📘 PZT P–E Loop Playground

A lightweight modeling and visualization toolkit for exploring PZT polarization behavior
(Samizo-Lab / TCAD Pre-Analysis Sandbox)

Links

Language	GitHub Pages 🌐	GitHub 💻
🇺🇸 English

📌 Overview

This repository provides a Python-based playground for exploring how three key factors:

• Film Thickness
• Composition (Zr/Ti ratio)
• Annealing Temperature

affect the polarization behavior of PZT ferroelectric films, including:

• P–E Hysteresis Loops (closed-loop generation)
• P–V conversion (device-level)
• Thickness variation
• Composition variation (Zr-rich ↔ Ti-rich)
• Annealing temperature variation
• 3D/Contour mapping of Pm
• S–E Butterfly Curves

The goal is rapid exploration using simplified physical models, serving as a conceptual bridge toward full TCAD simulations.

📁 Repository Structure

tcad_playground_pzt/
│
├── fig/                           # All generated figures
│   ├── pzt_pe_hysteresis_1d.png
│   ├── pzt_pe_tvar_PE.png
│   ├── pzt_pe_tvar_PV.png
│   ├── pzt_pe_hysteresis_compvar_1d.png
│   ├── pzt_pe_hysteresis_annealvar_1d.png
│   ├── pzt_pm_surface.png
│   ├── pzt_se_butterfly_1d.png
│   └── ...
│
├── pzt_pe_hysteresis_1d.py           # Base P–E closed-loop model
├── pzt_pe_hysteresis_tvar_1d.py      # Thickness variation
├── pzt_pe_hysteresis_compvar_1d.py   # Composition variation
├── pzt_pe_hysteresis_annealvar_1d.py # Anneal temperature variation
├── pzt_pm_surface_3dmap.py           # Pm 3D surface map
├── pzt_se_butterfly_1d.py            # S–E butterfly curve
│
└── README.md

🔧 Requirements

Python 3.8+
numpy
matplotlib
scipy

▶ Usage

1. Generate a basic P–E hysteresis loop

python pzt_pe_hysteresis_1d.py

Output image:

fig/pzt_pe_hysteresis_1d.png

📈 Generated Figures (Examples)

■ P–E Hysteresis Loop

Parameters:

• Pm = 42 µC/cm²
• Pr = 30 µC/cm²
• Es auto-calculated from Pr

Example image: pzt_pe_hysteresis_1d.png

■ Thickness Variation → P–V Curve

Thicknesses: 1.0 / 1.2 / 1.4 µm

• P–E curve remains nearly unchanged
• P–V curve shifts due to voltage scaling (V = E·t)

Example: pzt_pe_tvar_PV.png

■ Composition Variation

Composition values:

• −0.10 (Zr-rich)
• 0.00 (Nominal)
• +0.10 (Ti-rich)

Modeled trend: Ti-rich → Higher Pm

Example: pzt_pe_hysteresis_compvar_1d.png

■ Annealing Temperature Variation

Anneal temps: 720 / 740 / 760 °C

Modeled trend: Peak Pm near 740 °C

Example: pzt_pe_hysteresis_annealvar_1d.png

■ Pm 3D Surface Map (Composition × Anneal Temp)

Smooth surface + contour map of Pm.

Example: pzt_pm_surface.png

■ S–E Butterfly Curve

Model:

• d₃₃ = 200 pm/V
• S = d₃₃ × E × sign(P)

Generates a classic butterfly curve.

Example: pzt_se_butterfly_1d.png

🧩 Modeling Philosophy

This sandbox focuses on exploratory modeling, not high-fidelity TCAD:

• No fitting to real measurements (optional future step)
• Intuitive exploration of 3-factor interactions
• Flexible control of Pm, Pr, Ec, Es
• Ready for extensions:
  • Pm(T)
  • Ec(Composition)
  • Finite-thickness effects
  • dP/dE differential modeling
  • Domain-switching physics

Workflow matches Samizo-Lab methodology: Exploration → Model Formulation → Experiment Fit → TCAD Linkage

📌 Future Work

• Curve fitting using experimental data
• Parameter bridging to COMSOL / Synopsys TCAD
• Integration of domain-switching physics
• D–E formulation support
• Fatigue & imprint modeling

🏁 Conclusion

• Visualizes how Thickness, Composition, and Anneal Temperature influence
  P–E, P–V, and Pm characteristics
• Supports design-space exploration before experiments or TCAD runs
• Provides a lightweight, flexible modeling environment for Samizo-Lab workflows

📈 Example Figures (PZT Ferroelectric Playground)

Below are sample outputs generated from the tcad_playground_pzt module,
illustrating how film thickness, composition, and annealing temperature
influence ferroelectric polarization behavior.

▶ P–E Hysteresis Loop (Anneal Temperature Variation)

This example shows how the polarization–electric field hysteresis loop shifts
with annealing temperature. A peak polarization typically appears near the
optimal crystallization temperature.

▶ Pm 3D Surface Map (Composition × Anneal Temperature)

A smooth 3D visualization of the spontaneous polarization ( P_m ),
sweeping both annealing temperature and composition (Zr/Ti ratio).
This helps explore design spaces prior to TCAD or experimental work.

▶ S–E Butterfly Curve (Strain–Electric Field)

The classic butterfly-shaped strain–electric field curve,
modeled using a simplified piezoelectric formulation:

Illustrates the nonlinear electromechanical response of PZT films.

📄 License

✍ Author

📌 Item	Details
Name	Shinichi Samizo
GitHub