Lecture 3. Diffusion. Reading: Chapter 3

Transcription

1 Lecure 3 ffuso Readg: haper 3 EE r. Ala oolle

2 Impury ffuso: Pfa paeed he dea of usg dffusos S ad Ge 195. ffusos are mos commoly used for: Whe o use ad whe o o use : ffusos sources clude: 1.) Bases, emers, ad ressors bpolar echology.) Form source ad dra regos ad dope polyslco gae/ercoec les MOS echology. 1.) Use whe damage from Io Implaao leads o uaccepable decreases Mory carrer lfeme, elecrcal jucos eed o be very deep, or a cheap easy soluo s eeded.) o o use for ulra-shallow jucos, majory carrer devces (use o mplaao sead) or oal mpury dose s crcal (e. MOSFET chael) 1.) hemcal source a vapor a hgh emperaure..) oped ode source (eher deposed a hgh emperaure or as a Sp o polymer). 3.) ffuso/aealg from a Io mplaed source. EE r. Ala oolle

3 Impury ffuso: Tradoal Tube Furace Baffles used o m gases Wafers Held a quarz boa Ho Furace EE r. Ala oolle

4 Impury ffuso: Fck s frs law saes ha mpures flow (wh flu J) oward a decrease cocerao, (, ) (1) J The dffuso coeffce,, also called dffusvy, or dffuso cosa, characerzes a parcular mpury s ressace o flow whe eposed o a mpury grade. We do o measure mpury grades or mpury flues. These quaes are dffcul o oba. Thus, usg he law of coservao of maer, (, ) J () Ths secod law smply saes ha he oal chage flu leavg a volume equals he me rae of chage he cocerao he volume. EE r. Ala oolle

5 EE r. Ala oolle Pluggg (1) o (), oe ca rewre Fck s frs law as Fck s secod law, (3) I cera specal cases, s depede of, (4) We wll eame varous soluos of hs dffereal equao laer. More geerally 3: (5) Noe ha geerally, =f( T,, ad eve ). ), ( ), ( ), ( ), ( Impury ffuso:

6 Impury ffuso: ffuso oeffce Wha dsgushes oe mpury from aoher s s dffusvy. osder he geeral case where a aom ca es as boh a subsuoal or ersal mpury. We ca defe a few erms: [N S ] = Solubly of he mpury a subsuoal se [N I ] = Solubly of he mpury a ersal se s = Subsuoal jump frequecy (~10 13 Hz, depeds o Temperaure, oher facors) = Iersal jump frequecy EE r. Ala oolle

7 Impury ffuso: ffuso oeffce N s N N s N N N s Fraco of me he mpury speds a he Subsuoal Lace ses Fraco of me he mpury speds a he Iersal Lace ses he he effecve jump frequecy ca be defed as, effecve s N s N N s I N I N N s EE r. Ala oolle

8 Impury ffuso: ffuso oeffce For a ersal, o defec mus be creaed before he mpury ca dffuse. Thus, he dffusvy s, E moo kt Iersal effecved e, where Emoo ~ where d s he dsace for a jump. For a subsuoal mpury o move, mus frs creae a vacacy-ersal par. Thus, ofe s moo s lmed by he eergy requred o creae he defec subsuoal effecve d e E defec creao E moo kt, where E defec creao ev for ~ 4 5 ev S for S Geerally, o e E k a Noe: o s assumed cosa bu fac has a slgh depedece o emperaure hrough he effecve erm. EE r. Ala oolle

9 Impury ffuso: ffuso Mechasms The dffusvy s depeda o he po defec reacos ha ake place. Several mechasms es: Iersal, vacacy, ersalcy, ad dssocave mechasms. Noe: he kckou mechasm s a subse of he full ersalcy mechasm bu does o requre he presece of self-ersals. EE r. Ala oolle

10 EE r. Ala oolle p p p p o osder smple vacacy dffuso: The dffusvy ca be cosdered a superposo of all he dffusvy of all dvdual vacacy speces (dffere charges): Rarely are hrd ad forh order erms mpora. Impury ffuso: ffuso oeffce Noe several Equao Errors he ole oes!

11 Impury ffuso: ffuso oeffce osder As vs B dffuso S: Arsec S s a mpora case where mulple dffusvy erms mus be cosdered. A hgh coceraos of As, >>. Thus, he frs erms mus be used. The dopg has ehaced he dffuso. A lower coceraos, <, ad oly he rsc dffusvy erm eeds o be cosdered. See eample 3.1 ampbell. Ths cocerao depede dffusvy leads o a seep drop he cocerao whe he cocerao becomes lower ha. (Traffc jam aalogy). a elevaed emperaure: ffusvy s hgher for coceraos hgher ha ad lower for coceraos below. Ths resuls a more abrup profle (preferred). EE r. Ala oolle

12 Impury ffuso: Phosphorous ffuso oeffce I realy, may dffusos are domaed by more ha jus vacacy reacos. Oher defec complees form. osder P S. A hgh coceraos, doubly charged vacaces, V -, combe wh ozed phosphorous, P + o form a comple, (PV) - These domae over sgly charged vacaces. Thus, A P-levels resulg a ferm eergy less ha 0.11 ev, he (PV) - par dsassocaes accordg o, ( 0 PV ) ( PV ) ( usable) e P V Ths resuls a ecess of V - resulg a kk rego. Ths ecess vacacy cocerao leads o a ehaced dffusvy he al rego. EE r. Ala oolle

13 Impury ffuso: Phosphorous ffuso profle Epeced dffuso profle IF phosphorous was govered by smple rsc dffuso process. EE r. Ala oolle

14 Soluos of he Basc ffuso Equao: (, ) (, ) May useful soluos es The mahemacs of ffuso, d Ed., Joh. Frak (1975). Three mpora cases es: 1.) Ife Source (o-depleg) Assumpo (ofe ermed Predeposo ) Soluo s, Boudary codos for equao 4, for (0,0)=0, (0,>0)= S, ad (fy,)=0 z ( z, ) Serfc, where Sqr() s kow as he characersc dffuso legh, S s he fed surface cocerao ad erfc s kow as he complmeary error fuco. The dose, Q(), wh us=[cm - ] s defed as, Q T, z, dz 0 0 ad he juco deph for a cosa bulk cocerao, B, s, erfc( ) 1 erf ( ) Noe: Ofe he erf s abulaed bu o erfc j erfc 1 B s 0 bulk me j EE r. Ala oolle

15 (, ) Soluos of he Basc ffuso Equao: (, ).) Fe Source (depleg) Assumpo (ofe ermed rve ) Boudary codos for equao 4, for (z,0)=0 for z>0, d(0,)/dz=0, ad (fy,)=0 ad dose (area uder he curves o he lower rgh), Q T = cosa. Soluo s a Gaussa, z, Q T e z 4 The surface cocerao deplees as, s 0, Q T ad he juco deph s, j 4 l B Q T bulk me j EE r. Ala oolle

16 Soluos of he Basc ffuso Equao: omparso of Ife Source ad Fe Source ffuso Ife Source: osa surface solubly lm Fe Source: osa surface cocerao slope bu me varyg cocerao EE r. Ala oolle

17 Soluos of he Basc ffuso Equao: 3.) Two sep dffuso 1.) Predeposo wh small 1 (T) ad 1.) Tur off Impury Source 3.) Odze he wafer 4.) Tur up he emperaure (drve ) wh large (T) ad If ( 1 1 ) 0.5 << ( ) 0.5 ===> gaussa If ( 1 1 ) 0.5 >> ( ) 0.5 ===> erfc Thus, z, 1, U (1U ) 0, 1 e 1 du U 0 1U where he egral s kow as he smh egral 11 EE r. Ala oolle

18 Elecrc Feld Ehaceme: orrecos o ffuso Theory The elecrc feld creaed by he ozed mpures causes ehaced dffuso due o drf. Nrdzao Ehaceme/Reardao: 1, where0 1 Eposure of he S surface o NH 3 jecs ecess vacaces => ehacg vacacy mechasm dffuso (As), decreasg ersalcy mechasm dffuso (less S Iersals due o rappg by vacaces) Odao Ehaceme/Reardao: Eposure of he S surface o a odzg process jecs ecess S-Iersals => ehacg ersalcy mechasm dffuso (P ad B), decreasg vacacy mechasm dffuso Sce he odao rae s me depede, he dffusvy becomes me depede dode d Where he secod erm s he odao duced dffuso coeffce chage, o s he hckess of he ode, s me, =~ for S ad s a proporoaly cosa EE r. Ala oolle

19 orrecos o ffuso Theory ffuso o oher Maerals: ffuso s ehaced polycrysalle maerals due o dffuso dow gra boudares. ffuso s slower SO. Thus, SO s a ecelle hgh emperaure dffuso mask. ffuso haracerzao Ofe mes, he dffuso s characerzed by he shee ressace R s q 0 1 ( ) ( z) dz where s he cocerao depede mobly, ad s he cocerao EE r. Ala oolle

20 Supporg Iformao EE r. Ala oolle

21 Supporg Iformao EE r. Ala oolle

22 Supporg Iformao EE r. Ala oolle