EE5342 – Semiconductor Device Modeling and Characterization Lecture 20 March 31, 2010

1. EE5342 – Semiconductor Device Modeling and CharacterizationLecture 20March 31, 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

2. Schedule Change • Classes WILL be held on • 4/5/10 • 4/7/10 • Dr. Russell will be filling in • The previously scheduled make-up classes will be cancelled • 4/16/10 (Friday) • 4/23/10 (Friday) • Project 2 Test changed to W 4/28/10

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

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

5. 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

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

7. 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

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

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

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

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

12. Values for gate workfunction, fm

13. Values for fmswith metal gate

14. Values for fmswith silicon gate

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

16. 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

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

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

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

20. 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

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

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

23. Calculation of thethreshold cond, VT

24. Equations forVT calculation

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

26. 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

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

28. 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

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

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

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

32. Q’d,max and xd,max forbiased MOS capacitor Fig 8.11** |Q’d,max|/q (cm-2) xd,max (microns)

33. Fully biased n-channel VT calc

35. Computing thethreshold voltage

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

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

39. Fully biased p-channel VT calc

40. p-channel VT forVC = VB = 0 Fig 10.21*

41. Ion implantation

42. “Dotted box” approx

44. Mobilities

45. Differential chargesfor low and high freq high freq. From Fig 10.27*

46. Ideal low-freqC-V relationship Fig 10.25*

47. Comparison of lowand high freq C-V Fig 10.28*

48. Effect of Q’ss onthe C-V relationship Fig 10.29*

49. n-channel enhancementMOSFET in ohmic region 0< VT< VG Channel VS = 0 0< VD< VDS,sat EOx,x> 0 e-e- e- e- e- n+ n+ Depl Reg p-substrate Acceptors VB < 0

50. Conductance ofinverted channel • Q’n = - C’Ox(VGC-VT) • n’s = C’Ox(VGC-VT)/q, (# inv elect/cm2) • The conductivity sn = (n’s/t) q mn • G = sn(Wt/L) = n’s q mn (W/L) = 1/R, so • I = V/R = dV/dR, dR = dL/(n’sqmnW)