Physics of Very High Frequency (VHF) Capacitively Coupled Plasma Discharges

Transcription

1 Physcs of Vry Hgh Frquncy (VHF) Capactvly Coupld Plasma Dschargs Shahd Rauf, Kallol Bra, Stv Shannon, and Kn Collns Appld Matrals, Inc., Sunnyval, CA AVS 54 th Intrnatonal Symposum Sattl, WA Octobr 15-19, 2007.

2 Agnda Introducton Computatonal Modl Plasma Dynamcs at Vry Hgh Frquncy Influnc of Chambr Dsgn Influnc of Plasma Chmstry Conclusons

3 Introducton Strngnt procssng rqurmnts hav ld to th dvlopmnt of vry hgh frquncy (VHF) capactvly coupld plasma (CCP) tchrs n rcnt yars. Larg lctrod szs and hgh frquncs dctat that lctromagntc ffcts can play a major rol n dtrmnng plasma spatal profl. Elctromagntc ffcts n CCPs hav prvously bn nvstgatd usng analytcal modls by Lbrman 1 and Chabrt. 2 In ths papr, w dscrb a 2-dmnsonal computatonal plasma modl that slf-consstntly consdrs lctromagntc ffcts n th opraton of VHF CCPs. Th modl s usd to undrstand dscharg bhavor n Ar plasmas opratng at 180 MHz. It s found that plasma spatal profl s nfluncd by both lctrostatc and lctromagntc ffcts, whr lctromagntc ffcts pull th plasma towards th chambr cntr whl lctrostatc ffcts ar mor domnant at th lctrod dg. 1. M. A. Lbrman t al, Plasma Sourcs Sc. Tchnol. 11, 283 (2002). 2. P. Chabrt t al, Phys. Plasmas 11, 1775 (2004).

4 Computatonal Modl - 1 Th computatonal modl conssts of th followng quatons: Contnuty quaton (chargd spcs): Contnuty quaton (nutral spcs): Elctron nrgy consrvaton quaton: Maxwll quatons: t B E = t E J B o o + = ε μ μ 0 = B ε = ρ E S n E q q n D t n = μ S n D t n = = T Γ T n n P t n T λ κ

5 Computatonal Modl - 2 Th followng potntal formulaton s usd to solv th Maxwll quatons: B = A E A = φ A = 0 t Maxwll quatons ar thn transformd nto: ( ε φ) = ρ εμo 2 2 A 2 A t A σμo t = μ J o φ + εμo + μoσ φ t (2) Th coupld st of Eq. and contnuty quatons for chargd spcs ar solvd mplctly n tm. Equaton (2) s solvd n frquncy doman usng slf-consstntly computd currnts and potntal. Th modl s capabl of addrssng n harmoncs and 3 harmoncs ar consdrd n ths papr.

6 Trmnology E Elctrostatc lctrc fld = φ A t Elctromagntc lctrc fld Elctron total powr dposton: P = J E dv V Elctromagntc powr dposton: 2 P ( EM ) = σω V A 2 dv Elctrostatc powr dposton: P ( ES) = P P ( EM )

7 Plasma Dynamcs at VHF - 1 At 100 W, pak n lctron dnsty occurs at th chambr cntr. Tm-avragd lctrcal potntal (φ (0) ) s small. n (Max = m -3 ) SO 2 φ (0) (Max = 35.7 V, Mn = V) φ RF C 15 cm RF currnt flowng through th plasma gnrats a standng wav n th ntr-lctrod gap. 3.8 cm J z (Max = A/m 2 ) A z (Max = V s/m) 100 mt, 100 W, Ar, 180 MHz

8 Plasma Dynamcs at VHF - 2 Wth a larg plasma dnsty, shaths ar thn and lctrons gan substantal nrgy n th shath/pr-shath rgon (lctrostatc powr dposton). Elctrons ar also hatd n th cntr of th chambr by th lctromagntc standng wav (lctromagntc powr dposton). Plasma profl s strongly nfluncd by lctromagntc powr dposton, whch occurs ovr th bulk of th plasma rgon. φ (Max = V) P (ES) (Max = W/m -3 ) ωa z (Max = V/m) P (EM) (Max = W/m -3 ) 100 mt, 100 W, Ar, 180 MHz

9 Effct of RF Powr on Ar Plasma Charactrstcs - 1 Ion Sat. Currnt (a.u.) Exprmntal and computatonal rsults show that pak n plasma dnsty movs towards lctrod dg as RF powr s ncrasd Langmur Prob Mas. 100 mt, 1.25, 162 MHz 400 W 800 W 600 W 1000 W 1500 W 200 W Radus (cm) [] (Max = m -3 ) 50 W [] (Max = m -3 ) 100 W [] (Max = m -3 ) 200 W [] (Max = m -3 ) 400 W [] (Max = m -3 ) 1000 W 100 mt, Ar, 180 MHz

10 Effct of RF Powr on Ar Plasma Charactrstcs W 800 W J r (Max = 52.9 A/m 2 ) J r (Max = A/m 2 ) A r 1) (Max = V s/m) A r 1) (Max = V s/m) A z (Max = V s/m) A z (Max = V s/m) P (EM) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) 100 mt, Ar, 180 MHz

11 Effct of Intr-Elctrod Gap - 1 Plasma s mor unform at smallr ntr-lctrod gap. Plasma dnsty ncrass n th cntr of th chambr as th gap s ncrasd. Ths s du to largr loss at smallr gaps wth an ffctvly largr ara/volum rato [] (Max = m -3 ) [] (Max = m -3 ) [] (Max = m -3 ) mt, Ar, 100 W, 180 MHz

12 Effct of Intr-Elctrod Gap - 2 Plasma s mor unform at smallr gaps bcaus lctrostatc ffcts ar strongr, plasma producd at th lctrod dg has lss opportunty to dffus to chambr cntr, and lctromagntc powr dposton s ovr a smallr volum A z (Max = V s/m) A z (Max = V s/m) P (ES) (Max = W/m -3 ) P (ES) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) 100 mt, Ar, 100 W, 180 MHz

13 Effct of Lowr Elctrod Radus - 1 Plasma s qut unform ovr th lowr lctrod f th lowr lctrod radus s 10 cm. Elctromagntc ffcts mov th plasma to chambr cntr as lctrod sz s ncrasd. Plasma s mor ntns wth a smallr lowr lctrod for a gvn nput powr as th powr s dpostd ovr a smallr volum. [] (Max = m -3 ) 22.5 cm [] (Max = m -3 ) 15 cm [] (Max = m -3 ) 10 cm 100 mt, Ar, 100 W, 180 MHz

14 Effct of Lowr Elctrod Radus - 2 Elctrostatc ffcts ar rlatvly mor mportant wth a smallr lowr lctrod. 10 cm 22.5 cm A z (Max = V s/m) A z (Max = V s/m) P (ES) (Max = W/m -3 ) P (ES) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) 100 mt, Ar, 100 W, 180 MHz

15 Effct of SF 6 Addton to Ar - 1 Elctron dnsty dcrass consdrably as SF 6 s addd to an Ar plasma. Elctron dnsty pak movs towards th lctrod dg wth SF 6 addton Langmur Prob Mas. SF 6 0% [] (Max = m -3 ) Elctron Dnsty (m -3 ) % SF 6 5% SF 6 10% SF 6 15% SF 6 20% SF Radus (cm) 10% 20% 30% [] (Max = m -3 ) [] (Max = m -3 ) [] (Max = m -3 ) 500 W, 50 mt, Ar/SF 6, 3.76, 160 MHz 100 mt, 100 W, Ar/SF 6, 180 MHz

16 Effct of SF 6 Addton to Ar - 2 SF 6 s hghly lctrongatv and ngatv on dnsty s ordrs of magntud largr than lctron dnsty wth > 10% SF 6. Major ngatv ons ar SF 6- and SF 5-. Ar + s th domnant postv on. 100% Ar 70% Ar, 30% SF 6 [] (Max = m -3 ) [] (Max = m -3 ) [Ar + ] (Max = m -3 ) [Ar + ] (Max = m -3 ) [SF 6- ] (Max = m -3 ) 100 mt, 100 W, Ar/SF 6, 180 MHz

17 Effct of SF 6 Addton to Ar - 3 As n dcrass wth SF 6 addton, largr RF potntal s ndd to dlvr th sam powr n th plasma, makng lctrostatc ffcts mor mportant. Smultanously, currnt through th plasma dcrass makng lctromagntc ffcts wakr. 100% Ar 70% Ar, 30% SF 6 φ (Max = V) φ (Max = V) P (ES) (Max = W/m -3 ) P (ES) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) 100 mt, 100 W, Ar/SF 6, 180 MHz

18 Effct of Uppr Elctrod Radus 100 W - 1 As long as th uppr lctrod s largr than th lowr lctrod, uppr lctrod sz has lttl mpact on th plasma dstrbuton undr condtons whr lctromagntc standng wav ffcts ar domnant. [] (Max = m -3 ) [] (Max = m -3 ) 17.8 cm 20.1 cm [] (Max = m -3 ) 22.4 cm 100 mt, Ar, 100 W, 180 MHz

19 Effct of Uppr Elctrod Radus 100 W - 2 Uppr lctrod sz has lttl mpact on powr dposton or lctromagntc flds. A z (Max = V s/m) 17.8 cm 22.4 cm A z (Max = V s/m) P (ES) (Max = W/m -3 ) P (ES) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) P (EM) (Max = W/m -3 ) 100 mt, Ar, 100 W, 180 MHz

20 Effct of Uppr Elctrod Radus 800 W At larg RF powrs whr lctron dnsty s larg and lctromagntc ffcts bcom wakr, uppr lctrod sz has lttl mpact on plasma dstrbuton nar th chambr cntr. Plasma at th lowr lctrod dg starts gttng prturbd whn uppr lctrod sz bcoms comparabl to lowr lctrod sz. [] (Max = m -3 ) [] (Max = m -3 ) [] (Max = m -3 ) 17.8 cm 20.1 cm 22.4 cm 100 mt, Ar, 800 W, 180 MHz

21 Conclusons A slf-consstnt 2-dmnsonal plasma modl that ncluds th full st of Maxwll quatons s usd to undrstand th bhavor of VHF capactvly coupld plasmas. Plasma spatal profl s nfluncd by both lctrostatc and lctromagntc ffcts, whr lctromagntc ffcts pull th plasma towards th chambr cntr whl lctrostatc ffcts ar mor domnant at th lctrod dg. Currnt through th dscharg crats a standng lctromagntc wav n th chambr, whch pulls th plasma towards th cntr at low RF powrs. As RF powr s ncrasd, nductv ffcts bcom mportant and plasma dnsty pak movs towards th lctrod dg. Th rlatv mportanc of lctrostatc ffcts can b ncrasd by dcrasng ntr-lctrod gap.