A novel method for simultaneous measurement of thickness, refractive index, bow, and warp of a large
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.