MEMS 003 - CMUT ultrasound send / receive

Model definition

In this example, a model with two CMUT (Capacitive micromachined ultrasonic transducers) facing each other is considered. One of the CMUTs is an emitter and the other is a receiver. Between them, a volume of water is modeled as a medium. Below is an image of the model geometry.

 

Simulation setup guide

Here, you’ll find a simplified guide on setting up this simulation in Quanscient Allsolve.

Step 0 - Define shared expressions

In this example, it is useful to first define some shared expressions. These shared expressions will then be used to create the geometry. In addition, the shared expressions can later be edited to easily modify the geometry.

Start out in the Properties section by defining the following shared expressions:

Name	Description	Expression
thmem	Membrane thickness	1e-6
radmem	Membrane radius	20e-6
cmutdist	Distance between emitter and receiver CMUT	0.5e-3/3
thgap	Vacuum gap thickness	200e-9
VDC	Direct current voltage	50
freq	AC signal frequency	10e6
VAC	Alternating current voltage	2*sin(2*pi*freq/2*t)*sin(2*pi*freq/2*t)

 

Step 1 - Create the geometry

Geometric entity tags

Geometric entities (volumes, surfaces, curves and points) are referenced using tags throughout this tutorial.

Carefully replicate the geometry construction steps below in order to have correct tags. Incorrect entity tags can lead to errors or unexpected behavior during simulations.

In the Model section, create the model geometry by creating geometry elements as detailed below. Create the elements in the same order as listed.

1. First, create cylinders for the top and bottom CMUT, as well as the water medium:

Name	Element type	Geometric variable	Value
membranebot	Cylinder	Center point, (x, y, z)	(0, 0, 0)
		Radius	radmem
		Height	thmem
		Rotation, (x, y, z)	(90, 0, 0)

Name	Element type	Geometric variable	Value
vacuumgapbot	Cylinder	Center point, (x, y, z)	(0, 0, -thgap/2-thmem/2)
		Radius	radmem
		Height	thgap
		Rotation, (x, y, z)	(90, 0, 0)

Name	Element type	Geometric variable	Value
water	Cylinder	Center point, (x, y, z)	(0, 0, cmutdist/2+thmem/2)
		Radius	cmutdist/2
		Height	cmutdist
		Rotation, (x, y, z)	(90, 0, 0)

Name	Element type	Geometric variable	Value
membranetop	Cylinder	Center point, (x, y, z)	(0, 0, cmutdist+thmem)
		Radius	radmem
		Height	thmem
		Rotation, (x, y, z)	(90, 0, 0)

Name	Element type	Geometric variable	Value
vacuumgaptop	Cylinder	Center point, (x, y, z)	(0, 0, cmutdist+thmem+thgap/2+thmem/2)
		Radius	radmem
		Height	thgap
		Rotation, (x, y, z)	(90, 0, 0)

 

2. Then, create a box that divides the cylinders along the Y-axis:

Name	Element type	Geometric variable	Value
box	Box	Center point, (x, y, z)	(cmutdist/2, 0, cmutdist/2)
		Size, (x, y, z)	(cmutdist, 2*cmutdist, 2*cmutdist)
		Rotation, (x, y, z)	(0, 0, 0)

At this point, your model should look like in the image below:

 

3. Next, use the fragment all operation. Now, all the cylinders should be split into 2 volumes along the Y-axis.

 

4. Then, use the remove operation to remove the unnecessary box (tag 11). Now, your model geometry is finished.

 

Step 2 - Define the materials

Proceed to the Properties section to define the materials.

Pick the Water material from the materials database and assign it to both halves of the water cylinder (volumes 5 and 6). Save the target as a shared region.

Next, pick the Monocrystalline silicon material from the materials database. As the target, select volumes 1, 2, 7 and 8. Save the target as a shared region. image

Finally, pick the Vacuum material from the materials database. As the target, select volumes 3, 4, 9 and 10. Save the target as a shared region.

Now, your model materials are defined.

 

Step 3 - Define the physics

Proceed to the Physics section to define the physics.

For this CMUT simulation, Solid mechanics, Electrostatics and Acoustic waves physics are required.

1 - Solid mechanics:

• As solid mechanics target, select the shared region Monocrystalline silicon target.
• Add Clamp.
  • As clamp target, select surfaces 1, 5, 22 and 25.

2 - Electrostatics:

• As electrostatics target, select volumes 1 - 4 and 7 - 10.
• Add Constraint, and name it as Ground.
  • As target, set surfaces 10, 12, 29 and 31.
  • Set constraint value to 0.
• Add Constraint, and name it as Signal.
  • As target, set surfaces 4 and 6.
  • Set constraint value to VDC+VAC.
• Add Lump V/Q.
  • As lump V/Q target, set surfaces 17 and 21.
  • Set Voltage to VDC.

3 - Acoustic waves:

• As acoustic waves target, select the water volumes (tags 5 and 6).
• Add Perfectly matched layer.
  • As target, set surfaces 13 and 18.
• Add the Acoustic structure solid mechanics coupling.

Now, your simulation physics are defined.

 

Step 4 - Set up the mesh

Proceed to the Simulations section and create a new mesh:

• Set Mesh quality to Expert settings.
• Set Max size to 1e-5.
• Click Apply & mesh.

 

Step 5 - Simulate

In the Simulations section, create a new simulation with the following options:

• Set Analysis type to Transient.
• Set Timestep algorithm to Generalized alpha.
• Set Start time to 0.
• Set End time to 5e-7.
• Set Timestep size to 1e-8.
• Set Solver mode to Iterative solver.
  • Set Relative residual tolerance to 1e-6.
• Set Node type as 4 CPU, 64 GB.
• As the Mesh, select the mesh you created.
• In Output:
  • Add pressure field p.
  • Add custom value output with name Capacitance measured.
    • Output expression: lump.Q/lump.V.

Run the simulation by clicking Not Run.

 

Step 6 - Visualize

In the Simulations section, add plots and visualizations to see results.

An example plot and visualization are in the images below: