The Austrian Science Fund (FWF) approved my project proposal entitled "3D Solution of the Boltzmann Equation on Supercomputers". This project will fund my scientific work for three more years, with prospective start in mid 2017. Here is a brief summary of what this project is about.

Since the FWF encourages researchers to Open Science, especially since the money is ultimately provided by tax payers, I publish the relevant project proposal here. The initial project proposal was submitted in March 2015. Despite fairly good reviews, the committee did not approve the project. In October 2015, I submitted a revised project proposal (overview of changes), which the committee approved based on the positive reviews received in May 2016.

## Boltzmann Equation for Semiconductors

The project agenda is centered around the numerical solution of the semi-classical Boltzmann transport equation for semiconductors, which describes the motion of electrons and holes. In contrast to conventional approaches such as the drift-diffusion model, a solution of the Boltzmann transport equation not only provides information about the density of electrons or holes at a particular location in the device, but also their distribution with respect to momentum. This allows for more accurate simulations of semiconductor devices, ultimately increasing reliability and performance. Typical application areas include the automotive sector, where power devices are essential for starting your car engine.

## Supercomputing

Because the distribution of electrons and holes with respect to momentum is computed at each point in the semiconductor device, the computations require a lot of computational resources. For a fully three-dimensional device simulation (e.g. a FinFET) with 100 grid points for each of the three spatial coordinates, one has to compute the distribution with respect to momentum for each of the 1 million grid points. If one approximates the three-dimensional momentum space with the same 1 million grid points as the spatial domain, one would need several thousand Terabytes of memory to run one simulation. With the spherical harmonics expansion approach, we can bring these requirements down to about a Terabyte only, which is available on supercomputers today. However, in order to use such supercomputers, parallel algorithms need to be developed to use the computational resources efficiently. Such algorithms have not been developed or studied for the spherical harmonics expansion method yet. This research project will fill this gap. At the end of the project, we expect to run the most accurate simulations conducted so far on hundreds of nodes of a supercomputer such as the Vienna Scientific Cluster, making use of modern parallel hardware such as Intel's Xeon Phi line or graphics processing units. The results will be available to the general public not only in the form of research papers, but also in the free open source simulator ViennaSHE. Contributions will also flow back to ViennaCL and PETSc, on which the future developments in ViennaSHE will be based.

## Resources

- Initial project proposal (not approved)
- Reviews for inital proposal
- Revised project proposal (approved)
- Overview of changes in revision
- Reviews for revised proposal

*This blog post is for calendar week 13 of my weekly blogging series for 2016.*