Focus control is a critical technology in the semiconductor manufacturing process, as it directly influences wafer exposure quality. The wafer height map is measured by a level sensor on the measurement side of a dual-stage lithography tool, allowing the wafer stage to adjust its vertical position to align with the projection lens’s best focal plane. The height map surface is typically generated using numerical methods based on the wafer’s height data. However, due to noise in the raw height data, the vertical trajectories derived from this data cannot be directly implemented by the wafer stage control system. In static exposure, the wafer map consists of a series of fitting planes, each corresponding to the size of the exposure slit, which helps to mitigate the negative influence of high-frequency spatial noise. In this study, we propose a reconstruction method for wafer maps based on parametric surface to address the aforementioned issues. This method can establish an analytical representation of the wafer map using a parametric surface algorithm, suitable for dynamic exposure scenarios.

The level sensor is based on the triangulation method, which converts vertical position into relative displacement of the images of grating marks, including projection and detection gratings. The image of the projection grating on the wafer’s top surface, referred to as the measurement spot, characterizes the 3D topography of the wafer surface. The light source is a halogen lamp with a wavelength spectrum of 600 to 1000 nm. Both the projection and detection optics use double telecentric designs to reduce diffraction effects. To enhance robustness and measurement accuracy, the level sensor operates on a difference measurement principle. The detection grating image is split into two polarization beams (E-channel and O-channel), each detected by separate optical-electronic detectors. The raw height, without any calibrations, is computed using the normalized difference in light intensities between the E-channel and O-channel. The linear height of the measurement spot is determined, and optic nonlinear errors are corrected through online calibration. Nine independent measurement spots are arranged in a line, with the total width equal to the exposure field width. The raw height of the wafer surface is obtained through field-by-field scanning by the level sensor. To reduce high frequency spatial noise, the height map is generated by averaging the raw height samples along the scanning direction. The full wafer characteristics can then be analyzed using this height map. For static exposure, the Die height map is divided into several rectangular areas based on the exposure slit length in the scanning direction, and the average plane for each area is fitted using the least squares method. This creates a local Die map composed of a serial of independent planes. The vertical trajectories for the wafer stage are calculated based on the total height and tilt of each plane, resulting in discontinuous trajectories within the local Die field. In contrast, the parametric wafer map, used for dynamic exposure, is generated using bi-quartic B-spline surfaces and skinning algorithms. The scanning direction and spot direction are referred to as u-direction and v-direction, respectively, with the section lines corresponding to the height map samples along scanning direction. Uniform knot vectors are used in both directions to ensure consistency with the skinning method. Control point vectors are determined by solving equations that incorporate interpolation and boundary conditions, with the parametric Die map described by multiplying B-spline basis functions. The entire wafer map is constructed by piecing together the independent Die maps, and vertical trajectories for the wafer stage are calculated based on the average height and partial derivatives of the Die surface. The moving average of focus error (MAFE) and moving standard deviation of focus error (MSDFE) are calculated to evaluate the focus error, which is defined as the average difference between the image plane and wafer height in the exposure area.

The height map and wafer map are tested and validated using a focus experimental platform consisting of a level sensor, a mechanical frame, a metrology frame, a wafer stage, and a laser interferometer. The test sample is a 200 mm bare wafer secured by a vacuum chuck. The height and wafer maps are created to showcase the full wafer characteristics (Figs. 6 and 7). The parametric wafer map for the sample wafer is reconstructed using a field-by-field scanning strategy. Experimental results demonstrate that the local Die map is continuous and smooth in both the scanning and spot directions (Fig. 9). The vertical trajectories of the wafer stage for static exposure and dynamic exposure are calculated and compared (Figs. 8 and 10). MAFE and MSDFE are employed to assess the focus error of the parametric wafer map (Fig. 11). Compared to the static exposure wafer map, the Z/Rx/Ry motion trajectories are smoother and reduce the specification requirements for the wafer stage.

A parametric wafer map reconstruction method using a bi-quartic B-spline surface is proposed to improve exposure efficiency in dynamic exposure scenarios. The wafer map achieves continuity and smoothness in both the scanning and spot directions within each Die field, and vertical motion trajectories for the wafer stage are calculated directly. The lithography and focus control experimental platform is built to assess and verify the reconstruction accuracy of the parametric wafer map. The experimental results for MAFE and MSDFE range from -35.8 to 13.3 nm and from 5.9 to 41.4 nm, respectively. The parametric wafer map effectively reduces the spatial noise in the raw height signal, and the motion trajectories generated by the parametric surface are advantageous for focus control in the lithography machine. Future work will focus on the reconstruction method for wafer edge Die, which are irregularly shaped and partially overlap with the image plane.