Rapid scattering simulation of objects in imaging using edge domain decomposition

Abstract

A complex two-dimensional layout of a photomask or other three-dimensional object is systematically decomposed into a finite number of elementary two-dimensional objects with the ability to cause one-dimensional changes in light transmission properties. An algorithmic implementation of this can take the form of creation of a look-up table that stores all the scattering information of all two-dimensional objects needed for the synthesis of the electromagnetic scattered field from the original three-dimensional object. The domain is decomposed into edges, where pre-calculated electromagnetic field from the diffraction of isolated edges is recycled in the synthesis of the near diffracted field from arbitrary two-dimensional diffracting geometries. The invention has particular applicability in die-to-database inspection where an actual image of a mask is compared with a synthesized image that takes imaging artifacts of comers, edges and proximity into account. Another application is optical proximity correction which consists of evaluating the image of every feature on a mask and improving it by introducing edge shifts and iteratively adjusting the amounts of these shifts.

What is claimed is: 
     
       1. A method for simulation of light scattering in large three dimensional objects in a optical imaging system comprising the steps of:
 a) decomposing a three dimensional object into a plurality of elementary two dimensional objects, 
 b) defining the two dimensional objects by edges of the objects, 
 c) applying edge domain decomposition for the edges of the to two dimensional objects corresponding to a three dimensional object to identify light scattering by the associated one dimensional edges, and 
 d) summing scattered light from all edges to simulate light scattering in two three dimensions. 
 
     
     
       2. The method of  claim 1  and further including: e) spectrally mapping the edge domain decomposition. 
     
     
       3. The method of  claim 2  wherein the three dimensional object comprises a photo mask with multiple and interconnected openings. 
     
     
       4. The method of  claim 3  wherein step c) applying edge domain decomposition includes computational methods which speed-up calculations through use of table look-up of previously calculated objects and filtering that sequentially invokes more rigorous simulation as needed. 
     
     
       5. The method of  claim 4  wherein an electromagnetic field from the diffraction of isolated edges is recycled in the synthesis of a near diffracted field for arbitrary two dimensional diffracting geometries. 
     
     
       6. The method of  claim 5  wherein the a scattered field from all edges are summed to simulate light scattering in by the two three dimensional objects object. 
     
     
       7. The method of  claim 6  wherein scattered light is polarized and step c) applying edge domain decomposition includes separate decomposition for light parallel to edges (TE) and for light perpendicular (TM) to edges. 
     
     
       8. The method of  claim 7  wherein step c) applying edge domain decomposition includes pre-simulating all distinct edges in the object with all possible illumination directions and field polarizations. 
     
     
       9. The method of  claim 8  further comprising decomposing the three dimensional object into a plurality of the elementary two dimensional objects, wherein in step a) the two dimensional objects comprise rectangles. 
     
     
       10. The method of  claim 9  wherein the object is a phase shifting mask and step c) of pre-simulating light scattering from edges includes phase effects of etch depths in defining the phase shifting mask. 
     
     
       11. The method of  claim 10  wherein the simulation of light scattering is based on through the a lens optical spectra. 
     
     
       12. The method of  claim 10  wherein the simulation of light scattering is based on a raised cosine function for the optical spectra. 
     
     
       13. The method of  claim 10  wherein the simulation of light scattering is based on a Gaussian function for the optical spectra. 
     
     
       14. The method of  claim 10  wherein the simulation of light scattering is based on a rect-function for the optical spectra. 
     
     
       15. The method of  claim 3  wherein the object is a phase shifting mask and step c) applying edge domain decomposition includes pre-simulating light scattering from edges and includes phase effects of etch depths in defining the phase shifting mask. 
     
     
       16. The method of  claim 15  wherein scattered light is polarized and step c) includes separate decomposition for light parallel to edges (TB) (TE) and for light perpendicular (TM) to edges. 
     
     
       17. The method of  claim 16  wherein step c) applying edge domain decomposition includes pre-simulating all distinct edges in the object with all possible illumination directions and field polarizations. 
     
     
       18. The method of  claim 1  wherein step c) applying edge domain decomposition includes pre-simulating all distinct edges in the object with all possible illumination directions and field polarizations. 
     
     
       19. A method comprising:
 applying edge-domain decomposition to the a plurality of one-dimensional edges derived from a three-dimensional object to identify light scattering by the one-dimensional edges; and   using a computer, summing scattered light from the one-dimensional edges to simulate the light scattering by the three-dimensional object.   
     
     
       20. The method of claim 19, further comprising spectrally mapping the edge domain decomposition. 
     
     
       21. The method of claim 19, wherein the three dimensional object comprises a photo mask with multiple and interconnected openings. 
     
     
       22. The method of claim 19, wherein the applying edge-domain decomposition comprises using computational methods that speed up calculations by using lookup tables of previously calculated objects and filtering that sequentially invokes more rigorous simulation as needed. 
     
     
       23. The method of claim 19, wherein an electromagnetic field from diffraction of isolated edges is recycled in synthesis of a near diffracted field for arbitrary two-dimensional diffracting geometries. 
     
     
       24. The method of claim 19, wherein one or more scattered fields from the one-dimensional edges are summed to simulate the light scattering by the three-dimensional object. 
     
     
       25. The method of claim 19, wherein the scattered light is polarized and the applying edge-domain decomposition includes performing separate decompositions for light parallel to the one-dimensional edges (TE) and for light perpendicular (TM) to the one-dimensional edges. 
     
     
       26. The method of claim 19, wherein the applying edge-domain decomposition includes distinct edges in the three-dimensional object with one or more possible illumination directions and field polarizations. 
     
     
       27. The method of claim 26, wherein the three-dimensional object is a phase-shifting mask and the pre-simulating accounts for phase effects of etch depths in the phase shifting mask. 
     
     
       28. The method of claim 19, wherein two-dimensional objects defining the three-dimensional object comprise rectangles. 
     
     
       29. The method of claim 19, wherein the applying edge-domain decomposition is based on through-the-lens optical spectra. 
     
     
       30. The method of claim 19, wherein the applying edge-domain decomposition is based on a raised cosine function for optical spectra. 
     
     
       31. The method of claim 19, wherein the applying edge-domain decomposition is based on a Gaussian function for optical spectra. 
     
     
       32. The method of claim 19, wherein the applying edge-domain decomposition is based on a rect-function for optical spectra. 
     
     
       33. The method of claim 19, wherein:
 the three-dimensional object is a phase shifting mask, and   the applying edge-domain decomposition includes pre-simulating light scattering from the one-dimensional edges and phase effects of etch depths in the phase shifting mask.   
     
     
       34. The method of claim 33, wherein:
 the scattered light is polarized; and   the applying edge-domain decomposition includes performing separate decompositions for light parallel to the one-dimensional edges (TE) and for light perpendicular (TM) to the one-dimensional edges.   
     
     
       35. The method of claim 34, wherein the applying edge-domain decomposition includes pre-simulating distinct edges in the three-dimensional object with a plurality of possible illumination directions and field polarizations. 
     
     
       36. The method of claim 19, wherein the applying edge-domain decomposition includes pre-simulating distinct one-dimensional edges in the three-dimensional object with a plurality of pre-selected possible illumination directions and field polarizations. 
     
     
       37. A non-transitory computer-readable storage medium storing computer-executable instructions for causing a computer to perform a method comprising:
 applying edge-domain decomposition to a plurality of one-dimensional edges composing a three-dimensional object to identify light scattering by the one-dimensional edges; and   summing scattered light from the one-dimensional edges to simulate the light scattering by the three-dimensional object.   
     
     
       38. The non-transitory computer-readable storage medium of claim 37, wherein the method further comprises spectrally mapping the edge domain decomposition. 
     
     
       39. The non-transitory computer-readable storage medium of claim 37, wherein the three dimensional object comprises a photo mask with multiple and interconnected openings. 
     
     
       40. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition comprises using computational methods that speed up calculations by using look-up tables of previously calculated objects and filtering that sequentially invokes more rigorous simulation as needed. 
     
     
       41. The non-transitory computer-readable storage medium of claim 37, wherein an electromagnetic field from diffraction of isolated edges is recycled in synthesis of a near diffracted field for arbitrary two-dimensional diffracting geometries. 
     
     
       42. The non-transitory computer-readable storage medium of claim 37, wherein one or more scattered fields from the one-dimensional edges are summed to simulate the light scattering by the three-dimensional object. 
     
     
       43. The non-transitory computer-readable storage medium of claim 37, wherein the scattered light is polarized and the applying edge-domain decomposition includes performing separate decompositions for light parallel to the one-dimensional edges (TE) and for light perpendicular (TM) to the one-dimensional edges. 
     
     
       44. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition includes pre-simulating distinct edges in the three-dimensional object with one or more possible illumination directions and field polarizations. 
     
     
       45. The non-transitory computer-readable storage medium of claim 37, wherein two-dimensional objects defining the three-dimensional object comprise rectangles. 
     
     
       46. The non-transitory computer-readable storage medium of claim 44, wherein the three-dimensional object is a phase-shifting mask and the pre-simulating accounts for phase effects of etch depths in the phase shifting mask. 
     
     
       47. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition is based on through-the-lens optical spectra. 
     
     
       48. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition is based on a raised cosine function for optical spectra. 
     
     
       49. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition is based on a Gaussian function for optical spectra. 
     
     
       50. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition is based on a rect-function for optical spectra. 
     
     
       51. The non-transitory computer-readable storage medium of claim 37, wherein:
 the three-dimensional object is a phase shifting mask, and   the applying edge-domain decomposition includes pre-simulating light scattering from the one-dimensional edges and phase effects of etch depths in the phase shifting mask.   
     
     
       52. The non-transitory computer-readable storage medium of claim 51, wherein:
 the scattered light is polarized, and   the applying edge-domain decomposition includes performing separate decompositions for light parallel to the one-dimensional edges (TE) and for light perpendicular (TM) to the one-dimensional edges.   
     
     
       53. The non-transitory computer-readable storage medium of claim 52, wherein the applying edge-domain decomposition includes pre-simulating distinct edges in the three-dimensional object with a plurality of possible illumination directions and field polarizations. 
     
     
       54. The non-transitory computer-readable storage medium of claim 37, wherein the applying edge-domain decomposition includes pre-simulating distinct one-dimensional edges in the three-dimensional object with a plurality of pre-selected possible illumination directions and field polarizations. 
     
     
       55. A method of simulating an aerial image projected by a multiple-opening mask having a plane defined by an X-axis and a Y-axis, comprising:
 receiving layout data representing physical dimensions of one or more openings in the mask;   producing first scattered field data for a selected one of the openings using a first two-dimensional model oriented along the X-axis;   producing second scattered field data for the selected opening using a second two-dimensional model oriented along the Y-axis;   producing third scattered field data for the selected opening using a Kirchoff mask model; and   using a computer, producing composite scattered field data for the selected opening from the first scattered field data, the second scattered field data, and the third scattered field data.   
     
     
       56. The method of claim 55, wherein the layout data includes data concerning phase shift properties of the one or more openings. 
     
     
       57. The method of claim 55, wherein the layout data includes data concerning binary mask properties of the one or more openings. 
     
     
       58. The method of claim 55, wherein the X-axis is oriented in a TM direction for a polarized electromagnetic wave to be transmitted through the selected opening and the Y-axis is oriented in a TE direction for the polarized electromagnetic wave. 
     
     
       59. The method of claim 55, wherein the method further comprises decomposing the data representing the physical dimensions of the one or more openings into data defining the one or more openings as rectangles. 
     
     
       60. The method of claim 59, wherein the decomposing produces mutually disjoint rectangles. 
     
     
       61. The method of claim 55, further comprising performing optical proximity correction using the composite scattered field data. 
     
     
       62. The method of claim 55, further comprising performing die-to-database inspection using the composite scattered field data. 
     
     
       63. The method of claim 55, wherein the producing the composite scattered field data is performed by linearly combining the first scattered field data, the second scattered field data, and the third scattered field data. 
     
     
       64. The method of claim 55, wherein the first scattered field data and the second scattered field data are produced using pre-calculated values stored in one or more look-up tables. 
     
     
       65. A non-transitory computer-readable storage medium storing computer-executable instructions for causing a computer to perform a method of simulating an aerial image projected by a multiple-opening mask having a plane defined by an X-axis and a Y-axis, the method comprising:
 receiving layout data representing physical dimensions of one or more openings in the mask;   producing first scattered field data for a selected one of the openings using a first two-dimensional model oriented along the X-axis;   producing second scattered field data for the selected opening using a second two-dimensional model oriented along the Y-axis;   producing third scattered field data for the selected opening using a Kirchoff mask model; and   producing composite scattered field data for the selected opening from the first scattered field data, the second scattered field data, and the third scattered field data.   
     
     
       66. The non-transitory computer-readable storage medium of claim 65, wherein the layout data includes data concerning phase shift properties of the one or more openings. 
     
     
       67. The non-transitory computer-readable storage medium of claim 65, wherein the layout data includes data concerning binary mask properties of the one or more openings. 
     
     
       68. The non-transitory computer-readable storage medium of claim 65, wherein the X-axis is oriented in a TM direction for a polarized electromagnetic wave to be transmitted through the selected opening and the Y-axis is oriented in a TE direction for the polarized electromagnetic wave. 
     
     
       69. The non-transitory computer-readable storage medium of claim 65, wherein the method further comprises decomposing the data representing the physical dimensions of the one or more openings into data defining the one or more openings as rectangles. 
     
     
       70. The non-transitory computer-readable storage medium of claim 69, wherein the decomposing produces mutually disjoint rectangles. 
     
     
       71. The non-transitory computer-readable storage medium of claim 65, wherein the method further comprises performing optical proximity correction using the composite scattered field data. 
     
     
       72. The non-transitory computer-readable storage medium of claim 65, wherein the method further comprises performing die-to-database inspection using the composite scattered field data. 
     
     
       73. The non-transitory computer-readable storage medium of claim 65, wherein the producing the composite scattered field data is performed by linearly combining the first scattered field data, the second scattered field data, and the third scattered field data. 
     
     
       74. The non-transitory computer-readable storage medium of claim 65, wherein the first scattered field data and the second scattered field data are produced using pre-calculated values stored in one or more look-up tables. 
     
     
       75. A method of performing optical proximity correction for a mask, comprising:
 receiving layout data representing the mask, the layout data defining polygons and phase assignments;   assigning edge types to edges of one or more of the polygons, wherein the edge type for a respective edge is based at least in part on phase assignment data for an area adjacent to the respective edge;   simulating an aerial image produced by the mask using two-dimensional models for the edges of the one or more polygons, wherein the two-dimensional models are selected based at least in part on the respective edge types of the edges and wherein the simulating produces edge image intensities; and   using a computer, modifying the layout data by applying an optical proximity correction method to the layout data using the aerial image.   
     
     
       76. The method of claim 75, wherein the edge type is one of a Cr-layer/0° edge, a Cr-layer/90° edge, a Cr-layer/270° edge, a 0°/90° edge, or a 0°/270° edge. 
     
     
       77. The method of claim 75, further comprising decomposing one or more of the polygons in the layout data into mutually disjoint rectangles. 
     
     
       78. The method of claim 75, wherein the polygons comprise non-Manhattan geometries. 
     
     
       79. The method of claim 75, wherein the aerial image is simulated as being produced by quadrupole illumination. 
     
     
       80. The method of claim 75, wherein the modifying includes adding one or more of an edge shift or a sub-resolution assist feature to the layout data. 
     
     
       81. The method of claim 75, wherein the simulating ignores corner effects. 
     
     
       82. The method of claim 75, wherein the simulating includes using one or more look-up tables to determine the aerial image. 
     
     
       83. The method of claim 82, wherein the one or more look-up tables are generated by calculating electromagnetic field solutions. 
     
     
       84. A non-transitory computer-readable storage medium storing computer-executable instructions for causing a computer to perform an optical proximity correction method for a mask, the method comprising:
 receiving layout data representing the mask, the layout data defining polygons and phase assignments;   assigning edge types to edges of one or more of the polygons, wherein the edge type for a respective edge is based at least in part on phase assignment data for an area adjacent to the respective edge;   simulating an aerial image produced by the mask using two-dimensional models for the edges of the one or more polygons, wherein the two-dimensional models are selected based at least in part on the respective edge types of the edges and wherein the simulating produces edge image intensities; and   modifying the layout data by applying an optical proximity correction method to the layout data using the aerial image.   
     
     
       85. The non-transitory computer-readable storage medium of claim 84, wherein the edge type is one of a Cr-layer/0° edge, a Cr-layer/90° edge, a Cr-layer/270° edge, a 0°/90° edge, or a 0°/270° edge. 
     
     
       86. The non-transitory computer-readable storage medium of claim 84, wherein the method further comprises decomposing one or more of the polygons in the layout data into mutually disjoint rectangles. 
     
     
       87. The non-transitory computer-readable storage medium of claim 84, wherein the polygons comprise non-Manhattan geometries. 
     
     
       88. The non-transitory computer-readable storage medium of claim 84, wherein the aerial image is simulated as being produced by quadrupole illumination. 
     
     
       89. The non-transitory computer-readable storage medium of claim 84, wherein the modifying includes adding one or more of an edge shift or a sub-resolution assist feature to the layout data. 
     
     
       90. The non-transitory computer-readable storage medium of claim 84, wherein the simulating ignores corner effects. 
     
     
       91. The non-transitory computer-readable storage medium of claim 84, wherein the simulating includes using one or more look-up tables to determine the aerial image. 
     
     
       92. The non-transitory computer-readable storage medium of claim 91, wherein the one or more look-up tables are generated by calculating electromagnetic field. 
     
     
       93. A method of inspecting a mask, comprising:
 receiving data produced by scanning a beam across a surface of the mask and imaging scattered electromagnetic fields that result from the scanning; and   comparing the received data to benchmark data, wherein the benchmark data is produced by applying an edge domain decomposition method (EDDM) to layout data representing the mask.   
     
     
       94. The method of claim 93, wherein the benchmark data is produced at substantially a same time as the scanning. 
     
     
       95. The method of claim 93, further comprising generating a database storing the benchmark data. 
     
     
       96. The method of claim 93, wherein the benchmark data represents a defect-free version of the mask. 
     
     
       97. The method of claim 93, further comprising outputting a signal indicating whether the mask is defective based on the comparing. 
     
     
       98. The method of claim 93, wherein the benchmark data includes data produced by:
 defining a defect-free area of the mask;   simulating the defect-free area of the mask using the EDDM; and   simulating a defect within the defect-free area of the mask.   
     
     
       99. The method of claim 98, wherein the simulating a defect includes evaluating an aerial critical dimension (CD). 
     
     
       100. A non-transitory computer-readable storage medium storing computer-executable instructions for causing a computer to perform a method, the method comprising comparing received data to benchmark data, wherein the received data is produced at least in part by scanning a beam across a surface of a mask to produce a scattered electromagnetic field, and wherein the benchmark data is produced at least in part by applying an edge domain decomposition method (EDDM) to layout data representing the mask. 
     
     
       101. The non-transitory computer-readable storage medium of claim 100, wherein the benchmark data is produced at substantially a same time as the scanning. 
     
     
       102. The non-transitory computer-readable storage medium of claim 100, wherein the benchmark data is stored in a database. 
     
     
       103. The non-transitory computer-readable storage medium of claim 100, wherein the benchmark data represents a defect-free version of the mask. 
     
     
       104. The non-transitory computer-readable storage medium of claim 100, wherein the method further comprises, based on the comparing, outputting a signal indicating whether the mask is defective. 
     
     
       105. The non-transitory computer-readable storage medium of claim 100, wherein the benchmark data includes data produced by:
 defining a defect-free area of the mask;   simulating the defect-free area of the mask using the EDDM; and   simulating a defect within the defect-free area of the mask.   
     
     
       106. The non-transitory computer-readable storage medium of claim 105, wherein the simulating a defect includes evaluating an aerial critical dimension (CD). 
     
     
       107. A method for simulating light scattering by a three-dimensional object in an optical imaging system, the method comprising:
 applying edge-domain decomposition to the three-dimensional object to identify light scattering by one-dimensional edges that define the three-dimensional object; and   using a computer, summing scattered light from all the edges to simulate light scattering in two dimensions.