Lithography Modeling And Applications

Abstract

The manufacturing of integrated circuits relies on the use of lithography simulation to predict the image of the mask created on the wafer. Such predictions can be used for example to assess the quality of the images, verify the manufacturability of such images, perform using OPC necessary correction of the mask data to achieve images close to the targets, optimize the printing parameters such as the illumination source, or globally optimize the source and the mask to achieve better printability. This disclosure provides a technique based on the association of at least one kernel function per source region or source point. Each kernel function can be directly convoluted with a mask image to create a prediction of the wafer image. As the kernel functions are associated with the source, the source can be easily changed to create new models. The optical system can be fully described by computing the possible kernels for all possible source points and all possible numerical apertures. Therefore this technique is ideally suited for source-mask optimization as well as source-mask-numerical aperture optimization, and their associated applications.

1 . (canceled) 
     
     
         2 . A method, comprising:
 modeling an illumination source as a set of discrete source components, wherein different combinations of one or more of the discrete source components represent respective configurations of the illumination source; and   for each respective one of the discrete source components, using a microprocessor-based system to
 compute a projection function for an optical system dependent on the respective discrete source component, 
 combine the projection function with a mask function representing a semiconductor mask, to obtain a mask representation representing exposure of a semiconductor assembly from the semiconductor mask which is attributable to the respective discrete source component, and 
 store the mask representation attributable to the respective discrete source component in microprocessor-based-system-readable storage; 
   wherein the mask representations for the respective discrete source components are adapted for linear combination to model exposure of the semiconductor assembly from the semiconductor mask attributable to any one of the respective configurations of the illumination source.   
     
     
         3 . The method of  claim 2 , further comprising:
 combining the mask representations for at least two of the discrete source components to model a specific one of the respective configurations of the illumination source, and storing a digital representation for the model for the specific one in microprocessor-based-system-readable storage.   
     
     
         4 . The method of  claim 3 , further comprising:
 using the digital representation within an optical proximity correction (OPC) process, including modifying at least one of placement of the semiconductor mask relative to a projection axis or a layout for the semiconductor mask.   
     
     
         5 . The method of  claim 3 , wherein:
 modeling the illumination source as a set of discrete source components includes modeling each discrete source component as a point source; and   combining the mask representations for at least two of the discrete source components and storing the digital representation include combining the mask representations for at least two source points and storing the digital representation in a manner that models use of a specific one of the respective configurations as a discrete selection of point sources.   
     
     
         6 . The method of  claim 2 , wherein:
 each mask representation is structured in a manner that models polarization attributable to at least one of the optical system or illumination of the semiconductor mask.   
     
     
         7 . The method of  claim 2 , wherein:
 each mask representation is structured in a manner that models defocus attributable to at least one of the optical system or the semiconductor mask in a photoresist layer.   
     
     
         8 . The method of  claim 2 , wherein:
 the mask function represents the entire semiconductor mask.   
     
     
         9 . The method of  claim 2 , wherein:
 the mask function represents one of plural subset regions of the mask; and   the method further comprises repeating using the microprocessor-based-system to combine the projection function with the mask function for each one of the plural subset regions of the semiconductor mask and to store the mask representation in a manner where data is stored representing each of the plural subset regions of the semiconductor mask for each discrete source component.   
     
     
         10 . The method of  claim 2 , wherein:
 the projection function is specific to a corresponding one of the discrete source components; and   using the microprocessor-based system to combine includes convolving the projection function with the mask function.   
     
     
         11 . An apparatus, comprising:
 means for modeling an illumination source as a set of discrete source components, wherein different combinations of one or more the discrete source components represent respective configurations of the illumination source; and   means for, for each respective one of the discrete source components,
 computing a projection function for an optical system dependent on the respective discrete source component, 
 combining the projection function with a mask function representing a semiconductor mask, to obtain a mask representation representing exposure of a semiconductor assembly from the semiconductor mask which is attributable to the respective discrete source component, and 
 storing the mask representation attributable to the respective discrete source component in microprocessor-based-system-readable storage; 
   wherein the mask representations for the respective discrete source components are adapted for linear combination to model exposure of the semiconductor assembly from the semiconductor mask attributable to using any of the respective configurations of the illumination source.   
     
     
         12 . An apparatus comprising instructions stored on non-transitory machine readable media, the instructions when executed adapted to cause a machine to:
 model an illumination source as a set of discrete source components, wherein different combinations of one or more of the discrete source components represent respective configurations of the illumination source; and   for each respective one of the discrete source components,
 compute a projection function for an optical system dependent on the respective discrete source component, 
 combine the projection function with a mask function representing a semiconductor mask, to obtain a mask representation representing exposure of a semiconductor assembly from the semiconductor mask which is attributable to the respective discrete source component, and 
 store the mask representation attributable to the respective discrete source component in machine-readable storage; 
   wherein the mask representations for the respective discrete source components are adapted for linear combination to model exposure of the semiconductor assembly from the semiconductor mask attributable to using any of the respective configurations of the illumination source.   
     
     
         13 . The apparatus of  claim 12 , wherein the instructions are adapted to, when executed, further cause the machine to:
 combine the mask representations for at least two of the discrete source components to model a specific one of the respective configurations of the illumination source, and store a digital representation for the model for the specific one in machine-readable storage.   
     
     
         14 . The apparatus of  claim 13 , wherein the instructions are adapted to, when executed, further cause the machine to:
 use the digital representation within an optical proximity correction (OPC) process, by modifying at least one of placement of the semiconductor mask relative to a projection axis or a layout for the semiconductor mask.   
     
     
         15 . The apparatus of  claim 13 , wherein the instructions are adapted to, when executed, further cause the machine to:
 model each discrete source component as a point source; and   combine the mask representations and store the digital representation by combining the mask representations for at least two source points, and storing the digital representation in a manner that models use of a specific one of the respective configurations as a discrete selection of point sources.   
     
     
         16 . The apparatus of  claim 12 , wherein:
 each mask representation is structured in a manner that models polarization attributable to at least one of the optical system or illumination of the semiconductor mask.   
     
     
         17 . The apparatus of  claim 12 , wherein:
 each mask representation is structured in a manner that models defocus attributable to at least one of the optical system or the semiconductor mask in a photoresist layer.   
     
     
         18 . The apparatus of  claim 12 , wherein:
 the mask function represents the entire semiconductor mask.   
     
     
         19 . The apparatus of  claim 12 , wherein:
 the mask function represents one of plural subset regions of the mask; and   the instructions are adapted to, when executed, further cause the machine to repeat the combination of the projection function with the mask function for each one of the plural subset regions of the semiconductor mask, and the storing of the mask representation, in a manner where data is stored representing each of the plural subset regions of the semiconductor mask for each discrete source component.   
     
     
         20 . The apparatus of  claim 12 , wherein the projection function is specific to a corresponding one of the discrete source components and wherein the instructions are adapted to, when executed, further cause the machine to:
 combine by convolving the projection function with the mask function.   
     
     
         21 . The apparatus of  claim 12 , embodied as optical proximity correction (OPC) software.