Optical metrology model optimization for repetitive structures

Abstract

An optical metrology model for a repetitive structure is optimized by selecting one or more profile parameters using one or more selection criteria. One or more termination criteria are set, the one or more termination criteria comprising measures of stability of the optical metrology model. The profile shape features of the repetitive structure are characterized using the one or more selected profile parameters. The optical metrology model is optimized using a set of values for the one or more selected profile parameters. One or more profile parameters of the profile of the repetitive structure are determined using the optimized optical metrology model and one or more measured diffraction signals. Values of the one or more termination criteria are calculated using the one or more determined profile parameters. When the calculated values of the one or more termination criteria do not match the one or more set termination criteria, the selection of the one or more profile parameters and/or the characterization of the profile shape features of the repetitive structure are revised.

1 . A method of optimizing an optical metrology model for a repetitive structure, the optical metrology model having profile parameters, the method comprising:
 a) selecting a set of profile parameters using one or more selection criteria, wherein the optical metrology model is defined by the set of profile parameters to characterize the profile of the repetitive structure;   b) setting one or more termination criteria, the one or more termination criteria comprising a measure of stability of the optical metrology model;   c) extracting values of profile parameters of the profile of the repetitive structure using the optical metrology model and one or more measured diffraction signals, wherein the one or more measured diffraction signals were obtained by measuring diffraction signals from an actual repetitive structure using an optical metrology device;   d) calculating the measure of stability using the extracted values to test the stability of the optical metrology model; and   e) when the calculated measure of stability does not match the one or more set termination criteria, revising the selection of one or more profile parameters in the set and/or the characterization of the profile shape features of the repetitive structure, and iterating c), d), and e).   
   
   
       2 . The method of  claim 1 , wherein the set of selected profile parameters includes a first pitch parameter in a first dimension and a second pitch parameter in a second dimension, wherein the first and second dimensions are orthogonal. 
   
   
       3 . The method of  claim 2 , wherein the first pitch parameter and the second pitch parameter are set to constants during an initial iteration of steps c)-e), and wherein the first pitch parameter and the second pitch parameter are allowed to float during subsequent iterations of steps c)-e). 
   
   
       4 . The method of  claim 1 , wherein the one or more selection criteria include sensitivity of simulated diffraction signals to changes of the selected profile parameters and/or correlation of a selected profile parameter to other profile parameters. 
   
   
       5 . The method of  claim 4 , wherein the one or more selection criteria include low sensitivity of diffraction signals resulting from changes of the selected profile parameter. 
   
   
       6 . The method of  claim 4 , wherein the one or more selection criteria include high correlation of a selected profile parameter to other profile parameters. 
   
   
       7 . The method of  claim 4 , wherein the one or more selection criteria include low sensitivity of diffraction signals and high correlation of a selected profile parameter to other profile parameters. 
   
   
       8 . The method of  claim 4 , wherein the sensitivity of diffraction signals include cost function of two diffraction signals per unit change of the selected profile parameter or sum-squared error between two diffraction signals per unit change of the selected profile parameter. 
   
   
       9 . The method of  claim 4 , wherein the correlation of diffraction signals includes correlation coefficients of a selected profile parameter compared to all other profile parameters. 
   
   
       10 . The method of  claim 4 , wherein sensitivity of simulated diffraction signals to changes of the selected profile parameters and/or correlation of selected profile parameters to other profile parameters are determined by:
 a) calculations using data obtained using the optical metrology model;   b) calculations using data obtained using process simulation; and/or   c) calculations using historical data from a similar application.   
   
   
       11 . The method of  claim 1 , wherein the one or more termination criteria include checking that profile parameters falling within established ranges, that variance targets of determined profile parameters compared to reference values, target ratios of maximum to minimum eigenvalues, and/or singularity measures are met. 
   
   
       12 . The method of  claim 1 , wherein the profile shape of the repetitive structure is characterized by:
 utilizing mathematical algorithms that integrate physical dimension limits of the selected profile parameters.   
   
   
       13 . The method of  claim 12 , wherein the selected profile parameters include cross-sectional view parameters for shape features. 
   
   
       14 . The method of  claim 13 , wherein cross-sectional view parameters for shape features include top rounding, footing, undercutting, T-topping, and/or a hemisphere. 
   
   
       15 . The method of  claim 14 , wherein the mathematical algorithm for cross-sectional view parameters for shape features includes distance ratio. 
   
   
       16 . The method of  claim 15 , wherein the distance ratio is calculated using a length attribute of the shape feature and a proximate cross-sectional view profile parameter. 
   
   
       17 . The method of  claim 16 , wherein the proximate cross-sectional view parameter includes one or more of a top critical dimension, a middle critical dimension, a bottom critical dimension, and/or radius of a hemisphere. 
   
   
       18 . The method of  claim 17 , wherein:
 if one shape feature includes top-rounding, the distance ratio is calculated using the horizontal length of the top-rounded feature on one side and the top critical dimension;   if one shape feature includes T-topping, the distance ratio is calculated using the horizontal length of the T-top feature on one side and the top critical dimension;   if one shape feature includes footing, the distance ratio is calculated using the horizontal length of the footing feature on one side and the bottom critical dimension;   if one shape feature includes undercutting, the distance ratio is calculated using the horizontal length of the undercut feature on one side and the top critical dimension, the middle critical dimension or the bottom critical dimension, and   if one shape feature includes a hemisphere, the distance ratio is calculated using the horizontal length of the radius of the hemisphere feature and the top critical dimension.   
   
   
       19 . The method of  claim 1 , wherein the repetitive structure is a two-dimensional grating. 
   
   
       20 . The method of  claim 1 , wherein the repetitive structure comprises contact holes, posts, vias, and/or trenches. 
   
   
       21 . The method of  claim 1 , wherein the repetitive structure comprises two or more features in a unit cell. 
   
   
       22 . A system for optimizing an optical metrology model for use in modeling repetitive structures in a wafer, the system comprising:
 an optical metrology model optimizer configured to:
 select a set of profile parameters using one or more selection criteria, wherein the optical metrology model I defined by the set of profile parameters to characterize the profile of the repetitive structure; 
 set one or more termination criteria, the one or more termination criteria comprising a measure of stability of the optical metrology model; 
 extract values of profile parameters of the profile of the repetitive structure using the optical metrology model and one or more measured diffraction signals, wherein the one or more measured diffraction signals were obtained by measuring diffraction signals from an actual repetitive structure using an optical metrology device; and 
 calculate the measure of stability using the extracted values to test the stability of the optical metrology model; 
   a comparator configured to determine if one or more termination criteria are met by the calculated measure of stability; and   a model adjuster configured to revise the selection the set of one or more profile parameters in the set and/or the characterization of the profile shape features of the repetitive structure.   
   
   
       23 . The system of  claim 22 , wherein the set of selected profile parameters includes a first pitch parameter in a first dimension and a second pitch parameter in a second dimension, wherein the first and second dimensions are orthogonal. 
   
   
       24 . The system of  claim 23 , wherein the first pitch parameter and the second pitch parameter are set to constants during an initial iteration of optimizing the optical metrology model, and wherein the first pitch parameter and the second pitch parameter are allowed to float during subsequent iterations of optimizing the optical metrology model. 
   
   
       25 . The system of  claim 22 , wherein the one or more selection criteria include sensitivity of simulated diffraction signals to changes of the selected profile parameters and/or correlation of a selected profile parameter to other profile parameters. 
   
   
       26 . The system of  claim 22 , wherein the profile shape of the repetitive structure is characterized by:
 utilizing mathematical algorithms that integrate physical dimension limits of the selected profile parameters.   
   
   
       27 . The system of  claim 26 , wherein the selected profile parameters include cross-sectional view parameters for shape features. 
   
   
       28 . The system of  claim 27 , wherein cross-sectional view parameters for shape features include top rounding, footing, undercutting, T-topping, and/or a hemisphere. 
   
   
       29 . The system of  claim 28 , wherein the mathematical algorithm for cross-sectional view parameters for shape features includes distance ratio. 
   
   
       30 . The system of  claim 29 , wherein the distance ratio is calculated using a length attribute of the shape feature and a proximate cross-sectional view profile parameter. 
   
   
       31 . The system of  claim 30 , wherein the proximate cross-sectional view parameter includes one or more of a top critical dimension, a middle critical dimension, a bottom critical dimension, and/or radius of a hemisphere. 
   
   
       32 . The system of  claim 31 , wherein:
 if one shape feature includes top-rounding, the distance ratio is calculated using the horizontal length of the top-rounded feature on one side and the top critical dimension;   if one shape feature includes T-topping, the distance ratio is calculated using the horizontal length of the T-top feature on one side and the top critical dimension;   if one shape feature includes footing, the distance ratio is calculated using the horizontal length of the footing feature on one side and the bottom critical dimension;   if one shape feature includes undercutting, the distance ratio is calculated using the horizontal length of the undercut feature on one side and the top critical dimension, the middle critical dimension or the bottom critical dimension, and   if one shape feature includes a hemisphere, the distance ratio is calculated using the horizontal length of the radius of the hemisphere feature and the top critical dimension.   
   
   
       33 . The system of  claim 22 , wherein the repetitive structure is a two-dimensional grating. 
   
   
       34 . The system of  claim 22 , wherein the repetitive structure comprises contact holes, posts, vias, and/or trenches. 
   
   
       35 . The system of  claim 22 , wherein the repetitive structure comprises two or more features in a unit cell. 
   
   
       36 . A computer-readable storage medium containing computer executable instructions for causing a computer to optimize selection of profile parameters of an optical metrology model for use in modeling repetitive structures in a wafer, comprising instructions for:
 a) selecting a set of profile parameters using one or more selection criteria, wherein the optical metrology model is defined by the set of profile parameters to characterize the profile of the repetitive structure;   b) setting one or more termination criteria, the one or more termination criteria comprising a measure of stability of the optical metrology model;   c) extracting values of profile parameters of the profile of the repetitive structure using the optical metrology model and one or more measured diffraction signals, wherein the one or more measured diffraction signals were obtained by measuring diffraction signals from an actual repetitive structure using an optical metrology device;   d) calculating the measure of stability using the extracted values to test the stability of the optical metrology model; and   e) when the calculated measure of stability does not match the one or more set termination criteria, revising the selection of one or more profile parameters in the set and/or the characterization of the profile shape features of the repetitive structure, and iterating c), d), and e).   
   
   
       37 . The computer-readable storage medium of  claim 36 , wherein the set of selected profile parameters includes a first pitch parameter in a first dimension and a second pitch parameter in a second dimension, wherein the first and second dimensions are orthogonal. 
   
   
       38 . The computer-readable storage medium of  claim 37 , wherein the first pitch parameter and the second pitch parameter are set to constants during an initial iteration of steps c)-e), and wherein the first pitch parameter and the second pitch parameter are allowed to float during subsequent iterations of steps c)-e). 
   
   
       39 . The computer-readable storage medium of  claim 36 , wherein the one or more selection criteria include sensitivity of simulated diffraction signals to changes of the selected profile parameters and/or correlation of a selected profile parameter to other profile parameters. 
   
   
       40 . The computer-readable storage medium of  claim 36 , wherein the profile shape of the repetitive structure is characterized by:
 utilizing mathematical algorithms that integrate physical dimension limits of the selected profile parameters.   
   
   
       41 . The computer-readable storage medium of  claim 40 , wherein the selected profile parameters include cross-sectional view parameters for shape features. 
   
   
       42 . The computer-readable storage medium of  claim 41 , wherein cross-sectional view parameters for shape features include top rounding, footing, undercutting, T-topping, and/or a hemisphere. 
   
   
       43 . The computer-readable storage medium of  claim 42 , wherein the mathematical algorithm for cross-sectional view parameters for shape features includes distance ratio. 
   
   
       44 . The computer-readable storage medium of  claim 43 , wherein the distance ratio is calculated using a length attribute of the shape feature and a proximate cross-sectional view profile parameter. 
   
   
       45 . The computer-readable storage medium of  claim 44 , wherein the proximate cross-sectional view parameter includes one or more of a top critical dimension, a middle critical dimension, a bottom critical dimension, and/or radius of a hemisphere. 
   
   
       46 . The computer-readable storage medium of  claim 45 , wherein:
 if one shape feature includes top-rounding, the distance ratio is calculated using the horizontal length of the top-rounded feature on one side and the top critical dimension;   if one shape feature includes T-topping, the distance ratio is calculated using the horizontal length of the T-top feature on one side and the top critical dimension;   if one shape feature includes footing, the distance ratio is calculated using the horizontal length of the footing feature on one side and the bottom critical dimension;   if one shape feature includes undercutting, the distance ratio is calculated using the horizontal length of the undercut feature on one side and the top critical dimension, the middle critical dimension or the bottom critical dimension, and   if one shape feature includes a hemisphere, the distance ratio is calculated using the horizontal length of the radius of the hemisphere feature and the top critical dimension.   
   
   
       47 . The computer-readable storage medium of  claim 36 , wherein the repetitive structure is a two-dimensional grating. 
   
   
       48 . The computer-readable storage medium of  claim 36 , wherein the repetitive structure comprises contact holes, posts, vias, and/or trenches. 
   
   
       49 . The computer-readable storage medium of  claim 36 , wherein the repetitive structure comprises two or more features in a unit cell.