Physical and Chemical Deposition of Materials

Physical Vapor Deposition (PVD) is used to deposit thin films of material onto surfaces. In this process, the gas-phase precursor is condensed onto the surface of the substrate. Chemical Vapor Deposition (CVD) also involves the deposition of a gas-phase precursor material onto a surface, however, this process occurs through chemical reactions at the surface of the substrate. These processes are commonly used in semiconductor wafer processing, for microfabrication processes and in other applications where thin films are needed. Many of these processes take place at low pressure and involve flows over features with small length scales, which places the associated flow fields in the transitional or non-continuum flow regimes. The direct simulation Monte Carlo (DSMC) method is appropriate for the simulation of these types of flows, which are in translational nonequilibrium, and is used in this project.

Since the DSMC method has been mainly used for the simulation of external, hypersonic flow fields, new physical models need to be developed in order to simulate low-pressure flows that are used for materials processing. This ongoing project is a collaboration with an industry partner to develop the physical models necessary to apply the DSMC method to the solution of materials processing flows, and to incorporate these models into a tool with a much broader multi-physics capability.

One of the first challenges in this project is to develop boundary conditions that allow the subsonic, internal flow fields that exist in PVD and CVD reactors to be modeled. The subsonic outlet boundary is treated as a porous wall, with a variable porosity that is controlled using a simple feedback loop. The porosity is adjusted until the pressure in the cells along the outlet boundary equals the specified pressure. This approach has been used in the past to model the behaviour of vacuum pumps [1],[2]. The ability to model an inlet boundary by specifying either pressure and temperature (labeled Type 1), or total mass flow and temperature (labeled Type 2 or 3), has also been implemented. The implementation of the Type 1 inlet follows the form presented in [3]. A Type 2 mass flow inlet utilizes the assumption that the mass flux is uniformly distributed across the inlet area to compute the inlet density. A Type 3 mass flow inlet utilizes the assumption that the velocity across the inlet is uniform to compute the inlet velocity, and is implemented as presented in [4]. A limitation of the Type 3 implementation is that it requires communication of macroscopic information between processors during a parallel simulation, while the Type 2 inlet condition does not.

The new boundary conditions are validated by computing the flow field in a long, high aspect ratio microchannel, and comparing the predicted macroscopic properties to the analytical solution of the flow field [5]. Figure 1 (left) shows the predicted pressure along the centerline of the channel, as well as the analytical result. Use of the Type 3 boundary condition results in a slight under-prediction of the centerline pressure. Figure 1 (right) shows the predicted axial velocity along the centerline of the channel. Both of the boundary conditions that involve specifying mass flow (Types 2 and 3), yield an unphysical velocity profile immediately downstream of the inlet. This is likely due to the assumptions made about the uniformity of mass flux or velocity in the implementation of these boundary conditions. It is necessary to make assumptions of this nature since mass flow is an integrated, or total, quantity that is specified for the entire inlet area.

Figure 1:Predicted pressure (left) and axial velocity (right) along the centerline of the channel (dash, dash-dot and dash-dot-dot lines), and analytical results (solid line).


Erin Farbar


This work is funded by an industrial contract.


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