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piezod

Modeling and optimization of piezoresistive and piezoelectric sensors and actuators.

Installation

pip install piezod

For development:

git clone https://github.com/MicrosystemsLab/PiezoD.git
cd PiezoD/python
uv sync

Usage

from piezod import CantileverEpitaxy

# Create cantilever and set geometry
c = CantileverEpitaxy()
c.l = 300e-6  # length: 300 um
c.w = 44e-6   # width: 44 um
c.t = 89e-9   # thickness: 89 nm
c.fluid = "water"

# Calculate properties
print(f"Stiffness: {c.stiffness() * 1e3:.3f} mN/m")
print(f"Resonant frequency: {c.omega_vacuum_hz() / 1e3:.1f} kHz")
freq_hz, Q = c.omega_damped_hz_and_Q()
print(f"Damped frequency: {freq_hz / 1e3:.1f} kHz, Q = {Q:.1f}")

Run the example:

uv run python examples/quickstart.py

Development

Install dependencies:

uv sync

Run tests:

uv run pytest

Lint and format:

uvx ruff check src tests --fix && uvx ruff format src tests

Type check:

uvx ty check src

Doping profile convention

doping_profile() on every cantilever subclass returns (z, active_doping, total_doping):

  • total_doping: total concentration max(dopant_species, substrate_background_cm3) (cm^-3). Floors at the substrate so plotting code shows the implant peak rolling down into the substrate floor directly.
  • active_doping: net active resistor carriers (cm^-3) = max(0, electrically_active_dopant - substrate_background_cm3). Goes to zero below the junction. Used internally by all carrier integrals (Nz, sheet_resistance, beta).

The substrate is always counter-doped to the piezoresistor. Set the substrate concentration via the substrate_background_cm3 attribute on Cantilever (or the equivalent kwarg on PiezoresistorFromProfile); the default is 1e15 cm^-3. The TSUPREM-4 lookup table's baked-in 1.36e15 cm^-3 substrate is subtracted at load time so the tsuprem4 and dopedealer sources share the same underlying dopant convention.

Use cantilever.plot_doping_profile() for a quick total + net active overlay with the junction marked.

Documentation

See the main project documentation at github.com/MicrosystemsLab/PiezoD.

Citation

If you use piezod in your research, please cite:

Joseph C. Doll, Sung-Jin Park and Beth L. Pruitt Design optimization of piezoresistive cantilevers for force sensing in air and water Journal of Applied Physics 106.6 (2009): 064310-064310.

License

GPL-3.0-or-later