In the digital era, silicon wafers are the core foundational materials for the electronics and optoelectronics industries, and their thickness plays a crucial role in device performance, process stability, and product reliability. Silicon wafer thickness directly relates to electrical characteristics, thermal conductivity, and mechanical strength, and affects the consistency of key manufacturing processes such as lithography and etching. Improper thickness control can easily lead to stress concentration, warpage, or even device failure, thereby reducing yield. Therefore, achieving high-precision measurement and control of silicon wafer thickness is a critical prerequisite for ensuring quality and reliability in advanced manufacturing.
In this study, a spectral-domain low-coherence interferometry method was used to construct the measurement optical path (Fig.2), and an aiming module (Fig.3) was introduced to address the issue of system dead zone, thereby improving the stability and clarity of interference fringe acquisition. Given that raw interference signals could not be directly used for distance calculation, this study introduced a fringe-contrast-based signal extraction algorithm to screen and obtain the optimal interference spectrum. The raw interference fringe signals acquired by the spectral-domain low-coherence interferometry system were first processed. To address the random noise and local fluctuations in single-frame interference signals, spectral signal extraction was performed on the interference fringes (Fig.7), and a multi-frame averaging method was applied to obtain the mean spectral signal as the final signal (Fig.9d), thereby effectively improving the signal-to-noise ratio and enhancing signal stability. Based on this, a method based on the phase information of the interference signal was used for system wavelength calibration (Fig.11). By establishing a correspondence between the interference fringe phase and pixel position, the calibration of spectral sampling points was achieved. According to the wavelength calibration results, the interference signal, originally uniformly sampled in the pixel domain, was mapped to the wavenumber domain, and the non-uniformly spaced wavenumber data were resampled (Fig.12) to meet the equal-spacing requirement of the Fourier transform. Additionally, windowing was applied to suppress spectral leakage and sidelobe interference (Fig.13), and finally the Fourier transform distance spectrum of the interference signal was obtained. However, due to factors such as system noise, sampling errors, and window functions, the distance spectrum obtained by Fourier transform was only an approximate estimation of the target position. To further improve distance localization accuracy, this study proposed a feature-point-driven adaptive spline interpolation algorithm, which extracted key feature points from the distance spectrum and adaptively constructed a spline interpolation model to achieve high-precision estimation of the peak position.
To verify the effectiveness of the proposed algorithm, simulation-based comparative analysis was conducted between the proposed method and commonly used methods, including the energy centroid method and the hill-climbing search algorithm. The results demonstrated that the proposed algorithm outperformed the compared methods in terms of average error and stability, with an average error reduction of approximately 72.5% compared to the hill-climbing search algorithm. For experimental validation, a complete measurement optical system for silicon wafer thickness was established, and the measurement results were compared with those obtained from a spectral confocal system as the reference value. The relative error of the measurement results was less than 1%, meeting the accuracy requirements for engineering applications. To further evaluate the reliability of the measurement system, a single-point repeatability experiment was conducted on the same silicon wafer, yielding 100 sets of measurement data (Fig.17). The range was 1.01 μm and the standard deviation was 0.302 μm, indicating that the system had good repeatability. Further analysis of the sources of repeatability error revealed that in high spatial frequency regions, where interference fringes were dense and the signal spatial gradient was large, environmental disturbances and system noise were easily amplified significantly, resulting in relatively poor repeatability. In low spatial frequency regions, where interference fringes were sparse, the system exhibited weaker noise transfer characteristics, and thus the measurement results showed better repeatability.
To meet the requirements of silicon wafer thickness measurement, this study proposes and implements a silicon wafer thickness measurement scheme based on spectral-domain low-coherence interferometry, with improvements and innovations in signal processing and distance localization algorithms. The results demonstrate that this method can achieve high-precision measurement of silicon wafer thickness, with the measurement error meeting engineering application requirements, while also demonstrating stability and repeatability. The experimental and simulation results verify the advantages of the proposed algorithm over traditional methods in terms of measurement accuracy, providing a valuable reference for the application of spectral-domain low-coherence interferometry in silicon wafer thickness measurement and related precision measurement fields.
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