Transcript Piezoresistive Sensors - Principles, Materials
Chang Liu
Piezoresistive Sensors Principles, Materials, Fabrication and Applications
Chang Liu Micro Actuators, Sensors, Systems Group University of Illinois at Urbana-Champaign
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).
R
l A dR
A dL
L A d
L dA A
2
dR
R dL
L d
dA 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
m
*
d
2
E h
/
dk
2 s
q t m
* Chang Liu Crystal bandgap structure
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 R
G
L L G
R R
l
R
R l
stress
s
E
Material Metal foil Semiconductor (crystal) Diffused semiconductor 1-5 80-150 10-200 Gauge factor Chang Liu 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 changed significantly by the stress. The gauge metals, factor the is resistivity believed is to not 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 – 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.
Chang Liu An interactive guide can be found at http://www.measurementsgroup.com/guide/index.htm
MASS UIUC
Chang Liu
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
MASS UIUC
Chang Liu
Two Primary Classes of Piezo-resistor Configuration 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.
-22 -20 -18 -16 -14 -12 -10 -8 -8 -6 -4 -2 N type Phosphorous doped Si 10 19 10 20 10 21 30 28 26 24 22 20 18 16 14 12 10 8 P type Boron doped Si 10 19 10 20 10 21 Chang Liu
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 position sensing 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 m m 2 ). 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
Chang Liu
The piezoresistive coefficients
• Ohm’s law in matrix form • The relation between changes of resistivity and the applied stress and strain
MASS UIUC
Chang Liu
Piezoresistivity Components 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.
R s
R
R V out
R
1
R
2
R
2
R
3
R
4
R
4
V in V out
R
(
R R
R
)
R
2
R
V in
2
R R
R
1 2
V in
2
R R
R
( 2 (
R R
R
2
R
) ) 2
V in
Chang Liu
V out
2
R
R
/ 2
R V in
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 4
w
x
4 2 4
w
x
2
y
2 4
w
y
4
p D
Differential eq.
For displacement.
w
m
1
n
1
a mn
cos 2
mx a
1 cos 2
ny b
s
x
(
x
,
y
) 4 2
t a
2 1
E
m 2
m
1
n
1
a mn
m
2 cos( 2
m
x
)
a
m
n
2 cos( 2
ny
)
a
(
m
2 m
n
2 ) cos( 2
m
x a
)( 2
n
y a
Chang Liu
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
Chang Liu
Fabrication Process (Continued) MASS UIUC
Chang Liu
MASS UIUC
Chang Liu
Piezoresistive Accelerometer 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 dx
y
ds
y
y
/ 1
M EI
y
"
x s
max (
y
t
2 )
Mt
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
The moment applied at the fixed end of the beam is
a M
F
(
l
L
) 2 • • Therefore the maximum strain, which is the strain experienced by the resistor, is max 2
Mt EI F Ewt L
3 2
t
6
F
(
l
Ewt
3
L
2 )
t
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
6
GF
(
l
Ewt
2
L
) 2 6
Gm
(
l
Ewt
2
L
) 2
a
Chang Liu
MASS UIUC
Chang Liu
Stress state analysis example MASS UIUC
Chang Liu
Stress state analysis example MASS UIUC