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]. 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.
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
An important deposition technique for a variety of materials involves the use of an electron beam to vaporize metallic atoms from a solid ingot. This study considers the deposition of super-conducting films of YBa2Cu3O7-x that are of great technological interest in numerous applications. The background pressure in an experimental deposition chamber is maintained at 2~5E-5 Torr using vacuum pumps. Atoms are vaporized from yttrium, barium and copper ingots by a high-energy electron beam, and the vapor jets proceed through the low-pressure chamber toward a deposition substrate. A critical component for the process is the manner in which the atoms are transported from the ingot molten surfaces to the substrate. There is a need to understand in detail the gas dynamics of the expansion process. The direct simulation Monte Carlo (DSMC) method has been used to simulate the three dimensional gas dynamic process. Besides the translational energy mode, the atomic electronic energy is taken into account. Some important issues such as the atomic collision cross-sections for metal vapors and hyperfine electronic structure of atomic absorption spectra are addressed.
Figure 1 shows the total number density field given by DSMC calculation. The source fluxes (mol cm-2s-1) are Y: Ba: Cu=0.84: 1.86: 2.52. The atoms that vaporize from the surfaces of the yttrium, barium and copper ingots, at the bottom of the figure, quickly undergo expansion in the deposition chamber that results in a rapid decrease of the number density. The flow is therefore brought into the non-continuum regime that needs to be studied based on the kinetic viewpoint.
Figures 2 compares DSMC deposition thickness profiles along the symmetrical line of the substrate with measured data for two cases where only the yttrium source is evaporating. The source fluxes are 8.4E-7 and 1.1E-5 mol cm-2s-1, respectively, and the corresponding experimental deposition time are 30 and 12 minutes. The DSMC profiles agree very well with the measurement. Because of few collisions between the atoms for the case with the low evaporation rate, the collision-less distribution is close to the DSMC and measured results. For the high evaporation rate case, however, the collision-less distribution is much lower than the DSMC and measured results. The collisions impede to some extend atomic diffusion to the block plates and chamber wall that are assumed to be perfectly sticking, which is well satisfied because the plate and wall temperatures are low in the study. Therefore the possibility of the atoms to transport from the vaporized ingot surface to the substrate is increased by the atomic collisions.
Figure 3 compares DSMC and measured atomic absorption spectra at two frequencies along an aperture close to the substrate symmetrical line for the high evaporation rate case of pure yttrium, i.e. only the yttrium source evaporates at rate of 1.1E-5 mol cm-2s-1. Because of the different hyperfine electronic structures at the central frequency of 668nm and 679nm, the peak structures are inclined to the right and left, respectively. The DSMC and measured Doppler widths and peak structure details are in excellent agreement.
Investigators
Jing Fan, Postdoctoral Associate
Iain D. Boyd, Associate Professor
Acknowledgments
This work was developed as part of the Office of Naval Research/3M "Models, Sensors, and Controls for E-Beam Deposition" program, Agreement No. N00014-98-3-0015. The content does not necessarily reflect the position or policy of the Government and no official endorsement should be inferred.
Publications
- Fan, J., Boyd, I.D. and Shelton, C., Monte Carlo Modeling of YBCO Vapor Deposition, Presented at 22nd Rarefield Gas Dynamics Symposium, July 2000, Sydney, Australia.
- Fan, J., Boyd, I.D. and Shelton, C., Monte Carlo Modeling of Electron Physical Vapor Deposition of Yttrium, Journal of vacuum Science and Technology, Vol. 18, No. 6, Nov/Dec 2000.
Introduction
Thin films and the processes employed to fabricate them play an increasingly important role in a variety of technologies. The use of supersonic molecular beams as sources represents a novel approach to thin film growth. It has been demonstrated that the surface reaction probability can be greatly enhanced by increasing reactant kinetic energy, which can be readily achieved by using supersonic molecular beams. The goal of this study is to obtain better understanding of collimated molecular beams and to provide accurate predictions of experiments being conducted in the School of Chemical Engineering at Cornell University. The ultimate goal of our work is to help to optimize the deposition process.
The current study considers expansion of a mixture of 1% disilane (Si2H6) and 99% H2 from a nozzle orifice, through a conical skimmer, and into the growth chamber. Silicon film is deposited over the substrate surface. The direct simulation Monte Carlo method (DSMC) is employed to simulate this flow. An adaptive unstructured triangular grid is used to capture the density drop in the expansion flow. Models are under development for more accurate simulation.
Acknowledgements
This work was funded by the National Science Foundation.
Publications
- Chen, G., Boyd, I. D., Roadman, S. E. and Engstrom, J. R., "Monte Carlo Analysis of a Hyperthermal Silicon Deposition Process," J. Vacuum Science Technol. A, Vol. 16, No. 2, pp 689-699, 1998.
- Chen, G. and Boyd, I.D., "Monte Carlo Simulation of Silicon Thin Film Deposition Using Supersonic Molecular Beams," 20th International Symposium on Rarefied Gas Dynamics, Beijing, August, 1996.
- Chen, G. and Boyd, I.D., "Numerical Scale-Up Study of Silicon Deposition Using 2D Slit Nozzle Sources," Materials Science in Semiconductor Processing, Vol. 1, 1998, pp. 141-152.
- Chen, G. and Boyd, I.D., "Modeling of Silicon Deposition Process Scale-Up Employing Axisymmetric Ring Nozzle Sources," Journal of Vacuum Science and Technology A, Vol. 17, 1999, pp. 970-977.
- Chen, G., Boyd, I.D., and Engstrom, J.R., "Three Dimensional Modeling of Silicon Deposition Process Scale-Up Employing Supersonic Jets," Journal of Vacuum Science and Technology A, Vol. 17, 1999, pp. 978-985.
Introduction
Pulsed laser deposition (PLD) involves a laser ablation 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 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.
Figure 1. Schematic of PLD. (Image credit: Tedsanders, Wikimedia Commons, CC0 1.0)
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 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.
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.
(a) 
(b) 
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.
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.
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.
Investigators
Ronald Chan
References
[1] S. S. Harilal, C. V. Bindhu, M. S. Tillack, F. Najmabadi and A. C. Gaeris, “Internal structure and expansion dynamics of laser ablation plumes into ambient gases,” Journal of Applied Physics, Vol. 93, pp. 2380–2388, 2003.
[2] H. Yuan, A. B. Gojani, I. B. Gornushkin, X. Wang, D. Liu and M. Rong, “Dynamics of laser-induced plasma splitting,” Optics and Lasers in Engineering, Vol. 124, 105832, 2020.