Question and Answers
Q: Why does the 1D model take >10s? One would assume that the computational effort is comparable to a typical Mason model (transmission line based), which runs in milliseconds.
A: An analytical method like Mason’s or KLM is always going to be quicker than FEA for the simple problems which they are designed. That said, much of the quoted runtime for the 1D simulation was actually overhead from features like graphics. The simulation runs in under 3 seconds on a single core, meaning that we can run >10 simulations per second on the hardware we used for the optimization study.
Q: Were your substrate edges terminated by air/vacuum, or some sort of non-reflecting materials/boundary conditions?
A: In this simple example we fixed the edges of the model. However, it would be very easy to extend this model to consider more of the substrate, or to apply absorbing conditions if desired. The computationally intensive part of the calculation is the electrical solve (more below), which means that adding more of the substrate is relatively cheap.
Q: Can you us PML to remove artifacts due to the substrate edge?
A: We use an absorbing boundary condition that acts very similarly to a PML, and this could be applied to the substrate edge. We also have impedance boundary conditions.
Q: How is does “Q=3000” map to the AlN material parameters?
A: That was the Q of the material properties of AlN that we used, however there maybe variations in those properties.
Q: Ok, but Q may be different for different kinds of waves (long. vs. shear) … but there’s only one Q number?
A: Two Q values – one for longitudinal waves and one for shear waves. Lumped values based on mechanical losses. Could include dielectric losses as well. Update: Damping is something that we’re asked about quite a lot, as we take a slightly different approach than people are used to seeing from frequency domain solvers. The question that people usually want to know is “is it accurate”. We’ve done a great deal of work on the characterization of piezoelectric materials, including single crystal piezoelectrics, and what we see is that when the properties are right, the results match. I’ve included the impedance response of a PZT disc that we characterized to demonstrate the kind of accuracy that can be achieved.
Q: What are the lateral boundary conditions in the 3D model?
A: They are fixed in this model.
Q: The 2D is surprisingly fast – can you comment on mesh element dimensions?
A: On the order of 10’s of thousands of elements in the 2D model, 15 elements per wavelength at the shortest wavelength of interest. Will followup with actual mesh dimensions. Update: 2D model used 3,156 elements, which is a tiny model for PZFlex, hence the fast runtime.
Q: Is the number of time steps the same as the number of frequency points? If not, how many time steps do you need for the 514 frequency points?
A: Num of time steps and f points are related, but the length of the time step is also important. Models we used ran at ~4,500 cycles at the frequency of interest ~1.8 GHz. As a rough estimate, we would do 15/20 timesteps per cycle, so potentially, a model could use >10K cycles. Because the sim cycles are relatively cheap, they do not have a large impact on actual compute time. Update: In this case the 2D model actually performed 132,674 timesteps. This was because the model was meshed for the shear velocity in the plate, rather than the longitudinal, meaning a shorter timestep.
Q: I am assuming your simulation time increases a lot when the Q increases since the impulse response duration increases with Q. Is it right?
A: Yes – this is accurate. In narrow band, high Q devices, we would run the sim for many thousands of cycles (e.g. 4,500 cycles). The type of solver allows us to expand to very large modes in 3D and not run out of memory.
Q: Does PZFlex run on a GPU board?
A: There are development branches of PZFlex that are GPU compatible, and we have a roadmap to bring this into the release code. However, at the moment Pzflex runs on CPU architecture with SMP and MPI options.
Q: In the fast 3D sims: did you get the Q of all the modes right?
A: In this case, we did not have experimental results to compare against, so we compared them to each other. We would certainly like more direct comparisons with real-world results.
Q: Does PZflex predict resonator Q factors correctly?
A: Customers that do this day in/day out get very good agreement with their experimental results. Q of different modes comes down to matrial properties and fidelity to device geometries.
Q: Did you try to simulate SMR devices?
A: We have explored SMRs in the past for certain customers. Most of our work is unfortunately under NDA, but we can provide private demos if this is an interest of yours.
Q: You need much bigger meshes for SMRs than FBARs
A:That’s true although bear in mind that the substrate does not require an electromechanical solve. In PZFlex simulations you can limit the electromechanical solution to the piezoelectric areas of the model, avoiding unnecessary computation. Mechanical areas are relatively cheap, so we don’t find SMR simulation unduly challenging.