We are excited to share the results of one of our papers that was presented at the virtual IEEE International Ultrasonic Symposium this year! This work focused on how a generic digital twin can be used to replace the need for FBAR simulations and can predict series and parallel resonance frequencies in a fraction of a second.
Usually serial feedback optimization loops are used for the design of these resonator devices. However, evaluation of numerical models is a time-consuming process and is the bottleneck of the flow.
We propose a workflow that replaces the traditional simulation stage with a machine learning / AI model: the time requirement of the simulation stage in the optimization cycle suddenly shrinks, resulting in a direct speed-up and quicker turnover.
For simplicity, we started with 1D and 2D device models, to be able to assess the computational need for the input data size of the AI algorithms. As the device is symmetric, only half was simulated. For the 1D model – which is an infinite extension of the 2D model – the airgap isolates the resonator structure from the substrate, and therefore it can be neglected. The models are illustrated in Fig. 1.
In all models, the size of the resonator area was selected to achieve 50 Ω impedance at resonance. (This can be simply obtained assuming a parallel plate capacitor with relative permittivity of 9.5 for the aluminum nitride layer.)
For the various material properties, please refer to the paper itself.
Mesh and runtime setup
We carried out mesh convergence analysis to select an appropriate mesh for resolving results with required precision. As Fig. 2. shows, mesh sizes around 35 elements per wavelength result in already around 0.05% error in both the series and parallel resonance frequencies and was selected for the mesh.
A similar investigation was carried out for the runtime. As a time-domain simulation is used, it is important to let all energy dissipate from the system to appropriately resolve the impedance. Fig. 3. illustrates that 2500 cycles runtime is enough to have virtually no change in results compared to a much longer (10,000 cycles) simulation.
Input variables of the three thicknesses (bottom electrode, aluminum nitride and top electrode) were all varied in a linear random distribution with ±10% variance around the nominal values (0.25 micron for electrodes and 0.85 micron for piezo). For the 1D model, in total 400 simulations, for the 2D model, 100 simulations were carried out.
Three groups of regression algorithms were tried:
- Decision tree / random forest
- Linear regression / ridge / hyperparameter tuning etc.
- Neural network
The training time of these is shown in Fig. 4, while the relative error is shown in Fig. 5.
From these graphs, the following conclusions can be drawn: the fastest training time is associated with the linear regression and decision tree models; however, their performance is not the best, especially comparing to neural networks.
Looking at the real data vs predicted data graphs for these models (Fig. 6. and Fig. 7.), the non-linear response between thicknesses and resonance frequencies cannot be picked up properly by linear regression algorithms, creating a curved response (Fig. 6.). The tree-based models are better performing on classification tasks in general, the noisy response is due to that, when used for regression problems (Fig. 7.).
The best performance was associated with the neural networks (Fig. 8.). Here 20 sec training time (that is exactly one simulation time) was enough to generate a 3-15-10-10-2 neuron system that estimates resonance frequencies with better than 0.04% error. For the 2D models, the data size was dropped from 400 to 100 simulations only, and consequently the error increased slightly to 0.1%.
We see this method as an alternative to traditional approaches in resonator optimization and filter design. Next steps of the work include additional layers, the inclusion of material properties as sweep variables and converging towards 3D models.
Try it out yourself!
Attached to this blog post are model files and a Jupyter notebook. We encourage the reader to pick random layer thicknesses, run both the OnScale simulation model (requires our MATLAB® Toolbox) and the Jupyter notebook predictor to see excellent agreement between the two.
The paper is available on IEEE Explore as G. Simon, G. B. Hantos, M. S. Patel, A. Tweedie, and G. Harvey, “Machine Learning Enabled FBAR Digital Twin for Rapid Optimization”.
This work has been carried out in collaboration with Heriot-Watt University in Edinburgh.
Learn about Project BreathEasy – Project BreathEasy is a collaboration between engineers, scientists, doctors, and simulation experts to create actionable Digital Twin solutions to assist doctors making critical ventilation decisions during the COVID-19 global outbreak. Project BreathEasy was begun in March 2020 by OnScale, a Cloud Simulation company, and LEXMA, and advanced computational fluid dynamics (CFD) solver company. The two companies prepared early proofs-of-concept (POCs) for Digital Twins of human lungs using real, anonymized COVID-19 patient data like CT and xray imaging.