the resistor, is
 max
 L
F  l  t 6 F (l  L )t
Mt
2
2

 

3
3
Ewt
2 EI
Ewt
6
• The strain is applied in the longitudinal direction of the resistor.
Assuming the gauge factor is G, the change in resistance is
R
 G   max
R
Chang Liu
L
L 

6GF (l  )  6Gm(l  ) 
2 
2 a

2
Ewt 2
 Ewt





MASS
UIUC
Stress state analysis example
Chang Liu
MASS
UIUC
Stress state analysis example
Chang Liu
MASS
UIUC