EECS130 Integrated Circuit DevicesAnnouncementsSlide Number 3Slide Number 4Qualitative Solution - DefinitionsEmitter Region FormulationBase Region FormulationCollector Region FormulationCurrent FormulationEmitter Region SolutionCollector Region SolutionBase Region SolutionBase Region Solution (cont’d)Base Region Solution (cont’d)Terminal CurrentsSimplificationSimplified AnalysisQuestion:Performance ParametersBase width modulationBase-Width ModulationBase-Width Modulation by Collector VoltageBase-Width Modulation by Collector VoltageEECS130 Integrated Circuit DevicesProfessor Ali Javey11/20/2007BJTs- Lecture 4Reading Assignment: Chapter 11Announcements•HW9 is due now.PN Junction Review: Carrier concentration profile under biaspn = pn0 + Δpn (x)np = np0 +Δnp (x)Δpn (xn )Δnp (-xp )pn0np0nn0pp0–xp xnQuestion: how does this curve look for reverse bias?x0N-side P-sideJtotalJpNJnPx0N-side P-sideJtotalJpNJnPJpPJnNPN Junction Review: Current ProfileQualitative Solution - DefinitionsNE = NAEDE = DNτE = τnLE = LNnE0 = np0 = ni2/NENB = NDBDB = DPτB = τpLB = LPpB0 = pn0 = ni2/NBNC = NACDC = DNτC = τnLC = LNnC0 = np0 = ni2/NCEmitter Region Formulation• Diffusion equation:• Boundary ConditionsEEEndxndEDτΔΔ−=22"0)1()0"(0)"(/0−==Δ=∞→ΔkTqVEEEEBenxnxnBase Region Formulation• Diffusion equation:• Boundary ConditionsBBBpdxndBDτΔΔ−=220)1()()1()0(/0/0−=Δ−=ΔkTqVBBkTqVBBCBEBepWpeppCollector Region Formulation• Diffusion equation:• Boundary ConditionsCCCndxndCDτΔΔ−=22'0)1()0'(0)'(/0−==Δ=∞→ΔkTqVCCCCBenxnxnCurrent Formulation0""=Δ−=xdxndEEnEqADI0=Δ−=xdxpdBEpBqADIWxdxpdBCpBqADI=Δ−=0''=Δ=xdxndCCnCqADIEmitter Region Solution• The solution of: is:• From the boundary conditions: we have: and:EEEndxndEDτΔΔ−=22"0EELxLxEeAeAxn/"2/"1)"( +=Δ−)1()0"(0)"(/0−==Δ=∞→ΔkTqVEEEEBenxnxnEEBLxkTqVEEeenxn/"/0)1()"(−−=Δ)1(/0−−=kTqVELDEnEBEEenqAICollector Region Solution• The solution of: is:• From the boundary conditions: we have: and:CCLxLxCeAeAxn/'2/'1)'( +=Δ−CCBLxkTqVCCeenxn/'/0)1()'(−−=Δ)1(/0−−=kTqVCLDCnCBCCenqAICCCndxndCDτΔΔ−=22'0)1()0'(0)'(/0−==Δ=∞→ΔkTqVCCCCBenxnxnBase Region Solution• The solution of: is:• From the boundary conditions: we have: BBLxLxBeAeAxp/2/1)( +=Δ−BBBpdxndBDτΔΔ−=220)1()()1()0(/0/0−=Δ−=ΔkTqVBBkTqVBBCBEBepWpepp()()BLWBLWBLxBLxCBBLWBLWBLxwBLxWEBeeeekTqVBeeeekTqVBBepepxp///////)(/)()1()1()(/0/0−−−−−−−−−−−+−=ΔBase Region Solution (cont’d)• Now, we know:• Therefore, we can write: as:()2sinhξξξ−−=ee()()BLWBLWBLxBLxCBBLWBLWBLxwBLxWEBeeeekTqVBeeeekTqVBBepepxp///////)(/)()1()1()(/0/0−−−−−−−−−−−+−=Δ()[]()[]()BBCBBBEBLWLxkTqVBLWLxWkTqVBBepepxpsinhsinh)1(sinhsinh)1()(/0/0−+−=Δ−Base Region Solution (cont’d)• Now, we know:• Therefore, we have: and:()2coshξξξ−+=ee()[]1)1(/)/sinh(1/)/sinh(/cosh(0)−−−=kTqVLWkTqVLWLWBLDEpCBBEBBBBBeepqAI()[]1)1(/)/sinh(/cosh(/)/sinh(10)−−−=kTqVLWLWkTqVLWBLDCpCBBBEBBBBeepqAITerminal Currents• We know:• Therefore:()[]1)1(/)/sinh(1/)/sinh(/cosh(0)−−−=kTqVLWkTqVLWLWBLDEpCBBEBBBBBeepqAI)1(/0−−=kTqVELDEnEBEEenqAI()[]1)1(/)/sinh(/cosh(/)/sinh(10)−−−=kTqVLWLWkTqVLWBLDCpCBBBEBBBBeepqAI)1(/0−−=kTqVCLDCnCBCCenqAI()()()[]1)1(/)/sinh(10/)/sinh(/cosh(00)−−−+=kTqVLWBLDkTqVLWLWBLDELDECBBBBEBBBBBEEepepnqAI()()()[]1)1(/)/sinh(/cosh(00/)/sinh(10)−+−−=kTqVLWLWBLDCLDkTqVLWBLDCCBBBBBCCEBBBBepnepqAIQuestion: What is IB ?Simplification• In real BJTs, we make W << LB so that we have a high gain. Then, we note:• So, we have:()()11cosh1sinh22<<+→<<→ξξξξξξKK()()WxkTqVBWxkTqVBBCBEBepepxp)1(1)1()(/0/0−+−−≅ΔSimplified AnalysisConsider the carrier distribution in a forward active pnp transistor pB0nE0nC0Emitter Base CollectornC (0)pB (0)nE (0)Question: why does the carrier concentration show linear dependence in the base?Question:• Plot carrier distribution profile for a BJT under cut-off.Performance Parameters()()()2212212211111111BEEBBEBEEBBEBEEBBELWLWNNDDdcLWLWNNDDdcLWTLWNNDD+=++=+=+=βααγBase width modulationWhen the reverse bias applied to the C-B junction increases, the C-B depletion width increases and W decreases. Thus, thecollector current, IC increases. This is also known as “EarlyEffect”. More prominent in narrow-base transistors.ICVEC3 mA2 mA1 mAOutput resistance :CACECIVVIr =⎟⎟⎠⎞⎜⎜⎝⎛∂∂≡−10A large VA (i.e. a larger ro ) is desirable for voltage gainIB3ICVCE0VA(b)VA : Early VoltageIB2IB1Base-Width Modulation(Depletion region in collector is not shown)How can we reduce the base-width modulation effect?N+ PN emitter basecollector VCECEWB3WB2WB1 xn'} reduction of base width VCE1< VCE2<VCE3B VBEBase-Width Modulation by Collector VoltageThe base-width modulation effect is reduced if we(A) Increase the base width,(B) Increase the base doping concentration, NB , or(C) Decrease the collector doping concentration, NC .Which of the above is the most acceptable action?N+ PN emitter basecollector VCECEWB3WB2WB1 xn'} reduction of base width VCE1< VCE2<VCE3B VBEBase-Width Modulation by Collector
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