Monte Carlo Simulation in Statistical Design Kit

Overview Monte Carlo simulation in statistical design kit 2. Practical demonstration in Cadence 3. Simulation and Measurement

Monte Carlo Simulation Monte Carlo simulation in statistical design kit Monte Carlo Simulation ... allows the random variation of - process parameters - mismatch parameters - process & mismatch parameters

Monte Carlo process simulation Monte Carlo simulation in statistical design kit Monte Carlo process simulation Wafer production will always show some variation of techno- logical parameters The MC process simulation is the adequate tool to give an early estimation how it will affect the circuits function.

Monte Carlo process simulation Monte Carlo simulation in statistical design kit Monte Carlo process simulation ... dw_rpyhl_skew rcs_rpyhl_skew rsh_rpyhl_skew a_wc_skew_nsic a_be0_skew_nsic r_nsu_skew_nsic r_nbl_skew_nsic r_ncx_skew_nsic r_nci_skew_nsic r_wb_skew_nsic r_jbei_skew_nsic r_nbei_skew_nsic For each simulation run a new random set of process parameters is generated and is valid for all active and passive components in the circuit

Monte Carlo mismatch simulation Monte Carlo simulation in statistical design kit Monte Carlo mismatch simulation Even optimum layout cannot completely avoid mismatch between components. The MC mismatch analysis gives insight in the effect of these slight variations.

Monte Carlo mismatch simulation Monte Carlo simulation in statistical design kit Monte Carlo mismatch simulation For each device an individual mismatch random variable is generated and is valid only for a single run. The mismatch property can be set globally or for selected devices only.

Monte Carlo process & mismatch simulation Monte Carlo simulation in statistical design kit Monte Carlo process & mismatch simulation In addition to the global random process parameter set each device gets an individual mismatch random variable. This combined simulation will give an estimation of a real wafer fabrication

Monte Carlo Tool Demonstration Monte Carlo simulation in statistical design kit Monte Carlo Tool Demonstration

Monte Carlo simulation in statistical design kit Testbench

Operational Amplifier V1 Monte Carlo simulation in statistical design kit Operational Amplifier V1

Opamp V1 Mismatch and Process Variation Monte Carlo simulation in statistical design kit Opamp V1 Mismatch and Process Variation

Sweep of Process Parameter Model Setup Monte Carlo simulation in statistical design kit Sweep of Process Parameter Model Setup

Sweep of Process Parameter Model Setup Monte Carlo simulation in statistical design kit Sweep of Process Parameter Model Setup

Variation of Process Parameter with Corner Tool Monte Carlo simulation in statistical design kit Variation of Process Parameter with Corner Tool

Variation of Process Parameter with Corner Tool Monte Carlo simulation in statistical design kit Variation of Process Parameter with Corner Tool

Sweep of Process Parameter Monte Carlo simulation in statistical design kit Sweep of Process Parameter

Opamp V1 Mismatch and Process Variation Monte Carlo simulation in statistical design kit Opamp V1 Mismatch and Process Variation

Add base current compensation Monte Carlo simulation in statistical design kit Circuit optimisation Step 1: Add base current compensation

Circuit optimisation Step 1 Monte Carlo simulation in statistical design kit Circuit optimisation Step 1

Circuit optimisation Step 2: Add buffer stage Monte Carlo simulation in statistical design kit Circuit optimisation Step 2: Add buffer stage

Circuit optimisation Step 2 Monte Carlo simulation in statistical design kit Circuit optimisation Step 2

Adjust bias current and add cascode stage Monte Carlo simulation in statistical design kit Circuit optimisation Step 3: Adjust bias current and add cascode stage

Circuit optimisation Step 3 Monte Carlo simulation in statistical design kit Circuit optimisation Step 3

Improvement in DC-Offset Monte Carlo simulation in statistical design kit Improvement in DC-Offset

Overview Monte Carlo simulation in statistical design kit DC-Offset N = 1000 simulation runs Simulation MM Proc MM&Proc before optimisation 3.82 22.77 24.94mV after optimisation 1.16 0.09 1.16mV

Identify critical components and process parameters Monte Carlo simulation in statistical design kit Identify critical components and process parameters - Run sensitivity analysis - MC Simulation with individual mismatch enable - Perform correlation check after process simulation in Monte Carlo Tool - sweep of single process parameters

Rules of thumb for Design Monte Carlo simulation in statistical design kit Rules of thumb for Design Wide spread at Mismatch Simulation: -> Increase area factor of critical components Wide spread at Process Simulation: -> Check circuit topology e.g.: - add base current compensation - add cascode or buffer stage

Simulation and Measurement Monte Carlo simulation in statistical design kit Simulation and Measurement

Monte Carlo simulation in statistical design kit Circuit Topology

First approach to DC-Offset compensation with dummy stage Monte Carlo simulation in statistical design kit First approach to DC-Offset compensation with dummy stage

Results from first Silicon Monte Carlo simulation in statistical design kit Results from first Silicon First silicon of a test circuit did show a wide spreading of DC offsets especially in high gain mode. The yield was unacceptable low : DC offset voltages Specification: +/- 20mV First silicon : ~ 40mV (1-sigma)

Typical DC Offset Distribution (Wafer probing) Monte Carlo simulation in statistical design kit Typical DC Offset Distribution (Wafer probing) 1-Sigma 38.7mV

Resimulation: Mismatch & Process Variation Monte Carlo simulation in statistical design kit Resimulation: Mismatch & Process Variation

Redesign Monte Carlo simulation in statistical design kit Evaluation of the circuit without statistical models is possible - but takes a lot of time. Monte Carlo Analysis with new statistical design kit provides a fast insight in the circuits behaviour at mismatch and process variation. The conformity of measurement and simulation is rather good

Circuit improvements Monte Carlo simulation in statistical design kit - enlarge area factor at critical elements - add base current compensation - decrease current of differential amplifier to limit influence of beta variation - limit influence of early effect by cascode stages and dummy amps - revise the complete channel topology and gain chain (omit dummy OP stage)

Redesign without dummy stage but OP design improved Monte Carlo simulation in statistical design kit Redesign without dummy stage but OP design improved

New Design: Mismatch & Process Variation Monte Carlo simulation in statistical design kit New Design: Mismatch & Process Variation

Overview Monte Carlo simulation in statistical design kit DC Offset @ Opamp output (300 simulation runs) Simulation Measurement MM Proc MM&Proc Wafer First Design 13.6 32.9 32.9mV 38.7mV New Design 6.3 0.8 5.9mV ?

More Information Monte Carlo simulation in statistical design kit [1] Kraus, W. : PCM- and Physics-Based Statistical BJT Modeling Using HICUM and TRADICA, 6th HICUM Workshop, 2006 [2] Schröter, M., Wittkopf, H., Kraus, W. : Statistical modeling of high-frequency bipolar transistors, Proc. BCTM, pp 54 - 61, 2005