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Understanding the Ideal 2-Terminal MOS Capacitor for Semiconductor Devices

This lecture by Professor Ronald L. Carter provides a comprehensive overview of the ideal 2-terminal MOS capacitor, focusing on diode conduction and related band models. Key topics include the gate voltage relationship, depletion regions in p-type silicon, and the onset of strong inversion. Additionally, the lecture covers the equivalent circuit for depletion, capacitance calculations, and significant parameters influencing MOS device behavior. Understanding these concepts is essential for students and professionals working with semiconductor devices and integrated circuits.

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Understanding the Ideal 2-Terminal MOS Capacitor for Semiconductor Devices

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  1. EE 5340Semiconductor Device TheoryLecture 24 – 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. Depletion for p-Si, Vgate> VFB Vgate> VFB -xox SiO2 EOx,x> 0 0 DeplReg Acceptors p-type Si tsub Vsub= 0 x

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

  7. 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

  8. Inversion for p-SiVgate>VTh>VFB Vgate> VFB EOx,x> 0 e- e- e- e- e- Acceptors DeplReg Vsub= 0

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

  10. 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

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

  12. 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

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

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

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

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

  17. Values for gate workfunction, fm

  18. Values for fmswith metal gate

  19. Values for fmswith silicon gate

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

  21. 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

  22. 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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