Kernel function generation method, optical proximity correction method using the kernel function, and mask manufacturing method including the optical proximity correction method

An optical proximity correction (OPC) method comprising:

• providing data of a cell layout according to a plurality of factors for a pattern;
• calculating, by one or more processors, a respective critical dimension (CD) error of the pattern for each factor of the plurality of factors under varying conditions of remaining factors of the plurality of factors;
• generating, by the one or more processors, and for each CD error, individual kernel functions that simulate an impact of each factor of the plurality of factors on the CD error;
• generating, by the one or more processors, a combined kernel function by applying weights to the individual kernel functions and multiplying the individual kernel functions;
• generating, by the one or more processors, an OPC model by using the combined kernel function;
• performing, by the one or more processors, a simulation by using the OPC model;
• and
• exposing a mask substrate based on a result of the simulation.

A method of manufacturing a mask, the method comprising:

• obtaining an optical proximity corrected (OPC-ed) layout by performing an optical proximity correction (OPC) method using a kernel function;
• performing an optical rule check (ORC) on the OPC-ed layout;
• transferring a final OPC-ed layout that has passed the ORC, as mask tape-out (MTO) design data;
• preparing mask data based on the MTO design data;
• and
• exposing a mask substrate based on the mask data,
• wherein obtaining the OPC-ed layout comprises
• providing data of a cell layout according to a plurality of factors for a pattern,
• calculating, by one or more processors, a respective critical dimension (CD) error of the pattern for each factor of the plurality of factors under varying conditions of remaining factors of the plurality of factors,
• generating, by the one or more processors, and for each CD error, individual kernel functions that simulate an impact of each factor of the plurality of factors on the CD error,
• generating, by the one or more processors, a combined kernel function by applying weights to the individual kernel functions and multiplying the individual kernel functions,
• generating, by the one or more processors, an OPC model by using the combined kernel function, and
• performing, by the one or more processors, a simulation by using the OPC model.