Author(s)

Yi Wang

Affiliation(s)

School of Mathematics and Statistics, Hubei University of Education, Wuhan 430205, Hubei, China.

Corresponding Author

Yi Wang

ABSTRACT

This paper focuses on the precise measurement of epitaxial layer thickness in silicon carbide wafers. An ideal mathematical model based on infrared interference and its solution algorithm were constructed and solved. To construct the ideal mathematical model for epitaxial layer thickness measurement, the study first analyzes the physical principles of reflection and refraction of infrared light at the epitaxial layer-substrate interface. Utilizing Snell's law and trigonometric functions, it derives formulas for calculating optical path difference and phase difference. By establishing the conditions for wave interference maxima and minima, the theoretical formula for calculating epitaxial layer thickness was ultimately derived, successfully establishing a mathematical framework under the idealized assumption of only two reflections. Building upon this ideal model, for the thickness measurement algorithm design task, the study first performed standardized preprocessing on the provided spectral data, including S-G smoothing filtering, effectively reducing noise interference. Subsequently, a peak localization and selection algorithm was applied to precisely identify and jointly utilize the extreme points of all 60 interference fringes. To resolve the integer ambiguity issue for interference order m, a traversal optimization algorithm was designed. By searching for the m value that minimizes the variance of the thickness calculation sequence, the optimal interference order was coherently determined. Finally, the least-squares fitting optimization technique yielded an average epitaxial layer thickness of approximately 11.61 μm. A four-dimensional reliability assessment—encompassing parameter sensitivity, data integrity, theoretical consistency, and computational stability—validated the algorithm's exceptional robustness and reliability within the idealized model framework.

KEYWORDS

Silicon carbide epitaxial layer; Infrared interferometry; Least-squares method

CITE THIS PAPER

Yi Wang. Precise measurement of silicon carbide epitaxial layer thickness based on infrared interference principle and least squares optimization algorithm. World Journal of Engineering Research. 2026, 4(1): 19-28. DOI: https://doi.org/10.61784/wjer3074.

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