In this study, an optical method that allows simultaneous thickness measurements of two different layers distributed over a broad thickness range from several tens of nanometers to a few millimeters based on the integration of a spectroscopic reflectometer and a spectral-domain interferometer is proposed. Regarding the optical configuration of the integrated system, various factors, such as the operating spectral band, the measurement beam paths, and the illumination beam type, were considered to match the measurement positions and effectively separate two measurement signals acquired using both measurement techniques. Furthermore, for the thickness measurement algorithm, a model-based analysis method for high-precision substrate thickness measurements in thin-film specimens was designed to minimize the measurement error caused by thin films, and it was confirmed that the error is decreased significantly to less than 8 nm as compared to that when using a Fourier-transform analysis. The ability to undertake simultaneous thickness measurements of both layers using the proposed system was successfully verified on a specimen consisting of silicon dioxide thin film with nominal thicknesses of 100 nm and 150 nm and a 450 μm-thick silicon substrate, resulting in the exact separation between the two layers. From measurement uncertainty evaluation of a thin-film, a substrate in a thin-film specimen, and a single substrate, the uncertainties were estimated to be 0.12 nm for the thin-film, 0.094 μm for the substrate in a thin-film specimen, and 0.076 μm for the substrate. The measurement performance of thicknesses distributed on multi-scale was verified through comparative measurements using standard measurement equipment for several reference samples.
The importance of dimensional metrology has gradually emerged from fundamental research to high-technology industries. In the era of the fourth industrial revolution, absolute distance measurements are required to cope with various applications, such as unmanned vehicles, intelligent robots, and positioning sensors for smart factories. In such cases, the size, weight, power, and cost (SWaP-C) should essentially be restricted. In this paper, sub-100 nm precision distance measurements based on an amplitude-modulated continuous-wave laser (AMCW) with an all-fiber photonic microwave mixing technique is proposed and realized potentially to satisfy SWaP-C requirements. Short and long target distances of 0.879 m and 8.198 m were measured by detecting the phase delay of 15 GHz modulation frequencies. According to our measurement results, the repeatability could reach 43 nm at an average time of 1 s, a result not previously achieved by conventional AMCW laser distance measurement methods. Moreover, the performance by the proposed method in terms of Allan deviation is competitive with most frequency-comb-based absolute distance measurement methods, even with a simple configuration. Because the proposed method has a simple configuration such that it can be easily utilized and demonstrated on a chip-scale platform using CMOS-compatible silicon photonics, it is expected to herald new possibilities, leading to the practical realization of a fully integrated chip-scale LIDAR system.
In this study, an optical system for simultaneous measurement of physical thickness, group refractive index, bow, and warp of a large silicon wafer is first proposed based on a reflection-type spectral-domain interferometer. Such key parameters are determined by combining four different optical path differences measured at each sampling point throughout two-axis sample scanning within area of 250 mm by 250 mm. To overcome the measurement limitations by the deflection of a free, unclamped large-sized wafer, two optical path differences representing the surface profiles of both sides are utilized to facilitate the thickness and refractive index measurements insensitive to sample inclination. For verification of the proposed method, a 300-mm diameter silicon wafer with nominal thickness of 775 μm was used as a test sample. For measuring the bow and warp with gravity effect compensation, a silicon wafer was measured once again after turning over. Through theoretical analysis on the changes of optical path differences with the wafer tilted based on the measured surface profiles, it was verified that the effect of wafer bending on thickness and refractive index measurements can be ignored. The measurement uncertainties (k=1) of physical thickness, group refractive index, bow, and warp were evaluated to be approximately 0.692 μm, 0.003, 0.416 μm, and 0.589 μm, respectively.