MAGNETICALLY ENHANCED MULTIPLE
FREQUENCY CAPACITIVELY COUPLED
PLASMAS: DYNAMICS AND STRATEGIES
Yang Yang and Mark J. Kushner
Iowa State University
Department of Electrical and Computer Engineering
Ames, IA 50011
http://uigelz.ece.iastate.edu
October 2005
GEC05_MJK_01
mjk@iastate.edu
AGENDA
 Introduction to Magnetically Enhanced Reactive Ion Etching
(MERIE) reactors and two-frequency plasma sources.
 Description of Model
 Scaling parameters for single frequency MERIE
 Scaling of 2f-MERIE Properties
 Concluding Remarks
 Acknowledgement: Semiconductor Research Corp., National
Science Foundation, Applied Materials Inc.
GEC05_MJK_02
Iowa State University
Optical and Discharge Physics
MERIE PLASMA SOURCES
 Magnetically Enhanced Reactive Ion Etching plasma sources
use transverse static magnetic fields in capacitively coupled
discharges for confinement to increase plasma density.
 D. Cheng et al, US Patent 4,842,683
 M. Buie et al, JVST A 16, 1464 (1998)
GEC05_MJK_03
Iowa State University
Optical and Discharge Physics
SCALING OF MERIE SYSTEMS
• General scalings: More confinement due to B-field has geometric
and kinetics effects.
•
•
More positive bias with B-field
G. Y. Yeom, et al JAP 65, 3825 (1989)
GEC05_MJK_04
•
•
Larger [e], Te with B-field
S. V. Avtaeva, et al JPD 30, 3000 (1997)
Iowa State University
Optical and Discharge Physics
MULTIPLE FREQUENCY CCPs
• Dual frequency CCPs: goals of separately controlling fluxes and
ion energy distributions; and providing additional tuning of IEDs.
•
Ar/CF4/N2=80/10/10, 30 mTorr
• Even with constant LF voltage, IEDs depend on HF properties due
to change in sheath thickness and plasma potential
•
V. Georgieva and A. Bogaerts, JAP 98, 023308 (2005)
GEC05_MJK_05
Iowa State University
Optical and Discharge Physics
MULTIPLE FREQUENCY MERIEs
• Question to answer in this presentation:
• What unique considerations come to light when combining
magnetic enhancement, such as in a MERIE, with dualfrequency excitation?
• Ground Rules:
• A computational investigation to illuminate physics.
• Ar only in this presentation. Mixtures for another talk.
• Power vs Voltage is important! We are varying power not
voltage.
GEC05_MJK_06
Iowa State University
Optical and Discharge Physics
MODELING OF DUAL FREQUENCY MERIE
 2-dimensional Hybrid Model
 Electron energy equation for bulk electrons
 Monte Carlo Simulation for high energy secondary
electrons from biased surfaces
 Continuity, Momentum and Energy (temperature) equations
for all neutral and ion species.
 Poisson equation for electrostatic potential
 Circuit model for bias
 Monte Carlo Simulation for ion transport to obtain IEADs
GEC05_MJK_07
Iowa State University
Optical and Discharge Physics
ELECTRON ENERGY TRANSPORT
3

5

 ne kTe  / t  S Te   LTe       kTe   Te   Te   S EB
2

2

  qne  e  E  D  ne
S(Te)
L(Te)

(Te)
SEB
=
=
=
=
=
Power deposition from electric fields
Electron power loss due to collisions
Electron flux
Electron thermal conductivity tensor
Power source source from beam electrons
 All transport coefficients are tensors:
  2  Br2

m m
1
A  Ao
  Bz  Br B

2
q  2  B  

   B  Br Bz

i   m 

,
q/m
GEC05_MJK_08
Bz  Br B
 2  B2
 Br  B Bz
 B  Br Bz 

Br  B Bz 
 2  Bz2 
Ao  isotropic
Iowa State University
Optical and Discharge Physics
PLASMA CHEMISTRY, TRANSPORT AND ELECTROSTATICS
 Continuity, momentum and energy equations are solved for each species
(with jump conditions at boundaries)

 Ni
   ( N i vi )  Si  S EB
t


 N i vi  1
qi N i   
 kNiTi     N i vi vi  
E  vi  B     i
t
mi
mi
mj
 

N i N j vi  v j  ij


j
mi  m j
 N i i 
Nq
   Qi  Pi   U i    ( N i U i i ) 
E2
t
mi (   )
mij
N i qi2 2

Es   3
N i N j Rij k B (T j  Ti )   3 N i N j Rij k BT j
mi i
mi  m j
j
j
2
i i i
2
2
i
 Implicit solution of Poisson’s equation


 

   t  t   -  s   qi N i - t   q i  i 
i
i


GEC05_MJK_ 09
Iowa State University
Optical and Discharge Physics
IMPROVEMENTS FOR LARGE MAGNETIC FIELDS
 Poisson’s equation is solved using a semi-emplicit technique
where charge densities are predicted at future times.
  g t    m t 




   t  t   


  t   qi   i t'       j  t  t  
i materials
 e ,ions


 Predictor-corrector methods are used where fluxes at future
times are approximated using past histories or Jacobian
elements are used.

d t  1 2 t 
ion t'    t   t
dt


 df e t  
e t'   f e ne t , t    
 t  t    t 
 d 
GEC05_MJK_10
Iowa State University
Optical and Discharge Physics
MERIE REACTOR
 The model reactor is based on a TEL Design having a
transverse magnetic field.
 K. Kubota et al, US Patent 6,190,495 (2001)
GEC05_MJK_11
Iowa State University
Optical and Discharge Physics
MERIE REACTOR: MODEL REPRESENTATION
Shower Head
HEIGHT (cm)
4
B-Field
Conductive Wafer
2
Powered Substrate
Focus Ring
Pump
0
0
10
RADIUS (cm)
20
 2-D, Cylindrically Symmetric
 Magnetic field is purely radial, an approximation validated
by 2-D Cartesian comparisons.
GEC05_MJK_12
Iowa State University
Optical and Discharge Physics
MERIE: Ar+ DENSITY vs
MAGNETIC FIELD
 Increasing B-field shifts
plasma towards center and
increases density.
 Large B-fields (> 100 G)
decrease density.
 Plasma is localized closer to
wafer.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC05_MJK_13
Iowa State University
Optical and Discharge Physics
MERIE: CONFINEMENT OF IONIZATION
 The localization of plasma density near the powered electrode
with large B-fields is due to the confinement of secondary
electrons and more localized heating of bulk electrons.
 Ionization Sources
 Ionization by secondary
electrons is uniform
across the gap at low Bfield; localized at high
B-field.
 Secondary Electrons
 Ar, 40 mTorr, 100 W, 10 MHz
GEC05_MJK_14
 Bulk Electrons
Iowa State University
Optical and Discharge Physics
MERIE: SHEATH REVERSAL
AND THICKENING
 As the magnetic field
increases, the electrons
become less mobile than ions
across the magnetic field lines.
 The result is a reversal of the
electric field in the sheath and
sheath thickening.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC05_MJK_15
Iowa State University
Optical and Discharge Physics
MERIE dc BIAS,RF VOLTAGE
 The dc bias generally
becomes more positive with
increasing B-field as the
mobility of electrons
decreases relative to ions.
 Constant power, decreasing
ion flux, increasing bias
voltage  More resistive
plasma.
 VPlasma – Vdc decreases with
bias (sheath voltage….)
 Ar, 40 mTorr, 100 W, 10 MHz
GEC05_MJK_16
Iowa State University
Optical and Discharge Physics
Ar+ ENERGY AND ANGLE DISTRIBUTIONS
 The more positive dc bias reduces the sheath potential.
 The resulting IEAD is
lower in energy and
broader.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC05_MJK_17
Iowa State University
Optical and Discharge Physics
2 FREQUENCY MERIE: GEOMETRY
 Ar, 40 mTorr, 300 sccm
 B (radial)
 Base Case Conditions:
 Low Frequency: 5 MHz, 500 W
 High Frequency: 40 MHz, 500 W
GEC05_MJK_18
Iowa State University
Optical and Discharge Physics
2-FREQUENCY CCP (B=0): ELECTRON SOURCES
 Mean free paths are long
and thermal conductivity
is high (and isotropic).
 Te is nearly uniform over
wafer. Bulk ionization
follows electron density.
 Secondary electrons
penetrate through
plasma.
 Ar, 40 mTorr, 300 sccm,
0 G, 5 MHz, 40 MHz
 LF: 500W, 193 V (dc: -22 V)
 HF: 500 W, 128 V
GEC05_MJK_19
Iowa State University
Optical and Discharge Physics
2-FREQUENCY MERIE (B=150G): ELECTRON SOURCES
 Short transverse mean
free paths (anisotropic
transport).
 Te , bulk ionization peak
in sheaths; convect in
parallel direction.
 Secondary electrons are
confined near sheath
(trapping on B-field).
 dc bias more positive;
voltages larger.
 Ar, 40 mTorr, 300 sccm, 150
G, 5 MHz, 40 MHz
 LF: 500W, 202 V (dc: -1 V)
 HF: 500 W, 140 V
GEC05_MJK_20
Iowa State University
Optical and Discharge Physics
ION DENSITIES: 2f-CCP vs 2f-MERIE
 B = 0 G (max 9 x 1010 cm-3)
 B = 150 G (max 1.3 x 1012 cm-3)
 MERIE achieves goal of increasing ion density due to confinement
of beam electrons and slowing transverse diffusion loss.
 Spatial distribution changes due to both transport and materials
effects.
 Ar, 40 mTorr, 300 sccm, 5 MHz, 40 MHz
 LF: 500W, HF: 500 W
GEC05_MJK_21
Iowa State University
Optical and Discharge Physics
2-FREQUENCY CCP (B=0): PLASMA POTENTIAL
 Time dependent
 Low Frequency
 High Frequency
 Sheaths maintain electropositive nature through LF and HF cycles.
 Bulk plasma potential is nearly flat and oscillates with both LF and HF
components.
 Ar, 40 mTorr, 0 G, 5 MHz, 40 MHz
 LF: 500W, 193 V (dc: -22 V)
 HF: 500 W, 128 V
GEC05_MJK_22
Iowa State University
Optical and Discharge Physics
2-FREQUENCY MERIE (B=150G): PLASMA POTENTIAL
 Time dependent
 Low Frequency
 High Frequency
 Sheaths are reversed through portions of both LF and HF cycles.
 Bulk electric field is significant to overcome low transverse mobility.
Plasma potential oscillates with both LF and HF components.
 Ar, 40 mTorr, 150 G, 5 MHz, 40 MHz
 LF: 500W, 202 V (dc: -1 V)
 HF: 500 W, 140 V
GEC05_MJK_23
Iowa State University
Optical and Discharge Physics
2f-CCP vs 2f-MERIE: ION FLUXES
 B=0G
 B = 150 G
 Larger electric fields to transport electrons results in significantly
larger variations in ion flux through cycles.
GEC05_MJK_24
 Ar, 40 mTorr, 5 MHz, 40 MHz
 LF: 500W, HF: 500 W
Iowa State University
Optical and Discharge Physics
MATERIALS AFFECT UNIFORMITY: PLASMA POTENTIAL
 B=0 G
 B = 150 G
 Surface potential of dielectrics is out
of phase with plasma potential.
 Ar, 40 mTorr, 5 MHz, 40 MHz
 LF: 500W, HF: 500 W
GEC05_MJK_25
Animation-GIF
Shower Head
4
HEIGHT (cm)
 Low mobility of electrons prevent
“steady state” charging of dielectrics.
B-Field
Conductive Wafer
2
Powered Substrate
Focus Ring
Pump
0
0
View
10
RADIUS (cm)
20
Iowa State University
Optical and Discharge Physics
SECONDARY EMISSION: IMPORTANT TO SCALING
 B=0G
 B = 100 G
 Scaling of ion flux with HF power is sublinear though better w/B-field.
 Increasing HF power reduces LF voltage for constant power.
 Poor utilization of secondary electrons.
 Power lost to excitation that does not translate to ionization.
GEC05_MJK_26
 Ar, 40 mTorr, 5 MHz, 40 MHz
 LF: 500W, HF: 500 W
Iowa State University
Optical and Discharge Physics
PLASMA PARAMETERS: MERIE B=0, 100 G, V=constant
340 V (p-p)
 B=0
400 V (p-p)
 B = 100 G
 B=0: Increasing  produces nominal increase in ion density and
decrease in power as secondary electrons are poorly utilized.
 B=100 G: Increasing  produces more ionization, larger ion
density and increase in power.
 Ar, 100 mTorr, 10 MHz
GEC05_MJK_27
Iowa State University
Optical and Discharge Physics
IEDS vs B-FIELD
 IEDs broaden and move
to lower energy with
increase in B-field and
more positive dc bias.
 Reversal of sheaths
slows ions, broaden
angle.
 Ar, 40 mTorr, 300 sccm, 150
G, 5 MHz, 40 MHz
 LF: 500W
 HF: 500 W
GEC05_MJK_19
GEC05_MJK_28
Iowa State University
Optical and Discharge Physics
IEDS vs LF POWER
 Ability to control IED
with LF power is
compromised in MERIE.
 Redistribution of voltage
dropped across sheath
and bulk
 Change in angular
distribution.
 Ar, 40 mTorr, 300 sccm,
 5 MHz, 40 MHz
 HF: 500 W
Iowa State University
Optical and Discharge Physics
GEC05_MJK_29
VOLTAGES vs HIGH FREQUENCY POWER
 B=0
 B = 100 G
 Maximum ion energy is V(LF)+V(HF)-V(dc).
 Increasing HF power increases V(HF) and ion current. For
constant LF power, V(LF) decreases.
 The maximum IED depends on relative increase in V(HF) and
decrease in V(LF). Except that…..
GEC05_MJK_30
 Ar, 40 mTorr, 5 MHz, 40 MHz
 LF: 500W
Iowa State University
Optical and Discharge Physics
VOLTAGES vs HIGH FREQUENCY POWER
 LF Sheath Potential
 B = 100 G
 More resistive plasma and field reversal in HF sheath consum
voltage otherwise be available for ion acceleration in LF sheath.
 The result is a decrease in sheath voltage with a B-field.
 Ar, 40 mTorr, 5 MHz, 40 MHz
 LF: 500W
GEC05_MJK_31
Iowa State University
Optical and Discharge Physics
IEDs vs HIGH FREQUENCY POWER
 B=0
 B = 150 G
 It appears that ability to maintain IED while changing HF power
is better without B-field.
 That is generally true….but you just got lucky.
GEC05_MJK_32
 Ar, 40 mTorr, 5 MHz, 40 MHz
 LF: 500W
Iowa State University
Optical and Discharge Physics
IEDS vs LF FREQUENCY
B=0
 IED narrows in energy
as LF decreases while
maintaining nearly the
same average energy.
 Scaling does not
significantly differ from
single frequency
system.
 Ar, 40 mTorr, 300 sccm,
 LF: 500 W
 HF 40 MHz: 500 W
GEC05_MJK_33
Iowa State University
Optical and Discharge Physics
PLASMA POTENTIAL vs
LF FREQUENCY (B=100 G)
 As the low frequency
increases…
 The fraction of the cycle
during which the LF sheath
is reversed increases.
 LF = 2.5 MHz
 Field reversal occurs in the
bulk as well as sheath to
attract sufficient electrons
across B-field.
 More phase dependent.
 Ar, 40 mTorr, 300 sccm,
 LF: 500 W
 HF 40 MHz: 500 W
 LF = 40 MHz
GEC05_MJK_34
Iowa State University
Optical and Discharge Physics
IEDS vs LF FREQUENCY
B=100 G
 As the low frequency
increases…
 The window for allowing ions
out of plasma narrows.
 The IED narrows and
broadens to a greater degree
than without B-field.
 Ar, 40 mTorr, 300 sccm,
 4 MHz, 40 MHz
 HF: 500 W
GEC05_MJK_35
Iowa State University
Optical and Discharge Physics
CONCLUDING REMARKS
 Scaling laws for an industrial MERIE reactor using 2-frequency
excitation were investigated.
 Reversal of sheaths LF and HF electrodes dominate behavior.
 IED shifted to lower energy
 Broadened in angle
 Increasing (more positive) bias
 Sensitivity to sheath reversal increases with increasing LF.
 Ability to maintain constant IED when varying HF power is
diminished in MERIE system
 Larger voltage drop across bulk plasma and HF sheath
leaves less voltage at LF electrode.
 Larger plasma resistance with B-field increases RC time
constant for charging surfaces thereby impacting uniformity.
GEC05_MJK_36
Iowa State University
Optical and Discharge Physics