Transcript Investigations of Magnetically Enhanced RIE

INVESTIGATIONS OF MAGNETICALLY
ENHANCED RIE REACTORS WITH ROTATING
(NON-UNIFORM) MAGNETIC FIELDS
Natalia Yu. Babaeva and Mark J. Kushner
University of Michigan
Department of Electrical Engineering and Computer Science
Ann Arbor, MI 48109
http://uigelz.eecs.umich.edu
[email protected]
61st Annual Gaseous Electronics Conference
Dallas, Texas
October 13–17, 2008
GEC08_MERIE
AGENDA
 Introduction to Magnetically Enhanced Reactive Ion Etching
(MERIE) reactors.
 Description of Model
 Uniform and tilted magnetic field
 Uniform and graded solenoids
 Concluding Remarks
 Acknowledgement: Semiconductor Research Corp., Applied
Materials Inc., Tokyo Electron, Ltd.
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
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.
 The B-field is usually non-uniform across the wafer. Rotating
the field averages out non-uniformities in plasma properties.
 D. Cheng et al, US Patent 4,842,683
 M. Buie et al, JVST A 16, 1464 (1998)
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
CONSEQUENCES OF NON-UNIFORM B-FIELD
 What are the consequences on plasma properties (uniformity,
ion energy and angular distributions) resulting from “side-toside” variations in B-field?
 This is a 3-d problem…Our computational investigation is
performed with a 2-dimensional model in Cartesian coordinates.
 Enables assessment of side-to-side variations.
 Does not capture closed paths that might occur in 3-d
cylindrical coordinates.
 Restrict investigation to pure argon to isolate plasma effects.
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
MODELING OF MERIE
 2-dimensional Hybrid Model
 Electron energy equation for bulk electrons
 Continuity, Momentum and Energy (temperature) equations
for all neutral and ion species.
 Poisson equation for electrostatic potential
 Circuit model for bias
 Tensor transport coefficients.
 Monte Carlo Simulation
 Secondary electrons from biased surfaces
 Ion transport to surfaces to obtain IEADs
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
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 in time domain:
  2  Br2

1
A  Ao
  Bz  Br B

2
2
   B  

  B  Br Bz
Bz  Br B
 2  B2
 Br  B Bz
 B  Br Bz 

Br  B Bz 
 2  Bz2 
Ao  isotropic
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
IMPROVEMENTS FOR LARGE MAGNETIC FIELDS
 Poisson’s equation is solved using a semi-Implicit 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.

d t  1 2 t 
ion t'    t   t
dt


 df e t  
e t'   f e ne t , t    
 t  t    t 
 d 
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
REVIEW: MERIE REACTOR RADIALLY SYMMETRY
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.
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
Ar+ DENSITY vs
MAGNETIC FIELD
 Increasing B-field shifts
plasma towards center and
increases density.
 Decreasing Larmor radius
localizes sheath heating closer
to wafer.
 Plasma is localized closer to
wafer.
 Large B-fields (> 100 G)
decrease density due to
diffusion losses of Ar*
 Ar, 40 mTorr, 100W, 10 MHz
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
SHEATH REVERSAL, THICKENING, IEDs
 As the magnetic field increases, the electrons
become less mobile than ions.
 Electric field in the sheath reverses, sheath
thickens, IEDs lower in energy and broaden.
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
“SIDE-TO-SIDE” MERIE WITH SOLENOID COILS
 Actual Aspect
Ratio
 2-d Cartesian Geometry
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
Ar+ vs UNIFORM
B-FIELD ANGLE
 Uniform but tilted Bfield.
 Low cross field
mobility increases
plasma density and
plasma stretches
along field lines.
 Tilt of B-field
increases maximum
density while
plasma aligns with
field.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
Te vs UNIFORM BFIELD ANGLE
 With B=0, E-field
enhancement at edges
produces local
maximum in Te.
 With B > 0, sheath
heating is constrained
to layer near
substrate.
 Tilt reduces Te above
wafer where plasma
density is maximum
and sheath thickness
shrinks.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
BULK IONIZATION vs
B-FIELD ANGLE
 With B=0, edge
enhancement in Te
translates to local
maximum in bulk
ionization.
 With B > 0, confining
of sheath heated
electrons and low
transverse mobility
elongates ionization.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC08_MERIE
 Tilt localizes ionization
on one side of the
wafer.
University of Michigan
Institute for Plasma Science
and Engineering
BEAM IONIZATION vs
B-FIELD ANGLE
 With B=0, mean free
paths of secondary
electrons exceed gap
spacing.
 With B > 0, secondary
electrons are confined
near electrodes.
 Tilt in B-field shifts
secondary sources in
opposite directions
top-and-bottom.
 Ar, 40 mTorr, 100 W, 10 MHz
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
PLASMA POTENTIAL
 Plasma potential reflects tilt in B-field with local perturbations
due to positive charging of dielectrics by more mobile ions.
 Uniform (0o)
 Slanted (4o)
 Graded
Solenoid
Animation Slide
 Ar, 40 mTorr, 100 W, 10 MHz, 100 G
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
IEAD (CENTER) vs UNIFORM B-FIELD ANGLE
 IEDs broaden and
move to lower energy
with increase in B-field
due to sheath reversal.
 Tilt in B-field broadens
angular distribution
and produces angular
asymmetries.
 With a large tilt,
plasma potential has
time average tilt
leading to angular
assymetries.
 Ar, 40 mTorr, 100 W, 10 MHz, 100 G
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
IEADs ACROSS WAFER
vs B-FIELD ANGLE
 With tilts of  5o
significant side-to-side
variation in IEAD across
wafer.
 Broadening in energy of
IEAD results from
thinner sheath and less
of sheath reversal.
 Angular asymmetry
most severe at low
energies.
 Ar, 40 mTorr, 100 W,
 100 G, 10 MHz,
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
Ar+: UNIFORM AND GRADED SOLENOIDS
 Side-to-side plasma
density is highly
sensitive to small axial
gradients in B-field.
 With graded solenoid,
plasma density peaks
in divergent, lower Bfield.
 For a fixed power, a
larger fractional power
is deposited in the
less resistive region.
 Ar, 40 mTorr, 200 W, 10 MHz
 100 G: 0.5 cm above left position
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
Te, IONIZATION SOURCES: GRADED SOLENOIDS
 Beam ionization also
penetrates further on
the weak field side.
 Total ionization is
larger inspite of lower
electron temperature.
 Ar, 40 mTorr, 200 W, 10 MHz
 100 G: 0.5 cm above left position
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
PLASMA POTENTIAL
 Plasma potential reflects tilt in B-field with local perturbations
due to positive charging of dielectrics by more mobile ions.
 Uniform (0o)
 Slanted (4o)
 Graded
Solenoid
Animation Slide
 Ar, 40 mTorr, 100 W, 10 MHz, 100 G
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
IEADs: UNIFORM AND GRADED SOLENOID
 Graded solenoid
produces side-toside variation in
IEAD.
 Higher plasma
density, thinner
sheath and weaker
B-field (reduced
field reversal)
broaden energy.
 Ar, 40 mTorr, 200 W, 10 MHz
 100 G: 0.5 cm above left position
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering
CONCLUDING REMARKS
 “Side-to-side” plasma uniformity and IEADs were
computationally investigated MERIEs to provide insights to
rotating magnetic field systems.
 Tilt of 100 G magnetic fields of 5-10o are sufficient to skew
plasma density and produce position dependent IEADs.
 Solenoids with only a few percent variation in B-field also
produce side-to-side variations.
 Plasma density peaks in divergent, low B-field regions due to
being less resistive to axial current.
GEC08_MERIE
University of Michigan
Institute for Plasma Science
and Engineering