Study of Some Basic Transport Coefficients in Noble-Gas Discharge Plasmas

Transcription

1 Egypt. J. Solids, Vol. (30), No. (1), (2007) 137 Study of Som Basic Transport Cofficints in Nobl-Gas Discharg Plasmas M. H. Elghazaly, S. Solyman and A. M. Abdl baky Dpartmnt of Physics, Faculty of Scinc, Univrsity of Zagazig, Zagazig, Egypt Th transport cofficints, lctrical and thrmal conductivitis, hav bn calculatd in argon and hlium glow discharg plasmas. Th lctron collision frquncy nds to by know [In ordr to calculat th transport cofficints]. Th thr collision mchanisms, lctron-nutral, lctron-ion and lctron-lctron collision frquncis, ar all invstigatd. Th most important intrnal paramtrs of th plasma which hav a dirct baring on th calculation of th collision frquncy ar th lctron tmpratur and dnsity, and nutral atom dnsity. Th lctron tmpratur and lctron dnsity wr dtrmind from masurmnts takn with a doubl Langmuir prob. Th doubl prob was placd into th diffrnt rgions of th glow discharg from th cathod surfac to th anod. Th masurd lctron tmpratur ar about ( V) at discharg voltag of 400 volt for two diffrnt argon prssurs 13.3 and 26.6 Pa, and ( V) for hlium discharg at 750 volt and 53.2 and 79.8 Pa, rspctivly. Th lctron dnsity, ovr th prssur and voltag rangs mployd abov, ar about ( x10 9 cm -3 ) and ( x10 9 cm -3 ) for argon and hlium plasmas, rspctivly. In addition, th nutral atom dnsity, n n, is computd from th gas prssur and tmpratur using idal gas law. Calculatd rsults of lctrical and thrmal conductivitis and thir ratios, Widmann-Franz ratios, ar rprsntd graphically as functions of lctron tmpratur, with th gas prssur as paramtr. It was found that lctron nrgy gratly affcts th plasma transport cofficints. 1- Introduction: Th fundamntal proprtis of plasma ar markdly dpndnt upon th intractions of th plasma particls with th forc filds xisting insid it. Our intrst is in wakly ionizd plasmas, sinc a glow-discharg is a slfsustaining, wakly ionizd plasma that mits light (i.., it glows). In ths plasmas th lctrons tnd to dominat th situation, sinc thy rspond quickly to th influnc of lctric and magntic filds, in viw of thir low inrtia [1].

2 M. H. Elghazaly t al. 138 Low-prssur, wakly ionizd nobl-gas glow discharg plasmas ar vry frquntly subjct of both basic and applid rsarch and widly usd in industrial tchnological procsss. Low-prssur (0.13 Pa to 1333 Pa), cold (gas tmpratur 300 to 500 K), wakly ionizd (dgr of ionization 10-6 to 10-1 and th charg-nutral intractions dominat ovr th multipl coulomb intractions) glow discharg plasmas ar usd xtnsivly in th procssing of lctronic matrials, spcially for tching and dposition of thin films. Also, application was found in surfac modification,.g., hardning and corrosion rsistanc [2]. Procsss rlatd to th transport of mass, momntum, nrgy and chargs in plasma ar gnrally calld transport phnomna. Thr xist gnral quations dscribing ths diffrnt phnomna, and th spcial ffcts ar charactrizd by cofficints gnrally calld transport cofficints [3]. Ths transport cofficints can b valuatd whn th momntum transfr collision frquncy is known. Diffrnt typs of collision procsss hav a dominant influnc on th transport proprtis of th plasma. For th lctrons, a varity of diffrnt collision mchanisms is of importanc. Elastic collisions ar rsponsibl for momntum loss and limit th lctric as wll as th hat conductivity. Th most dominant mchanism, causing a loss of lctron momntum, is lastic lctronnutral collisions [4]. Transport phnomna in plasmas can b promotd by xtrnal and intrnal forcs. In spatially homognous plasma undr th influnc of xtrnal forcs, a drifting of th lctrons can occur. This motion inducd by xtrnal forcs is rfrrd to as mobility. Sinc th lctrons hav lctric charg, thir motion implis in conduction of lctricity whn actd upon by an xtrnal lctric fild. On th othr hand, th lctrons also hav kintic nrgy associatd with thir random thrmal motion, thir drift implis in th transport of thrmal nrgy and thrfor in hat conduction [1]. Th goal of this work is th calculation of th basic transport cofficints (lctrical and thrmal conductivitis) for argon and hlium plasmas. To dduc th transport cofficints, w nd only know th momntum transfr collision frquncy of th plasma spcis. Elctron-nutral collisions, lctron-ion collisions and lctron-lctron collisions ar all invstigatd. Elctron tmpratur and dnsity, and nutral atom dnsity ar all w nd to know for th valuation of th lctron collision frquncis. Thrfor, w prsnt in our articl th masurmnts of th lctron

3 Egypt. J. Solids, Vol. (30), No. (1), (2007) 139 tmpratur and lctron dnsity by mans of th Langmuir prob tchniqu, in addition to thrmal coupl for nutral gas tmpratur. 2. Transport Cofficints Study of th conductivity of th plasma can b achivd by solving th quation of motion for ach plasma spcis. Bcaus lctrons hav far lowr masss than ions, thy hav far highr typical spds at fixd tmpratur and ar much mor asily acclratd; i.., thy ar much mor mobil. As a rsult, it is th motion of th lctrons, not th ions, that is rsponsibl for th transport of hat and lctricity through plasma [5]. Th lctron transport cofficints, th lctrical conductivity, σ, and th thrmal conductivity, κ, ar valuatd using thir basic dfinitions [6]. σ 2 = (1) m ν n κ n k 2 = B (2) m ν T whr and m is th charg and mass of lctron, rspctivly, n is th lctron dnsity, T is th lctron tmpratur, k B is th Boltzmann constant and ν is th lctron collision frquncy. Th collisions btwn lctronnutral, lctron-ion and lctron-lctron play an important rol. Hnc, w may assum that th ovrall lctron collision frquncy, ν, is th sum of th lctron-nutral collision frquncy, lctron-ion frquncy and lctronlctron collision frquncy ν = ν + ν + ν (3) n i Th plasma-nutral collision usually dtrmins th kintics of th motion. Th lctron-nutral collision frquncy is givn as [7] ν = (4) n nn σ nυ th n n is th nutral atom dnsity, σ n th lctron-nutral collision cross-sction and υ is th lctron thrmal vlocity. In practical units, th lctron-nutral th collision frquncy is givn by [1] n σ n nnt ν = (5)

4 M. H. Elghazaly t al. 140 (T in K, n n in m -3 and σ n is th sum of th radii of th colliding particls). Th lctron-ion collision frquncy was dscribd by th Spitzr- Harm formula [8]. ν i 4 n ln Λ = (6) 3 2 4πε m ( T ) whr ε 0 is th prmittivity of vacuum and lnλ is th Coulomb logarithm givn as: ln Λ = 23 ln n T 2 (7) 10 In practical units, th lctron-ion collision frquncy is givn by [1] 6 2 ν = n T 3 ln Λ (8) i i T Λ = (9) 1 2 n Elctron-lctron collision frquncy was basd on th wll known xprssion [9] ν 2ν 3. Exprimntal St-up: i Th xprimntal st-up is dsignd to produc stady stat lowprssur, dirct currnt glow discharg plasma. Fig. (1) rprsnts a schmatic diagram of th xprimntal quipmnt and th lctrical circuit. Th discharg sourc is a Pyrx cylindrical tub with 20 cm innr diamtr and 26 cm in lngth. A flang mountd two aluminum shts wr sald at both nds of th tub. A stationary DC-glow discharg was gnratd btwn th lctrod systm which was mad movabl forward and backward insid th tub. It consists of two paralll coppr lctrods with 7 cm diamtr. Th axial distanc btwn th lctrods kps fixd at 7 cm apart. Th tub vacuation is carrid out using a gas rotary pump to about 10-3 torr. Argon and hlium ar usd hr as plasma-forming gas during masurmnt to avoid possibl ngativ ffct of complx chmical ractions whn a non-inrt gas is applid [10]. Th gas discharg was run from 2 kv dc powr supply with a rhostat ballast. Th discharg currnt was varid btwn 2 and 20 ma.

5 Egypt. J. Solids, Vol. (30), No. (1), (2007) 141 Fig. (1): A schmatic diagram for (a) th xprimntal quipmnt and (b) Th lctric circuit. In low-prssur glow discharg plasmas, Langmuir probs as a diagnostic tool ar known for thir ability to provid local masurmnts of vry important plasma paramtrs, namly th lctron dnsity and lctron tmpratur [11 & 12]. Th doubl prob usd hr consists of two idntical cylindrical tungstn wir of 0.19 mm diamtr and a lngth of 2 mm. Th sparating distanc btwn th two lctrod cntrs was 2 mm. Masurmnts wr mad at a discharg voltag of 400 V for two diffrnt argon gas prssurs: p = 13.3 and p = 26.6 Pa, and 750 V for two

6 M. H. Elghazaly t al. 142 diffrnt hlium gas prssurs: p = 53.2 and p = 79.8 Pa, rspctivly. For ach fixd bias point, th prob currnt and voltag wr masurd at ach spatial (axial) location from th cathod surfac to th anod in th discharg chambr. Fig. (2) shows a typical doubl-prob I-V charactristic curv. Maximum currnt through th doubl-prob circuit is dtrmind by positiv ion saturation currnts (i p1,2 ) to both probs. Th lctron tmpratur T has bn dtrmind from a quit simpl rlation btwn th paramtr Γ, dfind as [13 & 14], i p Γ = 1 (10) i2 and th potntial diffrnc btwn probs V: ln Γ ~ V (11) kt That is, th rciprocal valu of th slop of th smi-log plot ln Γ(V) vrsus V quals th lctron tmpratur in V. Fig. (2): (a) Typical doubl prob charactristic curv and (b) Elctron tmpratur.

7 Egypt. J. Solids, Vol. (30), No. (1), (2007) 143 Th lctron dnsity n =n i has bn dtrmind from th ion saturation currnt, I p =I is of th doubl-prob charactristic curv using [15]. I = n υ A (12) is i i, th whr A is th prob collcting ara and υ i,th is th ion thrmal spd givn by k T m 1, whr k B is Boltzmann s constant, T is th lctron ( ) 2 2 B i tmpratur and m i is th ion mass. Th nutral atom dnsity, n n, is computd from th gas prssur and tmpratur using idal gas law (n n = P / kt g ). Th nutral gas tmpratur, T g, in glow dischargs has bn studid prviously by mans of Dopplr broadning, thrmal coupl and via a manomtr prob [16,17]. Rcntly, Rayligh scattring of lasr radiation is usd to masur th nutral gas tmpratur [18]. In this work T g is ~ 300 K as masurd using a thrmal coupl. 4. Rsults and Discussion: Rgarding th low-prssur glow discharg plasma charactrization, on is concrnd with masuring th lctron tmpratur, T, th lctron dnsity, n and th nutral gas dnsity n n. To this purpos, a doubl Langmuir prob has bn usd, and th currnt-voltag (I-V) charactristic for argon and hlium glow dischargs, at diffrnt discharg voltag and gas prssur, along th tub axis from th cathod surfac to th anod wr masurd. Valus of th lctron tmpratur ar obtaind by th logarithmic plot mthod according to Eq. (10). Valus of Γ can b obtaind using th I-V charactristic curv, thn a plot of ln Γ against V yilds a straight lin, th slop of which givs th valu of T, Eq. (11). Th masurd valus of T ar about ( V) at discharg voltag of 400 volt for two diffrnt argon prssurs 13.3 and 26.6 Pa, and ( V) for hlium discharg at 750 V and 53.2 and 79.8 Pa, rspctivly. Th lctron dnsity, n, can also b obtaind from th ion saturation currnt, I p =I is of th doubl-prob I-V charactristic curv, with th valus of T dtrmind prviously, according to Eq.(12). Th lctron dnsity, ovr th prssur and voltag rangs mployd abov, ar about ( x10 9 cm -3 ) and ( x10 9 cm -3 ) for argon and hlium plasmas, rspctivly. Ovr th discharg voltag and prssur mployd in this work, valus of lctron tmpratur, T, and lctron dnsity, n, agr rasonably wll with othr valus givn in th litratur [19,20]. Th nutral atom dnsity, n n, is computd from th gas prssur and tmpratur using idal gas law (n n = P / kt g ). Th nutral gas tmpratur, T g, masurd using a thrmal coupl riss abov room tmpratur by about 20 K, and rachs a maximum of about 320 K at 2-4 mm from th cathod, undr th voltag and prssur invstigatd, thn it dcrass slightly to room tmpratur along th tub axis to th anod. Hnc, T g, is takn to b 300 K approximatly.

8 M. H. Elghazaly t al. 144 Calculations of th lctrical conductivity,σ, and thrmal conductivity, κ, using Eqs. (1) and (2) ncssitatd calculations of th lctron collision frquncis from Eqs. (5) to (9), rspctivly. With th xprimntal valus of T, n and n n which hav bn mployd also to calculatν, th valus of σ and κ wr calculatd. Th calculatd lctrical conductivity, σ, is plottd in Figs. 3(a) and 4(a) for argon and hlium plasmas. Figs. 3(a) and 4(a) show th tmpratur dpndnc of σ, with prssur as paramtr. Figur 3(a) clarifis th lctrical conductivity of argon plasma as a function of lctron tmpratur ranging from V at two diffrnt gas prssurs (13.3 and 26.6 Pa). This plot shows that σ riss in th rgion of low tmpraturs (T < 2.5 V). At highr lctron tmpraturs (T > 3 V) σ tnd to b constant. Quit similar bhavior of σ appar in Fig. 4(a) for hlium plasma at nutral gas prssurs of 53.2 and 79.8 Pa, and for an lctron tmpratur in th rang of 3-8 V. It can b sn that σ show a rapid incras in th rgion of tmpraturs btwn V. In th highr tmpratur rgion (abov 4 V) on can notic only a constant variation with tmpratur. Th rsults of th lctrical conductivity of argon and hlium plasmas ar insnsitiv to th changs in th high nrgy lctrons. Fig. (3): (a) Elctrical conductivity and (b) thrmal conductivity in Ar Plasma.

9 Egypt. J. Solids, Vol. (30), No. (1), (2007) 145 Figurs 3(b) and 4(b) show th tmpratur dpndnc of th calculatd thrmal conductivity, κ. Diffrnt compard to th cas of σ, th calculatd valus of κ ar virtually riss monotonically with th lctron tmpratur. Gnrally, th lctrical and thrmal conductivitis ar sn to incras with tmpratur, which is an asily comprhnsibl fatur ascribabl mainly to th incrasing thrmal ionization [21]. Fig. (4): (a) Elctrical conductivity and (b) thrmal conductivity in H Plasma.

10 M. H. Elghazaly t al. 146 Th prssur bhavior of th lctrical conductivity, σ, and thrmal conductivity, κ, show intrsting curvs in Figs. 3 and 4 for various lctron tmpraturs. It is clarly sn that, th calculatd valus of σ and κ ar virtually indpndnt of th prssur at lowr lctron tmpraturs (blow ~ 2.5 and 4 V for argon and hlium plasmas), at that it dcrass quit noticabl with th prssur abov that tmpraturs. Th inclusion of lctron collision frquncy may b significant in stablishing ths faturs shown in Figs. (3 & 4) [4]. Th bhaviour of th lctron collision frquncy ν (invrsly proportional to both σ and κ) is charactrizd by a gnral incras with nutral gas prssur. This corrsponds to an incrasing numbr of collisions. Howvr, proportionality is only obsrvd for vry small gas prssur (blow ~ 1 Pa). Dviations from a dirct proportionality bcom visibl spcially in th prssur rgim ovr 20 Pa in cas of low lctron tmpratur (2 V). Th gnral dpndnc of ν on th lctron tmpratur can b xplaind by a highr avrag vlocity with incrasing tmpratur. For highr tmpraturs, collision vnts bcom mor frqunt, which rsults in an incras of ν [4]. An important charactr is givn in Fig. (5) for argon discharg showing th tmpratur dpndnc of th ratio κ / σ with th prssur as paramtr. For hlium discharg, th sam valus of κ / σ was obtaind (s Fig. (5)), although gas prssur rang was highr than that of argon discharg. Th calculatd data in Fig. 5 show a good agrmnt with Widmann-Franz ratio, 2 2 κ σ = ( k )T. On th othr hand, Fig. (5) confirms that th ratio κ / σ is indpndnt on th gas prssur. Although, th gnral bhavior of th prsnt rsults of κ / σ agrs with th xpctd thortical law, thy diffr from that givn by Novaković t al. [9]. Fig. (5): Franz-Widmann ratio in Ar and H plasmas.

11 Egypt. J. Solids, Vol. (30), No. (1), (2007) 147 Finally, a comparison of th lctron collision frquncis, ν, calculatd via th xprimntal rsults of T, n and n n ar givn in Tabl (1) for argon discharg and Tabl 2 for hlium discharg, rspctivly. From th tabls it is clarly sn that, lctron-nutral collision frquncis, ν n, ovr th whol rang of lctron tmpraturs, ar so largr than th collision frquncis of lctrons with th chargd particls ν i and ν. So, th collisions with th ions in both argon and hlium dischargs ar rlativly insignificant in th whol lctron tmpratur rgion considrd hr. As xpctd, of th thr collision mchanisms studid hr, th lctron-nutral collisions play th main rol in valuating conductivity ovr othr ffcts which includ lctron-ion and lctron-lctron, with th xtra charactrization of low-prssur wakly ionizd glow discharg plasma. Tabl (1): Elctron tmpratur and collision frquncis in Ar plasma (P =13.3 Pa). T (V) ν n (xe8 s -1 ) ν i (x E5 s -1 ) ν (x E5 s -1 ) ν total (x E8 s -1 ) Tabl (2): Elctron tmpratur and collision frquncis in H plasma (P =79.8 Pa). T (V) ν n (x E8 s -1 ) ν i (x E4 s -1 ) ν (x E4 s -1 ) ν total (x E8 s -1 )

12 M. H. Elghazaly t al Conclusions: 1. W masurd th doubl prob I-V charactristic curv in both argon and hlium dischargs. From ths curvs w infrrd valus of th lctron tmpratur and dnsity. In our cas, th lctron tmpratur and dnsity for argon discharg is lowr than for hlium discharg. This may b du to th highr ionization potntial of hlium atom compard with its valu for argon atom. 2. High nrgy of th lctrons (lctron tmpratur, T ) implis high plasma conductivity. Th thrmal conductivity, κ, is virtually riss monotonically with lctron tmpratur. 3. Th lctrical conductivity, σ, is dominatd by low nrgy lctrons and insnsitiv to th changs in th high nrgy rgion. 4. Both lctrical and thrmal conductivity is indpndnt of th prssur at lowr lctron tmpratur, and dcrass noticably with th prssur at highr lctron tmpratur. 5. Widmann-Franz ratio is dirct proportional with lctron tmpratur and indpndnt on th gas prssur. 6. Elctron-nutral collisions play th main rol in valuating conductivity ovr othr collision ffcts, and offring th possibility to trat th glow discharg plasma as wakly ionizd. 7. Th most important rsult of this work is that, th simpl xprssions for σ and κ, Eqs. (1)and (2), dos not provid a sufficintly accurat valu of th plasma conductivitis, sinc thy basd on a scalar ffctiv lctron collision frquncy, ν, Eqs. (5) to (9). W bliv that to obtain mor accurat valus of σ and κ, a gnral form of th plasma s conductivity considring th ffctiv lctron collision frquncy, ν, rprsntd by th mor gnral form dpnding on th lctron nrgy distribution and th nrgy dpndnc of th corrsponding collision cross sction, Eq. (4), must b usd. Rfrncs: 1. J. A. Bittncourt, Fundamntals of plasma physics, Prgamon Prss, Oxford (1986). 2. D. P. Lymbropoulos and D. J. Economou, J. Rs. Natl. Stand. Tchnol. 100, 473 (1995). 3. H. W. Drawin, Collision and transport cross-sctions, In Plasma Diagnostics, Publishd by th Amrican Institut of Physics, Unitd Stat of Amrica, P. Schubrt, Modling and diagnostics of low prssur plasma dischargs,

13 Egypt. J. Solids, Vol. (30), No. (1), (2007) Z. Donko, P. Hartmann and K. Kutasi, On th rliability of low prssur Dcglow discharg modling, XXVIIth ICPIG, Eindhovn, th Nthrlands (2005). 6. M. Mitchnr and C. H. Krugr, Partially ionizd gass, Wily (1973). 7. Roy Subrata and B. P. Pandy, Elmnt basd hydrodynamic shath modl, 33rd Plasma dynamics and lasrs confrnc, Maui, Hawaii, (2002). 8. J. T. Gudmundsson and M. A. Librman, Plasma Sourcs Sci. Tchnol. 6, 540 (1997). 9. N. V. Novaković, S. M. Stojiković and D. Z. Gajić, Facta Univrsitatis Sris: Physics, Chmistry and Tchnology 3, 1 (2004). 10. Liu, C., Wang, J., Yu, K. I., Eliasson, B., Xia, Q., Xu, B. and Zhang, Y., J. Elctrostatics 54, 149 (2002). 11. D. Fang and R. K. Marcus, Spctrochm. Acta B45, 1053 (1990). 12. A. Bogarts, A. Quntmir, N. Jakubowski and R. Gijbls, Spctrochim. Acta B50, 1337 (1995). 13. E. O. Johnson and L. Maltr, Phys. Rv. 80, 58 (1950). 14. V. Margtić and D. Vža, Fizika A7 (2), 49 (1998). 15. C. Thompson, A.Barkan, N. D`Anglo and R. L. Mrlino, Phys. Plasmas 4, 2331 (1997). 16. S. K. Ohorodnik and W. W. Harrison, J. Anal. Atom. Spctrom. 9, 991 (1994). 17. N. I. Uzlac and F. Lis, Spctrochim. Acta B47, 877 (1992). 18. G. Gamz, A. Bogarts, F. Andrad and G. M. Hiftj, Spctrochim. Acta B59, 435 (2004). 19. E. Passoth, P. Kudrna, C. Csambal, M. Tichy and V. Hlbig, J. Phys. D: Appl. Phys. 30, 1763 (1997). 20. M. Blkin, J. A. Caruso, S. J. Cristophr and R. K. Marcus, Spctrochim. Acta B53, 1197 (1998). 21. R. N. V. Novaković, B. C. Milić, S. M. Stojiković and D. Z. Gajić, Facta Univrsitatis Sris: Physics, chmistry and tchnology 2, 285 (2003).