Application of Dimensional Analysis to Statistical Process Modeling
Abstract
This work explores the use of Dimensional Analysis as a technique fo r combining the benefits of empirical modeling and analytical modeling for physical processes. Two processes in the semiconductor industry, Low Pressure Chemical Vapor Deposition (LPCVD) of Polysilicon and LPCVD of Low Temperature Oxide, are dimensionally analyzed and experimenntally modeled. The group parameters that Dimensional Analysis yields are shown to be physically more significant than the primitive variables, that is variables that are directly and independently controlled, and therefore model processes much better. For each process, the best polynomial refression to experimental data is found for both the dimensionless parameters and the primitive variables. The average ratio of dimensionless parameter model F-tests to primitive variable model F-tests is 5:1 for polysilicon, and 2.25:1 for LTO. Also, and Application theorem, which measures the modeling and design of experiments gain yielded by Dimensional Analysis is presented. This Application theorem parallels the Pi theorem, but to fit the specific needs of manufacturing processes. The experimental aspect of this work involved minimizing the wafer to wafer variance of the Low Temperature Oxide process. This was achieved by designing and performing amd orthogonal array of eighteen experiments that charaterized the growth rate of the process. Models of the film deposition for eleven evenly distributed wafers were created and evaluated using the L18 array. These models were then used to calculate the wafer to wafer variance. The variance was reduced from eleven percent to six percent.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1989
- Accession Number
- ADA211881
Entities
People
- William P. Wehrle
Organizations
- Massachusetts Institute of Technology