MODELING PLASMA PROCESSING DISCHARGES
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1 MODELING PROCESSING DISCHARGES M.A. Lieberman Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA Collaborators: E. Kawamura, D.B. Graves, and A.J. Lichtenberg, UC Berkeley C. Lazzaroni and P. Chabert, Ecole Polytechnique, France J. Gudmundsson, Shanghai Jiao Tong U; Science Institute, U. Iceland A. Leblanc, ENS Cachan, France Jing Zhang, Donghua U, Shanghai, China Download this talk: lieber LiebermanPSC12 1
2 OUTLINE Fast computation of atmospheric pressure rf capacitive discharges Fluid model of E-H transition instability in electronegative inductive discharge LiebermanPSC12 2
3 ATMOSPHERIC PRESSURE CAPACITIVE RF DISCHARGE LiebermanPSC12 3
4 MOTIVATION Biomedical example of reactive oxygen species (Review article: H.W. Lee et al, J. Phys. D 44, , 2011) Applications to sterilization, cancer cell treatment, blood coagulation, wound healing Unique materials example of anatase crystalline TiO 2 (Review article: D. Mariotti and R.M. Sankaran, J. Phys. D, , 2010) (Anatase TiO 2 : H.G. Yang et al, Nature 453, 638, 2008) Applications to photonics crystals, photo/electrochromic devices, gas sensors, spintronic devices, anticancer or gene therapies, solar cells for electric energy or hydrogen production LiebermanPSC12 4
5 DISCHARGE CONFIGURATION Atmospheric pressure He or Ar with trace reactive gases 1D plane-parallel geometry ( mm gap) RF-driven (nominal MHz) ~ MHz He or Ar + Trace gas ~0.1 1 mm Reactive species LiebermanPSC12 5
6 EEPF TIME VARIATIONS He/N 2 fluid simulation with kinetic (Bolsig+) EEPF calculation Time variation Low temperature tail (J. Waskoenig, PhD Thesis, Queens U Belfast, 2010) Conclusions used in modeling The EEPF oscillates in time with the rf electron power absorbed The EEPF is Maxwellian below a break energy E b 20 V (metastable He excitation energy) The EEPF has a low temperature tail above the break energy LiebermanPSC12 6
7 HYBRID DISCHARGE MODEL Numerical solution of particle balances for each species dn j = G j L j dt G j = volume creation rate (2-body, 3-body and surfaces) L j = volume loss rate (2-body, 3-body, and surfaces) Analytical solutions of the discharge dynamics (homogeneous model) the time-varying T e (t) the effective rate coefficients K Coupling the analytical and numerical solutions = fast solution of the discharge equilibrium LiebermanPSC12 7
8 COMPARISON TO FLUID SIMULATION He/0.5%O 2 (16 species), 1mm gap, MHz Neutral (left) and charged (right) densities versus power (open symbols global model; solid symbols fluid results, Waskoenig, 2010) Reasonable agreement of model and fluid simulations 40 sec simulation time on fast laptop LiebermanPSC12 8
9 E/H (CAPACITIVE/INDUCTIVE) MODE TRANSITION INSTABILITY IN ELECTRONEGATIVE DISCHARGE LiebermanPSC12 9
10 MOTIVATION Low pressure inductive reactors for thin film processing Example: fabrication of CMOS transistors for microprocessors/memory Inductive reactors often operate near the E/H transition with electronegative feedstock gases Macroscopic instabilities observed in both commercial and research reactors LiebermanPSC12 10
11 E/H MODE TRANSITION Plasma resistance R e versus n e as I rf is varied A gap occurs between I rf = 7.5 and 8 A Measurements at 10 mtorr Cl 2 show gap region Previous measurements (many) and global models (many) indicate instability First calculation of E/H instability in fluid simulations n (m -3 ) e R (ohms) e e+17 1e+16 1e mtorr Cl 2 fluid simulation Capacitive (E-mode) I =7.5A rf Gap I =8A Inductive (H-mode) 0 1e+14 1e+15 1e+16 1e+17 Center n e (m-3) Malyshev & Donnelly (8/2001) measurements Gap region 1e LiebermanPSC12 abs 11 P (W) rf
12 BULK-FLUID/ANALYTIC-SHEATH MODEL Inductive reactor (Malyshev and Donnelly, ) z Axisymmetric cylindrical geometry 0.21 m Air (κ = 1) Center of symmetry (r = 0) Coils Quartz dielectric window (κ = 4) Plasma (κ = κ p) Quartz dielectric spacer (κ = 4) Perfectly conducting outer walls Sheath (κ = 1) Wafer chuck φ 0.18 m Electromagnetic field solve Fluid bulk plasma model Analytical sheath model Flow model of reactive gas Commercial software (COMSOL) (Kawamura et al, PSST 2011) r LiebermanPSC12 12
13 E/H TRANSITION INSTABILITY Example: 2.2 khz instability in 15 mtorr Cl 2 at I rf = 7.75 A, showing (a) n Cl (t), (b) n e (t), and (c) T e (t) At time t 1 the discharge enters capacitive mode From t 1 t 2 the discharge is in capacitive mode From t 2 t 3 the discharge makes a transition to inductive mode From t 3 t 4 the discharge is in inductive mode From t 4 t 1 the discharge makes a transition back into capacitive mode n (m -3 ) Cl -3 n (m ) e 1.1e+17 T (V) 1e+17 9e+16 8e+16 7e+16 6e e+16 8e+15 6e+15 4e+15 2e+15 e LiebermanPSC12 13 (a) (b) t t.. t (c) t.. 3. t t 3 4 t (s) t. 2 t 2 3. t t2 t t
14 T e (r,z) VERSUS t t = t 1 t = t 2 T e strongly localized near coil t 1 (enter E-mode): Te jumps to highest value t = t 3 t = t 4 t 2 t 4 (E-mode followed by transition to H-mode): T e decays in time LiebermanPSC12 14
15 n e weakly localized near coil t 1 (enter E-mode): n e rapidly decays with time n e (r,z)/n emax VERSUS t n emax = m 3 at t 1 n emax = m 3 at t 2 n emax = m 3 at t 3 n emax = m 3 at t 4 t 3 (enter H-mode): n e rapidly increases with time LiebermanPSC12 15
16 FLUID AND GLOBAL MODEL COMPARISON Intersection of dn e /dt = 0 and dn /dt = 0 curves equilibrium Slope dn /dn e of dn e /dt = 0 curve positive unstable dn e /dt = 0 Fluid simulatioṇ n (m 3 ) dn /dt = 0 Global model theory n e (m 3 ) Good agreement of fluid calculation and analytical global model LiebermanPSC12 16
17 NEUTRAL TIME AVERAGES OVER INSTABILITY Neutral species time variations are very small Time averages: Gas Temperature (K) Molar Cl Fraction T g rises to 530 K inside discharge Chlorine density varies significantly with radius LiebermanPSC12 17
18 SUMMARY A one-dimensional hybrid analytical-numerical global model of atmospheric pressure, rf-driven capacitive discharges was developed Coupling analytical solutions of the time-varying discharge and EEPF dynamics, and numerical solutions of the discharge chemistry, allows for a fast solution of the discharge equilibrium (Lazzaroni et al, to appear in PSST, 2012) The E/H transition instability has been found and studied in 2D fluid simulations The fluid instability dynamics is in good agreement with an analytical global model (Kawamura et al, submitted to PSST, 2012) Download this talk: lieber LiebermanPSC12 18
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