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A novel noncontact measurement method based on double-coil sensor is proposed for determining the thickness of copper (Cu) film on the silicon wafer in the process of stress free polishing (SFP). The double-coil sensor consists of two identical coaxial eddy current coils and corresponding auxiliary circuits, where the two coils are excited with the same sinusoidal signal and interact through the magnetic resonance coupling. The induced currents are produced in the Cu film through the electromagnetic coupling between double coils. The interaction equivalent circuit model of Cu film and two coils of double-coil sensor is discussed and the coil design and its lumped parameter extraction are analyzed. The linear relationship between the inductance difference of two coils and lift-off distance change (LODC) is formed and analyzed. By simulating the Cu film with different thicknesses sandwiched between two coils, the distribution and intensity of the magnetic field are presented. The slope of the relationship line between the inductance difference and the LODC is termed as SOR. Dependent on the LODC, the relationship between SOR and thickness of Cu film is extracted. Finally, the double-coil sensor is fabricated and the experiment is implemented. Different specimens with the thickness ranges from 100 to 500 nm are prepared and measured, where the measured maximum relative error is 4.7% and standard errors are between 2 and 13 nm. The experimental results demonstrate that the proposed measurement method is feasible and can confirm the thickness of Cu film on the silicon wafer. It is not only insensitive to the LODC but also can measure the thickness of less than $1~\mu \text{m}$ for Cu film on the silicon wafer.

Noncontact Thickness Measurement of Cu Film on Silicon Wafer Using Magnetic Resonance Coupling for Stress Free Polishing Application