Comparison of LPCVD Film Conformalities Predicted by Ballistic Transport‐Reaction and Continuum Diffusion‐Reaction Models

Abstract

Two models used for predicting film profile evolution during low pressure chemical vapor deposition in features on patterned substrates are compared; (i) a ballistic transport-reaction model (BTRM) in which transport between surfaces in a feature is "line of sight" and (it) a diffusion-reaction model (DRM) in which gas-phase transport is expressed in terms of concentration gradients and Knudsen diffusion. In order to compare the qualitative and quantitative predictions of the two models we use blanket tungsten deposition by the hydrogen reduction of tungsten hexafluoride in long (two-dimensional) rectangular trenches as an example. The two models are based on the same underlying assumptions: however, they differ in their treatment of molecular transport in features. For both models, film deposition occurs through heterogeneous gas-solid reactions, and profile evolution is two dimensional. The BTRM is formulated in terms of three-dimensional fluxes to the evolving film surface. These fluxes are expressed in terms of fluxes from all other points on the surface of the feature and from the source volume and are therefore "nonlocal." In the DRM, fluxes to the local surface are expressed in terms of local gas-phase concentrations. Because of the assumptions used to compute Knudsen diffusivity in the DRM, the transport occurs in one dimension. "Rules of thumb" relating qualitative changes in film conformality to changes in process conditions, derived using the governing equations of the two models, are the same and agree well with observed trends. Using a "relative reactant depletion criterion," both models predict the same ratio of partial pressures of reactants which maximizes film conformality. Quantitative step coverage predictions obtained from the BTRM simulations are consistently higher than those of the DRM.Process modeling is gaining importance in the microelectronics industry and has assumed multiple roles in process development, modification, and optimization. For example, low pressure chemical vapor deposited (LPCVD) process models are used to predict film conformality 1-9 as well as to develop novel process protocols to increase film cortformality and wafer throughput. 3,g Typical LPCVD systems are characterized by the presence of free molecular or Knudsen flow (high Knudsen numbers) within micronscale features and heterogeneous gas-solid reactions which lead to film growth. In recent years, two different physically based models of LPCVD processes have achieved reasonable success: (i) a "continuum-like" diffusion-reaction model (DRM), 14 and (it) a particle-based modified line-ofsight or ballistic transport-reaction model (BTRM). 44The BTRM has the advantage that its equations are derived from a strong fundamental basis; however, its application is restricted to low pressure processes. The advantage with the DRM is that it can be modified to simulate CVD processes at higher pressures (lower Knudsen numbers), in addition to the low pressure processes. Limitations of the DRM lie mainly in its treatment of mo...

Theory of Free Boundary Step Coverage in Chemical Vapor Deposition

“…Later it will be shown that for Ai > 15, Di is insensitive to X\, as is Ac-Therefore the variable diffusion model always predicts larger diffusion coefficients and better step coverage than eqs 34 and 35. This result is consistent with the BTRM model (Jain et al, 1993). If one uses a Dk which decreases with time as the walls close up, then the result would be somewhat below curve 3.…”

“…As one would expect on a physical basis, in the low-pressure region, our estimated diffusion coefficient is higher than the cross-sectionaverage Knudsen coefficient, which is based exclusively on side wall constraints. Thus in the LPCVD region the predicted step coverage is better than that of the Knudsen model, and this is consistent with line of sight results (Jain et al, 1993).…”

“…Then one equates the moles of reactant remaining on the wafer surface per unit time to form the film with the sticking coefficient times the bombardment flux for given process conditions as shown in eq 1. In some circumstances (Cale and Raupp, 1990a,b; Cale and Mohamed, 1991;Jain et al, 1993), the sticking coefficient is computed from a reaction mechanism based on an assumed sequence of reactions. In others (Cheng et al, 1989;Islamraja et al, 1991) a is chosen arbitrarily to match film profiles.…”

New therapies available for the treatment of type 2 diabetes

“…Coverage profiles inside nanostructures such as trenches and vias have been modeled in the literature using three different approaches; line‐of‐sight models,10, 24, 25 kinetic Monte Carlo simulations,26 and continuum approximations 27. Ballistic line‐of‐sight models are the most accurate representation under Knudsen flow conditions, where trajectories of gas species are dictated by wall collisions.…”

Chemical vapor deposition of titanium nitride thin films from tetrakis(dimethylamido)titanium and hydrazine as a coreactant

“…CVD processes with lower deposition temperatures may provide TiN films with improved step coverage for sub-0.25-m metallization schemes, because conformality is expected to improve with decreasing deposition temperature according to computer simulations of CVD. 25,34 This is a result of the decreased sticking coefficient of the precursors at lower deposition temperatures. Lowering the temperature for CVD TiN is also useful for improving coating processes in the cutting tool and hardcoatings industries.…”