1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization – EE5342 Lecture 34 – Spring 2011
Professor Ronald L. Carter

2. The npn Gummel-Poon Static ModelRC
ICC - IEC =
IS(exp(vBE/NFVt
- exp(vBC/NRVt)/QB B
RBB
ILC
IBR B’
ILE
IBF RE E
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3. 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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6. Values for fms with metal gate
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7. Values for fms with silicon gate
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8. Typical fms values
Fig 10.15*
fms
(V)
NB (cm-3)
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9. Flat band with oxide charge (approx. scale)
SiO2
p-Si
+<--Vox-->-
q(Vox)
Ec,Ox
q(ffp-cox)
q(fm-cox) Ex
Eg,ox~8eV
EFm Ec
EFi
EFp
q(VFB) Ev
VFB= VG-VB, when Si bands are flat Ev
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10. Flat-band parameters for n-channel (p-subst)
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11. Flat-band parameters for p-channel (n-subst)
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12. Inversion for p-Si Vgate>VTh>VFB
Vgate> VFB
EOx,x> 0
e- e- e- e- e-
Depl Reg
Acceptors
Vsub = 0
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13. Approximation concept “Onset of Strong Inv”
OSI = Onset of Strong Inversion occurs when ns = Na = ppo and VG = VTh
Assume ns = 0 for VG < VTh
Assume xdepl = xd,max for VG = VTh and it doesn’t increase for VG > VTh
Cd,min = eSi/xd,max for VG > VTh
Assume ns > 0 for VG > VTh
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14. MOS Bands at OSI p-substr = n-channel
Fig 10.9*
2q|fp|
qfp
xd,max
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15. Computing the D.R. W and Q at O.S.I.Ex
Emax x
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16. Calculation of the threshold cond, VT
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17. Equations for VT calculation
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18. Fully biased n-MOS capacitorVG
Channel if VG > VT VS VD
EOx,x> 0 n+
e- e- e- e- e- e- n+
p-substrate
Vsub=VB
Depl Reg
Acceptors y
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19. MOS energy bands at Si surface for n-channel
Fig 8.10**
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20. Computing the D.R. W and Q at O.S.I.Ex
Emax x
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21. Q’d,max and xd,max for biased MOS capacitor
Fig 8.11**
xd,max
(mm)
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22. Fully biased n- channel VT calc
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23. n-channel VT for VC = VB = 0
Fig 10.20*
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24. 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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