Multi-scale models for wafer surface evolution in chemical mechanical planarization
As device size decreases and circuit density increases, planarization technology becomes more and more important in semiconductor fabrication. Chemical mechanical planarization (CMP) has emerged as a new promising technique for its capability to achieve better local and global planarization of wafer surface. However, CMP process is sensitive to the pattern structure variation across a chip. The material removal rates are different for the regions with different pattern structure. Therefore, CMP obtains local planarization but generates global thickness variation. Two models, referred as Models I and II, are developed to investigate the pattern structure effect on the post-CMP wafer profile. Model I assumes that the pad asperities contact with the wafer directly. In developing this model, at first, the pressure distribution between a rough pad and a patterned wafer is evaluated based on Greenwood and Williamson model (1966); then, approaches are proposed to re-distribute the pressure due to pad bending to account for the effects of surrounding topography. The modified pressure is utilized in Archard's law (1953) to predict the local material removal rate and associated wafer surface evolution. This model has been verified against the experimental observations. A parametric study is conducted using this model to investigate the effects of pad roughness, bending ability, and influence length (which is defined the range of area over which the surrounding features affect the material removal rate at a given location). CMP designs for effective planarization are discussed based on Model I. Model II extends Model I to account for the abrasive particles effects. The wafer material removal is assumed to be primarily due to the slurry particles abrasion. Modeling is focused on a small region on the wafer surface. The contact pressure at this region is evaluated by Model I first. Then the material removed by a single active particle sliding over this region is estimated. After estimating the number of active particles sliding over this region during a time step, the total material removed from this region and the mean material removal rate can be calculated. By doing this across the whole wafer surface, the wafer profile evolution is obtained.