Acoustic lens design using ray tracing for high frequency ultrasonic inspection of semiconductor defects

Yu-Man Kim; Jong-Hyun Lee

doi:10.7776/ASK.2026.45.4.343

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2026 Vol.45, Issue 4 Preview Page Next Page

Acoustic lens design using ray tracing for high frequency ultrasonic inspection of semiconductor defects 반도체 결함 탐지용 초음파 검사를 위한 레이 추적법 이용 음향렌즈 설계

31 July 2026. pp. 343-349

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Abstract

In this study, a novel ray tracing method incorporating frequency-dependent effects is proposed. The validity of the proposed approach is verified by comparing the simulated acoustic field with that generated by a vibrating planar piston. For a spherical lens, three-dimensional acoustic field distributions near the focal region are analyzed, showing that the Depth of Focus (DOF) and Beam Diameter (BD) achieve approximately 85 % and over 95 % agreement with theoretical predictions, respectively. Furthermore, simulations of an aspherical lens demonstrate the feasibility of designing acoustic lenses with an extended DOF that is difficult to achieve using conventional spherical geometries. The proposed ray tracing method is particularly effective in environments where reflections by walls, ceiling, and floor are negligible, and it is well suited for the design of transducers and acoustic lenses used in ultrasonic semiconductor wafer inspection systems such as Scanning Acoustic Microscopy (SAM). All numerical computations in this study were performed using Python in the Google Colab environment.

Keywords

Scanning Acoustic Microscopy (SAM)

Ray tracing

Acoustic lens

Depth of Focus (DOF)

Beam Diameter (BD)

본 연구에서는 주파수 의존성을 고려한 새로운 레이 추적법을 제안하였다. 제안된 방법의 타당성은 평면 피스톤 진동에 의해 생성된 음장과의 비교를 통해 검증되었다. 구면 렌즈에 대한 시뮬레이션을 수행하여 초점 부근의 음장을 3차원적으로 분석하였으며, 그 결과 초점심도(Depth of Focus, DOF)는 이론값 대비 약 85 %, 빔 직경(Beam Diameter, BD)은 95 % 이상의 정확도를 보였다. 또한 비구면 렌즈에 대한 시뮬레이션을 통해, 기존 구면 렌즈로는 구현이 어려운 넓은 DOF를 갖는 음향렌즈 설계 및 제작 가능성을 확인하였다. 제안된 레이 추적법은 벽, 천장, 바닥 등에 의한 반사가 없는 환경에서 특히 효과적이며, 초음파 기반 반도체 웨이퍼 비파괴 검사 장비인 주사음향현미경(Scanning Acoustic Microscopy, SAM)에서 핵심 구성요소인 트랜스듀서 및 음향렌즈 설계에 유용하게 적용될 수 있다. 본 연구의 모든 수치 해석은 파이썬을 기반으로 구글 코랩 환경에서 수행되었다.

키워드

주사음향현미경(Scanning Acoustic Microscopy, SAM)

레이 추적법

음향렌즈

초점심도(Depth of Focus, DOF)

빔 직경(Beam Diameter, BD)

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Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 45
No :4
Pages :343-349
Received Date : 2026-04-10
Revised Date : 2026-05-29
Accepted Date : 2026-06-04
DOI :https://doi.org/10.7776/ASK.2026.45.4.343

The Journal of the Acoustical Society of KoreaISSN:1225-4428(Print) 2287-3775(Online)한국음향학회

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