Microelectronic Devices and Circuits
Microelectronic Devices and Circuits EL ENG 105
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This 19 page Class Notes was uploaded by Kris Heathcote on Thursday October 22, 2015. The Class Notes belongs to EL ENG 105 at University of California - Berkeley taught by Staff in Fall. Since its upload, it has received 41 views. For similar materials see /class/226760/el-eng-105-university-of-california-berkeley in Electrical Engineering at University of California - Berkeley.
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Date Created: 10/22/15
Lecture 21 BJTs Bipolar Junction Transistors Prof I S Smith mm muss Context Tn Monday s lecture we discussed minority injection in forward biased PN junctions Today we will discuss three terminal devices which use this effect for amplification called a B39ITs Bipolar Iunction Transistors mmm m EEES PMJ 5 5m Reading Today7s lecture will covering chapter 7 Bipolar Iunction Transistors BIT s Next we will start looking at amplifiers chapter 8 in the text mum m ms Unwergmatcaltuvma New F39MJ 5 5mm ecture Outline mam ch Review of minority current injection in PN Diode The BIT 7 1 BIT Physics 72 BIT EbersMoll Equations 73 BIT SmallSignal Model Unmmvcmm Beuelm muss PN diode Recornblnatlon 3 9 o As you increase the forward bias on a PN junction the banier keeping the holes from diffusing into the N side and keeping the electrons from diffusing to the P side is reduced o As the barrier height decreases the diffusion of carriers ross the barrier increases exponentially DevadmeMatEEES erwltn energy below barnerhelgnt Unwevsrtv etc Warm BeMElw PMJSSMM g diagram forward bias The numberof Electrons the denslty oreleelrons here l5 determlned by at ene g r y over here deterrnlnes the number otholes over here The number orho e5 overnere at tnls energy Forward bias 9 reduced barrier height so more minority carriers on both sides Depanmemavzzcs Unwevsm mca Warm BeMElw s gt Increased populatlon II o 39 39 The minority carrier concentrations at the edges of the depletion region will be given by pquot x xquot NAe qlt B VDgtquotT npx n P NDe qWB VDVkT l ote NA ande are the majority canier concentmtions on the other side of the junction with the assumption thatpn ltlt NL7 and n ltlt so note This neglects net recombination inside the depletion region DevadmenimEEES Unmnmmn New F39MJ 5 Mn 39 uasiNeutrality o Since the regions outside the depletion regions are going to be very close to electrically neutral called quasineutrality the number of maj ority carriers will increase slightly as well slightly because there are usually many more majority carriers than minority carriers anyway amer m N concentratlons Mlnonty camera dlstance hammersch Unwersmatcaltumla BeMElm ssp sioisspimm Mitzi 5565 105 sviinwu uaiiszi PMJSSMM Diffuse and Recombine o Once the minority carriers have been injected across the depletion region they will diffuse and they will recombine o They will recombine because now 17 gt quotZ and since recombination is proportional to pn it will now cause carriers to recombine at a rate faster than they are generated They will also diffuse into the other side because there are more of them the minority carriers at the edge of the depletion region than there are further in Depanmmmzzcs inweisnymcami Bemeim PMJSSMM Excess iniected minority carriers ping quot p side 11 side v n 2 L X px1gtnpn2quot 1 E Minority Carrier p Diffusion Length 39Wp 39Xp X W Once the minority carriers are inj ected into the other side of the 39unction the minority carrier concentration in the bulk region for forward bias is a decaying exponential Depanmemavzzcs Unwriswcami Bemelm secs 195 spiiiwmu usiiiszi Ambipolar diffusion o The diffusion constant for minority carriers is complicated by the fact that the minority carriers are dragged on or pulled by the majority carriers in a mechanism called ambipolar diffusion o There is a small E eld which keeps the excess holes and electrons together The ambipolar diffusion constant for minority carriers comes out to be the diffusion constant for the other mgr39ori39ty carriers in the cases Where the majority carriers greatly outnumber the minority carriers In other Words minority holes diffuse With DH and electrons with By o The minority diffusion length is a function of the ambipolar diffusion constant for the minority carriers as Well as the variability in the lifetime etc We will just take it to be a number mmmmzzcs UnwerSmatcaitnima Bemeim F39MJ s 5mm SteadyState Concentrations L 3 gtgtWnp ln Silicon it is easy for the diffusion length 39 much longer than the distance to the contacm if none of the diffusing holes and electrons recombine until they get to the contacm9 get a linear concentration gradient ping quot p side 11 side The upiiiaiiuii is assumed iiaps detects iiisis pin Depanmenmzzcs UnwerSmatcaitnima Bemeim seasweme Letitia Diode Current Densities F39MJ 55mm F39MJ 5 5m 1 IE k P W in VEB 7 7 7 dx x WP 7 2 llll VEC npn7 15 I Ennim lHl ullw in il t 1 e Underthis linear approximation We can ca ulate the current due to the holes diffusing ll ilo the N aide arid the electrons diffusing ll ilo the P Slde Notice that We are L15ng the electron diffusion constant forthe minority holes 0 A BJT transistor consists of a pair of diodes which d W W Nome that the owem have their junctions very close together so that the 1 qu due to the meted minority currents from onejunction go through the thin ix Minority carriers on middle layer to the otherJunction Ea h Sid are not equal M Lip But are propomona 0 They are called PNP or NPN transistors by the layers JP qu d To the carrier they are made up of X concentrations WWW Deva mentmEEES Unwersmatcaltwima Bemelm 5565 105 apt39na L vtuiizi PM 5 5n M 50 195 apnngm mnezi Bipolar Junction Transistor BJT Currents in a BJT F39MJ 5 5m o A BIT is physicallyjust two back to back PN diodes with three contacm but the current between the emitter and the collector is a minority carrier current in the base o Usually a B T is operated in a mode where one of the junctions is forward biased and the other is reverse biased oTh b39ddidquotmquot 39 o Essentially a forward biased diode is used to create te Everidllasle 0 e mlec mmonty Gamers a minori y current most of which then goes all the m 0 He m1 6 ller way across to the depletion region of another 0 The mmOr 1ty CaITIerS are then swept through the reverse biased diode The geometry can be such that almost all the current goes across to the second diode so that the controlling electrode doesn t have to supply much ofthe current maybe 1100 to 1400 reversed biased junction DevanmemavEEcs Unneisweanmn may DevanmentmEEES Unwersmatcaltwima Bemelm Currents in the BJT A BJT is ordinarily designed so that the minority carrier injection into the base is far larger than the minority carrier injection into the emitter It is also ordinarily designed such that almost all the minority carriers injected into the base make it lt he way across to the collector Band edge gram The band edge diagram for an N39PN transistor in operation P Lightly doped heavily doped cementum vnmrri Current controlled So the current is determined by the minority current ross the emitterbase junction g Icszjeu But since the majority ofthe minority current goes right through the base to the collector Ic s 71 And so the amount of cunent that must be supplied b the base is small compared to the cunent controlled mandarin Actual BJT Cross Sec Ic gtgt I tt39 wrtsillcon contact A u c nvld uxld tt nned layFL tctv cmutetteuicu mural mnlclc base 3 39 a n a sit some liuttittncnptt tttttsutotl melal mnmnl la wlleclqr DWpe sumate Vertical npn sandwlch pnp is usually a lateral structure n buried layout is a low resistance cont 5 i dlffuslon a aedeh nd base dlffuslon act lo collector determined by Vemcal distance between emitter PMJSSMM BJT Layout emitter edge of 6 buried layer n emitter areal AE intrinsic npn transistor mnemor o Emitter area most important layout parameter o Multi nger device also possible for reduced base resistance Deva mentatEEES Unmmmmm Beikelev PMJSSMM chematic Symbol The arrow on the symbol shows the controlling diode o Collector current is control by base currentlinearly a typical Value would be 100 because only one in 100 electrons would stop in the base instead ofrnaking it across to the co e o o Collector is controlled by baseemitter Voltage exponentially mmmmzzcs Unwersmatca mma Berkeley s 1 le NPN BJT model NJ 55m o A simple model for a NPN BJT pewtth ms Unmmmmm smiley NJ 55mm llector Characteristic 0 Ground emitter 0 Fix VCE 0 Drive base with fixed current IB 0 Measure the collector current mmth ms 39c 39cl39ar VCE VCE Unwersilyvvcaltamia Bemeley Th operating modes Forward active 7 EmitterBase forward biased 7 BaseColleetorreversebiased Satur ion e Both Juneuens are forward biased Reverse active e minerBase reverse biased e BaseColleetorforwardbiased e Transistor operaan is poor in this direction because is low lighter doping ofthe layer designedto be the collectormeans LhaLLhere is a lot ofminonty carrier injection out ofthe Base s s a r Characterlstlcs I5 39 M 3m Saiuvaimnw 39939quot Breakduwn Luw Ompm Resrsiarree 139quot serumqu 39n39 5 v m Lineavincvease Reverse Acme nquot M puuvTvans Fuvwavd Acme R egmn Very Hrgrr Output Resrs1anee R e Mk Xue Minnnly earners m base farm a unifnrm difqu duping r s raga rrarmmy camers injeded nm base is SaiuvaimnR egmn M lav W Output aesrsrarew Q r verse Acme rappyrransrsmr we am Er Itter Voltage Control Eveakduwn m umnunn w M Normd mm Expunemrai increase FurwavdAeiive Regmn Hrgr Output Resrs1anee us on Currents quotqu Draw blse wlloaor XEE I ma v6 0 x inn current Since emitter this current swamps nunhe current pnmnn due re nae 9M1 55m BJT Cu rrents Collector current is nearly identical to the magnitude of the emitter current define 570ng aF999 Kirchhoff 71E IC 15 DC Current Gain 10 iaFIE aFIB Ic a 10 1 1 1 DtF 5 F 17 001 Depanmemmzzcs mum m W New muss Origin of IF Baseemitterjunction some reverse injection of holes into the emitter 9 base current isn t zero Some electrons lost due to m l alo Typical aF m 99 F 100 Depanmmavzzcs magma quotm Bemelw mmmmms mam ch 5911 5 m o llector Current Diffusion of electrons across base resulm in V qD an 22250 n W W5 7 ananOAE IS 7 T 5 IC ISe 1 Unwergmatcaltuvma New 5911 5 5m Base Current In silicon recombination of carriers in the base can usually be neglected so the base current is mostly due to minority injection into the emitter Diffusion of holes across emitter results in 01 qD anO Wquot diff 7 n 7 JP qDP E P e kT 1 V52 18 quanOAE eqkT 71 WE Unwergmatcaltuvma Beuelm Current Gain qD mi 14 W F 1 4DpngA D pm W Mmsz base mm Maximize duping in 2mm rsMoll Equations measure EM parameters Exp Derivation Write emitter and collector currents in terms internal currents at two junc ions 1 7le emm 70 axldemm 1 1c arr emV 7171 eVlt VM 71 pl axle 0quot Equivalent Circuit ilding blocks diodes and I controlled 1 sources cl w cmm I I uV 4V391 I ule Lecture 21 BJTs Bipolar Junction Transistors Prof I S Smith mm muss Context In Friday s lecture we discussedBITs Bipolar Iunction Transistors Today we will find large signal models for the bipolar junction transistor and start exploring how to use transistors to make amplifiers and other analog devices mmm m EEES PMJ 5 5m Reading Today7s lecture will finish chapter 7 Bipolar Iunction Transistors BIT s Then we will start looking at amplifiers chapter 8 in the text mmmmms Unmmmmm New F39MJ 5 5mm ecture Outline BIT Physics 72 o BIT EbersMoll Equations 73 o BIT LargeSignal Models o BIT SmallSignal Models Next Circuits mam ch ummmmm Beuelm Stunnedan Currents in the BJT A BJT is ordinarily designed so that the minority carrier injection into the base is far larger than the minority carrier injection into the emitter It is also ordinarily designed such that almost all the minority carriers injected into the base make it it r he way across to the collecto Current controlled So the cunent is determined by the minority current across the emitterbase junction EVJ Ic s Ije quot But since the majority ofthe minority current goes right through the base to the collector Ic s 71 And so the amount of current that must be supplied by the base is small compared to the current controlled Ic gtgt I am ma nr mi nun is E m31miumsu BJT operating modes Forward active e EmitterrBase forward biased e BaserCollecLorrevasebiased Saturation e BoLh junctions are forward biased Reverse active 7 EmitterrBase reverse biased e BaseCollectorforwardbiased e Transistor operation is poor in this direction becauseb is low lighter doping othe layer designed to be the collector means thatthere is a lot ofminority carrier injection out othe Base collector Characteristics I3 i liAl l25iia and Saiuvailunm 2quot Eveakduwn Luw Output Peslsian 1 issiumiun n a l 5 M in Lineailneiease ReyeiseAetne iiiia puuvTYanSiStm in ijrsaim e VCHV39 FurwavdAciwe R eglun Veiy High Output Resistance The origin of current gain in BJT s The majority ofthe minority carriers lnjected from the emitter go across the base to the collector and are swept out by the electric fleld in the depletion region othe collectorr base Junction The base contact doem thave to supply that current to maintain the voltage othe baseiLhe voltage which is causing the current in the flrsi place entwhich does have to be supplied by the base Contact Comes from two mam sources Reeumhinatiun in the base En utten negleet in silieun lnieetiun erminunty camars intu the emitter Ifwe find the ratio othe cunent to the currentthat mustbe supplied by the base thatwlll give us the current gain to eggaeainaulieeinaz mumquot Diffusion Currents Mix umlx i warm Loiiuim wh The minority carriers injected into the base have a concentration gradient and thus a current since emitter do ing is higher this cu m ity m the base w the emltta Thls ls the source current gain as 312 mm empean new worm Diffusion Revisited Why is minonty currentprofile a linear functlor The diffusion cunent is proportional to the gadlmtxd ffus on constant since cunent is constantagradlent is constant Note that diffusion current density is controlled by Width of region base WidLh forBJT Dehslty hele tlled by putehtlal lhleetluh utealllels H ls pmpumunai in the number n maluvliy camevs ml The uthel slde utthe baiiiEi and ls EXpDnEMlainih the luweled halllel helliht 0quot hsliy aiihe enhiaei is H quot equai tn the enulllhllum 0 4 90 vaiue strung GR tea m4 E madmium51 worm BJT Currents Collector cunent is nearly identical to the magnitude ofthe emitter current de ne 1C eoFIE e 999 Kirchhoff r EICIE DC Current Gain 1c 0 p15 O F151c op o 999 I F 999 17097 E FIE BF 1709 001 9M1 55m Origin of IF Baseemitter junction some reverse injection of holes into the emitter 9 base current isn t zero Some electrons lost due to mbmallo In silicon can usually be neglected so the base current is mostly due to minority injection into the emitter 5911 5 5m Base Current recombination of carriers in the base of holes across emitter resulm in qu page 71 WE e fl We 8 kT d1 4D WE qu Pm 0 A WE q Va kT Unwergmatcaltuvma New 5911 5 5m Current Gain Depanmmavzzcs magma quotm emu mmmm Eats E B D1ffus1on diff 7 JP 7 13 Typical aF m 99 F 100 mummies mm m Mn WWW Em j o llector Current Diffusion of electrons across base resulm in 10 t I V E Jd ff qD dnp Dnnp o 9 quot quot dx W5 1 DnnFBDAE S WE Mr I C I Se 1 ananoAE in Down qupmAE Dy Pm WE WE MH Hmlze base Wldth i quot1250h Nor Pm i2 NM NM Maximize doping in emitter Unwergmatcaltuvma Beuelm le NPN BJT model A simple model for aNPN BJT 29139s 0 C l rsMoll Equations Ex 6 measure EM parameters Derivation Write emitter and collector currents in terms 0 fintemal currents at two junctions I 7146me 1 axldemm 1 1c 5amp1 emM7071 emVA 1 pl axle 0quot Equivalent Circuit c 1 i made cmmr I I uVK V39l IR lcslquNIJ l owl m m J x W l sitic capacitances To model devices adequately at high frequencies we need to account for the charge that we must move in or out ofthe devices In the PET this is clearly a capacitance but in a BJT the majority ofthe stored charge is in the form ofminority carriers which are diffusing across the device in forward operation but aren t there when the transistor is not conducting so obviously they must be extracted or allowed to diffuse away This stored charge can be modeled as a capacitance in small signal models i sion Capacitance ansconductance gm The total minority carrier charge for a onesided 1e t junction isareaoftriang b 1 1 w QWWA EbhrqA 3Wixwpxnpne inn tc 0 Sum Foraonesided junction he current is dominated a Q by theserninoritycarriers W Tm AD 7 1 q w t M W a N 92 on UDV E us D 9 W in Cuns am The transconductance is analogous to diode conductance WWW We rummage imam min t ntt 39 a n Capacitance cont conductance cont The proportionality constanthas units oftime Forwamwive mg sigml cmem 51 Q Wadi nfCSSESLESS TY ic Isewlt1vaVigt 2 Dtmlstun Cnsmctsnt a have means quiescent q Wprka M b pointnntchatge r o W 7 Twpmmkr ti leferentlanng and evaluatlng at Q V55 VCE the physical interpretation is that this is the ranszt Bic 1152mm 1 VCE WA time for the minority carriers to cross the ptype WEE g kT region Since the capacitance is related to charge Q n g as r i d 0v kT BE 5 I39c f VBEgtVCE ICAiC fVBEAvBEVCE A scent Point bias a 6 QVBEgtVCE3915 vaz t V52 m 9 CE 9 transconduclance variations in currents and voltages DepavwentaVEEES T Base Curren base terminal of a bipolar transistor To find the change in base current due in baseemitter voltage v 61395 In 6V5 9 6V5 7 gm 11 Vim F 7 61 7 are Q DepavwemavEEES 1c fVBEwaVoE m MJssmm ll otation Review Large signal VCE small signal DC bias small signal less messy Output conductance Remember the point of a small signal model is to produce a set of equations which relate the small to each other linearly gt and to create a linear equivalent circuit Universwymca mma may MJssmm ts Unlike a MOSFET there is a DC current into the 15 IC F IS Fqu kr1VCEVA to change are 1 g m 9 av 13F UniversWaVEa mm mm pm ssm mg lms I 13M 15 Is HA gtVcE V Since currenw are linearly related the derivative is a constant small signal large sign r mmmmms WWWmam Bevkelm pm ssm I ljm o ut Resistance r1T r 71761 frag 7gm avBEQ 1 avg 1 Hi gm o In practice the DC current gain 5 and the smallsignal current gain g are both highly variable 25 o Typical bias point DC collector current 100 uA r room ZSkQ lrnA R OOQ MOSFET mmmmms Unmwcmm Bevkelw put Resistance ro Why does current increase slightly with increasing VCE Answer Base wldth modulatlon similar to CLM forMOS Model Math lsa mess so introduce the Early voltage 1 ISEVBE WM 1VCEVA al Interpretation of r0 1 slupelm 1 nit w as quotth mmmees mom We mallSignal Model arasitic Capacitors Emitterbase is aforward biasedjunction 9 depletion capacitance C1 1 45mm Collectorbase is areverse biasedjunction 9 depletion capacltance Due to minority charge injection into base We have to account for the di usion capacitance as Well C sg T Cross Section SmallSignal Model Reverse biaseeiuneiiene r RealR Esistance twig n gamma eamei has noise Inn emmer mum mute eomaei a men tintmnpninm xternal Parasltlc Core transistor is the vertical region under the emitterc nt t minor Everything else is parasitic or unwanted External Pavasmcs Lateral BJT structure is also possib Circuits ore BJT Model Ll Reverse eiaeeeiunetien Ease T Culleduv Fieiienai Reeisianee nu noise eveiee biaeeeiunetien amp Dimisiem Capacitance EM When the inventors ofthe bipolar transistor rst got aworking device the rst thing they did was to build an audio ampli er to prove that the transistor was actually Working eture We can model most ofthe 1th the above oiiouit For low frequencies we can forgetthe capacitors Capacitors are nanelmearl MOS gate amp overlap caps are linear Given an ideal BJT stru action w ircuit An MOS Amplifier rmu s ana Supp y F aH V vamn V a 11 0mm swgna lI I WWW m
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