The Bipolar Transistor

Transcription

1 hater 2 The Biolar Trasistor hater 2 The Biolar Trasistor Bardee, Brattai ad Shockley develoed the Biolar Juctio Trasistor i 1947 at Bell Laboratories [1]. These researchers oticed that i certai exerimetal coditios the chage i collector voltage is roortioal to the chage i base curret; cosidered that the ratio betwee a voltage ad a curret is a resistace, this device has bee called trasfer resistor or trasistor. Sice the early 80s MOS techology has started substitutig the biolar oe i digital s fabricatio, so that at reset their usage is limited to secial alicatios. For the future it is foreseeable that MOS will relace etirely the BJT, due to the cotiual imrovemet of its erformace. Nevertheless BJT still remais the domiat rocess for liear ad mixed-sigal rocesses [2]. Moreover biolar microcircuits are the rimary s used i satellite alicatios, because of their good radiatio hardess. The most imortat arts that make use of biolars are oeratioal amlifiers, As, As, comarators, aalog switches, multilexers, voltage regulators ad ulse width modulators. Biolar s costitute owadays about 40% of the circuits used i satellite ad strategic missile systems that require radiatio hardess skills. 2.1 PN juctio A juctio [3] is ideally obtaied suerimosig two Silico layers with oosite sig doig, called -tye Silico ad -tye Silico. -tye is realized by Phoshorus 1 diffusio or imlatatio i Silico, ad -tye by use of Boro. While Silico itself is ot a coductor (the itrisic carrier cocetratio is about cm -3 at room temerature) doed Silico shows a certai coductivity due to the greater umber of carriers brought by the doat (the extrisic carrier cocetratio is about cm -3 ). Usually electros i -tye Silico are called majority carriers ad holes are called miority carriers (because the electros umber is about cm -3 # cm -3, while the holes are cm -3 ); the oosite haes for -tye Silico. A simle schematic of a juctio is give i Fig. 2.1 a). The charges i the circles are the fixed oes (doat) ad the others are free. 1 Silico belogs to the V grou i the eriodic table, Phoshorus to the V ad Boro to the. 13

2 hater 2 The Biolar Trasistor Figure 2. 1: juctio ad deletio regio formatio. deally at first 2 the juctio is everywhere eutral (all the doats maitai their outer electros) but after a while the diffusio ad the self-field effect lead to the situatio sketched i Fig. 2.1 b). Here a deletio regio has take lace ad the electrical otetial is ozero. The carriers see a otetial wall (about 0.7 V) ad sto overcomig the deletio regio. Alyig a icreasig forward voltage (i.e. with the + i ad the i ) oe lower the wall height util it disaears ad majority carriers ca cross the juctio (the diode is o). O the other side a reverse voltage make the wall bigger ad the diode is off. 2.2 Qualitative behavior of the laar trasistor its simlest form BJT is made of two juctios arraged back to back. So the ossible cofiguratios are the -- ad the --. The three Silico layers are called Emitter, Base ad ollector. order to get a simle idea of the rocesses ivolved i its oeratio we ca refer to Fig. 2.2 (-- trasistor). The ormal oeratig coditio is referred as forward active regio ad requires the emitter-base to be forward biased ad the collector-base to be reverse biased. this situatio electros from the emitter (majority carriers) are brought towards the collector; whe they reach the base there is o more electric field ad the motio takes lace by diffusio. the base electros are miority carriers. Electros die betwee few diffusio legths, so the base has to be arrow i order to allow electros flowig ito the collector. Oce reached the base-collector juctio they are swet across it by the reverse bias ad arrive ito the collector. Now i order to maitai the charge eutrality, some holes are ijected ito the collector; furthermore some holes are ijected ito the base to comesate holes recombied with electros. 2.e. whe uttig i cotact -Si with -Si 14

3 hater 2 The Biolar Trasistor Figure 2. 2: BJT currets i the forward active regio, simlified drawig Fially some holes come from base to emitter because of the forward bias. ollector holes of course do ot cross the juctio because of the reverse bias. The mai feature of the biolar trasistor is the curret amlificatio: we ca cosider the emitter-collector as the mai ie ad the base as a valve for curret cotrol i that ie. Actually if we igore the small recombiatio curret i base ad the holes ijected ito emitter, we ca write E 1 ) ( beig (1-) ~ 0.01 the fractio of electros which recombies i the base. Usig the Kirchoff s curret law with the symbols idicated i Fig. 2.2 we get 1 where E is the forward curret gai of the trasistor. Tyical values are E # 50y100. So emitter ad collector currets are roughly the same, while base curret is much smaller. Further, chagig base curret we get a imortat variatio i the mai ie curret. E B { E B B 2.3 The commo emitter curret gai this sectio we reset the basic relatios ivolved i trasistor gai calculatio. Alog the whole derivatio it will be cosidered just the oeratio i the forward active regio, which is the most commo way of usig BJTs. There is a imortat equatio (ofte called the Boltzma relatio) that will be used i the followig: e qv kt (1) 15

4 hater 2 The Biolar Trasistor Figure 2. 3: Electro cocetratio uder BE forward bias. t exresses the relatio betwee carriers at the juctio boudaries, beig the electro cocetratio i -tye Silico ad that oe i -tye (the same otatio works for holes) ad V the voltage across the juctio, or better across the sace charge regio (see Fig. 2.3). Our urose is to study the trasistor gai E, as said before. osidered that E (2) we are iterested i fidig out the currets ad their deedece o voltages. Trasistor currets are due to two effects: drift ad diffusio. rift takes lace whe a electric field is reset, ad the drift curret is drift qap E (3) where A is the cross-sectioal area, q the charge, the desity (or for holes). P is the mobility ad E the field. iffusio is due to carrier cocetratio gradiets ad has the shae (1) diffusio qa beig the diffusio coefficiet. There are 6 currets ivolved i E calculatios, as it is show i Fig. 2.4: the ormal diffusio curret, the reverse diffusio curret, the recombiatiogeeratio curret RG, the base recombiatio curret RB ; the surface curret S ad fially the collector leakage curret BO. At first we have to secify that the most imortat i ormal trasistor oeratio are ad RG. The others ca be cosidered as secodary (ad udesired) effects. fact is the electro flow from emitter to base. A fractio of it recombies i base ad the remaiig art goes to collector. So at this 0 th order aroximatio we would have B w w x RB (4) E B RB 16

5 hater 2 The Biolar Trasistor B is the holes ijectio from the ohmic cotact that maitais the charge eutrality. The E B order to get a high gai we should the reduce as much as ossible RB. Let s ow discuss the currets searately. The ormal diffusio curret is due to diffusio ad drift of miority carriers from base to collector. Of course these carriers come from the emitter, where they are the majority oes. The two situatios more likely to occur are rereseted i Fig The situatio a) is referred as low ijectio mode, which meas that trasistor carriers are egligible with resect to the doig level: RB RB N A (beig N A the accetor imurity cocetratio). The situatio b) is istead the high ijectio mode, whe ~ N A or >> N A. This classificatio also alies to holes i the -regios. Of course the schematic is quite rough ad ideed the ormal trasistor oeratio lies betwee these two extremes. The mai differece is due to the majority carrier role: i order to clarify it let s start writig the electrical eutrality of the base regio: N A W W b ³ 0 ³ # b W b 0 RB ( x) dx ( x) dx (5) with x at the base-emitter juctio. N A W b is the fixed accetor charge i cm -2 (see Fig. 2.1). this elemetary derivatio the base doig level is assumed costat. Figure 2. 4: BJT currets i the forward active regio. The trasistor draw has a radial shae; overcomig the simle ideal laar trasistor we discover the surface curret S that will be the mai roblem i ELRE. the icture arrows idicate electro flow. 17

6 hater 2 The Biolar Trasistor Figure 2. 5: Low ad High ijectio trasistor oeratio Substitutig itegrals i (5) with mea values we get N A (6) At low ijectio it is roughly # N A ; at hi ijectio it is #. So at low ijectio there is o hole desity gradiet. Moreover the free electros are very few comared to the holes, so the electric field i the base regio is egligible. This is why i Fig. 2.5a just diffusio is idicated. O the other side, at hi ijectio there is a hole desity gradiet which is rereseted i Fig. 2.5b. Here the holes kee driftig toward the collector. But the reverse bias i the B juctio makes them sto ad we get a situatio like the oe i Fig. 2.6: holes accumulate ear the B juctio, givig rise to a local chargig of the base. The result is a electric field that comesates the diffusio. Of course this field will iduce electro drift towards the collector, which adds to the diffusio see for the lowijectio case. Let s try ow to say the same thigs i a more rigorous way. Figure 2. 6: Hi ijectio electric field i the base regio due to hole cocetratio gradiet 18

7 hater 2 The Biolar Trasistor Startig with low ijectio, there is just diffusio ad the 1 equatio is w t w w w where W is the electro recombiatio lifetime. At equilibrium the time derivative is zero; usig the boudary coditios idicated i Fig. 2.7 we get the satial derivative at x = 0: w w x x 2 2 x W Wb coth L 1 0 L W 0 cosh L Here L is the electro diffusio legth defied as follows b 0 ¹ (7) (8) L 2 W (9) order to fid out ad 0 we use (1) ad the low ijectio aroximatio: is equal to the doig level so qv q( \ 0 V0 ) kt kt N e N e (10) while 0 comes from (10) with the alied exteral voltage V 0 = 0. Notice that i (10) the total voltage across the juctio is slitted i the juctio-voltage (all termial grouded) ad the alied oe. \0 is of the order of 0.7 V, while kt/q is about 26 mv at room temerature. t follows that for usual alied voltages (above 100 mv) we ca simlify (8) by as follows Fially usig (4) we get W coth b qv0 w L kt e 0 wx L x 0 Wb coth qv0 L kt qa 0e (12) L or also, if the base width is smaller tha the diffusio legth (which is the commo situatio), we ca use a aroximate exressio for the hyerbolic fuctio ad qv0 qa qa 0 kt e (13) Wb Wb This is the ormal diffusio curret at low ijectio. As said before it is the mai trasistor curret. order to take ito accout the high ijectio we should itroduce the drift curret. (11) 19

8 hater 2 The Biolar Trasistor Figure 2. 7: Boudary coditios for equatio (7) ombiig (3) ad (4) we get w qa qap E (14) wx The oly ukow here is the electric field, ad it ca be foud writig that the hole curret towards the collector is zero: hole drift = hole diffusio d qa qap E (15) dx Solvig for E: kt d l E (16) q dx (havig used the Eistei s relatio = PkT/q). Now we ca ut (16) ito (14) ad use the high ijectio aroximatio N A The we get qa 2 (17) W idicate as usual the electro cocetratio at the boudary. A comariso betwee (17) ad (13) shows that the drift cotributio to the ormal curret i high ijectio is the same as the diffusio oe (because,hi = 2,low ). As a fial ste we could fid out the emitter-base voltage deedece of at high ijectio, but it overcomes the aim of the reset overview. We just otice that the b 20

9 hater 2 The Biolar Trasistor resece of a electric field itroduces a voltage that has to be added to the juctio oe. ractice the total voltage deedece is o more like ex(qv be /kt) but becomes like ex(qv be /2kT). So far we have cosidered electro flow from the emitter to the collector, which is the ormal diffusio curret. The reverse diffusio curret is istead the hole flow from base to emitter due maily to diffusio. There are o holes comig from the collector because the B juctio is reverse biased. Hole distributio is sketched i Fig Evaluatig this curret i the emitter regio we do ot have to take ito accout a ossible electric field due to high ijectio i the base. So we ca make direct use of (12) with the suitable symbols for holes; further beig i the emitter, which is ofte thicker tha the diffusio legth, we ca substitute the hyerbolic fuctio with 1, gettig qa ' (18) L is of course related to the hole cocetratio o the other side of the juctio by the Boltzma relatio (1). Actually for the low ijectio case we have while at high ijectio it ca be show that 0 e qvbe kt 2 v (19) ad havig the same shae, oe could woder why << i ormal trasistor oeratio. This is due to the differet doig level i emitter ad i base: the former is somethig like 100 times the latter, ad this factor comes ito 0, 0 ad the mobilities. Of course this is a techological choice, because as said before the mai ie curret is, while adds to the base curret, thus reducig the gai. Figure 2. 8: Hole cocetratios i the forward active regio 21

10 hater 2 The Biolar Trasistor Figure 2. 9: Recombiatio of electros crossig the base The mai base curret comoet is the base recombiatio curret RB (see Fig. 2.4 for referece). This is due to the electro recombiatio i base whe goig from emitter to the collector. For a thi base the electro distributio is as i Fig Recombiatio takes lace with a lifetime W, so RB ( x) dxa qa Wb ³ 0 W 2 q W RB is a art of the base curret because durig recombiatio a hole is lost ad a ijectio from the base cotact occurs i order to reserve charge eutrality. RB ca also be exressed as follows RB t b W b ¹ beig t b the average base trasit time for electros. t is straightforward to get t b by comariso of (20) ad (21): W tb (22) 2 Oe should otice that t b deeds oly o base width ad doig levels (ad ot o ijectio level). Aother base curret comoet is the recombiatio geeratio curret RG, due to the electros from the emitter recombiig with doors i the BE deletio layers, to the holes recombiig with accetors, ad to the free electros ad holes recombiatio i that regio. A simle schematic of this situatio is i Fig A semi-emirical exressio is give by 2 b qv0 SkT 1. 5kT RG AXRi ie \ 0 where everythig is kow excet X, R i : X is the deletio width ad deeds o the alied voltage; R i is the itrisic carrier geeratio. b 2 L (20) (21) (23) 22

11 hater 2 The Biolar Trasistor Figure 2. 10: Recombiatio i the BE deletio layer The last base curret comoet is the surface curret S. The mechaism ivolved is similar to the revious oe. The differece is that the recombiatio takes lace ear the SiO 2 assivatio layer that overlies the emitter-base juctio (see Fig. 2.11). order to uderstad it we should quit the simle laar model ad cosider a more realistic trasistor like that oe sketched i Fig At the border betwee the SiO 2 isolatio layer ad the juctio there are lots of chemically active ceters that facilitate the recombiatio-geeratio of carriers. The weight of this curret comoet ca be very high; ideed S is the domiat comoet at low collector currets. A emirical exressio for the surface curret is give by qv0 2kT S S 0e The last curret we metioed is the collector leakage curret BO, that goes form collector to base through the B juctio reverse biased. At first we would imagie that such a curret is due to miority carrier diffusio, havig cosidered the miority distributio rereseted i Fig Nevertheless this cotributio is very small ad actually BO comes from electro-hole geeratio i the B juctio. fact at thermal equilibrium ad with o exteral voltage, recombiatio ad geeratio rate at the juctio are the same; (24) Figure Silico ioxide assivatio layer ad surface curret (detail from Fig. 2.4) 23

12 hater 2 The Biolar Trasistor while reverse biasig the B diode we get a carrier lack, ad geeratio (that does ot chage at all because deeds o Silico ad ot o carrier cocetratio) overcomes recombiatio. ue to the electric field i the juctio holes drift ito the base ad electros ito the collector. This way collector becomes egative ad hole ijectio from the cotact occurs. The result is a et hole flow from collector to base, as said above. order to accout for this curret we ca use the followig relatio qax R (25) BO beig AX B the B juctio volume ad i R i the geeratio rate i the volume uit. (25) we have eglected the recombiatio because the carrier cocetratio i the juctio is very low due to the reverse bias. At the ed of this review it is worth givig few orders of magitude. Tyical values for the currets cosidered are reorted i Table 2.1. Further we are ow able to write the recirocal gai as follows: havig used (21) ad cosidered that 1 E 1 B t b E W RB S B S ' i ' i RG BO RB # RG BO BO (26) (27) (28) Fig there is a lot of the iverse gai versus collector curret for a secific techology 4. We otice that as a referece value for the iverse gai oe ca use t b /W. Figure 2. 12: B juctio reverse biased ad thermally geerated curret ( BO ) 4 deed the techology cosidered is very old [4] but it is useful as a geeral examle. 24

13 hater 2 The Biolar Trasistor eviatios from this value occurs at low ad high currets: towards low collector curret the surface comoet becomes domiat ad icreases, thus reducig the gai. Towards high currets the iverse diffusio comoet is the most imortat 5. Rememberig (13), (18) ad (19) we see that ' v (29) ad this exlais the behavior i Fig urret Tyical values [A] 10-5 to to 10-1 RB 10-7 to 10-2 RG to 10-5 S to 10-5 BO Table 2. 1: Tyical values for BJT currets. order to kee i mid some umbers, we ca say that emitter ad collector currets rages from 0.1 to 1000 ma ad base curret is oe hudred times smaller. Figure 2. 13: The recirocal gai ad its comoets as a fuctio of the collector curret. 2.4 Layout examles revious sectios we have just cosidered a ideal trasistor obtaied by suerositio of three doed Silico layers. Now it is worth givig a brief overview of reset techologies, because it is well kow that trasistor behavior uder irradiatio strogly deeds o maufacturig choices. As 5 BO / is ot metioed because is egligible if comared to the other comoets. 6 Notice that metioed equatios hold for hi ijectio coditios, i.e. at hi collector curret here. 25

14 hater 2 The Biolar Trasistor said before the emitter is usually more heavily doed tha the base i order to get a big emitter efficiecy (i.e. the ratio / ). iffereces i doig levels are foud also i the collector-base juctio [4]: actually the deletio regio sreads i the lowest doed side of a juctio, so makig the base less doed tha collector we would get a base width very sesitive to the collector-base voltage, ad this should be avoided 7. So it seems that a better solutio would be to have a collector slightly doed; evertheless this way the collector resistace is icreased ad so the saturatio voltages 8. The solutio to this uzzle is rovided by the eitaxial layer. Usg a two-layers (low ad high doed resectively) collector with the lowest doed oe o the base side we get a base width quite stable because the deletio regio sreads ito the collector; further we get a low-resistace collector due to the hi-doed side. This is show i Fig The low-doed side of the collector is called eitaxial layer; the other oe is the substrate. By usig eitaxial layer we ca realize high frequecy, high voltage ad low saturatio voltage trasistors. Let s ow have a look to few commo trasistor shaes. Fig there is a sigle NPN trasistor (i.e. obtaied by a o-itegrated maufacturig rocess) with ei ad sub. The layers are realized by diffusio or io imlatatio of Boro ad Phoshorus o a Silico crystal. The Silico ioxide isolatio layer is grow by steam or oxyge reductio of the Silico. A high quality SiO 2 is recommeded i order to reduce radiatio damage: as we shall see later the oxide iflueces strogly the surface curret. Figure 2. 14: Eitaxial layer ad substrate 7 deed the base trasit time t b varies with the square of W b (22). Sice the cut-off frequecy of a trasistor is roughly f T #t b, a W b deedece o the collector voltage would lead to strog cutoff frequecy deedece o that voltage. 8 ollector resistace is directly related to its doig level as we ca easily imagie. Saturatio voltage is the voltage at the border betwee the forward active regio ad the saturatio regio that we did ot metio before. Oe could show that the greater the collector resistace the greater the saturatio voltage. 26

15 hater 2 The Biolar Trasistor Figure 2. 15: Plaar eitaxial trasistor 9 Fig the collector cotact is o the lower side of the trasistor. itegrated circuit fabricatio it is coveiet to ut all the cotacts o the same side (see Fig. 2.16). Nevertheless this could brig to arasitic trasversal currets. order to avoid it oe ca use a heavily doed buried layer with very low resistace that brigs the curret directly uder the collector, as it is show i Fig the same icture the -substrate is used i order to revet curret flow from adjacet trasistors i the same wafer; actually with the -ei it works as a so-called isolatio diode (two diodes arraged back to back). A more u to date omeclature for BJTs is the oe idicated i Fig (c) is called substrate trasistor ad is similar to the oe show i Fig (a) is similar to the oe i Fig ad is called vertical trasistor because the mai curret flow is i the u-dow directio. (b) is differet from both ad is kow as lateral: the mai flow is arallel to the surface (drive by the buried layer). The radiatio tolerace of the lateral trasistor is ot so good because of strog surface effects that will be discussed i ext hater. Ayway we ca easily uderstad that if the irradiatio acts maily o the surface, a device with ear-surface flow is more likely to be damaged tha oe with vertical flow. Figure 2. 16: laar eitaxial NPN trasistors: (1) is the mai curret flow ad (2) is the arasitic oe, reduced by the itroductio of the + buried layer. 9 The symbols + ad idicate a major or mior doig level. 27

16 hater 2 The Biolar Trasistor Figure 2. 17: Preset omeclature for trasistors. The last imrovemet to metio is cocered with the ohmic cotacts. Nowadays the Al cotact is ofte relaced with oe i Al/Polysilico, as Fig shows. This leads to faster devices ad elimiate a recombiatio curret at the Al/Si iterface, thus icreasig the gai ad the radiatio tolerace. Figure 2. 18: (a) Al cotacts o crystallie Si. (b) Polysilico emitter ad base. The Polysilico lies betwee the metallic cotact ad the Silico. Refereces [1] Lacaita, Samietro, ircuiti Elettroici, ittà Studi Edizioi 1997 [2] Emily, Total dose resose of Biolar Microcircuits, NSRE Short ourse 1996 [3] Beards, Aalog ad igital Electroics, Pretice Hall [4] Lari, Radiatio Effects i Semicoductor evices, Wiley