1EE105 - Fall 2006Microelectronic Devices and CircuitsProf. Jan M. Rabaey (jan@eecs)Lecture 23: Bipolar Junction TransistorModels (Chapter 7)2Administrative Midterm results Lab 7 this week – no lab next week Homework 10 due; homework 11 posted tomorrow One more homework after that Schedule for the rest of the semester– Week 12: Bipolar Transistor – Large and Small signal Model– Week 13 (Thanksgiving week) – CE, CB and CC amplifiers– Week 14: Emitter degeneration – frequency response– Week 15: Some more advanced topics and recap23Midterm2 Total: 20 Mean: 16.25 Standard Deviation: 6.35 Median: 17.88 Max: 25.000246810120-1.52-3.54-5.56-7.58-9.510-11.512-13.514-15.516-17.518-19.520-21.522-23.524-254The semester so far (Midterm 1+2)024681012024681012141618 Total: 20 Mean: 11.92 Standard Deviation: 4.37 Median: 12.52 Max: 19.07B = +/- 1235Ideal BJT Structure NPN or PNP sandwich (Two back-to-back diodes) How does current flow? Base is very thin. A good BJT satisfies the followingBase (P)Collector (N)Emitter (N)CIBIEI−BEV+−CEV+−Base (N)Emitter (P)Collector (P)EIBICI−EBV+−ECV+−CEII≈−CBII>>BEqVkTCSIIe≈6Operations Modes47Collector Characteristics (IB)Forward ActiveRegion (Very High Output Resistance)Saturation Region (Low Output Resistance)Reverse Active(Bad Transistor)BreakdownLinear Increase8Base-Emitter Voltage ControlExponential IncreaseForward ActiveRegion (High Output Resistance)Reverse Active(Bad Transistor)Saturation Region (Low Output Resistance)~0.3VBreakdown59Forward Active OperationxEB CWBCarrier ConcentrationDepletionRegions0Wpe0pc0nb0nb(0)10611Diffusion Currents Minority carriers in base form a uniform diffusion current. Since emitter doping is higher, this current swamps out the current portion due to the minority carriers injected from base12Origin of αFBase-emitter junction: some reverse injection of holes into the emitter Æ base current isn’t zero E B C Typical:Some electrons lost due to recombination.99Fα≈100Fβ≈713Current ComponentsxEBCICIEIB12 3electronsholes14BJT CurrentsCFEIIα=−Collector current is nearly identical to the (magnitude)of the emitter current … defineKCL: ECBIII−= +DC Current Gain:()CFE F B CIIIIαα=− = +1FCBFBFIIIαβα==−.999Fα=.9999991 .001FFFαβα===−815Collector CurrentDiffusion of electrons across base results in0BEqVpnpBdiffkTnnBdn qD nJqD edx W⎛⎞==⎜⎟⎝⎠BEqVkTCSIIe=0npB ESBqDn AIW⎛⎞=⎜⎟⎝⎠16Base CurrentDiffusion of holes across emitter results in01BEqVpnEdiffnEkTppEqD pdpJqD edx W⎛⎞⎛⎞=− = −⎜⎟⎜⎟⎝⎠⎝⎠01BEqVpnE EkTBEqD p AIeW⎛⎞⎛⎞=−⎜⎟⎜⎟⎝⎠⎝⎠917Current Gain00npBoEpBBCnEFpnEoEBpnEBEqD n AnWIDWqD p AIDpWWβ⎛⎞⎜⎟⎛⎞⎛⎞⎛⎞⎝⎠== =⎜⎟⎜⎟⎜⎟⎜⎟⎛⎞⎝⎠⎝⎠⎝⎠⎜⎟⎝⎠20,,20,,ipBABDEinEABDEnnNNnpNN⎛⎞==⎜⎟⎝⎠Minimize base widthMaximize doping in emitter18Large Signal Model xEBCWBCarrier Concentration0Wpe0nb0nb(0)pc0nb(W)xEBCWBCarrier Concentration0Wpe0nb0nb(0)pc0QSQAnb(W)xEBCWBCarrier Concentration0Wpe0nb0nb(0)pc0nb(W)xEB CWBCarrier ConcentrationDepletionRegions0Wpe0pc0nb0nb(0)Reverse ActiveForward ActiveSaturated Cutoff1019Ebers-Moll Equivalent CircuitWrite emitter and collector currents in termsof internal currents at two junctionsBuilding blocks: diodes and I-controlled I sources20Ebers-Moll EquationsDerivation: Write emitter and collector currents in termsof internal currents at two junctions()()//11BE th BC thVV VVEES RCSIIe Ieα=− − + −()()//11BE th BC thVV VVCFES CSIIe Ieα=−−−FES R CSIIαα=1121Forward Active RegionB-C junction is not forward-biased Æ IRis very smallTypical Values:0.7BEV =0.2CEV >22Simplified Ebers-MollForward-Active Case:Saturation: both diodes are forward-biases Æ batteries0.7BEV =CFBIIβ=BIBCECI0.7BEV =BIBCE0.1CEV =CI1223The Early EffectForward-activeSaturationVAVCEICVBE3VBE2VBE1Current in Forward-Active a Function impacted by VCEMain reason: Base-width modulationHence:/(1)BE thvVCS CEAiIe v V=+24Small-Signal ModelsAnalogy from MOSFET s.s. model:()BSDSGSDvvvfi ,,=()CEBECvvfi ,=1325Transconductance gm The transconductance is analogous to diode conductance26Transconductance (cont) Forward-active large-signal current:/(1 )BE thvVCS CEAiIe v V=+• Differentiating and evaluating at Q = (VBE, VCE )/(1 )BEqV kTCSCE ABEQdiqIeVVdv kT=+CCmBEQdiqIgdvkT==1427Comparison with MOSFET Typical bias point: drain/coll. current = 100 μA;Select (W/L) = 8/1, μnCox= 100 μA/V2 BJT: MOSFET:100μ4mS25mCmthIgV== =2DmGSTIgVV=−CCmthqIIgkTV==22 2 100μ 8 100μ 400μDmoxDGS TIWgCISVV Lμ== =×××=−28BJT Base CurrentsUnlike MOSFET, there is a DC current into thebase terminal of a bipolar transistor:()/(1 )BEqV kTBCF SF CEthIIIe VVββ== +To find the change in base current due to changein base-emitter voltage:1BBCmBE C BEQQQiiigvivβ∂∂∂==∂∂∂1529Small Signal Current GainCFBiiββΔ==Δ30Input Resistance rπ()11CmBBE BEQQigirvvπββ−∂∂== =∂∂In practice, the DC current gain βFand the small-signalcurrent gain βoare both highly variable (+/- 25%)Typical bias point: DC collector current = 100 μA1631Output Resistance roWhy does current increase slightly with increasing vCE?Model: introduce the Early voltage)1(/ACEVvSCVveIithBE+=Base (p)Emitter (n+)Collector (n)BW32Graphical Interpretation of roslope~1/roslope1733BJT Small-Signal
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