Analog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedAndrew R. NeureutherEECS 105 Microelectronics Devices and Circuits, Spring 2001Topics: F: MOS threshold voltageVersion 2/5/01Reading: HS 3.7-3.9. Light on math of the MOS capacitance (3.9.2)Lecture 8, February 2, 2001Analog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS Details1710=aN2010>dNmVVEgapn55021.12===+φ( )mVVp4201010ln026.01017=−=φ()()()mVmVVpnFB970420550 −=−−−=−−=+φφAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS-like Case RevisitedMobile ElectronsAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedCharge: MOS PrototypeEqual areaFor charge neutralityOXIDEGATE SUBSTRATEHas both a boundary and a distributed charge densityAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS Case: Depletion Discontinuity by factor of 3.9/11.7Change in slope by factor of 3.9/11.7Xdincreases as sqrt (VB)Parabolic shape VGB = 0.25V > VFB = -970 mVVGB< VTn = 0.6Vφφn+ + VGB= 550 +250 = 800 mVAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value Addedxρρ0(x)-toxMOS Cases Set by VGB xρρ0(x)-toxxρρ0(x)-toxxρρ0(x)-toxxd,maxInversionDepletionFlatbandAccumulationNo charge or electric field!Thin layer of mobile electrons!Negative lattice chargeThin layer of mobile holesThin layer of mobile holesVTn> VGB > VFBVGB = VFBVGB < VFBVGB > VTnVTn = 0.6VVFB = -970 mVAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS Case: Inversion-toxXd,maxxφ (x) 0φs,max = - φp = 420 mV VTn + φn+ -500 mV500 mV1 V1.5 VVoxVB,max VTn - VFBφp VGB= VTn = 0.6VMobile electronsMaximum bending of the potential is –φφp as n(x) makes layer of mobile electronsφφpφφpφ = 0 => = 0 => n = ni|2φ|2φp| =0.84VAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS Case: Flatband xxxρρ0(x)Eo(x)φφ0(x)= - 420 mVVGB= VFB= -φφn+φφp=- 970 mVPotential = φφpNo chargesNo ChargesNo change in potentialNo E fieldAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS Case: Accumulationρ(x)-toxx0QG- QG-toxE(x)0xEox QGεox-toxφ(x) 0x= VGB + φn+-750mV-500mV-250mV-1.0V-1.25V(accumulated holes)VGB - VFBchargedensityelectricfieldpotential+VGB< VFB = -970 mVMobile holesE field is from right to leftφφn+ + VFB= 550 –970 = -420 mVAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedMOS Case: Inversion-toxXd,maxxφ (x) 0φs,max = - φp = 420 mV VTn + φn+ -500 mV500 mV1 V1.5 VVoxVB,max VTn - VFBφp VGB= VTn= 0.6VMobile electronsMaximum bending of the potential is –φφp as n(x) makes layer of mobile electronsφφpφφpφ = 0 => = 0 => n = ni|2φ|2φp| =0.84VAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedCarrier Density vs. Position-toxXd,maxxφ (x) 0φs,max = - φp = 420 mV VTn + φn+ -500 mV500 mV1 V1.5 VVoxVB,max VTn - VFBφp φ = 0 => n = niReference levelφ = - φφp=> p = Nan = ni2/Naφ = + φφp=> p = ni2/Nan = ni2/p = ni2/p ni2/Na = NaLots of electronsno(x) = niexp [φφo(x)/ VTH]Analog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedGate Charge vs Gate VoltageAccumulation Depletion InversionThreshold 0.6VFlatband –0.97VCapacitanceGate ChargeVGBAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedThreshold Voltage VTn( )pAsoxpFBTnNqCVV φεφ 2212 −+−=)(pnFBV φφ −−=+oxsoxtCε=Start from no charge.Make mobile electron density equal hole density in substrateAccount for extra potential due to E field across oxide that terminates on lattice charge.()pAsdaBNqxqNQ φε 22max,max,−−=−=QB,maxis Boron lattice charge and is negative.Analog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedNMOS Example()pasBNqQ φε 22max,−−=()( )()()( )27171419max,/1067.184.0101085.87.11106.12 cmCxxxQB−−−−=−=( )()VxxNqCVpAsoxoxide725.07103.21067.12217=−−−=−−−=−φε()22718114/230103.2101501085.89.3maFFcmxcmxFcmxCoxµ===−−−−−Example pp. 139: Na= 1017; tox= 150Aφφn+= 550 mV φφp= -420 mVAnalog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedNMOS Example cont.( )pAsoxpFBTnNqCVV φεφ 2212 −+−=VmVmVmVVTn595.0725840970 =++−=Any excess gate voltage i.e. voltage above VTncreates additional mobile electrons.For each volt excess gate voltage()()2727/103.21103.2 cmCxVFcmxQMobile−−−==This is 1.4x1012 electrons/cm2Analog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value Addedn-type substrate (PMOS)Analog Integrated CircuitsOverview and Circuit Value AddedOverview and Circuit Value AddedThreshold Voltage VTp( )nDsoxnFBTpNqCVV φεφ 2212 −−=( )( ) ( )()VmVxxVTp695.1103.2101067.14202420550737−=−−−−=−−Example pp. 144: Nd= 1017; tox= 150Aφφn+= 550 mV φφn= 420 mVCOX= 2.3 x 10-7 F/cm2()( )( )( )( )( )27171419max,/1067.184.0101085.87.11106.1222cmCxxxNqQnDsB−−−===
View Full Document
Unlocking...