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Mathematics Group

Etching and Deposition in Semiconductor Process Manufacturing

We built a complete suite of mathematical and algorithmic tools to model etching and deposition in semiconductor manufacturing. Level set methods for interface motion are coupled to empirical flux laws, material-depending etch and deposition rates, re-emission profiles and pattern masks. These allow tracking of complex interfaces in plasma-enhanced chemical vapor deposition, ion-milling, and photolithography. Results were validated through careful comparison with experiment, and show the development of voids, needle-structures, three-dimensional faceting in sputter etching and deposition, and angle-dependent reemission profiles. These algorithms are now used worldwide to model the design and manufacture of semiconductors.