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WAVE AND ELECTROSTATIC COUPLING
IN 2-FREQUENCY
CAPACITIVELY COUPLED PLASMAS
UTILIZING A FULL MAXWELL SOLVER*
Yang Yanga) and Mark J. Kushnerb)
a)Department
of Electrical and Computer Engineering
Iowa State University, Ames, IA 50011, USA
[email protected]
b)Department
of Electrical Engineering and Computer Science
University of Michigan, Ann Arbor, MI 48109, USA
[email protected]
http://uigelz.eecs.umich.edu
October 2008
* Work supported by Semiconductor Research Corp., Applied
Materials and Tokyo Electron Ltd.
YY_MJK_AVS2008_01
AGENDA
 Wave effects in 2-frequency capacitively coupled plasma (2fCCP) sources
 Description of the model
 Base cases: Ar/CF4 = 90/10, HF = 10-150 MHz
 Scaling with:
 Fraction of CF4
 HF power
 Concluding remarks
YY_MJK_AVS2008_02
University of Michigan
Institute for Plasma Science
and Engineering
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
GOALS OF THE INVESTIGATION
 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
YY_MJK_AVS2008_04
University of Michigan
Institute for Plasma Science
and Engineering
METHODOLOGY OF THE MAXWELL SOLVER
 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. E  Em  
 Boundary conditions (BCs):
 EM field: Determined by rf sources.
 ES field: Determined by blocking capacitor (DC bias) or
applied DC voltages.
YY_MJK_AVS2008_05
University of Michigan
Institute for Plasma Science
and Engineering
FIRST PART: EM SOLUTION
 Launch rf fields where power is fed into the reactor.
 For cylindrical geometry, TM mode gives Er , Ez and H .
 Solve EM fields using FDTD techniques with Crank-Nicholson
scheme on a staggered mesh:
H 
Er E z

  0
z
r
t

H 
E
 J r   0 r r
z
t
1  rH  
E
 J z   0 r z
r r
t
 i 1, j 1
 i , j 1
Eri 1, j
Ezi , j
B i , j
Ezi 1, j
 i, j
Eri , j
 i 1, j
 Mesh is sub-divided for numerical stability.
YY_MJK_AVS2008_06
University of Michigan
Institute for Plasma Science
and Engineering
SECOND PART: ES SOLUTION
 Solve Poisson’s equation semi-implicitly:
d t , t  t 
  (t  t )   t  
t
dt
 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).
YY_MJK_AVS2008_07
University of Michigan
Institute for Plasma Science
and Engineering
HYBRID PLASMA EQUIPMENT MODEL (HPEM)
Electron Energy
Transport
Module
Te,S,μ
E, N
Fluid
Kinetics Module
Fluid equations
(continuity,
momentum,
energy)
Maxwell
Equations
 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
Plasma Chemistry
Monte Carlo
Module
YY_MJK_AVS2008_08
University of Michigan
Institute for Plasma Science
and Engineering
REACTOR GEOMETRY
 2D, cylindrically symmetric.
 Ar/CF4, 50 mTorr, 400 sccm
 Base conditions
 Ar/CF4 =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/CF4
mixture
 Ar, Ar*, Ar+
 CF4, CF3, CF2, CF, C2F4,
C2F6, F, F2
 CF3+, CF2+, CF+, F+
 e, CF3-, FUniversity of Michigan
Institute for Plasma Science
and Engineering
IEADs INCIDENT ON WAFER: 10/150 MHz
Center
 Total Ion
 Center
 Edge
Edge
 CF3
 Center
+
 Edge
 IEADs are separately
collected over
center&edge of wafer.
 From center to edge,
IEADs downshifted in
energy, broadened in
angle.
 Ar/CF4=90/10, 50 mTorr, 400 sccm
 HF: 150 MHz/300 W
 LF: 10 MHz/300 W
YY_MJK_AVS2008_10
University of Michigan
Institute for Plasma Science
and Engineering
IEADs INCIDENT ON WAFER: 10/100 MHz
Center
 Total Ion
 Center
 Edge
Edge
 CF3+
 Center
 Edge
 IEADs undergo less
change from center to
edge than 10/150 MHz.
 Ar/CF4=90/10, 50 mTorr, 400 sccm
 HF: 100 MHz/300 W
 LF: 10 MHz/300 W
YY_MJK_AVS2008_11
University of Michigan
Institute for Plasma Science
and Engineering
IEADs INCIDENT ON WAFER: 10/10 MHz
Center
 Total Ion
 Center
 Edge
Edge
 CF3+
 Center
 Edge
 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 …
 Ar/CF4=90/10, 50 mTorr, 400 sccm
 HF: 10 MHz/300 W
 LF: 10 MHz/300 W
YY_MJK_AVS2008_12
University of Michigan
Institute for Plasma Science
and Engineering
ELECTRON DENSITY: Ar/CF4 = 90/10
 HF = 50 MHz, Max = 5.9 x 1010 cm-3
 HF = 150 MHz, Max = 1.1 x 1011 cm-3
 Ar/CF4=90/10
 50 mTorr, 400 sccm
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 HF: 10-150 MHz/300 W
 LF: 10 MHz/300 W
 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.
University of Michigan
Institute for Plasma Science
and Engineering
AXIAL EM FIELD IN HF SHEATH
 HF = 50 MHz, Max = 410 V/cm
 Ar/CF4=90/10, 50 mTorr, 400 sccm
 HF: 10-150 MHz/300 W
 LF: 10 MHz/300 W
 HF = 150 MHz, Max = 355 V/cm
 |Ezm| = Magnitude of axial EM field’s first harmonic at HF.
 No electrostatic component in Ezm: purely electromagnetic.
 150 MHz: center peaked due to constructive interference of plasma
shortened wavelengths.
 50 MHz: Small edge peak.
YY_MJK_AVS2008_14
University of Michigan
Institute for Plasma Science
and Engineering
AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz
 |EZ| in HF (150 MHz) Sheath, Max = 1500 V/cm
 ANIMATION SLIDE-GIF
 |EZ| in LF(10 MHz) Sheath, Max = 1700 V/cm
 Significant change of |Ez| across HF sheath as evidence of traveling
wave.
 HF source also modulates E-field in LF sheath.
 Ar/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_15a
 HF: 150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
LF CYCLE AVERAGED
AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz
 |EZ| in HF (150 MHz) Sheath, Max = 450 V/cm
 |EZ| in LF(10 MHz) Sheath, Max = 750 V/cm
 Significant change of |Ez| across HF sheath as evidence of
constructive interference.
 Ar/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_15b
 HF: 150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
SPATIAL DISTRIBUTION OF NEGATIVE IONS
 [CF3- + F-]
 HF = 150 MHz, Max = 1.2 x 1011 cm-3
 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).
 [CF3- + F-] increases in the center.
 Ar/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_16
 HF: 10-150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
SPATIAL DISTRIBUTION OF POSITIVE IONS
 Ar+
 CF3+
 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.
 Ar/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_17
 HF: 10-150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Optical and Discharge Physics
ELECTRON IMPACT IONIZATION SOURCE FUNCTION
 HF = 10 MHz, Max = 2.1 x 1015 cm-3s-1
 HF = 50 MHz, Max = 6.3 x 1015 cm-3s-1
 HF = 100 MHz, Max = 4.2 x 1015 cm-3s-1
 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.
 HF = 150 MHz, Max = 3.8 x 1016 cm-3s-1
 Ar/CF4=90/10
 50 mTorr, 400 sccm
 HF: 10-150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Optical and Discharge Physics
YY_MJK_AVS2008_18
ION FLUXES INCIDENT ON WAFER
 Total Ion Flux
 CF3+ Flux
 Uniformity of incident ion fluxes and their IEADs are both
determined by plasma spatial distribution.
 Relative uniform fluxes and IEADs at 100 MHz.
 Ar/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_19
 HF: 10-150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
IEADs INCIDENT ON WAFER: Ar/CF4 = 80/20
Center
Edge
 Total Ion
 Inner
 Outer
 Inner
 CF3+
 Outer
 Less radial variation
across the wafer.
 More radial uniformity
of sheath thickness
and potential counts.
 Implicates adding CF4
improves plasma
uniformity.
 Ar/CF4=80/20, 50 mTorr, 400 sccm
 HF: 150 MHz/300 W
 LF: 10 MHz/300 W
YY_MJK_AVS2008_20
University of Michigan
Institute for Plasma Science
and Engineering
SCALING WITH FRACTION OF CF4 IN Ar/CF4: 10/150 MHz
 Pure Ar, Max = 3.8 x 1011 cm-3
 10% CF4, Max = 1.1 x 1011 cm-3
 20% CF4, Max = 4.8 x 1010 cm-3
 30% CF4, Max = 4.4 x 1010 cm-3
 With increasing fraction of CF4:
 [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.
 50 mTorr, 400 sccm
YY_MJK_AVS2008_21
 HF: 150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
ION FLUXES INCIDENT ON WAFER: 10/150 MHz
 Total Ion Flux
 CF3+ Flux
 Uniform [e] profile at 20% CF4 results in
 Radial uniformity of incident ion fluxes.
 Uniform radial profile of IEADs.
 50 mTorr, 400 sccm
YY_MJK_AVS2008_22
 HF: 150 MHz/300 W
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
SCALING TO HF POWER: 10/150 MHz
 [e]
 1000 W, [CF3- + F-]
 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/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_23
 HF: 50-150 MHz
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
IMPACT OF HF POWER ON
ION FLUXES ONTO WAFER
 Total Ions Flux
 Non-uniformity of ion fluxes onto the wafer also increases with
increasing HF power.
 Ar/CF4=90/10
 50 mTorr, 400 sccm
YY_MJK_AVS2008_24
 HF: 50-150 MHz
 LF: 10 MHz/300 W
University of Michigan
Institute for Plasma Science
and Engineering
TOTAL ION IEADs INCIDENT ON WAFER
Center
 300 W
 Center
 Edge
Edge
 1000 W
 Center
 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/CF4=90/10, 50 mTorr, 400 sccm
 HF: 150 MHz
 LF: 10 MHz/300 W
University of Michigan
Optical and Discharge Physics
YY_MJK_GEC2008_25
CONCLUDING REMARKS
 A full Maxwell solver separately solving for EM and ES fields was
developed and incorporated into the HPEM.
 For 2f-CCPs sustained in Ar/CF4=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 CF4 to 20% results in more uniform plasma
profile and IEADs incident on wafer.
 At HF = 150 MHz, increasing HF power increases plasma nonuniformity.
YY_MJK_AVS2008_26
University of Michigan
Institute for Plasma Science
and Engineering