Planarization length

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. 

A key component in CMP process characterization is the choice of test layout mask. For planarization length extraction, the test mask should... 

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. 

Fig. 23, Integrated density and step-height-dependent model parameter extraction approach. The outer loop finds the planarization length that best captures the density dependence, while the inner loop find the step-height model parameters that best explain up and down area polish data [48].

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]. 

D. Boning, D. Ouma, and J. Chung, Extraction of Planarization Length and Response Function in Chemical-Mechanical Polishing, Materials Research Society 1998 Spring Meeting, San Francisco, CA, May 1998. 

Why is the planarization length desirable at die size Will a planarization length at wafer diameter scale really be an advantage ... 

For very wide trenches (a large multiple of the pad thickness, depending on the hardness of the pad), the pad conforms easily to both the trench sides and the bottom, and except very close to the sides, the contact pressures and polishing rate are nearly equal. The planarization rate (the rate at which the step height is reduced) is therefore very low, and we could describe the feature as being larger than the pad planarization length. 

The optimization techniques are performed on mask design or processing level and approach planarity problems from different directions. Some of them reduce the pre-CMP topography, others reduce density variations or nonuniformity dimensions with respect to the planarization length, and still... 

Define the planarization length. What are typical planarization lengths for IC fabrication How does this relate to wafer-level 3D and wafer bonding ... 

For simplicity and to understand the STI mechanism, we introduce the following assumptions. First, the planarization length is zero, that is, there is no interaction between removal rates of patterned and blanket areas, and second, there is no dishing or recess at field oxide between active silicon nitrides in feature size level. On the basis of the above assumptions, STI CMP procedures can be divided into four steps as showm in Fig.2. The first step is defined as the period in which initial step heights of patterned area are perfectly eliminated. At this stage then erosion is generated due to the difference of removal rate between patterned and blanket area as showm in Fig.2(b). The second step is defined as the period in which the fully planarized oxide surface of patterned area is polished to expose the silicon nitride top surface. 

In previous work, we have formalized the notions of planarization length and planarization response function as key parameters that characterize a given CMP consumable set and process. Once extracted through experiments using carefully designed characterization mask sets, these parameters can be used to predict polish performance in CMP for arbitrary product layouts. The methodology has proven effective at predicting oxide interlevel dielectric planarization results. 

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 ... 

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