Stochastic Heating in RF capacitive discharges

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Marshall Price
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1 Stochatic Hating in RF capacitiv dicharg PTSG Sminar Emi Kawamura Thr ar two main mchanim for hating lctron in RF capacitiv dicharg: ohmic and tochatic hating. Plama ritivity du to lctron-nutral colliion lad to ohmic hating whil momntum tranfr from high voltag moving ath lad to tochatic hating. Thu, ohmic hating i mainly a ulk phnomna whil tochatic hating i localizd in th ath ara. In thi talk, w try to undrtand th natur of tochatic hating and how it dpnd on variou paramtr uch a prur, ath vlocity, frquncy and dnity profil.

2 Momntum tranfr from a moving ath In th La fram: Bfor Colliion Aftr Colliion n = n = n n = n = n u = u u f x (t) V m x x (t) V m x To find u f mov to fram whr x i at rt: Bfor Colliion Aftr Colliion u = u V = (u + V ) u f = u + V x x x x Tranfrring ack to th la fram, w hav u f = u f + V = u + 2V

3 2 Stochatic Hating I (L& L Ch. ) For ach colliion, E = m 2 (u2 f u 2 ) - flux incidnt on ath with vlocity u i, (u + V )f (u, t)du So, powr tranfr pr unit ara i S toc = m 2 (u2 f u 2 )(u + V )f (u, t)du Uing u f = u + 2V, S toc = 2m V (u + V ) 2 f (u, t)du Auming V = u co ωt and avraging ovr tim, S toc = 2m u 2 uf (u)du Auming a uniform dnity with f Maxwllian, th intgral i jut Γ = n v /4 S toc = 2 m u 2 n v For two ath, S toc = m u 2 n v

4 3 Stochatic Hating II (Kaganovich 24) Rcall that powr tranfr pr unit ara i S toc = m 2 (u2 f u 2 )(u + V )f (u, t)du - vlocity rlativ to moving ath i u = u V = (u + V ) Dfin g(u, t) = f ((u + V ), t) Tranfr to fram whr x i fixd (u u + V ), S toc = m 2 [(u + V ) 2 (u V ) 2 ]u g(u, t)du Simplifying and tim avraging, S toc = 2m V (t) If g(u ) i tationary, thn S toc = u 2 g(u, t)du For a uniform ion dnity profil, g(u ) i tationary (in th fixd x fram) Stochatic hating vani for uniform ion profil.

5 4 ν ff v. Prur for Moil and Uniform Fixd Ion J rf 2 S = S (p) + S = a ohm toc m ν ff l 2 2 n +8 (c-) νff +7 Moil Ion Fixd Unif. Ion Prur (mt) PIC imulation of currnt drivn Argon dicharg: J rf = 3 A/m 2, l =.5 m, A =. m 2, and f = 27.2 MHz. Ohmic hating at high p ν ff ν coll p Stochatic hating at low p No tochatic hating for uniform ion profil

6 5 Powr Dpoition J E Profil p = mt (Moil Ion) Ohmic and Stochatic Hating 5 S /S.56 toc a p = 3 mt (Moil Ion) 5 Stochatic Hating S /S.94 toc a p = 3 mt (Fixd Uniform Ion) 2 5 Ohmic Hating S toc /S a

7 6 Fixd Ion for Stochatic Hating Study 2+5 n /n =..5+5 Dnity(x) (m-3) DC ath voltag formd y partial load of lctron. High frquncy AC driv ocillat lctron aout. Mimic dual frquncy dicharg with f low =. W calculat powr dpoition y, S a = J E dx S ohm = m J 2 rfν coll 2 2 l dx n (L&L.2.24) S toc = S a S ohm.

8 toc toc 7 Stochatic Hating Ratio v. n /n and p = 3 mt, f = 27.2 MHz.8 u /v =.2, = 7.5mm S /(m u n v ) n /n p = 3 mt, f = 27.2 MHz n /n = 4, u /v = 6 % S /(m u n v ) n /n =.5, u /v = 9 % (mm) Stochatic hating ratio S toc /(m u 2 n v ) aturat a n /n No tochatic hating for n /n = (uniform ion profil). Stochatic hating ratio i indpndnt of.

9 toc 8 Stochatic Hating Ratio v. u / v 3 S /(m u n v ) n /n = 4., = 7.5 mm, f = 27.2 MHz p = 3 mt p = mt p = 3 mt y = 2/(u /v ) u /v (%) 3 S /(m u n v ) 2 toc n /n = 8., = 7.5 mm, p = 3 mt f = 27.2 MHz f = MHz f = 3.56 MHz y = 2/(u /v ) u /v (%) Bounc ronanc f = v /l 3 MHz. In th anc of ounc ronanc, S toc cal a u 2 At highr p, colliion wa out ounc ronanc.

10 2 toc 9 Stp and Continuou Profil at p = 3 mt Stp plama profil, p = 3 mt, f = 27 MHz =.75 m, u /v = 2%.5 Stp plama profil, p = 3mT, f = 27.2 MHz =.75m, u /v = 2% 2+5 n /n i =. Dnity (m-3) Continuou plama dnity, p = 3 mt, f = 27.2 MHz =.383 m, n /n = 5.85 S /(m u v n ) n /n Continuou plama dnity, p = 3 mt, f = 27.2 MHz =.383 m, n /n = Dnity (m-3) S /(m u v n ) toc u /v (%)

11 E av and J E for Stp and Continuou Profil J. 3 E (W/m ) for tp plama profil n /n = 2., =.75m, u /v =.2, f = 27.2 MHz E fild (V/m) for tp plama profil n /n = 2., =.75 m, u /v =.2, f = 27.2 MHz p = 3mT p = 3 mt +5 p = 3mT p = 3mT J. 3 E (W/m ) for continuou profil u /v =.2, f = 27.2 MHz E fild (V/m) for continuou profil u /v =.2, f = 27.2 MHz 2 p = 3mT, n /n = 5.75, = 6.7 mm p = 3mT, n /n = 5.85, = 3.83 mm 2 p = 3 mt, n /n = 5.75, = 6.7 mm p = 3 mt, n /n = 5.85, = 3.83 mm

Why is a E&M nature of light not sufficient to explain experiments?

Why is a E&M nature of light not sufficient to explain experiments? 1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt