1. Monte Carlo Simulation in Statistical Design Kit

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

3. 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

4. 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.

5. 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

6. 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.

7. 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.

8. 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

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

10. Monte Carlo simulation in statistical design kit
Testbench

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

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

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

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

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

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

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

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

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

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

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

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

23. 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

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

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

26. Overview Monte Carlo simulation in statistical design kit
DC-Offset N = 1000 simulation runs
Simulation
MM Proc MM&Proc
before optimisation mV
after optimisation mV

27. 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

28. 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

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

30. Monte Carlo simulation in statistical design kit
Circuit Topology

31. 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

32. 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)

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

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

35. 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

36. 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)

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

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

39. Overview Monte Carlo simulation in statistical design kit
DC Opamp output (300 simulation runs)
Simulation Measurement
MM Proc MM&Proc Wafer
First Design mV mV
New Design mV ?

40. 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 , 2005