Patricio Farrell
Coworkers:
Dilara Abdel, Daniel Fritsch, Yiannis Hadjimichael
Secretary:
Marion Lawrenz

Overview
The aim of this group is to develop and analyze physics preserving numerical techniques for innovative semiconductor devices. Few discoveries have shaped our modern society like semiconductors have. They are the backbone of every electronic device. A world without semiconductors is one without television, pacemakers, satellites, cell phones, air planes and computers - and by extension a world without the Internet, social media and online communication. New semiconductor techniques, materials and devices innovate established technologies. Among them are low-cost perovskites for next-generation solar cells, resource-efficient nanowires as well as accurate lasers for self-driving cars.
Mathematical research topics
- Numerical solution and simulation of nonlinear systems of partial differential equations
- Finite volume methods on Voronoi meshes
- Modified Scharfetter-Gummel techniques for nonlinear diffusion
- Drift-diffusion equations
- Charge transport in semiconductors, in particular coupling them to atomistic models as well as stress and strain
- Physics preserving numerical techniques
- Preconditioners and anisotropic meshing strategies
- High dimensional meshfree approximation for surrogate models
Applications
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Source: Pang Kakit (CC BY-SA 3.0) -
Highlights
- In April 2022, a MATH+ incubator project (Identifying and Efficiently Computing Band-Edge Energies for Charge Transport Simulations in Strained Materials) together with Costanza Manganelli and Christian Merdon will tackle band edge computations in strained semiconductors.
- In December 2021, Patricio Farrell was the GNCS visiting professor at SISSA, Italy
- Patricio Farrell was invited to be a plenary speaker at the ABPDE4 and Dilara Abdel presents a poster.
- During October/November 2021, Patricio Farrell was a CEMPI invited researcher at Inria, Lille and the University of Lille
- Dilara Abdel won a stipend (€1,500) by the science department of the French embassy ("Procope") to visit Inria Lille in October/November 2021
- Dilara Abdel and Yiannis Hadjimichael presented two separate posters at the AMaSiS 2021
- MATH+ AA2-10 project Electro-mechanical coupling for semiconductor devices together with Annegret Glitzky, Matthias Liero and Barbara Zwicknagl
- The Leibniz group is organizing a mini symposium at the SIAM Conference on Mathematical Aspects of Materials Science 2021 with the title Modelling and simulation of charge transport in perovskites. Dilara Abdel won a SIAM MS student travel award for attending the conference to give a talk.
- The Leibniz group presents two posters at the SIAM Conference on Computational Science and Engineering 2021. Dilara Abdel won a SIAM CSE student travel award for attending the conference to present a poster.
- Poster presented at the German Conference on Crystal Growth, Munich
- Two abstracts have been accepted to the NUSOD 2020 conference. One of them was voted among the top 10 contributions.
- MATH+ IP-TB-3 project Understanding doping variations in silicon crystals together with Nella Rotundo

Flexible Research Platform
