GEOMETRIC EFFECTS CONTRIBUTING TO ANTICIPATION OF THE BEVEL EDGE IN SPREADING RESISTANCE PROFILING D H Dickey nd R M Brennn Solecon Lbororie, Inc Reno, Nevd 89521 When preding reince probing re mde prior o he bevel edge, he d vlue obined re generlly ignored in ubequen proceing On bre urfce, hough, he incree in meured reince ofen oberved he bevel i pproched, i meningful nd my be cue of concern One of he ource of hi incree, referred o here nicipion of he bevel edge i due o geomeric effec: he runcion of pr of he conducive lyer by he bevel Under wor-ce condiion, he geomeric effec will incree meured reince by fcor of wo inufficien o ccoun for he order of mgniude incree oberved on ome ulrhllow profile In n effor o epre he geomeric effec from oher cue, we clcule i mgniude from imple imge model The clculion how he geomeric effec i minimized wih cloe probe pcing nd hllow bevel ngle, nd provide guideline for chooing uible bevelnglendpcing In figure 1, n illurion of preding reince probing ring on he originl urfce of beveled ilicon mple i hown If he urfce i bre nd he op conducive lyer i hin enough, he preding reince meuremen obined on he originl urfce ofen incree in vlue he bevel edge i pproched In figure 2, he expeced reince vlue for 1000Å juncion re hown The incree in reince hown were bed only on geomeric effec he runcion of pr of he conducive lyer by he bevel Noe he mgniude of he increeigreerwheneeperbevelngleiued Oher effec uch crrier pilling nd poible bevel urfce dmge re no conidered here lhough hey re imporn nd in ome ce, of greer conequence In hi figure nd he ubequen one, Guin 20 15 diribuion, urfce concenrion of 1x10 cm,bckground concenrion of 1x10 cm,ndprobe concrdiuofonemicronreumed 800W D Vlue Uully Dicrded originl urfce Thin Lyer Subre BEVEL EDGE BEVEL q V = 0005 vol Tungen crbide probe Expeced Spreding Reince 600 400 200 Bevel Angle: 20:1 200:1 1000:1 Aumpion mde: P+/n Guin Diribuion Surfce conc = 1e20 cm Subre conc = 1e15 cm Juncion deph = 1000Å Conc rdiu = 1 micron Probe pcing = 15 micron -25-20 -15-10 -5 BE Dince From Bevel Edge Figure 1 An illurion of preding reince profiling on beveled mple (The bevel ngle i ofen much mller hn indiced) Figure 2 Clculion for he geomeric effec indice n incree in reince he bevel edge i pproched Pge1of7
In figure 3, he probe pcing i vried Noe increing he probe pcing incree he meured reince nd he nicipion of he bevel edge In figure 4, he juncion deph i vried while minining he urfce 2 concenrion 1e20 cm A lyer wih hinner juncion will hen hve fewer crrier/cm nd hve higher meured reince Noe he nicipion of he bevel edge become greer he juncion become more hllow Expeced Spreding Reince 700 Probe Spcing: 600 500 400 300 200 100 0 Aumpion mde: P+/n Guin Diribuion Surfce conc = 1e20 cm Subre conc = 1e15 cm Juncion deph = 1000Å Conc rdiu = 1 micron Sine of bevel ngle =001 BE Dince From Bevel Edge Expeced Spreding Reince 700 600 500 400 300 200 100 Xj 0 BE Dince From Bevel Edge Figure 3 Clculion for he geomeric effec indice n incree in nicipion of he bevel edge for wider probe pcing Figure 4 Clculion for he geomeric effec indice n incree in nicipion of he bevel edge for more hllow rucure The chnge in reince i ffeced by he juncion deph, bevel ngle nd probe pcing Forunely, he bevel ngle nd juncion deph cn be linked o noher vlue lredy pprecied by he preding reince nly heonbeveldinceohejuncion, Xj/in(bevelngle) Alo,imybeuefuloconidernormlizedreince vlue he bevel edge, R BE/RNB where RBE i he clculed reince he bevel edge nd RNB i he clculed reince wih no bevel (or probing mde n infinie dince from he bevel edge) In figure 5, he nicipion of he bevel edge i ploed R BE/RNB nd compred o he on bevel dince o he juncion We believe hi chr my erve guideline for eiming he everiy of nicipion of he bevel edge due o he geomeric effec nd chooing uible bevel ngle nd pcing In generl, geomeric coniderion encourge mller bevel ngle ndlrgereppingincremen Pge2of7
200 Reince bevel edge Reince wih no bevel 175 150 R R BE NB = 125 100 On Bevel Dince From Bevel Edge o Juncion Figure 5 A guideline o nicipion of he bevel edge due o he geomeric effec funcion of bevel lengh o he juncion nd probe pcing Pge3of7
CALCULATIONS The conducive lyer i divided ino 100 ub-lyer Figure 6 illure he 2 ub-lyer nere he urfce The dince from he probe o he bevel edge i given L 0 The dince from he probe o he edge of he fir ub-lyer i L0 + / where i he hickne of he ub-lyer ndq i he bevel ngle (The mgniude of he bevel i grely exggered in he figure) The dince from he probe o he edge of he jh ub-lyer i L 0 + j / To fcilie undernding, he digrm in figure 5 i redrwn in figure 6 o lign he originl urfce o he horizonl nd o replce he bevel wih ep Clerly, one would expec he reince of ub-lyer o incree / decree The vlue / cn be increed (nd nicipion of he bevel edge reduced) if i i poible o reduce q, he bevel ngle L 0 L 1 BE L 2 q L 0 L 1 BE L 2 L 3 Figure 6 Illurion of he preding reince probe pproching he bevel edge The hin lyer h been divided ino 100 ub-lyer, wih only he fir hree hown The probe' curren line re limied only by he bevel Figure 7 A implificion of he previou figure The originl urfce w poiioned on he horizonl nd he bevel w replced by decending ep The miing porion of ech ub-lyer reduce he conducion nd incree he reince When he probe re everl probe pcing from he nere edge, he meured reince i: R = (Equion 1) where: R i he meured reince in ohm (herefer clled R NB for R no bevel ) r i he reiiviy in ohm-cm i he probe pcing i probe conc rdiu (umed o be 1 m ) i he lyer hickne in cm Probe 1 L Probe 2 The only edge cloe o he probe When he probe re dince L from one edge bu everl probe pcing from oher edge (ee figure 8), he meured reince i: R= (Eq 2) Figure 8 Illurion of he preding reince probe ner one edge When L i very lrge, R cn be found by uing equion 1 A L 0, R reche limi of wice he reince clculed from equion 1 For oher vlue of L, equion 2 hould be ued, NB NB A L R R nd by inpecion, R 2R L 0 Pge4of7
Reiiviy vlue were clculed fer Thurber Guindiribuion 2 2 -X Xj C(x) = C exp[ 4DT] nd DT = C 4ln C e l (3) + S B uing concenrion vlue deermined from he where: C(x) iheconcenriondephx 20 CS iheurfceconcenrione1x10 cm Xihedephincm DTiheproducofhediffuiviyndheime(clculedfromXj,CS, ndc B) Xj ihejunciondephincm 15 C ihebckgroundconcenrione1x10 cm B A p-ype lyer over n n-ype ubre w umed Since he urfce concenrion i 5 order of mgniude higher hn bckground, he conducnce lo due o he depleion region w conidered neglible A Guin 20 diribuion wih urfce concenrion of 1 x 10 cm w ued believing hi cued wor-ce nicipion ofhebeveledgemonghecommonlyoccurringulr-hllowprofile Someclculionweredoneuming complemenry error funcion nd urpriingly lile incree in he nicipion of he edge w noed Alo, 18 ome clculion were done uming CS = 1 x 10 cm wih urpriingly lile decree in nicipion of he beveledge SUMMARY The geomeric conribuion o nicipion of he bevel edge in preding reince profiling w dicued Clculion bed on imple imge model were ued o deermine i mgniude Shllow bevel ngle nd cloely pced probe help reduce i effec Under wor-ce condiion, he geomeric effec will incree he meured reince by fcor of wo inufficien o ccoun for he order of mgniude incree in meured reincehhvebeenobervedonomeulr-hllowprofileaguinprofilewihurfceconcenrion 20 of1x10 cm wued Bevelngle,probe pcing, nd juncion deph were vried The relionhip we found mo ueful w R BE/RNB ploed gin he on bevel dince o he juncion In wor-ce rucure, he me coniderionuggehmeuredreinceonhebevelmubecorrecedforhegeomericeffec REFERENCES 1 DHDickeyndJREhrein,NBSSpecilPublicion400-48,pp15-18(My1979) 2 DHDickey,ICSIT'92Conference,Tokyo,November10,1992 3Thurber,Mi,Liu,ndFilliben,NBSSpecilPublicion400-64,Tble10,p34ndTble14,p40 APPENDIX r Developmen of he Simple Imge From hin conducive lyer, he probe conc i umed o be cylinder of rdiu nd heigh Curren i umed o flow rdilly from he ide of he cylinder o he edge of he lyer The incremenl reince dr from r o dr cn be expreed he produc of he reiiviy nd incremenl lengh dr divided by he cro ecionl re 2p r or: Pge5of7
Appendix (coninued) Then, he reince R from he edge of cylinder of rdiu hrough he conducive lyer o dince from he cenerline of he probe conc cn be expreed : r dr R= 2 p ò r r = 2 ln p If poenil V i pplied o he probe cuing curren I, hen poenil will be V = A econd probe (P2) wih poenil -V i poiioned dince from he fir probe (P1) V -V P1 P2 V -V P1 P2 L Virul edge form by imge P3 nd P4 L V -V P3 P4 Pge6of7
Appendix (coninued) The poenil P1 due o P2 i - V + The poenil P1 due o P3 i + V - I The poenil P1 due o P4 i - V + I Summing he poenil P1, V1 = + V - V + + V - - V + The poenil P2 due o P1 i V - [ ] Ir V1 = + = - ln = 2p + [ ln ] The poenil P2 due o P3 i + V - The poenil P2 due o P4 i - V + I Summing he poenil P2, V2 = - V + V - + V - - V + [- - = + ln ] V2 = = Then V1 -V2 = + = [ ] The reince beween he probe, R= V1-V2 = [ ] r - I ln 2p [- - ] Pge7of7