Piezo electric Micro-machined Ultrasonic Transducers (pMUTS) consists of a thin PZT diaphragm typically formed on silicon substrates and are used in a wide range of sensing applications. Unlike cMUTS – no high voltage biasing is required for operation. OnScale allows a variety of outputs to be generated from a single run and directly correlated with experimental results.

1. pMUTs Modeling
CONFIDENTIAL

2. pMUTs
Piezoelectric micromachined ultrasonic transducers
Thin diaphragm typically formed on silicon substrates
Suitable for a range of broadband sensing applications
Microfabrication techniques make on-chip integration possible
Unlike cMUTs – no high voltage biasing is required for operation
Closer mechanical impedance to fluids enhances device efficiency
Capable of High Frequency operation over a wide bandwidth
2nd order vibrational
mode of a circular
pMUT element

3. Why OnScale?
Nonlinear response complicates analytical models but is
included in OnScale simulations
– This allows the simulation of harmonic distortion
Secondary effects can easily be included
– Rayleigh waves generated in backing which cause crosstalk
– Residual stress from manufacturing
Not as ‘mature’ as piezocomposites, so much simulation is
required to fully understand behaviour
– OnScale is very fast
Broadband, nonlinear behaviour requires an explicit,
nonlinear, transient analysis, which OnScale is ideally
suited for

4. Simple pMUT Example
Here we’ll construct a simple axisymmetric pMUT model
– Membrane thickness = 1μm
– Electrode thickness = 200 nm
– Substrate thickness = 3 μm
Mesh detail for simple axisymmetric pMUT model
– Cavity Depth = 3 μm
– Membrane radius = 22.5 μm
– Resonance Frequency ~ 27 MHz
Water
load
Si substrate
AlN active
layer
Molybdenum
electrodes
Cavity

5. Time Domain Analysis
Acoustic pressure Device displacement
Surface displacement Charge on electrode
Model Outputs

6. Model Outputs
This type of time domain analysis allows many outputs to be
generated, which can then be directly correlated with experiment
– Electrical impedance spectrum
– Maximum membrane displacement
– Membrane displacement spectrum
– Pressure in load
– Beam pattern
– Mode shapes
– Instantaneous and maximum stresses
Electrical impedance
spectrum
All of these outputs can be
generated from a single simulation

7. Pressure in Load
Extrapolation can be used to generate both time and frequency
domain plots of pressure in the load medium
Radial extrapolation used to create a directivity plot at device centre
frequency

8. Mode Shapes
27MHz Mode shape with surface displacement shown as colour
scale

9. Displacement Spectrum
Time domain data can easily be FFT’d to create spectra showing
device performance
27MHz Mode

10. Model performance
2D Model
Elements 14,014
Runtime 31 seconds
Memory 8 MB
Time steps 92,000
*Dell XPS 14Z Laptop – 2 Cores

11. pMUT Array Model
The previous model was extended to 3D to allow an array
of individual elements to be simulated
– Dimensions were the same as previously defined, but with square
elements, and a 5μm gap

12. Array Crosstalk Video

13. Effect of Crosstalk
Mechanical crosstalk on the surface of the device can
affect the beam pattern, narrowing the beam pattern
Element displacement
Element 4.5MHz Beam
Pattern

14. Array Model performance
3D Model
Elements 1.26 Million
Runtime 57 minutes
Memory 319 MB
Time steps 92,000
8 Core Desktop