In semiconductor manufacturing, Integrated circuits are produced by building functional modules on top of silicon disks called wafers. The increasing complexity of processes as the nano-technology advances has caused the wafer quality diagnosis even more difficult. Quality monitoring is usually performed via physical measurements and electric tests at selected (and limited) locations on the wafers. The relationship between the measurements and their corresponding locations can be modelled by a Universal Kriging model, including a polynomial trend and an interpolation based on a Gaussian process. A wafer-to-wafer comparison of the reconstructed patterns shall firstly reveal fundamental differences among the wafers such as the product types or process recipes. Furthermore, the impacts from manufacturing equipment, feedback/feedforward process regulations and real time process signals/states are also critical for the quality of wafer measurements. In this study, the spatial reconstruction of wafer measurements is firstly presented. The trend is modelled as a linear combination of Zernike polynomials (Zernike, 1934), in terms of a set of orthogonal functions over the circular domain, i.e. a wafer. Spatial correlation is also investigated in the model with a Gaussian process regression (Rasmussen and Williams, 2006). Links between the modelled patterns and corresponding process parameters are then established for key factors detection and wafer profile prediction. The proposed methodology is tested with industrial datasets.