Simultaneous Measurement of Thickness and Group Refractive Index Based on Differential White Light Interferometry

Abstract

Simultaneous measurement of thickness and refractive index is an important quality control scheme in high-end fabrication. However, the precise measurement of large-range thickness is still technically difficult. In this paper, we propose a high-precision simultaneous measurement method of thickness and group refractive index using differential white light interferometry. Using the bi-directional white light interferometer with a high dynamic range, we can get access to the optical paths on both sides of the specimen. We evaluate the performance of the proposed method by measuring specimens of three different materials, with different thicknesses ranging from 200 μm to 2000 μm. The measurement data are in good agreement with the nominal thickness, and the standard deviations of repeated measurements are ≤0.009 μm and ≤1.63×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> RIU for thickness and group refractive index respectively. In addition, we evaluate the impact of the temperature change on the group refractive index. A quasi-linear relationship between group refractive index and temperature is observed, and the slope of linear fit of silicon specimen around 20 °C is about 3.29×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> RIU/°C@1310 nm. We also analyze and summarize the main factors which may introduce uncertainty in the measurement results. The expanded uncertainties ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> =2) of measured thickness and group refractive index are ≤4.21×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> μm and ≤7.84×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> RIU respectively. The repeatability and uncertainty of group refractive index measurement both decrease as the thickness of specimen increases.