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 st 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) University of Michigan Institute for Plasma Science and 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 Michigan Institute for Plasma Science and Engineering GEC08_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 Michigan Institute for Plasma Science and Engineering GEC08_MERIE

ELECTRON ENERGY TRANSPORT S(T e )=Power deposition from electric fields L(T e ) =Electron power loss due to collisions  =Electron flux  (T e )=Electron thermal conductivity tensor S EB =Power source source from beam electrons  All transport coefficients are tensors in time domain: University of Michigan Institute for Plasma Science and Engineering GEC08_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. IMPROVEMENTS FOR LARGE MAGNETIC FIELDS University of Michigan Institute for Plasma Science and Engineering GEC08_MERIE

REVIEW: MERIE REACTOR RADIALLY SYMMETRY  2-D, Cylindrically Symmetric  Magnetic field is purely radial, an approximation validated by 2-D Cartesian comparisons. University of Michigan Institute for Plasma Science and Engineering GEC08_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 Michigan Institute for Plasma Science and Engineering GEC08_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 Michigan Institute for Plasma Science and Engineering GEC08_MERIE

“SIDE-TO-SIDE” MERIE WITH SOLENOID COILS  2-d Cartesian Geometry University of Michigan Institute for Plasma Science and Engineering  Actual Aspect Ratio GEC08_MERIE

Ar + vs UNIFORM B-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 Michigan Institute for Plasma Science and Engineering GEC08_MERIE

 Ar, 40 mTorr, 100 W, 10 MHz  With B=0, E-field enhancement at edges produces local maximum in T e.  With B > 0, sheath heating is constrained to layer near substrate.  Tilt reduces T e above wafer where plasma density is maximum and sheath thickness shrinks. T e vs UNIFORM B- FIELD ANGLE University of Michigan Institute for Plasma Science and Engineering GEC08_MERIE

 Ar, 40 mTorr, 100 W, 10 MHz BULK IONIZATION vs B-FIELD ANGLE University of Michigan Institute for Plasma Science and Engineering GEC08_MERIE  With B=0, edge enhancement in T e 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 Michigan Institute for Plasma Science and Engineering GEC08_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 (0 o ) Animation Slide University of Michigan Institute for Plasma Science and Engineering  Slanted (4 o )  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 Michigan Institute for Plasma Science and Engineering GEC08_MERIE  Ar, 40 mTorr, 100 W, 10 MHz, 100 G

IEADs ACROSS WAFER vs B-FIELD ANGLE  With tilts of  5 o 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 Michigan Institute for Plasma Science and Engineering GEC08_MERIE

Ar + : UNIFORM AND GRADED SOLENOIDS University of Michigan Institute for Plasma Science and Engineering GEC08_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.

T e, IONIZATION SOURCES: GRADED SOLENOIDS University of Michigan Institute for Plasma Science and Engineering GEC08_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 (0 o ) Animation Slide University of Michigan Institute for Plasma Science and Engineering  Slanted (4 o )  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 Michigan Institute for Plasma Science and Engineering GEC08_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 5-10 o 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 Michigan Institute for Plasma Science and Engineering GEC08_MERIE