# Stitching-Based Resolution Enhancement in Wavefront Phase Measurement of Silicon Wafer Surfaces
## 5 Conclusions  
The shrinking size of electronic devices has driven an urgent demand for advanced metrology techniques capable of high-resolution and high-throughput inspection of silicon wafers. In this work, we introduce an advanced wavefront phase sensor that demonstrates  
Figure 16: The global shape is shown with the second order removed. Die-to-wafer bonding and non die-to-wafer bonding dies enumeration. The measure was downsampled in order to speed up the die detection (**left**). Angle differences between the best fit plane of the red dashed area and the best fit plane of the area between the red and black dashed lines (**right**).  
Figure 17: Residual stress in film, provided by Equation (8). All values above 600 MPa and below \(-600\) MPa have been neglected, as they are caused by the gradient of discontinuities in the die shape.  
exceptional metrological performance. The system achieves sub-nanometer axial resolution, specifically below 1 nm, and lateral resolution around 7.56 \(\upmu\)m across diverse silicon wafer samples. Such precision is critical for addressing key industry challenges, including defect detection in die-to-wafer bonding, coplanarity measurement, and residual stress analysis from thin-film deposition processes. These functionalities are vital in ensuring the structural integrity, operational reliability, and extended lifespan of semiconductor devices while mitigating risks of device failure and performance degradation.  
Our proposed system surpasses traditional interferometric methods by utilizing a partially coherent light source, which significantly enhances vibration tolerance. This represents a critical advantage in industrial environments prone to mechanical disturbances.  
Future research will address throughput optimization by investigating techniques for image overlap correction through advanced stitching algorithms, enabling seamless coverage of larger wafer areas. Additionally, an automated interchangeable lens system integrated with a precision linear translation stage is under development. This mechanism will allow for dynamic adjustment of focal lengths and pixel sizes, further enhancing the system's versatility and applicability to a wider range of inspection tasks.  
It is worth mentioning that the stitching process is performed on intensity images rather than on the final phase data. As a result, system-induced aberrations, referred to as bias, remain in the stitched output. This leads to inaccuracies in low-order frequencies; for this reason, the presented data are shown with the second-order polynomials removed. In future work, a method for mitigating this inaccuracy will be studied.  
In conclusion, our proposed system represents a significant advancement in silicon wafer metrology. Its unique features position it as a promising solution for next-generation semiconductor manufacturing, offering precise, efficient, and scalable inspection tailored to evolving industry demands.  
Conceptualization, J.M.T.-S. and K.I.-K.; methodology, J.M.T.-S. and K.I.-K.; software, K.I.-K.; validation, J.M.T.-S.; formal analysis, K.I.-K.; investigation, J.M.T.-S. and K.I.-K.; resources, K.I.-K.; data curation, K.I.-K.; writing--original draft preparation, K.I.-K.; writing--review and editing, [PERSON]-S.; visualization, K.I.-K.; supervision, [PERSON]-S. and [PERSON]-R.; project administration, [PERSON]-S. and J.M.R.-R.; funding acquisition, J.M.R.-R. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.