Comsol Multiphysics 在低溫電漿模擬之應用 ~My Little Journal with Simulation 多重物理 CAE 分析軟體 COMSOL Multiphysics CONFERENCE 用戶研討會 Nov 9, 2012 台灣大學化工系徐振哲
Start of Plasma Plasma: ionized gas with equal amount of positive and negative charges. 1928: Named plasma 1932: Nobel prize in Chemistry "for his discoveries and investigations in surface chemistry." Irvine Langmuir I. Langmuir, Proc. Natl. Acad. Sci. U. S. A. (1928)
Key Process Features Closed System Gas In O + Power Ar e - Ar + O O 2 O 2 + Gas Out Kinetics Path e-: heated by the power, initiate reactions in parallel, e.g. ionization, dissociation, etc. Reactive neutral species: gassurface or gas-gas reactions Ions: sometimes energetic. Open System Gas In Power e - O 2 O + O Out Key Process Parameters Operating pressure and atmosphere Type of power Plasma Characteristics Species temperature, density and their distribution in time and in space.
Why Complicated Electric Field E(t,space) Electrons Active Species n e (t,space) T e (t,space) n i (t,space) T i (t,space) Ions n n (t,space) T n (t,space) and Multiple species
My Little Journey of Simulation 2002~2006 @ UC Berkeley Femlab 2.0 ~ Femlab 3.2 Modeling of Low Pressure Inductively Coupled Plasmas
System Description Experimental System Diagnostic ICP Multiple Diagnostics Fits 6-in wafer Well-defined boundaries Stainless steel walls and dielectric top plate Axisymmetric Model 2D, Fluid Model Ar/O 2 ICP as the preliminary test Femlab TM and Matlab TM Coupled neutral and plasma model Easy to share / access Easy to extend
Model Formulation: Equation System Overall Neutral Continuity (p) Neutral Species j mass balance (wj) Neutral Momentum Balance (u,v) Neutral Energy Balance (T) Ion Continuity (n i,j, n ineg,j ) Electron Energy (Te) Holmholtz Wave Equation (E θ ) rr [ τ] = p ( ρvv ) r ( w ) j v ρdj wj = rj ρ r r ( q ) = ( ρvcvt ) p( v) + Sn n t ij t 3 2 ( ρ v ) = R n Τe + ( Dij *( nij ± nij Τi r r r neete + Qe = ee Γ ω c r e n n E e r + P 2 2 ( E) θ = K Eθ iωµ 2 0J ext, θ e e )) = r ij abs
Model Formulation: Numerical Scheme Solve for u,v,p,t Solve for w j Solve for E θ Able to handle over 9 neutral species, and 8 charged species (totally 22 equations) with PC (~1GB memory). 6 neutral,4 ions species and 15 equations in current Ar/O 2 model. Convergence: No Solve for n i,j, Te Converged? Yes one iteration < 20min. Need < 10 iterations. Robust, and easy to converge.
Model Formulation: Ar/O 2 ICP Details Chemistries Neutral Species: ground state Ar, O 2, O, and metastable O 2 (a 1, b 1 Σ) and O( 1 D) Ion Species: Ar +, O 2+, O +, O - Major reactions: Ionization, excitation, dissociation, electron impact attachment, charge exchange. All cross sections and rate coefficients were taken from the literature. Model and Experiment Comparison n e profile, center n e, and T e, n O, total ion flux and composition at the wall.
150W, 10mT ne (cm -3 ) Validation: n e and T e : Ar/O 2 Plasmas Te (ev) 4 3 2 Te,eff Te2 Te1 Te Modeling 0.0 0.5 1.0 O 2 /(O 2 +Ar) 2.5x10 11 2.0x10 11 1.5x10 11 1.0x10 11 5.0x10 10 0.0 ne, Exp ne, Modeling 0.0 0.5 1.0 O 2 /(O 2 +Ar) Maxwellian EEPF at O 2 /(O 2 +Ar) > 0.75. Better T e prediction Better n e prediction Good prediction in pure O 2 plasmas. ne (cm -3 ) Te (ev) 6 4 2 1.5x10 11 1.0x10 11 5.0x10 10 C.C. Hsu, et al.,j. Phys. D-Appl. Phys., 39 (2006) 3272. 150W Pure O 2 500W 150W 500W 0.0 0 10 20 30 40 Pressure (mt)
My Little Journey of Simulation 2006~2007 @ UCLA Comsol Multiphysics 3.3 Solving an industrial problem
2006~2007 UCLA Advisor: Dr. Jane P. Chang Modeling Commercial Etching Tool to Explain Etching Behavior Spatial-Resolved Quantities: Neutral density, Ion flux, etc. Identify Critical Parameters: Power, DC ratio. 1.20E+017 Low DC Ratio 1.00E+017 Ion Density (cm-3) DPS-II 8.00E+016 High DC Ratio 6.00E+016 4.00E+016 2.00E+016 0.00E+000 0.00 0.05 0.10 0.15 Radial Position (m) Center Edge High DC Ratio Low DC Ratio Courtesy of Cypress Semiconductor
My Little Journey of Simulation 2007~ @ NTU Comsol Multiphysics 3.5a Modeling of Atmospheric Pressure Plasma Jet
Experimental Apparatus Arc Plasma Jet Voltage probe Current Probe Power source: - DC pulsed power, applied voltage (power source output) up to 350V. transformer Pulsed power source thermocouple lens Gas OES V t on t off time t on : pulse on time t off : pulse off time Duty cycle : t on /t off (25kHz, 8/32μs) Process gases: -N 2, (O 2, Air), with flow rate 10 s slm. Diagnostic tools: - High voltage probe - Current probe - Optical Emission Spectrometer - Thermocouple (Al 2 O 3 covered)
Ambient Air Effects With air Without air Intensity (a.u.) x10 3 Intensity (a.u.) x 10 3 25 20 15 10 5 0 30 slm 0 1 2 25 70 slm 3 4 20 15 10 5 70 slm 30 slm N 2 1 st positive (579.11 nm) 0 0 1 2 3 4 Distance from exit (cm) Without ambient air, the jet length and its width increase significantly, so does the emission intensity. Emission increases initially then decays with the increase of the distance High flow rate shows a higher reactivity regardless of the absence of the ambient air. Reactivity: controlled by power density and the decay process Ambient air diffusion significantly influence the plasma characteristics.
Equation System Overall equation of continuity Momentum balance Species equation of continuity Energy balance v ρv = R vv ( ρvv ) v = p τ r w v D w + w D w = r ( ) ( ρ ρ ρ ) j j j j n j j j v v v ρvu = q p + S n ( ˆ ) ( ) Correction of the diffusivity Sc () t = ν D () t () t DT 0.009au Boundary conditions mostly by convention: symmetric, no slip, convective flux, constant temperature
Model Chemistry Upstream: electron-impact reactions and heavy particle reactions Downstream: heavy particle reactions electrons are kinetically unimportant at the downstream.
AP Jet Downstream Modeling Model Geometry Use fluid model to simulate each individual species. Each species has its own continuity equation, and exchanges mass through collision. Species included: N 2, N, 4 excited N 2, O 2, O, NO, NO 2 and N 2 O. Over 10 coupled different equations. Use MatlabTM and Comsol Multiphysics TM to solve the equation system. Assuming constant ne and Te at the upstream. Cases with and without ambient air diffusion. Cases with high and low flow rate.
Model Validation With air Without air Clearly demonstrate the effect of the ambient air diffusion, mostly due to N 2 * + O 2 N 2 + 2 O I.H. Tsai, C.C. Hsu, IEEE Trans. Plasma Sci., 38 (2010) 3387
My Little Journey of Simulation 2007~ @ NTU Comsol Multiphysics 3.5a Modeling of Dielectric Barrier Discharge
Model Formulation Model Geometry Continuity Equation (e, N 2+, N 4+, N 2 *) Poisson Equation Equation System Surface charging 0 n t i i + Γ = eσ qn ε i i i 2 = ε V d ε φ+ φ= σs l db 0 S i S σ = ± eγ dt j Dielectric barrier at both electrodes. Not solving the dielectric barrier. Consider surface charging using Gauss law. Using AC power source Quantities vary with time.
Boundary Conditions Continuity Equations: 1 Γe n = ne vth, e hs ( γi, j Γi, j) ( γn, j Γn, j) 4 j j 1 Γ i n = hs µ i ni E+ ni vth, i 4 1 Γn n = nn vth, n 4 1 E n> 0 where hs = 0 E n 0 γ: secondary electron emission coefficient v th : thermal velocity h s : switching function, considers the direction of the E-field Poisson Equation ε d σs ( φ V ) φ = l ε 0 ( ) where σ = q Γ dt s i i V = 0 or V sin( ωt) σ s : surface charging ε d : dielectric constant of the dielectric barrier ε 0 : vacuum vacuum permittivity l: dielectric layer thickness (2 mm on both sides) 0
Plasma Chemistry Species included: e - 3 + 3 3 1 -, N 2+, N 4+, excited N 2 ( A Σ u B Π g C Π u a ' Π ) Not include: N and N + u due to small amount and unimportant kinetically. Electron-Impact Reaction Heavy Particle Reactions R10 N 2 + e N 2+ + 2 e R30 N 2 (a) + N 2 2N 2 R11 N 2 + e N 2 (A) + e R31 N 2 (a) + N 2 N 2 (B) + N 2 R12 N 2 + e N 2 (a) + e R34 N 2 (A) + N 2 (A) N 2 (C) + N 2 R13 N 2 + e N 2 (B) + e R35 N 2 (A) + N 2 (A) N 2 (B) + N 2 R14 N 2 + e N 2 (C) + e R36 N 2 (C) N 2 (B) R20 N 2+ + e N 2 R37 N 2 (C) + N 2 N 2 (a) + N 2 R21 N 2+ + e N 2 R38 N 2 (B) N 2 (A) + hv R25 N 4+ + e N 2 (C) + N2 R39 N 2 (B) + N 2 N 2 (A) + N 2 R32 N 2 (a) + N 2 (a) N 4+ + e R33 N 2 (a) + N 2 (A) N 4+ + e
Neutral Kinetics Time-Averaged Densities Center line condition: 15 kv, 30 khz, 1.25 mm Gap ng(1/m 3 ) 10 21 10 20 10 19 10 18 10 17 10 16 10 15 10 14 N 2 (A) N 2 (a) N 2 (B) N 2 (C) 0 0.2 0.4 0.6 0.8 1 1.2 position (m) x 10-3 N 2 (A) appears to be the dominant excited state N 2, as reported in the literature same trend for most conditions. Major formation mechanism are electronimpact excitation. Rather flat profile in the bulk as a result of high pressure (AP) Rapidly drop at the electrode surface due to surface quenching reaction Simulation shows the density is more sensitive to the bulk reaction rates than to the surface quenching coefficient.
Plasma Structure Charged Species Center line condition: 15 kv, 30 khz, 1.25 mm Gap t=0~0.04t t=0~0.04t 10 18 Averaged n e, gap=0.75~1.5 mm ne(1/m 3 ) 10 18 10 16 10 14 ni(1/m 3 ) 10 18 10 16 10 14 ne(1/m 3 ) 10 17 10 16 10 15 10 14 Increase the gap 10 13 0 0.2 0.4 0.6 0.8 1 normalized distance Averaged n i, gap=0.75~1.5 mm 10 18 10 12 10 12 0 0.5 1 position (m) x 10-3 0 0.5 1 position (m) x 10-3 Non-smooth averaged n e due to its rapid with time. More significant change in n e than in n i Oscillation of ne is clearly seen. ni(1/m 3 ) 10 17 10 16 Increase the gap 0 0.2 0.4 0.6 0.8 1 normalized distance
Plasma to Non-Plasma Transition t=0.0t 15 kv, 30 khz, Small gap (0.75 mm) t=0.25t t=0.50t t=0.75t 10 18 10 18 10 18 10 18 ne, ni(1/m 3 ) 10 16 10 14 ne, ni(1/m 3 ) 10 16 10 14 ne, ni(1/m 3 ) 10 16 10 14 ne, ni(1/m 3 ) 10 16 10 14 10 12 0 5 x (m) x 10-4 10 12 Y. B. Golubovskii, et al., J. Phys. D-Appl. Phys. 36, 39-49 (2003). 0 5 x (m) x 10-4 10 12 0 5 x (m) x 10-4 0 5 x (m) x 10-4 10 12 At small gap (<0.75 mm), no quasi-neutral region is seen throughout the power period. Similar behavior is seen in the literature for He plasmas. Non-plasma region sometimes terms Townsend discharge in the literature. Suggesting smaller gap does not necessarily lead to a higher density (reactivity).
Conclusion Comsol Multiphysics is a viable PDE solver to handle complex systems. Able to simulate low/high pressure, steady state/ transient behavior of low temperature plasmas Numerical simulation allows for better understanding and clearer observation of phenomena and physics, especially those not accessible by experimental work. Having a tool (computer program) in hand is very important to scientific researchers/students.