IC-CAP Statistics Package

The IC-CAP statistics package (available only on HP-UX and Solaris platforms) provides conventional parametric analysis and a patented non-parametric boundary analysis that was developed by Agilent EEsof EDA. The parametric analysis includes Principal Component Analysis (PCA), Principal Factor Analysis (PFA), and multiple linear regression.

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From the main IC-CAP window, you can click on
the Statistics Icon to open the Statistic Interface.
You can automate data import from IC-CAP
extractions directly or import your data from
an external source.

Parametric Analysis

With parametric analysis, it is easy to identify the best model parameters to track in electrical test or to build models that predict SPICE parameters or independent factors. These features help circuit designers and process engineers to improve yields and design more robust products.

To perform parametric analysis, each parameter distribution is first transformed into a Gaussian distribution. A correlation analysis is performed to determine a correlation coefficient matrix. The correlation coefficients provide a numerical measure of the amount of variation in a variable that is attributable to another variable.

To simulate a large number of correlated model parameters, they must be reduced to a smaller number of independent parameters representing the original data set statistical behavior. The main data reduction methods that are used in statistical analysis are PCA, PFA, and Unweighted Least Squares (ULS). The IC-CAP statistics package automatically generates model files from corner or Monte Carlo analysis. In addition, a new method for generating worst-case model candidates called boundary modeling was introduced in IC-CAP release 5.0.

Monte Carlo Analysis

Monte Carlo analysis provides an efficient solution to problems involving elements of uncertainty, which are too complex to be solved by strict analytical methods. Instead of calculating all possible combinations, this method uses a small set of randomly generated values to approximate a solution.

Corner Modeling

Corner modeling is used to select worst-case models from a given data set. This method computes the dependent parameters of a data set to arrive at a set of correlated parameters. Traditional worst-case modeling uses corner models. Corner modeling chooses a set of extreme values at the outside of the real multi-dimensional probability density function (PDF) and requires 2n simulations for an n-dimensional problem.

Parametric Boundary Modeling

Boundary modeling chooses those extreme values at the boundary of the real multidimensional PDF and only needs 2n simulations for an n-dimensional problem. For example, if you chose 10 factors, the number of simulations would be 20, compared to 1024 using corner models. Boundary modeling is an efficient and unique technique to help designers avoid over-designed devices or circuits.

Non-Parametric Analysis

This non-parametric boundary modeling technique was developed and patented to Agilent EEsof. Unlike other statistical analysis tools, which only handle Gaussian distributions, the non-parametric analysis in IC-CAP uses a new technique to handle any arbitrary data distributions, Gaussian or non-Gaussian, and complete the nominal and boundary models.

Details on the non-parametric boundary modeling technique are available in the following article:

• Dan Stoneking, Agilent Technologies, Improving the manufacturability of electronic designs, IEEE Spectrum, June 1999.

Non-parametric analysis works for any data from any arbitrary stochastic process. Such processes need not be Gaussian or have any analytical probability density function. The data can be unimodal or multimodal, residing in a single cluster or multiple clusters with no dimensional limitations. In addition, this method does not create any new model parameter set but uses the original data set. Working with the original data avoids the problem of information being lost during data transformation (as with transformation of raw data into a Gaussian distribution).

The non-parametric statistics analysis starts by selecting a nominal point and by choosing boundary points from an arbitrary user-supplied data collection. The nominal point is the point that has the highest estimated local density and the boundary points are those that have the estimated local density greater than some threshold value. The threshold value is determined by specifying the enclosure percentage, which is, under certain circumstances, related to the yield.

To perform non-parametric analysis, you can specify the number of boundary points, diversity over sampling, threshold percentage enclosed and density estimate percentage.

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Non-parametric analysis results showing the
parameter values of the nominal device
(best case) and boundary devices (worst case).

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Plot showing the nominal and boundary devices.

Typical Statistical Analysis Procedure

A typical statistical analysis procedure in IC-CAP has the following steps:

1. Import the ASCII formatted database that has measured or extracted data.
2. Analyze the data to see if it is a Gaussian distribution.
3. Transform data and remove outliers as needed.

For Gaussian distribution, perform parametric analysis:

1. Perform correlation analysis to see the relationship between each pair of parameters.
2. Compute factor loadings based on PCA or PFA.
3. Build the statistical models relating the model parameters to the independent factors or dominent parameters.
4. Generate Monte Carlo, corner, or boundary models Simulate to find the worst-case models.

Perform non-parametric analysis:

1. Start directly from the measured database or from the non-Gaussian distribution.
2. Calculate density measure estimates for all data points.
3. Compute nominal and boundary models.

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