EECS240 – Spring 2008Lecture 3: MOS Models for DesignElad AlonDept. of EECSEECS240 Lecture 3 2Why Modeling?• Analog circuits more sensitive to detailed transistor behavior• Precise currents, voltages, etc. matter • Digital circuits have much larger “margin of error”• Models allow us to reason about circuits• Provide window into the physical device and process• “Experiments” with SPICE much easier to do EECS240 Lecture 3 3Levels of Abstraction• Best abstraction depends on questions you want to answer• Digital functionality: • MOSFET is a switch• Digital performance:• MOSFET is a current source and a switch• Analog characteristics:• MOSFET described by BSIM with 400 parameters?• MOSFET described by measurement results?EECS240 Lecture 3 4Why not Square Law?• Square law model most widely known:• But, totally inadequate for “short-channel”behavior • Also doesn’t capture moderate inversion• (i.e., in between sub-threshold and strong inversion)()2,12Dsat n ox GS thWICVVLµ=⋅ ⋅ ⋅ ⋅ −EECS240 Lecture 3 5Square Law Model Assumptions• Charge density determined only by vertical field• Drift velocity set only by lateral field• Neglect diffusion currents (“magic” Vth)• Constant mobility• And many more…EECS240 Lecture 3 6A Real TransistorUltra-thin Gate DielectricDirect Tunneling CurrentQuantum EffectsPocket ImplantReverse short channel effectSlower output resistance scaling with LGate ElectrodeGate DepletionQuantum EffectShort Channel EffectsVelocity Saturation and OvershootSource-end Velocity LimitS/D EngineeringS/D resistancesS/D leakageRetrograde DopingBody effectEECS240 Lecture 3 7Now What?• Rely purely on simulator to tell us how devices behave?• Models not always based on real measurements• Model extraction is hard• Models inherently compromise accuracy for speed• Need to know about important effects• So that know what to look for• Model might be wrong, or doesn’t automatically include some effects• E.g., gate leakageEECS240 Lecture 3 8Output Resistance: CLM• “Channel Length Modulation”• Depletion region varies with VDS• Changes effective channel length• If perturbation is small:EECS240 Lecture 3 9Output Resistance: DIBL• “Drain Induced Barrier Lowering”• Drain controls the channel too• Charge gets imaged – lowers effective Vth• Model with Vth= Vth0- ηVDSEECS240 Lecture 3 10Output Resistance: SCBE• “Substrate Current Body Effect”• At high electric fields, get “hot” electrons• Have enough energy to knock electrons off Si lattice (impact ionization)• Extra e=-h+pairs – extra (substrate) current• Models usually empiricalEECS240 Lecture 3 11Output Resistance Mechanisms• All effects active simultaneously• CLM at relatively low fields• DIBL dominates for high fields• SCBE at very high fieldsSource: BSIM3v3 ManualEECS240 Lecture 3 12Velocity Saturation• Drift velocity initially increases linearly with field• Eventually carriers hit a “speed limit”• In the limit, IDα (VGS-Vth)EECS240 Lecture 3 13Vertical Field Mobility Reduction• Mobility actually depends on gate field• “Hard to run when there is wind blowing you sideways (into a wall)”• More technical explanation:• E-field pushes carriers close to the surface • Enhanced scattering lowers mobilityEECS240 Lecture 3 14Halo DopingSource: R. Dutton and C.-H. ChoiEECS240 Lecture 3 15Reverse Short-Channel EffectSource: R. Dutton and C.-H. ChoiEECS240 Lecture 3 16Sub-Threshold Region• Current doesn’t really go to 0 at VGS= Vth• Lateral BJT:log( )EECS240 Lecture 3 17Weak Inversion Channel Potential• “Base” controlled through capacitive divider• Non-ideality factor of channel control n > 1:• (n varies somewhat with bias – const. approx. usually OK)EECS240 Lecture 3 18Weak Inversion Current• Current set by diffusion – borrow BJT equation:EECS240 Lecture 3 19Operating in Weak Inversion• Usually considered “slow”:• “large” CGSfor “little” current drive (see later)• But, weak (or moderate) inversion becoming more common:• Low power• Submicron L means “high speed” even in weak inversion• Not well modeled, matching poor:• VTHmismatch amplified exponentially• Avoid in mirrorsEECS240 Lecture 3 20Moderate Inversion• Moderate inversion: both drift and diffusioncontribute to the current.• Closed form equations for this region don’t really exist.weakstrongmoderateinversionEECS240 Lecture 3 21Patching Models?• Have “good” models for weak inversion and strong inversion. • Why not just interpolate in between?• Example (EKV):EECS240 Lecture 3 22BSIM• Berkeley Short-channel IGFET Model (BSIM)• Industry standard model for modern devices• BSIM3v3 is model for this course• Typically 40-100 parameters• Advanced software and expertise needed to perform extractionEECS240 Lecture 3 23BSIM “Hand Calculation” Model• Requires many, many, many… assumptions• Vertical mobility degradation:• Velocity saturation:Define:oxdtUAu =mobility degradation coefficient1V5.0−≈dufor tox=10nm02UvEsatC=critical E-field for velocity saturationV/cm1024×≈CE(typical value)Define:EECS240 Lecture 3 24Strong Inversion Current()()()⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−⎟⎠⎞⎜⎝⎛++−+−=TGcdTGdTGDsatVVLEuVVuVVV111() ()⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+−+=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+−+⎟⎠⎞⎜⎝⎛−−=LEVVVuILEVVVuVVVVLWCICDTGdlongDlinCDTGdDDTGoxDlin11112)(0µ()() ()⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−⎟⎠⎞⎜⎝⎛++=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−⎟⎠⎞⎜⎝⎛++−=TGCdlongDsatTGCdTGoxDsatVVLEuIVVLEuVVLWCI111112)(20µEECS240 Lecture 3 25Equations of Derivatives• Required parameters()()[](){}()[]()()()[](){}()[]TGdCLMlongDsatTGTGdDsatDTGTGdCLMoxTGTGdDsatDoutVVulPILVVVVuVVVVVVuWlPCLVVVVuVVr−+−−++−=−−+−−++−=11112)(202µjoxxtl 3=with() ()()⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−⎟⎠⎞⎜⎝⎛+++−=⎥⎥⎦⎤⎢⎢⎣⎡+−=TGCdTGDsatlongDsatDsatTGDsatmsatVVLEuVVIIIVVIg11111)(W, L, TOX, U0, UA, VSAT, VTH0, PCLM, XJEECS240 Lecture 3 26Fitting Results0.001.002.003.004.005.006.000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2.0Full BSIM3Hand calculationVG(V)ID(mA)VD=1.8VVD=0.1V0.001.002.003.004.005.006.007.000 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.82.0ID(mA)VD(V)VG=2.0VVG=1.0VFullBSIM3Hand