Semiconductor Device Modeling and Characterization EE5342, Lecture 22 Spring 2003

1. Semiconductor Device Modeling and CharacterizationEE5342, Lecture 22Spring 2003 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. Band models (approx. scale) metal silicon dioxide p-type s/c Eo Eo qcox ~ 0.95 eV Eo qcSi= 4.0eV qfm= 4.28 eV for Al Ec qfs,p Eg,ox ~ 8 eV Ec EFm EFi EFp Ev Ev

22. 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

23. 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