Planarization length determination

In the simplest case, a square area can be used to determine the effective density across the mask, as shown in Fig. 11. Density to be assigned to the coordinates at the center of the window is equal to the ratio of raised to total area of the square window. The length of each side of the square is then defined as the planarization length this square region approximates the deformation characteristics of the pad and process. The size of the square (or the planarization length) is determined experimentally by varying the square size until the effective density calculation results in predicted thickness values that best fit experimentally measured polish data when used in the thickness evolution model. 

Figure 17 shows the effective density using the elliptic filter with a characteristic length of 2.9 mm. The optimal length must be determined for each consumable set and process conditions since the planarization length is dependent not only on the polish pad type but also on the polish process conditions, notably the down force. 

The calibration phase focuses on the determination of the planarization length itself. This is a crucial characterization phase since once the planarization length is determined, the effective density, and thus the thickness evolution, can be determined for any layout of interest polished under similar process conditions. The determination of planarization length is an iterative process. First, an initial approximate length is chosen. This is used to determine the effective density as detailed in the previous subsection. The calculated effective density is then used in the model to compute predicted oxide thicknesses, which are then compared to measured thickness data. A sum of square error minimization scheme is used to determine when an acceptably small error is achieved by gradient descent on the choice of planarization length. 

The integrated modeling methodology is useful for several applications. These include the ability to determine the optimal amount of material to deposit before CMP, the provision of an effective characterization scheme through the use of planarization length as a process performance monitor [29, 55], and the correct prediction of post-CMP ILD thickness variation, which is useful for assessing the impaet of such variation on circuit performance [24,56]. 

The ability to accurately model die pattern evolution as discussed in this paper provides a solution applicable to the ran by run control of multi-product patterned wafers [13]. As shown in Fig. 10, a feedback control loop incorporating the integrated density and step-height pattern dependent model was developed. For each device type, an appropriate set of model parameters (including effective blanket rate BR and planarization length) were determined. The model for the effective blanket rate includes a term Delta(n) that is updated on each run n to track the tool drift in rate over time due to pad and consumable wear ... 

The crystal structure of the potassium salt of 1,3,5,7-tetramethylcyclootatetraene dianion has been determined by X-ray dififaction. ° The eight-membered ring is planar, with aromatic C—C bond lengths of about 1.41 A without significant alternation. The spectroscopic and structural studies lead to the conclusion that the cyclooctatetraene dianion is a stabilized delocalized structure. 

Organic thionylamines have planar, cis structures (9.9) in the solid state and in solution, as determined by X-ray crystallography and N NMR spectroscopy, respectively. The gas-phase structures of the parent compound HNSO and MeNSO have been determined by microwave spectroscopy. The S=N and S=0 double bond lengths are 1.51-1.52 and 1.45-1.47 A, respectively. The bond angle [Pg.168]

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