Monte carlo simulation

®

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

®

Monte Carlo simulation in statistical design kit

Opamp V1 Mismatch and Process Variation

®

Monte Carlo simulation in statistical design kit

Sweep of Process Parameter Model Setup

®

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

®

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

®

Monte Carlo simulation in statistical design kit

Circuit optimisation Step 2

®

Monte Carlo simulation in statistical design kit

Circuit optimisation

Step 3:

Adjust bias current andadd cascode stage

®

Monte Carlo simulation in statistical design kit

Circuit optimisation Step 3

®

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

®

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