Wafer Test Measurement Correlation Analysis

Introduction

Rigorous wafer testing processes such as wafer acceptance testing often come with large amounts of data, which can be challenging to analyze and make meaning of. This application addresses this challenge by measuring the strength of association, calculated as the Cramer's V measure, between streamed wafer test measurement data and a chosen target variable. In turn, this identifies which sensors and parameters are most correlated with a failed test. With these insights, users will gain direction and guidance on where to prioritize their troubleshooting efforts. Having streamed data also allows these correlations to be monitored in real time, and facilitates quick, data-driven decision making.

To explore this dashboard yourself, check it out on our demo gallery. The demo gallery contains a version where streaming is not enabled; for a full demo, please email datascience@spotfire.com.

What is the Cramer’s V measure?

Cramer's V measures the strength of association between two variables, and ranges from 0 to 1, with 0 meaning no association, and 1 meaning a very strong association. Traditionally, Cramer’s V is applied to categorical data, but with additional preprocessing (binning and ranking), the measure can be applied to continuous data as well. Additionally, bias correction has been incorporated, which is especially beneficial for calculating correlations on smaller datasets.

Click here to read more about the Cramer's V measure.

Example Data and Use Case

In this demo, we are working with data that contains wafer test measurements. Each row is a wafer from a particular lot having test measurements collected from 6 sensors, each measuring 15 parameters. In total, each wafer will have 90 test measurement columns. There is also a binary outcome variable, with values indicating if the test had a "normal" or "abnormal" result, along with a visual failure code if a visual abnormality was detected by an operator.

Examples of parameter measurements include voltage, current, probe pad thickness, resistance, and more. A full set of example parameter measurements can be found in the demo.

Demo Walkthrough

Explore & Configure

This page provides an overview of the data we are working with. It contains a preview of what that data looks like, as well as a sample schema to provide some more context of what types of parameters we could be looking at. On the right is where you can configure your data. There are two modes this data can be viewed in: streaming and historical data. Configuring streaming data cannot fully be done in Spotfire; access to the streaming application is also required for full configuration. Configuring historical data means that tests have already been run, and now, association values can be calculated on the entire dataset at once. For configuring streaming data, you can select your window size - this is the maximum number of rows that will be used in the Cramer’s V calculations. The window will always move in increments of one row, but this can be configured based on if you want more or less recent data to be included in the calculations.

For configuring historical data, you configure your index column, target column, and measurement columns.

Then, click configure and get a confirmation message that your inputs have been configured.

Cramer’s V Results (Streaming)

This page is where the Cramer’s V association calculations are displayed for streaming data. To start, you can control the stream and receive a confirmation message on whether the stream is started, stopped, paused, or resumed. Whether the stream is actively running or not, you can change how you’d like to view the first plot. You can either view a particular sensor, see all sensors, or just highlight the top 5, a midrange which you can select, and the rest of the measurements.

On the right hand side, the Cramer’s V values are compared to a theoretical chi-square distribution. The idea here is that because the Cramer’s V measurement is based on the chi-square measure, it follows the same logic that a completely random set of values, i.e. where each column is considered independent of the target variable, then it would follow a chi-square distribution. By seeing a strong deviation from the chi-square distribution, this shows that there’s some significant association happening between some of the measurement columns and the target variable.

At the bottom is a heat map of the Cramer’s V values by sensor and parameter - lighter colors have lower values and darker colors have higher values, i.e. a stronger association.

Cramer’s V Results (Historical)

This page is where the Cramer’s V association calculations are displayed for historical data. Similar to the streaming page, you can change how you’d like to view the first plot. You can either view a particular sensor, see all sensors, or just highlight the top 5, a midrange which the user can select, and the rest of the measurements. The other plots and annotations are also identical to the streaming version of this page.

In this case, we are highlighting the measurements from Sensor 4, and are seeing very high correlations, indicating that we may want to further investigate what is being measured at Sensor 4 and if it is causing the test failures.

To continue onto the next portion of the app, you must mark columns of interest on either results page.

Parameter Drilldown

On this page, a user is looking at the rows they marked on the previous page. We can compare what the median values are across parameters, trellised by if it was a normal or abnormal result. With this page, users can get an idea of what parameters and subsequent values could be cause for further investigation and understanding.

Visual Failure Codes

On this last page, we are looking into the visual failure codes recorded in our data. We have a pareto chart and a spider plot to give users more insight as to what visual failure codes are most common, and if there are particular lots that they appear more frequently in.

Across the different pages, users will have a better understanding of their test measurement data and gain better guidance and direction on where to invest their troubleshooting efforts.