SOURCES OF NON-EQUILIBRIUM IN PLASMA MATERIALS PROCESSING*

Transcription

1 SOURCES OF NON-EQUILIBRIUM IN PLASMA MATERIALS PROCESSING* Mak J. Kushne Unvesty of Illnos Dept. of Electcal and Compute Engneeng 1406 W. Geen St. Ubana, IL USA June 2003 * Wok suppoted by Natonal Scence Foundaton, Semconducto Reseach Cop., Electc Powe Reseach Insttute, Appled Mateals. ISPC03_01

2 AGENDA Souces of non-equlbum n plasma pocessng Examples of non-equlbum Electon tanspot and electomagnetcs Wall chemsty and plasma knetcs Electostatcs n mcodschages Concludng Remaks ISPC03_02 Unvesty of Illnos Optcal and Dschage Physcs

3 SO WHAT DO WE MEAN BY (NON-)EQUILIBRIUM? Non-equlbum n plasma pocessng descbes many phenomena, fom electon tanspot to chemcal knetcs. Mathematcally..If F s a souce functon fo quantty N(t) havng dampng constant τ, then N(t)/(F o τ) dn dt () t N() t = F τ t N() t = Foτ 1 exp τ o t / τ ISPC03_03 Unvesty of Illnos Optcal and Dschage Physcs

4 NONEQUILIBRIUM IN ELECTRON TRANSPORT Electon tanspot s govened by Boltzmann s equaton, whch descbes non-equlbum evoluton of EED n space and tme. df ( ε,,t) qe(,t) f = v f ( ε,,t) v f ( ε,,t) + dt m t e Should collsons and advecton domnate, spatally dependent steady state tme solutons ae obtaned. f qe df v f v f >>, f = F( E() t,n() t ) t m dt c e Solutons may be adabatc to slow changes n electc feld o denstes of collson patnes. c ISPC03_04 Unvesty of Illnos Optcal and Dschage Physcs

5 NONEQUILIBRIUM IN ELECTRON TRANSPORT When collsons dsspate enegy (and momentum) n dstances (o tmes) small compaed to advecton, the Local Feld appoxmaton s obtaned. f t c qe m e v f >> v f, f () = F( E(),N() ) Non-equlbum s only manfested by changes n E and N. ISPC03_05 Unvesty of Illnos Optcal and Dschage Physcs

6 NONEQUILIBRIUM IN NEUTRAL (ION) TRANSPORT Nonequlbum n neutal flow often esults fom slp of dected momenta at low pessue. ( ρ v ) t N t = P = φ + S, φ = ρ v ( ρvv ) τ fj j ( v v j ) + S j / α m v v j ISPC03_06 If α v x, the veloctes equlbate and a sngle flud esults. j >> N = φ, φ = ρv / m, ρ = ρ t N t ( ρv) t = P = φ, ( ρvv) φ = N v D N τ + S o N N o Unvesty of Illnos Optcal and Dschage Physcs

7 NONEQUILIBRIUM IN CHEMICAL KINETICS Nonequlbum n chemcal knetcs (.e., the souce functon) esults fom eacton ates beng slow compaed to convecton. S = N N t = φ + S ( φ ) γ ( φ ) N jkj + N j Nlk jl + j j, l l l β l ( ) If S >> N v x, denstes become functons of only local themodynamc paametes (EOS). No = Nov, N = f ( No,T ) t Slowly vayng bounday condtons such as wall passvaton poduce long tem nonequlbum. ISPC03_07 Unvesty of Illnos Optcal and Dschage Physcs

8 NONEQUILIBRIUM IN ELECTROMAGNETICS Electomagnetcs ae govened by Maxwell s equatons. In the fequency doman, 1 ε E + J plasma + J 2 antenna µ t 2 ( ( ) ) ( E ) 2 + E = Although a quas-steady hamonc state soluton, non-equlbum occus though the consequences of E on plasma tanspot. E = ρ ε o = 0 Equlbum = q ( dn dt ) dt 0 Nonequlbum These tems most often poduce electostatc waves. ISPC03_08 Unvesty of Illnos Optcal and Dschage Physcs

9 NONEQUILIBRIUM IN ELECTROMAGNETICS Nonequlbum often occus though the feedback between the E-felds, electon tanspot and plasma geneated cuent. Cuents whch ae lnealy popotonal to felds equlbum J plasma (,t) = σ (,t) E(,t ) = σ (,t) E ( )exp( ωt + φ ( ) ) o J Cuents whch have complex elatonshps to electon (o on tanspot) ntated at emote stes nonequlbum plasma (,t) = G(,t,',t' ) σ ( ',t' ) E( ',t' )d' dt' q ( N v ) = In ICP systems, ths esults n non-monotonc decay of E- felds. ISPC03_09 Unvesty of Illnos Optcal and Dschage Physcs

10 ELECTROSTATIC NONEQUILIBRIUM The self sheldng of plasmas though the geneaton of self estong electc felds povdes electostatc equlbum. φ = q µ Φ D N Self estong electc felds ultmately poduce quasneutalty and ambpola tanspot. q N 0 φ = ε Φ = q ambpola In systems whee dmensons ae commensuate wth Debye lengths and sheldng s ncomplete, electostatc nonequlbum occus. D N N ISPC03_10 Unvesty of Illnos Optcal and Dschage Physcs

11 EXAMPLES OF NON-EQUILIBRIUM Electomagnetc non-equlbum: Anomalous skn depth Chemcal non-equlbum: Evolvng wall passvaton Electostatc nonequlbum: Mcodschages ISPC03_11 Unvesty of Illnos Optcal and Dschage Physcs

12 f BIASED INDUCTIVELY COUPLED PLASMAS Inductvely Coupled Plasmas (ICPs) wth f basng ae used hee. < 10s mto, 10s MHz, 100s W kw, electon denstes of cm SOLENOID DOME HEIGHT (cm) 0 GAS INJECTORS BULK PLASMA f BIASED SUBSTRATE WAFER PUMP PORT RADIUS (cm) s COILS s POWER SUPPLY ADVMET_1002_10 POWER SUPPLY Unvesty of Illnos Optcal and Dschage Physcs

13 Unvesty of Illnos Optcal and Dschage Physcs ELECTROMAGNETICS MODEL The wave equaton s solved n the fequency doman wth tenso conductvtes. The electostatc tem s addessed usng a petubaton to the electon densty. Conducton cuents ae knetcally deved to account fo noncollsonal effects. ( ) ( ) t J E t E E E + + = + σ ε µ µ = = = ω τ σ ε ε ρ q E n n q E e e 1 /, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) t v qn t J t v e e v o φ ω φ ω + = + = exp exp, J e ISPC03_12

14 Contnuum: 3 2 ELECTRON ENERGY TRANSPORT 5 n ekte / t = S + 2 ( Te ) L( Te ) ΦkTe κ ( Te ) Te SEB whee S(T e ) = Powe deposton fom electc felds L(T e ) = Electon powe loss due to collsons Φ = Electon flux κ(t e ) = Electon themal conductvty tenso S EB = Powe souce souce fom beam electons Knetc: A Monte Calo Smulaton s used to deve f ( ε,, t) ncludng electon-electon collsons usng electomagnetc and electostatc felds. ISPC03_13 Unvesty of Illnos Optcal and Dschage Physcs

15 Unvesty of Illnos Optcal and Dschage Physcs PLASMA CHEMISTRY, TRANSPORT AND ELECTROSTATICS Contnuty, momentum and enegy equatons fo each speces, and ste balance models fo suface chemsty. Implct soluton of Posson s equaton. ( ) ( ) + = + Φ q t - - s N q t t φ ρ ε S N t N + = ) v ( ( ) ( ) ( ) ( ) B v E m N q N v v kn T m t N v µ + + = 1 ( ) j j j j m m j v v N N m j ν + ( ) ) ( ) U ( U Q E m N q N P t N ω ν ν ε ε + = ± j j B j j j j B j j j j s T k R N N T T k R N N m m m E m N q 3 ) ( ν ISPC03_14

16 FORCES ON ELECTRONS IN ICPs vθ B R, B Z B R Eθ δ vθ x B R λs Es Inductve E-feld povdes azmuthal acceleaton; depth 1-3 cm. δ = Electostatc (capactve) penetates (100s µm to mm) Non-lnea Loentz Foce 1 2 ( m ( e µ n ) 2 e 1 ( ) 2 2 λ S 10λ D, λd = kte ( 8πnee ) F = v θ o e B f ISPC03_35 Unvesty of Illnos Optcal and Dschage Physcs

17 ANAMOLOUS SKIN EFFECT AND POWER DEPOSITION Collsonal heatng: λ mfp < δ skn, J e (, t) = σ, Anomalous skn effect: (, t) E( t) Ref: V. Godyak, Electon Knetcs of Glow Dschages EIND_0502_12 J e λ mfp (, t) = σ F = > δ (, ', t, t' ) E( ', t' ) v skn B Electons eceve (postve) and delve (negatve) powe fom/to the E-feld. E-feld s non-monotonc. d ' dt' Unvesty of Illnos Optcal and Dschage Physcs

18 ELECTRON DENSITY: A, 10 mto, 200 W, 7 MHz 4 3 [e] cm EXP. R =0 cm (x 0.75) EXP. R =4 cm (x 0.75) HEIGHT (cm) Model s about 20% below expements. Ths lkely has to do wth detals of the sheath model. ISPC03_15 V. Godyak et al, J. Appl. Phys. 85, 703 (1999); pvate communcaton Unvesty of Illnos Optcal and Dschage Physcs

19 TIME DEPENDENCE OF THE EED Tme vaaton of the EED s mostly at hghe eneges whee electons ae moe collsonal. Dynamcs ae domnantly n the electomagnetc skn depth whee both collsonal and non-lnea Loentz Foces) peak. The second hamonc domnates these dynamcs. SNLA_0102_10 A, 10 mto, 100 W, 7 MHz, = 4 cm ANIMATION SLIDE Unvesty of Illnos Optcal and Dschage Physcs

20 TIME DEPENDENCE OF THE EED: 2 nd HARMONIC Electons n skn depth quckly ncease n enegy and ae launched nto the bulk plasma. Undegong collsons whle tavesng the eacto, they degade n enegy. Those suvvng clmb the opposte sheath, exchangng knetc fo potental enegy. Seveal pulses ae n tanst smultaneously. Electon tanspot nonequlbum! ISPC03_36 A, 10 mto, 100 W, 7 MHz, = 4 cm Ampltude of 2 nd Hamonc ANIMATION SLIDE Unvesty of Illnos Optcal and Dschage Physcs

21 2 nd HARMONIC OF EED WITHOUT LORENTZ FORCE Excludng v x B tems, the non-lnea Loentz Foce s emoved. Electons ae altenately heated and cooled n the skn depth, out of phase wth E θ, wth some collsonal heatng. Hgh enegy electons do not popagate (othe than by dffuson) outsde the skn laye. Ampltude of 2 nd Hamonc SNLA_0102_12 A, 10 mto, 100 W, 7 MHz, = 4 cm ANIMATION SLIDE Unvesty of Illnos Optcal and Dschage Physcs

22 2 nd HARMONIC OF EED: 1 mto, 3 MHz By deceasng fequency, B f nceases, the skn depth lengthens and NLF nceases. Lowe pessue extends the electon mean fee path. Sgnfcant modulaton extends to lowe eneges. Ampltude of 2 nd Hamonc SNLA_0102_14 A, 1 mto, 100 W, 3 MHz, = 4 cm ANIMATION SLIDE Unvesty of Illnos Optcal and Dschage Physcs

23 TIME DEPENDENCE OF EED: 1 mto, 3 MHz At educed pessue and fequency, the condtons fo the nonlnea skn effect ae fulflled. The EED s essentally depleted of low enegy electons n the skn laye. SNLA_0102_15 A, 1 mto, 100 W, 3 MHz, = 4 cm ANIMATION SLIDE Unvesty of Illnos Optcal and Dschage Physcs

24 COLLISIONLESS TRANSPORT ELECTRIC FIELDS E θ exhbts extema and nodes esultng fom ths noncollsonal tanspot. Sheets of electons wth dffeent phases povde cuent souces ntefeng o enfocng the electc feld fo the next sheet. Axal tanspot esults fom foces. v B f Electomagnetc nonequlbum! ANIMATION SLIDE ISPC03_37 A, 10 mto, 7 MHz, 100 W Unvesty of Illnos Optcal and Dschage Physcs

25 POSITIVE POWER DEPOSITION: POSITIVE AND NEGATIVE The end esult s egons of postve and negatve powe deposton. NEGATIVE SNLA_0102_19 A, 10 mto, 7 MHz, 100 W Unvesty of Illnos Optcal and Dschage Physcs

26 POWER DEPOSITION vs FREQUENCY The shote skn depth at hgh fequency poduces moe layes of negatve powe deposton of lage magntude. Ref: Godyak, PRL (1997) 6.7 MHz (5x W/cm 3 ) A, 10 mto, 200 W 13.4 MHz (8x W/cm 3 ) SNLA_0102_32 MIN MAX Unvesty of Illnos Optcal and Dschage Physcs

27 TIME DEPENDENCE OF A IONIZATION: PRESSURE Although B f may be nealy the same, at lage P, v θ and meanfee-paths ae smalle, leadng to lowe hamonc ampltudes. 5 mto 20 mto 6 x x cm -3 s x x cm -3 s -1 A/N 2 =60/40, 10 MHz ANIMATION SLIDE SNLA_0102_29 MIN MAX Unvesty of Illnos Optcal and Dschage Physcs

28 EXAMPLES OF NON-EQUILIBRIUM Electomagnetc non-equlbum: Anomalous skn depth Chemcal non-equlbum: Evolvng wall passvaton Electostatc nonequlbum: Mcodschages ISPC03_16 Unvesty of Illnos Optcal and Dschage Physcs

29 SURFACE CHEMISTRY OF S ETCHING IN Cl 2 PLASMAS Etchng of S n Cl 2 plasmas poceeds by passvaton of S stes, followed by on actvated emoval of SCl n etch poduct. Cl Cl M + SCl n S SCl SCl n S Etch poducts depost on eacto walls. Cl atom ecombnaton and SCl n stckng slows on the passvated sufaces. Cl Cl2 SCln SCln Cl Cl SCln SCln Wall SCln (SCln)2 (SCln)m Wall ISPC03_17 Unvesty of Illnos Optcal and Dschage Physcs

30 Emsson Ion Flux Passvaton LONG TERM PASSIVATION OF WALLS Expemental measuements of optcal emsson, on flux and etch ates dung Cl etchng of S have long tem behavo. Tansents ae coelated wth nceasng flm thckness on walls, educng stckng coeffcents fo Cl and SCl. ICP, Cl 2, 10 mto, 800 W. Plasma-suface chemcal nonequlbum! ISPC03_18 S. J. Ullal, T. W. Km, V. Vahed and E. S. Aydl, JVSTA 21, 589 (2003) Unvesty of Illnos Optcal and Dschage Physcs

31 CHEMICAL NONEQUILIBRIUM: A/Cl 2 WITH WALL PASSIVATION Computatonally contast A/Cl 2 ICPs etchng S wth SCl 2 poduct, wth/wthout wall passvaton. Implement a multstep passvaton model begnnng wth SCl 2 polymezaton. Hghe degee of polymezaton educes Cl eassocaton. Wthout wall passvaton: Cl wall Cl 2, p = 0.3 Wth fnal wall passvaton: Cl wall Cl 2, p = 0.01 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm ISPC03_19 Unvesty of Illnos Optcal and Dschage Physcs

32 [SCl 2 ] WITH/WITHOUT WALL PASSIVATION Wthout passvaton, SCl 2 has a longe esdence tme and bulds to hghe denstes. Note momentum tansfe fom jettng nozzle. ISPC03_21 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm Unvesty of Illnos Optcal and Dschage Physcs

33 [SCl 2 ] TRANSIENT WITH/WITHOUT WALL PASSIVATION SCl 2 ntally stcks to walls n both cases. As passvaton pogesses, the stckng coeffcent deceases. Wth Passvaton Wthout Passvaton ANIMATION SLIDE ISPC03_24 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm Unvesty of Illnos Optcal and Dschage Physcs

34 [Cl] WITH/WITHOUT WALL PASSIVATION Passvaton educes Cl losses on the walls, nceasng ts densty and makng pumpng the lagest loss. ISPC03_23 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm Unvesty of Illnos Optcal and Dschage Physcs

35 [Cl] TRANSIENT WITH WALL PASSIVATION When walls ae clean, Cl eassocaton s a lage snk. As the walls passvate, suface losses decease (except to wafe). ANIMATION SLIDE ISPC03_25 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm Unvesty of Illnos Optcal and Dschage Physcs

36 [Cl 2 ] WITH/WITHOUT WALL PASSIVATION Wthout passvaton, Cl 2 has souces at walls, asng ts densty. In both cases, dssocaton facton s lage. ISPC03_22 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm Unvesty of Illnos Optcal and Dschage Physcs

37 [e] WITH/WITHOUT WALL PASSIVATION Wthout wall passvaton, souces Cl 2 fom the walls ae lage, esultng n moe dssocatve attachment and lowe [e]. ISPC03_20 A/Cl 2 = 80/20, 10 mto, 400 W, 200 sccm Unvesty of Illnos Optcal and Dschage Physcs

38 EXAMPLES OF NON-EQUILIBRIUM Electomagnetc non-equlbum: Anomalous skn depth Chemcal non-equlbum: Evolvng wall passvaton Electostatc non-equlbum: Mcodschages ISPC03_26 Unvesty of Illnos Optcal and Dschage Physcs

39 MICRODISCHARGE PLASMA SOURCES Mcodschages ae plasma devces whch leveage pd scalng to opeate dc atmosphec glows 10s 100s µm n sze. MEMS fabcaton technques enable nnovatve stuctues fo dsplays and detectos. Although smla to PDP cells, MDs ae dc devces whch lagely ely on nonequlbum beam components of the EED. Electostatc nonequlbum esults fom the small sze. Debye lengths and cathode falls ae commensuate wth sze of devces. L 1/ 2 ( 2V ε / ( qn )) m cathode Fall = c 0 I µ ISPC03_27 1/ 2 T ev λd 750 cm 10µ m, 3 ne( cm ) Unvesty of Illnos Optcal and Dschage Physcs

40 PYRAMIDAL MICRODISCHARGE DEVICES S MDs wth 10s µm pyamdal cavtes dsplay nonequlbum behavo: Townsend to negatve glow tanstons. Small sze also mples electostatc nonequlbum. Delectc Slcon Cathode Plasma Anode S.-J. Pak, et al., J. Sel. Topcs Quant. Electon 8, 387 (2002); Appl. Phys. Lett. 78, 419 (2001). ISPC03_28 Unvesty of Illnos Optcal and Dschage Physcs

41 Unvesty of Illnos Optcal and Dschage Physcs Chaged patcle contnuty (fluxes by Shafette-Gummel fom) Posson s Equaton fo Electc Potental Bulk contnuum electon enegy tanspot and MCS beam. Neutal contnuty and enegy tanspot. ( ) ( ) S N D qn t N + Φ = v v µ ρ V ρ S Φ ε + = ( ) e e e e q j, T 2 5 N n E j t n φ λ εϕ κ ε = = ( ) g o o P T t ct, S N N DN v t N + = + = κ ρ 2-D MODELING OF MICRODISCHARGE SOURCES ISPC03_29

42 DESCRIPTION OF MODEL: MCS MESHING Tanspot of enegetc seconday electons s addessed wth a Monte Calo Smulaton. ISPC03_30 Supempose Catesan MCS mesh on unstuctued flud mesh. Constuct Geens functons fo ntepolaton between meshes. Electons and the pogeny ae followed untl slowng nto bulk plasma o leavng MCS volume. Electon enegy dstbuton s computed on MCS mesh. EED poduces souce functons fo electon mpact pocesses whch ae ntepolated to flud mesh. Unvesty of Illnos Optcal and Dschage Physcs

43 MODEL GEOMETRY: S PYRAMID MICRODISCHARGE Investgatons of a cylndcally symmetc S pyamd MD. Typcal meshes have 5, nodes, dynamc ange of ISPC03_31 Unvesty of Illnos Optcal and Dschage Physcs

44 BASE CASE: Ne, 600 To, 50 µm DIAMETER Optmum condtons poduces lage enough chage densty to wap electc potental nto cathode well. In spte of lage Te, onzaton s domnated by beam electons. ISPC03_32 Ne, 600 To, 50 µm damete, 200 V, 1 MΩ Unvesty of Illnos Optcal and Dschage Physcs

45 BASE CASE: CHARGED PARTICLE DENSITIES Thee ae few egons of quas-neutalty o whch ae postve column-lke. [e] > cm -3 fo 10s µa. Excted state denstes >10 15 cm -3 ae commensuate wth macoscopc pulsed dschage devces. ISPC03_33 Ne, 600 To, 50 µm damete, 200 V, 1 MΩ Unvesty of Illnos Optcal and Dschage Physcs

46 ELECTRON DENSITY vs PRESSURE The dschage becomes moe confned at hghe pessues due to shote stoppng length of beam electons. Ne, 50 µm damete, V, 1 MΩ ISPC03_34 Unvesty of Illnos Optcal and Dschage Physcs

47 BEAM vs BULK: NONEQUILIBRIUM IONIZATION SOURCES The theshold fo Ne Ne ++ s 41 ev. Montong S[Ne ++ ]/S[Ne + ] sgnals MD tanstons fom Townsend-lke to negatve glow-lke. Negatve glow-lke exctaton occus wth P < 550 To. ISPC03_35 Ne, 50 µm damete, V, 1 MΩ Unvesty of Illnos Optcal and Dschage Physcs

48 SCALING WITH SIZE: pd, j = CONSTANT Pd scalng should not be a steadfast expectaton. Sheath popetes scale wth absolute plasma densty and not pd. Scalng eques caeful ballastng to keep [e] and sheath popetes constant. ISPC03_36 Ne, 200 V, 1 MΩ Unvesty of Illnos Optcal and Dschage Physcs

49 SCALING WITH SIZE: pd, ballast = CONSTANT When keepng ballast constant, j deceases n lage devces, esultng n lowe electon densty, less sheldng, moe electostatc equlbum. Electon cloud pops out of cavty. ISPC03_37 Ne, 200 V, 1 MΩ Unvesty of Illnos Optcal and Dschage Physcs

50 CONCLUDING REMARKS and ACKNOWLEDGEMENTS Nonequlbum n plasma pocessng s eveywhee you look Electomagnetcs Plasma dynamcs Suface chemsty Electostatcs The development of computatonal and expemental technques to esolve non-equlbum wll contnue to be mpotant n mpovng ou fundamental undestandng of these pocesses. Collaboatos D. Alex Vasenkov M. Avnd Sankaan ISPC03_31 Unvesty of Illnos Optcal and Dschage Physcs