Heracles

Heracles is a physics-based compact model for HfO2-based ferroelectric capacitors. It includes thermal models, interface layers and accurately reproduces several device phenomena, such as transient polarization switching and capacitance hysteresis. Heracles consists of a stateful and computationally efficient non-equilibrium thermodynamics description of the device behaviour, allowing for efficient Monte Carlo simulations even in larger analog CMOS circuits. This makes Heracles suitable for Design-Technology Co-Optimization (DTCO) approaches to (analog) compute-in-memory, neuromorphic systems or sensory circuit design.

Examples

A Verilog-A implementation that is tested in Cadence Spectre is available, including Monte-Carlo parameters. The parameters were extracted from measurement data by the Department of Electrical Engineering of IIT Bombay, as seen in the article cited below.

Virtuoso

To use the model in Cadence Virtuoso, create a cell called fecap with a symbol view (type schematicSymbol) and rename this symbol view to spectre. Create a symbol with 2 inout pins named te and be. Then, in the Virtuoso main window, open Tools/CDF/Edit and load cdf.il. Now import the model card in your Maestro test bench via Setup/Model Libraries, for example fehlings2024.scs for the model card of the source citation. In Setup/environment (or in the hierachy editor when used) make sure that the spectre view is included in switch and stop lists.

Alternatively create a veriloga view and paste in the source code, then import the model card in Maestro. Keep in mind that in this way mismatch Monte Carlo simulations may not work, depending on your Virtuoso configuration and CMOS PDK.

Ngspice

There is a compiled osdi binary shipped with every release, see the releases tab. You can find ngspice-based testbenches in the repository heracles-testbenches.

Documentation

Heracles Documentation

The documentation is still work in progress.

Contributing

Acknowledgements

This work was supported by the European Research Council (ERC) through the European’s Union Horizon Europe Research and Innovation Programme under Grant Agreement No 101042585. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

Citation

If you find Heracles useful in your work, please cite the following source:

@article{fehlings2025heracles,
  author={Fehlings, Luca and Hanif Ali, Md and Gibertini, Paolo and Gallicchio, Egidio A. and Ganguly, Udayan and Deshpande, Veeresh and Covi, Erika},
  journal={IEEE Transactions on Electron Devices}, 
  title={Heracles: A HfO2 Ferroelectric Capacitor Compact Model for Efficient Circuit Simulations}, 
  year={2025},
  volume={72},
  number={11},
  pages={6009-6014},
  keywords={Integrated circuit modeling;Switches;Capacitance;Electrodes;Computational modeling;Semiconductor device modeling;Hafnium compounds;Charge carrier density;Load modeling;Leakage currents;Compact model;ferroelectric devices;HfO2;nonvolatile memory;semiconductor device modeling;SPICE},
  doi={10.1109/TED.2025.3615577}}