A fundamental feature scale model for low pressure deposition processes

Abstract

The integro-differential equations which govern free molecular flow and low pressure chemical vapor deposition in long rectangular trenches are reviewed. The model equations are used to simulate the deposition of tungsten by hydrogen reduction of tungsten hexafluoride, with reactive sticking coefficients determined by local deposition conditions. Numerical solution of the governing equations provides film profiles and deposition rate profiles as a function of position in the trench at any time until the trench mouth closes. The impact of the operating conditions on step coverage is discussed in relation to reactive sticking factors. Calculated tungsten step coverages for three selected realistic initial trench shapes highlight the importance of establishing a consistent method for reporting step coverages. We introduce the percentage of feature fill as a measure of step coverage. To allow evaluation of the quantitative predictive ability of a model, cross-sectional scanning electron micrographs are required in general.

Multiscale modeling in chemical vapor deposition processes: Coupling reactor scale with feature scale computations

“…For this type of features the surface integral of Eq. (5) can be reduced (Cale et al, 1991;Kokkoris et al, 2006;Singh et al, 1992) to a line integral. In this work, we use the reduced expressions for infinite length trenches (Kokkoris et al, 2006).…”

“…S E,i varies locally from surface to surface inside the feature and surface reaction kinetics are used for its calculation (Section 3.2). Q i (x, x 0 ) is the differential transmission probability (Cale et al, 1991) from x 0 to x which incorporates geometric characteristics (orientation, visibility and distance of the elementary surfaces at x and x 0 ) as well as the reemission mechanism of species i (Cale and Mahadev, 1996;Kokkoris et al, 2006). The direct flux at a surface at x depends on (a) the solid angle O(x), through which the surface is visible to the bulk phase of the reactor, (b) the orientation of the surface which is defined by the unit normal vector at x, n(x), and (c) the flux distribution of the species in the bulk phase and above the patterned wafer, C bulk,i (y, j).…”

“…In the first approach the calculation is numerical; the second approach is stochastic. According to the first approach for FSM, the transport of species has been dealt with either continuum (in the sense that their mathematical formulation is a set of integral equations) ballistic models (Cale et al, 1991;Cale and Mahadev, 1996) when Kn41, or continuum diffusion models (Liao and Cale, 1994) when Kn51, and recently with numerically solving Boltzmann equation in the transition regime Gobbert and Cale, 2007). For the interaction of species with the local surfaces, empirical expressions for the surface reaction rate or Langmuir type surface models (Xenidou et al, 2004) have been exploited.…”

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

“…A third approach is the so-called 'ballistic transportreaction' model [57,58]. It is based on the analogy between diffuse reflection and absorption of photons on gray surfaces, and the scattering and adsorption of molecules on walls.…”

A Homogenization Technique for the Boltzmann Equation for Low Pressure Chemical Vapor Deposition

“…The deposition surface necessarily involves a microstructure given by the electrical components of the future microchip. Classical models for this process include reactor scale models [17] with a typical length scale of over 10 cm, which model the gas flow throughout the chemical reactor, and feature scale models [3] with a typical length scale of under 1 µm, which focus on the evolution of the film profile inside an individual feature.…”