A3D Hybrid Model of ahelicon Source +
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1 A3D Hybrid Model of ahelicon Source + Eric R. Keiter* and Mark J. Kushner** Department of Electrical and Computer Engineering 146 W. Green St., Urbana, IL 6181 USA 1st Gaseous Electronics Conference October Work supported by Semiconductor Research Corp. and AFOSR/DARPA. * mjk@uiuc.edu ** Present Address: Sandia National Labs, Albuquerque, NM, USA
2 Agenda!!!!! Abstract ModelDescription -waveequation -tensorconductivity Results,NagoyaTypeIIIcoil Results,M=Coil Conclusions Gec98_Helicon1
3 Abstract As the semiconductor industry moves to larger wafer sizes ($>$3mm) effecient new plasma sources which are capable of maintaining process uniformity at large scale will be needed. Helicon sources have been proposedasapossiblealternativetoinductivelycoupledplasmasources, duetohighefficiency,andthepowerdepositionnotbeinglimitedtoaskin depth. Additionally, helicon plasmas operate at very low pressure, so particulate contamination is minimal. In this paper, we present results fromanumericalstudyofaheliconsource. Thethreedimensionalhybrid plasmaequipmentmodel(hpem3d)hasbeenextendedtoincludeacold plasmatensorconductivityintheelectromagnetics(em)module. Astatic magneticfield isgenerated byasolenoid whichsurrounds thecylindrical reactor geometry and is simulated by solving for the vector potential. Transport of charged and neutral species is handled with a fluid simulation. By varying parameters such as the static magnetic field magnitude,reactorgeometry,andcoilconfiguration,weareabletomodify thepowerdepositionprofile. Thisinturndeterminesthedownstreamion and neutral flux uniformity. We find that for larger magnetic fields, the powerdepositionpenetratesmoredeeplyintothebulkplasma. Gec98_Helicon2
4 Scehmatic of 3D Hybrid Plasma Equipment Model (HPEM-3D)! HPEM-3D combines modules which address different physics or different timescales. E(r,z, θ) Magneto- Statics Module Circuit Module I,V Electromagnetics Module σ(r,z, θ ) E(r,z, θ) B(r,z, θ) Electron Energy Equation/ Boltzmann Module N(r,z, θ) P(r,z, θ) Φ(r,z, θ ) T(r,z, e θ) S(r,z, θ) µ (r,z, θ ) Electron Transport (Continuity) Ion Transport (Continuity, Momentum) Surface Kinetics Ambipolar Transport/ Sheath Poisson Solution Gec98_Helicon3
5 Electric Field Module: Wave Equation! The electric field module of the HPEM-3D is responsible for solving the 3D frequency domain wave equation: 2 E = µ ε ω E iµ ωj iωµ σe ant a f 2! The left hand side is replaced by: E = E E where the first term is neglected.! The conductivity, σ,is the cold plasma tensor conductivity (see next slide)! The finite difference form of the wave equation results in alarge matrix equation, whichis solved using ageneralized minimum residual method.!!! The Helicon wavelength can be estimated by If λ is small compared to reactor size, the numerical solution of the wave equation is difficult, as the problem is less well conditioned. The matrix problem is solved using the generalized minimum residual method. λ = 1. x1 2 B ωrn Gec98_Helicon4
6 Conductivity Tensor! The plasma current in the wave equation is handled by acold plasma tensor conductivity: σ = σ mv qa α 1 + B m 2 2 c h F G H 2 2 α + B αb + B B αb + B B r z r θ θ r z 2 2 αb + B B α + B αb + B B z r θ θ r θ z 2 2 θ r z r θ z z αb + B B αb + B B α + B I J K α = a iω q + v / m m f σ 2 = q m mv m! The addition of the static magnetic field results in alarger,less well conditioned matrix problem.! If the static magnetic field is predominantly in the z-direction, the (3,3) term of the tensor dominates Gec98_Helicon
7 Antenna Configuration! Two different antenna configurations were used: Nagoya Type III Double Ring (m=) J J! The Nagoya Type III is commonly used in laboratory Helicon plasmas, where it has been shown to produce an m=1 mode under the right conditions.! The Double Ring configuration was tested here to see if using it would resultin am=heliconmode. Gec98_Helicon6
8 Reactor Geometry 3 3 Side (r,z) view Showerhead Solenoid Top (r, θ)view, m= coil 2 1 Antenna Coil Dielectric Reactor wall Solenoid Top (r, θ)view, Nagoya Type III coil Coil Wafer! Antenna coil can either be the m= or Nagoya Type III configuration Gec98_Helicon Solenoid Coil
9 Plasma Parameters! M=cases: Pressure:.mTorr TotalPowerDeposition: 12Watts StaticMagneticField:,6,9Gauss Gas:Argon ReactorHeight:3cm ReactorRadius:1cm! NagoyaTypeIIIcases: Pressure:.mTorr TotalPowerDeposition: 6Watts StaticMagneticField:,3,6Gauss Gas:Argon ReactorHeight:3cm ReactorRadius:1cm Gec98_Helicon8
10 No Static Magnetic Field (B=), Nagoya Type III Coil AR 3.8E E E E E E E E E E E E E E E E+7.113E E E+7 1E+7 E-MAG Argon Ion Density (cm-3) Electric Field Total Magnitude With no magnetostatic field, the plasma is in purely inductive mode. The power deposition is confined near the coil. Gec98_Helicon1
11 No Static Magnetic Field (B=), Nagoya Type III Coil E E E E E E E E E E E E E E E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: With no magnetostatic field, the plasma is in purely inductive mode. Gec98_Helicon11
12 No Static Magnetic Field (B=), Nagoya Type III Coil Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: With no magnetostatic field, the plasma is in purely inductive mode. Gec98_Helicon12
13 Static Magnetic Field (B=3 G), Nagoya Type III Coil AR 1.2E E E E E E E E E E E E E E E E E E E+7 1E+7 E-MAG Argon Ion Density (cm-3) Electric Field Total Magnitude With the addition of a magnetostatic field, power deposition extends downstream away from the coils. Gec98_Helicon13
14 Static Magnetic Field (B=3 G), Nagoya Type III Coil E E E E E E E E E E E+1.447E E E E E-.4132E E E E E E E-6 1E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: With the addition of a magnetostatic field, power deposition extends downstream from the coils. Power deposition near the theta component of the coils is reduced. Gec98_Helicon14
15 Static Magnetic Field (B=3 G), Nagoya Type III Coil E E E E E E E E E E E E E E E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: With the addition of a magnetostatic field, power deposition extends downstream from the coils. The addition of a Bz magnetic field results in the power deposition mostly being near the z component of the coil. Gec98_Helicon
16 Static Magnetic Field (B=6 G), Nagoya Type III Coil AR E E E E E E E E E E E E E E E E E E E+7 1E+7 E-MAG Argon Ion Density (cm -3 ) Electric Field Total Magnitude With the addition of a magnetostatic field, power deposition extends downstream away from the coils. Gec98_Helicon16
17 Static Magnetic Field (B=6 G), Nagoya Type III Coil E E E E E E E E E E E+1.447E E E E E E E E E E E E E E-7 1E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: With the addition of a magnetostatic field, power deposition extends downstream away from the coils. Enhanced power deposition near z- component of the coils. Gec98_Helicon17
18 Static Magnetic Field (B=6 G), Nagoya Type III Coil E E E E E E E E E E E E E E E Argon Ion Density (cm -3 ) Top view: Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) With the addition of a magnetostatic field, power deposition extends downstream from the coils. The addition of a Bz magnetic field results in the power deposition mostly being near the z component of the coil. Gec98_Helicon18
19 No Static Magnetic Field (B=), M= Coil.84667E E E E E E E E+1.716E E E E E E E E+8.689E E E+7 1E Argon Ion Density (cm-3) Electric Field Total Magnitude (Log V/cm) With no magnetostatic field, the plasma is in purely inductive mode. Gec98_Helicon19
20 No Static Magnetic Field (B=), M= Coil E E E E E E E E E E E E E E E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: With no magnetostatic field, the plasma is in purely inductive mode. Gec98_Helicon2
21 Static Magnetic Field: B=6 G, M= Coil.3348E E E E+1.398E+1 3.4E E E E E E E E E E E E E E+7 1E Argon Ion Density (cm -3 ) Electric Field Total Magnitude The addition of the magnetic field (B z =6G), the electrons tend to follow the magnetic field lines, and the heating region becomes elongated down the z-axis. Gec98_Helicon21
22 Static Magnetic Field: B=6 G, M= Coil E E E E E E E E E E E E E E E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: The addition of the magnetic field (B z =6G), the electrons tend to follow the magnetic field lines, and the heating region becomes elongated down the z-axis. Gec98_Helicon22
23 Static Magnetic Field: B=9 G, M= Coil.33429E E E E E E E E E E E E+8.11E E E E E E E+7 1E Argon Ion Density (cm -3 ) Electric Field Total Magnitude As the magnetic field increases from 6 Gauss to 9 Gauss, the electric field penetration increases. Gec98_Helicon23
24 Static Magnetic Field: B=9 G, M= Coil E E E E E E E E E E E E E E E Argon Ion Density (cm -3 ) Electric Field Total Magnitude Total Power Deposition (Log Watt/cm -3 ) Top view: As the magnetic field increases from 6 Gauss to 9 Gauss, the electric field penetration increases. Gec98_Helicon2
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