RQURMNS FOR FFCN RANSSOR OPRAON r 1. AN so that the fudametal basis of trasistor atio, that of a urret otrolled by a small voltage flowig aross a large resistor to geerate a large voltage is maitaied. G R i his is ot true beause, a. mitter jetio effiiey, α. is omosed to two urret omoets, ad. is desirable beause it is the omoet that ijets miority arriers ito the -C jutio ad emerges as. is the eletro urret ijeted ito the emitter from the base. his is a arasiti urret as it does ot otribute to olletor urret,. herefore we defie a figure of merit (whih we will alulate shortly) alled MR NJCON FFCNCY, α, where α + he maximum (ad desirable value of α is 1 ad is ahieved whe 0. b. AS RANSPOR FACOR, α Of the hole flux emitted from the emitter, a ertai fratio is lost due to reombiatio i the -tye base. However, if the width of the eutral base, is made muh smaller tha the average distae a miority arrier travels before reombiig,, the the robability of reombiatio is redued. R out x 0 w x w << 55
So what does the harge rofile i the base regio look like? US H CONNUY QUAON. the absee of eletri field this redues to the diffusio equatio d D Net reombiatio 0 if << dx Use a oordiate system show i the figure above where the eutral base ommees at x 0 ad eds @ x. he solutio of d d ( x) x D 0 is the same as D 0 ad is 1 dx dx. his is a liear derease i the harge rofile with boudary oditios that @ x 0 is. herefore the harge rofile i the biolar trasistor a be itured as x ( x ) e 0 0 x 0 x 0 x 0 x ( x) 1 C x ( x ) 0 1 e he saliet features are (i) A exoetial dro-off i the ijeted miority rofile as the emitter thikess is muh larger tha a diffusio legth for eletros x ( x ) e [like a ovetioal diode] (ii) A liear derease i the miority (hole oetratio i the base x ( x) 1 w beause we egleted reombiatio. (iii) A traditioal derease i the miority arrier oetratio ( x) i the olletor as x determied by reverse biased oditios ( x ) 0 1 e NO CAN CACUA A H CURRNS CAUS KNO H CHARG PROFS. Reall that we wat whih requires α 1 ad α 1. geeral the urret gai α is defied as α α α ad α AN α 1 56
CACUANG α ( A 1m ) 1 α + N N 1 + d d qd x 0 : N qd x 0 dx dx qd : qd qvbe qvbe 0 k k OR qd e 1 : qd 0 e 1 D 0 D 0 Usig the aw of Mass Atio i i 0 & 0 NA ND where N & N D A Aetor oetratio i the -tye emitter Door oetratio i the base D A For α 1 we eed 0 D N D N Also e Need << 1 α r r for α 1 NA >> 1 ND Calulatig AS RANSPOR FACOR, α. olleted hole urret α ijeted hole urret where is the hole urret lost due to reombiatio i the base. 57
e assumed for alulatig the hole rofile i the base the reombiatio was zero. his gave us a liear rofile. atuality, the fiite (through very small) reombiatio that does our (as << 1 but ot 0) auses the hole rofile to sag as show below beause holes are lost to reombiatio. ( x) No reombiatio ith reombiatio Differee is beause of holes lost to reombiatio C ottom lie: the loss of holes erturbs the rofile a bit but it is essetially liear therefore validatig our assumtio. Or Negletig reombiatio is fie to alulate the olletor urret as the sloe of the rofile (whih determies ) is ot erturbed substatially. i.e. qd ut to alulate r we have to aout for reombiatio. his is doe elegatly usig harge otrol aalysis. the reombiatio urret arises from the re-suly of eletros i the base lost to, r reombiatio with the holes. he rate at whih holes reombie is give by Q τ. ase here Qis the stored harge of holes i the base ad τ is the lifetime of the miority holes. Qa be alulated as Q 1 Q Area of the harge triagle 58
qv Q 1 be k r 0 e 1 τ τ e ow defie urret gai, β, to be δ 1) gives us β r. ut + β r qd 1 β qd τ Dτ β β as Dτ for δ 1 he relatioshi betwee β ad α β COMMON-MR CURRN GAN α COMMON-AS CURRN GAN egletig (by roerly desigig C V out Vi i out R β COMMON-AS V ut voltage betwee mitter ad ase i V Outut voltage measured betwee Colletor ad ase out AS is the ommo termial ; α i out Note: α α δ f δ 1 the α α V i i R C out V out Commo mitter Cofiguratio Here V is alied betwee the base ad emitter ad the i outut voltage measured betwee olletor ad emitter. he emitter is the ommo termial. he iut urret, ad the outut urret, i out out β i 59
geeral (Kirhoff's aw) usig & 1 1 1 α OR β yially: β>10, α>0.9 1 α herefore if δ 1 the sie α 1+ as 0 α 1 + α α we get from β, α α 1 + 1 as exeted beause reombiatio 0 SUMMARY DSGNNG GOOD POAR RANSSORS N A δ 1 >> 1 N D << 1 α << 1 1 DCRAS H AS HCKNSS, NCRAS H AS MNORY CARRR FM, NCRAS MR DOPNG. 60