A computational framework for modelling grain-structure evolution in three dimensions

Abstract

We describe a simulation framework designed to track individual grains in a material during simulations of formation, processing and usage. The framework, which we call parallel level-set environment for nanoscale topography evolution, is designed to fill the clear and present need to account for grain structure in understanding and predicting the performance of structures in some products, such as metal lines in integrated circuits. It is the realization of ‘grain continuum’ models of films by Cale et al. and can be used to complement discrete atomistic simulations and to link them to continuum simulations. We demonstrate the use of multiple level-set methods to track islands nucleated on substrates, during growth and impingement to form a polycrystalline film. Individual grains in the film are defined in the finite-element data structure. We briefly discuss how this simulation tool might be used in an integrated multiscale process simulation environment previously described by Bloomfield et al. to establish a link from atomistic simulations upwards to feature-, pattern- and reactor-scale simulations.

Acknowledgements

The authors thank Leonard J. Borucki, Dibyendu Datta, Hanchen Huang, Andrew Kuprat, Kenneth E. Jansen, Ottmar Klaas and Mark S. Shephard for some very useful discussions. We would like to acknowledge the Microelectronics Advanced Research Corporation (MARCO), Defense Advanced Research Projects Agency and the New York State Office of Science, Technology and Academic Research (NYSTAR) for their support of this work through the Focus Center—New York, Rensselaer: Interconnections for Gigascale Integration.

Notes

†Email: [email protected].

† Throughout this work, the term ‘material’ is used to indicate any piecewise continuous region across which a property of interest varies continuously. Thus, if the distinguishing property is crystallographic orientation, different materials correspond to different grains.

Figure 2. Sign convention for level-set scalar fields for (a) two-phase and (b) many-phase systems. Note that the number of phases is greater than the number of level sets for two-phase systems and equal to the number of level sets for many-phase systems.

Additional information

Notes on contributors

Timothy S. Cale†

†Email: [email protected].