Basic Statistical Analysis and Yield Calculations

Basic Statistical Analysis and Yield Calculations Dr. Jos? Ernesto Rayas-S?nchez October 17, 2007

Basic Statistical Analysis and Yield Calculations

Dr. Jos? Ernesto Rayas S?nchez

1

Outline

Sources of design-performance uncertainty

Design and development processes

Design for manufacturability

A general formulation to statistical analysis

Tolerance and acceptability regions

Yield definitions

Calculating the yield

Statistical distributions and tolerances

Nominal optimization vs yield optimization

Dr. J.E. Rayas S?nchez

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Basic Statistical Analysis and Yield Calculations Dr. Jos? Ernesto Rayas-S?nchez October 17, 2007

Sources of Design-Performance Uncertainty

FROM THE DESIGN PROCESS

Modeling errors Numerical errors (simulation errors)

FROM THE MANUFACTURING PROCESS

Environmental effects Component aging Fabrication imprecision

FROM THE TESTING PROCESS

Measurement noise Calibration errors Measurement errors

Dr. J.E. Rayas S?nchez

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Typical Design and Development Process

Structure and components

Start

Develop initial design

Hand calculations

CAD simulations

Manufacture prototype Redesign

reject

Test

pass

End

Dr. J.E. Rayas S?nchez

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Basic Statistical Analysis and Yield Calculations Dr. Jos? Ernesto Rayas-S?nchez October 17, 2007

Improving the Design and Development Process

Structure and components

Start

Hand calculations

Parameter statistics

Manufacturing and test models

Develop initial design Manufacture prototype

Redesign

CAD simulations, yield analysis and

optimization

reject

Test

pass

End

Dr. J.E. Rayas S?nchez

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Design for Manufacturability

Start Choose structure and

components Assign initial parameter values

Simulate performance

Optimize performance

Performance

no

acceptable?

yes Analize yield

Yield acceptable? no

yes End to manufacture...

Optimize yield

Dr. J.E. Rayas S?nchez

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Basic Statistical Analysis and Yield Calculations Dr. Jos? Ernesto Rayas-S?nchez October 17, 2007

Achieving a High Yield

By numerical methods (yield optimization): for a given structure, find a nominal solution that best suit the manufacturing tolerances - $

By developing new structures: find a structure (topology, components, materials) less sensitive to manufacturing tolerances - $$$$

By controlling (increasing precision of) the manufacturing process - $$$$$$$$$$

Dr. J.E. Rayas S?nchez

7

A General Formulation to Statistical Analysis

It is assumed that the circuit topology and the component types are already selected by the designer and are fixed

y t represent the t parameters of the electronic circuit that are subject to statistical fluctuations

The optimization variables are restricted to a region X of valid design parameters

x X n represent the n optimization variables of the electronic circuit to be optimized

y includes all the elements in x (n m)

The elements in y not included in x are considered pre-

assigned parameters, contained in vector p m, with

m=t-n

Dr. J.E. Rayas S?nchez

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Basic Statistical Analysis and Yield Calculations Dr. Jos? Ernesto Rayas-S?nchez October 17, 2007

A Formulation to Statistical Analysis (cont)

The parameters of the k-th manufactured device, outcome

yk, are actually spread around the nominal point y according to their statistical distributions and tolerances

These parameters can be represented as

y j = y + y j

j = 1, 2, ... N

where N is the number of outcomes, and yj represents a random variation for the j-th outcome

Dr. J.E. Rayas S?nchez

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A Formulation to Statistical Analysis (cont)

The circuit responses are denoted by R(y) r where r is the number of responses to be optimized

The statistical analysis of a circuit around a nominal point y consists of realizing N simulations of R(yj) for j = 1 to N (also called Monte Carlo analysis)

The number of outcomes N must be sufficiently large to have statistical significance

Dr. J.E. Rayas S?nchez

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