Interferometric Microscopic Measurement Method for Encapsulated Structures Via Dual-arm Differential Adjustable Compensation

Encapsulation is a critical step in semiconductor manufacturing， providing chips with a stable and protected operational environment through integration into compatible external structures. High-precision and non-destructive surface morphology measurement of transparent encapsulated devices is essential， as it enables early detection of latent defects， supports process optimization， and ensures long-term device reliability. However， conventional white light interferometric microscopy faces inherent limitations when applied to encapsulated samples. Existing optical-path compensation schemes offer only restricted compensation ranges， and even small residual mismatches between the encapsulation layer and the compensation glass can introduce monochromatic aberrations and chromatic dispersion. These residual errors degrade fringe contrast， distort the recovered phase， and can ultimately lead to failure in reconstructing surface morphology.To address these challenges， we propose a dual-arm differential adjustable compensation strategy for white light interferometric microscopy. The method is designed to address the thickness mismatch and material dispersion when measuring encapsulated microstructures. The system incorporates two independently adjustable compensators： a plate compensator inserted into the test arm and a pair of wedge plates placed in the reference arm. The wedge plates provide a thickness adjustment range from 4.8 mm to 5.2 mm enabling the system to realize a continuously adjustable compensation range. The two compensators form a continuously adjustable configuration capable of correcting up to 400 μm of thickness deviation. This design supports stable compensation for encapsulation thicknesses from 0 mm to 5.2 mm. A 2.5× Michelson-type interferometric objective is employed in order to conveniently separate monochromatic aberrations from chromatic dispersion， thereby enabling a focused investigation of dispersion-induced phase distortions and the effectiveness of the proposed compensation strategy.Theoretical modelling and numerical simulations were conducted to assess the feasibility and robustness of the proposed compensation strategy. The modelling incorporated the spectral characteristics of the light source， the refractive-index dispersion of the encapsulation materials， and the numerical aperture of the interferometric objective. A detailed quantitative analysis was carried out to evaluate the influence of light-source bandwidth， the intensity ratio between the two interferometric arms， and residual thickness mismatch on the achievable fringe contrast. The results highlight the necessity of incorporating adjustable wedge plates to achieve continuous and precise dispersion compensation. Based on the simulation outcomes， acceptable tolerance ranges for the residual mismatch were derived， providing practical design guidelines for implementing adjustable dispersion compensation in interferometric microscopy platforms.Experimental validation was conducted using three representative classes of samples to verify the measurement accuracy and system stability. In addition to validating measurement accuracy， these experiments were also designed to evaluate the long-term operational stability of the compensation mechanism， especially under varying encapsulation thicknesses. First， a Bruker RM1722 roughness standard was used to evaluate surface roughness under encapsulation. The dynamic adjustment of the wedge plates in the reference arm effectively preserved high-contrast fringes. The encapsulated sample exhibited an arithmetic average roughness of （0.63 ± 0.003） nm， which closely matched the value of （0.61 ± 0.004） nm for the unpackaged sample. Second， a standard SHS-23008 step height specimen was measured beneath a 1 mm K9 cover plate to simulate the encapsulation condition. The reconstructed step height was （9.272±0.021） μm， demonstrating both the accuracy of the compensation method and the robustness of the phase retrieval process. Finally， the technique was applied to TO-packaged photodiodes to characterize the surface morphology of the encapsulated chip region. The arithmetic mean height and root mean square height of the surface were 3.855 nm and 3.892， respectively， indicating the good fabrication quality. These comprehensive results confirm that the proposed dual-arm differential adjustable interferometric method is feasible， reliable， and highly accurate for characterizing the surface morphology of transparent encapsulated microstructures. The demonstrated performance establishes the method as an effective and practical solution for high-precision， non-contact morphology evaluation of transparent encapsulated devices.