Micro and Nano Engineering Center


At Michigan State University


PLASMA MODELING

Modeling studies of both microwave plasma source and microwave materials processing machines are performed in the MNEC Center. Various plasma sources have been modeled ranging from a small 3.5 cm diameter discharge source operated below 1 mTorr to diamond CVD deposition sources operated above 100 Torr. The microwave fields are solved in these models using a finite-difference time-domain (FDTD) method. For the plasma discharges both particle and fluid models have been utilized. 

One emphasis of the modeling work is to achieve self-consistent solutions of both the microwave fields and the plasma discharge. The modeling effort has produced zero-dimensional (global) models, two-dimensional models, and three-dimensional models.

The objectives of the modeling study include:

  •  Improving the understanding of the microwave heating and the operational stability of microwave discharges and microwave heating processes.
  •  Developing models to assist in the design of microwave plasma/materials processing machines and processes.
  •  Developing control models that describe the microwave plasma/materials processing machines for feedback control systems.


One recent microwave plasma modeling project was a collaboration between Michigan State University and the University of Paris-Nord/LIMHP-CNRS Laboratory in France. This  collaboration produced a self-consistent two-dimensional model of hydrogen discharges operating in a microwave plasma source at pressures ranging from 10 to 80 Torr. This model was compared to a variety of experimental measurements on the plasma source, including microwave electric field strengths, plasma gas temperatures, and atomic hydrogen concentrations.
 

2D Self-Consistent Model for Hydrogen Plasmas Obtained in a Microwave Discharge Reactor 

(Ref: K. Hassouni, T. A. Grotjohn, and A. Gicquel, J. Appl. Phys., 86, pp. 134-151, 1999)

Self-Consistent Coupling between Electromagnetic Field and Plasma Distributions

 

1. H2 Plasma model :

    • 9 species : H2, H, H*(n=2), H*(n=3), H+, H2+, H3+, H-and e-
    • Three energy modes : gas, vibration, and electron
    •  35 reactions
    2. Electromagnetic model (Maxwell) yields : 
     
    • E, H components using FDTD approach
    • The self consistent absorbed power density

 

2D Self-Consistent hydrogen plasma model

Plasma behavior at various input powers for a pressure of 2500 Pa
 

References

Plasma Modeling:

    1) T. A. Grotjohn, "Numerical Modeling of a Compact ECR Ion Source," Review of Scientific Instruments,  vol. 63, pp. 2535-2537, 1992.

    2) T. A. Grotjohn, W. Tan, V. Gopinath, A. K. Srivastava, and J. Asmussen, " Modeling the Electromagnetic Excitation of a Compact ECR Ion/Free Radical Source,"  Rev. Scientific Instruments, vol. 65, pp. 1761-1765, 1994.

    3) W. Tan and T. A. Grotjohn, "Modeling the Electromagnetic Excitation of a Microwave Cavity Plasma Reactor,"  J. of Vacuum Sci. and Technol., vol. A-12, pp. 1216-1220, 1994.

    4) V. P. Gopinath and T. A. Grotjohn, "Three-Dimensional Electromagnetic PIC Model of a Compact ECR Plasma Source," IEEE Trans. on Plasma Science, vol. 23, pp. 602-608, 1995.

    5) W. Tan and T. A. Grotjohn, "Modeling the Electromagnetic Field and Plasma Discharge in a
    Microwave Plasma Diamond Deposition Reactor,"  Diamond and Related Materials, vol. 4, pp. 1145-1154, 1995.

    6) T. A. Grotjohn, G. L. King, and W. Tan, "Microwave Plasma Processing Machine Modeling and Diagnostics for Plasma Assisted Chemical Vapor Deposition," J. Moscow Physical Society, 5, 55, 1995.

    7) T. A. Grotjohn, "Modeling the Electron Heating in a Compact ECR Ion Source," Review of Scientific Instruments, vol. 67, pp. 921-923, 1996.

    8) P. Mak, M.-H. Tsai, J. Natarajan, B. L. Wright, T. A. Grotjohn, F. M. A. Salam, M. Siegel, and J. Asmussen, "Investigation of Multipolar Electron Cyclotron Resonance Plasma Source Sensors and Models for Plasma Control,"  J. of Vacuum Sci. and Technol., vol. A-14, pp. 1894-1900, 1996.

    9) F. M. Salam, C. Piwek, G. Erten, T. Grotjohn, and J. Asmussen, "Modeling of a Plasma Processing Machine for Semiconductor Wafer Etching using Energy-Functions-Based Neural Networks, IEEE Trans. on Control Systems Technology, 5, no. 6 , pp. 598-613, 1997.

    10) J. Asmussen, T. A. Grotjohn, P. U. Mak, and M. A. Perrin, "The Design and Application of Electron Cyclotron Resonance Discharges," IEEE Trans. on Plasma Science, vol 25, pp. 1196-1221, Dec. 1997.

    11) T. A. Grotjohn, "Modeling electromagnetic fields for the excitation of microwave discharges used for materials processing," J. Phys. IV France, vol. 8, pp. 61-79, 1998.

    12) K. Hassouni, T. A. Grotjohn, and A. Gicquel, "Self-consistent Microwave Field and Plasma Discharge Simulations for a Moderate Pressure Hydrogen Discharge Reactor," J. Appl. Phys. , vol. 86, pp. 134-151, 1999.