Measurement methodology of advanced nanostructures
A parameterized geometric model of a structure can be determined based on spectra from a wafer metrology tool. The structure can have geometry-induced anisotropic effects. Dispersion parameters of the structure can be determined from the parameterized geometric model. This can enable metrology techniques to measure nanostructures that have geometries and relative positions with surrounding structures that induce non-negligible anisotropic effects. These techniques can be used to characterize process steps involving metal and semiconductor targets in semiconductor manufacturing of, for example, FinFETs or and gate-all-around field-effect transistors.
1. A method comprising:
receiving spectra at a processor, wherein the spectra are from an area of a semiconductor wafer that includes a structure, wherein the spectra are measured by a wafer metrology tool, and wherein the structure has geometry-induced anisotropic effects;
generating a parameterized geometric model of the structure using the processor;
assigning anisotropic material properties to the parameterized geometric model using the processor;
determining dispersion parameters of the structure on the wafer using the parameterized geometric model with the processor, wherein the dispersion parameters include anisotropic dispersion parameters, and wherein anisotropic dielectric components of the dispersion parameters are provided by one or more reference theoretical or empirical dispersion models; and
determining at least one geometric parameter or anisotropic material parameter from the parameterized geometric model using the processor.
2. The method of claim 1 , further comprising measuring the spectra with the wafer metrology tool.
3. The method of claim 1 , wherein the dispersion parameters include an anisotropic tensor matrix.
4. The method of claim 1 , wherein the reference theoretical or empirical dispersion models represent dependency of the dispersion parameters on contributing factors to anisotropy.
5. The method of claim 1 , wherein the at least one geometric parameter or anisotropic material parameter is determined using a regression.
6. The method of claim 1 , wherein the at least one geometric parameter or anisotropic material parameter is determined using machine learning.
7. The method of claim 1 , wherein the dispersion parameters are modeled using a biaxial model or a uniaxial model.
8. The method of claim 7 , wherein dielectric components of the biaxial model or the uniaxial model are provided by at least one reference dispersion model.
9. The method of claim 1 , wherein the anisotropic material properties include at least one of electron density, material density, or chemical composition.
10. The method of claim 1 , wherein the anisotropic dispersion parameters are parametrized using correction parameters.
11. The method of claim 10 , wherein the correction parameters represent shifts or scales of an original anisotropic dispersion.
12. The method of claim 1 , wherein the dispersion parameters are determined by a process including:
generating a spectral design of experiments using the parameterized geometric model, a dispersion model, and a simulator, wherein at least one of the geometric parameters and dispersion parameters are distributed within predetermined ranges;
training a statistical model to determine a relationship between the spectra and at least one parameter related to geometric and/or material parameters of the structure; and
predicting parameters of interest of the structure from the spectra using the statistical model.
13. The method in claim 1 , wherein the dispersion parameters are determined by at least one of optimization or regression minimizing a spectral difference between modeled and measured versions of the spectra and by perturbing the parameterized geometric model and the dispersion parameters.
14. The method in claim 1 , further comprising one or more feedback operations that use learning based upon comparing simulated spectra and the spectra to adjust parameters in the parameterized geometric model, a dispersion model, and/or a geometric configuration.
15. The method of claim 1 , further comprising predicting anisotropic dispersions using the spectra.
16. A computer program product comprising a non-transitory computer readable storage medium having a computer readable program embodied therewith, the computer readable program configured to carry out the method of claim 1 .
17. A system comprising:
an electronic data storage unit; and
a processor in electronic communication with the electronic data storage unit and a wafer metrology tool, wherein the processor is configured to:
generate a parameterized geometric model of a structure, wherein the spectra are from an area of a semiconductor wafer that includes a structure, wherein the spectra are measured by a wafer metrology tool, and wherein the structure has geometry-induced anisotropic effects;
assign anisotropic material properties to the parameterized geometric model;
determine dispersion parameters of the structure on the wafer using the parameterized geometric model, wherein the dispersion parameters include anisotropic dispersion parameters, and wherein anisotropic dielectric components of the dispersion parameters are provided by one or more reference theoretical or empirical dispersion models; and
determine at least one geometric parameter or anisotropic material parameter from the parameterized geometric model.
18. The system of claim 17 , wherein the processor and the electronic data storage unit are disposed in the wafer metrology tool.
19. A non-transitory computer-readable storage medium, comprising one or more programs for executing a simulator comprising:
a parameterized geometric model of a structure, wherein the spectra are from an area of a semiconductor wafer that includes a structure, wherein the spectra are measured by a wafer metrology tool, wherein the structure has geometry-induced anisotropic effects, and wherein the parameterized geometric model, using a processor, is configured to:
have anisotropic material properties assigned;
determine dispersion parameters of the structure on the wafer, wherein the dispersion parameters include anisotropic dispersion parameters, and wherein anisotropic dielectric components of the dispersion parameters are provided by one or more reference theoretical or empirical dispersion models;
determine at least one geometric parameter or anisotropic material parameter; and
predict anisotropic dispersions based on the spectra.
20. The system of claim 17 , wherein the dispersion parameters are determined by a process including:
generating a spectral design of experiments using the parameterized geometric model, a dispersion model, and a simulator, wherein at least one of the geometric parameters and dispersion parameters are distributed within predetermined ranges;
training a statistical model to determine a relationship between the spectra and at least one parameter related to geometric and/or material parameters of the structure; and
predicting parameters of interest of the structure from the spectra using the statistical model.