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WEIGHTING FUNCTION TO ENHANCE
MEASURED DIFFRACTION SIGNALS IN
OPTICAL METROLOGY
BACKGROUND 5
1. Field
The present application relates to optical metrology, and, more particularly, to defining a weighting function to enhance measured diffraction signals used in optical metrology. 10
2. Related Art
Optical metrology involves directing an incident beam at a feature on a wafer, measuring the resulting diffraction signal, and analyzing the measured diffraction signal to determine various characteristics of the feature. In semiconductor 15 manufacturing, optical metrology is typically used for quality assurance. For example, after fabricating a periodic grating in proximity to a semiconductor chip on a semiconductor wafer, an optical metrology system is used to determine the profile of the periodic grating. By determining the profile of the peri- 20 odic grating, the quality of the fabrication process utilized to form the periodic grating, and by extension the semiconductor chip proximate the periodic grating, can be evaluated.
For a number of reasons, the measured diffraction signal may be weak. For example, the measured diffraction signal 25 may include noise related to the hardware used to obtain the measured diffraction signal and to the feature being measured. A weak measured diffraction signal may decrease the accuracy of the optical metrology process.
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SUMMARY
In one exemplary embodiment, a weighting function is obtained to enhance measured diffraction signals used in optical metrology. To obtain the weighting function, a mea- 35 sured diffraction signal is obtained. The measured diffraction signal was measured from a site on a wafer using a photometric device. A first weighting function is defined based on noise that exists in the measured diffraction signal. A second weighting function is defined based on accuracy of the mea- 40 sured diffraction signal. A third weighting function is defined based on sensitivity of the measured diffraction signal. A fourth weighting function is defined based on one or more of the first, second, and third weighting functions.
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DESCRIPTION OF DRAWING FIGURES
The present application can be best understood by reference to the following description taken in conjunction with the accompanying drawing figures, in which like parts may be 50 referred to by like numerals:
FIG. 1 depicts an exemplary optical metrology system;
FIGS. 2A-2E depict various optical metrology models of a structure;
FIG. 3 depicts an exemplary noise profile; 55
FIG. 4 depicts exemplary weighting functions;
FIG. 5 depicts another exemplary noise profile;
FIG. 6 depicts an exemplary measured diffraction signal and an exemplary simulated diffraction signal; go
FIG. 7 depicts an exemplary error profile;
FIG. 8 depicts an exemplary weighting function;
FIG. 9 depicts a set of measured diffraction signals;
FIG. 10 depicts a set of transformed diffraction signals;
FIG. 11 depicts ratios of the transformed diffractions sig- 65 nals depicted in FIG. 10 and the measured diffraction signals depicted in FIG. 9; and
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FIGS. 12, 13, 14 depict results of exemplary focus/exposure wafers (FEM) analysis.
DETAILED DESCRIPTION
The following description sets forth numerous specific configurations, parameters, and the like. It should be recognized, however, that such description is not intended as a limitation on the scope of the present invention, but is instead provided as a description of exemplary embodiments.
1. Optical Metrology
With reference to FIG. 1, an optical metrology system 100 can be used to examine and analyze a structure formed on a wafer. For example, optical metrology system 100 can be used to determine the profile of a periodic grating 102 formed on wafer 104. As described earlier, periodic grating 102 can be formed in test areas on wafer 104, such as adjacent to a device formed on wafer 104. Alternatively, periodic grating 102 can be formed in an area of the device that does not interfere with the operation of the device or along scribe lines on wafer 104.
As depicted in FIG. 1, optical metrology system 100 can include a photometric device with a source 106 and a detector 112. Periodic grating 102 is illuminated by an incident beam 108 from source 106. In the present exemplary embodiment, incident beam 108 is directed onto periodic grating 102 at an
angle of incidence 6,. with respect to normal n of periodic grating 102 and an azimuth angle <I> (i.e., the angle between the plane of incidence beam 108 and the direction of the periodicity of periodic grating 102). Diffracted beam 110
leaves at an angle of Qd with respect to normal n and is received by detector 112. Detector 112 converts the diffracted beam 110 into a measured diffraction signal.
To determine the profile of periodic grating 102, optical metrology system 100 includes a processing module 114 configured to receive the measured diffraction signal and analyze the measured diffraction signal. The profile of periodic grating 102 can then be determined using a library-based optical metrology process or a regression-based optical metrology process. Additionally, other linear or non-linear profile extraction techniques are contemplated.
It should be recognized that optical metrology system 100 can be used to examine and analyze various types of structures other than periodic grating 102, such as a thin film layer, features of the actual device, and the like. Additionally, a library-based optical metrology process or a regression-based optical metrology process can be used to determine various characteristics other than profile, such as the thickness of a thin film layer.
2. Library-Based Optical Metrology Process
In a library-based optical metrology process, the measured diffraction signal is compared to a library of simulated diffraction signals. More specifically, each simulated diffraction signal in the library is associated with an optical metrology model of the feature. When a match is made between the measured diffraction signal and one of the simulated diffraction signals in the library or when the difference of the measured diffraction signal and one of the simulated diffraction signals is within a preset or matching criterion, the optical metrology model associated with the matching simulated diffraction signal is presumed to represent the feature. The matching simulated diffraction signal and/or optical metrology model can then be utilized to determine whether the feature has been fabricated according to specifications.
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Thus, with reference again to FIG. 1, in one exemplary embodiment, after obtaining a measured diffraction signal, processing module 114 then compares the measured diffraction signal to simulated diffraction signals stored in a library 116. Each simulated diffraction signal in library 116 can be 5 associated with an optical metrology model. Thus, when a match is made between the measured diffraction signal and one of the simulated diffraction signals in library 116, the optical metrology model associated with the matching simulated diffraction signal can be presumed to represent the 10 actual profile of periodic grating 102.
The set of optical metrology models stored in library 116 can be generated by characterizing the profile of periodic grating 102 using a set of profile parameters, then varying the set of profile parameters to generate optical metrology mod- 15 els of varying shapes and dimensions. The process of characterizing a profile using a set of profile parameters can be referred to as parameterizing.
For example, as depicted in FIG. 2A, assume that the profile of a feature is characterized using optical metrology 20 model 200 with profile parameters hi and wl that define its height and width, respectively. As depicted in FIGS. 2B to 2E, additional shapes and features of the profile can be characterized by increasing the number of profile parameters used in optical metrology model 200. For example, as depicted in 25 FIG. 2B, optical metrology model 200 can include profile parameters hi, wl, and w2 that define its height, bottom width, and top width, respectively. Note that the width of optical metrology model 200 can be referred to as the critical dimension (CD). For example, in FIG. 2B, profile parameter 30 wl and w2 can be described as defining the bottom CD and top CD, respectively, of optical metrology model 200.
As described above, the set of optical metrology models stored in library 116 (FIG. 1) can be generated by varying the profile parameters used in the optical metrology model. For 35 example, with reference to FIG. 2B, by varying profile parameters hi, wl, and w2, optical metrology models of varying shapes and dimensions can be generated. Note that one, two, or all three profile parameters can be varied relative to one another. 40
With reference again to FIG. 1, the number of optical metrology models and corresponding simulated diffraction signals in the set of optical metrology models and simulated diffraction signals stored in library 116 (i.e., the resolution and/or range of library 116) depends, in part, on the range 45 over which the set of profile parameters and the increment at which the set of profile parameters are varied. In one exemplary embodiment, the optical metrology models and the simulated diffraction signals stored in library 116 are generated prior to obtaining a measured diffraction signal from an 50 actual feature. Thus, the range and increment (i.e., the range and resolution) used in generating library 116 can be selected based on familiarity with the fabrication process for a feature and what the range of variance is likely to be. The range and/or resolution of library 116 can also be selected based on 55 empirical measures, such as measurements using AFM, X-SEM, and the like.
For a more detailed description of a library-based process, see U.S. patent application Ser. No. 09/907,488, titled GENERATION OF A LIBRARY OF PERIODIC GRATING DIF- 60 FRACTION SIGNALS, filed on Jul. 16,2001, which is incorporated herein by reference in its entirety.
3. Regression-Based Optical Metrology Process
In a regression-based optical metrology process, the mea- 65 sured diffraction signal is compared to a simulated diffraction signal (i.e., a trial diffraction signal). The simulated diffrac
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tion signal is generated prior to the comparison using a set of profile parameters (i.e., trial profile parameters) for an optical metrology model. If the measured diffraction signal and the simulated diffraction signal do not match or when the difference of the measured diffraction signal and one of the simulated diffraction signals is not within a preset or matching criterion, another simulated diffraction signal is generated using another set of profile parameters for another optical metrology model, then the measured diffraction signal and the newly generated simulated diffraction signal are compared. When the measured diffraction signal and the simulated diffraction signal match or when the difference of the measured diffraction signal and one of the simulated diffraction signals is within a preset or matching criterion, the optical metrology model associated with the matching simulated diffraction signal is presumed to represent the actual feature. The matching simulated diffraction signal and/or optical metrology model can then be utilized to determine whether the feature has been fabricated according to specifications.
Thus, with reference again to FIG. 1, in one exemplary embodiment, processing module 114 can generate a simulated diffraction signal for an optical metrology model, and then compare the measured diffraction signal to the simulated diffraction signal. As described above, if the measured diffraction signal and the simulated diffraction signal do not match or when the difference of the measured diffraction signal and one of the simulated diffraction signals is not within a preset or matching criterion, then processing module 114 can iteratively generate another simulated diffraction signal for another optical metrology model. In one exemplary embodiment, the subsequently generated simulated diffraction signal can be generated using an optimization algorithm, such as global optimization techniques, which includes simulated annealing, and local optimization techniques, which includes steepest descent algorithm.
In one exemplary embodiment, the simulated diffraction signals and optical metrology models can be stored in a library 116 (i.e., a dynamic library). The simulated diffraction signals and optical metrology models stored in library 116 can then be subsequently used in matching the measured diffraction signal.
For a more detailed description of a regression-based process, see U.S. patent application Ser. No. 09/923,578, titled METHOD AND SYSTEM OF DYNAMIC LEARNING THROUGH A REGRESSION-BASED LIBRARY GENERATION PROCESS, filed on Aug. 6, 2001, now U.S. Pat. No. 6,785,638, issued Aug. 31, 2004, which is incorporated herein by reference in its entirety.
4. Rigorous Coupled Wave Analysis
As described above, simulated diffraction signals are generated to be compared to measured diffraction signals. In one exemplary embodiment, simulated diffraction signals can be generated by applying Maxwell's equations, which can be solved using various numerical analysis techniques, including rigorous coupled-wave analysis (RCWA). For a more detailed description of RCWA, see U.S. patent application Ser. No. 09/770,997, titled CACHING OF INTRA-LAYER CALCULATIONS FOR RAPID RIGOROUS COUPLEDWAVE ANALYSES, filed on Jan. 25,2001, now U.S. Pat. No. 6,891,626, issued May 10,2005, which is incorporated herein by reference in its entirety.
5. Machine Learning Systems
In one exemplary embodiment, simulated diffraction signals can be generated using a machine learning system employing a machine learning algorithm, such as backpropagation, radial basis function, support vector, kernel
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