The equations governing reacting flow impinging on a static or rotating surface are discussed in this chapter. The surface is assumed to be a reactive surface, where chemical vapor deposition (CVD) may occur. Such configurations (that is, shower-head, single-wafer reactors) are commonly used in semiconductor wafer processing. The governing equations and assumptions described in this chapter pertain to the following two Ansys Chemkin Reactor Models:

In a rotating-disk reactor a heated substrate spins (at typical speeds of 1000 rpm or more) in an enclosure through which the reactants flow. The rotating disk geometry has the important property that in certain operating regimes [111] the species and temperature gradients normal to the disk are equal everywhere on the disk. Thus, such a configuration has great potential for highly uniform chemical vapor deposition (CVD), [112], [113], [114] and commercial rotating disk reactors are common, particularly for materials processing in the microelectronics industry.

In certain operating regimes, the equations describing the complex three-dimensional spiral fluid motion can be solved by a separation-of-variables transformation[114] , [105] that reduces the equations to a system of ordinary differential equations. Strictly speaking, the transformation is only valid for an unconfined infinite-radius disk and buoyancy-free flow. Furthermore, only some boundary conditions are consistent with the transformation (for example, temperature, gas-phase composition and approach velocity all specified to be independent of radius at some distance above the disk). Fortunately, however, the transformed equations still provide a very good practical approximation to the flow in a finite-radius reactor over a large fraction of the disk (up to ~90% of the disk radius) when the reactor operating parameters are properly chosen, that is, high rotation rates.[111]

In the limit of zero rotation rate, the rotating disk flow reduces to a stagnation-point flow, for which a similar separation-of-variables transformation is also available. Such flow configurations ("pedestal reactors") also find use in CVD reactors.

This chapter reviews the rotating-disk/stagnation-point flow equations. An infinite-radius disk rotating below a fluid medium is a classic problem in fluid mechanics.[105] , [106] , [115] Under these ideal conditions this problem has a solution that is an exact solution of the Navier-Stokes equations. Consequently, the heat and mass transfer near an infinite-radius rotating disk have been extensively studied. [116], [117] For CVD applications, Olander [118] used a rotating disk to study deposition in the germanium-iodide system. Pollard and Newman[114] performed a theoretical study of the deposition of Si from SiCI₄ on a rotating-disk susceptor. They extended the von Karman similarity solution for isothermal flow[105] by adding energy and species equations and incorporating temperature-dependent fluid properties to obtain an ordinary differential equation boundary-value problem for the heat, mass and momentum transfer. Hitchman, et al. [119] studied epitaxial Si deposition from SiCI₄ in a rotating-disk reactor and analyzed their results in terms of the infinite-disk solution.

Consider a solid rotating surface of infinite extent in the plane (Figure 15.1: Sketch of the infinite-radius disk and inlet boundary conditions ) separated from a facing, parallel, porous, non-rotating surface by a distance . A forced flow with purely axial velocity emerges from the porous surface and is directed toward the rotating one. The flow at approximates the inlet flow conditions in a cylindrical, rotating-disk CVD reactor. The finite domain in the present case results in a nonzero value of the radial pressure gradient.

Analysis by Evans and Greif[111] combined the stagnation and rotating disk flows for the situation of an infinite-radius, porous, non-rotating disk separated by a distance from an infinite-radius, nonporous, heated, rotating disk. This combination of flows provides a good approximation to the flow field in a rotating disk reactor. The Evans and Greif analysis was used as a foundation for the Ansys Chemkin stagnation-flow and rotating-disk transport model. However, the Chemkin model also incorporates a species conservation equation for each species that occurs in the gas phase, with Gas-phase Kinetics and Surface Kinetics contributions. These equations account for convective and diffusive transport of species, as well as production and consumption of species by elementary chemical reactions.