Meta-surface characterization
Phase deviations are determined from measurements of different diffraction orders. Undesired-order focal spots provide an indication of fabrication or design errors, such as, for example, over-etching, under-etching, and incorrect nanoelement sizes (which sometimes manifest as “library shift errors”), among others. By calculating deviations in determined phase profiles in comparison to a desired phase profile, which can be done from measurements of various diffraction orders, and correlating the calculated deviations in phase profiles with certain types of fabrication or design errors, the disclosed systems and processes provide accurate, cost-effective, efficient, and scalable approaches for mass production of meta-surfaces.
1 . A process for identifying fabrication or design errors in meta-surfaces, the process comprising:
illuminating a meta-surface being evaluated with a light source to produce diffracted light comprising a desired-order diffraction profile and at least one undesired-order diffraction profile; and
measuring, with at least one photodetector optically positioned to receive the diffracted light, a phase profile of the evaluated meta-surface, comprising:
measuring desired-order intensity values in the desired-order diffraction profile; and
measuring undesired-order intensity values in the at least one undesired-order diffraction profile;
calculating a deviation of the measured phase profile from a desired phase profile; and
correlating the calculated deviation with a fabrication error or design error of the evaluated meta-surface.
2 . The process of claim 1 , wherein measuring the undesired-order intensity values comprises at least one selected from the group consisting of:
measuring zero-order intensity values in a zero-order diffraction profile having a zero-order transmission; and
measuring higher-order intensity values in a higher-order diffraction profile having a higher-order focal spot or within a higher diffraction order in an angular spectrum.
3 . The process of claim 2 , wherein measuring the higher-order diffraction profile comprises at least one selected from the group consisting of:
measuring second-order intensity values in a second-order diffraction profile having a second-order focal spot or within a second diffraction order in the angular spectrum;
measuring third-order intensity values in a third-order diffraction profile having a third-order focal spot or within a third diffraction order in the angular spectrum; and
measuring fourth-order intensity values in a fourth-order diffraction profile having a fourth-order focal spot or within a fourth diffraction order in the angular spectrum.
4 . The process of claim 3 , wherein calculating the deviation of the measured phase profile from the desired phase profile comprises:
determining a normalized first-order intensity at the a first-order focal spot or within a first diffraction order in the angular spectrum;
determining a normalized zero-order intensity at the zero-order transmission;
comparing the normalized first-order intensity with the normalized zero-order intensity; and
determining whether the normalized zero-order intensity is greater than the normalized first-order intensity.
5 . The process of claim 4 , wherein correlating the calculated deviation with the fabrication error comprises:
correlating the calculated deviation with an under-etching fabrication error in response to the normalized zero-order intensity being greater than the normalized first-order intensity.
6 . The process of claim 3 , wherein calculating the deviation of the measured phase profile from the desired phase profile comprises:
determining a normalized first-order intensity at a first-order focal spot or within a first diffraction order in the angular spectrum;
determining a normalized second-order intensity at the second-order focal spot or within the second diffraction order in the angular spectrum;
comparing the normalized first-order intensity with the normalized second-order intensity; and
determining whether the normalized second-order intensity is greater than the normalized first-order intensity.
7 . The process of claim 6 , wherein correlating the calculated deviation with the fabrication error comprises:
correlating the calculated deviation with an over-etching fabrication error in response to the normalized second-order intensity being greater than the normalized first-order intensity.
8 . The process of claim 3 , wherein calculating the deviation of the measured phase profile from the desired phase profile comprises: determining a normalized first-order intensity at a first-order focal spot or within a first diffraction order in the angular spectrum; determining a normalized zero-order intensity at the zero-order transmission; determining a normalized second-order intensity at the second-order focal spot or within the second diffraction order in the angular spectrum; comparing the normalized first-order intensity with the normalized second-order intensity; comparing the normalized first-order intensity with the normalized zero-order intensity; comparing the normalized second-order intensity with the normalized zero-order intensity; determining whether the normalized second-order intensity is greater than the normalized first-order intensity (2nd >1st); determining whether the normalized zero-order intensity is greater than the normalized first-order intensity (0th >1st); and determining whether the normalized second-order intensity is greater than the normalized zero-order intensity (2nd >0th).
9 . The process of claim 8 , wherein correlating the calculated deviation with the fabrication error comprises:
calculating a linear error associated with the calculated deviation;
calculating a quadratic error associated with the calculated deviation; and
calculating a cubic error associated with the calculated deviation.
10 . The process of claim 9 , wherein correlating the calculated deviation with the fabrication error comprises:
correlating a library shift error with a combination of:
the calculated linear error;
the calculated quadratic error; and
the calculated cubic error.
11 . The process of claim 10 , wherein calculating the deviation further comprises:
determining that a cubic error of at least twenty-five percent (≥25%) exists when:
2nd >1st; and
0th >1st.
12 . The process of claim 10 , wherein calculating the deviation further comprises:
determining that a negative cubic error of at least twenty-five percent (≥25%) exists when 2nd >0th >1st.
13 . The process of claim 10 , wherein calculating the deviation further comprises:
determining that a positive cubic error of greater than twenty-five percent (≥25%) exists when 0th >2nd >1st.
14 . The process of claim 1 , wherein measuring the phase profile comprises measuring the phase profile of a whole area of the meta-surface.
15 . The process of claim 1 , wherein measuring the phase profile comprises measuring the phase profile of a sub-section of the meta-surface.
16 . The process of claim 1 , wherein measuring the phase profile comprises measuring the phase profile of a whole area of the meta-surface, thereby allowing for rasterized analysis of the phase profiles for the whole area.
17 . The process of the claim 1 , wherein measuring the phase profile comprises measuring the phase profile of a sub-section of the meta-surface, thereby allowing for rasterized analysis of the phase profiles for the sub-section.
18 . The process of claim 1 , wherein measuring the phase profile comprises measuring the phase profile at multiple positions around a focal position for each focal order.
19 . The process of claim 18 , wherein each focal order comprises:
a wanted focal order; and
an unwanted focal order.
20 . The process of claim 18 , further comprising:
measuring a positive phase error associated with each focal order; and
measuring a negative phase error associated with each focal order.