Materials Processing
Deposition of many important materials such as semi-conductors is performed using energetic jets under low pressure conditions. In addition, materials that have been deposited, such as silicon, are often processed into specific shapes using a low-pressure plasma. The numerical methods that we develop in NGPDL primarily for aerospace applications therefore also find application in materials processing systems as described by the projects in this section.
Introduction
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].听Figure 1 (left) shows the predicted pressure along the centerline of the channel, as well as the analytical result.听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.听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.
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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).
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Investigators
Erin Farbar
Acknowledgments
This work is funded by an industrial contract.
References
- Font, G. I. and Boyd, I. D., "Numerical study of the effects of reactor geometry on a chlorine plasma helicon etch reactor," Journal of Vacuum Science and Technology A, Vol. 15, No. 2, pp. 313-319, 1997.
- Chen, G., Boyd, I. D., Roadman, S. E., and Engstrom, J. R., "Monte Carlo analysis of a hyperthermal silicon deposition process," Journal of Vacuum Science and Technology A, Vol. 16, No. 2, pp. 689-699, 1998
- Cai, C., Boyd, I. D., Fan, J. and Candler, G. V., "Direct Simulation Methods for Low-Speed Microchannel Flows," Journal of Thermophysics and Heat Transfer, Vol. 14, No. 3, pp. 368-378, 2000.
- Wu, J-S., Lee, F. and Wong, S-C., "Pressure Boundary Treatment in Micromechanical Devices Using The Direct Simulation Monte Carlo Method," JSME International Journal Series B, Vol.44, No. 3, pp. 339-450, 2001.
- Arkilic, E. B. and Schmidt, M. A., "Gaseous Flip Flow in Long Microchannels," Journal of Microelectromechanical Systems, Vol.6, No. 2, pp. 167-178, 1997
Introduction
Micro-electronic circuit wafers are typically manufactured using plasma etch reactors. Manufacturing is accomplished by depositing layers of conducting or insulating material onto a silicon wafer and then etching circuit features into them. The etch process involves bombarding the silicon wafer with a reactive neutral gas and an ion stream in a near-vaccum condition to carve out circuit features in a preferred direction. In order to improve the manufacturing process, increase yield, and raise quality, the flow field inside a chlorine plasma etch reactor is under study.
The goal of this research is to aid in the understanding of how the manufacturing control parameters affect the physical processes inside a low pressure plasma etch reactor. The flow inside the reactor varies from continuum flow to near free molecular flow. In addition, electromagnetic effects are important due to rf heating, magnetic confinement, and wafer potential bias acceleration. In order to correctly model the convective and diffusive transport as well as the chemistry and electromagnetic effects, particle methods (DSMC-PIC) are used. Computations are carried out on a massively parallel architecture IBM SP2. The work is done in collaboration with industrial partners who provide the specifics of reactor design and experimental data.
Numerical simulation allows the full characterization of both neutral and ion behavior inside the reactor. With simulation, it is also possible to study etch reactor design changes before building of hardware.
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Acknowledgment
This work was funded by the Advanced Research Projects Agency (ARPA).
Publications
- Font, G. I. and Boyd, I.D., "Numerical Study of the Effects of Reactor Geometry on a Chlorine Helicon Plasma Etch Reactor," AIAA 96-0591, 34th Aerospace Sciences Meeting & Exhibit, Jan. 1996.
- Font, G.I. and Boyd, I.D., "Numerical Study of Reactor Geometry Effects on a Chlorine Plasma Helicon Etch Reactor," Journal of Vacuum Science and Technology A, Vol. 15, 1997, pp. 313-319.
- Font, G.I., Boyd, I.D., and Balakrishnan, J., "Effects of Wall Recombination on the Etch Rate and Plasma Composition of an Etch Reactor," Journal of Vacuum Science and Technology A., Vol. 16, 1998, pp. 2057-2064.
Introduction
Pulsed laser deposition (PLD) involves a听laser ablation听procedure, where a laser pulse interacts with a material surface to induce the formation of a plasma plume that expands away from the surface. This plume contains material that is eventually deposited on an opposing substrate similar to听previous deposition processes studied in NGPDL. The interaction of the plume with a background gas influences the efficiency of the deposition process and is associated with a myriad of accompanying physical mechanisms. For example, a plume expanding into ambient gas of low pressure around 100 mTorr exhibits plume splitting and sharpening [1]. A definitive mechanistic explanation for laser-induced plasma plume splitting remains an active area of research [2]. The splitting of the plume into fast and slow components influences the geometry of the plume and can lead to effects on deposition characteristics that may be of industrial relevance.
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Figure 1. Schematic of PLD. (Image credit: Tedsanders, Wikimedia Commons, CC0 1.0)
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Methods
Plasma behavior may be simulated using particle methods such as particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC), or Eulerian methods such as the direct kinetic (DK) method that directly solves the Boltzmann or Vlasov equation. Both methods have been听previously studied in NGPDL. The DK method does not suffer from the statistical noise inherent to particle methods and is suitable for time-varying problems. In addition, it is able to effectively simulate rarefied regions where particle methods may have sparse populations depending on the initial and flow conditions. In PLD, the plume of interest expands unsteadily into an initially rarefied region, making the DK method well suited to the problem.
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Results
The development of a DK method for two atomic species with their charged counterparts is underway. A DK method for two neutral atomic species with cross collisions has been developed as an intermediary step to this goal. The following plots reveal the nature of these cross collisions.
Figure 2(a) plots the initial atomic number densities in a two-species population residing in a one-dimensional domain, while Figure 2(b) plots the corresponding number densities after some time has elapsed. The dense plume diffuses and expands to the right, while some of the background gas is also accelerated to the right due to cross collisions.
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Figure 2. (a) Initial atomic number densities in a two-species population as functions of space. (b) Corresponding number densities after some time has elapsed.
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As a verification exercise for the cross-collisions routine, three setups with identical total number densities were initialized and allowed to evolve in time. Their total number densities after some time has elapsed are plotted in Figure 3. The single-species configuration and the two-species configuration with cross collisions agree to a reasonable extent as expected, while the total number density in the two-species configuration without cross collisions diffuses more quickly with fewer collisions to inhibit the expansion process.
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Figure 3. Comparison of total number densities in a single-species population, a two-species population with cross collisions, and a two-species population without cross collisions, at the same time instance as in Figure 2(b). Here, the two-species configurations include two identical constituents for an apples-to-apples comparison with the single-species configuration.
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Investigators
Ronald Chan
References
[1] S. S. Harilal, C. V. Bindhu, M. S. Tillack, F. Najmabadi and A. C. Gaeris, 鈥淚nternal structure and expansion dynamics of laser ablation plumes into ambient gases,鈥 Journal of Applied Physics, Vol. 93, pp. 2380鈥2388, 2003.
[2] H. Yuan, A. B. Gojani, I. B. Gornushkin, X. Wang, D. Liu and M. Rong, 鈥淒ynamics of laser-induced plasma splitting,鈥 Optics and Lasers in Engineering, Vol. 124, 105832, 2020.