INVESTIGATIONS OF MAGNETICALLY ENHANCED RIE REACTORS WITH ROTATING (NON-UNIFORM) MAGNETIC FIELDS

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.


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



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:



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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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

T (

cm)

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0

2

Shower Head

PumpFocus RingPowered Substrate

Conductive Wafer

B-Field



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



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.



“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.




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




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.

Tilt localizes ionization on one side of the wafer.

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.

PLASMA POTENTIAL

Uniform (0o)

Animation Slide


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.



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,



Ar+: UNIFORM AND GRADED SOLENOIDS



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



Beam ionization also penetrates further on the weak field side.

Total ionization is larger inspite of lower electron temperature.


PLASMA POTENTIAL

Uniform (0o)

Animation Slide


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.




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.



INVESTIGATIONS OF MAGNETICALLY ENHANCED RIE REACTORS WITH ROTATING (NON-UNIFORM) MAGNETIC FIELDS

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