Modeling Defect Mediated Dopant Diffusion in Silicon.

Abstract

The current understanding of dopant diffusion in silicon comes from the synthesis of experimental and computational research. Dopant diffusion is mediated by defects, and the relevant physical phenomena range over many time and length scales, necessitating a multi-scale modeling approach. In this work, we focus on two essential aspects, (1) the accuracy of atomistic methods for calculating defect parameters, and (2) an accelerated kinetic Monte Carlo (KMC) method, which we use to investigate the effects of percolating dopant-defect interactions on diffusion.

We use continuum linear elasticity to quantify the effects of boundary conditions on atomistic calculations of defect energies and volume tensors. It predicts that when using periodic boundary conditions with zero average stress, energies converge with the inverse of system size and relaxation volume tensors are independent of supercell size or symmetry. We verify the linear elastic prediction in the far field of atomistic calculations by calculating the formation energy and volume tensor for vacancy and interstitial defects in silicon using the Stillinger-Weber empirical potential. In practice, both defect energies and relaxation volume tensors converge with the inverse of system size because changes in the bonding at the defect affect the elastic moduli.

We also introduce an accelerated KMC method which automatically determines which states comprise trapping energy basins, allowing simulations to reach very long times compared to standard KMC simulations. We validate the accelerated method by performing simulations of V-As cluster dissolution and comparing to standard KMC simulations. Then we apply the method to highly time and concentration dependent vacancy-mediated As diffusion in Si. At high As concentrations, percolating dopant interactions lead to limited increased diffusivity, but the effect is limited in magnitude and duration as immobile clusters form quickly. The energy basin algorithms for accelerating KMC simulations may be very useful in a wide variety of applications. By considering issues such as grouping isolated diffusing species and collecting data when the exact location of the system within an energy basin is not resolved, we provide an example that can be followed when applying this method to other systems.