Free molecular transport and deposition in cylindrical features

A Clausing‐like integral equation is derived which applies to both low pressure chemical vapor deposition (CVD) and physical vapor deposition (PVD) in cylindrical contact holes; i.e., over the full range of sticking coefficient (0–1). A steady state assumption is implicit in the formulation. In the absence of film deposition, the flux to the surface is spatially uniform. Analytical expressions are presented for the initial deposition profiles for PVD (unity sticking coefficient). Numerical inversions of the integral equations provide initial deposition profiles for CVD (low sticking coefficients). Initial deposition profiles exhibit poor uniformity in PVD and high uniformity in CVD, in agreement with empirical evidence. The results provide a test for proposed Monte Carlo simulations which are based on the same assumptions.