First-principles calculation of self-diffusion, arsenic diffusion, and surface segregation in silicon

Integrated circuit device densities have increased more than 2000 times since Gordon Moore's observation of exponential growth in 1965. Modern devices are thus sensitive to minute variations in diffusion, such as the transient-enhanced diffusivity resulting from ion implantation, concentration-dependent diffusivity of dopants due to changes in the Fermi level, and the effects of high stresses and stress gradients (resulting from thermal oxidation and other surface treatments). Arsenic diffusion and self-diffusion in Si are caused by both types of intrinsic defects, vacancies and self-interstitials. Surprisingly, the mechanisms of Si self-diffusion remain unclear: equilibrium defect concentrations are too low to measure, and defect diffusivities are obscured by the relatively large concentrations of C and O traps.; The aim of the present work is to develop a physically based, quantitative understanding of dopant diffusion during IC processing, as well as the non-equilibrium limits to dopant concentrations. Density functional theory, a first-principles techniques, has been used (with the PW91 functional) to calculate properties of intrinsic defects not directly accessible to experiment. Density functional calculations of the formation enthalpies and volumes of vacancies and interstitials in silicon are presented in each low-energy geometry and charge state. The effect of pressure (up to 30 kbar) and doping (moving the Fermi level from the valence band maximum to the conduction band minimum) on the stability and diffusivity of defects is discussed. In the presence of electronic or optical excitation, both defects are mobile even at cryogenic temperatures. Vacancy diffusion is found to be enhanced by n-type doping, while p-type doping inhibits interstitial migration. Relaxation volume tensors extracted from these calculations express the response of the defects to non-hydrostatic stress states.; The interstitial-mediated diffusion of As is shown to have a similar activation barrier to vacancy-mediated diffusion, despite much lower binding energies. The presence of multiple low-energy As interstitial configurations suggests a high diffusion entropy.