Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ Semiconductor Device Modeling and Characterization EE5342, Lecture 20 -Sp 2002 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L20 28Mar02

Equivalent circuit above 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 L20 28Mar02

MOS surface states** p- substr = n-channel L20 28Mar02

n-substr accumulation (p-channel) Fig 10.7a* L20 28Mar02

n-substrate depletion (p-channel) Fig 10.7b* L20 28Mar02

n-substrate inversion (p-channel) Fig 10.7* L20 28Mar02

Ideal 2-terminal MOS capacitor/diode conducting gate, area = LW Vgate=VG -xox SiO2 y L silicon substrate tsub Vsub=VB x L20 28Mar02

Band models (approx. scale) metal silicon dioxide p-type s/c Eo qcox ~ 0.95 eV Eo Eo qcSi= 4.0eV qfm= 4.28 eV for Al Ec qfs,p Eg,ox ~ 8 eV EFm Ec EFp EFi Ev Ev L20 28Mar02

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 L20 28Mar02

Values for gate work function, fm L20 28Mar02

Values for fms with metal gate L20 28Mar02

Values for fms with silicon gate L20 28Mar02

Experimental values for fms Fig 10.15* L20 28Mar02

Calculation of the threshold cond, VT L20 28Mar02

Equations for VT calculation L20 28Mar02

Fully biased n-MOS capacitor VG 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 L20 28Mar02 L

Effect of contacts, VS and VD L20 28Mar02

Computing the D.R. width at O.S.I. Ex Emax x L20 28Mar02

Computing the threshold voltage L20 28Mar02

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Fully biased MOS capacitor in inversion Channel VG>VT VS=VC VD=VC EOx,x> 0 n+ e- e- e- e- e- e- n+ p-substrate Vsub=VB Depl Reg Acceptors y L20 28Mar02 L

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 L20 28Mar02

Flat-band parameters for n-channel (p-subst) L20 28Mar02

MOS energy bands at Si surface for n-channel Fig 8.10** L20 28Mar02

Fully biased n- channel VT calc L20 28Mar02

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 L20 28Mar02