System and method for generating and analyzing roughness measurements
Systems and methods are disclosed that remove noise from roughness measurements to determine roughness of a feature in a pattern structure. In one embodiment, a method for determining roughness of a feature in a pattern structure includes generating, using an imaging device, a set of one or more images, each including measured linescan information that includes noise. The method also includes detecting edges of the features within the pattern structure of each image without filtering the images, generating a biased power spectral density (PSD) dataset representing feature geometry information corresponding to the edge detection measurements, evaluating a high-frequency portion of the biased PSD dataset to determine a noise model for predicting noise over all frequencies of the biased PSD dataset, and subtracting the noise predicted by the determined noise model from a biased roughness measure to obtain an unbiased roughness measure.
1. A method for determining roughness of a feature in a pattern structure, the method comprising;
generating, using an imaging device, a set of one or more images, each image of the set including an instance of a feature within a respective pattern structure, each image including measured linescan information corresponding to the pattern structure that includes noise;
detecting edges of the features within the pattern structure of each image of the set without filtering the images;
generating a power spectral density (PSD) dataset representing feature geometry information corresponding to the edge detection measurements of the set of images;
defining a threshold range and a threshold height;
generating a baseline PSD dataset for a portion of the PSD dataset, by smoothly connecting a first PSD value of the portion of the PSD dataset and a second PSD value of the portion of the PSD dataset, wherein the first PSD value and the second PSD value are separated by the threshold range;
determining that a difference between a third PSD value of the portion of the PSD dataset and the baseline is greater than the threshold height; and
replacing the portion of the PSD dataset with the baseline PSD dataset.
2. The method of claim 1 , further comprising:
identifying the portion of the PSD dataset as a spike associated with a photomask feature; and
performing a roughness measurement of the photomask feature based on the portion of the PSD dataset.
3. The method of claim 1 , further comprising defining the threshold height based on the overall statistical uncertainty in values of the PSD dataset.
4. The method of claim 1 , further comprising defining the threshold range as three frequency increments.
5. The method of claim 1 , further comprising:
evaluating the PSD dataset comprising a first bump to determine a first model and a bump model; and
fitting the first model and the bump model to the PSD dataset to create a best fit model.
6. The method of claim 5 , wherein the bump model is of the form:
PSD bump ( f )= Ae −(f−f c ) 2 /2σ w 2
wherein PSD bump represents the first bump in the PSD dataset, A represents an amplitude of the first bump, f c represents a center frequency of the first bump, and σ w represents the width of the first bump.
7. The method of claim 5 , further comprising:
determining an area of the first bump from the best fit model, the first bump defining an area above the first model, wherein the area defines a magnitude of a phenomenon associated with the first bump.
8. The method of claim 7 , further comprising identifying the magnitude of the phenomenon as a measure of a variance of a wiggle.
9. The method of claim 1 , further comprising:
identifying the portion of the PSD dataset as a spike associated with a topography of a wafer; and
evaluating the portion of the PSD dataset to assess the topography of the wafer.
10. The method of claim 1 , further comprising:
unbiasing the PSD dataset by subtracting PSD noise to create an unbiased PSD dataset,
wherein the PSD dataset comprises at least one selected from the group consisting of: a biased PSD dataset and the unbiased PSD dataset.
11. A system for determining roughness of a feature in a pattern structure, the system comprising:
an imaging device configured to generate a set of one or more images, each image of the set including an instance of a feature within a respective pattern structure, each image including measured linescan information corresponding to the pattern structure that includes noise; and
a processor operatively coupled to the imaging device;
a memory coupled to the processor;
the memory storing a program that, when executed by the processor, causes the processor to:
receive the measured linescan information from the imaging device;
detect edges of the features within the pattern structure of each image of the set without filtering the images to create edge detection measurement of the set of images;
generate a biased power spectral density (PSD) dataset corresponding to the edge detection measurements of the set of images;
evaluate a first bump in the PSD dataset to create a bump model; and
fit a first model and the bump model to the PSD dataset to create a best fit model.
12. The system of claim 11 , wherein to evaluate the first bump, the program further causes the processor to apply a bump model in the form:
PSD bump ( f )= Ae −(f−f c ) 2 /2σ w 2
wherein PSD bump represents the first bump in the PSD dataset, A represents an amplitude of the first bump, f c represents a center frequency of the first bump, and σ w represents the width of the first bump.
13. The system of claim 11 , wherein the program further causes the processor to determine an area of the first bump from the best fit model, the first bump defining an area above the first model, wherein the area defines a measure of a variance of a wiggle.
14. The system of claim 11 , wherein the program further causes the processor to:
define a threshold range and a threshold height;
generate a baseline for a portion of the PSD dataset by smoothly connecting a first PSD value of the portion of the portion of the PSD dataset and a second PSD value of the portion of the PSD dataset, wherein the first PSD value and the second PSD value are separated by a threshold range;
determine that a difference between a third PSD value of the portion of the PSD dataset and the baseline is greater than the threshold height; and
replace the portion of the PSD dataset with the baseline for the portion of the PSD dataset.
15. The system of claim 12 , wherein the program further causes the processor to:
identify the portion of the PSD dataset as a spike associated with a topography of a wafer; and
evaluate the portion of the PSD dataset to assess the topography of the wafer.
16. The system of claim 14 , wherein the program causes the processor to define the threshold height based on the overall statistical uncertainty in values of the PSD dataset.
17. The system of claim 11 , wherein the program further causes the processor to:
identify the first bump as associated with a photomask feature; and
perform a roughness measurement of the photomask feature based on the bump model.
18. The system of claim 11 , wherein the program further causes the processor to:
unbias the PSD dataset by subtracting PSD noise to create an unbiased PSD dataset,
wherein the PSD dataset comprises at least one selected from the group consisting of: a biased PSD dataset and the unbiased PSD dataset.
19. A non-transitory computer readable storage media storing instructions that, when executed by a processor, cause the processor to:
generate, using an imaging device, a set of one or more images, each image of the set including an instance of a feature within a respective pattern structure, each image including measured linescan information corresponding to the pattern structure that includes noise;
detect edges of the features within the pattern structure of each image of the set without filtering the images;
generate a biased power spectral density (PSD) dataset representing feature geometry information corresponding to the edge detection measurements of the set of images;
evaluate a first bump in the PSD dataset to create a bump model; and
fit a first model and the bump model to the PSD dataset to create a best fit model.
20. The non-transitory computer readable storage media of claim 19 , wherein the instructions further cause the processor to apply a bump model in the form:
PSD bump ( f )= Ae −(f−f c ) 2 /2σ w 2
wherein PSD bump represents the first bump in the PSD dataset, A represents an amplitude of the first bump, f c represents a center frequency of the first bump, and σ w represents the width of the first bump.
21. The non-transitory computer readable storage media of claim 19 , wherein the instruction further cause the processor to determine an area of the first bump from the best fit model, the first bump defining an area above the first model, wherein the area defines a measure of a variance of a wiggle.
22. The non-transitory computer readable storage media of claim 19 , wherein the instructions further cause the processor to:
define a threshold range and a threshold height;
generate a baseline for a portion of the PSD dataset by smoothly connecting a first PSD value of the portion of the portion of the PSD dataset and a second PSD value of the portion of the PSD dataset, wherein the first PSD value and the second PSD value are separated by a threshold range;
determine that a difference between a third PSD value of the portion of the PSD dataset and the baseline is greater than the threshold height; and
replace the portion of the PSD dataset with the baseline for the portion of the PSD dataset.
23. The non-transitory computer readable storage media of claim 19 , wherein the instructions further cause the processor to:
unbias the PSD dataset by subtracting PSD noise to create an unbiased PSD dataset,
wherein the PSD dataset comprises at least one selected form the group consisting of: a biased PSD dataset and the unbiased PSD dataset.