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Semiconductor Device Modeling and Characterization – EE5342 Lecture 31 – Spring 2011

Semiconductor Device Modeling and Characterization – EE5342 Lecture 31 – Spring 2011. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/. Ideal 2-terminal MOS capacitor/diode. conducting gate, area = LW. V gate. -x ox. SiO 2. 0. y. 0. L. silicon substrate. t sub.

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Semiconductor Device Modeling and Characterization – EE5342 Lecture 31 – Spring 2011

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  1. Semiconductor Device Modeling and Characterization – EE5342 Lecture 31 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

  2. Ideal 2-terminalMOS capacitor/diode conducting gate, area = LW Vgate -xox SiO2 0 y 0 L silicon substrate tsub Vsub x

  3. Band models (approx. scale) metal silicon dioxide p-type s/c Eo Eo qcox ~ 0.95 eV Eo qcSi= 4.05eV qfm= 4.1 eV for Al Ec qfs,p Eg,ox ~ 8 eV Ec EFm EFi EFp Ev Ev

  4. Flat band condition (approx. scale) Al 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

  5. Equivalent circuitfor 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

  6. Accumulation forVgate< VFB Vgate< VFB -xox SiO2 EOx,x<0 0 holes p-type Si tsub Vsub = 0 x

  7. Accumulationp-Si, Vgs < VFB Fig 10.4a*

  8. Equivalent circuitfor accumulation • Accum depth analogous to the accum Debye length = LD,acc = [eVt/(qps)]1/2 • Accum cap, C’acc = eSi/LD,acc • Oxide cap, C’Ox = eOx/xOx • Net C is the series comb C’Ox C’acc

  9. Depletion for p-Si, Vgate> VFB Vgate> VFB -xox SiO2 EOx,x> 0 0 Depl Reg Acceptors p-type Si tsub Vsub = 0 x

  10. Depletion forp-Si, Vgate> VFB Fig 10.4b*

  11. Equivalent circuitfor depletion • Depl depth given by the usual formula = xdepl = [2eSi(Vbb)/(qNa)]1/2 • Depl cap, C’depl = eSi/xdepl • Oxide cap, C’Ox = eOx/xOx • Net C is the series comb C’Ox C’depl

  12. Inversion for p-SiVgate>VTh>VFB Vgate> VFB EOx,x> 0 e- e- e- e- e- Acceptors Depl Reg Vsub = 0

  13. Inversion for p-SiVgate>VTh>VFB Fig 10.5*

  14. 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

  15. MOS Bands at OSIp-substr = n-channel Fig 10.9*

  16. Equivalent circuitabove OSI • Depl depth given by the maximum depl = xd,max = [2eSi|2fp|/(qNa)]1/2 • Depl cap, C’d,min = eSi/xd,max • Oxide cap, C’Ox = eOx/xOx • Net C is the series comb C’Ox C’d,min

  17. MOS surface states**p- substr = n-channel

  18. n-substr accumulation (p-channel) Fig 10.7a*

  19. n-substrate depletion(p-channel) Fig 10.7b*

  20. n-substrate inversion(p-channel) Fig 10.7*

  21. Values for gate workfunction, fm

  22. Values for fmswith metal gate

  23. Values for fmswith silicon gate

  24. fms (V) Fig 10.15* NB (cm-3) Typical fms values

  25. Flat band with oxidecharge (approx. scale) Al SiO2 p-Si +<--Vox-->- q(Vox) Ec,Ox q(ffp-cox) Ex q(fm-cox) Eg,ox~8eV Ec EFm EFi EFp q(VFB) Ev VFB= VG-VB, when Si bands are flat Ev

  26. Flat-band parametersfor n-channel (p-subst)

  27. Flat-band parametersfor p-channel (n-subst)

  28. Inversion for p-SiVgate>VTh>VFB Vgate> VFB EOx,x> 0 e- e- e- e- e- Acceptors Depl Reg Vsub = 0

  29. 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

  30. Fig 10.9* qfp 2q|fp| xd,max MOS Bands at OSIp-substr = n-channel

  31. Computing the D.R. W and Q at O.S.I. Ex Emax x

  32. Calculation of thethreshold cond, VT

  33. Equations forVT calculation

  34. Fully biased n-MOScapacitor VG Channel if VG > VT VS VD EOx,x> 0 e- e- e- e- e- e- n+ n+ p-substrate Vsub=VB Depl Reg Acceptors y 0 L

  35. MOS energy bands atSi surface for n-channel Fig 8.10**

  36. Ex Emax x Computing the D.R. W and Q at O.S.I.

  37. Q’d,max and xd,max forbiased MOS capacitor Fig 8.11** xd,max (mm)

  38. Fully biased n-channel VT calc

  39. n-channel VT forVC = VB = 0 Fig 10.20*

  40. 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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