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 YYANG_AVS2007_01 * Work supported by Semiconductor Research Corp., Applied Materials and NSF.

2. Iowa State University Optical and Discharge Physics 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/Cl 2  Concluding Remarks YYANG_AVS2007_02

3. Iowa State University Optical and Discharge Physics WAVE EFFECTS IN hf-CCP SOURCES YYANG_AVS2007_03 A. Perret et al, Appl. Phys. Lett. 83, 243(2003)  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.

4.  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 GOALS OF THE INVESTIGATION

5. Iowa State University Optical and Discharge Physics YYANG_AVS2007_05 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 E s, N Fluid Kinetics Module Fluid equations (continuity, momentum, energy) Maxwell Equations Te,S, μ Electron Energy Transport Module Boltzmann equation

6. Iowa State University Optical and Discharge Physics FULL-WAVE MAXWELL SOLVER YYANG_AVS2007_06  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:  In 2D cylindrical coordinates,, solved on a staggered mesh using sparse matrix techniques.  E field :  Scalar potential :

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

8. Iowa State University Optical and Discharge Physics YYANG_AVS2007_08 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.

9. Iowa State University Optical and Discharge Physics YYANG_AVS2007_09 NORMALIZATION OF SPARSE MATRIX  Normalized vector and scalar potentials solved in same matrix. = 00

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

11. ELECTRON DENSITY YYANG_AVS2007_11 Iowa State University Optical and Discharge Physics  [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  Maxwell Solution  Electrostatic Poisson Solution

12. ELECTRON HEATING YYANG_AVS2007_12 Iowa State University Optical and Discharge Physics  Bulk ionization follows electron density as T e is fairly uniform.  With MS, lower T e 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  Maxwell Solution  Electrostatic Poisson Solution

13. YYANG_AVS2007_13 Iowa State University Optical and Discharge Physics  Maxwell Solution  Axial field  Electrostatic Poisson Solution - 170 V/cm – 260 V/cm  Radial field - 89 V/cm – 24 V/cm  Axial field - 130 V/cm – 250 V/cm CYCLE AVERAGED ELECTRIC FIELD  Ar, 50 mTorr, 200 sccm  160 MHz, 300 W, 48 V  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.

14. YYANG_AVS2007_14 Iowa State University Optical and Discharge Physics  Maxwell Solution  Azimuthal - 0.07 G – 0.07 G  Scalar Potential - 61 V – 54 V  Electrostatic Poisson Solution  Potential - 65 V – 45 V  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. Animation Slide POTENTIAL AND MAGNETIC FIELD  Ar, 50 mTorr, 200 sccm  160 MHz, 300 W, 48 V

15. YYANG_AVS2007_14b Iowa State University Optical and Discharge Physics  Maxwell Solution  Azimuthal Max = 0.09 G  Scalar Potential - 14 V – 30 V  Electrostatic Poisson Solution  Potential - 19 V – 25 V CYCLE AVERAGED MAGNETIC FIELD  Ar, 50 mTorr, 200 sccm  160 MHz, 300 W, 48 V  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.

16. Iowa State University Optical and Discharge Physics SCALING WITH FREQUENCY YYANG_AVS2007_15  Maxwell Solution  Ar, 50 mTorr  200 sccm  300 W  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.

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

18. Iowa State University Optical and Discharge Physics ION FLUX YYANG_AVS2007_17  Ar  50 mTorr  200 sccm  Maxwell Solution  Electron density  Experiment  Ion saturation current G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006)  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.

19. Iowa State University Optical and Discharge Physics YYANG_AVS2007_18 2-FREQUENCY CCP  Ar, 50 mTorr, 200 sccm  Electron density  Single frequency at 160 MHz, 300 W  Dual frequency  10/160 MHz, 500/500 W  Ar has center peaked [e] for single frequency (160 MHz/300 W).  dfCCP (P LF =P HF ) 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.

20. Iowa State University Optical and Discharge Physics YYANG_AVS2007_19  Ar/Cl 2 dual frequency have similar effect of reduced importance of wave effects.  Increasing Cl 2 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 ELECTRONEGATIVE DISCHARGE: Ar/Cl 2

21. Iowa State University Optical and Discharge Physics YYANG_AVS2007_19 ELECTRONEGATIVE DISCHARGE: Ar/Cl 2  Electron density  Ar/Cl 2 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

22. Iowa State University Optical and Discharge Physics YYANG_AVS2007_20 POWER DEPOSITION  Ar/Cl 2 = 80/20, more bulk power deposition due to lower electron density.  Lower [e] produces smaller axial current, smaller A r, A z and longer wavelength.  Ratio of inductive to capacitive field decreases.  Power deposition  Ratio: inductive to capacitive field  50 mTorr, 200 sccm  LF: 10 MHz/500 W HF: 160 MHz/ 500 W

23. Iowa State University Optical and Discharge Physics YYANG_AVS2007_22 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 Cl 2 reduces wave effects by lengthening wavelength and increasing bulk electron heating.