## Statistical Parameter and Yield Analysis

**Spayn**^{™} is a statistical modeling tool for analyzing variances from model parameter
extraction sequences, electrical test routines, and circuit test measurements.
Spayn helps to identify the relationship between device or circuit performance
variations and the process fluctuations.

## Key Features

- Automatic generation of worst-case and corner SPICE models
- Advanced principal factor / component analysis
- Identification of inter-relationship among groups of parameters
- Statistical process control, process monitor, and yield analysis
- Advanced Wafer Map displaying wafer-to-wafer and die-to-die variances
- Seamless integration with fast SmartSpice API for statistical circuit design
- Flexible data input,
output, append, merge, and split options with histogram, 2D & 3D scatter
plot, and response surface model display options

- Silvaco's strong encryption is available to protect valuable customer and third party intellectual property.

## Spayn Objective

Spayn is a statistical analysis software package tailored for the semiconductor industry. It is applied for two main fields:

- Characterization
- Process Control/Analysis

Spread in performance of analogue or digital circuits is largely due to inherent fluctuation in the manufacturing process. Achieving statistical control is fundamental to product quality.

Spayn is the ideal statistical modeling tool for analyzing variances from model parameter extraction sequences, electrical test routines, and circuit test measurements

Spayn performs statistical analyses on parametric data, and helps determine the complex relationships between circuit design and process fabrication parameters.

## Spayn Users

- Parameter Extraction and Circuit Simulator Support Personnel
- Device Modeling Engineers
- Circuit Designers
- Process Development / Integration Engineers

## Spayn Applications

Used standalone, or linked to a circuit simulator, Spayn is a user-friendly tool requiring little detailed knowledge of statistics and no user-created programs.

Usage from SPICE parameter extraction, process development and integration, product, and yield engineers, to circuit designers.

Spayn
is a simple, powerful, and affordable tool for statistical modeling and process
control.

## Data Filtering

Spayn is capable of managing a large number of Attributes, Parameters and Samples, limited only by workstation memory and processor performance. To deal with large data sets, Spayn provides a powerful filtering concept allowing selection of samples to reduce the number of data sets used. "Filter by Attributes" allows definition offilters based on data set attributes. "Filter by Parameters" can be used to further reduce the number of data sets by specifying limits on the parameter values.

Even with a spreadsheet table, it can be tedious and numbing to work with all data. To address this, Spayn provides filters to precisely select samples and reduce the number of data sets in use. Filtering can be done at the Attributes or Parameters level. First, "Filter by Attributes" defines database identification selection key. Second, "Filter by Parameters" defines value limits to reduce the number of sets that satisfy criteria.

Powerful "Filter by Attribute" dialog. Choose among different filtering methods. |
Subset of dataset definition using powerful "Filter by Parameters." Some tools such as ’compute limits,’ ‘histogram plot,’ Automatic Filter,’ help build the Filter. |

## Statistical Analysis, Data Management and Visualization

Spayn accepts Utmost IV-generated SPICE model library formats, Virtual Wafer Fab format, and other industry formats (RS/1TM, CSV, MS EXCELTM). Spayn offers unique and extremely fast relational database search, merge, append, and split capabilities. Many built-in general purpose statistical analysis features aid in the examination of parametric data: Gaussian, exponential, log-normal, and Gamma distributions.

Scatter plots analyze the relationship between parameters by using the least squares method to fit linear, logarithmic, parabolic, reciprocal, hyperbolic, exponential, power, root, or 3rd order polynomial. The resulting error residuals, ANOVA information and correlation coefficients are generated. The “Golden Device feature” allows you to calculate which observation or observations in a particular database most closely match the mean, based on some dissimilarity measure.

Response surface model of regression are displayed using TonyPlot | Histogram plot with attributes for selected parameters highlighted |

The contour plot displays ellipses representing +s, +2s, and + 3s distribution of parameters | The relationship among any three selected parameters can be viewed in 3D |

Multiple linear regression capabilities generate equations that relate one selected parameter to other sets of user-defined parameters. SPICE models card can be generated for any point in a scattergram Plot. The SmartSpice link and the user Netlist feature allow running simulation for each SPICE models card.

Significant correlations are highlighted in red.

## Advanced PCA/PFA – Principal Component and Factor Analysis

Spayn identifies dominant parameters and/or factors of variations. The data is then automatically grouped so that each parameter in a specific group is controlled by the same source of variation. Analysis of each parameter group then identifies relationships between process input, process monitoring, device, circuit, and manufacturing parameters within the group.

The following analysis features are available:

- Advanced Principal Component and Factor Analysis
- Dominant parameter identification
- VARIMAX and QUARTIMAX rotations
- Histograms or scatter plots using components/ factors
- PCA parameter weights and sensitivity analysis
- Unique user-defined dominant parameter selection and equations.

PCA/PFA capabilities allows you to define dominant parameters or identify them automatically, and then generate linear or non-linear equations | Powerful factor analysis, coupled with built-in SPICE model equations, delivers unmatched statistical modeling capabilities |

## Worst-Case and Corner SPICE Model Generation

Spayn generates equations relating each parameter under analysis to the uncorrelated dominant factors or dominant parameters. These independent variables are interactively or automatically perturbed to produce realistic “corner” and “worst-case” models using built-in SPICE model equations.

User-defined, Monte Carlo (left figure), corner (right figure), or worst-case simulations can be performed using the fast SmartSpice API. Single device or very complex circuits can be simulated and many types of analysis are possible. |

## Statistical Process Control and Yield Analysis

Spayn can be used to determine the underlying statistical nature of IC manufacturing processes and their impact on device performance.

Spayn creates statistical process control (SPC) and process monitor (PM) charts to track the variation of dominant parameters or factors over selected wafers or lots. SPC charts plot and store Shewhart mean and range/sigma data with the parameters grouped in terms of their attributes.

Spayn helps to identify
an efficient process monitoring strategy by identifying the minimum set of
dominant factors that must be monitored in production
in order to control the yield. Process monitoring charts are then used
to view
these parameters.

SPICE models are generated using built-in SPICE. Models can then be used to run simulations directly from PM charts. |

Wafer Map displays parameters, or any other measured data together with their distributions over die locations |

Golden Device feature calculate which observation or observations most closely match the mean, based on some dissimilarity measure. i.e., the measured device that best describes the given database.

computed and Attributes displayed

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