Implementation and Performance Evaluation of a Bivariate Cut-HDMR Metamodel for Semiconductor Packaging Design...

Area of Science:

• Engineering
• Computational Science
• Materials Science

Background:

• Metamodeling is crucial for optimizing complex engineering designs.
• High Dimensional Model Representation (HDMR) offers a framework for analyzing high-dimensional problems.
• Semiconductor packaging design involves numerous variables, necessitating efficient modeling techniques.

Purpose of the Study:

• To implement and evaluate the Bivariate Cut High Dimensional Model Representation (HDMR) technique for a 10-variable semiconductor packaging design problem.
• To compare the performance of Bivariate Cut HDMR against the Central Composite Design (CCD) metamodeling approach.
• To analyze the efficiency and accuracy of Bivariate Cut HDMR in terms of sample point usage and predictive error.

Main Methods:

• Implementation of Bivariate Cut HDMR considering up to second-order interactions.
• Utilizing three uniformly distributed sample points (s=3) with quadratic spline interpolation for component functions.
• Direct comparison with a metamodel based on Central Composite Design (CCD).
• Performance evaluation using R-squared and Relative Average Absolute Error (RAAE) metrics.

Main Results:

• Bivariate Cut HDMR achieved accuracy comparable to CCD.
• Bivariate Cut HDMR required only one-fifth of the sample points used by CCD (201 vs. 1045 points).
• The technique demonstrated robust performance in predicting outcomes for the semiconductor packaging design.

Conclusions:

• Bivariate Cut HDMR is a highly efficient metamodeling technique for high-dimensional problems like semiconductor packaging design.
• The method offers a significant reduction in computational cost without sacrificing predictive accuracy.
• Further investigation into sampling schemes and prediction planes can elucidate the technique's effectiveness.