LIBRARY GENERATION WITH DERIVATIVES IN OPTICAL METROLOGY
Methods of library generation with derivatives for optical metrology are described. For example, a method of generating a library for optical metrology includes determining a function of a parameter data set for one or more repeating structures on a semiconductor substrate or wafer. The method also includes determining a first derivative of the function of the parameter data set. The method also includes providing a spectral library based on both the function and the first derivative of the function.
1 . A method of generating a library for optical metrology, the method comprising:
determining a function of a parameter data set for one or more repeating structures on a semiconductor substrate or wafer;
determining a first derivative of the function of the parameter data set; and
providing a spectral library based on both the function and the first derivative of the function.
2 . The method of claim 1 , wherein determining the first derivative comprises determining an analytical derivative of the function of the parameter data set.
3 . The method of claim 1 , wherein determining the first derivative comprises determining a numerical derivative of the function of the parameter data set.
4 . The method of claim 1 , the method further comprising:
determining a higher order derivative of the function of the parameter data set, wherein providing the spectral library is further based on the higher order derivative of the function.
5 . The method of claim 1 , wherein determining the first derivative comprises determining both an analytical derivative and a numerical derivative of the function of the parameter data set.
6 . The method of claim 1 , wherein determining the function of the parameter data set comprises determining a function of a shape profile of the one or more repeating structures.
7 . The method of claim 1 , wherein determining the function of the parameter data set comprises determining a function of a material composition of the one or more repeating structures.
8 . The method of claim 1 , wherein providing the spectral library comprises training a neural network using both the function and the first derivative of the function.
9 . The method of claim 1 , wherein the spectral library comprises a simulated spectrum, the method further comprising:
comparing the simulated spectrum to a sample spectrum.
10 . A non-transitory machine-accessible storage medium having instructions stored thereon which cause a data processing system to perform a method of generating a library for optical metrology, the method comprising:
determining a function of a parameter data set for one or more repeating structures on a semiconductor substrate or wafer;
determining a first derivative of the function of the parameter data set; and
providing a spectral library based on both the function and the first derivative of the function.
11 . The non-transitory storage medium as in claim 10 , wherein determining the first derivative comprises determining an analytical derivative of the function of the parameter data set.
12 . The non-transitory storage medium as in claim 10 , wherein determining the first derivative comprises determining a numerical derivative of the function of the parameter data set.
13 . The non-transitory storage medium as in claim 10 , the method further comprising:
determining a higher order derivative of the function of the parameter data set, wherein providing the spectral library is further based on the higher order derivative of the function.
14 . The non-transitory storage medium as in claim 10 , wherein determining the first derivative comprises determining both an analytical derivative and a numerical derivative of the function of the parameter data set.
15 . The non-transitory storage medium as in claim 10 , wherein determining the function of the parameter data set comprises determining a function of a shape profile of the one or more repeating structures.
16 . The non-transitory storage medium as in claim 10 , wherein determining the function of the parameter data set comprises determining a function of a material composition of the one or more repeating structures.
17 . The non-transitory storage medium as in claim 10 , wherein providing the spectral library comprises training a neural network using both the function and the first derivative of the function.
18 . The non-transitory storage medium as in claim 10 , wherein the spectral library comprises a simulated spectrum, the method further comprising:
comparing the simulated spectrum to a sample spectrum.
19 . A system to generate a simulated diffraction signal to determine process parameters of a wafer application to fabricate a structure on a wafer using optical metrology, the system comprising:
a fabrication cluster configured to perform a wafer application to fabricate a structure on a wafer, wherein one or more process parameters characterize behavior of structure shape or layer thickness when the structure undergoes processing operations in the wafer application performed using the fabrication cluster;
an optical metrology system configured to determine the one or more process parameters of the wafer application, the optical metrology system comprising:
a beam source and detector configured to measure a diffraction signal of the structure;
a spectral library of simulated diffraction signals, the spectral library based on both a function and a first derivative of the function of a parameter data set of a plurality of model structures; and
a processor configured to determine, from the plurality of model structures, a model of the structure.
20 . The system of claim 19 , wherein the first derivative is an analytical derivative.
21 . The system of claim 19 , wherein the first derivative is a numerical derivative.
22 . The system of claim 19 , wherein the spectral library is further based on a higher order derivative of the function of the parameter data set.
23 . The system of claim 19 , wherein the processor is further configured to compare a simulated spectrum of the spectral library with a sample spectrum of the structure.