Free molecular transport and deposition in long rectangular trenches

Integral equations are derived which describe free molecular flow and simultaneous film deposition in long rectangular trenches. The equations apply to flow in the absence of deposition and to both low-pressure chemical vapor deposition (LPCVD) and physical vapor deposition (PVD), i.e., over the full range of reactant sticking coefficient from zero to unity. 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 along the trench sides and bottom for PVD (unity sticking coefficient). Numerical inversion of the integral equations provides initial deposition profiles for LPCVD (low sticking coefficient). The calculated initial deposition profiles are consistent with empirical results which typically show poor uniformity in PVD and high uniformity in LPCVD, and also compare well with Monte Carlo based simulations of deposition processes.