Full wafer map response surface models for combinatorial chemical vapor deposition reactor operations

A computational toolbox was developed to perform full wafer response surface modeling of combinatorial chemical vapor deposition wafers. It consists of a library of MATLAB object-oriented functions that are based on accurate quadrature methods. The toolbox was tested using three sets of artificially generated wafers. Once the validity of the toolbox was demonstrated, it was used to model tungsten deposition with a Spatially Programmable CVD reactor. As a result, a model of the form T = b 1(sqh2s1) + b 2(sqh2s2) + b 3(sqh2s3) + b 14(sqh2s1)(gap) + b24(sqh2s2)( gap) + b34(sqh2 s3)(gap) was considered the most appropriate fit to the data. This model takes into account the systems kinetics (it uses the square root of the hydrogen flow), the gas flows into each one of the reactor segments and the inter-segment gas diffusivity.