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TOOL SCALE AND FEATURE SCALE MODELS 15 addition, there must be extensive sets of comparisons between experimental measurements and model predictions in order to validate the models that are proposed. An important feature alluded to in Chapter 1 is the role of the mid-level, between the tool scale (tens to hundreds of centimeters) and the microfeature level (~ 1 µm). This mid-level involves effects near the edge of the wafer, the effects of pattern area loading on the wafer, and similar phenomena. The length scale is typically less than 1 cm (on the order of the size of a single chip) but greater than 10 µm. This is an awkward intermediate scale, since resolving tool scale simulations on a scale of ~ 0.1 cm or less becomes very expensive computationally. Further work is needed to develop strategies to couple models of various length scales. Capabilities Needed for Tool Scale Models Tool scale models need to be capable of predicting the behavior and uniformity of the plasma sufficiently well that the following effects can be modeled: 1. Alternative chemistries, 2. Pressure, 3. Power, 4. Gas flow and composition, 5. Changing geometrical configuration (tool shape, wafer edges, clamps), 6. Chamber wall effects: seasoning and cleaning, and 7. Applied magnetic field. In order that the models be useful, the minimum requirement is that the models capture the qualitative trends. In addition, they must be set up in such a way that they can be coupled conveniently to the feature scale models, discussed below. Barriers to Using Tool Scale Models Some of the barriers to the use of current-generation tool scale models are listed below:2 1. There is a lack of mature models that include physical accuracy, computational accuracy, and robustness. Physical accuracy refers to the accuracy of the underlying equations and assumptions in the model. Computational accuracy refers to possible problems with actually solving the equations in the model. For example, finite difference or finite element methods' solutions to discretized equations do not always correspond to the solution of the original differential equation. Robustness refers to loss of convergence, "touchy" solutions, and similar problems. Robustness is a nontrivial issue to overcome when highly coupled, nonlinear equations are being solved, as in the case of glow discharge plasmas. 2. There is a lack of integration among different parts of the simulation codes. This means that models of the tool geometry, the grid generators, the visualization tools, the graphical interfaces, and other design tools are not linked together in convenient ways. 3. There is a lack of commercial software suppliers. Commercial software suppliers provide documentation, consistent support, model updates, and continuous development. Generally, these features are lacking in university and national laboratory codes (although exceptions exist). 4. There is a lack of a database. All simulations require information about various processes occurring within the system being modeled. In the case of plasma models, this requirement includes information regarding electron-impact phenomena, ion-neutral collisions (e.g. ion-molecule reactions), neutral- neutral reactions, and the various processes occurring at surfaces bounding the plasma.
