MOSFET Simulation ModelsRigorous Modeling“Compact Models”Types of Compact ModelsTable ModelsEmpirical ModelsPhysical ModelsCommon Compact Models for IC SimulationsBSIM Model (e.g. BSIM3v3)EKV Model (e.g. EKV 2.6 Model)PSP ModelSmoothing FunctionEKV Model (Simplified)Statistical ModelingMonte Carlo SimulationCorner Simulations (PVT Corners)Process VariationSupply Voltage VariationTemperature Variation1MOSFET Simulation ModelsDr. David W. GrahamWest Virginia UniversityLane Department of Computer Science and Electrical Engineering© 2010 David W. Graham2Rigorous Modeling• Requires 3D modeling equations• Finite-element analysis (coupled PDEs for thousands of small elements)• Great for designing devices• Unusable for circuit design– Simulations take far too long– Æ Need a faster simulation model for circuit design3“Compact Models”• Simplification of the finite-element analysis approach• Include only what needs to be included– This is a tough job in developing simulation models– Models have to be simple enough to simulate fast, but complex enough to permit design– Tradeoff between simulation speed and model accuracy/complexity• We use “compact models” in SPICE4Types of Compact Models1. Table Models2. Empirical Models3. Physical Models5Table Models• Look-up-table approach• Contains currents (+ maybe small-signal parameters) for a given bias condition• Fast simulation– No need to solve complicated equations– May use interpolation• Easy to develop– Simply characterize your device• Provides current value regardless of the mechanism causing it– Not concerned with the physics• Cannot be used to predict changes if parameters change– e.g. if W or L change, a completely new table is required• Rarely used for sophisticated design6Empirical Models• Relies on curve fitting• Can use any equation that adequately fits the data• Parameters have no physical meaning– e.g. coefficient to the curve-fit polynomial• Fairly easy to characterize devices and extract the curve-fit parameters• Purely empirical models are rarely used– Typically they help other types of models to model real devices– Some device characteristics are very hard to model analytically7Physical Models• Based on device physics• Parameters have a physical meaning– e.g. flat-band voltage, substrate doping, etc.• Hard to develop• Typically result in the best simulation results• Can be used to predict the performance for changing parameters• May require significant overhead for changing process technology8Common Compact Models for IC Simulations1. BSIM Model2. EKV Model3. PSP Model9BSIM Model (e.g. BSIM3v3)• From UC Berkeley• Most widely used model in industry (currently)• Performance– Very good for strong inversion– Okay for weak inversion (improving)– Poor performance in moderate inversion• Mixture of empirical and physical models• Typically >100 parameters• Parameters available from foundry10EKV Model (e.g. EKV 2.6 Model)• Developed by 3 Swiss engineers– Enz, Krummenacher, and Vittoz• Originally developed to be a better hand-calculation model for low-power circuit design• Used primarily in low-power circuit-design, but its influence is growing• Performance– Works well in strong inversion– Works very well in weak inversion– Decent in moderate inversion• Physical model– Only 18 parameters– Each parameter has physical significance– Therefore, parameter extraction is a simpler process11PSP Model• Developed jointly by Penn St. (now ASU) and Philips Research• Slated to become the “next industry standard”– Decided by the Compact Modeling Council– Not widely used yet, but will soon be• Based on “charge-sheet modeling”– i.e. it is based upon looking at the surface potential• Physical Model12Smoothing Function• Modeling moderate inversion is hard• Given strong-inversion and weak-inversion models, how do we go between the two? – i.e. How can best approximate moderate-inversion operation?• Æ Use a smoothing function that incorporates both weak and strong inversion– Only one side (e.g. weak inv.) is “revealed” under a given set of biasing conditions– EKV model is particularly suited to this approach13EKV Model (Simplified)()()⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+−⎟⎟⎠⎞⎜⎜⎝⎛+=−−−−TdTgTsTgUVVVUVVVTeeUKI222221log1log22κκκSmoothing Function⎟⎠⎞⎜⎝⎛+221logxeInterpolates smoothly between exponential and quadratic relationshipwhen x<0()()κμκκκTTTsbgUVoxTUVVVfeCUIeII020102−−−+=≈ wherewhen x>0()()212sTbgfVVVVKI −−−−≈κκκκ14Statistical Modeling• Designs must be robust to process variations (e.g. mismatch, variations in doping, variations in Vdd , etc.)• Many degrees of freedom and parameters that can be varied• Monte Carlo simulation is a popular choice for statistical modeling15Monte Carlo Simulation• Define a given set of possible ranges for parameters– e.g. substrate doping, VT , Vdd• Randomly pick a subset of the values within the range• Perform simulations• Is design within tolerance?– If YES – Done– If NO – Modify design16Corner Simulations (PVT Corners)• Special case of Monte Carlo simulations• Looking for the best and worst case scenarios of varying parameters• Vary 3 specific parameters– Process– Supply Voltage– Temperature17Process Variation• Deviations in the fabrication process• Examples include– Doping concentrations– Oxide thickness– Diffusion depths– W and L sizes– (Usually described as “fast” or “slow” transistors)• Caused by non uniform conditions during fabrication18Supply Voltage Variation• If Vdd changes, it could significantly alter the performance of a circuit– i.e. change current, gm , etc. • Vdd could also vary by location on an IC• Could significantly affect “overhead” and power consumption19Temperature Variation• Temperature can change due to – Environment– Heat caused by other parts of the IC (i.e. temperature gradients caused by self heating)• As Temperature increases– Mobility ↓– VT ↓– UT