DISSERTATION zur Erlangung des Grades Doktor der Naturwissenschaften an der Fakultät für Physik und Astronomie der Ruhr-Universität Bochum

Transcription

1 Invstigation of ICP RF dischargs by mans of a Langmuir prob DISSERTATION zur Erlangung ds Grads Doktor dr Naturwissnschaftn an dr Fakultät für Physik und Astronomi dr Ruhr-Univrsität Bochum von Shailndra Vikram Singh aus Varanasi Bochum 2004

2 Dissrtation ingricht am: Tag dr mündlichn Prüfung: Rfrnt: Prof. Dr. H. Soltwisch Korfrnt: Prof. Dr. P. Awakowicz

3 Contnt: CHAPTER 1. INTRODUCTION AND MOTIVATION 5 CHAPTER 2. THE RF PLASMAS Introduction Capacitivly coupld plasmas (CCP) Inductivly coupld plasma (ICP) 12 E-mod 13 H-mod 14 Hybrid mod 14 CHAPTER 3. THE SHEATH AND THE ELECTRON DISTRIBUTION FUNCTION Shath formation in a low tmpratur plasma Bohm critrion and Prshath RF shaths Elctron distribution function 18 CHAPTER 4. BASICS OF DIAGNOSTICS Langmuir Probs 24 Masurmnt Principl Prob thory Elctron saturation currnt calculation Elctron rtarding currnt calculation Ion saturation currnt Evaluation of plasma paramtrs Elctron Distribution Functions Plasma and floating potntial Elctron tmpratur Elctron dnsity dtrmination Rogowski Coil Capacitor dividr 40 CHAPTER 5. EXPERIMENTAL SETUP Th plasma ractor Capacitivly coupld plasma (CCP) ractor Inductivly coupld plasma (ICP) ractor 44 Faraday shild 45 Matching ntwork 46 Antnna coil Elctrical charactrization of ICP Currnt prob (Rogowski coil) 49

4 5.3.2 Voltag masuring dvic Langmuir Prob Systm Problms associatd with th prob masurmnt Prob tip contamination RF distortion Low frquncy nois 60 CHAPTER 6. LANGMUIR PROBE MEASUREMENTS AND COMPARISON WITH A MODEL Masurmnts in th CCP Masurmnts in th ICP and thir comparison with modls Modling Masurmnts in a pur ICP discharg 67 Elctron dnsity 69 Elctron distribution function 71 EEPF vs radial position 71 EEPF vs. powr 72 EEPF vs. prssur 73 Comparison of th EEPF with th non-local approach Global Modl 77 Chargd particl balanc to obtain th lctron tmpratur 78 Powr balanc to obtain th plasma dnsity 79 CHAPTER 7. CHARACTERIZATION OF THE MODE TRANSITION REGION OF THE ICP DISCHARGE Extrnal Charactrization of th ICP discharg 84 Th RF currnt and voltag masurmnts 85 Faraday shild 85 Comparison btwn th thr diffrnt arrangmnts 87 Discussion Plasma lctron paramtrs nar mod transition rgions 91 Effct of Faraday shilding 91 Elctron plasma paramtrs dmonstrating hystrsis Transformr modl Th EEPF clos to th mod transition 99 Poynting vctor in H-mod 104 Poynting vctor in E-mod 104 Poynting vctor in transition rgion 105 Extra componnt j(e r B z E z B r ) 105 An stimation 106 CHAPTER 8. SUMMARY AND OUTLOOK 109 BIBLIOGRAPHY: 111 4

5 Chaptr 1. Introduction and motivation It was Irving Langmuir ( ) who namd partially ionizd gass (containing background nutral gas particls as wll) th Plasma [1, 2, 3]. Howvr, th trm plasma initially bcam popular for th fully ionizd gass containing just fr ions and lctrons. Mor prcisly, a plasma is an ionizd gas which has a significant numbr (sufficint to affct its lctrical proprtis and bhavior) of lctrically chargd and nutral particls. A plasma is quasi-nutral in natur and xhibits collctiv bhavior [4]. Contrary to th constitunts of solids, liquids and gass, particls in plasma (particularly lctrons) hav substantially high tmpratur. Plasma is charactristically so diffrnt from th othr thr known stats of mattr that it is oftn rfrrd as th Fourth Stat of Mattr. It is blivd that 99 % of th univrs is in th plasma stat. According to th particl s tmpratur, plasmas ar distinguishd. Plasmas, whr all particls (lctrons, ions and nutrals) hav locally an idntical tmpratur ar dfind as local thrmal quilibrium (LTE) plasmas, and th dischargs with a larg diffrnc of tmpratur btwn th light lctrons (vry high tmpratur, fw 10,000 K) and th havy nutrals and ions (vry low tmpratur, around room tmpratur) ar calld non-local thrmal quilibrium (non-lte) plasmas [5]. Th thrmal vlocity of lctrons in LTE as wll as in non-lte dischargs is much highr than th ion thrmal vlocity bcaus of thir mass diffrnc. Hnc, in an vry laboratory plasma th fastmoving lctron s flux to th wall is highr than that of th slow ions. Within a vry short tim lctrons nar th wall ar lost lading to a positivly chargd layr calld shath around th walls and lctrods. Shaths ar of quit importanc in tchnological applications and in th undrstanding of th bulk procsss. Th nutral background gas in partially ionizd plasma can consist of atoms, molculs and vn radicals which, similar to ions, can b xcitd and d-xcitd to and from, various allowd nrgy lvls. Th molculs, molcular ions and radicals can b dissociatd and abov all ths background particls can vn gt ionizd du to th collisions. Th ssntial mchanisms in th plasma ar xcitation and rlaxation, dissociation, ionization and rcombination, and to maintain th stady stat of lctron and ion dnsitis th rcombination and surfac loss procsss must b compnsatd by th ionization procsss. To achiv this, balancd condition an xtrnal powr sourc is rquird. Vry oftn th plasmas, and spcially low tmpratur and low (and modrat) dnsity plasmas ar namd aftr thir gnrating sourcs lik dirct currnt (dc plasmas), radiofrquncy (RF plasmas), microwav plasma tc.

6 Chaptr 1. Introduction and motivation Nowadays plasma s domstic and industrial applications ar numrous and divrs [6, 7]. In gnral du to thir distinct bhaviors LTE plasmas ar mployd at th placs whr normous hat is rquird lik cutting and wlding, whras non-lte plasmas ar usd whr high nrgy ions and nutrals might intrfr with th procsss. Ractiv non-lte plasmas (with appropriat prcursor gas) ar widly usd in surfac modification applications. Plasma procssing is usd for th tratmnt of txtils, for lighting facilitis, for mchanical tools to improv durability and for production of microchips. In th rcnt past plasmas hav bn mployd to produc solar clls or plasma display panls (PDP) for flat scrns and to crat rsistant and bio-compatibl coatings on bio-implants. A grat dmand in th tchnological applications has attractd a lot of rsarchrs to includ complx and chmically ractiv (low tmpratur and low prssur) non-lte plasmas. Ths plasmas hav th advantag to modify surfac proprtis in a rgion which is not accssibl undr thrmodynamic quilibrium. It is this non quilibrium bhavior along with th chmical complxity of ractiv plasmas which is rsponsibl for th difficultis in finding an appropriat dscription and bttr undrstanding of discharg procsss involvd. For th undrstanding of th fundamntal procsss it is th simpl gass (nobl gass, spcially H and Ar) which ar still bing usd, and it has to b mntiond that aftr dcads of rsarch a complt dscription of discharg proprtis for vn simpl gass hav still not compltly bn achivd. Th spcific aim of our group is to invstigat capacitivly and inductivly coupld low prssur RF dischargs with mthan, oxygn, hlium, argon and thir mixturs as sourc gass. Argon and hlium ar gass which ar wll invstigatd and ar having lctron impact ractions as th main procsss whras mthan, oxygn and thir mixtur (vn with H and Ar) lad to vry complicatd chmically ractiv plasmas. Bcaus of limitd scintific work don with ractiv gass and du to th natur of th procsss involvd, information about lmntary quantitis lik raction cross sctions and sticking cofficints ar limitd and th availabl valus hav rlativly high uncrtainty. Low prssur mthan plasmas ar usd for carbon film dposition, howvr, admixtur of oxygn in a mthan plasma dcids th surfac proprtis of th dpositd layr nding up from a soft amorphous to diamond lik hard carbon coating [8, 9]. Th quality of ths dpositd layrs, which is of tchnical importanc dpnds on a varity of intracting intrnal (bulk) paramtrs of th discharg lik th lctron dnsity, lctron tmpratur, nutral gas tmpratur, spcis concntrations, ion flux, ion nrgy and potntial distribution and ovr and abov on lctron nrgy distribution function. Mor prcisly th scintific intrst of our group lis in th physical and chmical 6

7 Chaptr 1. Introduction and motivation proprtis of th bulk plasma and spcially in mthan-oxygn plasmas. To rach to any propr conclusion in any laboratory plasma it is quit important to know how th powr, applid through xtrnal mans, is coupld into th plasma. This lads to th scond important dirction of our rsarch. For this vry purpos it is quit important to invstigat simpl plasmas (of hlium and argon) to undrstand th bhavior undr rlativly simpl discharg conditions. And, as was mntiond arlir, aftr dcads of work not vn ths simpl plasmas ar compltly undrstood. So to masur all th dsird paramtrs of any plasma and to covr a wid rang of diffrnt conditions will lad to a rathr hard and nvr nding journy and this lads to th third dirction of our rsarch and compls us to prdict th phnomna on th basis of limitd xprimntal rsults. In th prsnt work Langmuir prob masurmnts hav bn prformd in two discharg chambrs oprating undr diffrnt RF coupling mchanisms. Th first on is a asymmtrical capacitivly coupld paralll-plat ractor and th scond on is an inductivly coupld Gasous Elctronics confrnc (GEC) rfrnc cll. Th us of ths diffrnt typs of ractor offrs th opportunity to obsrv influnc of diffrnt hating mchanisms. This work is mainly concntratd on th inductivly coupld plasmas (ICP). In practic an inductiv sourc xhibits th prsnc of two diffrnt oprational rgims: on corrsponds to th pur inductiv coupling (H-mod), anothr on is charactrizd by capacitiv coupling (E-mod) and xhibits proprtis typical for capacitiv discharg [10]. Th H-mod is charactrisd by high lctron dnsity ( cm -3 ) whras, in E-mod lctron dnsity is narly two ordrs lowr. Th jump btwn E- to H-mod and H- to E-mod occurs at diffrnt powrs lading to th hystrsis. All th masurmnts prsntd in this work hav bn prformd with argon as a fd gas. For th study of th hating mchanisms involvd and th othr plasma procsss, th knowldg of Elctron Enrgy Distribution Function (EEDF) is ssntial. In this thsis, th mphasis has bn put on th undrstanding of th mod transition and th hystrsis in th ICP discharg. Th masurmnts prformd in pur H-mod hav bn compard with a 2-D modl dvlopd in th fram work of our group (Ivanov [36]). In ordr to achiv pur H-mod coupling two diffrnt Faraday shilds hav bn studid and th rsults hav bn compard to th non-shildd stup. Th comparison btwn th modl and, th prob masurmnts for th stup with th bst prforming Faraday shild has bn usd to undrstand th hating mchanism involvd in th H- mod. This modl is dvlopd to dscrib only th pur H-mod. In ordr to undrstand th lss invstigatd E-mod which is by natur mor clos to CCP discharg, a st of masurmnts hav bn don in th CCP discharg. 7

8 Chaptr 1. Introduction and motivation Th H-mod of th ICP discharg is charactrizd by th currnt flowing in th antnna, whras th E-mod is sustaind by th lctrostatic coupling du to th voltag drop across th antnna. Th antnna currnts and th voltags hav bn masurd using a Rogowski coil and a capacitiv voltag prob, rspctivly. Ths currnt and voltag probs hav bn dvlopd in th fram of this work. In th prsnt work a sris of masurmnts hav bn prformd clos to th mod transition rgion. Th masurd antnna paramtrs hav bn compard with a transformr modl. Finally, with th hlp of th discharg paramtrs lik th EEDF, th plasma and th floating potntials and th lctron dnsity and xtrnal paramtrs lik antnna currnt and voltags hav bn usd to undrstand th mod transition and to giv a possibl xplanation for th hystrsis. Th prsntd thsis is structurd in such a way that a short introduction to gnral faturs of RF dischargs is givn in th scond chaptr. It includs th gnral proprtis of capacitivly and inductivly coupld plasmas. Th third chaptr covrs a brif introduction to th shath bhavior in RF plasmas and dals with an ovrviw on th lctron nrgy distribution function. Th subsqunt chaptr xplains th thoris involvd with th usd diagnostic tools in th prsnt work. It starts with a dscription of Orbital Motion Limitd Thory (OML) thory usd to obtain th plasma paramtrs form th Langmuir prob masurmnts. This chaptr also covrs th basics of th Rogowski coil and capacitiv voltag prob. Th fifth chaptr covrs th tchnical dtails of th xprimntal stup and th diagnostics, and covrs brifly th problms associatd with th Langmuir prob masurmnts. Th sixth chaptr concntrats on th Langmuir prob masurmnts in th capacitivly coupld dischargs and th pur ICP dischargs. Th masurd rsults hav bn compard with a global modl and a mor dtaild 2-D simulation. Along with th rsults and th discussion, th dtail of th modl is also prsntd in this chaptr. Th scond last chaptr covrs th masurmnts of xtrnal paramtrs namly th antnna currnt and th voltag drop across th powrd nd and th groundd nd of th antnna. This chaptr includs th ffct of th Faraday shild implmntation and a dtaild invstigation of th plasma paramtrs with th hlp of prob masurmnts ar prsntd, too. In this chaptr a hypothsis is proposd to xplain th mchanism of hystrsis. Finally, in th last and th ighth chaptr th summry and outlook is prsntd. 8

9 Chaptr 2. Th RF plasmas Equation Chaptr 2 Sction Introduction Innovativ industrial applications of gas dischargs and limitations of DC dischargs ld rsarchrs towards radio frquncy (ƒ MHz) dischargs [11, 12]. Chmically ractiv RF dischargs ar oftn usd for tching and dposition of thin solid layrs on a substrat attachd to on of th lctrods. RF plasmas ar of spcial us whn th layr to b tratd is a smiconductor or an insulator bcaus th DC discharg currnt cannot b sustaind undr ths conditions [13]. And an altrnating currnt is rquird providd frquncy of this altrnating currnt must b chosn high nough that th chargs cratd in first half of th cycl ar not lost whn th currnt gos through zro. Thus to fulfill this condition typically ndd frquncis ar abov 50 khz. In this work an RF lctromagntic sourc with a standard frquncy, ƒ rf of MHz, which is dfind by intrnational communication authoritis undr unshildd nvironmnt to avoid intrfrnc with communication channls, has bn chosn. Broadly, RF dischargs ar classifid by thir driving frquncy, ω rf = 2πƒ rf and th way this RF fild is coupld to induc th corrsponding lctromagntic fild into th discharg spac. On th basis of how th fild is coupling to discharg spac, RF dischargs ar subdividd into two kinds, namly inductivly coupld and capacitivly coupld plasmas [12]. A distinction on th basis of driving frquncy ω rf is mad with its rlativ magnitud to th lctron plasma frquncy, plasma frquncy, 2 ω pi ( ni M i ε 0 ) 2 ω p ( n m ε 0 ) = and th ion =. Th first rgion is charactrizd by ω p >> ωpi >> ωrf, calld low frquncy rgim, whr both ion and lctron motion is modulatd by th applid fild, whras th scond rgim, calld high frquncy rgim with th condition ω pi << ωrf << ωp is distinguishd by immobil ions. Mor prcisly, in high frquncy rgim it is only th lctrons which follow th applid fild and th ions rmain too slow to follow ths fast changs. Th prsnt work is prformd at th standard frquncy (lis in th high frquncy rgim) for both kind of dischargs i.. capacitivly coupld and inductivly coupld plasmas. Bfor going in dtail of dscribing capacitivly coupld and inductivly coupld plasma dischargs it may b usful to rcall som lctro-tchnical facts about plasmas. Firstly it is known that an lctromagntic wav in a conductor is confind on th surfac and its pntration is limitd to th skin dpth dpnding on th fr lctron dnsity [14].

10 Chaptr 2. Th RF plasmas Similarly, plasma s skin dpth is lctron dnsity dpndnt and its dpndnc will b discussd latr in dtail. Scondly th plasma impdanc, whr R p is th plasma rsistanc and or inductiv [11]. 2.2 Capacitivly coupld plasmas (CCP) Z p is a complx quantity Z p = Rp + jx p (2.1) X p is th ractanc which can ithr b capacitiv Capacitivly coupld RF dischargs consist of two paralll lctrods sparatd by a small gap into which th plasma gas is fd, and RF currnts and voltags ar introducd through capacitiv shaths built across th lctrods. Th lctrod s shap and dimnsion can b idntical, calld symmtrical or can b asymmtrical and thir importanc is du to th rsultant shath in th stady discharg condition. Th prsnt work is don on th discharg cll with circular paralll lctrods of similar dimnsion but th groundd lctrod is largr including th walls of th chambr which ar groundd too. A typical schm of a CCP sourc is shown in figur 2.1. Figur 2.1: Sktch of th asymmtrical capacitivly coupld plasma and th quivalnt circuit. Th powr supply of th CCP sourc is always coupld through an impdanc matchr (calld Matching ntwork ) to th powrd lctrod [15]. Th lattr is rquird bcaus vry (RF) gnrator has fixd output ral impdanc (typically and in our cas, too, it is 50 Ω), whras gas dischargs along with th ractor rsult to a complx impdanc and hav to b matchd with th gnrator. A good (losslss) matching is 10

11 Chaptr 2. Th RF plasmas achivd whn th matching ntwork transforms th complx impdanc of th load (discharg and discharg chambr) to th ral impdanc of th RF gnrator (50 Ω). Matching ntworks consist of a combination of two tunabl capacitors and a coil and hav twofold advantags. Firstly last loss to hav bttr coupling fficincy and scondly to avoid rflctd powr (loss) which can vn damag th gnrator itslf. Furthr dtails of th matching ntwork will b discussd latr. Th physical mchanism for th plasma ignition is wll undrstood for RF dischargs [16, 11, 13]. Spcifically in CCP dischargs th fr lctrons containd in th ractor volum, producd by cosmic rays, gt acclratd in th prsnc of an applid altrnating lctric fild. Ths lctrons kp on colliding with th ambint nutral gas particls and sufficintly high nrgy (highly acclratd) lctrons kp on crating nw chargs and vntually gas brakdown occurs. At th driving frquncy of MHz principally only th lctrons follow th RF fild and gain nrgy, whras th havy ions rmain too immobil racting to such a fast chang and rmain at room tmpratur. This naturally occurring mchanism kps RF dischargs far from thrmal quilibrium. In a symmtrically oscillating fild it is actually th collisions (with nutrals) which allow th lctrons to gain nrgy. Du to th collisions, lctrons following th (acclrating and dclrating) RF cycls ar knockd out (of th fild lins) with a rsultant incras in thrmal nrgy. In absnc of collisions oscillating lctrons will hav no gain or loss of nrgy on an avrag In a CCP (a low prssur, wakly ionizd non-lte) lctrons do not shar thir gaind nrgy with th much havir ions and nutrals through lastic collisions, bcaus th frquncy of such collisions is not high nough and th nrgy transfr in lastic collisions is proportional to thir mass ratio. Th lctrons loos thir nrgy mainly in inlastic collisions, lik xcitation, dissociation and ionization. So, to achiv a slf sustaind discharg condition th chargd particl losss hav to b compnsatd by th lctron impact ionization in th bulk. Th nrgy transfr dpnds on th RF currnts and voltags in th plasma bulk and shath. And nrgy transfr to th plasma can b achivd in svral ways rsulting in diffrnt plasma rgims [13]. At low voltags and low prssur whn plasma dnsity is low th currnt through th non conductiv shath is only displacmnt currnt and th basic hating mchanism is ohmic du to th conduction currnt in th bulk. This mod of plasma hating is calld α-rgim bcaus of its rsmblancs to th DC positiv column (with th first Townsnd cofficint, α). It is charactrizd by a slf-consistnt and slf-sustaind plasma bulk and larg shath impdanc rsulting in a rlativly small discharg currnt. 11

12 Chaptr 2. Th RF plasmas With incras in applid voltag to th powrd lctrod th charg dnsity incrass and with furthr incras plasma starts to ntr th rgion whr scondary lctron mission from th lctrod bcoms vry important. Scondary lctrons, producd nar th lctrod in th shath rgion, gt strongly acclratd during most of th RF cycl raching vry high nrgy. In prsnc of sufficint nutrals in th shath ths high nrgy lctrons ar abl to ioniz so many nutrals that an lctron avalanch dvlops in th shath rsulting into a flux of high nrgy lctrons into th plasma bulk. At a sufficintly high prssur and powr (voltag to th lctrod) ths lctrons can vn ovrtak th ionization procsss in th plasma bulk and th plasma ntrs in a diffrnt hating rgim calld γ-rgim, charactrizd by rlativly high dnsity and low tmpratur. So th slf-consistncy in this mod is achivd considring both th bulk and th shath as wll and contrary to α rgim, it has much smallr shath impdanc and a comparativly high currnt dnsity. Th α to γ transition is smooth [13] in argon or in havy gass but it can vn b quit drastic spcially in light gass lik hlium and hydrogn. Anothr hating mchanism obsrvd in CCP is collisionlss hating, also calld stochastic hating [13, 17] and was firstly obsrvd in vry low prssur whr collisions ar narly ngligibl and th plasma hating is a rsult of lctron shath intraction. In this mod lctrons collid with th oscillating shath dg and gain nrgy on an avrag ovr an RF cycl and ar abl to sustain th discharg. 2.3 Inductivly coupld plasma (ICP) In an inductivly coupld plasma th RF powr is coupld through an antnna (inductor), instad of a circular lctrod, which producs an lctromagntic fild and acts lik a powrd lctrod. This antnna can b a conductor of diffrnt gomtris (hlical or spiral-lik conductor) and is placd adjacnt to (or immrsd insid) th discharg rgion [18, 19]. In this work th uppr lctrod is rplacd by a fiv-turn planar coil (pancak configuration) coupld through a quartz window without having a dirct contact to th ionizd gas. Th ICP dischargs ar run at rlativly low prssur and ar charactrizd by high dnsity, low lctron tmpratur (compard to CCP) and vry thin and low voltag shaths. 12

13 Chaptr 2. Th RF plasmas Figur 2.2: Sktch of inductivly coupld plasma. Lik in CCPs th RF gnrators in ICPs ar coupld through a matching ntwork to th antnna lctrod. In our cas it is th middl nd of th pancak configuration which is powrd, whras th outr nd is groundd. For th fficint coupling in th prsnc of th matching ntwork th antnna coil is drivn undr th lctrical rsonanc condition at th driving frquncy (13.56 MHz) and for th impdanc of 50 Ω. Th impdanc matching causs high currnts to flow in th inductiv lmnt (du to this rason any inductiv lmnt is avoidd in th matching ntwork of an ICP). Sinc th magnitud and rat of chang of this currnt is vry high a magntic flux is gnratd in th adjacnt plasma rgion within th skin dpth. This ffct is found to b dominant at high powrs. Anothr ffct of th lctrical rsonanc condition is a high potntial across th antnna nds. Such RF potntials ar coupld in a sam fashion lik in th CCP and ar dominant at rlativly low powrs. To undrstand th powr coupling mchanism in th ICP dischargs it is quit ncssary to sparat ths to ffcts. E-mod Th so calld E-mod or dark mod du to th coupling and th apparanc, rspctivly, is distinguishd by low lctron dnsity m -3 (in Ar plasmas) [10]. Th lctrostatic E-fild is gnratd bcaus of a high potntial drop (btwn th powrd and groundd nd of th antnna coil) at th oprating rsonanc condition, and th obsrvabl shath du to low dnsity rsults th plasma to bhav vry similar to low dnsity CCP dischargs. Th fficincy of powr coupling into th plasma in E-mod is dtrmind by th antnna plasma capacitanc and by th magnitud of th antnna voltag. Th basic hating mchanism is similar to capacitivly coupld dischargs. This lctrostatic coupling can b rducd by using a groundd Faraday shild [20, 21] (to b dscribd latr in dtail) placd btwn coil and plasma. 13

14 Chaptr 2. Th RF plasmas H-mod With incras in powr at a crtain thrshold th plasma gos to th high dnsity mod (H-mod, oftn calld pur inductiv mod), whr azimuthal lctric filds blow antnna coil ar rsponsibl for th plasma gnration. Th plasma in this mod is charactrizd by high dnsity (maximum cm -3 ), high luminosity, ngligibl (and low voltag) shaths and rlativly low plasma potntial and man lctron nrgy. According to Faraday s law, E = B / t, th tim varying magntic fild inducd du to th RF currnt in th coil inducs an azimuthal RF lctric fild in th plasma. Th inducd RF lctric fild in th plasma rgion inducs an RF currnt in th conducting plasma in th opposit dirction to th coils currnt, similar to an lctrical transformr. Th fficincy of powr coupling in th H-mod is basd on th transformr activity btwn th plasma currnt and th antnna currnt. Th inducd plasma lctric filds acclrat or hat th lctrons and whn ths acclratd lctrons collid with th fd gas som of thm rsults into ionization. In this mod th hating mchanisms in th plasma ar bulk ohmic hating as wll as collisionlss stochastic hating [22]. For a pur ICP in th absnc of lctrostatic coupling (i.. in prsnc of good faraday shilding) it is practically impossibl to ignit th discharg without any xtrnal sourc of lctrons. In th prsnt work, whnvr th Faraday shild was in us, an ignitr was installd working lik a spark plug [23]. Hybrid mod As xplaind arlir with incrasing powr th systm gos from E- to H-mod at a crtain thrshold whras th rvrs procss dos not happn at th sam powr but at a lowr powr lading to an hystrsis ffct [24]. It is found that nithr th E-mod nor th H-mod of an ICP discharg is pur [24] but, th prsnc of th hybrid mod is dominant clos to mod transition and hystrsis rgion. This work is vry much dvotd to undrstand th mod transitions and th hystrsis. Attmpts hav bn mad to undrstand th transitions and hystrsis on th basis of th transformr modl [25] whr th plasma is considrd as singl turn coil and its transformr activity with th antnna is studid. Th capacitiv branch of hating is also introducd to undrstand th plasma undr E-mod. Nvrthlss, until today a slf consistnt xplanation of th hystrsis is missing. Exprimntally it has bn found xprimntally that th mod transition points ar dpndnt on th coil gomtry, on th quality of th faraday shild, on th distanc btwn th antnna coil and th plasma, on stray lmnts du to physical boundaris and abov all on th fd gass [26]. Sinc thr has not bn any vidnt work rlating this physics problm to any chmical or surfac phnomnon argon was usd as a fd gas to avoid furthr complications in th prsnt work. 14

15 Chaptr 3. Th shath and th lctron distribution function Equation Chaptr 3 Sction Shath formation in a low tmpratur plasma In a low prssur RF dischargs, with T >> T i, it is an stablishd fact that quasinutrality vanishs nar th surfacs which ar in contact with th plasma. Assuming a plasma of singly ionizd atomic gas (.g. argon), whr n and n ar th lctron and ion dnsity in th bulk rspctivly; th thrmal lctron flux ( Γ = i 1 4 nv ) to th xposd 1 surfac is much highr than that of th ion flux ( Γ i = nv i i ), whr v and v i ar th man lctron and man ion spd rspctivly. In th balancd condition whn Γ =Γ, th quasi-nutrality would hav bn undisturbd bcaus of th fact that th lctron-ion pair hitting th wall ar lost togthr [4]. In rality, for th plasma with T >> T, Γ >>Γ i th fast laving lctrons lav th quasi-nutral bulk at a positiv potntial calld plasma potntial, 4. On th othr hand, a floating surfac in contact with th plasma starts to dvlop a ngativ potntial rlativ to th potntial of th quasinutral plasma bulk potntial, bcaus of comparativly mor lctrons rach th xposd surfac. This rlativ ngativ voltag soon rachs th lvl that it starts to rpl impinging lctrons and attract ions stablishing th balanc of lctron and ion flux to th floating surfac. Undr this balancd condition th dvlopd potntial on any surfac is th potntial at which any lctrically unbiasd surfac floats and hnc is calld th floating potntial, surfacs, w hav V f V p V p V f. Sinc this potntial dvlops to oppos th lctron raching < V. Du to th dvlopd ngativ potntial at th floating p surfacs a nt positiv charg accumulats in front of th walls. This positiv charg rgion is calld th shath. Th thicknss of ths shaths dpnds on th scrning ability of th plasma to any xtrnal prturbations, and it is confind within fw Dby 2 lngths, ( λd ε0kt n ) =. Th positiv ion shath is charactrizd by high ion dnsity compard to th lctron dnsity whr latr dcays within th ordrs of Dby lngth to shild th lctrons from th wall. Shaths dvlop around a biasd surfac as wll but th charactr of th shath on a biasd surfac dpnds on th applid potntial. An lctrically biasd Langmuir prob is th bst xampl, whr a positivly chargd (ion) shath dvlops around a ngativly i i

16 Chaptr 3. Th shath and th lctron distribution function biasd prob surfac and a ngativly chargd (lctron) shath dvlops on a positivly biasd prob [27]. Th stimation of ion shath thicknss can b mad using Child-Langmuir law [11] for spac-charg-limitd currnt dnsity j flowing btwn two plans sparatd by a distanc s with a potntial U btwn thm. In th cas of plasma, s is th shath thicknss with on plan as shath dg, and th Child-Langmuir law rads 4ε 0 2 j = 9 M i (hr ε 0 is th vacuum prmittivity constant and U s 2 M i is th mass of th ion). (3.1) Bohm critrion and Prshath It has bn obsrvd [28] that th masurd ion flux and th thortically obtaind 1 ion flux using Γ i = nv i i through th ion shath had a grat discrpancy. As a mattr of 4 fact, th abov rlation is basd on th assumption that th shath trminats at th plan (shath dg) whr lctron dnsity bcoms qual to ion dnsity. But in ordr for th potntial in th shath to dcras monotonically as w mov from th plasma towards th boundary (and to gt th xact ion flux), ions must ntr th shath with a vry high vlocity [] calld Bohm vlocity, u B. Th common dscription [11] for xtraction of ions from th stationary plasma bulk is basd on th Poisson quation assuming Maxwllian distributd lctrons with an lctron tmpratur, T. For th plasma boundary condition it is assumd that th lctron dnsity dcrass xponntially with dcrasing potntial across th shath (i.. n xp( ( V V ) / kt ) ). Th ions oby th continuity quation, maning ion dnsity s p f dcrass with incrasing vlocity of th ions. Following th abov mntiond stps [28] on rachs to a condition for ion vlocity at th shath dg calld Bohm critrion [29]. u 1 kt 2 s ub =, M i (3.2) From th abov quation it is clar that th ion vlocity in th shath is dfind by th lctron currnt not by th ion tmpratur. As a natural consqunc of th basic physics, thr must xist a rgion btwn th nutral plasma and th non-nutral shath whr ions could gt acclratd. This transition rgion, bcaus of which th ions gain Bohm vlocity at th shath dg ar calld prshath. 16

17 Chaptr 3. Th shath and th lctron distribution function Prshath formd in th plasma has a potntial drop on th ordr of rgion quasi-nutrality is still valid ( n kt. In this = n i ) but th charg dnsity dcrass, a dtaild dscription of prshath can found in [29]. Now assuming n s bing th charg dnsity at th shath dg th ion currnt dnsity can b stimatd at th shath dg j = n u (3.3) With th hlp of qn. (3.1) and (3.3) th shath thicknss can b calculatd as s B U s = λ d. 3 kt Furthrmor, th potntial drop across th shath V p (3.4) V f can b achivd balancing th ion and lctron flux at th wall. Th ion flux bing calculatd using Bohm 1 vlocity Γ i = ns( kt Mi) and th lctron flux Γ = 4 nv s xp( V ( p Vf ) / kt ), which rsults V p kt M i Vf = ln. (3.5) 2 2π m RF shaths Th abov discussion has bn prcdd undr dc discharg conditions for th simplicity. Howvr, in RF (at MHz) dischargs along with th lctrons, discharg potntials also oscillats [30, 31] with th applid frquncy. This all changs th natur of th shath. Although th vry basic bhavior rmains th sam on tim avrag, th shath starts to xpand and contract with tim du to lctron motion. Du to th oscillating natur of th lctrons in th bulk and th shath boundary thy intract btwn ach othr and, as discussd in th last chaptr, this intraction is quit involvd in th lctron hating mchanism (stochastic hating). Th basic natur of shaths in ICP and CCP dischargs ar quit diffrnt du to thir coupling mchanism. In a capacitivly coupld discharg, dirct fild lins ar prsnt btwn th RF powrd lctrod and th plasma (or th groundd lctrod, if prsnt). Th changing polarity of this fild kps th lctrons changing thir dirction of motion. Consquntly th potntial of bulk plasma as wll as th positiv ion shaths ar spatially and tmporally rf-modulatd. Du to this RF modulatd high potntial across th shath of a Langmuir prob tip, th prob masurmnts in RF plasmas ar comparativly difficult (will b discussd in dtails in chaptr 4 & 5). In absnc of any collisions th ions prsnt in th shath xprinc an RF modulatd fild with a maxima and a minima. 17

18 Chaptr 3. Th shath and th lctron distribution function Consquntly ion nrgy distribution at th surfac in an RF discharg is charactrizd by a low and a high nrgy paks calld a saddl structur distribution [32]. In a pur inductivly coupld discharg (maning in absnc of any suprimposd lctrostatic coupling), th lctric fild lins ar azimuthal contrary to th dirct pntrating axial fild in CCP. Lik th lctromagntic fild propagation in any conductor, th fild lins in th plasma ar only abl to pntrat within th skin dpth. Thrfor th lctric fild lins ar closd within th discharg and hnc principally no RF voltag variation occurs across th shaths. Th shaths in inductivly coupld plasmas ar vry much lik a convntional DC shath with a low and constant potntial diffrnc across it. Sinc th powr coupling is limitd with in th skin dpth vn th plasma potntial also is compltly RF indpndnt. Howvr, as sn in th prvious chaptr, th ICP is always suprimposd with a lctrostatic coupling, and th shaths in this cas ar no longr DC. 3.2 Elctron distribution function To rprsnt a givn spcis in plasma or in any statistical systm a distribution rr function, f (, r υ,) t is usd. In an ionizd gas th vlocity distribution of th lctrons is of fundamntal importanc as th discharg currnt is mainly lctron currnt. Espcially in low prssur RF plasmas, xcitation and ionization of th gas atoms or molculs is in larg xtnt causd by lctrons. Onc th lctron distribution function (EDF) is obtaind, all th lctron-dpndnt paramtrs lik lctron mobility, diffusivitis and raction rats can b dtrmind [33, 34, 11, 12]. Th prsntd introduction on distribution function will b rfrrd to lctrons r r only. Assum an lctron vlocity distribution function f (, r υ,) t, which tlls th r r distribution of th lctrons in a six-dimnsional position and vlocity phas spac ( r, υ ) at a momnt t [35, 27]. Th numbr of lctrons pr unit volum in vlocity spac with th vlocity componnts along x, y and z spatial coordinats btwn υ x andυ x + dυ x, υ y and υ y + dυ y and υ z and υz + dυ z at a tim t is f ( xyz,,, υx, υy, υz, td ) υxdυydυ z. (3.6) r Th lctron dnsity n= n( r, t) at tim t and at a position r is obtaind by intgrating rr f (, r υ,) t ovr vlocity spac, that is r rr 3 nrt (,) = f(, rυ,) tdυ. (3.7) 18

19 Chaptr 3. Th shath and th lctron distribution function Frquntly vlocity distribution functions ar normalizd with rspct to dnsity: r r r f (, r υ,) t = n(,)(, r t f $ r r r υ,), t (3.8) whr f$ (, r rr υ,) t is calld normalizd lctron vlocity distribution function, with 3 f $ (, r r r υ,) t d υ = 1. (3.9) For isotropic distribution it is usful to introduc anothr function g( υ ) which is dpndnt only on th absolut valu of vlocity and is such that [35, 11] r r 3 g( υ) dυ = f( r, υ, t) d. (3.10) υ 0 This xprssion can asily b achivd by assuming a sphrical systm of coordinats in vlocity spac and intgrat ovr all angular coordinats. Sinc th volum lmnt (for vlocity) in a sphrical systm is givn by b rwrittn as [12] 3 2 d υ υ sin( θ) dθdφd 2 2 g( ) d π π υ υ = dφ sin( θ) dθ f( r, υ, t) υ d = υ, quation (3.10) can υ (3.11) For th isotropic f (, r υ,) t in th vlocity spac abov quation solly dpnds on valu of vlocity lading to rlation g 2 ( υ) 4 πυ f( υ). = (3.12) Th abov quation is nothing but a rlation btwn lctron nrgy distribution function (EEDF) and th lctron vlocity distribution function f ( υ ). Th lctron (kintic) nrgy distribution function can b obtaind in trms of nrgy by rplacing dυ 2 by dε whr kintic nrgy, ε = 1/2m υ. 4π 2ε 2ε g( ε ) = f( ) m m m (3.13) A thortical calculation and modling of th kintic bhavior is out of th scop of this thsis. But, a comparison will b mad with th obtaind rsults of a co-workr [36] for th similar plasma conditions in argon dischargs. This part is only mant to undrstand th basic procsss and th dfind trms usd in this work. So, by now only th rprsntation of th lctron distribution function was discussd but to gt any physical undrstanding of th lctron kintics, its tim bhavior r r 3 should b closly chckd. Undr non-stady conditions f (, r υ,) t d υ varis with tim du to following rasons. 1. Elctrons from outsid of collisions and vis vrsa. 3 d υ will b scattrd into 3 d υ as a rsult of 19

20 Chaptr 3. Th shath and th lctron distribution function 2. Elctrons from insid th lmntary volum will b lost as a rsult of diffusion procsss producd by gradints in f ( r, υ, t). 3. Elctrons from insid 3 d υ will b lost as a rsult of xtrnal forcs acting on thm. Including all th abov mntiond points th lctron transfr rat maning th numbr of lctrons that pass out of d 3 υ pr scond pr unit volum as a rsult of xtrnal forc satisfis Boltzmann quation [33, 34, 35]. rr rr f (, r υ,) t rr X rr f(, r υ,) t + υ r f(, r υ,) t + υ f(, r υ,) t = t m t c (3.14) Whr X is xtrnal forc (for applid lctromagntic sourc it can b simply Lorntz forc) acting on lctrons, and υ dnots gradint in vlocity spac. Cration and dstruction of particls (by impact ionization, rcombination or chmical ractions) r r f (, r υ,) t ar includd in th right hand sid collision oprator, t, c rr rr rr f(, r υ,) t f(, r υ,) t f(, r υ,) t = + t t t. (3.15) c lastic inlastic Undr th condition of thrmodynamic quilibrium whr lctrons and havy particls hav narly th sam tmpratur th distribution functions ar Maxwllian. Our intrst lis in RF plasmas which ar far away from thrmodynamic quilibrium du to th applid RF lctric fild. This applid RF lctric fild at a frquncy of MHz acts as a sourc to produc thrmodynamic non-quilibrium rsulting into vry highnrgy lctrons and cold ions. Sinc any applid fild has a dirctional dominanc, th flow of lctrons is no mor isotropic in prsnc of any (hr RF) fild in plasmas. Espcially lctrons (bcaus of lightnss) dvlop a drift vlocity υ d in th dirction of applid fild rsulting into anisotropy in th background isotropic random thrmal vlocity υ. This sction of work is dvotd to brifly undrstand th anisotropy causd in lctron vlocity distribution du to th applid fild. Lt us start with th rlativly simpl cas of a uniform DC lctric fild E as a sourc for producing disquilibrium in a homognous plasma (th spac gradints causd du to th walls and diffusion flows ar ngligibl, f (, r rr υ,) t r = 0) whr th spac gradint trm in th Boltzmann quation (3.14) can b nglctd (th ffct of oscillating filds and spatial gradints will b discussd latr) [36, 12] 20

21 Chaptr 3. Th shath and th lctron distribution function rr rr f (, r υ,) t E rr f(, r υ,) t υ f(, r υ,) t = t m t. (3.16) In abov mntiond conditions th EVDF dpnd only on th vlocity υ and on th angl θ btwn th dirction of vlocity υ and th applid lctric fild c E. Th dirctional applid lctric fild will rsult in an avrag dirctional drift vlocity. Assuming that th anisotropy causd in EVDF du to modratly strong applid E fild lads to vry low angl θ dpndnc, th nrgy gaind by th lctrons from th lctric fild pr collision is much smallr than th man thrmal nrgy of th lctrons, i.. th drift vlocity, υ d and thrmal vlocity,υ satisfy, υd / υ << 1. Thrfor angular dpndnc of th EVDF, f ( θ, r υ, t) can b rprsntd by a sris xpansion in trms of Lgndr Polynomials [35] and th xpansion can b truncatd aftr th scond trm. This wll known mthod is also calld two trm xpansion [35, 12]. r υd f ( θ, υ,) t = f0(,) υ t + cos( θ) f1(,) υ t = f0(,) υ t + f1(,) υ t (3.17) υ Substituting th abov rlation in quation (3.12), an absolut vlocity dpndnt function g( υ ) can b obtaind for a sphrical coordinat systm 2π π r r 2 g( υ) dυ = [ f ( υ, t) + cos( θ) f ( υ, t)] υ sin( θ) dυd d. (3.18) This quation lads to θ φ g = f t that mans f 0 ( υ, t) contributs for isotropic 2 ( υ) 4 πυ 0( υ, ) quantitis which dfins th avrag lctron nrgy and th avrag valu of any othr nrgy dpndnt quantity. Howvr, th scond trm f 1 ( υ, t) is th dirctd componnt of distribution function calld th anisotropic EVDF componnt. It givs th avrag valus of quantitis pointing along th fild lik currnt or vlocity componnt paralll to th applid lctric fild E 2 [ (, ) (, ) ] u = υcosθ = υcosθ f υ t + f υ t cosθ υ sinθdυdθdφ 0 1 4π 3 = υ f 0 1( υ) dυ 3. (3.19) Momnt mthod is usd to sparat th isotropic and th anisotropic part of qn. (3.16). Th first quation for th functions f 0 and f 1 is found by substituting qn (3.17) in quation (3.16) and multiplying th rsultant quation by d(cosθ) and intgrating it ovr all valus of cosθ from -1 to 1. f E t 3m υ υ ( υ f ) = S. (3.20) 0 21

22 Chaptr 3. Th shath and th lctron distribution function Th scond quation can b obtaind by substituting (3.17) again in quation (3.16) but multiplying th rsultant quation by cosθ d(cosθ) and intgrating it also ovr all valus of cosθ. ( f ) t m υ f1 E 0 = S. 1 (3.21) Th trms S contain collision of lctrons with atoms, ions and among ach othr. For a plasma with rlativly low dgr of ionization collisions btwn lctron-lctron can b nglctd th only collision btwn lctrons and background havy gas particls ar th dominant. Prcisly th collision trm distribution function S 1 rprsnts momntum transfr and th f charactrizs th fraction of lctrons moving in th dirction 1 paralll to th applid fild. Now sinc collisions lads to a substantial chang in th dirction of lctron motion so th charactristic tim of variation in f 1 must b of th ordr of tim btwn th collisions [35]. And th variation rat δ f t 1 δ must dpnd on th product of f by th collision frquncy 1 ν n, (i.. ν 1 n trm S 0 S f 1 ). Whras, th collision dfins th nrgy transfr and is dpndnt on nrgy transfr cofficint ( κ = 2m M ) along with th variation rat in th isotropic part f 0 (i.. S0 κnνn f0) n i [35]. Now without going in furthr dtails of collision trms and assuming no inlastic collision undr stationary condition w com to a vry important quation [11] 3 m 2 M E 3 υ 2 ' ' f0 = Axp ν nυdυ. (3.22) Exprssion (3.22) dpnds on ν n, which can b vlocity dpndnt lading ν ( ) n νn υ or a vlocity indpndnt transport collision frquncy ν n = const. At a constant collision frquncy ν n = const th distribution function is Maxwllian irrspctiv of th applid fild strngth. Maxwllian distribution function f rprsnts m lctrons of common tmpratur tmpratur kt M E m ν n i. For kintic nrgy kt = and constant ( ) 32 distribution function gm( ε ) can b writtn as in [11] g m ε 1 2 = 2 mυ, lctron A= m 2π kt Maxwll nrgy m ε ( ε ) = xp 2π kt kt. (3.23) 22

23 Chaptr 3. Th shath and th lctron distribution function ( ν n υλ n Now considring th scond cas whr collision frquncy is vlocity dpndnt = ) but th man fr path lngth of lctrons is constant ( λ n = const ). Undr ths circumstancs th nrgy distribution function turns out to b g D m m 3m ε ( ε ) = xp 2 2π M, (3.24) 2ε0 M ε0 and is calld a Druyvstyn distribution function, whr ε ( 0 = λ E) is th nrgy gaind by lctrons ovr a distanc λ m. Exprimntally obsrvd distribution functions can b of any shap and ar oftn fittd with ε g( ε ) xp ε0 α n (3.25) whr (Maxwllian )1 α 2 ( Druyvstyn). Anothr vry oftn ncountrd distribution function for our kind of plasma is bi-maxwllian whr th tail and had of th distribution functions hav vry distinct tmpratur and can b rprsntd as Whr L T ε ε g( ε ) = Axp Bxp L + kt kt H. (3.26) is th tmpratur of low nrgy part and H T rprsnts high nrgy lctron s tmpratur of a bi-maxwllian distribution function. Abov mntiond non- Maxwllian distribution functions do not rprsnt th lctrons of sam tmpratur and ar rprsntd by thir avrag nrgy ε of lctrons. Now coming closr to th rality of RF plasma, maning that th assumd applid lctric fild is oscillating homognous lctric fild ( E = E cos 0 ωrf t) instad of constant fild is assumd. In such cas th isotropic distribution function f 0 can b xtractd from th sam quation (3.22) just by rplacing homognous, constant E fild to an ffctiv lctric fild. E E ν n = ff ν n + ωrf Th influnc of th ffctiv fild. (3.27) E dpnd on th ratio ωrf ν n, and is considrd in dtails, in a work in th fram of our group [8]. In a low tmpratur plasma, th diffusion towards th wall dominats th plasma procss. In such cas an additional diffusion fild trm will b addd to abov rlation [37, 38]. ff 23

24 Chaptr 4. Basics of diagnostics Equation Chaptr 4 Sction 0 This chaptr of th thsis will covr a dtaild dscription of th thoris involvd with th diagnostics usd in th prsnt work. Broadly, th diagnostic tchniqus usd in this thsis can b dividd in to two catgoris. First catgory contains th Langmuir prob which is insrtd in th plasma, to masur bulk plasma paramtrs. Whras, th othr tools, Rogowski coil (a currnt prob) and capacitiv voltag prob, ar installd out of th plasma volum to charactriz th powr coupling. Th first sction of this chaptr is dvotd to Langmuir prob s basics and th thory usd to xtract plasma paramtrs followd by th scond sction dscribing th basics of Rogowski coil and capacitiv voltag prob. 4.1 Langmuir Probs As was dmonstratd in th prvious chaptrs chargd particls and spcially lctrons play a vry important rol in low tmpratur, low prssur RF plasmas. In ths dischargs nrgy is coupld to th plasma through th acclration of lctrons dominating th bulk procsss. By contrast, th ion s nrgy, thir dnsity and distribution play a substantial rol in th plasma boundary procsss which ar dcisiv factors in surfac procssing plasmas. This work is mostly rstrictd to th masurmnts of plasma paramtrs associatd with th lctrons using an lctrostatic prob. Elctrostatic probs ar undisputdly th oldst and most widly usd diagnostic tools in plasma physics. Th tchnical and first thortical xplanation of th lctrostatic prob was dvlopd by I. Langmuir [39, 40], and hnc it is widly known as Langmuir prob. Principally in its simplst form a Langmuir prob is just a conducting wir insrtd in th plasma, whos currnt-voltag charactristic I ( V ) is masurd with rspct to rfrnc lctrod. Th rsulting prob charactristic is analyzd using an appropriat prob thory which crats a connction btwn th masurd I( V ) charactristic curv and th paramtrs of th undisturbd plasma. Th plasma paramtrs which can asily b obtaind using masurd charactristic curv and appropriat prob thory ar floating potntial ( V f ), plasma potntial ( V ), lctron tmpratur ( T ), lctron dnsity ( n ) and lctron nrgy distribution function ( f ( ε ) ). Probs ar asy to construct and ar vry flxibl with th dimnsion but th simplicity in th tchnical part has to compromis a lot with xtrmly complicatd thoris involvd. That mans vry asily obtaind data can b badly intrprtd in p

25 Chaptr 4. Basics of diagnostics absnc of implmntation of an appropriat thory. Anothr and th biggst problm associatd with prob masurmnts is du to its physical prsnc in th discharg. Th plasma has a basic natur to shilding any xtrnal prturbation (within som Dby lngth) but in rality this shilding ffct is nvr so localizd [4] (and can b far wors in magntizd plasmas). So to say physical prsnc of prob vntually affcts a lot to th surrounding discharg condition. On th othr hand advantags ovr diagnostic tools lik Thomson scattring, microwav intrfromtr and optical mission spctroscopy is, its low cost and its ability to do local masurmnts. Howvr, th othr tchniqus ithr ar vry high budgt or provid only th volum avragd paramtrs. Figur 4.1: Masurmnt principl of Langmuir prob. Masurmnt Principl A Langmuir prob systm consists of a small conducting lctrod calld prob tip, which is insrtd into th plasma at th dsird location of masurmnt and an xtrnal control unit (fig. 4.1). Th prob tip can b of any shap but oftn planar, sphrical or cylindrical shaps ar chosn du to th limitations of thortical dscription. In th prsnt work cylindrical tungstn wirs of diffrnt diamtrs ranging µm and lngth of 5-10 mm wr usd lik lctrod [41]. Th prob tip is kpt vry clos to an lctrically insulatd floating lctrod. Th xtrnal lctrical circuit associatd with th control unit allows th variation of th prob (tip) voltag V with rspct to th rfrnc lctrod (in our cas it is th groundd lctrod of th ractor itslf) to obtain th ion and lctron currnt. Th obtaind rlation btwn th prob currnt and th applid prob voltag I = f( V) is calld th prob charactristic. 25

26 Chaptr 4. Basics of diagnostics Figur 4.2. Schmatic of a typical prob currnt-voltag charactristic. As discussd in sction (3.1), th introducd prob tip in to th plasma will soon b surroundd by a plasma shath laving th bulk plasma (aftr th shath dg) at a positiv plasma potntial ( V p ). Th applid DC potntial to th tip with rspct to th shath dg potntial (i.. plasma potntial) can b rprsntd by U= V V p. Furthrmor, at a floating stat th voltag drop across th shath acts as a barrir to approaching lctrons (or rathr attract ions), making ion and lctron flux qual at th floating potntial ( V f ). In th I V curv (fig. 4.2) th point of qual ion-lctron flux can b idntifid at th point whr magnitud of currnt is zro. For th complt xplanation and undrstanding of th I according to th applid voltag [42, 43]. V curv, it is dividd into thr rgions (A) Ion saturation currnt ( I is, ) rgion ( V < Vf and U << kt ): th voltag applid to th prob tip in this rgion is ngativ with rspct to th floating potntial. Also th valu of U (potntial barrir for th lctrons) is much largr than th lctron tmpratur, so that not vn th fastst lctrons can rach th prob tip. Hnc, lctron contribution to th currnt in this rgion is zro. On th othr hand in this rgion bcaus of high ngativ potntial across th shath th positiv ions ar attractd to th prob 26

27 Chaptr 4. Basics of diagnostics surfac and contribut to th currnt flow. Th prob acts lik an attracting lctrod for th ions, and making th tip vn furthr ngativ will soon saturat th ion currnt. (B). Elctron rplling currnt ( I r, ) rgion ( U < kt and Vf < V < Vp ): with incras in applid voltag V th lctrons with sufficintly larg nrgy succd to ovrcom th potntial barrir (U ) and rach th prob surfac and start to rduc th modulus valu of th currnt compting with th ion flux. In this rang th lctrons compt with th barrir voltag U. That mans furthr incras in V maks th potntial barrir U vn smallr for th lctrons and vn rlativly lss nrgy lctrons also start to rach at th prob surfac. At th sam tim in this rgion th positiv ions start to fl a rplling potntial and at th floating potntial V f th ion currnt and th lctron currnt to th prob surfac bcoms qual (nt currnt contribution bcoms zro). With an vn furthr dcras in potntial barrir U (by incrasing th positiv bias V ) th currnt riss stply sinc mor and mor lctrons with vn lss and lss nrgy contribut to th currnt. Finally, at th bias voltag V = V p, th potntial barrir U bcoms zro and th prob surfac floats at th surrounding potntial and th lctrons xprincs no barrir to rach th surfac. Actually anothr part of th currnt blonging to th ion currnt is ion rplling currnt ( I ir, ) rgion whr V < Vf but lying bfor th ion saturation rgion whr U < kt. Th ion nrgy in our plasma is so low that th ion saturation currnt is comparativly ngligibl to th lctron saturation currnt. Furthrmor, in th ion rplling rgion whr high nrgy lctrons ar still abl to ovrcom th potntial barrir and contribut mor than th ions to th currnt and hnc this rgion can b considrd as xtndd lctron rplling currnt rgion. Bcaus of that th rplling currnt in this work is calculatd by taking diffrnc btwn th total currnt and th ion saturation currnt. V (C) Elctron saturation currnt ( I s, ) rgion ( V > V p and U > 0 ): in this rgion is vn highr than th surrounding (plasma) potntial rsulting in a ngativ shath around th prob tip. Undr this condition all th lctrons raching ngativ lctron shath gt attractd and th currnt vntually saturats. Vp 4.2 Prob thory This part faturs th thory, how diffrnt parts of currnt Iir,, Ir,, Iis,, I s, (of an xprimntally obtaind I V curv) can b xplaind and usd in ordr to xtract th 27