- Email: [email protected]
Magnetic fields in magnetron sputtering systems
S.,'h+ce and C,Jor#n.t's /i'¢kt,#++~v..+711+93) I - 5
I
Magnetic fields in magnetron sputtering systems + M. J. Murphy, D. C. Cameron. M. Z. Karim and M. S. J. Hashmi IJllbllll ( ;/.I | .tl frxtl.i (J/,t~.¢'; hi /)tdll.I 9 ' II ('/lllll!,
IR¢~iv~ May 29, 19921
Abstract i~t~lll]). ~l lalmputer-aidcd-design ll,ll:k;sb~ has been ll.~¢dto d~'nerib~ Ih¢ tllll[Inl2til: kid ill [i-tliii ill it planar malgnetron ,~.xk:nl I I ] .lilll2h l¢¢hnlqul5 )idd la~'dknl resull+ lind die icry Ilexibl~: I)islld~ilnlag'~ are Iilitl the p:nuJls life rural) ntilllerieaL i1 I;ikl.,~ hllk" arid some eXl~.i,e m pr~ipei'l', tllillSC Ihls kind d mlfllar¢ ~l~d commerciitl l%leklig~ ~.';nlhi/VCF} espen~k.¢. Allalyll¢ ¢xprt'xsllins b r Ihe li¢ld in [fOlll o[ a rlhlllilf lllti[n¢Iron shotild tilor¢ ¢:i~ill. f~l¢ililal¢ th¢or¢liu':il anal)~i~ of nla~.n01r~.lno['tl.,rahon Ih¢) ~'.ould ,the k' till/fill Io the thin Iilm r~arehd [al.'u'druth de, ignillg a llla[tl¢lflin n)'slt'ltl, The meLJlo,.|sprl.'~ellled licit' appJ.% lo CllCLilllr lind i'~¢t;lllgultlr matRet [it-ometfic~, hut Jl;ll,C much hl'oader llFIIl~Jlcllbihl.'. "l hi/ rCstllk are ¢;1~il) O.lcnded to ml.lltll~]¢ Illil~lldlhlll ct,nli~uIralion:,. Th¢lr¢ lin~ limillllionn liA I ~ tniiterials x'.,hi~2hcan k' IP.t~dand/111 lh~, rfla~n¢ii.2~¢Ollldl).. hui Ih¢~¢ are ikll lliidul) k'qridlXC
I. I n t r o d u c t i o n
The m o t i v a t i o n for the work to be described in this paper was the desire o f the atithors to have a simple. accurate u n d e r s t a n d i n g of the m a g n e t i c field in magnetrtm spulicring s)'slem~. ,quc'h underslandlng is helpful t',cca!.is¢ tile Inal~lletic licid strength and direction are crilical protons par:.lnlelcrs. 1he lield ul the ,,puller h i l e d ,,Llrfaee inilucllCCS sputter rate and target erosion unili~lUllty 1.2] W i l h Ihe advcrll d tlllbalallced m;lgnetron> [J. 4] it 1"~2CtilllC clear thai Ihc licld al the ,~tlhSlrale gill, ice ik also hnportcull l h i , is bccitl~,C Ihe licld afl-eci~ Ilic pla,,nla ttcn,,il) in Ihc ~ i d n i i ) uf the nubqr,llc, h¢ilcc
lhe ion Ilux to tile substrate and therefore the Iilm properties. Siich ioi1 b o m b a r d m e n t is essential ill the
production of high qualily hard coatings. Furthermore. in multiple magnetron s$'.,,tems tile polarities of the tnztgnets ill a given m a g n e t r o n with respect to the polarities of the m a g n e t s in n e i g h b o u r i n g ii1;.igllelrOllS ,hould I~ t a k e n into accoull(. It has been d c m o n q r a t c d that tile p l > m t l density is h m c r in s)stenls where ,i nlagncir(m face,; its m i r r o r image than %vhcn it face; i k ot~pt~nile II. $1 This i~ because the kilter conligurulioil alltms field lines belwecll Ihc iTla~nelrorls tO link Lip and I~rm a ma~nctie eleetren Irap which enhances pklsm:t dentil}' t'll21WCCll the nla~netroll ~, II is tic;Jr Ihcn lhal ihu' role d ihc maellClic Iictd m IllagllCirUll 5,yslCill.n 1~.e~,olvillg to L~ccomc quite ~2ol/Iplcs. ,\ g o d theoretical description d these fields would be tl,C[tll. One xvay to get Stlch it description Is to IBc il -ll.ipd prc~l.t:ial al ihc Iq(h IlilCi n;tlinn,il t'onft'rcncc" lln ~.khlliulT1ell t Oallll[~s ;i:ld ]hin i Illll~. Sail I)icg,l+ ( .Jl+ t '.~,'L ,~.rtil ~, ill. b J.47
il?
maBnetic C A D package. There are a nun+l~r or referrals to, a n d explicil account s of, Ihe use of such paekuges in the literature [ 1 . 6 , 7]. Such m e t h d s are generally ba,,ed
on finite elemerit or b o u n d a r y element technique;. The.,. are both accurate and flexible. The) can be used lot analysing complicated magnetic gcomclrie,. 1 heir di,,advdnlugen tlrc lhal Ihe ,diwarc is u'x['K.'axp,c ;llld ~ellClall} lleeds it large conll"ltllCr on which to run 11 1;Ike, ~PlII, exi~rtise and con,,idcruble time to uv+_',ol,ai,dl.', m )-I) an.d}si~..The qtlalllilativercsulb roll}al',pl) to tile111,x~ncJroI1 ill qtieslltm N.I'.. the) ;tic Iltlnle[ic lind I,ick ~Clleldlll} I Jllqead q,I I,tklllg thin rolllc '-.,.l."d e c l d d t~ It'. ,Ind tim! Llll,I]}IIC nOJtltlOtl~ (L~r ~OILIIIOlI~ ~]IICI1 xxcrt' ,It leA< strui.~Jllk)rx*.'ard to COllll)Utr21 Jol stnlpJc m;l~lletron eollligurations. The major part t~f lhis lusk xva:, Itlad¢ gtai~htfor,.',ard
by the uvailahility d" ex:acl result,, for
certain rectangular nlagnct t?.pcs and the Iamiliarit}' t',f tile ealculalion for eylimhical and a n n u l a r I } p 6 The paper is o r g a m s e d as Ioikm,,. Nu.dion 2 gl',.,..'., a,3 uL'counl of lhc 1,4asori~. ~h'¢ certain magnds can b? I r c a i d analyticall). In Section 3 ix dencr~hetl the nl¢lltod o f caJcLllalion b r cxlindrical ilnd annulilr nl;.l[~llCln and itx:ail;.lblere~ulk for regtallgUl;Ir tll;Iglle|'~ .¢leCtlOll a illuqrate ~, ihc a p p l i c i t i o n d lhe',ee..lUaliorlx in ditT¢.'re;u llldgllCll't)ll conligllration~, xqlilq o'Mghl~lOIl~ *t[C gl~Cll in Section 5
2. N l a g n c l s
lhc ,apcrating i~in~e d a pcrmancnl nl,i~[ic| It,',o11 Ih¢ dema~nelisation cur',e in the ,,ccond q u a d r a i l l d 11~¢ hystel'¢'qS loop. ( ' h a r a c t c r i s l i e tlenla~lldisa|lO[1 '~Ul'~C,
I I%q
I I.cu,r Salu u.~ XII l~gl> r...n-I
M. ,I. Murplw et aL ,' Magnctic field.~ i,t mag+letron spl ler n.k, s)'.~ emx
for various magnetic materials are shown in Fig. I. Generally speaking AI-Ni-Co magnets have a high remanent field, but a low cocrcivity. In contrast, ferrites have t'~.~sonable coercivity, but relatively low remanent field. Rare earth samarium cobalt an~ neodymium iron boron magnets have high remancnce together wilh high coercivity. These magnets have demagnetisation curves that are linear over a large range with a B to H ratio close to the permeability of air j+n. Substantial reverse fields are necessary to drive the magnet into the non-linear region. The magnet is uniformly magnetised throughout its volume. This combination of properties allows these magnets to be treated as if they have an effective magnetic charge density at either pole with an air gap in between. Thus, calculation of the magnetic field at a point outside these magnets becomes a matter of integrating over the sheet surface charge at both poles. Also the supcrposition principle applies such that contributions to the field at a poinl from various magnets may be added vectorially to yield the total field. Bonded rare earths and some ferritcs may be similarly treated but they demagnetise more easily. Rare earths can be used in an open magnetic circuit as is done for example in magnetic buckets. Such geometries sugged the open circuit operation of magnctrons too, since in the absence of soft magnetic materials calculation of the magnetic fields is straightforward.
3. Calculations and formulae If H is the magnetic field intensity then in the absence of currents a magnetic sealer potenti:d Ii is defined hy
H=
-VI"
Ill
The following relations apply outside and inside the magnet respectively.
B = ~o I I
(2a)
g,c., = 1+~,M
i2b)
wht:re B is the magnetic flux density, it 0 is the permeability of free space, B,~,,, is the remanent field and M is the magnetisation. The surface charge density is given by (3)
a =/*oMn
where n is the unit surface normal. By analogy with the electrostatic field
v = L i"u
41t J I r -
/
-gOO,.800-"iDO.-l~l~-500-.400-3~O-~)0.100
,.°o
4n/.+,,
f
j IR ~- r,I
(4)
where R and R, are the field and source position vectors respectively and m is the unit vector in the direction M. Consider now the case of a uniformly magnetised cylinder with M parallel to the axis. In Fig, 2 can bc seen two disks of charge one at each end of the cylinder. Taking the upper surface, from (2a) and 14) the magnetic field is
B.~
--
B=
,lr,
f'r,, 2 h R , dR, V" Jn I R - R~I
(5)
For an annulus it is only necessary to change the limits of integration. R,t is thc magnet radius. IR - R,I can be expanded out by the triangle rule and then expressed in L'~.endrc polynomials to yield B = - / ~ "2~ ' V r ,~, ~" i r'' ~.,-T Rt
(61
~herc R. (R..)is ,5c smaller (largeri t~f IRI .rid IR.I.
1400
The notation is thu~ of re[ ~ which cover,, a ,,imilar example. For the far geld case with IRI > IR, I,
1200
B=-"'s'-'~-V
B
2
5
'
rd
,
~'
1.2
_R'.':
J~~-c"o(I + 2JR I + :
P~(0)Pt(cos0)
lO0O
and for the near field with !RI < IR, I.
~x~ g 5
e = --~L,m v
2
(" r' "+'~"+.'t--i+ IIR I. t P+(OlP,IcosO)
17)
(Sl
0
oemagne~ng toroe 0 ~ / ~ Fi B I ('hat~l+t¢llshL '*lCma~nClis,ttloll uul+u's f, tr '. ;tI'II~U~ m a g n e t i c n~:llCrlilJ~ 11. &Inteo: 2. ~tnixottOpll: b,lrlu111 tcrritc: 3. b o n d e d S n l ( ' o : J, S i n ( ' . . '~. N d l c B I
(d)
n
[h)
l+g. 2 t;l) Th+ .:ylltldrl~:+d rl+ilgilt:t t:alt;ulalltltl ~2¢o111¢tr) The olt~itx is Jou+illed ,It ~hl: cc;llrc or" d 111;I.1~1112 J'IICC I!~1 [ h c r¢clilll~'al;iF [na~llL:~ ~2'~'0nICI;')" ',~J~h IhL' o[1~.111 I~;ahXJ al lhL' n~a~lCl centre
M. J. Afurphy el ,d. , ,$fagttetit" fields i~t m a g n e t r o n splatering xy~tent~
there will be an extra factor of - I since ran= -1. Adding the contributions from both surfaces gix,es the total magnetic field land its components; at a point. Sitace the :-component of magnetic hield at the substrate is important, we state the following simple expression for the on axis field o'~'ing to a di~ of charge. ,=
~ -
r~.~_q,.,
i
:>o
19)
--
N
0
--
--
--
--
These results contain all that is necessary to descril~ the magnetic field in front of a "standard' circular
magnetron Iwithout the backing plate) as will be described in the next section. Taking advantage of the straightforward mathematical properties of these magnets is not a new idea [% II]. The case of a uniformly magnetised rectangular magnet has been described by Ono et al. [12] (using an equivalent current model) and Trow [13]. The following results, which are str:'ightforward to apply, are taken from ref. 13. The relevant diagram is Fig. 2(b).
B~= ~(-In(y+ B,../I
(I0)
r))
F;g. 3. Ca]cubting for an aclual magnctron m;~r,e~ ;~'*a~
03i!illlllllllIIIlllll!
0.25
0.2
0.15
/r-~\\ 0.05
4n (2 '
"
\(:-
The.~ equations are the result of rectangular monopole sheet and between the limits ~ = ~ _+_I..,: 2. : + I.: 2 where I.,. L,. and L. ;,re
y-)q:
4-x'-,/)
an integration over a should be e~aluatcd v = y + I-, :2 and -- = the ~imensluns of the
magnet m the respective directions. The .~g~ function cquals I if the argument is greater titan or equal to 0 else - I and r = ( x " + ?.,2+ :2)t.-'. The origin is at the magnet centre.
4. Method and results
The method of calculation for an actual magnetron magnet array is .~imple and is illustrated in Fig. 3. Figure 4 shows the results for a cross-section through a circular magnetron magnet array. "The arro','~s represent Ihe direction of the magnetic field. i-'igurc 5 shows the results for a cross-section th:ough a rectangular unbalanced magnetron. The field caused lB. the outer magnet dominates that by the inner Clearly hiehlighted is a "null point' of zero magnetic field on the :-~lxis about 7 cm in front of the magnetron. This is interesting because it suggests that v, crc the substrate placed at this position, the ion bombardment might be less than if it were placed 15 cm away ~;'here the field is
% ~. ~, ~ '~ t /
~',,'~ 1 T
r
I / ' ~ I I'%. '%1'I I ~ t P ,"
% 'i i' t ~',"
0 L--__~
49.04 -0.02
~.06
0
0.02
-- ......
0.04 008
I i g .1 Rc,uh for ,i o r ~ u l . l t rll.l~nCIiLql ~ l l h mncr n,.agncI of rAdltt, onlm m
The ,lnl~l])ll s InlIC[ f . l d l l l , l. (lll',f, ffl .llld 'hV I~(11.~; I,ICI,].
In 0 O44 i11
~ t ~ I~
!
tI
I
}L
l - l g 5 Magnetic field cfo~,~,-'~¢¢llon of ,in t]nbd|~tliLvd l¢c,angliklr magncl,g~n magnet ilrfa) & ¢onMdcrablc range o~cr ~hlCh lhL" hc~C i~ ¢ a k I% Nuun d]Ic~;tl', In front of Ih¢ III.I~TICIIOH
.~.f. J
4
.~.'lllrpllJ" 1'[ { d . .
Magnetw ~iehl~ , , aaf:nefron splinering ,~'xtems
1
(~ 4k08 -0.04.0J01
0
0,02 0 . 0 4 0.~8
1 roT. This could be an important fi.lm growth consideration. The position of the null point will vary as the degree of unbalance changes and it will retreat from the magnetron as the size of the inner magnet incrca~s with respect to the outer. Figures 6(a) and 61b) show the results for a crosssection through mirrored and closed field dual magnetron configurations as described by Wong et el. [ I ] The field link-up in the latter geometry is clearly visible. The z-component of field at the centre betw~'en the two opposed magnetrons is 2 mT. Figure 7 shows a fully thr~-dimensionaI field for a tee'angular magnet array on a plane roughly correspovding to a target surface. This illustratcs the uniformity of magnetic field along the length of the array and also the "end effects'. It also emphasizes the capability of an analytic approach to solve three-dimensional multiple magnetron problems in a straightforward general iTlannel.
5. Conc; :sion
" l!!i!!i o I.. ~,,~.'(~, ~ -0.04 ~
"-". ""-'~-r O
~
t
004
..
I 112 {~ [;tI %1+tgn:~'llc fic!d cr~,+-~¢~tlOn lot ;i tllll¢tlrt2t~ I.t+llL~tllA~ltSll. ,.~I \ l ; , ~ n d l ~ . ticld ¢~lll~igllhlt}tlll for ,HI t'ppo~',i ~tlrl!i~llr:ltlll'l
.-,.,ktt{ 1t,,--
It ha., been sho',vn that it is possible to understand simple magnetron magnet geometries, both circular and rcctat,gular, in a straightforward fashion. The effects of varying magnet nun',ber,L sizes and positions can be ca.~ily investigated Interacting multiple magneh'on systems can al,,n bc investig;,'cd in either tw,.~ or three dimensions. Ira backing plate is not used then the results should be exact. Wc believe this work will bc useful Io researchers faced ~ilh the problem of building their ( ~ n magnetron. ku,'lhcrmorc, man 3 theoretical results to date depend on a knowledge of the magnetic lield in Iront of the target surface. The result.,; should thcrc;'ore be useful to theorists and cxpertmcntalists alike. Acknowledgments Tbc aulhors appreciate the time and interest of Dr Michael Hopkins. Tiffs work ~as supported by the EC BRrrE programmc under contract BRITE RIIB. 0221. CIHt. References
i ,~ - ~ Ih:ct2.~hlllCllM~ln.l] %Ik'l~. i1[ lilt" til.l!~n~ll~ llckl ,,:: ;t pldllC ¢~,rt¢-I~tnldltl ~ Io ,i l,lrg¢l ~lll [LI,~V
I NI ~1. \~,ouE. ~,~, i) hptoul and b t. Rt~hdc..burl ( ,ml H'O,mfl.. qo (l~gll 121 -~ I'~ I~ ~*Vill14. I1~ .I I %"l~%cn i{lld ~.V Kern feud.). 1II111 IFhli Ph)('(,~x¢.~..~l~adcmlc life.'%% N Y . 197X. pp I~1 173 I~ Wmd<~w..f I~. S,I 7c{ hm,L -I .¢ (6! I 1'),%5I 21(.S 4 B W m d o ~ illld (; |. I|atdJllt2 .I I'., .'q~ lc(hm,I .i. ," (31 I }l)X*)l 12"r? W I) ~pr,~ul I ) } RLIOIllk. M I- (ir,d~am and 15 [ R,}hdc. ~i,rl (',,(J: l'r, l m , , i J3 44 I I{;b~ll 2711
,'X.f+J. Murph): el al, I M~,netic /ields i. magm'lron spultcrin~, s)~t~'ms
6 A. E. Wcndt, M, A. Lieberman and H. Mouth, J. Vac. Sci. Tvchmd. 4.6 43) 11988) 1827. 7 C. M. Pcrlov and J. R B.'auer. I~/','/'~Trmc~..Vla~Jlet, 32 l.~) 11~)~6) 831. x j. D jackson, c l u ~ . u l E.k'(trIM~'no.li{ ~. John Wil¢'~, NY. 2nd ¢dn. I07.~.p 9 .i. 9 J. B. Y. Tsui, D. J, Idcn. K. J. Strngl and A. J. Evcrs./£E£ Tva,s. M~'.. ? (1972) I ~ .
I0 K. Halbach, ,%.1 /n~frlmz Mcl/l.J,/, I I ] , Sala and Y. Into, 3 |n'.r. [l,~fr
:o9 II~gil I ~.aL, .I;,n /~1 HJf, t ~14 I"~o1 ! ""
{in Jap,'llff~sc ) I .~ Y O . o . Y . H;~kamJI;L T s ; . o ,rod [ It.l.hm~,,h, Tr( hm,t 4. : (41 [IqSg) .~7n4
I
I.;,
x,
13 J. R. Trow. Ph.D. Tlu,si~+, Uni,,'ersily of Californi;L I~rkclcy. r9~c5 L'~wrence Bcrkctcy Lab. RCr~rl NO. LI~L-I~I ~6.
I
Magnetic fields in magnetron sputtering systems + M. J. Murphy, D. C. Cameron. M. Z. Karim and M. S. J. Hashmi IJllbllll ( ;/.I | .tl frxtl.i (J/,t~.¢'; hi /)tdll.I 9 ' II ('/lllll!,
IR¢~iv~ May 29, 19921
Abstract i~t~lll]). ~l lalmputer-aidcd-design ll,ll:k;sb~ has been ll.~¢dto d~'nerib~ Ih¢ tllll[Inl2til: kid ill [i-tliii ill it planar malgnetron ,~.xk:nl I I ] .lilll2h l¢¢hnlqul5 )idd la~'dknl resull+ lind die icry Ilexibl~: I)islld~ilnlag'~ are Iilitl the p:nuJls life rural) ntilllerieaL i1 I;ikl.,~ hllk" arid some eXl~.i,e m pr~ipei'l', tllillSC Ihls kind d mlfllar¢ ~l~d commerciitl l%leklig~ ~.';nlhi/VCF} espen~k.¢. Allalyll¢ ¢xprt'xsllins b r Ihe li¢ld in [fOlll o[ a rlhlllilf lllti[n¢Iron shotild tilor¢ ¢:i~ill. f~l¢ililal¢ th¢or¢liu':il anal)~i~ of nla~.n01r~.lno['tl.,rahon Ih¢) ~'.ould ,the k' till/fill Io the thin Iilm r~arehd [al.'u'druth de, ignillg a llla[tl¢lflin n)'slt'ltl, The meLJlo,.|sprl.'~ellled licit' appJ.% lo CllCLilllr lind i'~¢t;lllgultlr matRet [it-ometfic~, hut Jl;ll,C much hl'oader llFIIl~Jlcllbihl.'. "l hi/ rCstllk are ¢;1~il) O.lcnded to ml.lltll~]¢ Illil~lldlhlll ct,nli~uIralion:,. Th¢lr¢ lin~ limillllionn liA I ~ tniiterials x'.,hi~2hcan k' IP.t~dand/111 lh~, rfla~n¢ii.2~¢Ollldl).. hui Ih¢~¢ are ikll lliidul) k'qridlXC
I. I n t r o d u c t i o n
The m o t i v a t i o n for the work to be described in this paper was the desire o f the atithors to have a simple. accurate u n d e r s t a n d i n g of the m a g n e t i c field in magnetrtm spulicring s)'slem~. ,quc'h underslandlng is helpful t',cca!.is¢ tile Inal~lletic licid strength and direction are crilical protons par:.lnlelcrs. 1he lield ul the ,,puller h i l e d ,,Llrfaee inilucllCCS sputter rate and target erosion unili~lUllty 1.2] W i l h Ihe advcrll d tlllbalallced m;lgnetron> [J. 4] it 1"~2CtilllC clear thai Ihc licld al the ,~tlhSlrale gill, ice ik also hnportcull l h i , is bccitl~,C Ihe licld afl-eci~ Ilic pla,,nla ttcn,,il) in Ihc ~ i d n i i ) uf the nubqr,llc, h¢ilcc
lhe ion Ilux to tile substrate and therefore the Iilm properties. Siich ioi1 b o m b a r d m e n t is essential ill the
production of high qualily hard coatings. Furthermore. in multiple magnetron s$'.,,tems tile polarities of the tnztgnets ill a given m a g n e t r o n with respect to the polarities of the m a g n e t s in n e i g h b o u r i n g ii1;.igllelrOllS ,hould I~ t a k e n into accoull(. It has been d c m o n q r a t c d that tile p l > m t l density is h m c r in s)stenls where ,i nlagncir(m face,; its m i r r o r image than %vhcn it face; i k ot~pt~nile II. $1 This i~ because the kilter conligurulioil alltms field lines belwecll Ihc iTla~nelrorls tO link Lip and I~rm a ma~nctie eleetren Irap which enhances pklsm:t dentil}' t'll21WCCll the nla~netroll ~, II is tic;Jr Ihcn lhal ihu' role d ihc maellClic Iictd m IllagllCirUll 5,yslCill.n 1~.e~,olvillg to L~ccomc quite ~2ol/Iplcs. ,\ g o d theoretical description d these fields would be tl,C[tll. One xvay to get Stlch it description Is to IBc il -ll.ipd prc~l.t:ial al ihc Iq(h IlilCi n;tlinn,il t'onft'rcncc" lln ~.khlliulT1ell t Oallll[~s ;i:ld ]hin i Illll~. Sail I)icg,l+ ( .Jl+ t '.~,'L ,~.rtil ~, ill. b J.47
il?
maBnetic C A D package. There are a nun+l~r or referrals to, a n d explicil account s of, Ihe use of such paekuges in the literature [ 1 . 6 , 7]. Such m e t h d s are generally ba,,ed
on finite elemerit or b o u n d a r y element technique;. The.,. are both accurate and flexible. The) can be used lot analysing complicated magnetic gcomclrie,. 1 heir di,,advdnlugen tlrc lhal Ihe ,diwarc is u'x['K.'axp,c ;llld ~ellClall} lleeds it large conll"ltllCr on which to run 11 1;Ike, ~PlII, exi~rtise and con,,idcruble time to uv+_',ol,ai,dl.', m )-I) an.d}si~..The qtlalllilativercsulb roll}al',pl) to tile111,x~ncJroI1 ill qtieslltm N.I'.. the) ;tic Iltlnle[ic lind I,ick ~Clleldlll} I Jllqead q,I I,tklllg thin rolllc '-.,.l."d e c l d d t~ It'. ,Ind tim! Llll,I]}IIC nOJtltlOtl~ (L~r ~OILIIIOlI~ ~]IICI1 xxcrt' ,It leA< strui.~Jllk)rx*.'ard to COllll)Utr21 Jol stnlpJc m;l~lletron eollligurations. The major part t~f lhis lusk xva:, Itlad¢ gtai~htfor,.',ard
by the uvailahility d" ex:acl result,, for
certain rectangular nlagnct t?.pcs and the Iamiliarit}' t',f tile ealculalion for eylimhical and a n n u l a r I } p 6 The paper is o r g a m s e d as Ioikm,,. Nu.dion 2 gl',.,..'., a,3 uL'counl of lhc 1,4asori~. ~h'¢ certain magnds can b? I r c a i d analyticall). In Section 3 ix dencr~hetl the nl¢lltod o f caJcLllalion b r cxlindrical ilnd annulilr nl;.l[~llCln and itx:ail;.lblere~ulk for regtallgUl;Ir tll;Iglle|'~ .¢leCtlOll a illuqrate ~, ihc a p p l i c i t i o n d lhe',ee..lUaliorlx in ditT¢.'re;u llldgllCll't)ll conligllration~, xqlilq o'Mghl~lOIl~ *t[C gl~Cll in Section 5
2. N l a g n c l s
lhc ,apcrating i~in~e d a pcrmancnl nl,i~[ic| It,',o11 Ih¢ dema~nelisation cur',e in the ,,ccond q u a d r a i l l d 11~¢ hystel'¢'qS loop. ( ' h a r a c t c r i s l i e tlenla~lldisa|lO[1 '~Ul'~C,
I I%q
I I.cu,r Salu u.~ XII l~gl> r...n-I
M. ,I. Murplw et aL ,' Magnctic field.~ i,t mag+letron spl ler n.k, s)'.~ emx
for various magnetic materials are shown in Fig. I. Generally speaking AI-Ni-Co magnets have a high remanent field, but a low cocrcivity. In contrast, ferrites have t'~.~sonable coercivity, but relatively low remanent field. Rare earth samarium cobalt an~ neodymium iron boron magnets have high remancnce together wilh high coercivity. These magnets have demagnetisation curves that are linear over a large range with a B to H ratio close to the permeability of air j+n. Substantial reverse fields are necessary to drive the magnet into the non-linear region. The magnet is uniformly magnetised throughout its volume. This combination of properties allows these magnets to be treated as if they have an effective magnetic charge density at either pole with an air gap in between. Thus, calculation of the magnetic field at a point outside these magnets becomes a matter of integrating over the sheet surface charge at both poles. Also the supcrposition principle applies such that contributions to the field at a poinl from various magnets may be added vectorially to yield the total field. Bonded rare earths and some ferritcs may be similarly treated but they demagnetise more easily. Rare earths can be used in an open magnetic circuit as is done for example in magnetic buckets. Such geometries sugged the open circuit operation of magnctrons too, since in the absence of soft magnetic materials calculation of the magnetic fields is straightforward.
3. Calculations and formulae If H is the magnetic field intensity then in the absence of currents a magnetic sealer potenti:d Ii is defined hy
H=
-VI"
Ill
The following relations apply outside and inside the magnet respectively.
B = ~o I I
(2a)
g,c., = 1+~,M
i2b)
wht:re B is the magnetic flux density, it 0 is the permeability of free space, B,~,,, is the remanent field and M is the magnetisation. The surface charge density is given by (3)
a =/*oMn
where n is the unit surface normal. By analogy with the electrostatic field
v = L i"u
41t J I r -
/
-gOO,.800-"iDO.-l~l~-500-.400-3~O-~)0.100
,.°o
4n/.+,,
f
j IR ~- r,I
(4)
where R and R, are the field and source position vectors respectively and m is the unit vector in the direction M. Consider now the case of a uniformly magnetised cylinder with M parallel to the axis. In Fig, 2 can bc seen two disks of charge one at each end of the cylinder. Taking the upper surface, from (2a) and 14) the magnetic field is
B.~
--
B=
,lr,
f'r,, 2 h R , dR, V" Jn I R - R~I
(5)
For an annulus it is only necessary to change the limits of integration. R,t is thc magnet radius. IR - R,I can be expanded out by the triangle rule and then expressed in L'~.endrc polynomials to yield B = - / ~ "2~ ' V r ,~, ~" i r'' ~.,-T Rt
(61
~herc R. (R..)is ,5c smaller (largeri t~f IRI .rid IR.I.
1400
The notation is thu~ of re[ ~ which cover,, a ,,imilar example. For the far geld case with IRI > IR, I,
1200
B=-"'s'-'~-V
B
2
5
'
rd
,
~'
1.2
_R'.':
J~~-c"o(I + 2JR I + :
P~(0)Pt(cos0)
lO0O
and for the near field with !RI < IR, I.
~x~ g 5
e = --~L,m v
2
(" r' "+'~"+.'t--i+ IIR I. t P+(OlP,IcosO)
17)
(Sl
0
oemagne~ng toroe 0 ~ / ~ Fi B I ('hat~l+t¢llshL '*lCma~nClis,ttloll uul+u's f, tr '. ;tI'II~U~ m a g n e t i c n~:llCrlilJ~ 11. &Inteo: 2. ~tnixottOpll: b,lrlu111 tcrritc: 3. b o n d e d S n l ( ' o : J, S i n ( ' . . '~. N d l c B I
(d)
n
[h)
l+g. 2 t;l) Th+ .:ylltldrl~:+d rl+ilgilt:t t:alt;ulalltltl ~2¢o111¢tr) The olt~itx is Jou+illed ,It ~hl: cc;llrc or" d 111;I.1~1112 J'IICC I!~1 [ h c r¢clilll~'al;iF [na~llL:~ ~2'~'0nICI;')" ',~J~h IhL' o[1~.111 I~;ahXJ al lhL' n~a~lCl centre
M. J. Afurphy el ,d. , ,$fagttetit" fields i~t m a g n e t r o n splatering xy~tent~
there will be an extra factor of - I since ran= -1. Adding the contributions from both surfaces gix,es the total magnetic field land its components; at a point. Sitace the :-component of magnetic hield at the substrate is important, we state the following simple expression for the on axis field o'~'ing to a di~ of charge. ,=
~ -
r~.~_q,.,
i
:>o
19)
--
N
0
--
--
--
--
These results contain all that is necessary to descril~ the magnetic field in front of a "standard' circular
magnetron Iwithout the backing plate) as will be described in the next section. Taking advantage of the straightforward mathematical properties of these magnets is not a new idea [% II]. The case of a uniformly magnetised rectangular magnet has been described by Ono et al. [12] (using an equivalent current model) and Trow [13]. The following results, which are str:'ightforward to apply, are taken from ref. 13. The relevant diagram is Fig. 2(b).
B~= ~(-In(y+ B,../I
(I0)
r))
F;g. 3. Ca]cubting for an aclual magnctron m;~r,e~ ;~'*a~
03i!illlllllllIIIlllll!
0.25
0.2
0.15
/r-~\\ 0.05
4n (2 '
"
\(:-
The.~ equations are the result of rectangular monopole sheet and between the limits ~ = ~ _+_I..,: 2. : + I.: 2 where I.,. L,. and L. ;,re
y-)q:
4-x'-,/)
an integration over a should be e~aluatcd v = y + I-, :2 and -- = the ~imensluns of the
magnet m the respective directions. The .~g~ function cquals I if the argument is greater titan or equal to 0 else - I and r = ( x " + ?.,2+ :2)t.-'. The origin is at the magnet centre.
4. Method and results
The method of calculation for an actual magnetron magnet array is .~imple and is illustrated in Fig. 3. Figure 4 shows the results for a cross-section through a circular magnetron magnet array. "The arro','~s represent Ihe direction of the magnetic field. i-'igurc 5 shows the results for a cross-section th:ough a rectangular unbalanced magnetron. The field caused lB. the outer magnet dominates that by the inner Clearly hiehlighted is a "null point' of zero magnetic field on the :-~lxis about 7 cm in front of the magnetron. This is interesting because it suggests that v, crc the substrate placed at this position, the ion bombardment might be less than if it were placed 15 cm away ~;'here the field is
% ~. ~, ~ '~ t /
~',,'~ 1 T
r
I / ' ~ I I'%. '%1'I I ~ t P ,"
% 'i i' t ~',"
0 L--__~
49.04 -0.02
~.06
0
0.02
-- ......
0.04 008
I i g .1 Rc,uh for ,i o r ~ u l . l t rll.l~nCIiLql ~ l l h mncr n,.agncI of rAdltt, onlm m
The ,lnl~l])ll s InlIC[ f . l d l l l , l. (lll',f, ffl .llld 'hV I~(11.~; I,ICI,].
In 0 O44 i11
~ t ~ I~
!
tI
I
}L
l - l g 5 Magnetic field cfo~,~,-'~¢¢llon of ,in t]nbd|~tliLvd l¢c,angliklr magncl,g~n magnet ilrfa) & ¢onMdcrablc range o~cr ~hlCh lhL" hc~C i~ ¢ a k I% Nuun d]Ic~;tl', In front of Ih¢ III.I~TICIIOH
.~.f. J
4
.~.'lllrpllJ" 1'[ { d . .
Magnetw ~iehl~ , , aaf:nefron splinering ,~'xtems
1
(~ 4k08 -0.04.0J01
0
0,02 0 . 0 4 0.~8
1 roT. This could be an important fi.lm growth consideration. The position of the null point will vary as the degree of unbalance changes and it will retreat from the magnetron as the size of the inner magnet incrca~s with respect to the outer. Figures 6(a) and 61b) show the results for a crosssection through mirrored and closed field dual magnetron configurations as described by Wong et el. [ I ] The field link-up in the latter geometry is clearly visible. The z-component of field at the centre betw~'en the two opposed magnetrons is 2 mT. Figure 7 shows a fully thr~-dimensionaI field for a tee'angular magnet array on a plane roughly correspovding to a target surface. This illustratcs the uniformity of magnetic field along the length of the array and also the "end effects'. It also emphasizes the capability of an analytic approach to solve three-dimensional multiple magnetron problems in a straightforward general iTlannel.
5. Conc; :sion
" l!!i!!i o I.. ~,,~.'(~, ~ -0.04 ~
"-". ""-'~-r O
~
t
004
..
I 112 {~ [;tI %1+tgn:~'llc fic!d cr~,+-~¢~tlOn lot ;i tllll¢tlrt2t~ I.t+llL~tllA~ltSll. ,.~I \ l ; , ~ n d l ~ . ticld ¢~lll~igllhlt}tlll for ,HI t'ppo~',i ~tlrl!i~llr:ltlll'l
.-,.,ktt{ 1t,,--
It ha., been sho',vn that it is possible to understand simple magnetron magnet geometries, both circular and rcctat,gular, in a straightforward fashion. The effects of varying magnet nun',ber,L sizes and positions can be ca.~ily investigated Interacting multiple magneh'on systems can al,,n bc investig;,'cd in either tw,.~ or three dimensions. Ira backing plate is not used then the results should be exact. Wc believe this work will bc useful Io researchers faced ~ilh the problem of building their ( ~ n magnetron. ku,'lhcrmorc, man 3 theoretical results to date depend on a knowledge of the magnetic lield in Iront of the target surface. The result.,; should thcrc;'ore be useful to theorists and cxpertmcntalists alike. Acknowledgments Tbc aulhors appreciate the time and interest of Dr Michael Hopkins. Tiffs work ~as supported by the EC BRrrE programmc under contract BRITE RIIB. 0221. CIHt. References
i ,~ - ~ Ih:ct2.~hlllCllM~ln.l] %Ik'l~. i1[ lilt" til.l!~n~ll~ llckl ,,:: ;t pldllC ¢~,rt¢-I~tnldltl ~ Io ,i l,lrg¢l ~lll [LI,~V
I NI ~1. \~,ouE. ~,~, i) hptoul and b t. Rt~hdc..burl ( ,ml H'O,mfl.. qo (l~gll 121 -~ I'~ I~ ~*Vill14. I1~ .I I %"l~%cn i{lld ~.V Kern feud.). 1II111 IFhli Ph)('(,~x¢.~..~l~adcmlc life.'%% N Y . 197X. pp I~1 173 I~ Wmd<~w..f I~. S,I 7c{ hm,L -I .¢ (6! I 1'),%5I 21(.S 4 B W m d o ~ illld (; |. I|atdJllt2 .I I'., .'q~ lc(hm,I .i. ," (31 I }l)X*)l 12"r? W I) ~pr,~ul I ) } RLIOIllk. M I- (ir,d~am and 15 [ R,}hdc. ~i,rl (',,(J: l'r, l m , , i J3 44 I I{;b~ll 2711
,'X.f+J. Murph): el al, I M~,netic /ields i. magm'lron spultcrin~, s)~t~'ms
6 A. E. Wcndt, M, A. Lieberman and H. Mouth, J. Vac. Sci. Tvchmd. 4.6 43) 11988) 1827. 7 C. M. Pcrlov and J. R B.'auer. I~/','/'~Trmc~..Vla~Jlet, 32 l.~) 11~)~6) 831. x j. D jackson, c l u ~ . u l E.k'(trIM~'no.li{ ~. John Wil¢'~, NY. 2nd ¢dn. I07.~.p 9 .i. 9 J. B. Y. Tsui, D. J, Idcn. K. J. Strngl and A. J. Evcrs./£E£ Tva,s. M~'.. ? (1972) I ~ .
I0 K. Halbach, ,%.1 /n~frlmz Mcl/l.J,/, I I ] , Sala and Y. Into, 3 |n'.r. [l,~fr
:o9 II~gil I ~.aL, .I;,n /~1 HJf, t ~14 I"~o1 ! ""
{in Jap,'llff~sc ) I .~ Y O . o . Y . H;~kamJI;L T s ; . o ,rod [ It.l.hm~,,h, Tr( hm,t 4. : (41 [IqSg) .~7n4
I
I.;,
x,
13 J. R. Trow. Ph.D. Tlu,si~+, Uni,,'ersily of Californi;L I~rkclcy. r9~c5 L'~wrence Bcrkctcy Lab. RCr~rl NO. LI~L-I~I ~6.