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MIT 6 012 - Lecture Notes

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6.012 - Microelectronic Devices and Circuits Lecture 7 - Bipolar Junction Transistors - Outline • Announcements First Hour Exam - Oct. 7, 7:30-9:30 pm; thru 10/2/09, PS #4 • Review/Diode model wrap-upExponential diode: iD(vAB) = IS (eqvAB/kT -1) (holes) (electrons) with IS ≡ A q ni2 [(Dh/NDn wn*) + (De/NAp wp*)] Observations: Saturation current, IS, goes down as doping levels go up Injection is predominantly into more lightly doped side Asymmetrical diodes: the action is on the lightly doped side Diffusion charge stores; diffusion capacitance: (Recitation topic) Excess carriers in quasi-neutral region = Stored charge • Bipolar junction transistor operation and modelingBipolar junction transistor structure Qualitative description of operation: 1. Visualizing the carrier fluxes (using npn as the example) 2. The control function 3. Design objectives Operation in forward active region, vBE > 0, vBC < 0: δE, δB, βF, IES Clif Fonstad, 10/1/09 Lecture 7 - Slide 1Biased p-n junctions: current flow, cont. The saturation current of three diode types:! iD= Aqni2DhNDnwn,eff+DeNApwp,eff" # $ % & ' eqvAB/kT-1[ ] IS's dependence on the relative sizes of w and Lmin Short-base diode, wn << Lh, wp << Le: ! Jh(xn) = qni2NDnDhwn" xn( )eqvAB/kT-1[ ]Je(-xp) = qni2NApDewp" xp( )eqvAB/kT-1[ ]# $ % % & % % iD= Aqni2DhNDnwn" xn( )+DeNApwp" xp( )' ( ) ) * + , , eqvAB/kT-1[ ] p’(x), n’(x) x xn-xp-wp wn n’(-xp) p’(xn) ! Jh(xn) = qni2NDnDhLheqvAB/kT-1[ ]Je(-xp) = qni2NApDeLeeqvAB/kT-1[ ]" # $ $ % $ $ iD= Aqni2DhNDnLh+DeNApLe& ' ( ) * + eqvAB/kT-1[ ] p’(x), n’(x) x x-x-wnpp wn n’(-xp) p’(xn) Long-base diode, wn >> Lh, wp >> Le: General diode: Hole injection into n-side Electron injection into p-side Clif Fonstad, 10/1/09 ! Note : wn,eff" Lhtanh wn- xn( ), wp,eff" Letanh wp- xp( ) Lecture 7 - Slide 2Asymmetrically doped junctions: an important special case Current flow impact/issues A p+-n junction (NAp >> NDn): ! " Aqni2DhNDnwn,effeqvAB/kT-1[ ] Hole injection into n-side ! iD= Aqni2DhNDnwn,eff+DeNApwp,eff" # $ % & ' eqvAB/kT-1[ ]An n+-p junction (NDn >> NAp): Electron injection into p-side ! iD= Aqni2DhNDnwn,eff+DeNApwp,eff" # $ % & ' eqvAB/kT-1[ ]( Aqni2DeNApwp,effeqvAB/kT-1[ ] Note that in both cases the minority carrier injection is predominately intothe lightly doped side. Note also that it is the doping level of the more lightly doped junction thatdetermines the magnitude of the current, and as the doping level on thelightly doped side decreases, the magnitude of the current increases. Two very important and useful observations!! Clif Fonstad, 10/1/09 Lecture 7 - Slide 3Biased p-n junctions: excess minority carrier (diffusion) charge stores Diffusion charge store, and diffusion capacitance: Using example of asymmetrically doped p+-n diode p’(x), n’(x) p’(xn) Charge storedon n-side (holesNote: Assumingnegligible charge stored on p-side n’(-xp) x -w -xand electrons) x wp p n n Notice that the stored positive charge (the excess holes) and thestored negative charge (the excess electrons) occupy the same volume in space (between x = xn and x = wn)! ! qA,DF(vAB) = Aq p'(xn) " p'(wn)[ ]wn" xn[ ]2# Aqni2NDneqvAB/kT"1[ ]wn,eff2The charge stored depends non-linearly on vAB. As we did in the case of the depletion charge store, we define an incremental linear equivalent diffusion capacitance, Cdf(VAB), as: Clif Fonstad, 10/1/09 Lecture 7 - Slide 4 ! Cdf(VAB) "#qA,DF#vABvAB=VAB$ Aq22kTwn,effni2NDneqvAB/kTp’(x), n’(x) p’(xn)Diffusion capacitance, cont.: Excess holes and electrons stored on the n-side n’(-xp)x -wp -xp xn wn A very useful way to write the diffusion capacitance is in terms of the bias current, ID: ! ID" Aqni2DhNDnwn,effeqVAB/kT#1[ ]" Aqni2DhNDnwn,effeqVAB/kT for VAB>> kTTo do this, first divide Cdf by ID to get: ! Cdf(VAB)ID(VAB)"Aq22kTwn,effni2NDneqVAB/kTAqni2DhNDnwn,effeqVAB/kT! Cdf(VAB) "wn,eff22Dhq ID(VAB)kTIsolating Cdf, we have: ! =qwn,eff22kT Dh* Notice that the area of the device, A, does not appearClif Fonstad, 10/1/09 Lecture 7 - Slide 5explicitly in this expression. Only the total current!d/2 -d/2 qA qB( = -qA) xn -xp qA qB ( = -Q A) -qNAp qNDn ! qAB,DF(vAB) " Aqni2DhNDnwn,effeqVAB/kT#1[ ] =wn,eff22DhiD(vAB) Comparing charge stores; small-signal linear equivalent capacitors: Parallel plate capacitorρ(x) x ! qA,PP= A"dvABCpp(VAB) #$qA,PP$vABvAB=VAB=A"dDepletion region charge store! qA,DP(vAB) = "A 2q#Si$b" vAB[ ]NApNDnNAp+ NDn[ ]Cdp(VAB) = Aq#Si2$b" VAB[ ]NApNDnNAp+ NDn[ ]=A#Siw(VAB)ρ(x) xQNR region diffusion charge store Clif Fonstad, 10/1/09 Lecture 7 - Slide 6 qA, qB (=-qA) p’(x), n’(x) x xn-xp-wp wn n’(-xp) p’(xn) Note: Approximate because we areonly accounting for the chargestore on the lightly doped side. ! Cdf(VAB) "wn,eff22Dhq ID(VAB)kTp-n diode: large signal model including charge stores BAIBSqABNon-linear resistive element Non-linear capacitive element qAB: Excess carriers on p-side + excess carriers on n-side + junction depletion charge. small signal linear equivalent circuit ! gd"#iD#vABvAB=VAB$0 for VAB< 0qIDkTfor VAB>> kT /q% & ' ( ' Cd(VAB) "#qAB#vABvAB=VAB$CdpVAB( )for VAB< 0CdpVAB( )+ CdfVAB( )for VAB>> kT /q% & ( bagdCdClif Fonstad, 10/1/09 Lecture 7 - Slide 7Moving on to transistors! Amplifiers/Inverters: back to 6.002 vT(t) =VT + vt(t) VCCvOUT+-vIN+-+-RTDSGRD vT(t) =VT + vt(t) VCCvOUT+-vIN+-+-RTCEBRCAn MOS amplifier A bipolar amplifier or inverter: or inverter: the transistor is an the transistor is an n-channel MOSFET npn BJT Clif Fonstad, 10/1/09 Lecture 7 - Slide 8npn BJT: Connecting with the n-channel MOSFET from 6.002 A very similar behavior*, and very similar uses. vDSiDSaturation (FAR)CutoffLinearorTriodeiD ! K [vGS - VT(vBS)]2/2!iBvBEvCEiC0.6 V0.2 VForward Active RegionFARCutoffCutoffSaturationiC ! !F iBvCE > 0.2 ViB ! IBSeqVBE/kTInput curveOutput familyMOSFET BJT BEC+––+vBEvCEiBiCGSD+––+vGSvDSiGiDClif Fonstad, 10/1/09 Lecture 7 - Slide 9 * At its output each device looks like a current source controlled by the input signal.How do we make a BJT? Basic Bipolar Junction Transistor (BJT) - cross-section n+ n p Collector, C Base, B Emitter, E Al Al Si SiO2 An npn BJTAdapted from Fig. 8.1 in Text The heart of the device, and what we will model How does it work?Clif Fonstad, 10/1/09 Lecture 7 - Slide 10Bipolar Junction Transistors: basic operation and modeling… … how the base-emitter voltage, vBE, controls the


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MIT 6 012 - Lecture Notes

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