MIT6_012F09_lec07

MIT6_012F09_lec07 - 6.012 Microelectronic Devices and...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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-up Exponential 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 modeling Bipolar junction transistor structure Qualitative description of operation: 1. Visualizing the carrier fluxes 2. The control function 3. Design objectives Operation in forward active region, vBE > 0, vBC < 0: δE, δB, βF, IES (using npn as the example) Clif Fonstad, 10/1/09 Lecture 7 - Slide 1 Biased p-n junctions: current flow, cont. The saturation current of three diode types: IS's dependence on the relative sizes of w and Lmin p’(x), n’(x) p’(xn) Short-base diode, wn << Lh, wp << Le: n’(-xp) x # -wp -xp xn wn n2 Dh qv AB / kT i J h (x n ) = q e - 1] % [ ' * % N Dn ( w n " x n ) Dh De 2 , [e qv AB / kT - 1] + $ iD = Aqn i ) 2 n De ) N Dn ( w n " x n ) N Ap ( w p " x p ) , ( + J e (-x p ) = q i [e qv AB / kT - 1] % N Ap ( w p " x p ) % & p’(x), n’(x) p’(xn) Long-base diode, wn >> Lh, wp >> Le: n’(-xp) " -wp -xp xn wn n 2 Dh qv AB / kT i J h (x n ) = q - 1] $ [e &D $ N Dn Lh De ) qv AB / kT 2 h + - 1] # iD = Aqn i ( + [e n 2 De qv AB / kT N Dn Lh N Ap Le * ' J e (-x p ) = q i - 1] $ [e $ N Ap Le % General diode: x "D De % qv AB / kT h iD = Aqn $ + - 1] ' [e # N Dn w n ,eff N Ap w p ,eff & 2 i ! Hole injection into n-side Clif Fonstad, 10/1/09 ! Electron injection into p-side Note : w n ,eff " Lh tanh( w n - x n ), w p ,eff " Le tanh( w p - x p ) Lecture 7 - Slide 2 Asymmetrically doped junctions: an important special case Current flow impact/issues A p+-n junction (NAp >> NDn): "D Dh De % qv AB / kT 2 2 h iD = Aqn i $ + - 1] " Aqn i ' [e [e qv AB / kT - 1] N Dn w n ,eff # N Dn w n ,eff N Ap w p ,eff & Hole injection into n-side ! An n+-p junction (NDn >> NAp): "D De % ! AB / kT De 2 h iD = Aqn i $ + - 1] ( Aqn 2 ' [e qv [e qv AB / kT - 1] i N Ap w p ,eff # N Dn w n ,eff N Ap w p ,eff & Electron injection into p-side ! Note that in both cases the minority carrier injection is predominately into the lightly doped side. Note also that it is the doping level of the more lightly doped junction that determines the magnitude of the current, and as the doping level on the lightly doped side decreases, the magnitude of the current increases. Two very important and useful observations!! Clif Fonstad, 10/1/09 Lecture 7 - Slide 3 Biased 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’ ( x n ) Charge stored on n-side (holes and electrons) Note: Assuming negligible charge stored on p-side n’(-xp) -wp -xp x xn wn Notice that the stored positive charge (the excess holes) and the stored negative charge (the excess electrons) occupy the same volume in space (between x = xn and x = wn)! qA ,DF (v AB ) = Aq[ p' ( x n ) " p' ( w n )] ! [w n " x n ] 2 # w n ,eff n i2 qv AB / kT Aq " 1] [e N Dn 2 The 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: #qA ,DF Cdf (VAB ) " #v AB Clif Fonstad, 10/1/09 $ v AB = VAB q2 n i2 qv AB / kT A w n ,eff e 2 kT N Dn Lecture 7 - Slide 4 p’(x), n’(x) Diffusion capacitance, cont.: p’(xn) Excess holes and electrons stored on the n-side n’(-xp) -wp -xp x xn wn A very useful way to write the diffusion capacitance is in terms of the bias current, ID: ID " Aqn i2 Dh D [e qVAB / kT # 1] " Aqni2 N wh e qVAB / kT for VAB >> kT N Dn w n ,eff Dn n , eff To do this, first divide Cdf by ID to get: q2 n i2 qVAB / kT A w n ,eff e Cdf (VAB ) 2 kT N Dn " Dh ID (VAB ) Aqn i2 e qVAB / kT N Dn w n ,eff ! Isolating Cdf, we have: ! Clif Fonstad, 10/1/09 = 2 q w n ,eff 2 kT Dh 2 w n ,eff q ID (VAB ) Cdf (VAB ) " ! 2 Dh kT * Notice that the area of the device, A, does not appear explicitly in this expression. Only the total current! ! Lecture 7 - Slide 5 Comparing charge stores; small-signal linear equivalent capacitors: " qA ,PP = A v AB d Parallel plate capacitor ρ(x) qA d/2 $qA ,PP C pp (VAB ) # $v AB x -d/2 qB( = -qA) Depletion region charge store ρ(x) qNDn v AB = VAB A" d qA ,DP (v AB ) = " A 2q#Si [$ b " v AB ] ! qB -xp = N Ap N Dn [N Ap + N Dn ] ( = -Q A ) x xn qA Cdp (VAB ) = A -qNAp N Ap N Dn q#Si 2[$ b " VAB ] [ N Ap + N Dn ] = A #Si w (VAB ) QNR region diffusion charge store p’(x), n’(x) p’(xn) ! qA, qB (=-qA) Note: Approximate because we are only accounting for the charge store on the lightly doped side. n’(-xp ) -wp -xp xn qAB ,DF (v AB ) " Aqn i2 x wn Cdf (VAB ) " Clif Fonstad, 10/1/09 ! Dh [e qVAB / kT # 1] N Dn w n ,eff 2 w n ,eff q ID (VAB ) 2 Dh kT = 2 w n ,eff iD (v AB ) 2 Dh Lecture 7 - Slide 6 p-n diode: large signal model including charge stores A qAB IBS Non-linear resistive element B qAB: Excess carriers on p-side + excess carriers on n-side + junction depletion charge. Non-linear capacitive element small signal linear equivalent circuit a Cd gd b Clif Fonstad, 10/1/09 #iD gd " #v AB v AB = VAB #qAB Cd (VAB ) " #v AB %0 ' $ & qID ' kT ( v AB = VAB for VAB < 0 for VAB >> kT / q % Cdp (VAB ) for VAB < 0 $& ( Cdp (VAB ) + Cdf (VAB ) for VAB >> kT / q Lecture 7 - Slide 7 ! Moving on to transistors! Amplifiers/Inverters: back to 6.002 V CC V CC RD RC D RT vT (t) = V T + vt (t) + - C + vIN - S vOUT An MOS amplifier or inverter: the transistor is an n-channel MOSFET Clif Fonstad, 10/1/09 RT + G - vT (t) = V T + vt (t) + - + B + vIN - vOUT E - A bipolar amplifier or inverter: the transistor is an npn BJT Lecture 7 - Slide 8 npn BJT: Connecting with the n-channel MOSFET from 6.002 A very similar behavior*, and very similar uses. iD MOSFET D Linear iD or Triode + iG Saturation (FAR) vDS G+ iD ! K [vGS - V T(vBS)]2/2! vGS – iC BJT C – S Cutoff + vDS iB Saturation vCE B+ iC i B vBE – – E FAR iB ! IBSe qV BE /kT vCE > 0.2 V Cutoff 0.6 V Input curve Clif Fonstad, 10/1/09 vBE Forward Active Region iC ! !F iB 0.2 V Cutoff vCE Output family 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 Base, B Emitter, E Al p SiO2 n+ n Si An npn BJT Adapted from Fig. 8.1 in Text Al Collector, C The heart of the device, and what we will model Clif Fonstad, 10/1/09 How does it work? Lecture 7 - Slide 10 Bipolar Junction Transistors: basic operation and modeling… … how the base-emitter voltage, vBE, controls the collector current, iC C iC Reverse biased vCB, the reverse bias on the collector-base junction, insures collection of those electrons injected across the E-B junction that reach the C-B junction as the collector current, iC n NDC B + vBE + C iC −E iB p NAB + B vCE n+ vBE NDE − E iE − Forward biased vBE, the bias on the emitter-base junction, controls the injection of electrons across the E-B junction into the base and toward the collector. A good way to envision this is to think "carrier fluxes": Clif Fonstad, 10/1/09 Next foil Lecture 7 - Slide 11 C iC vCE B + vBE n NDC − E iB iB p NAB + B The base supplies the small hole flux vBE E Hole flux B n+ NDE − Reverse biased BC junction collects electrons coming across the base from the emitter + iB C iC + C iC + Bipolar Junction Transistors: the carrier fluxes through an npn Electron flux vBE iE − − E iE − Forward biased n+-p EB junction emits electrons into the base towards the BC junction Our next task is to determine: Given a structure, what are iE(vBE,vCE), iC(vBE,vCE), and iB(vBE,vCE)? Clif Fonstad, 10/1/09 Lecture 7 - Slide 12 Bipolar Junction Transistors: basic operation and modeling… … how the base-emitter voltage, vBE, controls the collector current, iC vCE n NDE E vBE p NAB +B -w E − − Excess Carriers: iE iE + n NDC C iC iB wB 0 p!, n! Electron (ni2/NAB)(e qvBE/kT - 1) Electron flux 2/NDE)(e qvBE/kT - 1) (ni flux E E− − 0 (ohmic) + + Clif Fonstad, 10/1/09 vBE vBE 0 B B Hole ole flux H flux -wE 0 (vBC = 0) x wB + wC + + - iE C C iC 0 (ohmic) i C x wB iB iB wB + wC This is rigorous for vCB = 0, but also very good when vCB > 0. Lecture 7 - Slide 13 Bipolar Junction Transistors: basic operation and modeling… … how the base-emitter voltage, vBE, controls the collector current, iC vCE n NDE E vBE p NAB +B -w E − − Excess Carriers: iE iE + n NDC C iC iB wB 0 p!, n! Electron (ni2/NAB)(e qvBE/kT - 1) Electron flux 2/NDE)(e qvBE/kT - 1) (ni flux E E− − 0 (ohmic) + + Clif Fonstad, 10/1/09 vBE vBE 0 B B Hole flux Hole flux -wE 0 (vBC = 0) x wB + wC + + - iE C C iC 0 (ohmic) i C x wB iB iB wB + wC This is rigorous for vCB = 0, but also very good when vCB > 0. Lecture 7 - Slide 14 npn BJT: Forward active region operation, vBE > 0 and vBC ≤ 0 Excess Carriers: p!, n! (ni2/NAB)(e qvBE/kT - 1) (ni2/NDE)(e qvBE/kT - 1) 0 (ohmic) ~ 0 (vBC < 0) 0 (ohmic) x -wE wB wB + wC wB 0 wB + wC ie, ih Currents: -wE ihE [= !EieE] 0 x –iC [= ieE (1 – !B )] ieE } iE [= ieE + ieE = ieE (1 + !E)] Clif Fonstad, 10/1/09 –iB [= ihE + !B ieE = ieE (!E + !B )] Lecture 7 - Slide 15 npn BJT: Approximate model for iE(vBE,vBC) and iC(vBE,vBC) in forward active region, vBE>0, vBC<0 p!, n! (ni2/NAB)(e qvBE/kT - 1) (ni2/NDE)(e qvBE/kT - 1) 0 (ohmic) ~ 0 (vBC < 0) 0 (ohmic) x -wE wB + wC wB 0 The emitter current, iE Begin with the good current, the electron current into the base, ieE: ieE = " Aqn i2 De [e qVBE / kT " 1] N AB w B ,eff Next find the bad current, the hole current back into the emitter, ihE: ihE = " Aqn i2 ! Dh [e qVBE / kT " 1] N DE w E ,eff and write it as a fraction of ieE: ihE = Clif Fonstad, 10/1/09 ! N AB w B ,eff Dh ieE = "E ieE De N DE w E ,eff We'll define δE on the next foil. Lecture 7 - Slide 16 npn BJT: Approximate forward active region model, cont. ie, ih -wE ihE [= !EieE] iE [= ieE + ieE = ieE (1 + !E)] wB 0 wB + wC x –iC [= ieE (1 – !B )] ieE } –iB [= ihE + !B ieE = ieE (!E + !B )] The emitter current, iE, cont. In writing the last equation we introduced the emitter defect, δE: "E # w ihE DN = h $ AB $ B ,eff ieE De N DE w E ,eff To finish for now with the emitter current, we write it, iE, in terms of the emitter electron current, ieE: ! " ihE % iE = ieE + ihE = $1 + ' ieE = (1 + (E ) ieE # ieE & Clif Fonstad, 10/1/09 Lecture 7 - Slide 17 ! npn BJT: Approximate forward active region model, cont. ie, ih -wE wB 0 ihE [= !EieE] wB + wC x –iC [= ieE (1 – !B )] ieE iE [= ieE + ieE = ieE (1 + !E)] } –iB [= ihE + !B ieE = ieE (!E + !B )] The collector current, iC The collector current is the electron current from the emitter, ieE, minus the fraction that recombines in the base, δBieE: iC = (1 " #B ) ieE To find the fraction that recombine, i.e. the base defect, δB, we note that we can write the total recombination in the base, δBieE, ! as: wB "B ieE = # A q % 0 Clif Fonstad, 10/1/09 n' ( x ) dx $ eB Lecture 7 - Slide 18 ! npn BJT: Approximate forward active region model, cont. The base defect, δB If the recombination in the base is small (as it is in a good BJT) then the excess electron concentration will be nearly triangular and we can say: wB " 0 n ' (0) w B ,eff n ' ( x ) dx # 2 wB Thus "B = ! #Aq % 0 n' ( x ) dx $ eB ieE and ieE " # A q DeB n ' (0) w B ,eff n ' (0) w B ,eff # Aq 2 2 w B ,eff w B ,eff 2$ eB &! = = n ' (0) 2 DeB $ eB 2 L2 eB # A q DeB w B ,eff The collector current, iC, cont. Returning to the collector current, iC, we now want to relate it to the total emitter current: ! iC = "(1 " #B ) ieE $ (1 " #B ) i = "' i % iC = " FE iE = (1 + #E ) ieE & (1 + #E ) E with " F # Clif Fonstad, 10/1/09 ! (1 $ %B ) (1 + %E ) Lecture 7 - Slide 19 npn BJT: Approximate forward active region model, cont. So far... We have: #D De & qVBE / kT h iE = " Aqn % + " 1] ([e %N w ( $ DE E ,eff N AB w B ,eff ' #D De & qVBE / kT 2 h = " IES [e " 1] with IES = Aqn i % + ( %N w ( $ DE E ,eff N AB w B ,eff ' …and we have: iC (1 # &B ) iC " iE : iC = # $ F iE with $ F % # = iE (1 + &E ) ! These relationships can be represented by a simple circuit model: ! B iB + vBE 2 i C !FiF or "FiB iF IES –E Note: iF = -iE. Clif Fonstad, 10/1/09 iE = " iF iC = # F iF with iF = IES (1 " e qv BE / kT ) with # F $ " iC (1 " %B ) = iE (1 + %E ) iB = " iE " iC = (1 " # F )iF Looking at this circuit and these expressions, it is clear that to make iB small and |iC| ≈ |iE|, we must have αF ≈ 1. We look at this next. ! Lecture 7 - Slide 20 C iC C + npn BJT: Approximate forward active region model, cont. iC iB B + vBE Reverse biased BC junction collects electrons coming across the base from the emitter −E B The base supplies the small hole flux B iB + vBE Hole flux – + iB C !FiF or "FiB iF IES n+-p Forward biased EB junction emits electrons into the base towards the BC junction Electron flux vBE − E iE − E iE = " iF = " IES (1 " e qv BE / kT ) iC = # F iF iB = " iE " iC = (1 " # F )iF Clif Fonstad, 10/1/09 Lecture 7 - Slide 21 npn BJT: What our model tells us about device design. We have: "F = (1 # $B ) (1 + $E ) and the defects, δE and δB, are given by: ! "E Dh N AB w B ,eff = # # De N DE w E ,eff and "B # 2 w B ,eff 2 L2 eB We want αF to be as close to one as possible, and clearly the smaller we can make the defects, the closer αF will be ! ! to one. Thus making the defects small is the essence of good BJT design: Doping : npn with N DE >> N AB w B ,eff : very small LeB : very large and >> w B ,eff Clif Fonstad, 10/1/09 Lecture 7 - Slide 22 ! npn BJT: Well designed structure (Large βF, small δE and dB) δE and δB are small and αF is ≈ 1 when NDE >> NAB, wE << LhE, wB<<LeB p!, n! Excess Carriers: (ni2/NAB)(e qvBE/kT - 1) (ni2/NDE)(e qvBE/kT - 1) 0 (ohmic) 0 (vBC = 0) 0 (ohmic) x -wE wB + wC wB wB + wC ie, ih Currents: -wE ihE [= !EieE] iE [= ieE(1 + !E)] Clif Fonstad, 10/1/09 wB 0 0 x ieE –iC [= ieE(1 – !B ) " ieE] –iB [= iE – (– iC ) = ieE(!E + !B ) " ieE!E] Lecture 7 - Slide 23 npn BJT,cont.: more observations about F.A.R. model It is very common to think of iB, rather than iE, as the controlling current in a BJT. In this case we write iC as depending on iB: iE = " iF = "IES [e iC = # F iF iB = (1 " # F )iF qVBE / kT with "F # qV / kT qV / kT $ *iB = (1 " # F ) IES [e BE " 1] = IBS [e BE " 1] " 1] && & #F iC = iB = ) F iB %(+ (1 " # F ) && '& iE = " iC " iB = () F + 1) iB , $F (1 % &B ) = 1 % $ F (&E + &B ) and IBS " (1 # $ F ) IES = IES (% F + 1) Two circuit models that fit this behavior are the following: C ! !FiB B iB + IES vBE – Clif Fonstad, 10/1/09 E C ! iB B+ !FiB Note: "F = IBS vBE – E #F (# F + 1) Lecture 7 - Slide 24 ! npn BJT: Equivalent FAR models C !FiF B iBF B iB iF IES + vBE – C C !FiB iB B+ + vBE IES IES = Aqn i2 ( Dh N DE w E ,eff + De N AB w B ,eff ) " F = # F (# F + 1) IBS vBE –E #F "F = (1 $ # F ) E !FiB IBS C A useful model using a break-point diode: ! + vAB – Clif Fonstad, 10/1/09 A iD IS B ! + ≈ vAB – A iD VBE,ON B ! !FiB iB B –E = IES (" F + 1) + VBE,ON vBE – This is a very useful model to use when finding the bias point in a circuit. E Lecture 7 - Slide 25 npn BJT: The Ebers-Moll model The forward model is what we use most, but adding the reverse model we cover the entire range of possible operating conditions. Forward: B iBF + vBE C C Reverse: vBC !FiF ICS iR B iF IES iBR "D De % h IES = Aqn $ + ' $N w –E N AB w B ,eff ' # DE E ,eff & (1 ) *B ) , + = (1 ) *B ) (F = F (*E + *B ) (1 + *E ) 2 2 w B ,eff w B ,eff Dh N AB w B ,eff = , *B . = De N DE w E ,eff 2 De / e 2 L2 e αRiR *E , ihE ieE E – vBC ! Combined they form the full Ebers-Moll model: + B+ iF – 2 2 w B ,eff w B ,eff *B . = 2 De / e 2 L2 e ! !RiR vBE Clif Fonstad, 10/1/09 C ICS iR !FiF IES "D De % h ICS = Aqn $ + ' $N w ' # DC C ,eff N AB w B ,eff & (1 ) *B ) , + = (1 ) *B ) (R = R (*C + *B ) (1 + *C ) w i DN *C , hC = h - AB - B ,eff ieC De N DC wC ,eff 2 i 2 i E You are not responsible for this model. Note: iF = -iE(vBE,0) and iR = -iC(0,vBC). Lecture 7 - Slide 26 npn BJT: The Gummel-Poon model Another common model can be obtained from the Ebers-Moll model is the Gummel-Poon model: C C Forward: !FiF B iBF iF IES + vBE – = B iBF + vBE E IS " Combined they form the Gummel-Poon model: Clif Fonstad, 10/1/09 C !RiBR iBR E E = $ F IES = $ R ICS • Aside from the historical interest, another value this has for us in 6.012 is that it is an interesting exercise to show that the two forward circuits above are equivalent. B IS/!F #F #R IES = ICS # F + 1) # R + 1) ( ( ! IS/!R + !FiBF – – Reverse: vBC vBC – IS/!R iBR iBF IS/!F + B+ vBE – You even less responsible for this model. C !FiBF - !RiBR E Lecture 7 - Slide 27 6.012 - Microelectronic Devices and Circuits Lecture 7 - Bipolar Junction Transistors - Summary • Review/Junction diode model wrap-up Refer to "Lecture 6- Summary" for a good overview Diffusion capacitance: adds to depletion capacitance (p -n example) + In asym., short-base diodes: Cdf(VAB) ≈ (qID/kT)[(wn-xn)2/Dh] (area doesn't enter expression!) • Bipolar junction transistor operation and modeling C iC Currents (forward active): wB + wC (npn example) iE(vBE,0) = – IES (eqvBE/kT – 1) iC(vBE,0) = – αF iE(vBE,0) with αF ≡ [(1 – δB)/(1 + δE)] n – ––––––––––––––––––––––––––––––––––––––––– iB B + p Electron Flux Hole Flux vBE wB 0 -wE E Clif Fonstad, 10/1/09 iE (ratio of hole to electron current across E-B junction) Base defect, δB ≡ (wB2/2Le2) n+ – Emitter defect, δE ≡(DhNABwB*/DeNDEwE*) (fraction of injected electrons recombining in base) – ––––––––––––––––––––––––––––––––––––––––– n!, p! Also, iB(vBE,0) = [(dE + dB)/(1 + dE)] iE(vBE,0) and, iC(vBE,0) = bF iB(vBE,0), with bF º aF/(1 – aF) = [(1 – dB)/(dE + dB)] Lecture 7 - Slide 28 MIT OpenCourseWare http://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online