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 ScienceAnn 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 MichiganInstitute 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) University of Michigan
Institute for Plasma Scienceand Engineering
GEC08_MERIE
CONSEQUENCES OF NON-UNIFORM B-FIELD
What are the consequences on plasma properties (uniformity, ion energy and angular distributions) resulting from “side-to-side” 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.
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
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
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
ELECTRON ENERGY TRANSPORT
S(Te) = Power deposition from electric fields
L(Te) = Electron power loss due to collisions
= Electron flux(Te) = Electron thermal conductivity tensorSEB = Power source source from beam electrons
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All transport coefficients are tensors in time domain:
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Poisson’s equation is solved using a semi-Implicit technique where charge densities are predicted at future times.
Predictor-corrector methods are used where fluxes at future times are approximated using past histories or Jacobian elements.
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IMPROVEMENTS FOR LARGE MAGNETIC FIELDS
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University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
REVIEW: MERIE REACTOR RADIALLY SYMMETRY
2-D, Cylindrically Symmetric
Magnetic field is purely radial, an approximation validated by 2-D Cartesian comparisons.
RADIUS (cm)0 10 20
HE
IGH
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cm)
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Shower Head
PumpFocus RingPowered Substrate
Conductive Wafer
B-Field
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
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
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
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.
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
“SIDE-TO-SIDE” MERIE WITH SOLENOID COILS
2-d Cartesian Geometry University of MichiganInstitute for Plasma Science
and Engineering
Actual Aspect Ratio
GEC08_MERIE
Ar+ vs UNIFORMB-FIELD ANGLE
Ar, 40 mTorr, 100 W, 10 MHz
Uniform but tilted B-field.
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.
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar, 40 mTorr, 100 W, 10 MHz
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.
Te vs UNIFORM B-FIELD ANGLE
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar, 40 mTorr, 100 W, 10 MHz
BULK IONIZATION vs B-FIELD ANGLE
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
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.
Tilt localizes ionization on one side of the wafer.
BEAM IONIZATION vs B-FIELD ANGLE
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar, 40 mTorr, 100 W, 10 MHz
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.
PLASMA POTENTIAL
Uniform (0o)
Animation Slide
University of MichiganInstitute for Plasma Science
and Engineering
Slanted (4o)
Graded Solenoid
GEC08_MERIE
Ar, 40 mTorr, 100 W, 10 MHz, 100 G
Plasma potential reflects tilt in B-field with local perturbations due to positive charging of dielectrics by more mobile ions.
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.
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar, 40 mTorr, 100 W, 10 MHz, 100 G
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,
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar+: UNIFORM AND GRADED SOLENOIDS
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar, 40 mTorr, 200 W, 10 MHz 100 G: 0.5 cm above left position
Side-to-side plasma density is highly sensitive to small axial gradients in B-field.
With graded solenoid, plasma density peaks in divergent, lower B-field.
For a fixed power, a larger fractional power is deposited in the less resistive region.
Te, IONIZATION SOURCES: GRADED SOLENOIDS
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
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
PLASMA POTENTIAL
Uniform (0o)
Animation Slide
University of MichiganInstitute for Plasma Science
and Engineering
Slanted (4o)
Graded Solenoid
GEC08_MERIE
Ar, 40 mTorr, 100 W, 10 MHz, 100 G
Plasma potential reflects tilt in B-field with local perturbations due to positive charging of dielectrics by more mobile ions.
IEADs: UNIFORM AND GRADED SOLENOID
Graded solenoid produces side-to-side variation in IEAD.
Higher plasma density, thinner sheath and weaker B-field (reduced field reversal) broaden energy.
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE
Ar, 40 mTorr, 200 W, 10 MHz 100 G: 0.5 cm above left position
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.
University of MichiganInstitute for Plasma Science
and EngineeringGEC08_MERIE