# Engineering Acoustics/Piezoelectric Acoustic Sensor

## Introduction

Piezoelectric Acoustic Wave technology have been used for more than 60 years and offered many sensor applications, such as pressure sensors, chemical sensors, temperature sensors, mass sensors and so on. Their detection mechanism are based on acoustic wave vibration, as an acoustic wave is excited and propagates through or on the surface of the material, any changes to the characteristics of the propagation path affect the velocity and/or amplitude of the wave, changes in velocity/amplitude can be monitored by measuring the frequency or phase characteristics of the sensor and can then be correlated to the corresponding physical or chemical quantity being measured. [1] All acoustic waves sensors use a piezoelectric material to generate and detect acoustic waves. Piezoelectric material provides the link between electrical and mechanical phenomena which allow the electrical signal convert into mechanical acoustic wave and vice versa. Conventional piezoelectric materials involve quartz, LiNbO3, AlN and LiTaO3.

## Acoustic Wave Propagation Modes

Piezoelectric acoustic wave devices are described by the mode of wave propagation through or on a piezoelectric substrate. If the wave propagates on the surface of the substrate, it is known as a surface wave; and if wave propagating through the substrate is called a bulk wave.

### Mechanical waves in sensor devices

Mechanical waves for sensor applications are distinguished primarily by two different types: shear waves and compressional waves. Shear waves (also called S wave) have particle displacements that are normal to the direction of wave propagation, behave like real water waves, while compressional waves (also called P wave) are waves in which the displacement of the particle is in the same direction as the propagation direction of the wave[2].

## Acoustic Wave Technology

Surface acoustic wave (SAW) and bulk acoustic wave (BAW) are two most commonly used technologies in sensor applications.

### Surface Acoustic Wave

Surface Acoustic Wave was first discovered by Lord Rayleigh in 1887. Rayleigh Surface Acoustic Wave is composed of a longitudinal and a vertical shear component, the wave bound to the surface and decay exponentially with the distance from the surface. Therefore, the wave energy is confined on the surface, which is ideal for sensor application. The common structure of a SAW device contains piezoelectric material with interdigital transducers(IDT) patterned on top. An acoustic wave is excited and travels along the surface when an RF voltage is applied on the input IDT by piezoelectric effect. The operation frequency of the SAW device ranges from the MHz to GHz range mainly depending on the interdigital transducer’s design and piezoelectric material[3]:

${\displaystyle f_{res}={\frac {V_{R}}{\lambda }}}$
• where ${\displaystyle V_{R}}$ is Rayleigh wave velocity determined by material properties and λ is the wavelength defined as the periodicity of the IDT.

The figure below is SAW delay line configuration, which consists of two IDTs, one of them acting as the transmitter to generate acoustic waves, and the other as a receiver, the path between the IDTs is known as the delay-line. When electric signal is applied on the interdigitated electrodes(IDT) with alternate polarity as shown in Figure, resulting in alternating regions of tensile and compressive strain between fingers of the electrodes due to piezoelectric effect of material, then creating a mechanical wave at the surface, the mechanical wave will propagate in both directions from the input IDT, only half of the energy of the mechanical wave will propagate across the delay line in the direction of the output IDT. [4] The delay-line is sensing area, usually, the sensor material is deposited on the delay-line for chemical sensor to absorb the target analytics.

Surface acoustic wave resulting from opposing polarity of the electrodes of the IDT

#### Sensor Respnse

The surface acoustic wave is sensitive to changes in the surface properties of the medium in the delay-line, these changes will modulate the velocity and amplitude of the wave.

The surface wave velocity can be perturbed by various factors, each of which represents a possible sensor response[5]

${\displaystyle {\frac {\delta v}{v_{0}}}={\frac {1}{v_{0}}}({\frac {\delta v}{\delta m}}\Delta m+{\frac {\delta v}{\delta c}}\Delta c+{\frac {\delta v}{\delta T}}\Delta T+...)}$
• where ${\displaystyle v_{0}}$ is unperturbed wave velocity, ${\displaystyle m}$ is mass, ${\displaystyle T}$ is temperature and c is stiffness.

Therefore, this kind of devices can be used in mass, pressure and temperature sensing applications.

##### Mass sensor

One of the most used surface acoustic waves(SAW) sensor are mass sensor.

Example of application: Gas Sensor, Bio-sensor

The sensor material is deposited on the propagation path between the two IDTs. After exposure to a target analytes, the active sensing material of the sensor adsorption the molecules of analytes, which causes the mass of the sensing material to change and the surface acoustic wave to slow down on the propagation path due to mass loading. This causes a change in the delay time:

${\displaystyle \tau ={\frac {L_{path}}{V_{R}}}}$
• where ${\displaystyle L_{path}}$ is the length of propagation path. By tracking the delay time change at the receiver IDT, one can infer the concentration of the target analyte.
${\displaystyle \Delta \tau ={\frac {L_{path}}{V_{R}}}-{\frac {L_{path}}{V_{R^{'}}}}\propto concentration}$
##### Equivalent circuit

Mason’s Crossed-Field model is used to develop the equivalent electrical circuit for an one period of IDT fingers, by using frequency dependent resistance blocks, whose resistance is minimum for the center frequency of the SAW device and very high for remaining frequencies. Thus, the input energy propagates only for the frequencies in close proximity to the resonant frequency.

### Bulk Acoustic Wave

An bulk acoustic wave is the wave that travels through a piezoelectric material, as in a quartz delay line. Also known as volume acoustic wave. In same material, the wave velocity is higher for Bulk Acoustic Wave than Surface Acoustic Wave because SAW is composed of a longitudinal and a shear wave, the wave velocity is slower than both of them, while bulk acoustic wave contains either longitudinal or shear wave only, which is much faster.

#### Quartz Crystal Microbalance (QCM) technology

QCM is oldest and simplest acoustic wave device for mass sensor, it consists of a thin disk of AT-cut quartz with parallel circular electrodes patterned on both sides. The application of a voltage between these electrodes results in a shear deformation of the crystal[6].

Quartz resonators with front and back electrodes

The working principle is based on mass-loading which is similar to SAW sensor. Bulk adsorption of target analyte onto the coated crystal causes an increase in effective mass, which reduces the resonant frequency of the crystal, in direct proportion to the concentration of target analyte. For ideal sensing material, this sorption process is fully reversible with no long-term drift effect, giving a highly reliable and repeatable measurement[7].

The relation between the frequency shift and the mass-loading can be obtained from Sauerbrey equation developed by Prof. Dr. Günter Sauerbrey from Tiefenort, Germany, in 1959:

${\displaystyle \Delta f=-{\frac {2f_{0}^{2}}{A{\sqrt {\rho _{q}\mu _{q}}}}}\Delta m}$

• ${\displaystyle f_{0}}$ - resonant frequency depends on the wave velocity (v) and the piezoelectric material thickness, ${\displaystyle f_{0}={\frac {v}{2d}}}$
• ${\displaystyle \Delta f}$ - frequency change
• ${\displaystyle \Delta m}$ - mass change
• ${\displaystyle A}$ - active area
• ${\displaystyle \rho _{q}}$ - density of piezoelectric material
• ${\displaystyle \mu _{q}}$ -shear modulus of piezoelectric material

#### Thin-film Bulk Acoustic Resonator (FBAR) technology

FBAR is special case of QCM with piezoelectric films thicknesses ranging from only several micrometres down to tenth of micrometres resonate in the frequency range up to 10 GHz, since the mass sensitivity is proportional to resonance frequency, FBAR can achieve 3X mass sensitivity compared to QCM.

Thin-film bulk acoustic resonator(FBAR)

## Reference

1. Hoang T 2009 Design and realization of SAW pressure sensor using aluminium nitride Dissertation University Joseph Fourier, France
2. (60), H., (69), J., & (68), R. (n.d.). Mechanical waves and shear wave induction in soft tissuesteemCreated with Sketch. Retrieved April 13, 2018, from https://steemit.com/ultrasonography/@hagbardceline/mechanical-waves-and-shear-wave-induction-in-soft-tissue
3. H. Wohltjen, “Mechanism of operation and design considerations for surface acoustic wave device vapour sensors,” Sensors and Actuators, vol. 5, no. 4, pp. 307 – 325, 1984.
4. Kirschner J 2010 Surface acoustic wave sensors (SAWS): design for application (www.jaredkirschner.com/ uploads/9/6/1/0/9610588/saws.pdf)
5. Ricco, A.j., et al. “Surface acoustic wave gas sensor based on film conductivity changes.” Sensors and Actuators, vol. 8, no. 4, 1985, pp. 319–333., doi:10.1016/0250-6874(85)80031-7.
6. Hoang T 2009 Design and realization of SAW pressure sensor using aluminium nitride Dissertation University Joseph Fourier, France
7. http://www.michell.com/us/technology/quartz-crystal-microbalance.htm