ION ENERGY DISTRIBUTIONS IN
INDUCTIVELY COUPLED PLASMAS HAVING A
BIASED BOUNDARY ELECTRODE*
Michael D. Logue and Mark J. Kushner
Dept. of Electrical Engineering and Computer Science
University of Michigan, Ann Arbor, MI 48109, USA
mdlogue@umich.edu, mjkush@umich.edu
Hyungjoo Shin, Weiye Zhu, Lin Xu, Vincent M. Donnelly,
and Demetre J. Economou
University of Houston, Department of Chemical & Biomolecular
Engineering, Houston, TX 77204
November 2011
*
Work supported by SRC and US Dept. of Energy Office of Fusion Energy Sciences
GECNov2011
AGENDA
 Control Of Ion Distribution Functions
 Description of the Model and Geometry
 Ion Energy Distributions (IEDs) and Plasma Parameters for Pulsed ICP
 Pulsed ICP With Constant DC Boundary Electrode (BE) Bias
 Pulsed ICP With Pulsed DC Boundary Electrode (BE) Bias
 Concluding Remarks
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.
CONTROL OF ION DISTRIBUTION FUNCTIONS
 In plasma materials processing there is a need to
control the ion energy distributions (IEDs) to surfaces
with increasing precision.
 A recent development controlling of IEDs in inductively
coupled plasmas (ICPs) is use of a boundary electrode.
 A dc or pulsed dc bias to the boundary electrode shifts
the quasi-dc plasma potential and in turn the peak in the
IED incident onto grounded surfaces.
 Using results from a computational investigation, the
effect of pressure and BE bias (both dc and pulsed dc)
on plasma parameters and IEDs will be discussed.
 Example: Simulated IEDs and etch profiles for
Ar/Cl2=80/20, 10 mTorr, 300 W peak ICP power, 100 W
peak bias power, and 5 kHz pulse frequency, Duty
Cycle=50%
GECNov2011
 Agarwal, J. Vac. Sci. Technol. A, Vol 29 (2011)
University of Michigan
Institute for Plasma Science & Engr.
DESCRIPTION OF HPEM

 r 

E r ,  ,

Br , z r ,  

je r , 


k r , Te r 

S r 

S r 

ES ( r , z ,  )


Er , z r , N i r ,


ne r , Ti r 
 Modular simulator that combines fluid and kinetic approaches.
 Resolves cycle-dependent phenomena while using time-slicing
techniques to advance to the steady state.
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.

HPEM-EQUATIONS SOLVED - E r ,  
 Maxwell’s Equations – Frequency Domain Wave Equation



2

1
 1    E  J plasma  J antenna
    E      E  

2
t
t





 



E r , t   E r  expit , J antenna r , t   J r ,  

 


J plasma r ,     ion  E r ,    J e r ,  MCS
  

 Azimuthal antenna currents – retain only E, Brz
 Plasma currents
 Collisional ion currents
 Kinetically derived non-local electron currents capture
nonlocal effects.
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.

HPEM-EQUATIONS SOLVED - f  , r , 
 Electron Energy Distributions – Electron Monte Carlo Simulation
 
f v , r , t 

t
   
  
 
 
 
q Erz r   E r ,    v  Brz r ,  

 f v , r , t  
 v f v , r , t  
v f v , r , t   

m
t

c


 Cycle dependent electrostatic fields
 Phase dependent electromagnetic fields
 Electron-electron collisions using particle-mesh algorithm
 Phase resolved electron currents computed for wave equation
solution.
 Captures long-mean-free path and anomalous behavior.
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.

HPEM-EQUATIONS SOLVED - N r , 
Electrons, Ions, Neutrals:

 Ni
   ( Ni vi )  Si
t


 N i vi 
qi N i   
1
Ions, Neutrals:
  kNiTi      N i vi vi  
E  vi  B
t
mi
mi
mj
 
   i  
N i N j vi  v j  i , j
j mi  m j


 Ni i 
Ni qi2 i
2
Ions, Neutrals:
   Qi  Pi  U i    ( NiU i i ) 
E
t
mi ( i2   2 )
mj
Ni qi2 2

Es   3
Ni N j Rij kB (T j  Ti )   3Ni N j Rij kBT j
mi i
mi  m j
j
j

Electrons: e  Dene  e ne Erz or Scharfetter  GummelFluxes


 

Electrostatic Potential:    t  t   -  s   qi Ni - t   qi   i 
i
i


GECNov2011
University of Michigan
Institute for Plasma Science & Engr.
PLASMA CHEMISTRY MONTE CARLO MODULE
For species K
For (r,z) mesh cell I,J
Get Source Function for
Species K
Determine # of particles
To launch
For particle 1:Total Particles
Launch particle at random
time during rf cycle
Follow particles until a surface
Is hit. Include acceleration from
Fields and particle collisions
Collect statistics on particles
That hit specified surface
Go to top of particle loop
Go to top of mesh cell loop
Go to top of species loop
GECNov2011
 Pseudo-Particles are launched at
random times during the rf cycle
based on ion source functions vs
position.
 Trajectories are integrated based
on stored electric fields
interpolated as a function of time
during pulse period.
 Null collision techniques are used
to account for elastic and inelastic
collisions.
 Since transit time of ions may
exceed pulse period, the stored
electric fields during pulse are
treated as being periodic.
University of Michigan
Institute for Plasma Science & Engr.
BOUNDARY ELECTRODE ICP (BE-ICP): EXPERIMENT
 BE-ICP is a cylindrical
plasma driven by a
solenoidal coil.
 The biased electrode is at
the top boundary
consisting of annular rings.
 Ion energies measured by
retarding field energy
analyzer (RFEA).
 Electron, ion densities,
temperatures: Langmuir
probe
 Argon, 10s mTorr, 40 sccm
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.
PULSED BE-ICP
 In the BE-ICP system both the ICP power and the DC bias on the
boundary electrode can be independently pulsed.
 This can allow for greater tunability of the plasma parameters as
well as the IED
 Investigate effects of using pulsed ICP power with and without
pulsed dc bias on the boundary electrode
Duty Cycle
Pmax
Power(t)
Pave 
ICP Power
Envelope

Pt dt


1
0
ΔtBias
Pmin
 = 1/
GECNov2011
Boundary
Electrode
DC Bias(t)
Time
University of Michigan
Institute for Plasma Science & Engr.
BOUNDARY ELECTRODE
ICP (BE-ICP): MODEL
 Model representation of ICP system.
 RFEA is modeled as a flat, grounded
metal. Gridded structure is not be
resolved at this scale.
 Cylindrically symmetric model
resolves pump as annular port.
 Integration in time to a pulse-periodic
steady state.
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.
Te, Φ, ne DURING PULSE, ΔtBias = 42-60μs
 ne
 Electron density peaks
to 1012 cm-3. Plasma
potential controls the
IED.
GECNov2011
 Plasma Potential
 Te
Animation Slide
University of Michigan
Institute for Plasma Science & Engr.
Te, PLASMA POTENTIAL DURING PULSE PERIOD
 Model
 Experiment
 Te and  both have “overshoot” at beginning of
pulse period to re-establish plasma.
 Modulation of  affords opportunity to shape
IED.
 Applying pulsed BE bias will further modulate
, and so IED.
 Duty cycle = 20%, PRF = 10 kHz, P(pulse
average) = 120 W.
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.
• Model
IEDs – PULSED ICP WITH
DC BOUNDARY
 IEDs consist of 2 peaks: High energy peak
corresponding to large  during plasma on
period.
B
 Low energy peak due to smaller (and
falling)  during plasma off period.
A
B
 Experiment
B
 Ions “launched” during
plasma on period require tens
of s to reach substrate.
A
 High energy peak is broadened as ions sample
dynamics of  during transport to substrate.
Power(t)
A
Boundary Electrode
DC Bias (t)
Time
GECNov2011
 Vast majority of ionization
occurs during plasma on part
of cycle (20 s)
University of Michigan
Institute for Plasma Science & Engr.
• Model
IEDs – PULSED ICP WITH
PULSED DC BOUNDARY
B
 Energy of peak is independent of pressure
as  is determined by BE voltage.
A
 Magnitude of peak decreases at high
pressure due to collisionality, and
populates intermediate energies.
B
 Lower energy peak
decreases as pressure
increases due to increased
collision frequency
 Experiment
B
B
 Model predicts larger low
energy component (very
sensitive to acceptance
angle of RFEA vs energy.)
A
Power(t)
A
ΔtBias
Time
GECNov2011
Boundary Electrode
DC Bias (t)
University of Michigan
Institute for Plasma Science & Engr.
IEDs – PULSED ICP, PULSED
DC BOUNDARY IN EARLY
AFTERGLOW
• Model
B
A
 The positions of the peaks in the IEADs are
determined by the plasma potential 
during the plasma on period, and the
voltage of the BE.
B
 The magnitude of the peak
is determined by the length
of time the BE is on.
 Experiment
B
B
 Slight peak around 1.5 V in
model due to non-zero
minimum plasma potential.
A
Power(t)
A
ΔtBias
Time
GECNov2011
Boundary Electrode
DC Bias (t)
University of Michigan
Institute for Plasma Science & Engr.
IEDs – PULSED ICP WITH
PULSED DC BOUNDARY IN
LATE AFTERGLOW
• Model
B
A
 By moving pulse of BE to the late
afterglow, the low and high energy peaks
are more distinctively separate.
B
 Experiment
B
A
Power(t)
B
A
 The magnitude of the high
energy peak is controlled by
the length of the BE pulse.
ΔtBias
Time
GECNov2011
Boundary Electrode
DC Bias (t)
University of Michigan
Institute for Plasma Science & Engr.
CONCLUDING REMARKS
 The use of a dc biased boundary electrode in ICP allows for
control of the IED due to the shifting of the plasma potential by the
dc bias.
 Positive biases result in the increase of the IED peak energy by
nearly the applied bias while negative biases resulted in a small,
capped decrease in the IED peak energy.
 Pulsing the dc bias on the boundary electrode in the ICP afterglow
creates a narrower peak in the IED centered at approximately the
applied bias potential. The height of the peak is determined by
the length of the BE pulse.
 This allows tuning of the energy and height of the peak energy of
the IED.
GECNov2011
University of Michigan
Institute for Plasma Science & Engr.