Multiscale modeling of stress-mediated diffusion in silicon: Ab initio to continuum

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Abstract
In this letter, we present the development of a complete methodology to simulate the effects of general anisotropic nonuniform stress on dopant diffusion in silicon. The macroscopic diffusion equation is derived from microscopic transition-state theory; the microscopic parameters are calculated from first principles; a feature-scale stress-prediction methodology based on stress measurements in the relevant materials as a function of temperature has been developed. The developed methodology, implemented in a continuum solver, is used to investigate a TiN metal gate system. A compressive stress field is predicted in the substrate, resulting in an enhancement in lateral boron diffusion. This enhancement, which our model attributes mostly to solubility effects, is in good agreement with experiment.