NARRW GAP ELECTRNEGATIVE CAPACITIVE DISCHARGES AND STCHASTIC HEATING M.A. Lieberman Deartment of Electrical Engineering and Comuter Sciences University of California Berkeley, CA 9472 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 Motivation: widely used for thin film etch and deosition Download this talk: htt://www.eecs.berkeley.edu/ lieber LiebermanPSC13 1
UTLINE PIC simulations of narrow ga oxygen discharges Equilibrium discharge model Stochastic (collisionless) heating LiebermanPSC13 2
DISCHARGE CNFIGURATIN xygen at 1 1 mtorr, V rf = 5 2 V 1D lane-arallel geometry ( 1 1 cm ga length L) Usual model is stratified discharge with electronegative (EN) core and electroositive (EP) edge As L is decreased, the EP edge can disaear and new interesting henomena are found LiebermanPSC13 3
PIC SIMULATINS AND EQUILIBRIUM MDELING (Vary ga length L at =5 mtorr, V rf = 5 V) LiebermanPSC13 4
L=4.5 cm (EP EDGE EXISTS) 2e+16 1.5e+16 1e+16 5e+15 (a) Particle Density (m-3).1.2.3.4 1 1 + 2 2 + e (c) Temerature (V) Low Te e EN core EP edge Sheath.2.1 -.1 -.2 5 4 3 2 e + 2 (b) Current Density (A/m 2).1.2.3.4 Large os (d) Electron Heating (W/m 3) e Core flux.1.1.1.2.3.4 1-1 ohm.1.2.3.4 stoc Small neg LiebermanPSC13 5
L=2.5 cm (N EP EDGE) (a) Particle Density (m-3) (b) Current Density (A/m 2) 2e+16 1.5e+16 + 2 EN core No EP edge.4.2 e Core flux 1e+16 5e+15 1 1 e e.5.1.15.2.25 (c) Temerature (V) High Te e Sheath -.2 -.4 2 15 + 2.5.1.15.2.25 (d) Electron Heating (W/m 3) e 1.1 + 2.1.5.1.15.2.25 1 5-5 Small neg ohm Large os stoc.5.1.15.2.25 LiebermanPSC13 6
EEDF S AND DENSITY DETAILS (a) EEDF (a.u.) for L = 4.5 cm (b) EEDF (a.u.) for L = 2.5 cm 1 1 1 EP edge: bi-maxwellian 1 No EP edge: Maxwellian 1 1.1.1.1.1 5 1 15 2 25 Energy (ev).1 1 2 3 4 Energy (ev) 2e+15 (a) Densities (m-3) for L= 4.5 cm 1e+15 (b) Densities (m-3) for L= 2.5 cm 1.5e+15 1e+15 5e+14 n + - n - n e sheath edge n.1.2.3.4 8e+14 6e+14 Sheath begins at end of EP edge 4e+14 2e+14 n + - n - n e n ~ sheath edge Sheath begins inside EN core.5.1.15.2.25 LiebermanPSC13 7
TIME-VARYING DENSITY (L=2.5 cm, N EP EDGE) 1e+15 Electron density (m-3) at T/8 intervals + 2 5e+14 scillating electron cloud uncovers core Core 1 8 2 7 3 6 4 5 1 8 2 7 3 6 4 5.5.1.15.2.25 LiebermanPSC13 8
MDELING CNSIDERATINS EP edge exists (larger ga lengths L) Bi-Maxwellian EEDF About half the ion flux generated in sheath/ep edge Usual Child law rf sheath Usual ositive collisionless heating in sheath No EP edge (smaller ga lengths L) Maxwellian EEDF ver half the ion flux generated in sheath Attachment in sheath is imortant Unusual rf sheath containing negative ions Negative collisionless heating in sheath, ositive in core Models develoed: model with some inuts from PIC results self-consistent model LiebermanPSC13 9
MDEL WITH SME INPUTS FRM PIC Rate coefficients and collisional energy losses using PIC EEDF Power deosition in core from PIC results Solid lines (2-region model with EP edge); Dashed lines (1-region model without EP edge); circles (PIC results) (a) n e (m 3 ) at 1 mtorr, 5 V 1 16 1 15 1 14.4.6.8.1 1 16 1 15 L (m) (c) n e (m 3 ) at 5 mtorr, 5 V (b) n e (m 3 ) at 25 mtorr, 5 V 1 16 1 15 1 14 1 16 1 15.4.6.8.1 L (m) (d) n e (m 3 ) at 1 mtorr, 5 V 1 14.2.3.4.5.6 L (m) (e) n e (m 3 ) at 5 mtorr, 1 V 1 14.1.2.3.4.5 L (m) (f) n e (m 3 ) at 5 mtorr, 2 V Reasonable agreement between model and PIC results (submitted to Physics of Plasmas, 213) 1 16 1 15 1 14.2.3.4.5.6.2.25.3.35.4 L (m) L (m) LiebermanPSC13 1 1 16 1 15 1 14
STCHASTIC (CLLISINLESS) HEATING LiebermanPSC13 11
PIC RESULTS FR VARIUS GAPS L (5 mt, 5 V) Stochastic heating small at transition where EP edge disaears EP edge exists ositive heating in sheath, negative in core No EP edge negative heating in sheath, ositive in 5 4 3 S (W/m 2 ) 1 core.2.3.4.5.6 Large os (d) Electron Heating (W/m 3) e L=4.5 cm 2 15 1 2 5 Small 1 neg ohm ohm stoc stoc Small neg -5-1.1.2.3.4.5.1.15.2.25 LiebermanPSC13 12 1 2 1 1 S ohm S stoc L (m) (d) Electron Heating (W/m 3) L=2.5 cm e Large os
INTEGRATED S stoc (x) FR VARIUS GAPS L Integrate ower density stoc (x) from electrode toward discharge midlane Large L n e (core) > n e (sheath) ositive heating in sheath, negative heating in core Small L n e (sheath) > n e (core) negative heating in sheath, ositive heating in core LiebermanPSC13 13
TW-STEP DENSITY MDEL 1. I.D. Kaganovich, Phys. Rev. Lett. 89, 2656 (22). 2. E. Kawamura, M.A. Lieberman and A.J. Lichtenberg, Phys. Plasmas 13, 5356 (26). Use to investigate stochastic heating LiebermanPSC13 14
FIXED INS, PIC ELECTRNS (3 mt Ar, 13.56 MHz) (Models EN lasma with EP edge) (Models EN lasma with no EP edge) n i n i n e n e Sheath oscillation Sheath oscillation Positive Fermi kick? Positive low density kick? Negative high density kick? Negative high density kick? Positive low density kick? Negative Fermi kick? LiebermanPSC13 15
SUMMARY A transition from an EN discharge with an EP edge, to a narrower ga discharge with no EP edge, was investigated with PIC simulations and modeling The effects of a bi-maxwellian EEDF, with an EP edge, and sheath attachment and core uncovering, with no EP edge, need to be taken into account in modeling A transition from sheath to internal stochastic heating after the EP edge disaears is observed, and is being studied with a fixed ion, two-ste density, PIC simulation LiebermanPSC13 16