ECE606: Solid State Devices Lecture 18. Bipolar Transistors a) Introduction b) Design (I)

Transcription

1 606: Solid State Devices Lecture 18 ipolar Trasistors a) Itroductio b) Desig (I) Gerhard Klimeck 1 ackgroud ase! Poit cotact Germaium trasistor Ralph ray from Purdue missed the ivetio of trasistors. Trasistor research was also i advaced stages i urope (radar).

2 Shockley s ipolar Trasistors + emitter Double Diffused JT + p base -collector + + emitter p base collector + Moder ipolar Juctio Trasistors (JTs) ase mitter + ollector P- - SiGe itrisic base P+ + Dielectric trech Why do we eed all these desig? Trasistor speed icreases as the electro's travel distace is reduced SiGe Layer 4

3 Symbols ad ovetio Symbols + P Poly emitter Low-doped base P ollector PP ollector ollector dopig optimizatio ase mitter ase mitter I +I +I 0 (D) V +V +V 0 5 Outlie 1) quilibrium ad forward bad-diagram ) urrets i bipolar juctio trasistors 3) ber s Moll model 4) Itermediate Summary 5) urret gai i JTs 6) osideratios for base dopig 7) osideratios for collector dopig 8) oclusios RF: SDF, hapter 10 6

4 Topic Map Diode quilibrium D Small sigal Large Sigal ircuit s Schottky JT/HT MOS 7 ad Diagram at quilibrium + ( D A ) D q p + 1 J r + g t q p 1 J r + g t q J J qµ + qd P P P qpµ qd p P P P quilibrium D d/dt0 Small sigal d/dt ~ jωt Trasiet --- harge cotrol model 8

5 ad Diagram at quilibrium P homojuctio JT mitter ase ollector Vacuum level F χ 1 χ 3 χ V 9 lectrostatics i quilibrium x p, ε q k s 0 ( + ) V bi x p, k s ε 0 ( + ) q V bi x, k s ε0 ( + ) q V bi x, ε q k s 0 ( + ) V bi mitter ase ollector Two back to back p- juctio 10

6 Outlie 1) quilibrium ad forward bad-diagram ) urrets i bipolar juctio trasistors 3) ber s Moll model 4) Itermediate Summary 5) urret gai i JTs 6) osideratios for base dopig 7) osideratios for collector dopig 8) oclusios RF: SDF, hapter Topic Map quilibriu m D Small sigal Large Sigal ircuit s Diode Schottk y JT/H T MOS 1

7 ad Diagram with ias + ( D A ) D q p + 1 J r + g t q p 1 J r + g t q J J qµ + qd P P P qpµ qd p P P P o-equilibrium D d/dt0 Small sigal d/dt ~ jωt Trasiet --- harge cotrol model 13 lectrostatics i quilibrium ε x V V k s 0 p, bi q ( ) ( ) + k s ε 0 p, bi q x V V ( ) ( ) + ε x V V k s 0, bi q ( ) ( ) + ε x V V k s 0, bi q ( ) ( ) + mitter ase ollector V Assume curret flow is small fermi level is flat V 14

8 urret flow with ias Iput small amout of holes results i large amout of electro output V -F, F p, - V -F, 15 Moder MOSFT - Fudametal Limit looks similar to JT S Metal Oxide p Vg D + + log I d Threshold Vg S 60 mv/dec 0 V dd V g x

9 Moder MOSFT - Fudametal Limit looks similar to JT Vg S D Metal Oxide p + + log I d Threshold DOS(), log f() f ` Vg 0 S 60 mv/dec V dd V g x oordiates ad ovetio mitter ase ollector + P X X X 0 W,...,... D, A, D, D D,... D D,... D D P P,... p p,... 0 p p 0 Dopig Miority carrier diffusio Majority carriers 18

10 arrier Distributio i ase x x ( x) Ax D W W D i, qv, ( ) ( x i qv 1) 1 ( x x e + e 1) W W + i, qv (0 ) ( e 1) i, qv ( ) ( x W e 1) Assume o recombiatio. Start from miority carrier V V 19 ollector ad mitter lectro urret i, qv, ( ) ( x i qv 1) 1 ( x x e + e 1) W W d qd i, qv qd i, qv J, qd ( e 1) + ( e 1 dx ) W W W V J p, dp qdp dx V D W p i D qv ( e 1) 0

11 urret-voltage haracteristics ormal, Active Regio : Forward biased : Reverse biased J qd i, qd i, qv J, e 1 + e 1 W W log 10 J qv ( ) ( ) High-level ijectio series resistace, etc. I > 60 mv/dec. V W is ot idepedet of bias > arly ffect V same physics of diode, rollover 1 Outlie 1) quilibrium ad forward bad-diagram ) urrets i bipolar juctio trasistors 3) ber s Moll model 4) Itermediate Summary 5) urret gai i JTs 6) osideratios for base dopig 7) osideratios for collector dopig 8) oclusios RF: SDF, hapter 10

12 Hole diffusio i collector bers Moll Model + qd + qd i, qd i, i, qv I A e A e W W W ( qv 1) p ( 1) ( qv 1) ( qv 1) α I e I e F F 0 R0 I I c, +I c,p I F I R I I, +I,p I I α R I R I F qdp i, qd i, qd i, qv A + e + A e W W W qv qv ( 1) α R R ( 1) I e I e F 0 0 α F I I qv ( 1) ( 1) F R F 0 R0 ( qv 1) ( qv 1) I I e I I e Temperature depedet 3 ommo ase ofiguratio I F I R V (i) I P I V (out) I Juctio capacitace ad diffusio capacitace How would the model chage if this was a Schottky barrier JT? I α R I R α F I F The origial trasistor was a metal/ semicod / metal device o miority carriers, o diffusio capacitace but the rest about the same. ommo base cofiguratio provides power gai, but o curret gai. > mitter ad collector curret are idetical > o curret gai > ollector curret I ca be drive through large resistor > power gai Is there aother cofiguratio that ca deliver curret gai? I 4

13 ommo mitter ofiguratio I µ I V (i) P P+ I V (out) I αrir αfif I IF IR α F I F α I α I α F ( 1 α ) I I 1 α F F F F F F π IR F α I α I F F R R F F This is a practice problem 5 Itermediate Summary The physics of JT is most easily uderstood with referece to the physics of juctio diodes. The equatios ca be ecapsulated i simple equivalet circuit appropriate for dc, ac, ad large sigal applicatios. Desig of trasistors is far more complicated tha this simple model suggests > the ext lecture elemets For a terrific ad iterestig history of ivetio of the bipolar trasistor, read the book rystal Fire. 6

14 Outlie 1) quilibrium ad forward bad-diagram ) urrets i bipolar juctio trasistors 3) ber s Moll model 4) Itermediate Summary 5) urret gai i JTs 6) osideratios for base dopig 7) osideratios for collector dopig 8) oclusios RF: SDF, hapter 10 7 qd qd i, p i, qd i, qv I A + e A W W + W F 0 qv qv ( e 1) α RI R0 ( e 1) I qv ( 1) ( e 1) bers Moll Model qdp i, qd i, qv I A e + A e W W qv p ( 1) ( 1) I I F I R I α R I R I α F I F F R F 0 R0 ( qv 1) ( qv 1) I I e I I e qd i, qd i, qd i, qv I A e + A + e W W W qv ( 1) ( 1) qv qv ( 1) ( 1) α I e I e F F 0 R0 8

15 bers Moll Model (asic defiitio) saturatio regio I active regio I 0 V The bers-moll model describes both the active ad the saturatio regios of JT operatio. 9 Gummel Plot ad Output haracteristics The simultaeous plot of collector ad base curret vs. the base-emitter voltage o a semi-logarithmic scale is kow as a Gummel Plot. This plot is extremely useful i device characterizatio because it reflects o the quality of the emitter-base juctio while the base-collector bias is kept at a costat. A umber of other device parameters ca be ascertaied either quatitatively or qualitatively directly from the Gummel plot because of its semi-logarithmic ature For example the d.c gai, base ad collector ideality factors, series resistaces ad leakage currets. 30

16 Gummel Plot ad Output haracteristics I qd i, qv / kt qd i, qv / kt ( e 1) + ( e 1) A W W I qdp i, qv / kt ( e 1) A W D I I D ommo emitter urret Gai V 31 urret Gai ommo mitter curret gai.. I D I qd W W i, qv / kt qd i, ( qv / kt ) ( e 1) + ( e 1) qd i, qv / kt W ( e 1) V (i) I P+ P i, p i, D W W D I Will examie ommo ase curret gai.. I α D D I I I I D trasfer gai I I α D 1 α D V (i) I P+ P Properties are related (trasistor did ot chage ) I 3 V (out)

17 urret Gai D D W W D i, p i, High ijectio collector curret >roll-off ase curret does ot roll off 33 How to make a Good Silico Trasistor For a give mitter legth D D W W D i, p i, ~1, same material primarily determied by badgap Make-ase short (few mm i 1950s, 00 A ow) Wat high gradiet of carrier desity mitter dopig higher tha ase dopig ase dopig hard to cotrol mitter dopig easier 34

18 Dopig for Gai D D W W D i, p i, + P 35 Outlie 1) quilibrium ad forward bad-diagram ) urrets i bipolar juctio trasistors 3) ber s Moll model 4) Itermediate Summary 5) urret gai i JTs 6) osideratios for base dopig what s wrog with the previous recipe? 7) osideratios for collector dopig 8) oclusios RF: SDF, hapter 10 36

19 Problem of Low ase Dopig: urret rowdig V qd I J ( x) dx W I J x dx W i, ( ) qd p i, + p base -collector + qv ' ( x) ( e 1) qv ' ( x) ( e 1) V dx dx Double diffused juctio cofiguratio: mitter dopig must compesate / overcome the base dopig Low dopig i base > resistace alog the curret path > potetial drop > Determies the ijectio > Spatially depedet > More curret i the corers 37 Low ase Dopig: o-uiform Tur-o Sketches from text book + p base -collector + o-uiform curret iefficiet High curret at the edge ca cause bur-out Iterdigitated desigs for almost all high power trasistors (- distace miimized) 38

20 Low ase Dopig: urret rowdig + p base V -collector + We talked about how low dopig for the base ehaces the curret gai. ut there is a potetial dowside to this approach If the base dopig is kept to small values, it will have a high resistace: Lesser ability to coduct meas higher resistace 39 Low ase Dopig: urret rowdig + p base V -collector + o-zero base resistace results i a lateral potetial differece uder the emitter regio For a -p- trasistor as show, the potetial decreases from edge of the emitter towards the cetre (the emitter is highly doped ad ca be cosidered a equipotetial regio) 40

21 Low ase Dopig: urret rowdig + p base V -collector + The umber of electros ijected from emitter to base is expoetially depedet o base-emitter voltage With the lateral drop i the voltage i the base betwee the edge ad cetre of emitter, more carriers will be ijected at the edge tha the emitter cetre. 41 Low ase Dopig: urret rowdig Key facts: 1. urret crowdig is due to D ature of JTs. It is a fuctio of the dopig cocetratio 3. As dopig cocetratio icreases, resistivity decreases osequece: urret gai goes smaller mitter curret ijectio efficiecy decreases The larger curret desity ear the emitter may cause localized heatig ad high ijectio effects Possible Solutio: mitter widths are fabricated with a iter-digitated desig May arrow emitters coected i parallel to achieve the required emitter area 4

22 Low ase Dopig: o-uiform Tur-o Sketches from text book + p base -collector + o-uiform curret iefficiet High curret at the edge ca cause bur-out Iterdigitated desigs for almost all high power trasistors (- distace miimized) 43 Problem of Low ase Dopig: Puch-through + k s ε0 p, bi q x V V ( ) ( ) + k s ε0 p, bi q x V V ( ) ( ) + Low base dopig is ot a good idea! 44

23 D Problem of low ase-dopig: ase Width Modulatio lectrical base regio is smaller tha the metallurgical regio! D W i, p, p, c p i, W x x D ε x V V k s 0 p, bi q ( ) ( ) + + P ε x V V k s 0 p, bi q ( ) ( ) + Gai depeds o collector voltage (bad) Depletio regio width modulatio 45 Problem of Low ase-dopig: arly Voltage D D W W x x D i, p. p. p i, qd i, ( qv / kt ) qd i, ( qv / kt ) I, ( e 1) ( e 1) W ' + W ' di I I dv V + V V A A V about 1V V A ideally ifiity Jim arly device pioeer V A I I practice Ideally V 46

24 The arly Voltage PS1 I I practice Ideally V V A The collector curret depeds o V : For a fixed value of V, as V icreases, the reverse bias o the collector-base juctio icreases, hece the width of the depletio regio icreases. The quasi-eutral base width decreases collector curret icreases. Due to the arly effect, collector curret icreases with icreasig V, for a fixed value of V. 47 The arly Voltage PS I I practice Ideally V V A The arly voltage is obtaied by drawig a lie tagetial to the trasistor I-V characteristic at the poit of iterest. The arly voltage equals the horizotal distace betwee the poit chose o the I-V characteristics ad the itersectio betwee the tagetial lie ad the horizotal axis. arly voltage is idicated o the figure by the horizotal dotted lie 48

25 Puch-through ad arly Voltage di I I dv V + V V A A di d di dv d q W dv ( ) ( q W ) 1 di dq q dw dv 1 I q W q W V I I A qw VA eed higher ad W or + qd i, qd i, qv I e e W W ξ qv ( 1) ( 1) W di d ξ ζ dw dw W W I W 49 Outlie 1) quilibrium ad forward bad-diagram ) urrets i bipolar juctio trasistors 3) ber s Moll model 4) Itermediate Summary 5) urret gai i JTs 6) osideratios for base dopig 7) osideratios for collector dopig 8) oclusios RF: SDF, hapter 10 50

26 ollector Dopig W x x D D W i, p, p, p i, + P V A qw ase-ollector i reverse bias Majority carriers oly o diffusio capacitace Reduce capacitace Icrease x x κ sε 0 + x, p, If you wat low base dopig the reduce collector dopig eve more to icrease ollector depletio.. 51 but (!) Kirk ffect ad ase Pushout Space-harge Desity x p-ase -ollector + W - c + x W q V V x + x bi κ sε 0 x Space-harge Desity p-ase -ollector + W c W x ( + ) x ' ( ) x ' q ( + ) ' + ( ) V V x x ' bi κ sε0 J ' qυ sat x x x J 1 1 qυ J sat qυ sat Additioal charge! a be large compared to low dopig 5

27 Kirk ffect ad ase Pushout + emitter p base collector + Space-harge Desity p-ase -ollector + c x W W Space-harge p-ase -ollector c W W + x Space-harge p-ase -ollector + W WI W x c-c WS Icrease bias & curret Juctio lost High curret domiates collector dopig 53 Kirk ffect ad ase Pushout x ' x J 1+ qυ sat J 1 qυ sat J qυ J, crit sat K a ot reduce collector dopig arbitrarily without causig base pushout 54

28 Kirk ffect The Kirk effect occurs at high curret desities i a bipolar trasistor. The effect is due to the charge desity associated with the curret passig through the base-collector regio. As this charge desity exceeds the charge desity i the depletio regio the depletio regio ceases to exist. Istead, there will be a build-up of majority carriers from the base i the base-collector depletio regio. The dipole formed by the positively ad egatively charged ioized doors ad acceptors is pushed ito the collector ad replaced by positively charged ioized doors ad a egatively charged electro accumulatio layer, which is referred to as base push out. This effect occurs if the charge desity associated with the curret is larger tha the ioized impurity desity i the base-collector depletio regio. Assumig full ioizatio, this traslates ito the followig coditio o the collector curret desity. Key poit : Uder high curret ad low collector dopig the depletio approximatio is ivalid i the - juctio! Perhaps High Dopig i mitter? ad-gap arrowig reduces gai sigificatly D W W i, Dp i, g, / kt W V e g, / kt p V D W D e e g / kt (aski-like) Tuelig cause loss of base cotrol 56

29 Summary While basic trasistor operatio is simple, its optimum desig is ot. I geeral, good trasistor gai requires that the emitter dopig be larger tha base dopig, which i tur should be larger tha collector dopig. If the base dopig is too low, however, the trasistor suffers from curret crowdig, arly effects. If the collector dopig is too low, the we have Kirk effect (base push out) with reduced high-frequecy operatio ad if the emitter dopig is too high the the gai is reduced. 57