1. EE 5340 Semiconductor Device Theory Lecture 21 – Spring 2011
Professor Ronald L. Carter

2. Test 2 – Tuesday 05Apr11 11 AM Room 129 ERB Covering Lectures 11 to19
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3. 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
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4. E-M linking current model
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5. E-M linking current model (cont)
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6. E-M linking current model (cont)
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7. 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
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8. npn Base-width mod. (Early Effect)
Fig 9.15*
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9. Base-width modulation (Early Effect, cont.)
Fig 9.16*
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10. Emitter current crowding in base
Fig 9.21*
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11. Interdigitated base fixes emitter crowding
Fig 9.23*
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12. Base region high- level injection (npn)
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13. Effect of HLI in npn base region
Fig 9.17*
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14. Effect of HLI in npn base region (cont)
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15. Effect of HLI in npn base region (cont)
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16. Emitter region high- level injection (npn)
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17. Effect of HLI in npn emitter region
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18. Effect of HLI in npn base region
Figs 9.18 and 9.19*
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19. Bandgap narrowing effects
Fig 9.20*
Replaces ni2
throughout
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20. 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.
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21. 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.
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22. Hybrid-pi Circuit model
Fig 9.33*
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23. Gummel-Poon Static npn Circuit ModelB
RBB
ILC
IBR
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B’
ILE
IBF RE E
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24. 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
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25. Gummel Poon npn Model Equations
IBF = ISexpf(vBE/NFVt)/BF
ILE = ISEexpf(vBE/NEVt)
IBR = ISexpf(vBC/NRVt)/BR
ILC = ISCexpf(vBC/NCVt)
QB = (1 + vBC/VAF + vBE/VAR ) 
{½ + [¼ + (BFIBF/IKF + BRIBR/IKR)]1/2 }
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26. Charge components in the BJT
**From Getreau, Modeling the
Bipolar Transistor, Tektronix, Inc.
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27. 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
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28. BJT Characterization Forward GummeliC RC iB RE RB
vBEx
vBC
vBE + -
vBCx= 0 = vBC + iBRB - iCRC
vBEx = vBE +iBRB +(iB+iC)RE
iB = IBF + ILE =
ISexpf(vBE/NFVt)/BF
+ ISEexpf(vBE/NEVt)
iC = bFIBF/QB =
ISexpf(vBE/NFVt)/QB
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29. Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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30. BJT Characterization Reverse GummeliE RC iB RE RB
vBCx
vBC
vBE + -
vBEx= 0 = vBE + iBRB - iERE
vBCx = vBC +iBRB +(iB+iE)RC
iB = IBR + ILC =
ISexpf(vBC/NRVt)/BR
+ ISCexpf(vBC/NCVt)
iE = bRIBR/QB =
ISexpf(vBC/NRVt)/QB
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31. Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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32. 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.
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