Vacancy Formation during Vapor Deposition

A hybrid modeling approach combining two-dimensional atomistic molecular dynamics simulations of vacancy formation with a continuum analysis of vacancy diffusion has been used to predict the vacancy content of vapor deposited nickel as a function of deposition rate/temperature and incident flux energy/angle. The hybrid approach uses a previously developed molecular dynamics technique to obtain the vacancy concentration in the surface of a film formed during a brief period of very high rate deposition. The structure is then annealed and the decrease in surface vacancy concentration calculated by solving continuum diffusion equations. By varying the annealing period, a good approximation to the surface vacancy concentration as a function of deposition rate is obtained. The vacancy profile through the thickness of a thick film is then obtained by solving continuum diffusion equations using the surface vacancy concentration as a moving boundary condition. In contrast to molecular dynamics alone, the hybrid approach enables calculation of the vacancy content for arbitrary low deposition rates. It reveals the existence of a deposition rate dependent temperature where the vacancy content exhibits a minimum value. The 1 ppm iso-vacancy contour in the process variable space is found to be a very steep function of deposition rate and temperature, and depends only weakly on incident flux energy or angle.