Mesa 5.0's Physics-Based Model
Mesa 5.0's theory has been
proven to capture key physics involved during CMP, on the feature and
pattern scale. The model computes the point-wise contact force between
the pad and wafer, and then removes the wafer material at a rate proportional
to that stress, as illustrated in the figure below:
In the figure above, the wafer is pressing into the pad. Consequently, the pad is compressed and also bulges up between the wafer features. Of course, in reality the pad is extremely rough compared to the height of the wafer features. However, because only the tips of the rough pad features touch the wafer and because they are also in constant motion relative to the wafer, their effect can be averaged and modeled as a smooth pad surface.
The contact balances the stresses in the pad surface, the resulting contact stresses, and the overall down-force on the wafer as shown in the figure below.
The wafer displacement, which is an unknown, is determined computationally until the sum of the pad contact forces balance the process down-force. Each time the model tries a new wafer displacement, the shape of the pad has to be recalculated. The shape is computed based on an internal stress equalization algorithm that requires the stresses from the distorting springs to equalize.
Once the contact stresses are known for a particular point in time, they may be used along with a coefficient known as the Erosion Rate Coefficient (E) to compute the amount of material removed. The Erosion Rate Coefficient, which may be measured experimentally using blanket wafers, represents the blanket rate of material removal per pound of down-force. Its units are microns/second/pound of down-force.
Different Erosion Rate Coefficients may be used for different materials and slurries. For example, when performing a copper CMP simulation, an E value for each material-slurry combination can be specified. See the figure below.
Mesa has been successfully validated on Oxide, Copper, and STI processes. The Erosion Rate Coefficient is measured using inexpensive blanket wafers and the pad's spring constant values are obtained using TIR or feature-scale erosion profile data. The coefficients are only a function of the consumables and the process and their range of variation are fairly well predicted.