Surface Acoustic Wave Gas Sensor

A surface acoustic wave (SAW) is an acoustic wave propagating along the surface of a solid material. Its amplitude decays rapidly, often exponentially, with the depth of the material. SAWs are featured in many kinds of electronic components, including filters, oscillators, and sensors. SAW devices typically use electrodes on a piezoelectric material to convert an electric signal to a SAW, and back again.

In this model, you investigate the resonance frequencies of a SAW gas sensor. The sensor consists of an interdigitated transducer (IDT) etched onto a piezoelectric LiNbO3 (lithium niobate) substrate and covered with a thin polyisobutylene (PIB) film. The mass of the PIB film increases as PIB selectively adsorbs CH2Cl2 (dichloromethane, DCM) from air. This causes a shift in resonance which slightly lowers the resonance frequency for the same SAW mode.

Model Definition

Figure 1 shows a conceptual view of the gas sensor in this model.

Figure 1: SAW gas sensor, showing the IDT electrodes (in black), the thin PIB film (light gray), and the LiNbO3 substrate (dark gray). For the sake of clarity, the dimensions are not to scale and the IDT has fewer electrodes than in common devices. A slice of the geometry is removed to reveal the modeled unit cell (in white).

IDTs used in SAW devices may have hundreds of identical electrodes, and each electrode can be about 100 times longer than it is wide. You can therefore neglect the edge effects and reduce the model geometry to the periodic unit cell shown in Figure 2. The height of this cell does not have to extend all the way to the bottom of the substrate but only a few wavelengths down, so that the SAW has almost died out at the lower boundary.

Figure 2: The geometry of the SAW unit cell used in this model. A 500 nm PIB film covers two 1 μm-wide electrodes on top of the LiNbO3 substrate. The substrate domain has a total height of 12 μm.

Set up the model using the predefined Piezoelectricity multiphysics interface. In 2D, a Plane Strain assumption is used for the Solid Mechanics interface. Hence the out-of-plane strain component is zero. This should be a valid assumption, considering that the SAW is generated in the plane of the model and hence any variation in the out-of-plane direction can be considered minimal.

boundary conditions

In order to define the model, you need to apply structural and electrical boundary conditions.

As one can assume that the surface wave dies off within two to three wavelengths from the surface, the lower boundary is fixed. This enforces a zero structural displacement but does not contribute to any significant reflection from the lower boundary back into the bulk of the substrate as long as we are observing surface waves and in particular Rayleigh waves.

The electrodes have a much higher electrical conductivity compared to PIB and LiNbO3. Hence, one can expect each of the electrodes to be isopotential. This is why you do not need to model the domains that constitute the electrodes but can simply use appropriate boundary conditions on all the outer boundaries of each electrode to indicate what type of isopotential state it is in. The boundaries of the left terminal is set to electrical ground, and those of the right terminal are assigned to a Floating Potential with zero surface charge accumulation. This combination of electrical boundary conditions corresponds to an open circuit configuration, which is typically suitable for sensing applications.

Use periodic boundary conditions to dictate that the electric potential and displacements are the same along both vertical boundaries of the geometry. When using periodic boundary conditions, one needs to ensure that the mesh on the vertical boundaries on the left of the unit cell and the vertical boundaries on the right of the unit cell are identical. This is achieved by first creating the mesh on the vertical boundaries on the left and then using the Copy Edge feature to create the exact same mesh on the vertical boundaries on the right.

All other boundaries are left to the default boundary conditions which are Free for the Solid Mechanics interface and Zero Charge for the Electrostatics interface, respectively.

Material Properties

The substrate used in the simulation is YZ-cut LiNbO3 with the following properties (cited in Ref. 2):

•

Elasticity matrix:

•

Coupling matrix:

•

Relative permittivity:

The density of the PIB film is from Ref. 1. The Poisson’s ratio is considered to be 0.48, and the Young’s modulus is set to 10 GPa

The adsorption of DCM gas is represented as a slight increase of the overall density of the PIB film as shown in the following expression.

In this model, you use a parameter, switch, whose value can be either 0 or 1. This allows to solve the model for two cases; once without the effect of adsorbed gas and once with the effect of the adsorbed DCM gas in PIB.

When the sensor is exposed to 100 ppm of DCM in air at atmospheric pressure and room temperature, the “partial density” of DCM in the PIB film can be calculated from

where K = 10l.4821 (Ref. 1) is the air/PIB partition coefficient for DCM, M is its molar mass, and c

is its concentration in air. The DCM concentration, c in moles/m3 is computed using the Gas Law. Here c0 is the concentration in parts per million, p is the pressure, T is the temperature, and R is the gas constant. Any effects of the DCM adsorption on the material properties other than the density are neglected.

Most of the material properties and factors affecting them have been parameterized as shown in Table 1. This easily allows the model to be adapted for other materials and operating conditions.

Table 1: List of parameters.
Name	expression	description
p	1[atm]	Air pressure
T	25[degC]	Air temperature
c0	100	DCM concentration in ppm
c_DCM_air	10-6c0p/(R_const*T)	DCM concentration in air
M_DCM	84.93[g/mol]	Molar mass of DCM
K	10^1.4821	PIB/air partition constant for DCM
rho_DCM_PIB	KM_DCMc_DCM_air	Mass concentration of DCM in PIB
rho_PIB	0.918[g/cm^3]	Density of PIB
E_PIB	10[GPa]	Young's modulus of PIB
nu_PIB	0.48	Poisson’s ratio of PIB
eps_PIB	2.2	Relative permittivity of PIB
switch	0	Switch for adding DCM density
vR	3488[m/s]	Rayleigh wave velocity
width	4[um]	Width of unit cell
f0	vR/width	Estimated SAW frequency
t_PIB	0.5[um]	PIB thickness

Estimating the SAW frequency

The use of periodic boundary condition implies that the frequencies of interest correspond to wavelengths that are integer fractions of the width of the geometry. The lowest SAW eigenmode has its wavelength equal to the width of the geometry, that is, 4 μm. Using this along with the Rayleigh wave velocity for the given piezoelectric substrate material, one can find an estimate of the resonance frequency of interest. The information can be used in the eigenfrequency solver, which helps it to find out the resonance frequencies close to this estimated number. In this model, you use a YZ-cut LiNbO3 whose Rayleigh wave velocity (vR) is around 3488 m/s. This gives an estimate of the lowest SAW frequency (f0) to be 872 MHz.

Results and Discussion

The first and second eigenfrequencies evaluate to approximately 850 MHz and 855 MHz, respectively. Figure 3 and Figure 4 show the corresponding SAW modes. Figure 5 and Figure 6 show the electric potential distribution characteristics for these solutions.

Exposing the sensor to a 100 ppm concentration of DCM in air leads to a resonance frequency shift of approximately 200 Hz downward. This shift is computed by evaluating the resonance frequency before and after adding the density of adsorbed DCM to that of the PIB domain.

Note that the computational mesh is identical in both these solutions. This implies that the relative error of the frequency shift is similar to that of the resonance frequency itself. Thus, the shift is accurately evaluated despite being a few magnitudes smaller than the absolute error of the resonance frequency.

Figure 3: Deformed shape plot of the first SAW mode.

Figure 4: Deformed shape plot of the second SAW mode.

Figure 5: Electric potential distribution and deformations at first resonance, antisymmetric with respect to the center of each electrode.

Figure 6: Electric potential distribution at second resonance, symmetric with respect to the center of each electrode.

References

1. K. Ho, E.R. Lindgren, K.S. Rawlinson, L.K. McGrath, and J. L. Wright, “Development of a Surface Acoustic Wave Sensor for In-Situ Monitoring of Volatile Organic Compounds,” Sensors vol. 3, pp. 236–247, 2003.

2. S. Ahmadi, F. Hassani, C. Korman, M. Rahaman, and M. Zaghloul, “Characterization of Multi- and Single-layer Structure SAW Sensor,” Sensors 2004, Proceedings of IEEE, vol. 3, pp. 1129–1132, 2004.

MEMS_Module/Sensors/saw_gas_sensor

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Geometry 1

For quicker modeling, load the parameters from a file.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file saw_gas_sensor_parameters.txt.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type width.

In the text field, type 3*width+t_PIB.

Locate the section. In the text field, type -3*width.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (µm)
Layer 1	t_PIB

Select the check box.

Clear the check box.

Click

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type width/4.

In the text field, type 0.4*t_PIB.

Locate the section. In the text field, type width/8.

Click

Copy 1 (copy1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type width/2.

Click

Before creating materials, define the domains where each physics apply.

Solid Mechanics (solid)

Piezoelectric Material 1

In the window, under click .

In the window for , locate the section.

Click

Select Domain 1 only.

Electrostatics (es)

The electrical equations are not solved in the aluminum electrodes because they are assumed to be perfect conductors compared to LiNbO3 and PIB, and hence we consider them to be equipotential regions.

In the window, under click .

Select Domains 1 and 2 only.

Charge Conservation, Piezoelectric 1

In the window, under click .

Select Domain 1 only.

Materials

LiNbO3

In the window, under right-click and choose .

In the window for , type LiNbO3 in the text field.

Locate the section. Click

Select Domain 1 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Elasticity matrix, Voigt notation	{cE11, cE12, cE22, cE13, cE23, cE33, cE14, cE24, cE34, cE44, cE15, cE25, cE35, cE45, cE55, cE16, cE26, cE36, cE46, cE56, cE66} ; cEij = cEji	{242.4[GPa], 75.2[GPa], 203[GPa], 75.2[GPa], 57.3[GPa], 203[GPa], 0, 0, 0, 75.2[GPa], 0, 8.5[GPa], -8.5[GPa], 0, 59.5[GPa], 0, 0, 0, 8.5[GPa], 0, 59.5[GPa]}	Pa	Stress-charge form
Coupling matrix, Voigt notation	{eES11, eES21, eES31, eES12, eES22, eES32, eES13, eES23, eES33, eES14, eES24, eES34, eES15, eES25, eES35, eES16, eES26, eES36}	{1.33, 0, 0, 0.23, 0, -2.5, 0.23, 0, 2.5, 0, -2.5, 0, 0, 0, 3.7, 0, 3.7, 0}	C/m²	Stress-charge form
Relative permittivity	{epsilonrS11, epsilonrS22, epsilonrS33} ; epsilonrSij = 0	{28.7, 85.2, 85.2}	1	Stress-charge form
Density	rho	4647	kg/m³	Basic

Alternately, you can click the button below the table and use the matrix inputs to enter cE, e, and epsilonrS according to the material data shown under the section.

PIB

Right-click and choose .

In the window for , type PIB in the text field.

Select Domain 2 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	E_PIB	Pa	Basic
Poisson’s ratio	nu	nu_PIB	1	Basic
Density	rho	rho_PIB+switch*rho_DCM_PIB	kg/m³	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	eps_PIB	1	Basic

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Aluminum (mat3)

Select Domains 3 and 4 only.

Solid Mechanics (solid)

In the window, under click .

Fixed Constraint 1

In the toolbar, click

and choose .

Select Boundary 2 only.

Periodic Condition 1

In the toolbar, click

and choose .

Select Boundaries 1, 3, 16, and 17 only.

This defines periodic condition for the physics. By default, the periodicity type is set to for all dependent variables.

Electrostatics (es)

Ground the left electrode by applying boundary condition on its edges.

In the window, under click .

Ground 1

In the toolbar, click

and choose .

Select Boundaries 6–9 only.

Apply a on the edges of the right electrode.

Floating Potential 1

In the toolbar, click

and choose .

Select Boundaries 11–14 only.

Define periodic boundary condition for the physics.

Periodic Condition 1

In the toolbar, click

and choose .

Select Boundaries 1, 3, 16, and 17 only.

Mesh 1

Edge 1

In the toolbar, click

Select Boundaries 1 and 3 only.

Distribution 1

Right-click and choose .

Select Boundary 3 only.

In the window for , locate the section.

In the text field, type 4.

Edge 1

Define an increasing mesh size along the thickness of the piezoelectric substrate.

Distribution 2

In the window, right-click and choose .

Select Boundary 1 only.

In the window for , locate the section.

From the list, choose .

In the text field, type 25.

Select the check box.

Click

Copy Edge 1

In the window, right-click and choose .

Select Boundaries 1 and 3 only.

In the window for , locate the section.

Select the

toggle button.

Select Boundaries 16 and 17 only.

Free Quad 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domains 2–4 only.

Size 1

Right-click and choose .

In the window for , locate the section.

Click the button.

Locate the section. Select the check box.

In the associated text field, type t_PIB/4.

Mapped 1

In the toolbar, click

In the window for , click

Study 1

Set up a to solve the model with and without the adsorbed species on the sensor. The parameter switch is used to solve the model once without adding the density of DCM and once with the added density of adsorbed DCM in PIB.

Parametric Sweep

In the toolbar, click