Continuum model of thin film deposition incorporating finite atomic length scales

We show that surface evolution resulting from the deposition of discrete particles is intrinsically different from that produced by continuum processes. The atomistic effects have major consequences, even when observed at macroscopic length scales. We have elucidated some of the atomistic effects by comparing: (i) numerical simulations of thin film deposition using the continuum model, (ii) atomistic (Monte Carlo) models, and (iii) experiments on the sputter deposition of Ta onto a substrate containing etched vias. We have therefore developed a continuum model which incorporates finite atomic length scales. The model incorporates effects of atomic interactions, which lead to the capture of impinging atoms that pass near a point on the film. This capture effect results in "breadloafing" at sharp convex corners where the curvature is high. We have validated our model in idealized two-dimensional simulations and obtained improved qualitative agreement with both experiment and Monte Carlo atomistic simulations. In the case of deposition into a trench, the model predicts that the protruding material from breadloafing eventually merges above the trench, leaving an enclosed void. This effect is observed in experiments, but is not reproduced when using the standard continuum model. Finally, we have also developed and implemented a more general three-dimensional model which successfully results in the breadloafing effect.