Multi-component kernels for vector optical image simulation

A method comprising:

• combining first elements of an illumination profile of an illumination source of an optical system of a lithographic system and second elements of an exit pupil function of the optical system to form a generalized pupil function;
• determining a vector transmission cross coefficient (vector-TCC) matrix of the optical system of the lithographic system based on the generalized pupil function;
• performing an optical proximity correction (OPC) operation of a layout pattern of a photo mask, wherein the OPC operation uses the vector-TCC matrix to determine a projected pattern of the layout pattern of the photo mask on a wafer;
• performing an inverse lithographic transformation (ILT) operation of the layout pattern to generate an enhanced layout pattern, wherein the ILT operation uses the vector-TCC matrix to determine a projected pattern of the layout pattern of the photo mask on the wafer during the ILT operation;
• and
• producing the ILT enhanced layout pattern on a mask-blank to create a photo mask.

A lithographic system, comprising:

• a main controller;
• a photo mask;
• a mask enhancer coupled to the main controller;
• an optical system comprising an illumination source, wherein the optical system is coupled to the main controller;
• a mask projector coupled to the main controller and the mask enhancer and configured to produce a projection of the photo mask on a wafer;
• and
• an analyzer module coupled to the main controller, wherein the analyzer module is configured to receive a target layout pattern to be produced on the wafer,
• wherein the mask enhancer is coupled to the analyzer module through the main controller and is configured to receive the target layout pattern from the analyzer module and to perform one of an optical proximity correction (OPC) operation or an inverse lithographic transformation (ILT) operation of the target layout pattern,
• wherein the mask enhancer is configured to:
• combine first elements of an illumination profile of an illumination source of an optical system of a lithographic system and second elements of an exit pupil function of the optical system to form a generalized pupil function;
• and
• determine a vector transmission cross coefficient (vector-TCC) operator of the optical system of the lithographic system based on the generalized pupil function and a conjugate of the generalized pupil function,
• wherein the mask projector is configured to perform the projection of a photo mask on the wafer for the OPC operation or the ILT operation using the vector-TCC operator to determine a projected pattern of the photo mask on the wafer.