# Engineering Acoustics/Piezoelectric Acoustic Sensor

## Introduction

Piezoelectric Acoustic Wave technologies have been used for over 60
years. They have many applications for pressure, chemical concentration,
temperature or mass sensors. Their detection mechanism is based on
acoustic wave propagation. An acoustic wave is excited and propagates
through or on the surface of the material. 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 natural frequency or phase characteristics of the sensor,
which can then be correlated to the corresponding physical or chemical
quantity being measured. [^1] Acoustic waves sensors use piezoelectric
materials to generate and detect acoustic waves. Piezoelectric materials
provide the transduction between electrical and mechanical response
conversion of electrical signal into mechanical acoustic waves and vice
versa. Conventional piezoelectric materials includes 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 of 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, as for surface water waves. Compressional waves (also
called P wave) are waves in which the displacement of the particle is
along the same direction as the propagation direction of the wave[^2].

!Shear
wave\|400px
!Compressional
wave\|400px

## Acoustic Wave Technology

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

### Surface Acoustic Wave

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]:

```{=html}
<center>
```
$f_{res} = \frac{V_{R}}{\lambda}$

```{=html}
</center>
```
where $V_{R}$ 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 an electric signal is applied on the
interdigitated electrodes (IDT) with alternate polarity, as shown in
Figure, an alternating regions of tensile and compressive strain between
two fingers of the electrodes due to piezoelectric effect of material. A
mechanical wave is generated at the surface. The mechanical wave
propagates in both directions from the input IDT, only half of the
energy of the mechanical wave propagates 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 Sensor Interdigitated Transducer
Diagram\|700px
!Surface acoustic wave resulting from opposing polarity of the
electrodes of the IDT


The animation below is time-domain simulation for the 2D structure of
SAW device using COMSOL. The x,y-axis represent the position of model.
The small rectangles on top are electrodes.

!FEM model with SAW\|

#### Sensor Response

The surface acoustic wave is sensitive to changes in the surface
properties of the medium in the delay-line, these changes 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]

```{=html}
<center>
```
$\frac{\delta v}{v_{0}}= \frac{1}{v_{0}}(\frac{\delta v}{\delta m}\Delta m + \frac{\delta v}{\delta c}\Delta c + \frac{\delta v}{\delta T}\Delta T + ...)$

```{=html}
</center>
```
-   where $v_{0}$ is unperturbed wave velocity, $m$ is mass, $T$ 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 along the propagation path between the
two IDTs. After exposure to a target analytes (e.g. target gas), the
active sensing material of the sensor adsorbs the analytes molecules
only, which causes the mass of the sensing material to increase and the
surface acoustic wave speed to decrease on the propagation path due to
mass loading. This causes a change in the delay time[^6],

```{=html}
<center>
```
$\tau = \frac{L_{path}}{V_{R}}$

```{=html}
</center>
```
where $L_{path}$ 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.

```{=html}
<center>
```
$\Delta \tau = \frac{L_{path}}{V_{R}} - \frac{L_{path}}{V_{R^{'}}} \propto concentration$

```{=html}
</center>
```
##### Equivalent circuit

Mason's Crossed-Field model was used to develop the equivalent
electrical circuit for an one period of IDT fingers[^7]. Frequency
dependent resistance blocks were used. Resistance is minimum for the
center frequency of the SAW device, and very high for remaining
frequencies. Thus, the input energy propagates only at the frequencies
in near the resonant frequency. The equivalent circuit below is
implemented using ADS.

### Bulk Acoustic Wave

A bulk acoustic wave is a wave that travels through a piezoelectric
material, as in a quartz delay line. It is also known as a volume
acoustic wave. In some materials, the wave velocity is greater for bulk
acoustic waves than surface acoustic wave because SAW is composed of a
longitudinal and a shear wave. The wave velocity is lower than both of
them. Bulk acoustic waves contain either longitudinal or shear waves
only, and thus propagate faster.

#### Quartz Crystal Microbalance (QCM) technology

QCM is the oldest and simplest acoustic wave device for mass sensors. 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[^8].
!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[^9].

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

$\Delta f = -\frac{2f_{0}^2}{A \sqrt{\rho_{q}\mu_{q}}}\Delta m$[^10]

-   $f_{0}$ - resonant frequency depends on the wave velocity (v) and
    the piezoelectric material thickness, $f_{0} = \frac{v}{2d}$
-   $\Delta f$ - frequency change
-   $\Delta m$ - mass change
-   $A$ - active area
-   $\rho_{q}$ - density of piezoelectric material
-   $\mu_{q}$ -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
micrometers down to tenth of micrometers using MEMS technology. They
resonate in the frequency range up to 10 GHz. Their mass sensitivity is
proportional to their resonance frequency.
FBAR can achieve 3X
mass sensitivity compared to QCM. !Thin-film bulk acoustic
resonator(FBAR)_.png "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]: 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.

[^7]: Trang Hoang. Design and realization of SAW pressure sensor using
    Aluminum Nitride. Acoustics \[physics.class-ph\]. Université
    Joseph-Fourier - Grenoble I, 2009. English. `<tel-00540305>`{=html}

[^8]: Hoang T 2009 Design and realization of SAW pressure sensor using
    aluminium nitride Dissertation University Joseph Fourier, France

[^9]: <http://www.michell.com/us/technology/quartz-crystal-microbalance.htm>

[^10]:
    