Large area pattern erosion simulator

A method for simulating the performance of a system for chemical mechanical polishing of the surface of a workpiece by a moving pad, said method comprising the steps of:

• a) modeling the surface of the workpiece by a collection of nodes located in a plane w, each of said wafer nodes having a location defined by the Cartesian coordinates xwi, ywi, zwi;
• b) modeling the surface of the moving pad by a collection of nodes located in a plane P parallel to said plane w, each of said pad nodes having a location defined by the Cartesian coordinates xwi, ywi, zpi;
• c) establishing a first linear spring force at each of said pad nodes, said first linear spring force being expressed as a function of the deflection of the pad;
• d) establishing a second linear spring force on each of said pad nodes as a function of the connection distance of each pad node to an adjacent pad node;
• e) summing said first and second linear spring forces to determine the total force on each pad node;
• f) determining the rate of change of a wafer node coordinate zwi during small time segments as a function of the force applied by each pad node on a corresponding workpiece node;
• g) determining the deformation of each of said pad nodes during said small time segment, by the change in location of said pad node Cartesian coordinate zpi caused by the total force on each of said pad nodes on the surface of the workpiece;
• h) determining the erosion of each node on the workpiece surface in said small time segment by the change in location of each of said workpiece node Cartesian coordinate zwi.

A method for estimating the feature scale planarity that would result from a chemical mechanical polishing (CMP) process that uses a CMP system having a carrier element configured to hold a workpiece against a stack of polishing pads including a base pad and a top pad, said method comprising:

• a) obtaining an initial feature scale pattern associated with said workpiece;
• b) acquiring a deformation model of a polishing element associated with said CMP system;
• c) said deformation model including the steps of:
• 1) equating the base pad of a first abstract mathematical spring;
• 2) equating the top pad to a second abstract mathematical spring connected in series with said first abstract mathematical spring;
• and
• d) performing a modeling routine to thereby obtain a feature scale simulation result for said workpiece, said feature scale simulation result being responsive to said initial feature scale pattern and to said deformation model, and representing an estimate of said feature scale planarity.

A computer system for estimating the wafer scale uniformity and feature scale planarity that would result from a chemical mechanical polishing (CMP) process performed on a workpiece by a CMP system having a polishing pad stack with a base pad and a top pad, said system comprising:

• a processor operable to receive an initial feature scale pattern associated with the workpiece;
• wherein the processor is further operable to perform a modeling routine by equating the base pad to a first abstract mathematical spring, and by equating the top pad to a second abstract mathematical spring connected in series with said first abstract mathematical spring and by simulating the operation of the CMP system on the workpiece, based on the initial feature scale patter;
• thereby providing a
• wafer scale simulation result representing said wafer scale uniformity and a feature scale simulation result representing said feature scale planarity;
• and
• wherein the processor is further operable to compare at least one of said wafer scale simulation result and said feature scale simulation result to an empirical CMP result associated with said CMP process to thereby obtain a simulation error.

A computer system for estimating the wafer scale uniformity and feature scale planarity that would result from a chemical mechanical polishing (CMP) process performed on a workpiece by a CMP system having a polishing pad stack with a base pad and a top pad, said system comprising:

• a processor operable to receive an initial film thickness profile associated with the workpiece;
• wherein the processor is further operable to perform a modeling routine by equating the base pad to a first abstract mathematical spring and equating the top pad to a second abstract mathematical spring connected in series with said first abstract mathematical spring and by simulating the operation of the CMP system on the workpiece, based on the initial film thickness profile;
• thereby providing a
• wafer scale simulation result representing said wafer scale uniformity and a feature scale simulation result representing said feature scale planarity;
• and
• wherein the processor is further operable to compare at least one of said wafer scale simulation result and said feature scale simulation result to an empirical CMP result associated with said CMP process to thereby obtain a simulation error.