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®
Monte Carlo Simulation
in Statistical Design Kit
®
Monte Carlo simulation in statistical design kit
1. Monte Carlo Simulation
2. Practical demonstration in Cadence
3. Simulation and Measurement
Overview
®
... allows the random variation of
- process parameters
- mismatch parameters
- process & mismatch parameters
Monte Carlo simulation in statistical design kit
Monte Carlo 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 simulation in statistical design kit
Monte Carlo process simulation
®
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 simulation in statistical design kit
Monte Carlo process simulation
...dw_rpyhl_skewrcs_rpyhl_skewrsh_rpyhl_skewa_wc_skew_nsica_be0_skew_nsicr_nsu_skew_nsicr_nbl_skew_nsicr_ncx_skew_nsicr_nci_skew_nsicr_wb_skew_nsicr_jbei_skew_nsicr_nbei_skew_nsic ...
®
Even optimum layoutcannot completely avoid mismatch between components.
The MC mismatch analysis gives insight in the effect of these slight variations.
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 simulation in statistical design kit
Monte Carlo 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 simulation in statistical design kit
Monte Carlo process & mismatch
simulation
®
Monte Carlo Tool
Demonstration
Monte Carlo simulation in statistical design kit
®
Monte Carlo simulation in statistical design kit
Testbench
®
Monte Carlo simulation in statistical design kit
Operational Amplifier V1
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Monte Carlo simulation in statistical design kit
Opamp V1 Mismatch and Process Variation
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Monte Carlo simulation in statistical design kit
Sweep of Process Parameter Model Setup
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Monte Carlo simulation in statistical design kit
Sweep of Process Parameter Model Setup
®
Monte Carlo simulation in statistical design kit
Variation of Process Parameter with Corner Tool
®
Monte Carlo simulation in statistical design kit
Variation of
Process
Parameter
with
Corner
Tool
®
Monte Carlo simulation in statistical design kit
Sweep of Process Parameter
®
Monte Carlo simulation in statistical design kit
Opamp V1 Mismatch and Process Variation
®
Monte Carlo simulation in statistical design kit
Circuit optimisation
Step 1:
Add base current compensation
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Monte Carlo simulation in statistical design kit
Circuit optimisation Step 1
®
Monte Carlo simulation in statistical design kit
Circuit optimisation
Step 2:
Add buffer stage
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Monte Carlo simulation in statistical design kit
Circuit optimisation Step 2
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Monte Carlo simulation in statistical design kit
Circuit optimisation
Step 3:
Adjust bias current andadd cascode stage
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Monte Carlo simulation in statistical design kit
Circuit optimisation Step 3
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Monte Carlo simulation in statistical design kit
Improvement in DC-Offset
®
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
Monte Carlo simulation in statistical design kit
Overview
®
- Run sensitivity analysis
- MC Simulation with individual mismatch enable
- Perform correlation check after process simulation in Monte Carlo Tool
- sweep of single process parameters
Monte Carlo simulation in statistical design kit
Identify critical components and
process parameters
®
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
Monte Carlo simulation in statistical design kit
Rules of thumb for Design
®
Simulation and
Measurement
Monte Carlo simulation in statistical design kit
®
Monte Carlo simulation in statistical design kit
Circuit Topology
®
Monte Carlo simulation in statistical design kit
First approach to
DC-Offset
compensation
with dummy stage
®
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)
Monte Carlo simulation in statistical design kit
Results from first Silicon
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Typical DC Offset Distribution (Wafer probing)
1-Sigma 38.7mV
Monte Carlo simulation in statistical design kit
®
Monte Carlo simulation in statistical design kit
Resimulation: Mismatch & Process Variation
®
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
Monte Carlo simulation in statistical design kit
Redesign
®
- 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)
Monte Carlo simulation in statistical design kit
Circuit improvements
®
Monte Carlo simulation in statistical design kit
Redesign
without
dummy stage
but
OP design
improved
®
Monte Carlo simulation in statistical design kit
New Design: Mismatch & Process Variation
®
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 ?
Monte Carlo simulation in statistical design kit
Overview
®
Monte Carlo simulation in statistical design kit
More Information
[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