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EE 5340 Semiconductor Device Theory Lecture 21 – Spring 2011
Professor Ronald L. Carter
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Test 2 – Tuesday 05Apr11 11 AM Room 129 ERB Covering Lectures 11 to19
Open book - 1 legal text or ref., only. You may write notes in your book. Calculator allowed A cover sheet will be included with full instructions. For examples see ©rlc L21-07Apr2011
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npn BJT currents in the forward active region ©RLC
IC = JCAC IB=-(IE+IC ) JnE JnC IE = -JEAE JRB=JnE-JnC JpE JGC JRE JpC ©rlc L21-07Apr2011
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E-M linking current model
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E-M linking current model (cont)
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E-M linking current model (cont)
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More non-ideal effects in BJTs
Base-width modulation (FA: xB changes with changes in VBC) Current crowding in 2-dim base High-level injection (minority carriers g.t. dopant - especially in the base). Emitter Bandgap narrowing (NE ~ density of states at cond. band. edge) Junction breakdown at BC junction ©rlc L21-07Apr2011
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npn Base-width mod. (Early Effect)
Fig 9.15* ©rlc L21-07Apr2011
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Base-width modulation (Early Effect, cont.)
Fig 9.16* ©rlc L21-07Apr2011
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Emitter current crowding in base
Fig 9.21* ©rlc L21-07Apr2011
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Interdigitated base fixes emitter crowding
Fig 9.23* ©rlc L21-07Apr2011
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Base region high- level injection (npn)
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Effect of HLI in npn base region
Fig 9.17* ©rlc L21-07Apr2011
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Effect of HLI in npn base region (cont)
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Effect of HLI in npn base region (cont)
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Emitter region high- level injection (npn)
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Effect of HLI in npn emitter region
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Effect of HLI in npn base region
Figs 9.18 and 9.19* ©rlc L21-07Apr2011
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Bandgap narrowing effects
Fig 9.20* Replaces ni2 throughout ©rlc L21-07Apr2011
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Junction breakdown at BC junction
Reach-through or punch-through when WCB and/or WEB become large enough to reduce xB to zero Avalanche breakdown when Emax at EB junction or CB junction reaches Ecrit. ©rlc L21-07Apr2011
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Hybrid-pi circuit model
Adapted from linking current version of E-M model with parasitic Rs and CSubstr C-E branch is linking current B-E branch is the reduced B-E diode with diffusion (for and rev) resistance and capacitance and junction cap. B-C branch is the reduced B-C diode with diffusion (for and rev) resistance and capacitance and junction cap. ©rlc L21-07Apr2011
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Hybrid-pi Circuit model
Fig 9.33* ©rlc L21-07Apr2011
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Gummel-Poon Static npn Circuit Model
B RBB ILC IBR ICC - IEC = IS(exp(vBE/NFVt - exp(vBC/NRVt)/QB B’ ILE IBF RE E ©rlc L21-07Apr2011
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Gummel-Poon Static npn Circuit Model
Intrinsic Transistor RC B RBB ILC IBR ICC - IEC = {IS/QB}* {exp(vBE/NFVt)-exp(vBC/NRVt)} B’ ILE IBF RE E ©rlc L21-07Apr2011
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Gummel Poon npn Model Equations
IBF = ISexpf(vBE/NFVt)/BF ILE = ISEexpf(vBE/NEVt) IBR = ISexpf(vBC/NRVt)/BR ILC = ISCexpf(vBC/NCVt) QB = (1 + vBC/VAF + vBE/VAR ) {½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 } ©rlc L21-07Apr2011
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Charge components in the BJT
**From Getreau, Modeling the Bipolar Transistor, Tektronix, Inc. ©rlc L21-07Apr2011
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Gummel Poon Base Resistance
If IRB = 0, RBB = RBM+(RB-RBM)/QB If IRB > 0 RB = RBM + 3(RB-RBM)(tan(z)-z)/(ztan2(z)) [1+144iB/(p2IRB)]1/2-1 z = (24/p2)(iB/IRB)1/2 From An Accurate Mathematical Model for the Intrinsic Base Resistance of Bipolar Transistors, by Ciubotaru and Carter, Sol.-St.Electr. 41, pp , 1997. RBB = Rbmin + Rbmax/(1 + iB/IRB)aRB ©rlc L21-07Apr2011
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BJT Characterization Forward Gummel
iC RC iB RE RB vBEx vBC vBE + - vBCx= 0 = vBC + iBRB - iCRC vBEx = vBE +iBRB +(iB+iC)RE iB = IBF + ILE = ISexpf(vBE/NFVt)/BF + ISEexpf(vBE/NEVt) iC = bFIBF/QB = ISexpf(vBE/NFVt)/QB ©rlc L21-07Apr2011
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Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1 1/slope = 59.5 mV/dec
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BJT Characterization Reverse Gummel
iE RC iB RE RB vBCx vBC vBE + - vBEx= 0 = vBE + iBRB - iERE vBCx = vBC +iBRB +(iB+iE)RC iB = IBR + ILC = ISexpf(vBC/NRVt)/BR + ISCexpf(vBC/NCVt) iE = bRIBR/QB = ISexpf(vBC/NRVt)/QB ©rlc L21-07Apr2011
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Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1 1/slope = 59.5 mV/dec
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References * Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997. **Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986. ©rlc L21-07Apr2011
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