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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 YBa₂Cu₃O_7-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.

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Investigators

Jing Fan, Postdoctoral Associate
Iain D. Boyd, Associate Professor

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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.

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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

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��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.

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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��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, “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.