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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.

CMUT model

 

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:

NameDescriptionExpression
thmemMembrane thickness1e-6
radmemMembrane radius20e-6
cmutdistDistance between emitter and receiver CMUT0.5e-3/3
thgapVacuum gap thickness200e-9
VDCDirect current voltage50
freqAC signal frequency10e6
VACAlternating current voltage2*sin(2*pi*freq/2*t)*sin(2*pi*freq/2*t)

 

Step 1 - Create the geometry

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:
NameElement typeGeometric variableValue
membranebotCylinderCenter point, (x, y, z)(0, 0, 0)
Radiusradmem
Heightthmem
Rotation, (x, y, z)(90, 0, 0)
NameElement typeGeometric variableValue
vacuumgapbotCylinderCenter point, (x, y, z)(0, 0, -thgap/2-thmem/2)
Radiusradmem
Heightthgap
Rotation, (x, y, z)(90, 0, 0)
NameElement typeGeometric variableValue
waterCylinderCenter point, (x, y, z)(0, 0, cmutdist/2+thmem/2)
Radiuscmutdist/2
Heightcmutdist
Rotation, (x, y, z)(90, 0, 0)
NameElement typeGeometric variableValue
membranetopCylinderCenter point, (x, y, z)(0, 0, cmutdist+thmem)
Radiusradmem
Heightthmem
Rotation, (x, y, z)(90, 0, 0)
NameElement typeGeometric variableValue
vacuumgaptopCylinderCenter point, (x, y, z)(0, 0, cmutdist+thmem+thgap/2+thmem/2)
Radiusradmem
Heightthgap
Rotation, (x, y, z)(90, 0, 0)

 

  1. Then, create a box that divides the cylinders along the Y-axis:
NameElement typeGeometric variableValue
boxBoxCenter 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:

Model state

 

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

 

  1. 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:

Plot example

Visualization example