Jpn. J. Appl. Phys . Vol. 35 (199G) pp. 3845-3851 p.rl 1. No. 7. July 1996 A Comprehensive Study of High-Level Free-Carrier Injection in Bipolar Junction Transistors Y. YI,;E:, J. J. LIOU, A. OR.TIZ-CONDE I and F . GARCIA SANCHEZ I Depa"ment (II Elutriml and Comp"ter En,snsring , Univerrity (II Cenlf'lli Flond .. , Orl .. ndo, FL 3!!8J6, USA I Depa!'t .. mento de Eleclr6nic .. , Uniller,id..d S'mOn Bolivar, Coraeo. 1080. 1'. . Ver .. :: ....el.. { Recel\'(.od Seplclllbl!t 12, 1995; ILCcepted (or publi c ation April 10, 1996) Thi s paper presents a comprtlhensive study ou the eITecu of high· le vd. free-carrier' injection on the currenl UaDsport of bipolar junction transistors (BJTs). Detailed information fo r the free-carrier concentration , electric field. l1ud dri ft and dillusioll current components in the quasi.neutral base (QNB) under hi gb. l evel injection are calculated us ing the modified ambipolar transport equation aud using several difillteot apprc»ti.matioo5 for the majority·carrier current in the QNB , h is shown that high· le v el inj l:clion 1;1\1, cre:ate a large retarding field whicll is in tho: opposite of the built·in field the nonuni for m doping concentrat ioll. High-level injec tio:l abo enhanc es recombination in lhe QNB , thus resulting ill a pOlition.deptmdent mill ority-canier curreut in the re gion even if the bue is thin. Our result.s further suggest tuat the widely used zero cu.rrent gives tise to a larger error compared to other lesser known approximations, KEYWORDS; nmltonduttor device model i n, ; bipollr junction n lnsilJtort; hi,h·l ewl injection 1. Introduction Despi te the fact that· high-level inject ion of free carriers in the !emiconductor device is a long existing and widely known topic, such a mechanism has seldom been imple- mented properly in analytic device models. For example, in modeling the current transport in an advanced bipolar junction transistor (BJT) , it is conventionally assUlIlcd that tht' ma jorir.y-carriet current is absent throughout th e qu asi-neut ral base (QNB ). '-S) In addi tion . in ," " lAt in g t ile mlDority·carrier drift current, it is a COl practicr that only the built-in electric field associated with the nonuniform doping profile is considered. The effect of high-level injection is only accounted for in toe conventional model by modifying the carrier density at the edge of the space-charge region.' l will ot' shown in tbis study. these approaches fail to gi w an accurate description for the current transport in ad"a nceo n BJTs operating at high current levels, . The <t mbipolar transport equation (ATE), first devel· oped by Van Roosbroeek,T) is a useful tool to investi· gat e tht' moderate and high-level injection problems in semic on duc tor devices wi th uniform doping concentrtl- tions. B:uically. it is derived from t he el ectron and hol l' conrinuin' equations and th e co nditi on that charge in the quasi-neutral region even under the nO ll eoqu ili brium condition. For devices with nonuni· form doping profiles, such as the bipolar ju nction transis· tor. rht' ATE needs to be modified. T he solution to th(' mo dified .-\oTE requires numerical pro cedur es. unless it is sim p li fit' <"! using various approximationll sitch a ll low-lewel injen i oll :-.nd/or ?em electric field.- 1 papcr the high-level injcct ion charac· ter isti cs of B.JTs calculated numerically from the mod- ifi ed AT C. In particul ar , we investigi"lte the effccts of using diti('rent approximations for the majority-carrier currents in th e QNB. including the zero majority current used C'om'entionally, on the BJT model predictions under hi gb ·lc\"(' 1 in jection. A two-dimensional dcvicc simulatol c all(,(1 )'1[DlCI !o ' is also used t(J provid e the insight of ill thl' QXO . Results for the electric field, drift current, diffusion cWTent, and to- tal current in the QNB are presen ted and discussed, An accurate approach for modeling the collector current in- cluding high injection effect is aho suggested. 2, General Theory 8.Ild Ambipolar Tr8.llSpoft Equat ioD The basic semiconductor device equations are: 10 ) 8n (I) 8i = q \J J .. + G .. - R.. . : = - VJp +Gp -14 . J., = 91J..,n{ + qD" 'i7n, Jp = qJ.lpp{ - qD" 'i7p , _ V2V, = = (p-n+Nt - N;) , (I) (2) (3 ) (4) 15) where t he symbols have their usual meanings. For the quasi-neutral region, it can be assumed that charge neu· trality exists, and the space-charge density p in the region. is approximately zero. This is deri ved based on the us- sumpt ion tha t under the nonequilibrium condiiion, t he: net ch arge ill t.h e quasi. ne ut ral rep on is nol pe rturb ed notably beyond its equilibrium \'aiue. Let us focus on the quasi·nc utr al base (0:5 x $ we ) of an n+ / p/ n BJT. A Gaussian profile for the base doping concentrat ion NB is considered: N , (x ) = N. , ox p [- C :J I. 1 (0 ) where Non and /\ 'c are the peak base doping contentr .. · t ion and constnnt collcctor doping C'oncentration, respec· t ivel y. Because of the quasi-neutrality. the Poisson equation becomes redundant and Lln = Llp, dLln _ dLlp (i ) cb: - dz where .a n = n(x) - n o( x ) and at = p(x ) - Pu (x ) arc the excess electron and hole concentrations, respectively (llu = n? / I\'s alld Po = Nu are the equilibrium