# Publications

## Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory

Manuel Aldegunde, James R. Kermode, and Nicholas Zabaras, *J. Comput. Phys.* **311**, 173-195, doi:10.1016/j.jcp.2016.01.034

This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors.

## Energy conserving, self-force free Monte Carlo simulations of semiconductor devices on unstructured meshes

M. Aldegunde and K. Kalna, "Energy conserving, self-force free Monte Carlo simulations of semiconductor devices on unstructured meshes", Comput. Phys. Commun. **189**, pp. 31-36 (2015), doi:10.1016/j.cpc.2014.11.020

Unphysical self-forces resulting from the particle–mesh coupling occur when ensemble Monte Carlo simulations of semiconductor devices use an unstructured mesh to describe device geometry. We report on the development of a correction to the driving electric field on arbitrary meshes and show that self-forces can be virtually eliminated on a finite element mesh at a small additional computational cost. The developed methodology is included into a self-consistent 3D finite element Monte Carlo device simulator. We show the efficiency of the method simulating an isolated particle and obtaining kinetic energy conservation down to a magnitude of 10^{−10} meV. The methodology is later applied to a FinFET simulation to show what impact can be expected from the self-forces using traditional electric field interpolation strategies. We find that for a large enough ensemble of particles, the impact of self-forces on the final I_{D}–V_{G} is almost negligible.