Wafers in a semiconductor manufacturing process are subjected to many process steps which can induce stress variations across the wafer, e.g., thin film depositions, RTA processes, etc. These stress variations change the wafer shape, thus rendering them visible to the PWG metrology approach. A real manufacturing process might have many processing steps between layers, so the overlay error would be driven by the accumulated stress changes from all of those processes. For example, a critical overlay error between an active area (AA) patterned layer and a gate patterned layer, would need wafer shape data at AA lithography and also wafer shape data at gate lithography. Based on the preceding considerations, we now describe a novel metric from wafer shape data which can predict IPD of chucked wafers in the lithography scanner, leading to noncorrectable overlay errors. Figure 2 schematically outlines the calculation of this new metric which we call PIR. In order to make predictions of the overlay errors between pattern layer and pattern layer , we start with wafer shape measurements at both the layers. For each layer, we calculate a wafer shape gradient vector, and thus the measured wafer shape map creates a local slope vector map across the wafer. Next, a slope difference map is derived by subtracting the two local slope maps for layer and . Note that if the shape slope map for layer is the same as the slope map for layer , then the slope difference map will be zero, and no process-induced overlay error would be predicted. The slope difference map represents the expected IPD from the change in stress that occurred between layers and , including the change in the uniform stress component assuming that the wafer is pulled perfectly flat by the lithography tool chuck. The chucking performance depends on a combination of the chucking forces and the spatial wavelengths contained in the shape of the wafer being chucked and has been reported elsewhere.8 But constant magnification components, i.e., simple and components of Eq. (1), will be accurately corrected by the normal scanner alignment process. Therefore, we must subtract such correctable components from the shape slope difference map to obtain a shape slope residual (SSR) vector map, which will correlate most directly to realistic overlay error deviations. The “Scanner Corrections” box of Fig. 2 can mimic any type of alignment process, although most commonly the simple linear models of Eq. (1) are used. If higher-order corrections are applied by a scanner exposure tool then the SSR calculation can be modified to account for these corrections. The final step to predict the PIR is to multiply the SSR by a slope factor “,” which may vary for different processes and sources of stress. In general, we recommend determining from empirical data correlating overlay measurements and SSR data for the specific process under study. Typical values are the order of , meaning that an SSR of corresponds to an IPD of .