ECSE-6300 IC Fabrication Laboratory Lecture 6 Diffusion in Silicon. Lecture Outline

Transcription

1 ECSE-6300 IC Fabrcato Laboratory Lecture 6 ffuso Slco Prof. Resselaer Polytechc Isttute Troy, NY 1180 Offce: CII-69 Tel.: (518) e-mals: luj@rp.edu /dex.html 6-1 Lecture Outle Itroducto Models of ffuso Solds Fck s 1 ffuso Equatos ffusvtes Atomc ffuso Mechasms Measuremet Techques ffuso poly S ad SO ffuso Ehacemets ad Retardatos Note: The lecture sldes were prepared based o the orgal materals wrtte by Profs. T.P. Chow ad J.-Q. Lu 6-

2 ffuso Models Solds ffuso solds vsualzed as movemet of dffusat atoms by vacaces or selftersttals B ad P dffuse va a dual (vacacy ad tersttal) wth tersttal domat, whle As ad Sb dffuse va a vacacy mechasm Trastoal metal atoms st tersttal posto wthout bods wth matrx atoms dffuse va tersttal mechasm Vacacy ad tersttal Itersttalcy 6-3 Fck s 1 ffuso Equatos Fck s1 st Law of ffuso C( J x Fck s d dx Law of ffuso C( J ( t ) C( t x Whe the solute cocetrato s low, ~ costat ad the d Law reduces to C( C( t x Solutos are preseted most commo cases below : dffuso costat (cm /s ) C: Cocetrato (atoms/cm 3 ) J: dffuso flux (atoms/s. cm ) J 1 J A * Fck s theory o dffuso was publshed

3 Solutos of Fck s d Law wth Costat ffusvtes Costat Surface Cocetrato I.C.: C(0) = 0; B.C.: C(0, = C s ad C(, = 0 x C( Cserfc t Correspods to dopat dffuso wth doped glass Costat Total opat I.C.: C(0) = 0; B.C.: Q T C( exp t QT Cs C(0, t x 4t Correspods to pre-deposto wth o mplatato log C s log C s C( t C( t x x 6-5 Temperature epedece of ffusvty o exp E kt o : Frequecy factor related to atomc jumpg frequecy or lattce vbrato frequecy ad jumpg dstace of mpurty E ~ 3 to 4 ev (vacacy), 0.6 to 1. ev (tersttal) 6-6

4 Itrsc ffusvtes 1400 o C 1000 o C 780 o C exp o E kt As dffusvty s relatvely low good type dopat 6-7 Atomstc ffuso Mechasms Upper lmt of the dopat cocetrato, for whch s a costat, ca be estmated from trsc carrer cocetrato,, at the dffuso temperature. s ~costat whe C(x) < Impurty atom occupyg a substtutoal lattce ste ca be kcked out by a tersttal slco A S + I s A I Impurty atom leaves a substtutoal ste ad eters to a tersttal ste, creatg a vacacy A S A I + V 6-8

5 Pot efects ad opat Movemet rect Exchage Vacacy Mechasm A S A S V A S + I s A I A S A I + V I S A S V A S A I A I There are also may other possble mechasms 6-9 Solutos of Fck s d Law wth Cocetrato-epedet ffusvtes Approxmate Solutos: C Assumg trsc dffusvty at low cocetratos C( t C(y) ad y x/t Values of, ad C(y) are determed from I.C. ad B.C. Whe = 0, = ½, Boltzma Trasformato ( C) 1 C Co dc dy ydc where y = x/t 1/ 6-10

6 Solutos of Fck s d Law wth Cocetrato epedet ffusvtes Costat Total opat 1/ x ( Cs ( 1 xf C where QT Cs ( ( ) t ad ( ) Q T t xf ( 1 1 γ s related to the Gamma tegral. 1 = /3 ad = / Approxmatos for Vacacy- Cotrolled ffuso Mechasm Relatoshp btw the acceptor type vacacy cocetratos extrsc ad trsc S ca be expressed as Sce, because Geeral dffusvty expresso, cludg all possble combatos of mpurty pot defect teractos: o... p p

7 ffusvtes of B, P, As, ad Sb S o o o o E o exp kt... p p... oors (cm /s) (ev) Acceptors o E o o E o o E o + o E + o As P Sb B A Al A Ref.: W.R. Ruya ad K.E. Bea, Semcoductor Itegrated Crcut Processg Techology, Addso-Wesley, Readg, MA, Electrc Feld Effect o ffusvty Whe dopat atoms are ozed at the dffuso temperature, a local (teral) electrc feld s set up: kt 1 C E x q C x 0 1 ffuso flux C C J CEx C x x C C ( 1) h x x h h 1 q kt the max ehacemet E x ffusvty Ehacemet P S at 900 o C 6-14

8 Badgap Narrowg Effect o ffusvty ffusvty Reducto C s : surface cocetrato C z : emprcal costat Implat damage also causes badgap arrowg 6-15 ffuso for Hgh Cocetrato B, As ad P Boro Arsec Phosphorus P + V h c Tal Trasto Vacacy & Itersttal B p ffusvty at very hgh cocetrato Hgh cocetrato ~10 0 cm -3 Vacacy & Itersttal cluster As Feld ehacemet tal Vacacy, P + V = (PV) & Itersttal P C e 1 exp 3 s 3 0. ev kt 6-16

9 Grdg wheel Jucto Stag ad Four-Pot Probe Techque Jucto depth ca be obtaed by agle lappg at 1 to 5 ad chemcal stag (HF wth drops of HNO 3 ) -- The p-type rego s staed darker tha -type rego after strog llumato Sheet resstace (Ω/) R S = (V/I) C.F. Average resstvty ρ = R s x j For large d/s: C.F (-dmesoal fte shee s I V d s d I V a 6-17 Va der Pauw Techque Curret forced betwee adjacet cotacts whle voltage s measured across the other par. d l R 1,34 R F( Q) where d = sample thckess Q = R 1,34 / R 3,41, R 1,34 = V 1 /I 34, etc. Average R S over four dfferet pars of cotacts I Structure (b), F=Q=1, R s = (/l)r = 4.53R 3,41 arbtrary shape Photolthographcally pattered structure W eff = L(R s I 14 /V 3 ) -process tester Kelv resstor 6-18

10 epleto capactace C(V) for (a) & mpurty coc. C(x) at space-charge layer edge C-V Techque 1 s 3 C ( V ) dc( V ) C( x) x q dv C(V ) s s 1/ C( V ) Vb V L = q/kt The extrsc ebye Legth: s L qn B From C(V), C(x), ad L ca be derved Lmted to a few L away from the depleto layer edge at zero bas ad spatal resoluto wth a few L p + (or + p) dode Schottky dode MOS 6-19 Spreadg Resstace Proflg For a pot probe, the spreadg resstace s R sr = / a where a s related to the effectve electrcal cotact radus (ot the probe tp radus) Sestve to sample surface ad bevelg accuracy Correcto factors are eeded to covert the spreadg resstace to carrer cocetrato 6-0

11 ffuso Profle Measuremet Techques 6-1 Fast ffusats S Fast dffusats (e.g., Cu, Au, Fe) S form deep-level traps, ad affect the morty-carrer lfetme ad the jucto-leakage currets. 6-

12 ffuso Poly-S ffusvty poly S s domated by gra boudary dffuso ad hece s strogly flueced by the flm texture, whch are fuctos of flm deposto temperature, deposto rate ad flm thckess. Poly-gate dopg As mplats 650m thck LPCV poly-s o 40m oxde Reverse Aealg SIMS 6-3 As ad B ffuso Profles Poly-S Shallow jucto formato for emtters 6-4

13 ffusvtes SO Thermal SO serves a mask to prevet dffuso of mpurty atoms to S s low for B, As, P, Sb, etc. s hgh for H, He, OH, Na, O, ad Ga 6-5 ffuso Ehacemet/Retardato Oxdato-Ehaced ffuso of Boro 1100 o C wet O A = + (T, t, P O, oretato, etc.) 6-6

14 ffuso Ehacemet/Retardato 6-7 Fck s d Law of ffuso C( C( t x E o exp kt for Itrsc/Extrsc S E-fled effect Badgap arrowg effect Hgh cocetrato effect Measuremet Techques for ffuso Profle Jucto depth Sheet resstace (4-pt., VadePauw) Profle (C-V, Spreadg R, SIMS) Summary Vacacy ad tersttal ffuso results Fast dffusats S ffuso Poly-S ffuso SO Ehaced/retarded Itersttalcy 6-8