Patterned wafer modeling

In Section II, we focus first on wafer-scale models, including macroscopic or bulk polish models (e.g., via Preston s equation), as well as mechanistic and empirical approaches to model wafer-scale dependencies and sources of nonuniformity. In Section III, we turn to patterned wafer CMP modeling and discuss the pattern-dependent issues that have been examined we also discuss early work on feature-scale modeling. In Section IV, we focus on die-scale modeling efforts and issues in the context of dielectric planarization. In Section V, we examine issues in modeling pattern-dependent issues in metal polishing. Summary comments on the status and application of CMP modeling are offered in Section VI. 

Thus CMP pads play an important role in dishing of patterned wafers. The model presented here parameterizes CMP pads using Young s modulus, Poisson s ratio, and pad thickness plus an unusual fcstretch term. Control of these parameters could lead to improvements in dishing and erosion outcomes during polishing. 

Finally, after development of the two-step model and application of the model to blanket wafer polishing, we describe how the model may be applied to patterned wafer polishing and how the latter may differ from blanket polishing. 

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 model update is based on seven measurements on four die taken on each patterned wafer using the on-line Nova sensor. The updated blanket rate is then used in conjunction with the pattern dependent model to select the best time for the next wafer of either product type to achieve the desired average target thickness (estimated values from the pattern dependent model of a four die average of 252 sites). The experimental results for a control experiment across two different patterned wafer types is shown in Fig. 11, where we see that +/- lOOA control around the average target thickness has been achieved. 

The origin of this phenomenon can he traced to the drying step of the liquid development process. During the development step, after the resist-patterned wafer has been contacted with the developer solution for a given length of time and subsequently rinsed with deionized water, the level of the rinse liquid at some point attains a condition similar to that shown in Fig. 11.45, where the space between adjacent resist lines is partially filled with fluid. The fluid meniscus exhibits a curvamre due to the differences in pressure across the fluid interface that result from surface tension in the confined space between the resist lines. Tanaka et al. developed a cantilever beam mechanical model for describing pattern collapse. The Laplace equation relates the pressure differential across the meniscus... 

To predict the final oxide thickness in a pattern wafer, we used a model known as the MIT model proposed by Stine et al. (1997). Figure 2.27... 

Figure 4. SEM photo of EL Ni patterns produced using a high resolution grating mask. The experimental conditions for producing the patterned wafer were as described in the caption of Fig. 3. The micrograph was obtained using a Cambridge Model S200 electron microscope.

Other fluid dynamic models of slurry flow have also been developed by other workers [57]. Coppeta, Rodgers, Radzak, and coworkers examined slurry flow, both from a simulation point of view, and from an experimental angle [6,10,11]. A special test apparatus is used consisting of flourescent injections of die that is entrained beneath a glass wafer enabling observation of slurry flow patterns and residence time. Such studies are instrumental... 

D. Ouma, B. Stine, R. Divecha, D. Boning, J. Chung, G. Shinn, I. Ali, and J. Clark, Wafer-Scale Modeling of Pattern Effect in Oxide Chemical Mechanical Polishing, Proc. SPIE Microelectronic Man. Conf., Austin, TX, Oct. 1997. 

To enable reflectometry to provide accurate, reproducible, and efficient measurements, several factors must be considered. Choice of the substrate material, substrate modeling, number of measurements per wafer, choice of the measurement patterns, and the setup of the pattern recognition program are all critical to the measurement process, as discussed in the following. 

MIP features down to 1.5 pm on 4-in silicon wafers was reached (Fig. 6). A wide range of micrometric patterns with different geometries can be obtained, such as lines, spirals, circle matrices, and circular, squared, or hexagonal patterns (Fig. 6 bottom). Multiplexed chips containing three different polymers were also fabricated, paving the road to mass production of biomimetic chips. Fluorescence microscopy was used to test for the binding of fluorescent model analyte to the micropattems. 

Turner K, Spearing S. Modeling of direct wafer bonding effect of wafer bow and etch patterns. J Appl Phys 2002 92(12) 7658-7666. 

In reference 1-7 it was shown that the local removal for the up features was equal to the removal rate on a flat wafer (r) divided by the pattern density (a). If the pad surface could be modeled as incompressible this remains valid till the stmcture is completely planarized at the planarization time tp,. Afterwards the level is reduced at the same rate as the polishing rate on a flat wafer. Since the average pressure is always the same for an imit area in the case of perfect pad bending this calculation can be applied for all structures independent of the surroimding areas. This allows to calculate the WIDNU as the level difference between the area with the highest pattern density (b) and the lowest pattern density (e.g. a), i.e. 

The flow of a slurry in a CMP process has been investigated. This wafer-scale model provides the three dimensional flow field of the slurry, the spatial distribution of the local shear rate imposed on the wafer surface, and the streamline patterns which reflect the transport characteristics of the slurry. 

In this section, three example applications intimately related to the pattern dependent behavior of CMP are briefly discussed. First, we note the relative importance of die-level effects with respect to typical wafer-scale nonuniformity. Second, we describe recent application of the integrated density and step height model to the run by run control of ILD CMP. Finally, we summarize issues in the application of density models to prediction of shallow trench isolation. 

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