berkley_半導(dǎo)體工藝講義09

1、Dopant Diffusion(1) Predeposition* dose controlSOdopant gasDoped Si regionSiO2IStO2 oSO2seal surface with oxide(2) Drive-in* profile control (junction depth; concentration)>ote: IVedepoition by dirTmion can »Im)he replaced by a hxllaw imphntation MepPvoTetMW Nulhan Cicun買.V C Bokdey EE14)Lcc

2、hwc *9Dopant Diffusion Sources(a) Gas Source: AsH3, PH3, B2H6(b) Solid Source(c) Spin-on-glass(a) InGrs=a-© ® wcrsE-iE.-mpumyDifTusion Mechanisms70789 Nathan nKun»U C Berkdey EEZJ(b) Subs 三 u=ona-Lecture 3Agifie 30 A 一 ypn-id bubbnr JlrnmKcmcnto-r doping ui.=cc= waferc#mg & Pcx-J&

3、#163;Hlrce T-lc ga" 7-set u"5-g rnanow uomrD=ers (MFC).3orecMW Nathan n_cmfi U C Bok2.cy EEzyLecture $Diffusion Mechanisms : ( c) InterstitialcyFgUP 3.5 In interstitialcy diffusion an interstitial silicon alom displaces a substitutional impurity, driving it to an intcrshlial site where it

4、ditTuses some distance hcfore il returns to a substitutional sitePvoTcxmw NMhan Ccun買.V C Berkeley EEI4)Lecture *9DitTusion Mechanisms : (d) Kick-Out. (c) Frank TurnbullFigure 3.6 The kick-out (left) and Erank Turnbull mechanisms (right).Mathematics of DivisionFick's First Law:C(x)J(x,/)= -D

5、76; dxD : diffusion constant刃八Program Nulhan Cxun買.U C Berkeley EE14)LccUvc *9Using the Continuity Equation0 C(x,r)+y J()=0dtv7dedJd Joe)=>=Dd td x 8x( d xDiffusion EquationIfD is independent ofC (i.e., D is independent of x).dt dx2Concentration Independent Difliision EquationProfcnm Nnlhan Com買.

6、U C Bokclcy EEI4)LccUvc *9Temperature Dependence of DE A = activation energy in e V k = Holtzman constant=8.6 x 10 5 eV / kelvinD °、E A are tabulatedTenpefMirv C01XMIIIOOIOOO 900«00700eo04<K7 ot 0»1.0 l.lTemprmure. KXX>T(1C>PfofcsMW NMhan Cicun買.U C Berkeley EE14JLectin c *91

7、1Diffusion Coefficients of Impurities in SiA.Boundary Conditions.C7(x = 0,/) = CQ = solid solubility of the dopantC(x = x?/) = 0Initial Condition.C(XJ = O)=OSolid Soluhility of Common Impurities in SiZA Sateduf cvanmxi mUuo UD(writic> l mV n 畑 men ntwE 穴O IAI 4 fKPtoTcxmw Nslhan Ccun買.V C Berkele

8、y EEI4)Lecture *9C(x,/)=C0. 17叫昴丿2 y/ l)t = Characteristic distance for diffusion.Co 三 Surface Concentration (solid solubility- limit)Properties of Error Function erf(z) And Complementary Error Function erfc(z)erf (i).1 日2 <hvn 0eric (z) - 1 erf (z)af(0) = 0CT(l co) = 1erft-oo )=-71 e心eif(z)w zfa

9、 z«lpitetfc (z)»focz»iderf(z)deifc(z) 2.&-斗 e/erfc(y)<*>, zerfc(z)* 擊(i-e-z2) J erfc(z)dzPfotesMW NMhan Cicun買.V C Bcricdcy EEI4JLcchwc *911m vdiM ( aftz) can be kuiMl m oMdMMb(«l uMei. Udd mi fuy m oituifieri aud 仲"Ifymi bnv prnjrn>M<maythe folhwwc«mU 皿

10、 mmxwflte ! 1 »<M> 10、cvf(z) -* 1 - (a.T ®-T- 軻T，a«T*,>e '4.7 P-tJiWil(-0Jf4t2Q<92 七M(jìn)9<a36<< d 49JP2027/I! Predeposition dose/2/ Cone, gradient工=_£X 2/bLcchwc *9d xjDlProTecMW Nathan Ci<un買.V C Berkeley EEi4)B. Drivein Profile Boundary ConditionsC(x =

11、x,/)= 05Xx=0 Initial Conditionsx=0x Predep's (I)t)Shallow Prcdcp Approximation:C（xj = 0）（?-3（x）G2J（”u =prcdeff亦Solution of Drive-in Profile :C（x）/C0Good agreementApproximation .under-estimates cone hereHou good is the &、）approximation ?r J Dl prtdepJ Dt 亦* - inApproximation over-estimates co

12、ne. hereExact solutionDelta function.ApproximationSummary of Predep + DriveinD i = Diffusivity al Predep temperature l = Predep timeD、 = Diffusivity at Drive-in temperaturet2 = Drive-in timeC(x)心 l兀PfofetMW NMhan Cicun買.V C BokdcyEE14)Lcchn c *9Scmilog Plots of normalized Concentration versus depthD

13、rive-inFkfB 3.7» a luMtawi ctf drpiti tor (A) fwvdcpMMkm mJ <B> ilr)>c la Mumimh (<»rzlac ol thectun:tcmtK iSIfutkxi length.Diffusion of Gaussian Im plantation Profilee 2 <AR； JDt)C(x, t) =兀(ARf e 2 (ARp > 21»； + 2Dt)1Z2Note: 0 is the implantation doseProfesMW Nalhan

14、 Gicuiik. U C Bcricdcy EE14)LccUvc *9For reference onbDiffusion of Gaussian Implantation Profile (arbitrary Rp)QCThe exact solutions with - 0 at x - 0 ( i.e no dopant loss tluough surface)can be constnicted by adding another full gaussian placed at Rp (Method of ImagesC(x. t)We can see that in the l

15、imit (Dt),zl » Rp and AR. 0CC(xwt)-> (買Dtp ?"he half-gaussian dnve-in soluticn)The Thermal BudgetDopants will redistribute when subjected to various thermal cycles of IC processing steps. If the difTusion constants at each step are independent of dopant concentration, the diffusion equa

16、tion can be written as :Let 卩三0ac _ac agWhen we compare tliat to a standard difYusiim equation with 1) being time-5聰瓦帝 a.龜ac ap ao a2c m 心lhe diflusion equation becomes:石orProfesMw Nnlhan Cicun買.U C fkxkclcy EEI4)LccUvc *9lhe standard solution b、卩 will also satisfy the time-dependent D ditTusion equ

17、ation.ExampleConsider a senes of high-tcmpcraturc processing cycles at temperature T time duration t temperature T? time duration t?. etc. The corresponding diffusion constants will be D. D?、.Then, p = Dti+D2t2(Dt)cffccticThe sum of Dt products is sometimes referred to as the thermal budget' of

18、the process. For small dimension IC devices, dopant redistribution has to be minimized and we need low tlicmial budget processesThermal BudgetFor a complete process flowt only those steps with high i)t values arc importantPvofecMw NMhan Cicun買.U C BerkeleyEEI4)Lcctwc *9In in's Curvesp-typc Erfc*

19、 4 sets of curves "type l：rfcSee Jaesfr tex1 p-t pe half-gaussian n-t> pe hali-gaussianEstablish the explicit relationship betweenN (surface concentration) ox (junction depth).JN (background concentration).BR (sheet resistance).SOnce any three parameters are knoun the fourth one can be determined.Motivation to generate the In in's CurvesBoth NB(4-point-probc). RH (4-point probe) and 哥(junction staining) can be conveni