Wafer Map Distribution of Statistically Correlated Parameters

Introduction

E-test or SPICE model parameters are typically collected from devices taken from different lots and different production lines. These model data sets are normally statistically correlated. SPAYN can be used to perform various statistical analysis on these data sets, including Principal Component Analysis, in order to identify dominant model parameters for worst case analysis and/or yield enhancement. This article describes a new capability available in SPAYN: wafer map distribution of statistically correlated parameters.


Figure 1. Interactive die name editing capability is displayed.

Analysis of Sampled Wafer Lot Data By Using Wafer Map

This new wafer map feature provides a convenient tool for studying the boundary effects, getting statistical summary information for each lot, wafer, or any combination of these attributes, and providing the vertical or stack information at a particular die location.

The data sets used here as an example are complete SPICE level 3 NMOS and PMOS parameter sets extracted from wafer/die sampled from selected wafer lots. The parameter sets include extracted model parameters.

As a simple example, lets assume the user wants to display the average parameter values for NMOS threshold voltage VTO_N and PMOS threshold voltage VTO_P. The user needs to create a die location file for the dies in the selected data set, then the wafer map will display distribution of these parameters in color. The red color for example indicates the highest threshold voltage and the purple color indicates the lowest threshold voltage. Moving the mouse cursor around, the wafer map will display the location and average threshold voltage for each die location at the right column display panel of the wafer map. The color legend is displayed at the left corner of the wafer map. The color distribution across the wafer visually indicates any trends of parameter values as the wafers are coming from different manufacturing lines. One application for example is the display of boundary effects from different process steps.

 

A logarithmic scale of the parameter values is also available by pressing the toggle button at the right column of the wafer map.

Figure 2. Interactive attribute selection windows.

Additionally, a complete analysis of the boundary effects can be done for any combinations of the attributes related to the dies. For example, a user may want to investigate boundary effects for lot1, lot2, or for wafer1, or wafer1, wafer2, wafer3, of lot1 which coming from process 1. All analysis can be done by using convenient set up features on the wafer map coupled with the display of color or grayscale distribution of the dominant parameters on the wafer map.

Statistical information is available for display by turning on the summary button. Each time a parameter is selected for display, its corresponding parameter information window containing a complete statistical summary for that parameter will open along with its attribute combination. This information window displays all statistical information: the number of dies displayed, the name of the parameter, the scale of the parameter value, a list of all the estimated parameter values at each die location, and standard deviation of this estimated parameter value array, median, minimum, maximum values, lower and upper quintiles and interquantile range. Hardcopy option is available to print summary reports.

Aside from planar distribution, a vertical or stack information is also available and calculated at each die location. Move the mouse cursor to a die location of interest, select that die, and a die information window will pop up. This window contains the name and the location of this die and number of dies extracted at this location. Statistical summary is available for this die. This statistical summary can be used to study the wafer to wafer variation of parameter values at a particular die location.

A number of additional user friendly features are available. For example, a user can interactively edit the die location file by selecting the die of interest and entering the die name. When the edit is complete, the changes can be saved back into a file and later used for further analysis.

Figure 3. Statistical summary display for parameter values at all selected die locations.