Positron beam analysis of structurally ordered porosity in mesoporous silica thin films

Posi on beam analysis o s uc u ally o de ed po osi y in mesopo ous silica hin ilms A. an Veen a, *, R. Escoba Galindo a , H. Schu a , S.W.H. Eij a , C.V. Falub a , A.R. Balkenende b , F.K. de Theije b a De ec s in Ma e ials, In e acul y Reac o Ins i u e, Del Uni e si y o Technology, Mekelweg 15, NL-2629 JB Del , The Ne he lands b Philips Resea ch Labo a o ies, P o . Hols laan 4, NL-5656 AA, Eindho en, The Ne he lands Abs ac Posi on beam echniques ha e been employed o cha ac e ise low-kdielec ic silica based ilms, which ha e wo o h ee dimensional s uc u es o nanome e size po es. Po e ac ions a y om 5 o 50%. Posi ons implan ed in he laye slow down and e en ually annihila e wi h he elec ons om he laye . Howe e , in po es o he dielec ic ilms posi onium (Ps) is o med be o e annihila ion akes place. The wo s a es o Ps (pa a-posi onium (p-Ps) and o ho-posi onium (o-Ps)) a e o med wi h a he di e en li e imes o 125 ps and 142 ns, espec i ely. The beha iou o Ps in he po ous ma e ial can be desc ibed as ho pa icles wi h 1 eV ini ial kine ic ene gy, which lose hei ene gy by equen collisions wi h he a oms o he po e walls. When he po es a e in e connec ed o sepa a ed by hin walls allowing pe mea ion o he Ps some o he Ps will e use om he ilm in o he acuum. The 2D-ACAR echnique enables one o moni o he eloci y dis ibu ion o he annihila ing p-Ps and shows an inc easing ac ion o su ace emi ed p-Ps when posi ons a e implan ed close o he ilm su ace. Measu emen s o Dopple b oadening o 2-gamma annihila ion and de ec ion o 3-gamma e en s (o-Ps) gi e insigh in o he equency o o he annihila ion e en s. Combining he esul s, a comple e pic u e can be ob ained o he in e ac ions and anspo o he Ps pa icles in he ma e ial. By modelling he Ps beha iou in o ma ion is ob ained on s uc u al pa ame e s o he po ous ma e ial. A anspo model based on mul i ene gy g oup di usion o pa icles desc ibes he esul s well. #2003 Else ie B.V. All igh s ese ed. Keywo ds: Posi ons; Posi onium; Annihila ion; Silica; Po es and pe cola ion phenomena 1. In oduc ion Ma e ials wi h a low dielec ic cons an (kB/2.2) a e equi ed o u u e gene a ions o ICs, in o de o subs i u e he p esen dielec ic laye s in ul a la ge scale in eg a ed (ULSI) de ices. Candida es include, e.g. o ganic and ino ganic polyme s, and nanopo ous silica. A high po osi y o he ma e ial is necessa y o lowe he dielec ic cons an su icien ly. Fu he mo e, po e sizes should be small ( ypicallyB/5 nm). Cha ac e isa ion o he po ous s uc u e by a numbe o posi on annihila- ion echniques [1/4] has shown o be success ul. The majo i y o posi ons a e implan a ion in he ma e ial o m posi onium (Ps) in he po es. Since Ps can be conside ed as a e y ligh ace ‘a om’ wi h he physical size o a hyd ogen a om wande ing a ound in he po e s uc u e i can gi e in o ma ion on po e size and anspo o gas h ough he po ous s uc u e. In his s udy he emphasis will be on a desc ip ion o he Ps his o y in low-k hin ilms wi h well-de ined po es. The expe imen al me hods a e dep h selec i e Dopple b oadening and high esolu ion 2D-ACAR which mea- su e momen um dis ibu ions o annihila ing elec on/ posi on pai s and Ps in he ilms. A companion a icle desc ibes low-k ilms in which he composi ion o he in e nal su ace is modi ied [5]. 2. Sample p epa a ion and expe imen al p ocedu e The mesopo ous silica samples we e p oduced using solu ions con aining silicon alkoxides ( e ae hylo ho- silica e, TEOS) and a su ac an (ce yl ime hylammo- * Co esponding au ho . Tel.: /31-15-278-2801; ax: /31-15-278- 6422. E-mail add ess: a [email p o ec ed] .nl (A. an Veen). Ma e ials Science and Enginee ing B102 (2003) 2/7 www.else ie .com/loca e/mseb 0921-5107/03/$ - see on ma e #2003 Else ie B.V. All igh s ese ed. doi:10.1016/S0921-5107(02)00752-3 nium b omide, CTAB) o Plu onic F127 (e hylene oxide) 106 (p opylene oxide) 70 (e hylene oxide) 106 . Du ing coa ing deposi ion he sol en s e apo a e, micelles a e o med and he silicon alkoxide condenses o o m (o ganically modi ied) silica a ound he micelles. A well-o de ed po e s uc u e is ob ained once he micelles a e emo ed om he coa ing. The TEOS/CTAB sys em o ms a high po osi y a h ee dimensional (3D) hexagonal phase, while he TEOS/F127 sys em esul s a high po osi y in a wo dimensional (2D) hexagonal packing o cylinde s in he plane o he su ace. The six samples used in his s udy a e all hyd ophilic due o he p esence o silanol g oups a he in e nal po e su aces. The ilm p ope ies a e gi en in Table 1. The PBA expe imen s we e pe o med wi h he posi on beams a he Del Posi on Cen e [6,7]. The posi ons we e injec ed in he samples wi h ene gies uned be ween 100 eV and 30 keV. The maximum implan a ion ene gy co esponds o a ypical implan a- ion dep h o /2mm in ce amics o densi y 2.5 g cm 3 . All expe imen s we e ca ied ou a oom empe a u e unde a acuum o abou 10 6 Pa. The PBA esul s a e desc ibed in e ms o h ee pa ame e s (S,Wand -Ps) [8]. The Spa ame e indica es he ac ion o posi ons ha annihila es wi h low momen um elec ons ( alence o conduc ion elec ons). This pa ame e is ela ed o he open olume de ec s p esen in he sample (e.g. po es). The Wpa ame e indica es he ac ion o posi ons ha annihila es wi h high momen um elec- ons (co e elec ons). This pa ame e is ela ed o he chemical en i onmen whe e he annihila ion akes place. Bo h pa ame e s can be combined in S/W maps whe e he di e en annihila ion si es (laye s) can be dis inguished. The da a was analysed wi h he VEPFIT [7] p og am. The hi d pa ame e ( -Ps) ep esen s he ac ion o implan ed posi ons ha is ela ed o o ho- posi onium (o-Ps) sel -annihila ion and is obse ed by 3-gannihila ion. In he companion a icle he b anching o he posi ons in o di e en s a es is p esen ed [5]. Fo low-kcoa ings i e annihila ion s a es can be dis in- guished: pa a-posi onium (p-Ps), o-Ps annihila ion ia he po e wall, o-Ps sel -annihila ion, posi on annihila- ion inside he walls sepa a ing he po es, and he ac ion o Ps ha escapes om he ilm. The ac ion -Ps is de ined such ha o highly po ous ma e ial wi h la ge po es -Ps/100%. The 2D-ACAR me hod [9] measu es he de ia ion om collinea i y be ween he wo annihila ion pho ons. This de ia ion is o he o de o a ew milli adians. A high-in ensi y (10 8 e  s 1 ) uneable keV posi on beam POSH enables dep h-selec i e s udies in he (sub)- mic ome e ange. 2D-ACAR is measu ing exclusi ely 2-gannihila ion e en s and is able o esol ing p-Ps annihila ion and o de i e he momen um dis ibu ion o he annihila ing p-Ps. 3. Resul s In Fig. 1 he measu ed alues o S,W, and -Ps a e plo ed e sus he posi on ene gy o he six samples. In he ou h panel he S/W alues a e plo ed in a so called S/Wmap. The esul s a e ypical o a hin ilm on a silicon subs a e. Posi ons en e ing wi h a low ene gy a e implan ed e y shallowly and p obe he ou e su ace and, he e o e, yield di e en S,Wpa ame e s han hose in he ene gy ange 1/4 keV co esponding o implan a ion wi hin he ilms. Fo ene gies la ge han 4 keV a g adual ansi ion akes place o annihila- ion in he subs a e. Fi ing p ocedu es ( VEPFIT [6]) ha e been applied o de e mine he hickness (by weigh ) o he ilm. This hickness ag ees well wi h he weigh hickness de i ed om Table 1 (using hickness and densi y). Cha ac e is ic alues de i ed o Sand Wo all he ilms a e gi en in Table 1. They a e also indica ed in he S/Wmap o Fig. 2 o six o he ilms. The Ps ac ion a ies om e y low o abou 50% o he in es iga ed hyd ophilic samples. Resul s o hyd opho- bic ilms in [5] show e en highe alues o 85%. In gene al, he Ps ac ion inc eases wi h po osi y bu he ac ion is much highe o he high po osi y F127 wo dimensional s uc u e wi h la ge diame e cylinde s han o he CTAB h ee dimensional s uc u e wi h small diame e po es. A ypical esul ob ained wi h he 2D-ACAR se up o he F127 (2c) ilm is shown in Fig. 2. The momen um Table 1 Desc ip ion o he low-k ilms and measu ed posi on annihila ion pa ame e s Numbe Desc ip ion Thickness (nm) Po osi y (%) Po e size (nm) Densi y (g cm 3 )S el. laye W el. laye Ps 1a TEOS/CTAB 0.01 a R b 184 10.9 1 (0.5) 2.0 0.954 1.64 0 1b TEOS/CTAB 0.05 R 267 31.0 1 (0.5) 1.5 0.992 1.46 0.12 1c TEOS/CTAB 0.1 3D 338 46.3 1.75 (0.25) 1.2 1.010 1.40 0.12 2a TEOS/ F127 0.0005 R 190 7.4 1 (0.5) 2.0 0.982 1.56 0 2b TEOS/ F127 0.002 R 285 35.0 1 (0.5) 1.4 0.994 1.40 0.08 2c TEOS/ F127 0.005 2D 457 44.7 4.5 (0.5) 1.2 0.994 1.48 0.48 a Composi ion a io. b O de ing: R, andom; 2D, wo dimensional; 3D, h ee dimensional. A. an Veen e al. / Ma e ials Science and Enginee ing B102 (2003) 2 /73 dis ibu ion o he ilm implan ed wi h 3.5 keV posi ons shown in Fig. 2a e eals asymme y in he y-di ec ion (co esponding o he di ec ion ou wa d di ec ed om he su ace). Appa en ly, he dis ibu ion is composed o an iso opic and an aniso opic componen . I appea s ha he la e componen is a cosine momen um dis ibu ion (Fig. 2b) which can be assigned o p-Ps pa icles lying o he su ace, like a gas molecule e using om a hole in a olume con aining a low densi y Knudsen gas. The iso opic con ibu ion can be decomposed in o a na ow and a b oad componen . The na ow componen can be assigned o p-Ps ‘gas’ ha annihila es inside he po es. In Fig. 3 c oss-sec ions o he momen um dis ibu ion in xand ydi ec ion a e displayed o he ilm. Analysis o he momen um dis ibu ion shows ha he a e age ene gy o he Ps amoun s o 0.9 eV o shallowly implan ed and o 0.5 eV o 3.5 keV implan ed posi ons. An a e age momen um Fig. 1. Posi on annihila ion pa ame e s S,W, and -Ps plo ed as a unc ion o he a e age posi on implan a ion dep h, and an S,Wmap showing all he S,Wda a. Fo he CTAB-1c ilm he cha ac e is ic annihila ion s a es a e gi en: (1) su ace, (2) po ous ilm, (3) in e ace and (4) Si-subs a e. Fig. 2. Momen um dis ibu ions measu ed o sample 127 2c. A. an Veen e al. / Ma e ials Science and Enginee ing B102 (2003) 2 /74 o 10 3 m o c co esponds o an a e age Ps kine ic ene gy o 0.128 eV. 4. Posi onium slowing down and anspo in po ous SiO 2 The implan a ion p o ile o posi ons can be desc ibed by he so called Makho p o ile (a de i a i eo a Gaussian) which is also used o solids wi hou po es [8]. The po osi y is aken in o accoun by using he educed densi y o he po ous silica in he Makho exp ession. Posi ons do no slow down in he po es, only in he wall ma e ial. Ps is o med by combining one o he elec ons p oduced in he ack o he slowing down posi on wi h he he malised posi on. The Ps pa icle is a ac ed by he po es and is c ea ed wi h a kine ic ene gy o abou 1 eV, as ollows om Ps su ace emission o Ps om silica and om ACAR measu emen s on Ps in xe ogel [10]. Once Ps is o med, wi h he wo s a es p-Ps and o-Ps in a a io o 1/3, i will beha e as an a om in a Knudsen gas. The e a e only in e ac ions wi h he walls o he s uc u e bu no wi h o he Ps. The eason o his is he sho li e ime o Ps a e age li e imes o sel - annihila ion a e 125 ps o he p-Ps and 140 ns o o- Ps, espec i ely, when sel -annihila ion occu s. The annihila ion o p-Ps yields wo g- ays o abou 511 keV, he sel annihila ion o o-Ps yields h ee g- ays in he ene gy egion 0/511 keV. Annihila ion o o-Ps is accele a ed by a pick-o eac ion wi h he walls o he po es; subsequen ly, annihila ion by wo g- ays occu s. The anspo and cooling o he Ps can be desc ibed by app oxima ing he Ps anspo by di usion heo y. Le c(E,x, ) be he concen a ion o Ps a dep h xwi h ene gy Ea ime . A balance equa ion can hen be w i en as ollows: dc(x;E) d D(E)d2c(x;E) dx21 41 Vn(E) sOc(x;E)1 4 1 Vn(Eƒ) sOc(x;E)I(x)lPsc(x;E) d lpick-o c(x;E) whe e he i s e m a he igh hand side desc ibes he loss/gain by di usion ( he di usion coe icien Dis E dependen ), he second e m he loss a e by sca e ing (E0/E?), wi h inal ene gy E?/E/aa e one collision, and he hi d e m he g ow h a e by sca e ing (Eƒ0 / E) wi h ene gy Eƒ/aEa e one collision. In a collision wi h a oms in he mal mo ion also some ene gy will be ans e ed om he a om o he Ps; inally, his will lead o he malisa ion o he Ps. This is no ye included in he heo y. The ou h e m is he implan a ion a e which is ze o o EB/E 0 , he i h e m is he sel annihila ion a e and he six h e m he pick- o a e (impo an only o o-Ps), wi h d he pick-o laye in he po es wi h adius . The di usion coe icien can be desc ibed by D(E)/ 1/6l 2 n o 3D o de ed and 1/4l 2 n o 2D o de ed po e s uc u es, whe e lis he jump dis ance/dis ance be ween he wo cen es o neighbou ing ca i ies/ 2  /l w , wi h l w he hickness o he wall sepa a ing he po es. V is he a emp equency, in all di ec ions, o one Ps p esen in a ca i y olume V/4/3/p/ 3 , whe e V1/4 (1/V)n Ps O Owhe e Ps is he eloci y o he Ps de i ed Fig. 3. C oss-sec ions h ough momen um dis ibu ion measu ed by 2D-ACAR. (a) Momen um pe pendicula o he su ace, (b) momen um pa allel o he su ace. A. an Veen e al. / Ma e ials Science and Enginee ing B102 (2003) 2 /75 om he ene gy E,n Ps /V2eE/m Ps , and O is he ac ion o Ps ha is pene a ing h ough he walls o he ca i y gi en by O /O*/O,O* is he open o anspa en pa o he wall, s is he ac ion ha sca e s o he wall. The ac o 1/ais close o uni y because m Ps is much smalle han he mass o he wall a oms. I s lowes alue o maximum ene gy ans e , is 1/a/(1/m Ps /m a ) 2 /(1/m Ps /m a ) 2 /(1/4m Ps /m a ). The ene gy loss o Ps wi h ene gy Edu ing ime D equals 1/4(1/V)n(E) s O(collision equency)/D /E/a The bounda y condi ions a e gi en by e lec ion o Ps a he silicon subs a e in e ace a x/l:(dc/dx) x1 / 0. I is assumed ha Ps a he acuum side is emi ed in o he acuum: c (x0) /0. The emission a e is gi en by D(dc/dx). The ime dependen anspo equa ion is sol ed nume ically. 5. Discussion The abo e model applied o an o de ed 2D po e s uc u e (e.g. 127 2c) yields a wall hickness o 1.8 nm. The e ec i ep-Ps di usi i y is calcula ed o be 2 cm 2 s 1 , and he di usion leng h is 158 nm i he po e anspa ency pa ame e O /0.2 is aken. I ollows om he alue o he di usion leng h (o he same o de as he ilm hickness) ha a signi ican amoun o p-Ps c ea ed h oughou he ilm will escape om he su ace du ing i s limi ed li e ime. In [5] i is ound ha o a sample po osi y /45%, p-Ps e usion is obse ed. I is e y likely ha when walls ge hinne , i.e. a ew imes he s uc u al po e size in silica, Ps, which has an e ec i e, quan um mechanically de e mined, size o abou 0.8 nm when i is in in e ac ion wi h he silica s uc u e, will easily pe mea e. Nume ical esul s o anspo o p-Ps implan ed in such a po ous ilm a e gi en in Fig. 4. Time dependen ene gy dis ibu ions o p-Ps a a dep h o 200 nm a e plo ed which show he e olu ion o he ene gy om 1 eV a /0 o a b oad s a iona y ene gy dis ibu ion when equilib ium is es ablished be ween he implan a ion o posi ons and he annihila ion o p-Ps (a e age li e ime 125 ps). The bo om igu e shows he s a iona y ene gy dis ibu ions a a ying dep h. A e age ene gies a e 0.35 eV o he deep laye s and 0.41 eV o he shallow laye s. The ene gy dis ibu ions de ia e om he Maxwell/Bol z- mann dis ibu ion which applies o pa icles in he mal equilib ium. An impo an eason is ha a any ime ho Ps is in oduced in o he ilm. I seems ha he ene gy dis ibu ions can be desc ibed a he well by he sum o wo Maxwell/Bol zmann dis ibu ions, e.g. one wi h kT 1 /0.11 eV, and kT 2 /0.6 eV o he dis ibu ion wi h an a e age ene gy o 0.35 eV (no shown he e). The abo e model can be applied and used o i he measu ed ene gy and eloci y dis ibu ions, oge he wi h he o he pa ame e s measu ed in he posi on beam expe imen s. The model will yield ac ions o all annihila ing modes which con ibu e o he Sand W pa ame e s and he Ps ac ion. 6. Conclusions and inal ema ks Dep h selec i e posi on annihila ion s udies o low-k ilms show clea ly ha wi h inc easing po osi y o he ilms p-Ps c ea ed in he ilm is eme ging om he ilm. The eloci y dis ibu ion o he e using Ps and he Ps emaining in he ilm can be de e mined. Cooling o he Ps is slow and is de e mined by in e ac ion wi h he po e walls. The p esence o o-Ps indica es ha po es ha e g own beyond 4 nm size. Dopple b oadening pa a- me e s and Ps ac ion can be used o de e mine he Fig. 4. (a) Calcula ed ene gy dis ibu ions du ing slowing down o p- Ps in mesopo ous silica wi h po es o 5 nm and densi y 1 g cm 3 The Ps pa icles ha e an ini ial ene gy o 1 eV. The implan a ion o posi ons is con inuous wi h an ene gy o 3.5 keV a an a e age dep h o 300 nm. The ene gy dis ibu ion is plo ed a ime in e als o 37.5 ps. A e 500 ps a s a iona y s a e is a ained. (b) S a iona y ene gy dis ibu ions o di e en dep hs in he ilm. A e age ene gies a e indica ed. A Maxwell/Bol zmann dis ibu ion is shown wi h simila a e age ene gy. A. an Veen e al. / Ma e ials Science and Enginee ing B102 (2003) 2 /76 b anching in o all annihila ion channels which depend on he po ous s uc u e o he ilm. The model p esen ed he e will in he u u e be used o pe o m i s o he b anching a ios. Re e ences [1] M.P. Pe ko , M.H. Webe , K.G. Rodbell, K.P. Lynn, S.A. Cohen, J. Appl. Phys. 86 (1999) 3104/3109. [2] K.P. Rodbell, M.P. Pe ko , M.H. Webe , K.G. Lynn, W. Volksen, R.D. Mille , Ma e . Sci. Fo um 363 /365 (2000) 15/19. [3] T. Gessmann, M.P. Pe ko , M.H. Webe , K.G. Lynn, K.P. Rodbell, P. Asoka-Kuma , W. S oe l, R.H. Howell, Ma e . Sci. Fo um 363/365 (2000) 585/587. [4] J. Sun, D.W. Gidley, T.L. Dull, W.E. F ieze, A.F. Yee, E.T. Ryan, S. Lin, J. We zel, J. Appl. Phys. 89 (2001) 5138/5144. [5] R. Escoba Galindo, A. an Veen, S.W.H. Eij , C.V. Falub, H. Schu , A.R. Balkenende, F.K. de Theije, Ma e . Sc. Eng. B., his issue. [6] A. an Veen, J. T ace Mic op obe Techniques 8 (1&2) (1990) 1/ 29. [7] A. an Veen, H. Schu , J. de V ies, R.A. Hak oo , M.R. Ijpma, in: P.J. Schul z, G.R. Massoumi, P.J. Simpson (Eds.), Posi on Beams o Solids and su aces, AIP 218, 1990, pp. 171/196. [8] A. an Veen, H. Schu , P.E. Mijna ends, in: P. Coleman (Ed.), Posi on Beams and Thei Applica ions, Wo ld Scien i ic Publish- ing, 2000 (Chap e 6). [9] R.N. Wes , in: A. Dupasquie , A.P. Mills, J ., (Eds.), Posi on Spec oscopy o Solids, P oceedings o In e na ional School o Physics ‘En ico Fe mi’ Cou se CXXV’ IOS P ess, Ams e dam, 1995, 75/143. [10] Y. Nagashima, M. Kakimo o, T. Hyodo, K. Fujiwa a, A. Ichimu a, T. Chang, J. Deng, T. Akahane, T. Chiba, K. Suzuki, B.T.A. McKee, A.T. S ewa , Phys. Re . A 52 (1995) 258. A. an Veen e al. / Ma e ials Science and Enginee ing B102 (2003) 2 /77