Stagnation-Flow Chemical Vapor Deposition

Consider an atmospheric-pressure process to deposit a silicon film from a silane (SifLj) precursor. The showerhead-to-wafer distance is 3 cm. In this process a helium carrier gas makes up the bulk of the flow, with the active silane accounting for only 0.17% of the inlet mixture. The precursor gases enter the reactor at 300 K, but the wafer temperature and inlet velocity are varied to observe different process characteristics. 

For the purpose of this illustrative model, a particularly simple reaction mechanism is used. However, while not the complete mechanism used in practice, it captures the essential features of a silane process. Moreover it illustrates some of the competitive physical processes that characterize many CVD processes. The gas-phase reaction mechanism consists of a single, irreversible, decomposition reaction 

The surface reactions are based on sticking coefficients. Silylene (S1H2), which is very reactive, has a sticking coefficient of unity. The silane, which is much less reactive, has an activated sticking coefficient, given as 

The top panel of Fig. 17.2 (Ts = 800 K) reveals that there is very little decomposition of the silane in the gas phase, which is a result of the relatively low temperature. As a result the net growth rates should be expected to be quite low, since the silane sticking coefficient is so low. At a surface temperature of Ts = 1300 K, however, the decomposition of silane to silylene in the gas-phase boundary layer is nearly complete. The relatively high silylene concentrations should lead to high growth-rates. The peak in the silylene profile at about 1.5 mm above the surface results from the competition between production by the homogeneous decomposition reaction and consumption at the surface by heterogeneous reaction. 

The flux summary within the boxes in Fig. 17.2 shows the mass flux (g/cm2-s) of both the silane and silylene to the surface, resulting in deposition of silicon and release of volatile hydrogen. At low temperature, the film growth is primarily from silane, although it is quite low. By Ts = 925 K, there is sufficient silane decomposition that the surface fluxes of the two species are becoming comparable. At Ts = 1300 K, the silylene flux is dominant, carrying most of the silicon to the surface. 

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A further consequence of the upstream diffusion to the burner face could be heterogeneous reaction at the burner. Such reaction is likely on metal faces that may have catalytic activity. In this case the mass balance as stated in Eq. 16.99 must be altered by the incorporation of the surface reaction rate. In addition to the burner face in a flame configuration, an analogous situation is encountered in a stagnation-flow chemical-vapor-deposition reactor (as illustrated in Fig. 17.1). Here again, as flow rates are decreased or pressure is lowered, the enhanced diffusion tends to promote species to diffuse upstream toward the inlet manifold. 

Fig. 17.1 Illustration of a stagnation-flow chemical-vapor deposition process.

While our primary interest in this text is internal flow, there are certain similarities with the classic aerodynamics-motivated external flows. Broadly speaking, the stagnation flows discussed in Chapter 6 are classified as boundary layers where the outer flow that establishes the stagnation flow has a principal flow direction that is normal to the solid surface. Outside the boundary layer, there is typically an outer region in which viscous effects are negligible. Even in confined flows (e.g., a stagnation-flow chemical-vapor-deposition reactor), it is the existence of an inviscid outer region that is responsible for some of the relatively simple correlations of diffusive behavior in the boundary layer, like heat and mass transfer to the deposition surface. 

M.E. Coltrin, RJ. Kee, G.H. Evans, E. Meeks, FM. Rupley, and J.F. Grcar. Spin A Fortran Program for Modeling One-Dimensional Rotating-Disk/Stagnation-Flow Chemical Vapor Deposition Reactors. Technical Report SAND91-8003, Sandia National Laboratories, 1991. 

S. Joh and G.H. Evans. Heat Transfer and Flow Stability in a Rotating Disk Stagnation Flow Chemical Vapor Deposition Reactor. Numer. Heat Transf. Part A— Applications, 31 (8) 867—879,1997. 

Stagnation flows represent a very important class of flow configurations wherein the steady-state Navier-Stokes equations, together with thermal-energy and species-continuity equations, reduce to systems of ordinary-differential-equation boundary-value problems. Some of these flows have great practical value in applications, such as chemical-vapor-deposition reactors for electronic thin-film growth. They are also widely used in combustion research to study the effects of fluid-mechanical strain on flame behavior. 

For many applications, like chemical-vapor-deposition reactors, the semi-infinite outer flow is not an appropriate model. Reactors are often designed so that the incoming flow issues through a physical manifold that is parallel to the stagnation surface and separated by a fixed distance. Typically the manifolds (also called showerheads) are designed so that the axial velocity u is uniform, that is, independent of the radial position. Moreover, since the manifold is a solid material, the radial velocity at the manifold face is zero, due to the no-slip condition. One way to fabricate a showerhead manifold is to drill many small holes in a plate, thus causing a large pressure drop across the manifold relative to the pressure variations in the plenum upstream of the manifold and the reactor downstream of the manifold. A porous metal or ceramic plate would provide another way to fabricate the manifold. 

L.L. Raja, R.J. Kee, R. Serban, and L.R. Petzold. A Computational Algorithm for Dynamic Optimization of Chemical Vapor Deposition Processes in Stagnation Flow Reactors. J. Electrochem. Soc., 147 2718-2726,2000. 

Problem 11-6. Mass and Heat Transfer for Chemical Vapor Deposition. Consider the following model for chemical vapor deposition (CVD) on a surface. A reactive species is transported toward the surface by a 2D flow near a stagnation point, as illustrated in the figure. Far away from the surface the flow is given by... 

Raja LL, Kee RJ, Serban R, Petzold LR Computational algorithm for dynamic optimization of chemical vapor deposition processes in stagnation flow reactors, J Electrochem Soc 147 2718-2726, 2000. 

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