Computational surface profilometry and its applications in semiconductor inspection

Abstract

Non-contact surface profilometry techniques, especially the phase-measuring profilometry, have been evolved dramatically over recent years. Besides the simple triangulation configuration with a fringe pattern projection system and digital imaging system, efficient computational surface profilometry techniques have also drawn tremendous attention from both academia and a wide range of applications. In the semiconductor industry, high-precision and high-speed, automated optical inspection systems are urgently needed to ensure high quality of semiconductor devices and yield improvement on the production and assembly line. However, by assuming the measured object to be stationary, conventional approaches are not suitable for surface profilometry of moving objects. Moreover, different sources of error such as the low contrast fringe patterns on the measured object, the unevenness in the illumination and the perspective projection effect from the optics will decrease the performance of surface profilometry.

To meet these challenges, we have built fringe pattern projection prototypes with projector and camera arrays for surface profilometry of moving objects along the conveyor belt. This design helps to enlarge the field of view with parallel processing. In addition, we have presented an optimization framework to investigate the sources of the error for surface profilometry and generalize various computational surface profilometry approaches under different scenarios.

Under this framework, first, we investigate two important factors determining the precision of surface profilometry, namely, the condition number of the phaseshift matrix and the fringe contrast within the images of the projected fringe patterns. Then, a regularized phase-shift algorithm has been proposed to improve the reconstruction results at the low contrast regions such as on the substrate of the semiconductor devices. Second, we study the intensity fluctuation caused by the uneven illumination for surface profilometry of moving objects. After that, an illumination-reflectivity-focus model has been suggested to describe the unevenness and an illumination-invariant phase-shift algorithm has been developed to handle this uneven illumination effect. Third, the perspective projection effect from the optics also affects the accurate phase-shift estimation for a moving object. Therefore, we propose a general polynomial phase-measuring profilometry model to establish the relationship between the phase-shift and height variation for each measured point. Accordingly, a polynomial phase-shift algorithm with error compensation technique has been put forward to improve the performance of the surface profilometry for moving objects.

Both simulation and real experiments from the prototype have been conducted to verify the improvement on the performance of the proposed methodologies. Furthermore, these research results have demonstrated the effectiveness and efficiency of the presented optimization framework for investigating the sources of error for surface profilometry. Moreover, the proposed computational surface profilometry techniques and the corresponding fringe pattern projection systems have been used in automated optical inspection systems for yield improvement on the production line in the semiconductor industry.