Free molecular transport and deposition in long rectangular trenches

Abstract

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.

Multi-scale modeling of chemical vapor deposition processes for thin film technology

“…Free molecular flows at high Knudsen conditions ðKn410Þ can be modeled through line-of-sight-type models [57,179,180]. For the intermediate pressure ðKn ¼ 0:01210Þ ranges, neither of the approaches is suitable.…”

Planar Source Line‐of‐Sight Model with Automatically Adjusting Time Increment and Local Sticking Factors

“…[3] However, the use of local sticking factors increases the computational cost due to the iterative process by which a converged solution for the reaction-dependant surface fluxes is reached. This additional cost increases with aspect ratio and decreases with increased sticking factors.…”

“…The three models are the simplified hemispherical vapor source (HVS) model developed by Yun and Rhee, [1] the ballistic transport and reaction model (BTRM) of Cale and co-workers., [2][3][4] and the Monte Carlo (MC) method used by Rodgers and Jensen. [5] The goal of developing this new model, called the ballistic transport with local sticking factors (BTLSF) model, was to produce a simple but accurate ballistic transport-based feature-scale model where the initial deposition arrives from a source plane.…”

Kinetic description of flow past a micro-plate

“…The method uses ÔpropagatingÕ directions for tracking the transport of particles throughout phase space. This transport model is similar in spirit to earlier transition probability transport codes [9,[11][12][13][14][15]. Although earlier codes [13,14] are capable of handling arbitrary spatial meshes, they typically assume isotropic scattering and make other simplifying assumptions which reduce the computational overhead, making it possible to store large amounts of geometrical information typically needed.…”