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15 mosfet threshold voltage

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15 mosfet threshold voltage

  1. 1. 1Metal Oxide SemiconductorField Effect Transistor (MOSFET)Structure:metal oxidesemiconductorp+n nS G D
  2. 2. 2MOSFET operationp+n nSGDIf VG=0nAssuming VD=high, VS=0No current
  3. 3. 3p+n nSGDIf VG=highn+ + + +An n type channelis formedNow if VD=high, there is a currentflow between D and SGate voltage attractselectrons and pushesholes awayMOSFET operation
  4. 4. 4MOSFET structures and circuit symbolsp- type substr ateSour ce Dr ai nGateSubstr ateSi O2Dr ai nSour ce Sour ceDr ai nGateSour ceDr ai nBul kChannelDepl eti on r egi onn+n+(a) (b) (d)(c)(a) Schematic structure of n-channel MOSFET (NMOS) andcircuit symbols for (b) MOSFET, (c) n-channel MOSFET, and (d)n-channel MOSFET when the bulk (substrate) potential has tobe specified in a circuit.
  5. 5. 5Complementary MOSFET pairsSchematic structure of Complementary MOSFET (CMOS) andcircuit symbols for p-channel MOSFET (PMOS). Minuses andpluses show the depletion regions.p- type substr at en+Sour ce Dr ai nGateSubst r ateSi O2Sour ceDr ai nGateSour ceDr ai nBul kp+n- channel p- channeln- type wel lSi O2
  6. 6. 6Sub-threshold mode of MOSFET operation• VG = 0; the MOSFET conducting channelis not formedEcEF²E F1²E F2ChannelSource DrainEnergyDistanceIn the subthreshold regime, the MOSFET current is a small reverse currentthrough the source – substrate and drain – substrate p-n junctions;Only a small number of electrons can pass over the potential barrierseparating the drain and the source.VG = 0higher VGΦB( / )B kTST Sourcen n e− Φ≈ ×
  7. 7. 7In the sub-threshold regime, the channel current is very low and increasesexponentially with the gate bias.DrainSourceVG1VG2VG3VG1<VG2<VG3Gate-source voltage (V)1.81.41.00.60.2-0.20-10-8-610 2-4-2 0.05 VV ds = 3.0 VI t101010101010Sub-threshold mode of MOSFET operation( / )B kTST Sourcen n e− Φ≈ ×
  8. 8. 8At certain gate bias called the threshold voltage, the conductivity type underthe gate inverts and the barrier between the Source and the Draindisappears.Electrons can enter the region under the gate to form aconducting n-channel.At the gate voltages above the threshold, the gate and the channel form aMetal-Insulator-Semiconductor (MIS) capacitor.DrainSourceVG1VG2VG3VG1<VG2<VG3Gate-source voltage (V)1.81.41.00.60.2-0.20-10-8-610 2-4-2 0.05 VV ds = 3.0 VI t101010101010MOSFET threshold voltageVT
  9. 9. 9The free electron charge in the MOSFET channel (per unit area):Q1 = CGATE × (VG – VT)(assuming that at VG = VT the free electron concentration is zero)MOSFET above the threshold voltageqns = ci VGS − VT( )= ciVGT0/ /i i i ir ic d dε ε ε= =The sheet electron concentration above the threshold, nS is given by:In MOSFETs, the gate and channel form a MIS-capacitor,hence the capacitance per unit gate areaεi = εir ε0 is the total dielectric permittivity of the gate dielectric(usually, SiO2), εir is the relative dielectric permittivity of the gate dielectric.Total gate capacitance CG = ci ×A, where A is the gate area
  10. 10. 10Above the threshold, the sheet electron concentration and hencethe channel current increase linearly with the gate bias VG.Gate-source voltage (V)1.81.41.00.60.2-0.20-10-8-610 2-4-2 0.05 VV ds = 3.0 VI t101010101010MOSFET above the threshold voltageqns = ci VGS − VT( )= ciVGT
  11. 11. 11MOSFET Threshold Voltagesemiconductormetal oxidep+n nS G DDrainSource
  12. 12. 12Band Diagram at the MOS interfacesmetaloxidep+nnBefore ContactECEVEFsEiVacuum levelOXIDEMETAL SEMICONDUCTOREFmECEVqφmEgq χoxq χsq χs qφs
  13. 13. 13p+nnAfter ContactOXIDEMETAL SEMICONDUCTORECEVEFsEiEFmECEVECEVEFsEiEFmECEVMetal and semiconductor Fermi levels align byelectron transfer. Bending is the result of thepresence of transferred electron
  14. 14. 14VG>0p+nnVGECEVEFsEiEFmECEVVGVG<VFBECEVEFsEiEFmECEVVGVG=VFBECEVEFsEiEFmECEVVGFlat band VoltageGate voltage making the band flatVFB= φm-φs
  15. 15. 15Conductivity conversion in MOSFETECEVEFsEiVG=0p+VGnnECEVEFsEiVG ↑p+VGnnLess holes at theinterface, morebendingp typeLess p typeMore depletion
  16. 16. 16ECEVEFsEiVG ↑ ↑p+VGnnp typeLess p typen type InversionECEVEFsEiVG ↑ ↑ ↑p+VGnnp typeLess p typen type Strong InversionOnset ofChannelcreationChannelcreated
  17. 17. 17Inversion condition in MOSFETECEVEFsEiqφbqVsSurface potential Vsis controlled by the gate voltageAccumulationVs<0DepletionVs<φbOnset of inversionVs=φbInversionVs>φbStrong InversionVs>2φbbqkTip n eφ=Equilibrium hole concentration in the bulk of semiconductorqφb is the Fermi level offset fromthe mid-gap in the bulk materialWhen Vs = 2φb, n-concentration at the surfaceis the same as p-concentration in the bulk
  18. 18. 18Surface potential required to reachthe MOSFET thresholdWhen Vs = 2φb, n-concentration at the surfaceis the same as p-concentration in the bulkbqkTip n eφ=ECEVEFsEiVsT=2φbφbφbbqkTin n eφ=
  19. 19. 19Surface potential and gate voltageECEVEFsEiEFmECEVVGViVs• VG is the gate voltage, as source is grounded,VG=VGS• Vi is the voltage drop across the oxide/insulator• Vs is the surface potentialGS FB s iV V V V= + +
  20. 20. 20Voltage drop across the oxide layerECEVEFsEiEFmECEVVGViVsVi is the voltage drop across the oxide/insulatorGS FB s iV V V V= + +diiQVC=where Qd is the capacitor charge and Ci is the capacitance.Since the charges on the metal and semiconductor plates are the same,Qd can be calculated as the charge in semiconductor.The semiconductor charge is formed by the charge of the depletion regionGate electrode and semiconductor form theplates of the MOS capacitor.Voltage drop across the capacitor:
  21. 21. 21Voltage drop across the oxide layerECEVEFsEiEFmECEVVGViVsThe relation between the depletion region width W andthe applied voltage Vs:2d s a sQ qN Vε→ =22assq N WVε=2 saVWqNε=Form this,2 sd a aaVQ qN W qNqNε= =The depletion region charge (per unit area):
  22. 22. 22Voltage drop across the oxide layerECEVEFsEiEFmECEVVGViVsdiiQVc=is the depletion region charge per unit area,ci is the MOS-capacitor capacitance per unit area:sasd VqN2Q,where ε=di is the thickness of the oxide film under the gateiiicdε=
  23. 23. 23MOSFET threshold voltage (cont.)2 s a sGS FB siqN VV V Vcε= + +At the onset of strong inversion:( )( )2 22 s a bT FB biqNV Vcε φφ= + +2 2NT FB b bV V ϕ γ ϕ= + +Finally, the threshold voltage,2N s a iqN c/γ ε=where the body effect constant,The MOSFET threshold voltage is defined as the Gatevoltage leading to the strong inversion, i.e. Vs = 2φb
  24. 24. 24Effect of Body Biasp+n nVSVG VDVBS ≠0( )BSbNbFBT V22VV −ϕγ+ϕ+=the Threshold voltage,
  25. 25. 25Effect of Surface Statesp+n nVSVG VDVBS ≠0( )BSbNbissFBT V22CQVV −ϕγ+ϕ++=the Threshold voltage,During the oxide growth on Si, danglingbonds are created that contributes towanted trapped charges at the interface+ + + + + + + + + +Qss : surface state charges per unit area

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