A unified line-of-sight model of deposition in rectangular trenches

The integro-differential equations which describe free molecular flow in long rectangular trenches in the absence of deposition and to both low pressure chemical vapor deposition (LPCVD) and physical vapor deposition (PVD) are derived. A pseudosteady state assumption is implicit in the formulation, i.e., the feature dimensions change slowly relative to the time required for the flux to redistribute in response to the changes. Numerical solution of the governing equations provides film and deposition rate profiles as a function of deposition time until the trench is completely filled. Solutions are discussed for selected values of the sticking coefficient from zero to unity. The calculated film profiles are consistent with empirical results which typically show poor uniformity in PVD and step coverage increasing with decreasing sticking coefficient in LPCVD. Film profiles compare well with Monte Carlo based simulations of deposition processes.