ipolar Juctio Trasistors ipolar juctio trasistors (JT) ar activ 3-trmial dvics with aras of applicatios: amplifirs, switch tc. high-powr circuits high-spd logic circuits for high-spd computrs. JT structur: sadwich of altratig typ of Si-layrs p JT: squc of -p- pp JT: squc of p--p p JTs ar most widly usd. C N+ P N- N+ 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #1
a) 2d-cross-sctio of a p JT structur. A. C JT Structur Cotacts P N+ N-pi N+ P+ P+ N+ NPN Activ rgio P C o c t r a t i o ( c m -3 ) b) 1d-cross-sctio alog th itrisic dvic. 1.+21 1.+20 1.+19 1.+18 1.+17 1.+16 N+ mittr P as N- Collctor N+ urrid layr 1.+15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 D p t h ( u m ) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #2
. asic Faturs of C JT Structurs Th bas rgio is o-uiformly dopd. This rsults i a built-i ε fild across th bas which aids th trasport of from C. Parasitic lmts xist i a JT structur such as: bas rsistac, R from bas cotact to activ ara collctor rsistac, R C (prdomiatly through - layr). solatio must b providd btw adjact dvics: rvrs biasd PN juctios trch isolatio. Th N- collctor rgio adjact to th bas: rducs C C, improvs V C dcrass bas width modulatio by th collctor voltag but adds sris rsistac to th dvic. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #3
C. asic JT Opratio X N+ P N- N+ hols Most of th + + C 0.7 V forward bias 5 V rvrs bias Th JT opratio is as follows: A xtral voltag is applid across th - juctio to forward bias it ( 0.7 V) ar ijctd ito th bas by th mittr. (Also, hols ar ijctd ito th mittr but thir umbrs ar much smallr bcaus of th rlativ valus of N A, N D ). 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #4
asic Opratio f X << L N (diffusio lgth) i th bas, most of th ijctd - gt ito th collctor without rcombiig. A fw do rcombi; th hols cssary for this ar supplid as bas currt. Th rachig th collctor ar collctd across th C- juctio dpltio rgio. C C lctros flowig mittr to collctor C Hols ito mittr Rcombiig lctros Sic most of th ijctd - rach th collctor ad oly a fw hols ar ijctd ito th mittr, th rquird << C. Thrfor, th dvic has a substatial currt gai. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #5
asic Opratio - Drivatio of Currts ordr to driv th basic rlatioship for - currt flowig btw ad C, w assum that th dvic currt gai is high. 0 J p hol currt i bas 0 J p 0 qµ p pε x qd p (dp/dx) (1) ε x D µ p p 1 p dp dx q 1 p dp dx (2) For uiformly dopd bas, ε x 0 ad th - travllig through th bas will mov by diffusio oly. Howvr, i C trasistors dp/dx 0 ad ε x 0. Th dirctio of this fild aids - flow from C ad rtards - flow from C. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #6
asic Opratio - Drivatio of Currts Th - flow btw ad C is giv by: J qµ ε x + qd (d/dx) (3) Usig (2) i (3) w gt: J dp d µ q D (4) p dx dx + J qd p dp dx + p d dx Or, ( p) qd d J (5) p dx W itgrat (5) ovr th quasi-utral bas rgio of width x. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #7
asic Opratio - Drivatio of Currts N+ x d1 P x d2 N- C x J x o p q dx D x o x 0 d p dx dx x x J is pulld outsid th assumig o rcombiatio of - i th bas rgio, i.. J costat. J x o p q dx D p ( ) p( 0) x 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #8 (6) (7)
asic Opratio - Drivatio of Currts From PN juctio aalysis, th p-products at th dg of th dpltio rgios ar: J p p ( ) ( ) x q 2 i x o 2 i 2 i qv C qv 0 (8) D qv C pdx qv Now, th total charg i th u-dpltd bas rgio is giv by: x Q qa pdx (11) o 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #9 (9) (10)
asic Opratio - as Gumml Numbr ad, s q s 2 2 A Q qv C 2 i D qv (12) (13) This is a xtrmly importat rsult. Not that: 1 Usually, oly o of th two xpotial trms is importat sic o juctio is typically rvrs biasd. Wh th dvic is i saturatio, both juctios ar forward biasd ad both trms must b icludd. x Q 2 Th quatity, N A( x) dx is calld th bas Gumml umbr. qa o t is th total itgratd bas charg (atoms/cm 2 ). Sic 1/Q, it is importat to miimiz Q. Thrfor, C trasistors us low bas dopig lvls. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #10
JC (A/cm 2 ) C Vs. V Sic C juctio is rvrsd biasd th qv C / trm is gligibl ad w ca show from (12) ad (13): 1.-01 1.-02 1.-03 1.-04 1.-05 1.-06 1.-07 1.-08 1.-09 1.-10 2 2 2 q A D i qv 1 Q xpt dal JS 60mV 0.0 0.2 0.4 0.6 V (V) Dcad chag i JC (14) (14) prdicts that C vs. V is rlatd xpotially. Slop (/q)l(10) 60 mv/dcad (@ 25 o C) Rlatioship holds xtrmly wll for C trasistors ovr may dcads of currt. Grally, Q is obtaid by itgratio ovr th bas rgio. Thrfor, Q is typically wll cotrolld to ~ 10 12 cm -2 to giv high C for a giv V. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #11
D. Currt gai Lt us cosidr th factors that ca cotribut to bas currt i a JT: Rcombiatio i th utral bas rgio Hol ijctio ito th mittr Rcombiatio i th - spac charg rgio C lctros flowig mittr to collctor C Hols ito mittr Rcombiig lctros 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #12
1. Rcombiatio i th Nutral as Rgio Typically, som of th - travlig th bas will rcombi with majority carrir hols. (This is ot importat for modr C JTs). N+ P N p p o p Q p o p o f w assum that th bas is uiformly dopd so that ε x 0, th - currt ad cotiuity quatios ar: d p qa D (15) dx 2 d p p po D 0 (16) 2 d x τ 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #13
Rcombiatio i th Nutral as Rgio As w discussd for PN juctio, th gral solutio of ths quatios is: p po K 1 x/l + K 2 x/l (17) Th appropriat boudary coditios ar: p (x 0) po qv / p (x x ) 0 Usig ths boudary coditios w gt from (18): p p o q V x x sih L x sih L (18) Substitutig (18) ito (15) w gt mittr ad collctor currts. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #14
C qad L qa D as Trasport Factor L p p Th ratio of ths two currts is dfid as th bas trasport factor ad is giv by: α T C / sch(x /L ) (21) modr C JTs, X << L ad rcombiatio i th utral bas rgio is sigificatly low. f X << L, (19) rducs to our arlir xprssio for - currt (14) ad th bas trasport factor α T bcoms: α T 1 x 2 /2L 2 o o q V q V x 1 coth (19) L x 1csch L (20) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #15
a typical advacd JT, X 1 µm ad L 30 µm α T 0.9994. This valu of α T would imply a forward currt gai: β F C which is highr tha ormally obsrvd valu of β F i C JTs with 1 µm bas widths. Thus, α T is NOT usually a limitig factor i currt gai. Th bas currt du to α T is: as Trasport Factor α αt 1 α 2 q A i x qv 1 RC 2N Aτ whr τ is liftim i th bas. T C T > 1600 (22) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #16
2. Hol jctio ito th mittr Th domiat mchaism i limitig β i modr JTs is hol ijctio ito th from. Not that this procss must occur bcaus V dcrass th barrir to - flow from ad also th barrir for hol flow from. x x C x C p p p p p p x >> L p x << L p Th ijctd hol currts i ach cas com dirctly from th aalysis of log bas ad short bas diods ( dots mittr proprtis): q 2 D x >> L : qa V p p p i 1 (23) N D L p x << L p : p qa 2 i N D D p x q V 1 (24) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #17
mittr fficicy Th ijctio fficicy of th mittr is dfid as: 1 γ + p TOT p 1+ Th from (14) ad (24) w gt: 1 γ x N A D p 1+ x N D D (25) (26) (f X >> L or X >> L p, th L diod approximatios rplac X ad/or X with L or L p.) (26) is oly approximatly corrct i C structurs bcaus N A ad N D ar ot costat. Not that γ is mad clos to 1 by: (1) makig N D >> N A ; (2) X small; (3) X larg (prvt hol rcombiatio at cotact). 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #18
3. - Spac Charg Rcombiatio α T ad γ ar idpdt of V imply that th ratio of collctor to bas currt is a costat, idpdt of V i.. currt lvl. practic, th ratio of th two currts is NOT idpdt of C. At low lvls th domiat raso is rcombiatio i th - dpltio rgio. C ijctio rcombiatio * hol ijctio From PN juctio thory, w fid that som rcombiatio of th carrirs movig through th dpltio rgio will occur, causig a rcombiatio currt. 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #19
- Spac Charg Rcombiatio qaiw qv A RC 2 (27) 2τ o whr τ o is th liftim i th dpltio rgio. Not: This currt flows i th circuit ad dos ot dirctly affct C. Thus, as RC bcoms importat, th ratio of C / will chag. qv /2 dpdc is importat at low currt lvls. Summarizig our discussio of currt gai: 1 β C p + C + RC 1 2 A P + + 2 β D o N N x x D D x 2 L N A xw 2 D iτ q V 2 (28) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #20
. Mod of Opratios C N+ P N- N+ C JTs ar two back-to-back diods. C Four mods of JT opratios 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #21
1) Forward activ / ormal juctio forward biasd C juctio rvrsd biasd hr, C C β F 2) Rvrs activ Mod of Opratios, whr β F forward gai + V C vrs Saturatio - + V Cut-off Normal - juctio rvrs biasd ad C juctio forward biasd hr, rvrs gai, β F / 1 3) Saturatio rgio ad C ar forward biasd 4) Cut-off rgio ad C ar rvrsd biasd 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #22
F. asic JT Modl asic JT modl ca b drivd cosidrig two back-to-back diods as p-jt. 1) - juctio is forward bias: forward currt, F flows through - diod. α F F flows i th collctor hr, α F forward gai C / if V is +v 2) -C juctio is rvrs bias: rvrs currt, R flows through -C diod. α R R flows i th mittr a R R hr, α R rvrs gai / C if V is +v C F α F F 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #23 p R C C
M1 JT Modl: jctio Vrsio Th basic brs-moll modl (M1): α R R α F F O C O C F Trmial currts: O F + α R R (29) C α F F R (30) F α R R α F F + R (1 α F ) F + (1 α R ) R (1 α F ) F + (1 α R ) R (31) R 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #24
M1 JT Modl: jctio Vrsio W kow from currt flow aalysis: Hr F R C S CS qv qv C 1 1 S - saturatio currt; V - voltag CS C- saturatio currt; V C -C voltag Th trmial currts from (29), (30), (32), (33): C α F S S qv qv (32) (33) qv C 1 + α RCS 1 (34) qv 1 C CS 1 (35) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #25
M1 JT Modl: jctio Vrsio From rciprocity proprty: α F S α R CS S Thrfor, α C Agai, qv β F C forward currt gai α F /(1 α F ) β R C rvrs currt gai α R /(1 α R ) Sic S f( i 2 ) f(t) S S S F 1 + S 1 S α qv T ) T R qv C qv C k g 1 1 1 1 T T (36) (37) rf ( T ) S ( Trf (38) rf 3 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #26
22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #27 M1 JT Modl: jctio Vrsio Modl quatios: Whr α F β F /(1 + β F ) α R β R /(1 + β R ) Total fiv modl paramtrs: b F, b R, S, T rf, ad g ca b usd to dscrib basic JT dvic charactristics without parasitics. + 1 ) ( 1 ) ( 1 ) ( 1 ) ( T T T T qv C R S qv S C qv C S qv F S α α (36b) (37b) rf g T T k rf rf S S T T T T 1 1 3 ) ( ) ( (38)
M1 JT Modl: Trasport Vrsio Modl quatios (36) ad (37) ca b writt as: 1 CC + C α F 1 C CC + C α R Whr th rfrc sourc currts: CC C S S qv qv C 1 1 O 1 1 CC 1 + 1 α F α R C C CC /α F (39) (40) C O C 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #28 O CC C /α R (41)
M1 JT Modl: Noliar Hybrid-π From trasform modl (39) ad (40), w gt: 1 CC 1 CC ( CC C ) CT α F β (42) F 1 C C ( CC C ) 1 C CT α (43) R β R Whr th rfrc sourc currt is: qv qv C CT CC C S 1 1 Th diod currts ar: qv CC S 1 β F β F qv C S C 1 β β R R (44) (45) (46) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #29
M1 JT Modl: Noliar Hybrid-π Th modl: CT CC - C O C O C Th trmial currts: CC /β F O C /β R C CC β F C CT β R CC + β F β CT C R (47) (48) (49) 22-Ja-04 HO #6: LN 251 - ipolar Trasistors Saha #30