1. WAVE AND ELECTROSTATIC COUPLING IN 2-FREQUENCY CAPACITIVELY COUPLED PLASMAS UTILIZING A FULL MAXWELL SOLVER* Yang Yang a) and Mark J. Kushner b) a) Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011, USA yangying@iastate.edu b) Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, MI 48109, USA mjkush@umich.edu http://uigelz.eecs.umich.edu October 2008 YY_MJK_AVS2008_01 * Work supported by Semiconductor Research Corp., Applied Materials and Tokyo Electron Ltd.

2. AGENDA  Wave effects in 2-frequency capacitively coupled plasma (2f- CCP) sources  Description of the model  Base cases: Ar/CF 4 = 90/10, HF = 10-150 MHz  Scaling with:  Fraction of CF 4  HF power  Concluding remarks YY_MJK_AVS2008_02 University of Michigan Institute for Plasma Science and Engineering

3. WAVE EFFECTS IN HF-CCP SOURCES  Wave effects (i.e., propagation, constructive and destructive interference) in CCPs become important with increasing frequency and wafer size.  Wave effects can significantly affect the spatial distribution of power deposition and reactive fluxes. G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006) YY_MJK_AVS2008_03 University of Michigan Institute for Plasma Science and Engineering

4.  Relative contributions of wave and electrostatic edge effects determine the plasma distribution.  Plasma uniformity will be a function of frequency, mixture, power…  Results from a computational investigation of coupling of wave and electrostatic effects in two-frequency CCPs will be discussed :  Plasma properties  Radial variation of ion energy and angular distributions (IEADs) onto wafer GOALS OF THE INVESTIGATION YY_MJK_AVS2008_04 University of Michigan Institute for Plasma Science and Engineering

5.  Full-wave Maxwell solvers are challenging due to coupling between electromagnetic (EM) and sheath forming electrostatic (ES) fields.  EM fields are generated by rf sources and plasma currents while ES fields originate from charges.  We separately solve for EM and ES fields and sum the fields for plasma transport.  Boundary conditions (BCs):  EM field: Determined by rf sources.  ES field: Determined by blocking capacitor (DC bias) or applied DC voltages. METHODOLOGY OF THE MAXWELL SOLVER YY_MJK_AVS2008_05 University of Michigan Institute for Plasma Science and Engineering

6.  Launch rf fields where power is fed into the reactor.  For cylindrical geometry, TM mode gives E r, E z and H .  Solve EM fields using FDTD techniques with Crank-Nicholson scheme on a staggered mesh:  Mesh is sub-divided for numerical stability. FIRST PART: EM SOLUTION YY_MJK_AVS2008_06 University of Michigan Institute for Plasma Science and Engineering

7.  Solve Poisson ’ s equation semi-implicitly:  Boundary conditions on metal: self generated dc bias by plasma or applied dc voltage.  Implementation of this solver:  Specify the location that power is fed into the reactor.  Addressing multiple frequencies in time domain for arbitrary geometry.  First order BCs for artificial or nonreflecting boundaries (i.e., pump ports, dielectric windows). SECOND PART: ES SOLUTION YY_MJK_AVS2008_07 University of Michigan Institute for Plasma Science and Engineering

8. HYBRID PLASMA EQUIPMENT MODEL (HPEM)  Electron Energy Transport Module:  Electron Monte Carlo Simulation provides EEDs of bulk electrons  Separate MCS used for secondary, sheath accelerated electrons  Fluid Kinetics Module:  Heavy particle and electron continuity, momentum, energy  Maxwell’s Equation  Plasma Chemistry Monte Carlo Module:  IEADs onto wafer YY_MJK_AVS2008_08 E, N Fluid Kinetics Module Fluid equations (continuity, momentum, energy) Maxwell Equations Te,S, μ Electron Energy Transport Module Plasma Chemistry Monte Carlo Module University of Michigan Institute for Plasma Science and Engineering

9. REACTOR GEOMETRY  2D, cylindrically symmetric.  Ar/CF 4, 50 mTorr, 400 sccm  Base conditions  Ar/CF 4 =90/10  HF upper electrode: 10-150 MHz, 300 W  LF lower electrode: 10 MHz, 300 W  Specify power, adjust voltage. YY_MJK_AVS2008_09  Main species in Ar/CF 4 mixture  Ar, Ar*, Ar +  CF 4, CF 3, CF 2, CF, C 2 F 4, C 2 F 6, F, F 2  CF 3 +, CF 2 +, CF +, F +  e, CF 3 -, F - University of Michigan Institute for Plasma Science and Engineering

10. Center Edge IEADs INCIDENT ON WAFER: 10/150 MHz YY_MJK_AVS2008_10  Total Ion  CF 3 +  Center  Edge  IEADs are separately collected over center&edge of wafer.  From center to edge, IEADs downshifted in energy, broadened in angle.  Ar/CF 4 =90/10, 50 mTorr, 400 sccm  HF: 150 MHz/300 W  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering

11. Center Edge IEADs INCIDENT ON WAFER: 10/100 MHz YY_MJK_AVS2008_11  Total Ion  CF 3 +  Center  Edge  Ar/CF 4 =90/10, 50 mTorr, 400 sccm  HF: 100 MHz/300 W  LF: 10 MHz/300 W  IEADs undergo less change from center to edge than 10/150 MHz. University of Michigan Institute for Plasma Science and Engineering

12. Center Edge IEADs INCIDENT ON WAFER: 10/10 MHz YY_MJK_AVS2008_12  Total Ion  CF 3 +  Center  Edge  Ar/CF 4 =90/10, 50 mTorr, 400 sccm  HF: 10 MHz/300 W  LF: 10 MHz/300 W  Less radial change compare to 10/150 MHz case.  Why radial uniformity of IEADs changes with HF ?  Many factors may account for variation: sheath thickness, sheath potential, mixing of ions … University of Michigan Institute for Plasma Science and Engineering

13. ELECTRON DENSITY: Ar/CF 4 = 90/10  Changing HF results in different [e] profile, thereby giving different radial distribution of sheath thickness, potential...  [e] profile is determined by wave and electrostatic coupling.  HF = 150 MHz, Max = 1.1 x 10 11 cm -3  HF = 50 MHz, Max = 5.9 x 10 10 cm -3 YY_MJK_AVS2008_13 University of Michigan Institute for Plasma Science and Engineering  Ar/CF 4 =90/10  50 mTorr, 400 sccm  HF: 10-150 MHz/300 W  LF: 10 MHz/300 W

14. AXIAL EM FIELD IN HF SHEATH  HF = 50 MHz, Max = 410 V/cm  HF = 150 MHz, Max = 355 V/cm YY_MJK_AVS2008_14  |E zm | = Magnitude of axial EM field’s first harmonic at HF.  No electrostatic component in E zm : purely electromagnetic.  150 MHz: center peaked due to constructive interference of plasma shortened wavelengths.  50 MHz: Small edge peak.  Ar/CF 4 =90/10, 50 mTorr, 400 sccm  HF: 10-150 MHz/300 W  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering

15. AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz  |E Z | in LF(10 MHz) Sheath, Max = 1700 V/cm YY_MJK_AVS2008_15a  Significant change of |E z | across HF sheath as evidence of traveling wave.  HF source also modulates E-field in LF sheath. University of Michigan Institute for Plasma Science and Engineering  |E Z | in HF (150 MHz) Sheath, Max = 1500 V/cm  Ar/CF 4 =90/10  50 mTorr, 400 sccm  HF: 150 MHz/300 W  LF: 10 MHz/300 W  ANIMATION SLIDE-GIF

16. LF CYCLE AVERAGED AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz  |E Z | in LF(10 MHz) Sheath, Max = 750 V/cm YY_MJK_AVS2008_15b  Significant change of |E z | across HF sheath as evidence of constructive interference. University of Michigan Institute for Plasma Science and Engineering  |E Z | in HF (150 MHz) Sheath, Max = 450 V/cm  Ar/CF 4 =90/10  50 mTorr, 400 sccm  HF: 150 MHz/300 W  LF: 10 MHz/300 W

17. SPATIAL DISTRIBUTION OF NEGATIVE IONS YY_MJK_AVS2008_16  Ar/CF 4 =90/10  50 mTorr, 400 sccm  Finite wavelength effect at 150 MHz populates energetic electrons in the reactor center.  More favorable to attachment processes (threshold energies  3 eV) than ionization (threshold energies  11 eV).  [CF 3 - + F - ] increases in the center.  [CF 3 - + F - ]  HF: 10-150 MHz/300 W  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering  HF = 150 MHz, Max = 1.2 x 10 11 cm -3

18. SPATIAL DISTRIBUTION OF POSITIVE IONS University of Michigan Optical and Discharge Physics YY_MJK_AVS2008_17  Ar/CF 4 =90/10  50 mTorr, 400 sccm  Difference in radial profiles for different ions.  Different sheath transiting time due to differences in mass and sheath thickness.  Eventually translates to radial non-uniformity of IEADs.  CF 3 +  Ar +  HF: 10-150 MHz/300 W  LF: 10 MHz/300 W

19. ELECTRON IMPACT IONIZATION SOURCE FUNCTION University of Michigan Optical and Discharge Physics  HF = 10 MHz, Max = 2.1 x 10 15 cm -3 s -1  HF = 50 MHz, Max = 6.3 x 10 15 cm -3 s -1  HF = 100 MHz, Max = 4.2 x 10 15 cm -3 s -1  HF = 150 MHz, Max = 3.8 x 10 16 cm -3 s -1 YY_MJK_AVS2008_18  Source from bulk and secondary electrons.  50 MHz: bulk ionization from Ohmic heating, edge peaked due to electrostatic field enhancement..  150 MHz: ionization dominated by sheath accelerated electrons (stochastic heating).  100 MHz: has both features, but edge effect dominates.  Ar/CF 4 =90/10  50 mTorr, 400 sccm  HF: 10-150 MHz/300 W  LF: 10 MHz/300 W

20. ION FLUXES INCIDENT ON WAFER YY_MJK_AVS2008_19  Ar/CF 4 =90/10  50 mTorr, 400 sccm  Uniformity of incident ion fluxes and their IEADs are both determined by plasma spatial distribution.  Relative uniform fluxes and IEADs at 100 MHz.  CF 3 + Flux  HF: 10-150 MHz/300 W  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering  Total Ion Flux

21. CenterEdge IEADs INCIDENT ON WAFER: Ar/CF 4 = 80/20 YY_MJK_AVS2008_20  Total Ion  CF 3 +  Inner  Outer  Less radial variation across the wafer.  More radial uniformity of sheath thickness and potential counts.  Implicates adding CF 4 improves plasma uniformity.  Ar/CF 4 =80/20, 50 mTorr, 400 sccm  HF: 150 MHz/300 W  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering

22. SCALING WITH FRACTION OF CF 4 IN Ar/CF 4 : 10/150 MHz  Pure Ar, Max = 3.8 x 10 11 cm -3  10% CF 4, Max = 1.1 x 10 11 cm -3  20% CF 4, Max = 4.8 x 10 10 cm -3  30% CF 4, Max = 4.4 x 10 10 cm -3  50 mTorr, 400 sccm  HF: 150 MHz/300 W  LF: 10 MHz/300 W  With increasing fraction of CF 4 :  [e] decreases thereby decreasing conductivity.  Weakens constructive interference of EM fields by increasing wavelength.  Maximum of [e] shifts towards the HF electrode edge.  Skin depth also increases.  Increasing penetration of EM fields.  More uniform [e] profile results. YY_MJK_AVS2008_21 University of Michigan Institute for Plasma Science and Engineering

23. ION FLUXES INCIDENT ON WAFER: 10/150 MHz YY_MJK_AVS2008_22  50 mTorr, 400 sccm  Uniform [e] profile at 20% CF 4 results in  Radial uniformity of incident ion fluxes.  Uniform radial profile of IEADs.  CF 3 + Flux  Total Ion Flux  HF: 150 MHz/300 W  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering

24. SCALING TO HF POWER: 10/150 MHz YY_MJK_AVS2008_23  Increasing HF power reduces plasma uniformity.  Finite wavelength effect preferentially produces negative ions in the center.  With increasing [e], wave penetration is less affected in the radial direction due to the HF sheath, so [e] peak only moves 2 cm from 300 W to 1000 W.  Ar/CF 4 =90/10  50 mTorr, 400 sccm  HF: 50-150 MHz  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering  1000 W, [CF 3 - + F - ]  [e]

25. IMPACT OF HF POWER ON ION FLUXES ONTO WAFER YY_MJK_AVS2008_24  Non-uniformity of ion fluxes onto the wafer also increases with increasing HF power.  Ar/CF 4 =90/10  50 mTorr, 400 sccm  HF: 50-150 MHz  LF: 10 MHz/300 W University of Michigan Institute for Plasma Science and Engineering  Total Ions Flux

26. Center Edge TOTAL ION IEADs INCIDENT ON WAFER University of Michigan Optical and Discharge Physics YY_MJK_GEC2008_25  300 W  Center  Edge  Outer  More uniform IEADs at higher HF power.  With increasing HF power (increasing [e]), LF voltage decreases to keep LF power constant.  Diminishes radial variation of IEADs.  Ar/CF 4 =90/10, 50 mTorr, 400 sccm  HF: 150 MHz  LF: 10 MHz/300 W  1000 W

27. CONCLUDING REMARKS YY_MJK_AVS2008_26  A full Maxwell solver separately solving for EM and ES fields was developed and incorporated into the HPEM.  For 2f-CCPs sustained in Ar/CF 4 =90/10 mixture,  HF determines wave and electrostatic coupling which, in turn, determines plasma spatial distribution.  Non-uniform IEADs across the wafer at HF =150 MHz due to plasma non-uniformity.  Increasing fraction of CF 4 to 20% results in more uniform plasma profile and IEADs incident on wafer.  At HF = 150 MHz, increasing HF power increases plasma non- uniformity. University of Michigan Institute for Plasma Science and Engineering