Slide 1Ideal 2-terminal MOS capacitor/diodeMOS surface states** p- substr = n-channelMOS Bands at OSI p-substr = n-channelEquivalent circuit for accumulationEquivalent circuit for Flat-BandEquivalent circuit for depletionEquivalent circuit above OSIDifferential charges for low and high freqIdeal low-freq C-V relationshipComparison of low and high freq C-VEffect of Q’ss on the C-V relationshipFlat band condition (approx. scale)Flat-band parameters for n-channel (p-subst)Flat-band parameters for p-channel (n-subst)Typical fms valuesFlat band with oxide charge (approx. scale)Inversion for p-Si Vgate>VTh>VFBApproximation concept “Onset of Strong Inv”MOS Bands at OSI p-substr = n-channelComputing the D.R. W and Q at O.S.I.Calculation of the threshold cond, VTEquations for VT calculationFully biased n-MOS capacitorMOS energy bands at Si surface for n-channelComputing the D.R. W and Q at O.S.I.Q’d,max and xd,max for biased MOS capacitorFully biased n- channel VT calcn-channel VT for VC = VB = 0Fully biased p- channel VT calcp-channel VT for VC = VB = 0n-channel enhancement MOSFET in ohmic regionConductance of inverted channelBasic I-V relation for MOS channelI-V relation for n-MOS (ohmic reg)ReferencesComputing the D.R. W and Q at O.S.I.EE 5340Semiconductor Device TheoryLecture 25 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L25-21Apr20112Ideal 2-terminalMOS capacitor/diodex-xox0SiO2silicon substrateVgateVsubconducting gate,area = LWtsub0yL©rlc L25-21Apr20113MOS surface states**p- substr = n-channelVGSsSurf chg Carr DenVGS < VFB < 0s < 0 Accum. ps > NaVGS = VFB < 0s = Neutral ps = NaVFB < VGSs > 0 Depletion ps < NaVFB < VGS < VThs = |p| I ntrinsic ns = ps = niVGS < VThs > |p| Weak inv ni< ns < NaVGS = VThs = 2|p| O.S.I . ns = Na©rlc L25-21Apr20114MOS Bands at OSIp-substr = n-channelFig 10.9*2q|fp|qfpxd,max©rlc L25-21Apr20115Equivalent 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 combOxacctot'C1'C1'C1C’OxC’acc©rlc L25-21Apr20116Equivalent 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 combOxextr,Dtot'C1'C1'C1C’OxC’D,extr©rlc L25-21Apr20117Equivalent 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 combOxdepltot'C1'C1'C1C’OxC’depl©rlc L25-21Apr20118Equivalent 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 combOx,mindtot'C1'C1'C1C’OxC’d,min©rlc L25-21Apr20119Differential chargesfor low and high freqFrom Fig 10.27*high freq.©rlc L25-21Apr201110Ideal low-freqC-V relationshipFig 10.25*©rlc L25-21Apr201111Comparison of lowand high freq C-VFig 10.28*©rlc L25-21Apr201112Effect of Q’ss onthe C-V relationshipFig 10.29*©rlc L25-21Apr201113Flat band condition (approx. scale)Ec,OxEvAlSiO2p-Siq(fm-cox)= 3.15 eVEFmEFpEcEvEFiq(cox-cSi)=3.1eVEg,ox~8eVcond band-flat forVVV8.0 VeV8.0EETheneV85.0EEIfsgMSfpfmFBfpfmfpcqffp= 3.95eV©rlc L25-21Apr201114Flat-band parametersfor n-channel (p-subst)0nNlnVq2EnNNlnV gate, Si-poly n a Forden chg Ox/Si the is 'Q ,x'C'C'QV :substratepiatg2iactmssmsssOxOxOxOxssmsFB©rlc L25-21Apr201115Flat-band parametersfor p-channel (n-subst)0nNlnVq2EnNNlnVqE gate, Si-poly p a Forden chg Ox/Si the is 'Q ,x'Cchange) (no 'C'QV :substratenidtg2idvtmsgsmsssOxOxOxOxssmsFB©rlc L25-21Apr201116Fig 10.15*fms(V)NB (cm-3)Typical fms values©rlc L25-21Apr201117Flat band with oxidecharge (approx. scale)EvAlSiO2p-SiEFmEc,OxEg,ox~8eVEFpEcEvEFi'Ox'ssmsOxmsFBOxOxcOx'ssxssmssCQVVxVdxdEq1QEsurface gate the onis Q'Q' chargea cond FB at thenbound, Ox/Si the atis Q' charge a Ifq(ffp-cox)q(Vox)q(fm-cox)q(VFB)VFB= VG-VB, when Si bands are flatEx+<--Vox-->-©rlc L25-21Apr201118Inversion for p-SiVgate>VTh>VFBVgate> VFBVsub = 0EOx,x> 0inversion for threshold above E Induced depletes 0 E Induced 0xVESiSiOxOxx,Ox--AcceptorsDepl Reg e- e- e- e- e-©rlc L25-21Apr201119Approximation 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©rlc L25-21Apr201120MOS Bands at OSIp-substr = n-channelFig 10.9*2q|fp|qfpxd,max©rlc L25-21Apr201121Computing the D.R. W and Q at O.S.I.ExEmaxxaSixNqdxdE apSidqNx22,maxparea 2,max,max'dadxqNQ ©rlc L25-21Apr201122Calculation of thethreshold cond, VTOx the across Q' induce to addedvoltage the isV where V,VVsub)-p sub,-(n xNqQ' ischarge extra the and x of value the reached has region depletionThe inverted. is surface the whenreached is condition threshold Thed,maxFBTd,maxBd,maxd,max©rlc L25-21Apr201123Equations forVT calculationsubstr-n for 0 substr,- p for 0VqN22x ,xNqQ' 0nNV 0NnVCQ2VV substrnpdanpd,maxd,maxa,dd,maxidtnaitpOxdnpFBT,,',max,,ln,ln':,©rlc L25-21Apr201124Fully biased n-MOScapacitor0yLVGVsub=VBEOx,x> 0AcceptorsDepl Reg e- e- e- e- e- e- n+ n+VSVD p-substrateChannel if VG > VT©rlc L25-21Apr201125MOS energy bands atSi surface for n-channelFig 8.10**©rlc L25-21Apr201126Computing the D.R. W and Q at O.S.I.ExEmaxxaSixNqdxdE aSBpSidqNVVx)(22,max)(2SBpVVarea ,maxda,maxdxqNQ ©rlc L25-21Apr201127Q’d,max and xd,max forbiased MOS capacitorFig 8.11**xd,max(mm))2-d,max(cmqQ'©rlc L25-21Apr201128Fully biased n-channel VT calc 0V ,qNVV22x ,xNqQ' ,0NnlnVVV'C'Q2VVVVV
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