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<p>Silicon wafers serve as essential substrates for semiconductor chips, necessitating ultra-precise surface measurements to ensure device reliability. Optical interferometry has been widely employed for surface shape measurement due to its large-aperture, non-contact capabilities, and nanometer-level accuracy. Among various interferometric techniques, wavelength-modulation interferometer combined with phase-extraction methods enables surface shape measurement without mechanical movement of the target sample. However, existing approaches require multiple fringe patterns, additional phase unwrapping, and fail to adequately compensate for phase-shifting nonlinearity caused by environmental uncertainties. To address these limitations, deep learning-based methods have been explored for phase extraction. However, existing deep learning models often produce discontinuous phase distributions requiring post-processing or rely on fixed phase-shift intervals, limiting practical applicability. This study proposes a robust phase aberration estimation network (PAENet) that accurately extracts Zernike aberration coefficients from two raw fringe patterns with random phase shift. PAENet directly computes continuous phase distributions without pre- or post-processing and effectively eliminates systematic errors from phase-shifting nonlinearity. The training data incorporate various ranges of Zernike coefficients, reflecting the physical characteristics of actual fringe patterns. Simulation results demonstrated that PAENet achieves the lowest peak-to-valley (PV) and root-mean-square (RMS) errors compared to existing methods. In experimental fringe patterns in the surface profile measurements of silicon wafer, PAENet effectively suppressed systematic errors caused by phase-shifting nonlinearity, unlike conventional phase-extraction methods. Furthermore, PAENet demonstrated a repeatability error of 1.0812&#xa0;nm, significantly outperforming conventional approaches, including other deep learning-based methods.</p>

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Deep Learning-Based Phase Aberration Estimation for Ultra-Precise Silicon Wafer Metrology

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Hwan Kim,
  • Yangjin Kim,
  • Yusuke Ito,
  • Naohiko Sugita,
  • Mamoru Mitsuishi

摘要

Silicon wafers serve as essential substrates for semiconductor chips, necessitating ultra-precise surface measurements to ensure device reliability. Optical interferometry has been widely employed for surface shape measurement due to its large-aperture, non-contact capabilities, and nanometer-level accuracy. Among various interferometric techniques, wavelength-modulation interferometer combined with phase-extraction methods enables surface shape measurement without mechanical movement of the target sample. However, existing approaches require multiple fringe patterns, additional phase unwrapping, and fail to adequately compensate for phase-shifting nonlinearity caused by environmental uncertainties. To address these limitations, deep learning-based methods have been explored for phase extraction. However, existing deep learning models often produce discontinuous phase distributions requiring post-processing or rely on fixed phase-shift intervals, limiting practical applicability. This study proposes a robust phase aberration estimation network (PAENet) that accurately extracts Zernike aberration coefficients from two raw fringe patterns with random phase shift. PAENet directly computes continuous phase distributions without pre- or post-processing and effectively eliminates systematic errors from phase-shifting nonlinearity. The training data incorporate various ranges of Zernike coefficients, reflecting the physical characteristics of actual fringe patterns. Simulation results demonstrated that PAENet achieves the lowest peak-to-valley (PV) and root-mean-square (RMS) errors compared to existing methods. In experimental fringe patterns in the surface profile measurements of silicon wafer, PAENet effectively suppressed systematic errors caused by phase-shifting nonlinearity, unlike conventional phase-extraction methods. Furthermore, PAENet demonstrated a repeatability error of 1.0812 nm, significantly outperforming conventional approaches, including other deep learning-based methods.