mems-ana_demo
d33-dominant MEMS piezoelectric hysteresis visualization
This directory contains a frozen demo snapshot that visualizes the quasi-static out-of-plane displacement of a MEMS piezoelectric structure dominated by the piezoelectric coefficient d33, driven by a ferroelectric P–Ez hysteresis loop.
The purpose of this demo is not quantitative device design, but to provide a clear, reproducible reference showing how electrical hysteresis maps into mechanical displacement patterns.
🔗 Links
| Language | GitHub Pages 🌐 | GitHub 💻 |
|---|---|---|
| 🇺🇸 English |  |
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1. Electrical input: P–Ez hysteresis (V-only)
This figure shows the polarization–electric field (P–Ez) hysteresis loop used as the electrical input to the model.
- The analysis is voltage-driven only
- Electrical current and dynamic switching effects are not modeled
- The closed loop defines the rising and falling voltage branches consistently
This hysteresis is imposed as a fixed input condition for all subsequent results.
2. uz–V butterfly curve (d33-dominant, fixed scale)
This plot shows the resulting butterfly-shaped displacement–voltage response derived from the P–Ez hysteresis under a d33-dominant assumption.
- Vertical axis: out-of-plane displacement $u_z$
- Horizontal axis: applied voltage
- Visualization scale is fixed to 0–500 nm
The butterfly shape directly reflects the underlying ferroelectric hysteresis.
3. Static uz(x,y) mid-plane maps (absolute displacement)
These snapshots show the spatial distribution of $u_z(x,y)$ at the MEMS mid-plane for selected voltage points along the butterfly curve.
- Displacement is treated as ABSOLUTE $u_z$
- An offset at 0 V is allowed
- Mechanical boundary conditions are schematic / conceptual
All frames use the same color scale (0–500 nm) to allow direct comparison.
4. Dynamic response: uz(x,y) over voltage cycles
This animation shows the time evolution of $u_z(x,y)$ over multiple voltage cycles following the hysteresis loop.
- Rising and falling branches follow the P–Ez loop
- The response is quasi-static (no inertia or damping modeled)
- Intended for intuitive understanding, not transient accuracy
How to run
python -m pip install -e .
python examples/animate_uz_midplane_typical_d33.py
Scope and limitations
- Voltage-driven analysis only (current not modeled)
- d33-dominant piezoelectric response
- No losses, no nonlinear elasticity, no realistic anchors
- Boundary conditions are simplified for clarity
Status
- Stable
- Frozen demo snapshot
- Parameters are fixed to ensure reproducibility
Disclaimer
This demo is intended for conceptual understanding and visualization. Real device design and quantitative evaluation require additional physics, including electrical current, losses, nonlinear mechanics, and realistic boundary conditions.