2-DIMENSIONAL MODELING OF PULSED PLASMAS WITH AND WITHOUT SUBSTRATE BIAS USING MODERATE PARALLELISM*

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1 IEEE Pulsed Powe / Plasma Scence Confeence June 17 -, 1 Las Vegas, Nevada -DIMENSIONAL MODELING OF PULSED PLASMAS WITH AND WITHOUT SUBSTRATE BIAS USING MODERATE PARALLELISM* Pamod Subamonum** and Mak J. Kushne*** **Depatment of Chemcal Engneeng ***Depatment of Electcal and Compute Engneeng Unvesty of Illnos Ubana, IL 6181 emal: subamon@uuc.edu mk@uuc.edu *Wok suppoted by SRC, NSF and AFOSR/DARPA

2 AGENDA Intoducton Descpton of the modeately paallel model Valdaton Popetes of Pulsed Cl Plasmas Wth and wthout f substate bas Bas voltage Feedstock composton Conclusons ICOPS1_PRAMOD_1 Unvesty of Illnos Optcal and Dschage Physcs

3 PULSED ICP PLASMAS Pulsed plasmas Damage fee plasma etchng wth bette unfomty and ansotopy Impoved etch selectvty by modfyng the ato of chemcal speces Addtonal contollable degees of feedom : Duty cycle and modulaton fequency Reduce chage buldup on wafes and suppess notchng Reduced patcle geneaton n the plasma Cuent models fo nvestgatng pulsed opeaton ae typcally global o 1-dmensonal Dffcult to esolve long-tem tansents n mult-dmensonal plasma equpment models Modeately paallel algothms fo -dmensonal hybd models wee developed to nvestgate long tem tansents. ICOPS1_PRAMOD_ Unvesty of Illnos Optcal and Dschage Physcs

4 DESCRIPTION OF THE PARALLEL HYBRID MODEL The HPEM, a modula smulato, was paallelzed by employng a shaed memoy pogammng paadgm on a Symmetc Mult- Pocesso (SMP) machne. E,B S EMM EETM FKS The Electomagnetcs, Electon Monte Calo and Flud-knetcs Modules ae smultaneously executed on thee pocessos. The vaables updated n dffeent modules ae mmedately made avalable though shaed memoy fo use by othe modules. σ N SHARED MEMORY E,B σ S E,B,N E,N,σ S EMM EETM FKS E,N,σ Dynamc load balancng s mplemented to equal the tasks on dffeent pocessos. ICOPS1_PRAMOD_3 Unvesty of Illnos Optcal and Dschage Physcs

5 GOVERNING EQUATIONS IN HPEM ICOPS1_PRAMOD_4 Unvesty of Illnos Optcal and Dschage Physcs Contnuty (heavy speces) : Momentum (heavy speces) : Enegy (heavy speces) : Dft-dffuson (electon) : ( ) S N v t N + = ( ) ( ) ( ) ( ) + τ + = s s v v k N N v N v P m 1 B v E N m q t v N ( ) ± = B B B s B T k R N N T T k N N m m m T T k E m N q E m N q T N k t 3 ) ( ν λ ϕ ν ω ν ν ( ) e e e s e e e S n D E n t n + + µ =

6 Electons: GOVERNING EQUATIONS IN HPEM (contnued) Enegy k Te + ( ΓTe ) = Pheatng Ploss Monte Calo Smulaton dv dt = q m e e ( E + v x B) d = v dt ν ε = m e 1 σ,k k N Posson's equaton: ε Φ Wave equaton: Vecto potental: dρ(t) (t + t) = ρ(t) + t t = ρ(t) + q t[. ϕ + S ( ε E) ( E + J ) 1 σ E = + µ t t 1 A = B = A µ B s ] ICOPS1_PRAMOD_5 Unvesty of Illnos Optcal and Dschage Physcs

7 REACTOR GEOMETRY AND SIMULATION CONDITIONS Reacto geomety taken fom Malyshev et. al.* Base case condtons: Peak ICP powe: 6 W f bas: 5 V, 1 MHz PRF: 1 khz Cols Delectc Nozzle Refeence Pont Pessue: 1 mto Gas flow ate: 1 sccm Cl, A/Cl 6 Wafe Electode Pump Pot *M. V. Malyshev, V. M. Donnelly, Plasma Souces Sc. Technol. 9, 353 () ICOPS1_PRAMOD_6 Unvesty of Illnos Optcal and Dschage Physcs

8 DYNAMICS OF PULSED PLASMAS: ELECTRON DENSITY ICP powe at 1 MHz (f) s pulsed at PRF of 1 khz. Seveal pulses ae equed to attan peodc steady state [e] attans steady state value n the late actveglow coespondng to cw opeaton [e] decays seveal odes of magntude, as the electons ae lost due to dssocatve attachment Wth substate bas, [e] attans a steady state value n the late afte glow coespondng to capactve mode ICOPS1_PRAMOD_7A Electon Densty (cm -3 ) NO BIAS Cl, 1 mto, 6 W, 1 MHz, 1 khz/5% BIAS NO BIAS BIAS Tme (µs) Electon Densty Unvesty of Illnos Optcal and Dschage Physcs

9 DYNAMICS OF PULSED PLASMAS: ELECTRON TEMPERATURE T e peaks at the leadng edge, as the powe deposton occus nto a smalle nventoy of electons No substate bas esults n hghe peak T e, as the electons decay away seveal odes of magntude lowe n the late afteglow T e s smla dung late actveglow and ealy afteglow peod Wth substate bas, T e nceases n the late afteglow due to sheath heatng Electons themalze to gas tempeatue wthout substate bas ICOPS1_PRAMOD_7B Electon Tempeatue (ev) NO BIAS BIAS NO BIAS BIAS Tme (µs) Electon Tempeatue Unvesty of Illnos Optcal and Dschage Physcs

10 VALIDATION OF THE MODEL: PHYSICS Model esults compae well wth expements* Wth substate bas, T e ses to values above the steady state value Electon Tempeatue (ev) Exp. [e] Model Exp. 3.5 Te Model Tme (µs) Electon Densty (cm -3 ) Electon Tempeatue (ev) [e] Model 1 11 Exp. 1 1 Te Exp. 1 9 Model Tme (µs) Electon Densty (cm -3 ) Wthout f bas Wth f bas (5 V, 1 MHz) Cl, 1 mto, 6 W, 1 MHz, 1 khz/5% * M. V. Malyshev, V. M. Donnelly, Plasma Souces Sc. Technol. 9, 353 () ICOPS1_PRAMOD_8 Unvesty of Illnos Optcal and Dschage Physcs

11 SHEATH HEATING IN PULSED PLASMAS WITH SUBSTRATE BIAS Sheath heatng scales wth the squae of the sheath speed, v s Sheath thckness l scales as n e -1/ Sheath speed v s» w l Total sheath heatng H, theefoe scales as H ~ v s n e and s not a functon of electon densty Specfc heatng ate (pe electon), h, scales as H/n e ~ 1/n e As the electon densty decays, pmaly by dssocatve attachment to Cl, the sheath thckness l nceases Oscllatng sheath poduces a net ncease n specfc heatng ate h and hence an ncease n (o slowng n ate of decease n) T e ICOPS1_PRAMOD_9 Unvesty of Illnos Optcal and Dschage Physcs

12 Cl PULSED PLASMAS WITH AND WITHOUT RF BIAS: ELECTRON DENSITY 4 No Bas Bas The peak [e] mgates to below the cols dung "powe-on" whee the souce s maxmum. Heght (cm) 18 1 (a) 8 µs ON (d) 8 µs ON 6 [e] s smla wth and wthout substate bas dung the actveglow and ealy afteglow phase. As the powe s tuned off, n the ealy afteglow ambpola losses domnate ove geneaton of electons. Heght (cm) (b) 45 µs ON (c) 95 µs OFF (e) 45 µs ON (f) 95 µs OFF In the late afteglow, sheath heatng domnates and the plasma tanstons fom nductvely coupled to capactvely coupled mode wth substate bas. Heght (cm) Radus (cm) Radus (cm) 1 x 1 8 cm -3 1 x 1 11 cm -3 ICOPS1_PRAMOD_1 Unvesty of Illnos Optcal and Dschage Physcs

13 Cl PULSED PLASMAS WITH AND WITHOUT RF BIAS: ELECTRON TEMPERATURE The peak n T e at the leadng edge s due to powe deposton nto smalle nventoy of electons. Heght (cm) (a) 3 No Bas µ s ON Bas (d) 3 µs ON 6 Sheath heatng pevals, even afte 1 ms nto the powe-on peod, owng to low n e. At 45 ms, the T e pofle looks smla to no substate bas case Heght (cm) (b) 45 µs ON (e) 45 µ s ON Afte 5 ms nto the powe-off peod, sheath heatng begns Heght (cm) 18 1 (c) 95 µs OFF (f) 95 µ s OFF T e nceases n the late afteglow, as powe s deposted nto electons nea the substate by oscllatng sheath. ICOPS1_PRAMOD_ Radus (cm) Radus (cm).1 ev 1 ev Unvesty of Illnos Optcal and Dschage Physcs

14 EFFECT OF BIAS VOLTAGE AND ICP POWER ON ONSET TIME As the bas voltage s nceased, the onset tme to the capactve couplng mode, t c, deceases. Ths s attbuted to the geate sheath heatng at hghe bas voltages. As the ICP powe s vaed fom 45 W to 6 W, t c nceases as the peak electon densty n the late actve glow s hghe (thnne sheath). At hghe ICP powes, the plasma s moe dssocatng and less attachng, whch nceases the [e] n the late actve glow and nceases t c. Onset tme to capactve mode (µs) Cl pulsed plasma 1 mto, 1 sccm PRF: 1 khz Duty cycle: 5% Bas: 5 V 45 W 6 W Bas Voltage (V) ICOPS1_PRAMOD_1 Unvesty of Illnos Optcal and Dschage Physcs

15 EFFECT OF GAS MIXTURES ON ONSET TIME As the A facton s nceased, t c nceases sgnfcantly. Fo A/Cl =4/6, t c s longe than the pulse off tme, due to the hghe [e] n afteglow (thnne sheath). 6 A/Cl pulsed plasma 45 W, 1 mto 1 sccm PRF: 1 khz Duty cycle: 5% Bas: 5 V As sheath heatng s educed, negatve ons can be extacted dung the pulse off peod. Bas voltage, fequency and feedstock composton need to be optmzed to nvestgate the possblty of negatve on extacton wth substate bas. ICOPS1_PRAMOD_13 Electon Tempeatue (ev) Tme (µs) Unvesty of Illnos Optcal and Dschage Physcs

16 CONCLUSIONS A new -D hybd model was developed to addess tansents based on modeate computatonal paallelsm. Computatonal studes wee pefomed fo pulsed opeaton of Cl and A/Cl ICPs. T e at the leadng edge s nealy twce the steady state value. In electonegatve plasmas, electon-on plasma n the actveglow becomes on-on plasma n the afteglow. Fo pulsed Cl plasmas wth contnuous substate bas, sheath heatng was obseved to be pedomnant n the late afteglow. The t c nceases wth ICP powe as the plasma s moe dssocated n the late actveglow and t takes moe tme fo electon densty to decay away. The extacton of negatve ons n the afteglow s dffcult wth a contnuous substate bas as the sheaths typcally do not collapse. ICOPS1_PRAMOD_14 Unvesty of Illnos Optcal and Dschage Physcs