SAW 001 - Unit cell

What you’ll learn

• How to define anisotropic material properties (elasticity, permittivity, piezoelectric coupling) for a Lithium Niobate substrate.
• How to set up translational periodicity and piezoelectricity coupling between Solid mechanics and Electrostatics with Lump V/Q actuation.
• How to run both transient and harmonic simulations, sweep frequency, and plot impedance magnitude.

Prerequisites: complete any one step-by-step tutorial first so you are comfortable with the Allsolve project layout (Geometry, Physics, Simulations, Results).

Surface Acoustic Wave (SAW) devices play a crucial role in modern electronic systems, serving in applications ranging from wireless communication and sensing to signal processing and filters. Understanding and optimizing the performance of SAW devices requires comprehensive simulation techniques that accurately model their complex behavior under varying conditions.

Full-scale SAW device simulations can be computationally expensive, however. In this example, we demonstrate a streamlined approach using a unit cell of a single-port SAW filter. This simplified model, comprising a pair of aluminum electrodes (grey) on a Lithium Niobate (green) piezoelectric substrate, allows for rapid analysis of device performance while still capturing the essential physics.

Demo project: SAW unit cell

The model is set up to simulate a Y-cut, which can be rotated to the desired angle. The base design generates an shear horizontal (SH) mode at 852 MHz using a finger pitch of 1 μm.

Simulation setup guide

Here you’ll find a simplified, example case level guide for setting up a SAW unit cell simulation.

Step 1 - Define variables & functions

In the Common sidebar, define variables:

Name	Description	Expression
width	Cell width [m]	4e-6
thickness	Cell thickness [m]	1e-7
elec_height	Electrode height [m]	2e-7
subs_height	Substrate height [m]	12e-6
freq	Frequency [Hz]	8.7e8

Also define the following functions:

Name	Description	Arguments	Expression
Zreal	Real part of the impedance	Ir, Iim, Vr, Vim	(Vr*Ir+Vim*Iim)/(Ir*Ir+Iim*Iim)
Zim	Imaginary part of the impedance	Ir, Iim, Vr, Vim	(Vim*Ir-Vr*Iim)/(Ir*Ir+Iim*Iim)
Zmagnitude	Impedance magnitude	Ir, Iim, Vr, Vim	sqrt(Zreal(Ir,Iim,Vr,Vim)*Zreal(Ir,Iim,Vr,Vim)+Zim(Ir,Iim,Vr,Vim)*Zim(Ir,Iim,Vr,Vim))

Step 2 - Create the geometry

In the Geometry section, create the model geometry by building three boxes:

Name	Element type	Center point (m)	Size (m)	Rotation (deg)
substrate	Box	X: 0	X: width	X: 0
		Y: 0	Y: thickness	Y: 0
		Z: -subs_height/2	Z: subs_height	Z: 0

Name	Element type	Center point (m)	Size (m)	Rotation (deg)
electrode 1	Box	X: -width/4	X: width/4	X: 0
		Y: 0	Y: thickness	Y: 0
		Z: elec_height/2	Z: elec_height	Z: 0

Name	Element type	Center point (m)	Size (m)	Rotation (deg)
electrode 2	Box	X: width/4	X: width/4	X: 0
		Y: 0	Y: thickness	Y: 0
		Z: elec_height/2	Z: elec_height	Z: 0

Your model geometry is now finished, and should look like in the image below:

Step 3 - Define the materials

Go to the Physics section to define the model materials.

Material 1 - Aluminium

Assign Aluminium to the pair of small electrode volumes on top of the substrate.

Material 2 - Lithium Niobate

Create a new material with these general settings:

Name	Abbreviation	Description	Color	Target
LiNbO3	linbo3	Lithium Niobate	green	Substrate volume

Apply the settings to save your work on Lithium Niobate so far.

Then, define the LiNbO3 material properties:

• Density
  • 4647
• Elasticity matrix
  • ☑️ Anisotropic
  • [2.424e11, 0.752e11, 0.752e11, 0, 0, 0; 0.752e11, 2.03e11, 0.573e11, 0, 0.085e11, 0; 0.752e11, 0.573e11, 2.03e11, 0, -0.085e11, 0; 0, 0, 0, 0.752e11, 0, 0.085e11; 0, 0.085e11, -0.085e11, 0, 0.595e11, 0; 0, 0, 0, 0.085e11, 0, 0.595e11]
• Electric permittivity
  • ☑️ Anisotropic
  • [28.7 * epsilon0, 0, 0; 0, 85.2 * epsilon0, 0; 0, 0, 85.2 * epsilon0]
• Piezoelectric coupling matrix
  • ☑️ Anisotropic
  • [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]

Expression editor

Use the expression editor to add matrix valued material properties easily:

1. Click Switch to expression editor below the matrix editor.
2. Copy the matrix value as given above, and paste it to the expression editor.

All of your model materials are now defined.

Step 4 - Define the physics

Go to the Physics section to define the physics. First add the Solid mechanics and Electrostatics physics, and then move on to defining their interactions.

Physics 1 - Solid mechanics

• Let solid mechanics target default to the whole geometry.

• Add Clamp:

  Name	Interaction type	Target
  Clamp	Clamp	bottom surface of the substrate volume

• Add Periodicity:

  • As Target 1, select the left side surface of the substrate volume in the negative X-direction.
  • As Target 2, select the right side surface of the substrate volume in the positive X-direction.
  • In Parameters:
    • Set Type to Translation.
    • Set Translation direction [X; Y; Z] to [1; 0; 0].
    • Set Translation distance to width.

  

• Add Plain strain:

  Name	Interaction type	Target	Value
  Plain strain	Constraint	Substrate and electrode volumes	[0, 0; 1, 0; 0, 0]

Physics 2 - Electrostatics

• Let electrostatics target default to the whole geometry.

• Add Lump V/Q.

  • As lump V/Q target, select all surfaces on the left side (negative X-side) electrode.
  • Set Actuation mode to Voltage.
  • Set Voltage to wavelet(freq, 1.0).

• Add Periodicity, same as in Solid mechanics:

  • As Target 1, select the left side surface of the substrate volume.
  • As Target 2, select the right side surface of the substrate volume.
  • In Parameters:
    • Set Type as Translation.
    • Set Translation direction [X; Y; Z] to [1; 0; 0].
    • Set Translation distance as width.

  

• Add Constraint, and name it as Ground.

  • As Target, select the right side (positive X-side) electrode volume.
  • Set constraint value to 0.

• Add Piezoelectricity to couple electrostatics with Solid mechanics.

  • As Target, select the substrate volume.

Your physics are now defined.

Step 5 - Generate the mesh

Go to the Simulations section and create a new mesh:

• Set Autorefine to Disabled.
• Open the collapsible menu for Mesh element size.
• Set Max size to thickness*2.

Apply settings and mesh. Check the preview:

Structured meshing

Structured meshing is also available to make a mesh of regular hexahedrons (cuboids) which can be useful for a thin plate-like geometry such as this.

Step 6 - Simulate

In the Simulations section, create 2 simulations.

Simulation 1 - Transient

Simulation settings:

1. Set Analysis type to Transient.

2. Select timestepping settings as below:

   Timestep algorithm	Start time [s]	End time [s]	Timestep size [s]
   Generalized alpha	0	100/freq	0.05/freq

3. Set Solver mode to Direct solver.

4. As Mesh, select the mesh you created.

5. Add Outputs:

   Name	Output type	Expression
   Voltage	Custom value output	lump.V
   Charge	Custom value output	lump.Q
   Current	Custom value output	dt(lump.Q)

Simulation 2 - Harmonic

Simulation settings:

1. Set Analysis type to Harmonic.

2. Set Fundamental frequency to freq.

3. Set Solver mode to Direct solver.

4. As Mesh, select the mesh you created.

5. Add Inputs:

   Name	Input type	Expression
   freq sweep	Sweep over shared expression freq	linspace(8.3e8, 8.6e8, 50)

6. Add Outputs:

   Name	Output type	Expression
   impedance magnitude	Custom value output	Zmagnitude(getharmonic(2,dt(lump.Q)),getharmonic(3,dt(lump.Q)), getharmonic(2,lump.V), getharmonic(3,lump.V))*thickness

Run your simulations.

Step 7 - Plot results

In the Simulations section, add plots to see value output results. Some examples are given below.

Results 1 - Transient

Results 2 - Harmonic

Tip: Y-axis logarithmic scale & min/max

The Impedance magnitude values in this example vary logarithmically. To see the whole plot clearly, edit your Y-axis options to use the Logarithmic scale.

It might also be useful to edit the Y-axis Min/Max options to see the whole curve clearly.