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NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY CAPACITIVELY COUPLED PLASMAS*

NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yang Yang and Mark J. Kushner Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011 yangying@iastate.edu mjk@iastate.edu http://uigelz.ece.iastate.edu October 2007.

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NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY CAPACITIVELY COUPLED PLASMAS*

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  1. NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yang Yang and Mark J. Kushner Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011 yangying@iastate.edu mjk@iastate.edu http://uigelz.ece.iastate.edu October 2007 * Work supported by Semiconductor Research Corp., Applied Materials and NSF. YYANG_AVS2007_01

  2. AGENDA • Wave effects in hf capacitively coupled plasma (hf-CCP) sources • Description of the model • Base Case: 160 MHz, single frequency • Scaling of plasma properties with frequency • Scaling of dual frequency CCP (dfCCP) properties in Ar/Cl2 • Concluding Remarks Iowa State University Optical and Discharge Physics YYANG_AVS2007_02

  3. WAVE EFFECTS IN hf-CCP SOURCES • Wave effects in CPPs impact plasma uniformity at high frequencies: • Standing waves due to finite wavelength tend to produce center peaked plasma. • Skin effects due to high electron density tend to produce edge peaked profile. • Electrostatic edge effects still contribute. A. Perret et al, Appl. Phys. Lett. 83, 243(2003) Iowa State University Optical and Discharge Physics YYANG_AVS2007_03

  4. GOALS OF THE INVESTIGATION • Relative contributions of wave and electrostatic edge effects determine plasma distribution. • Electronegative additives complicate issue by changing relationship between power and plasma density. • Plasma uniformity will be a function of frequency, power, mixture… • In this talk, results from a computational investigation will be discussed: • Wave effects on plasma properties in hf-CCPs. • Roles of electronegative gases on uniformity. Iowa State University Optical and Discharge Physics YYANG_AVS2007_04

  5. HYBRID PLASMA EQUIPMENT MODEL (HPEM) • Electron Energy Transport Module: • Electron energy equation with Boltzmann equation derived transport coefficients. • MCS for secondary, sheath accelerated electrons • Fluid Kinetics Module: • Heavy particle and electron continuity, momentum, energy • Maxwell’s Equations in potential form Electron Energy Transport Module Boltzmann equation Te,S,μ Es, N Fluid Kinetics Module Fluid equations (continuity, momentum, energy) Maxwell Equations Iowa State University Optical and Discharge Physics YYANG_AVS2007_05

  6. FULL-WAVE MAXWELL SOLVER • A full-wave Maxwell equation solver has been developed to address finite wavelength wave effects. • Vector potential : • Coulomb Gauge : • With vector and scalar potential, Maxwell equations are: • Scalar potential : • In 2D cylindrical coordinates, , solved on a staggered mesh using sparse matrix techniques. • E field : Iowa State University Optical and Discharge Physics YYANG_AVS2007_06

  7. NUMERICAL REPRESENTATION OF EQUATIONS • Radial vector potential: • Axial vector potential: • Scalar potential: Iowa State University Optical and Discharge Physics YYANG_AVS2007_07

  8. TENSOR TRANSPORT COEFFICIENTS • With azimuthal magnetic field, the electron flux is given by where and are the tensor mobility and diffusivity. and electron momentum transfer collision frequency. • Fluxes of heavy particles given by momentum equations. Iowa State University Optical and Discharge Physics YYANG_AVS2007_08

  9. NORMALIZATION OF SPARSE MATRIX = 0 0 Normalized vector and scalar potentials solved in same matrix. Iowa State University Optical and Discharge Physics YYANG_AVS2007_09

  10. REACTOR GEOMETRY • Ar for single frequency. • Ar/Cl2 dual frequency • Ar, Ar*, Ar+ • Cl2, Cl, Cl* • Cl2+, Cl+, Cl- • e • 2D, cylindrically symmetric. • Ar, 50 mTorr, 200 sccm • Base case: 160 MHz, 300 W (upper electrode) • Specify power, adjust voltage. Iowa State University Optical and Discharge Physics YYANG_AVS2007_10

  11. ELECTRON DENSITY • Maxwell Solution • [e] peaked at center with Maxwell solution (MS) due to finite wave length effect. • With Poisson solution (PS), a flat [e] profile. • Less power penetrates into bulk plasma with MS. • Ar, 50 mTorr, 200 sccm • 160 MHz, 300 W, 48 V • Electrostatic Poisson Solution Iowa State University Optical and Discharge Physics YYANG_AVS2007_11

  12. ELECTRON HEATING • Maxwell Solution • Bulk ionization follows electron density as Te is fairly uniform. • With MS, lower Te obtained in the center due to reduced ohmic heating in high electron density region . • Ar, 50 mTorr, 200 sccm • 160 MHz, 300 W, 48 V • Electrostatic Poisson Solution Iowa State University Optical and Discharge Physics YYANG_AVS2007_12

  13. Maxwell Solution • Axial field CYCLE AVERAGED ELECTRIC FIELD - 170 V/cm – 260 V/cm • With MS, the cycle averaged axial electric field is stronger in the center in sheath region. • As such, standing wave effect mainly enhances stochastic heating in the center. • Relative weak radial electric field in the bulk plasma region. • Radial field - 89 V/cm – 24 V/cm • Electrostatic Poisson Solution • Axial field - 130 V/cm – 250 V/cm • Ar, 50 mTorr, 200 sccm • 160 MHz, 300 W, 48 V Iowa State University Optical and Discharge Physics YYANG_AVS2007_13

  14. Maxwell Solution • Azimuthal Animation Slide POTENTIAL AND MAGNETIC FIELD - 0.07 G – 0.07 G • Symmetric B due to out of phase sheath motion. • Magnitude of B is small and not major contributor here. • Similar scalar potential from MS as electrostatic potential from PS. • Scalar Potential - 61 V – 54 V • Electrostatic Poisson Solution • Potential - 65 V – 45 V • Ar, 50 mTorr, 200 sccm • 160 MHz, 300 W, 48 V Iowa State University Optical and Discharge Physics YYANG_AVS2007_14

  15. Maxwell Solution • Azimuthal CYCLE AVERAGED MAGNETIC FIELD Max = 0.09 G • Symmetric B due to out of phase sheath motion. • Magnitude of B is small and not major contributor here. • Similar scalar potential from MS as electrostatic potential from PS. • Scalar Potential - 14 V – 30 V • Electrostatic Poisson Solution • Potential - 19 V – 25 V • Ar, 50 mTorr, 200 sccm • 160 MHz, 300 W, 48 V Iowa State University Optical and Discharge Physics YYANG_AVS2007_14b

  16. SCALING WITH FREQUENCY • Maxwell Solution • Uniform [e] at 5 MHz for MS, similar to PS. • With increasing frequency, [e] profile undergoes transition from flat at 5 MHz, to edge peaked at intermediate frequencies, to center peaked at 160 MHz. • Wider edge peak with MS at 50 and 100 MHz . • Ar, 50 mTorr • 200 sccm • 300 W Iowa State University Optical and Discharge Physics YYANG_AVS2007_15

  17. Maxwell Solution COMPARISON WITH EXPERIMENT • Line integrated [e] • Ar • 50 mTorr • 200 sccm • Poisson Solution • [e] close to experiments from 5 to 100 MHz; Better match with MS. • PS radial [e] is not sensitive to frequency. G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006) Iowa State University Optical and Discharge Physics YYANG_AVS2007_16

  18. ION FLUX • Maxwell Solution • Electron density • Experiment • Ion saturation current • Ar • 50 mTorr • 200 sccm • MS transitions from uniform to edge peaked to center peaked from 5 MHz to at 160 MHz. • Skin effect and wave effects have different contributions with frequency. • Trends agree with experiment. G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006) Iowa State University Optical and Discharge Physics YYANG_AVS2007_17

  19. 2-FREQUENCY CCP • Ar has center peaked [e] for single frequency (160 MHz/300 W). • dfCCP (PLF=PHF) 10 MHz ionization source has uniform distribution. • Electrons are “seeded” where HF ionization might not occur (near edges) increasing skin effect. • Combined effects dominate over standing wave . • Edge high [e] with a small center peak is produced. • Electron density • Single frequency at 160 MHz, 300 W • Dual frequency • 10/160 MHz, 500/500 W • Ar, 50 mTorr, 200 sccm Iowa State University Optical and Discharge Physics YYANG_AVS2007_18

  20. ELECTRONEGATIVE DISCHARGE: Ar/Cl2 • Ar/Cl2 dual frequency have similar effect of reduced importance of wave effects. • Increasing Cl2 decreases electron density and reduces axial current. • Result is weakening of standing wave effect and skin effect. • 50 mTorr, 200 sccm • LF: 10 MHz/500 W, HF: 160 MHz/ 500 W Iowa State University Optical and Discharge Physics YYANG_AVS2007_19

  21. ELECTRONEGATIVE DISCHARGE: Ar/Cl2 • Electron density • Ar/Cl2 dual frequency • Decreasing importance of wave-effects produce edge-high electron densities. • 50 mTorr, 200 sccm • LF: 10 MHz/500 W HF: 160 MHz/ 500 W Iowa State University Optical and Discharge Physics YYANG_AVS2007_19

  22. Power deposition POWER DEPOSITION • Ar/Cl2 = 80/20, more bulk power deposition due to lower electron density. • Lower [e] produces smaller axial current, smaller Ar, Az and longer wavelength. • Ratio of inductive to capacitive field decreases. • Ratio: inductive to capacitive field • 50 mTorr, 200 sccm • LF: 10 MHz/500 W HF: 160 MHz/ 500 W Iowa State University Optical and Discharge Physics YYANG_AVS2007_20

  23. CONCLUDING REMARKS • A full Maxwell solver was developed and incorporated into HPEM; to resolve wave effects. • Experimental trends of transition of plasma density from flat to edge peaked to center peaked with increasing frequency are reproduced. • At low powers, azimuthal B is not a large contributor to electromagnetic effects. • Standing wave generally increases sheath fields at center of reactor. • With dual frequency excitation, low frequency provides ionization independent of wave effect. Seeding of electrons reduces severity of high frequency wave effect. • Adding Cl2 reduces wave effects by lengthening wavelength and increasing bulk electron heating. Iowa State University Optical and Discharge Physics YYANG_AVS2007_22

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