Lecture 11: Piezoelectric Sensors & Actuators - …mech466/MECH466-Lecture-11.pdf · During normal operation, a piezoelectric material is either strained (to create an electric potential)
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MECH 466Microelectromechanical Systems
University of VictoriaDept. of Mechanical Engineering
(b) Sensors [1] based on ‘quartz resonators’ to measure physical phenomena such as: temperature, applied force (stress) and fluid density, among others.
(c) Ultrasonic transceivers for marine sonar.(d) Ultrasound systems for non-invasive biomedical
imaging.(e) The needles of record players(f) microphones
In its natural state, a piezoelectric material, such as quartz, is likely in a polycrystalline configuration with grains (domains) that are randomly oriented in various directions, as shown:
Since the domains are randomly oriented, the ‘net’ piezoelectric effect due to strain (or applied voltage) is zero.
Magnified Image of Quartzite [Dept. of Geology and Geophysics, U. of Minnesota]
In order to create a ‘net’ piezoelectric effect, the material must be:
(a) a pure crystal (difficult to realize in most cases)
(b) the crystal domains must be brought into alignment
Poling: is a method aligning the crystal domains of piezoelectric materials.
During Poling, the material is exposed to a very strong electric field, and is simultaneously baked at an elevated temperature, which causes the domains to become aligned in the desired orientation.
This alignment (also known as polarization) is sensitive, and a material can become depolarized if it is subjected to extreme mechanical stress, electric fields or temperatures.
During normal operation, a piezoelectric material is either strained (to create an electric potential) or is subjected to an electric potential (to create a strain).
However, care must be taken to operate the material within the parameters specified by the manufacturer.
Electrical depolarization can occur if a piezoelectric material is subjected to extreme electric fields (or voltages) which will cause it to lose (or significantly degrade) its piezoelectric effects.
Mechanical depolarization can occur if a material is excessively strained to the point where the crystal domains are significantly disturbed.
Thermal depolarization can occur if a material subjected to temperatures beyond the ‘Curie point’ of the material. A safe operational temperature is about half the Curie point temp.
Consider operation with the ‘direct piezoelectric effect’
If a material is strained, a charge will build up on opposite faces of the crystal:
You can think of a piezoelectric crystal like a ‘capacitor’ that generates charge on the upper and lower surfaces when you strain it, as shown in the diagram.
Piezoelectric ceramics tend to be very good insulators (i.e. poor conductors), so the charge will tend to remain on the upper and lower surfaces.
Continuing on with our ‘capacitor analogy’...
It is well known that there will be some finite amount of electric leakage of charge from one surface to another. (i.e. even capacitors will eventually loose their charge).
More importantly, if we try to do work with the developed potential (+V), buy connecting it to a load, current will flow to do the work. Therefore, the accumulated charge will drain, and the developed potential will drop.
EdTD ε+=Where: D - Electrical Polarization (C/m2) T - Stress Vector (N/m2) d - Piezoelectric Coefficient Matrix ε - Electrical Permitivity Matrix (F/m) (*Note: this is NOT strain*) E - Electric Field Vector (V/m)
The direct effect of piezoelectricity can be simplified down to the following equation, in the absence of an external electric field (i.e. E=0).
The inverse effect of piezoelectricity can be simplified to the following expression, if there is no additional mechanical stress present (i.e. T=0). Where strain is related the electric field by:
The units of the piezoelectric constant, dij, are the units of electric displacement over the unit of the stress. Therefore:
Recall that:
Therefore the piezoelectric constant is a good way to measure the intensity of the piezoelectric effect, since we can think of it in terms of Columbs generated, per Newton applied.
€
V = Et
Where: V - Voltage E - Electric Field t - distance of interest through E
NColumb
mNmV
mF
TE
TDd ====
2
33 ][]][[
][][][ ε
ij
Si is symmetric and does not exhibit piezoelectricity.(Si: positive charge; bond electrons: negative change)
GaAs lattice is not symmetric and exhibits piezoelectricity.(However, GaAs has poor piezoelectric material properties)
Curie temperature- temperature above which the piezoelectric property will be lost.
Material purity- the piezoelectric constant is sensitive to the composition of the
material and can be damaged by defects.
Frequency response- most materials have sufficient leakage and cannot “hold” a DC
force. The DC response is therefore not superior but can be improved by materials deposition/preparation conditions.
Bulk vs thin film- bulk materials are easy to form but can not integrate with MEMS
or IC easily. Thin film materials are not as thick and overall displacement is limited.
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Bi-Layer Bending Configuration:
Where: Ap and Ae are the cross-section areas of the piezoelectric and the elastic layer, Ep and Ee are the Young’s modulus of the piezoelectric and the elastic layer, and tp and te are the thickness of the piezoelectric and the elastic layer
A patch of ZnO thin film is located near the base of a cantilever beam, as shown in the diagram below. The ZnO film is vertically sandwiched between two conducting films.
The length of the entire beam is l. It consists of two segments: A and B. Segment A is overlapped with the piezoelectric material while segment B is not. The length of segments A and B are lA and lB, respectively.
If the device is used as a force sensor, find the relationship between applied force F and the induced voltage.
Axis 3 of the deposited ZnO is normal to the front surface of the substrate it is deposited on. A transverse force would produce a longitudinal tensile stress in the piezoelectric element (along axis 1), which in turn produces an electric field and output voltage along axis 3.
The stress along the length of the piezoresistor is actually not uniform and changes with position. For simplicity, we assume the longitudinal stress is constant and equals the maximum stress value at the base. The maximum stress induced along the longitudinal direction of the cantilever is given by:
Where the stress component is parallel to axis 1.
According to Equation 2, the output electric polarization in the direction of axis 3 is:
The overall output voltage is then:
with Tpiezo being the thickness of the piezoelectric stack.