Cylindric decomposition for efficient mitigation of substrate deformation with film deposition and ion implantation

A system comprising:

• a memory;
• and
• a processing device communicatively coupled to the memory, the processing device to:
• obtain, using optical inspection data, an out-of-plane deformation (OPD) profile of a substrate;
• obtain a polynomial representation of the OPD profile to determine a plurality of polynomial coefficients, each of the plurality of polynomial coefficients characterizing a respective one of a plurality of elemental deformation shapes of the substrate;
• identify, based on at least a subset of the plurality of polynomial coefficients, one or more cylindric decompositions of a quadratic part of the OPD profile, wherein each of the one or more cylindric decompositions comprises a decomposition of the OPD profile into at least a parabolic deformation of the substrate and a cylindric deformation of the substrate;
• compute, using a selected cylindric decomposition of the one or more cylindric decompositions, one or more characteristics of a stress-compensation layer (SCL) for the substrate;
• cause the SCL to be deposited on the substrate;
• and
• cause the SCL to be exposed to a stress-mitigation beam.

A semiconductor manufacturing system comprising:

• one or more processing chambers to process a substrate;
• and
• a computing device to:
• obtain, using optical inspection data, an out-of-plane deformation (OPD) profile of the substrate;
• obtain a polynomial representation of the OPD profile to determine a plurality of polynomial coefficients, each of the plurality of polynomial coefficients characterizing a respective one of a plurality of elemental deformation shapes of the substrate;
• identify, based on at least a subset of the plurality of polynomial coefficients, one or more cylindric decompositions of a quadratic part of the OPD profile, wherein each of the one or more cylindric decompositions comprises a decomposition of the OPD profile into at least a parabolic deformation of the substrate and a cylindric deformation of the substrate;
• compute, using a selected cylindric decomposition of the one or more cylindric decompositions, one or more characteristics of a stress-compensation layer (SCL) for the substrate;
• cause the SCL to be deposited on the substrate;
• and
• cause the SCL to be exposed to a stress-mitigation beam.