In the semiconductor manufacturing industry, precision, reliability, and consistency are of utmost importance. Every aspect of production and quality control relies on accurate and repeatable measurements.

1. Gage Repeatability and
Reproducibility in Semiconductor
Manufacturing

2. In the semiconductor manufacturing industry, precision, reliability, and consistency are of
utmost importance. Every aspect of production and quality control relies on accurate and
repeatable measurements. To ensure the effectiveness of measurement systems and
processes, a rigorous measurement system analysis is required. The Gage Repeatability and
Reproducibility (Gage R&R) test, a key tool for such an analysis, is commonly used to verify
the capabilities of a measuring instrument.
Gage R&R is a statistical tool used to study the amount of variation in the measurement
system arising from the measurement device and the people taking the measurement. It
gives an understanding of the reliability of the measurement system by quantifying its
variance, and by comparing this variance with the overall variability observed.
Understanding and applying the concepts of Gage R&R will help in mitigating errors in the
process, and subsequently improve the quality of the final product.
This detailed technical guide will discuss the intricacies of Gage R&R and how it can be
effectively applied in the semiconductor manufacturing industry. Further, it will shed light
on interpreting the results and using them for better decision-making.

3. Gage R&R: The Concept
The Gage R&R test assesses the measurement system as a whole, including the instrument itself, the operator using it, and the
procedure for its use. It does not evaluate the product or component. The test is based on the idea that the variation in measurement
results originating from the instrument should be significantly smaller than the variations from the measured parts or components.
Two key elements in Gage R&R analysis are repeatability and reproducibility. Repeatability refers to the variation in repeated
measurements from the same instrument, operator, part, and time. Reproducibility refers to the variation in repeated measurements
when there are changes in conditions like different operators, or times.
For instance, in the context of a semiconductor manufacturing environment, repeatability could be how consistently a Scanning Electron
Microscope (SEM) measures a particular feature size on a wafer lot when used by the same operator and under the same conditions.
Reproducibility, on the other hand, might reflect how the SEM's measurements vary when used by different operators or at different
times.
However, Gage R&R goes beyond just these two factors. It also takes into account the operator's skill and understanding of the
measurement procedure, which can significantly impact the measurement results.
Requirements for a Gage R&R Test
To perform a Gage R&R test, the following requirements must be met:
Parts
A sample of 5-10 parts manufactured with varying dimensions. In the context of semiconductor manufacturing, these could be wafers
with varying feature sizes or other parameters of interest.
Operators
At least two operators are needed for the study to compare measurements. These could be quality control inspectors or machine
operators, depending on the specific use case.

4. Measurement System
The measurement system to be analyzed must be identified. This could range from an optical microscope to a more complex system such as an
Atomic Force Microscope (AFM), depending on the parameters being measured.
Measurement Repetitions
Three or more measurement repetitions for each part and each operator. The number of repetitions needed may depend on the variability in
the measurements and the precision required.
Statistical Software
Gage R&R procedure and analysis requires robust statistical software capable of handling computations. Popular software includes Minitab,
JMP, and even Excel with certain add-ins.
Gage R&R Procedure
An understanding of the mathematical models underpinning Gage R&R analysis is beneficial for interpreting results, but most calculations can
be performed using statistical software. The test uses the Analysis of Variance (ANOVA) method, specifically a balanced two-factor crossed-
random model.
The steps in conducting a Gage R&R study are as follows:
Data Collection: Gather measurements from each operator for each part, repeated as per the requirement (usually 3 or more times). This step
should follow a randomized order to eliminate bias.
Data Entry
Enter the collected data into the statistical software, ensuring it is properly structured for the Gage R&R analysis.
Analysis
Run the Gage R&R analysis, typically found in the Quality Tools or Measurement System Analysis menu in most statistical software.

5. Case Studies
Let's consider two examples of Gage R&R analysis in the context of yield in semiconductor manufacturing:
Case 1: A semiconductor manufacturer conducted a Gage R&R analysis on their high-resolution SEM used for measuring feature size on a
newly developed chip. They found that the percentage of total variation due to the measurement system was 25%. This indicated that
their SEM was not suitable for the task, and further investigation found that the SEM needed recalibration and maintenance.
Case 2: In another scenario, a semiconductor company conducted a Gage R&R study on their ellipsometer used for measuring the
thickness of oxide layers on a wafer. The study showed that the percentage of total variation due to the measurement system was only 8%,
suggesting that their measurement system was capable and effective.
These examples illustrate how to interpret Gage R&R test results and underline the importance of this tool in verifying the capability of
measurement processes in the semiconductor industry.
Conclusion
Gage R&R analysis plays a crucial role in the quality control and process improvement strategies of semiconductor manufacturing. By
accurately assessing the measurement system's capability, companies can ensure that their products meet the stringent requirements of
precision and repeatability demanded by the industry.
References
1. Measurement Systems Analysis (MSA), 4th Edition, AIAG (Automotive Industry Action Group) - This manual provides a
comprehensive understanding of MSA, including Gage R&R.
2. Wheeler, D.J. and Lyday, R.W. (1990). Evaluating the Measurement Process. Second Edition, SPC Press, Inc.
3. Pyzdek, T., & Keller, P. (2018). The Six Sigma handbook. McGraw-Hill Education.
4. "Guidance for Industry and FDA Staff: Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests", U.S.
Department of Health and Human Services, Food and Drug Administration, March 2007.