1. EE 5340 Semiconductor Device Theory Lecture 22 – Spring 2011
Professor Ronald L. Carter

2. Project Discussion – Ideal Diode equations
Ideal diode, Jsexpd(Va/(hVt))
ideality factor, h
Recombination, Js,recexp(Va/(2hVt))
appears in parallel with ideal term
High-level injection, (Js*JKF)1/2exp(Va/(2hVt))
SPICE model by modulating ideal Js term
Va = Vext - J*A*Rs = Vext - Idiode*Rs
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3. Project Discussion – Ideal Diode Forward Current Equations
Id = area·(Ifwd - Irev)
Ifwd = forward current = Inrm·Kinj + Irec·Kgen
Inrm = normal current = IS·(eVd/(N·Vt)-1)
if: IKF > 0
then: Kinj = (IKF/(IKF+Inrm))1/2
else: Kinj = 1
Irec = recombination current = ISR·(eVd/(NR·Vt)-1)
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4. SPICE Diode Model t Dinj Drec N~1, rd~N*Vt/iD rd*Cd = TT =
Cdepl given by CJO, VJ and M
Drec
N~2, rd~N*Vt/iD
rd*Cd = ?
Cdepl =? t
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5. Derivation Tips
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6. 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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7. 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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8. 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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9. Charge components in the BJT
**From Getreau, Modeling the
Bipolar Transistor, Tektronix, Inc.
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10. 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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11. 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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12. Ideal F-G Data iC and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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13. 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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14. Ideal R-G Data iE and iB (A) vs. vBE (V) N = 1  1/slope = 59.5 mV/dec
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15. Ideal 2-terminal MOS capacitor/diode
conducting gate,
area = LW
Vgate
-xox
SiO2 y L
silicon substrate
tsub
Vsub x
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16. Band models (approx. scale)
metal
silicon dioxide
p-type s/c Eo Eo Eo
qcox
~ 0.95 eV
qcSi= 4.05eV
qfm= 4.1 eV for Al Ec
qfs,p
Eg,ox
~ 8 eV
EFm Ec
EFp
EFi Ev Ev
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17. Flat band condition (approx. scale)
SiO2
p-Si
q(fm-cox)= 3.15 eV
q(cox-cSi)=3.1eV
Ec,Ox
qffp= 3.95eV
EFm Ec
Eg,ox~8eV
EFi
EFp Ev Ev
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18. Equivalent circuit for Flat-Band
Surface effect analogous to the extr Debye length = LD,extr = [eVt/(qNa)]1/2
Debye cap, C’D,extr = eSi/LD,extr
Oxide cap, C’Ox = eOx/xOx
Net C is the series comb
C’Ox
C’D,extr
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19. References
* Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997.
**Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986
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