6.012 Spring 2007Lecture 181Lecture 18The Bipolar Junction Transistor (II)Regimes of OperationOutline• Regimes of operation• Large-signal equivalent circuit model• Output characteristicsReading Assignment:Howe and Sodini; Chapter 7, Sections 7.3, 7.4 & 7.5Announcement:Quiz #2: April 25, 7:30-9:30 PM at Walker. Calculator Required. Open book.6.012 Spring 2007Lecture 1821. BJT: Regions of Operation• Forward active: device has high voltage gain and high β; • Reverse active: poor β; not useful;• Cut-off: negligible current: nearly an open circuit; • Saturation: device is flooded with minority carriers;– ⇒ takes time to get out of saturationsaturationreversecut-offforwardactiveVBCVBCVCEVBEVBEBCE+-+-+-6.012 Spring 2007Lecture 183Forward-Active Regime: VBE> 0, VBC<0n-Emitterp-Basen-CollectorIE<0IB>0IC>0VBE > 0VBC < 0Minority Carrier profiles (not to scale):npBpnEpnCnpBopnEopnCo0WB-XBEWB+XBC-WE-XBEWB+XBC+WCxemitter basecollector6.012 Spring 2007Lecture 184Forward-Active Regime: VBE> 0, VBC< 0• Emitter injects electrons into base, collector extracts (collects) electrons from base:IC= ISeVBEVth[]; IS=qAEnpBoDnWB• Base injects holes into emitter, holes recombine at emitter contact:IB=ISβFeVBEVth[]− 1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ;ISβF=qAEpnEoDpWE• Emitter current:IE=−IC− IB=−ISeVBEVth[]−ISβFeVBEVth[]−1⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ • State-of-the-art IC BJT’s today: IS≈ 0.1 - 1 fA• βF≈ 50 - 300.• βFhard to control tightly: ⇒ circuit design techniques required to be insensitive to variations in βF.βF=ICIB=npBo•DnWBpnEo•DpWE=NdEDnWENaBDpWB6.012 Spring 2007Lecture 185Reverse-Active Regime: VBE< 0, VBC> 0Minority Carrier Profiles (not to scale):n-Emitterp-Basen-CollectorIE>0IB>0IC<0VBE < 0VBC > 0npBpnEpnCnpBopnEopnCo0WB-XBEWB+XBC-WE-XBEWB+XBC+WCxemitter basecollector6.012 Spring 2007Lecture 186Reverse-Active Regime: VBE< 0, VBC> 0• Collector injects electrons into base, emitter extracts (collects) electrons from base:IE= ISeVBCVth[]; IS=qACnpBoDnWB• Base injects holes into collector, holes recombine at collector contact and buried layer:IB=ISβReVBCVth()−1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ;ISβR=qACpnCoDpWC• Collector current:IC=−IE− IB=−ISeVBCVth[]−ISβReVBCVth[]−1⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ • Typically, βR≈ 0.1 - 5 << βF.βR=IEIB=npBo•DnWBpnCo•DpWC=NdCDnWCNaBDpWB6.012 Spring 2007Lecture 187Cut-Off Regime: VBE< 0, VBC< 0Minority Carrier Profiles (not to scale):n-Emitterp-Basen-CollectorIE>0IB<0IC>0VBE < 0VBC < 0npBpnEpnCnpBopnEopnCo0WB-XBEWB+XBC-WE-XBEWB+XBC+WCxemitter basecollector6.012 Spring 2007Lecture 188Cut-Off Regime: VBE< 0, VBC< 0• Base extracts holes from emitter:IB1=−ISβF=−IE• Base extracts holes from collector:IB2=−ISβR=−IC• These are tiny leakage currents (≈10-15A).6.012 Spring 2007Lecture 189Saturation Regime: VBE> 0, VBC> 0Minority Carrier profiles (not to scale):n-Emitterp-Basen-CollectorIEIB<0ICVBE > 0VBC > 0npBpnEpnCnpBopnEopnCo0WB-XBEWB+XBC-WE-XBEWB+XBC+WCxemitter basecollector6.012 Spring 2007Lecture 1810Saturation Regime: VBE> 0, VBC> 0Saturation is superposition of forward active + reverse active:IC= ISeVBEVth[]− eVBCVth[]⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ −ISβReVBCVth[]− 1⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ IB=ISβFeVBEVth[]− 1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ +ISβReVBCVth[]− 1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ IE=−ISeVBEVth[]− eVBCVth[]⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ −ISβFeVBEVth[]−1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ •ICand IEcan have either sign, depending on relative magnitudes of VBEand VBCand βFand βR.6.012 Spring 2007Lecture 1811Saturation - The Flux Picture• Both junctions are injecting and collecting.• Electrons injected from emitter into base are collected by the collector as in Forward Active case.• Electrons injected from collector into the base are collected by the emitter as in Reverse Active case.• Holes injected into emitter recombine at ohmic contact as in Forward Active case.• Holes injected into collector recombine with electrons in the n+buried layer;;majority hole flux from base contact n+ buried layern-type collector p-type base n+emitter n+ polysiliconhole diffusion fluxmajority electron flux from collector contactto recombine with hole diffusion fluxmajority electron flux from collectorcontact supplying injection into base minority hole diffusion flux;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;majority electron fluxto collector contact electron diffusion majorityelectrons6.012 Spring 2007Lecture 18122. Large-signal equivalent circuit modelEquivalent-circuit model representation (non-linear hybrid-πmodel) [particular rendition of Ebers-Moll model in text]:System of equations that describes BJT operation:Three parameters in this model: IS, βF, and βR.IC= ISeVBEVth[]− eVBCVth[]⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ −ISβReVBCVth[]− 1⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ IB=ISβFeVBEVth[]− 1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ +ISβReVBCVth[]− 1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ IE=−ISeVBEVth[]− eVBCVth[]⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ −ISβFeVBEVth[]−1⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ BCEIBIRIFIS/βRIS/βFIEICβFIF - βRIR=IS[exp(qVBE/kT) - exp(qVBC/kT)]+-+-VBEVBC6.012 Spring 2007Lecture 1813Simplification of equivalent circuit model:• Reverse-active regime: VBE< 0, VBC> 0• Forward-active regime: VBE> 0, VBC< 0For today’s technology: VBE,on≈ 0.7 V. IBdepends on outside circuit.For today’s technology: VBC,on≈ 0.6 V BCEBCEVBE,onBCEEBCVBC,onISeVBEVth[]ISeVBCVth[]6.012 Spring 2007Lecture 1814Simplification of equivalent circuit model:• Cut-off regime: VBE< 0, VBC< 0• Saturation regime: VBE> 0, VBC> 0For today’s technology: VCE,sat≈ 0.1 V. ICand IBdepend on outside circuit.Only negligible leakage currents. BCEBCEVBE,onVBE,onVCE,satVBC,onVBC,onBCE+-BCE6.012 Spring 2007Lecture 18153. Output CharacteristicsCommon-emitter output characteristics:VCE=VCB+VBEVCE,satICIBIB=0006.012 Spring 2007Lecture 1816Common-Emitter Output Characteristics6.012 Spring 2007Lecture 1817What did we learn today?Summary of Key Concepts• Forward-active regime: For bias calculations:• Saturation Regime: For bias calculations:• Cut-off Regime: For bias
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