Method and apparatus for optically measuring periodic structures using orthogonal azimuthal sample orientations

Abstract

An optical metrology apparatus for measuring periodic structures using multiple incident azimuthal (phi) and polar (theta) incident angles is described. One embodiment provides the enhanced calculation speed for the special case of phi=90 incidence for 1-D (line and space) structures, which has the incident plane parallel to the grating lines, as opposed to the phi=0 classical mounting, which has incident plane perpendicular to the grating lines. The enhancement reduces the computation time of the phi=90 case to the same order as the corresponding phi=0 case, and in some cases the phi=90 case can be significantly faster. One advantageous configuration consists of two measurements for each sample structure, one perpendicular to the grating lines and one parallel. This provides additional information about the structure, equivalent to two simultaneous angles of incidence, without excessive increase in computation time. Alternately, in cases where the computation for phi=90 is faster than the corresponding phi=0 incidence, it may be advantageous to measure parallel to the grating lines only. In the case where two sets of incident angles are used, the incident light can be polarized to provide a total of four sets of data—R s 0 , R p 0 , R s 90 , R p 90 —for each incident polar angle, all from the same structure.

1 . A method of measuring characteristics of a diffraction grating structure, comprising:
 providing incident light comprising one or more multiple wavelengths;   providing the incident light in an incident plane of the light that is at a first azimuthal angle of phi=0 with respect to a plane perpendicular to the diffraction grating structure;   providing the incident light in the incident plane of the light that is at a second azimuthal angle of phi=90 with respect to a plane perpendicular to the diffraction grating structure;   detecting light reflected from the diffraction grating structure when the incident light is at the first azimuthal angle of effectively phi=0 and when the incident light is at the second azimuthal angle of effectively phi=90;   utilizing the detected light as part of a diffraction analysis; and   determining at least one characteristic of the diffraction grating structure by exploiting symmetry properties of the diffraction analysis such that the computation time for data at the second azimuthal angle is approximately the same as or is less than the computation time for data at the first azimuthal angle.   
     
     
         2 . The method of  claim 1 , wherein data is only collected at the first azimuthal angle and the second azimuthal angle. 
     
     
         3 . The method of  claim 1 , wherein the diffraction analysis comprises utilizing a rigorous coupled wave analysis. 
     
     
         4 . The method of  claim 3 , wherein the symmetry properties comprise symmetry properties of the Fourier expansions of the rigorous coupled wave (RCW) analysis for the second azimuthal angle, allowing RCW eigen- and boundary problems to be reduced in complexity. 
     
     
         5 . The method of  claim 4 , wherein a second azimuthal angle boundary problem is reduced to a 4(N+1)×4(N+1) system of equations and an eigen-problem is reduced to two (N+1)×(N+1) eigen-systems for a given truncation order, N. 
     
     
         6 . The method of  claim 2 , wherein four data sets are utilized in the diffraction analysis for each polar angle, the data sets being comprised of two different polarizations at each of the first and second azimuthal angles. 
     
     
         7 . The method of  claim 2 , further comprising utilizing multiple polar angles at each of the first and second azimuthal angles. 
     
     
         8 . The method of  claim 2 , wherein the determined characteristic is a geometrical characteristic. 
     
     
         9 . The method of  claim 8 , wherein the geometrical characteristic is a line width, height and/or depth. 
     
     
         10 . The method of  claim 2 , wherein computation time for data at the second azimuthal angle is at least 20% less than the computation time for data at the first azimuthal angle. 
     
     
         11 . The method of  claim 10 , wherein computation time for data at the second azimuthal angle is at least 30% less than the computation time for data at the first azimuthal angle. 
     
     
         12 . The method of  claim 1 , wherein the computation time for data at the second azimuthal angle is significantly reduced compared to a conventional computation at the second azimuthal angle. 
     
     
         13 . The method of  claim 12 , wherein the computation time for data at the second azimuthal angle is reduced by a factor of approximately 8 over a conventional calculation at the second azimuthal angle. 
     
     
         14 . The method of  claim 1 , wherein the incident light comprises multiple wavelengths of light. 
     
     
         15 . A method of characterizing a diffraction grating structure, comprising
 collecting a first set of reflected data from the grating structure by providing incident light at a first angle of azimuthal incidence with respect to the grating structure;   collecting a second set of reflected data from the grating structure by providing incident light at a second angle of azimuthal incidence with respect to the grating structure, the first and second angles being effectively orthogonal and the second angle of azimuthal incidence being different from zero;   analyzing a combination of at least the first and second set of reflected data; and   utilizing symmetrical characteristics of a diffraction analysis of the second angle of azimuthal incidence reflected data so as to reduce the computation complexity of the analysis of the second set of reflected data during the determination of at least one geometrical characteristic of the grating structure.   
     
     
         16 . The method of  claim 15 , where one or more of the sets of data are used to normalize other set(s) of data so that optical metrology data comprises ratios of reflected data collected for different incident conditions, avoiding the need to determine incident intensity via an absolute calibration process. 
     
     
         17 . The method of  claim 16 , wherein the optical metrology data comprises a first ratio of at least a portion of the first set of reflected data and at least a portion of the second set of reflected data. 
     
     
         18 . The method of  claim 17 , wherein the diffraction analysis comprises a regression or library lookup procedure that minimizes the difference between a calculated reflectance or diffraction efficiency ratio and a measured intensity ratio. 
     
     
         19 . The method of  claim 18 , wherein an inverse ratio is substituted in specific wavelength regions where the denominator of the first ratio is near zero. 
     
     
         20 . The method of  claim 19 , wherein a weighting function is used to equalize a contribution to a merit function regardless of a reflectance ratio magnitude. 
     
     
         21 . The method of  claim 18 , wherein data regions at which a denominator of the first ratio is near zero are dropped from the diffraction analysis. 
     
     
         22 . The method of  claim 15 , where one or more diffracted orders of reflected data are detected along with or instead of the 0'th order. 
     
     
         23 . The method of  claim 15 , wherein data is only collected at the first azimuthal angle and the second azimuthal angle. 
     
     
         24 . The method of  claim 23 , wherein the diffraction analysis comprises utilizing a rigorous coupled wave analysis. 
     
     
         25 . The method of  claim 15 , wherein four data sets are utilized in the diffraction analysis for each polar angle, the data sets being comprised of two different polarizations at each of the first and second azimuthal angles. 
     
     
         26 . The method of  claim 15 , further comprising utilizing multiple polar angles at each of the first and second azimuthal angles. 
     
     
         27 . The method of  claim 15 , wherein the diffraction analysis comprises utilizing a rigorous coupled wave analysis. 
     
     
         28 . The method of  claim 27 , wherein the symmetry properties comprise symmetry properties of the Fourier expansions of the rigorous coupled wave (RCW) analysis for the second azimuthal angle, allowing RCW eigen- and boundary problems to be reduced in complexity. 
     
     
         29 . The method of  claim 28 , wherein a second azimuthal angle boundary problem is reduced to a 4(N+1)×4(N+1) system of equations and an eigen-problem is reduced to two (N+1)×(N+1) eigen-systems for a given truncation order, N. 
     
     
         30 . An optical metrology system, comprising:
 a light source;   a sample having a diffraction grating, the light source providing incident light to the diffraction grating, the plane of incidence of the light with respect to the diffraction grating being changeable with respect to at least an azimuthal rotation;   a detector collecting data from light diffracted by the diffraction grating, the system being configured to collect data from the diffraction grating when the incident light is at the first azimuthal angle of phi=0 and when the incident light is at the second azimuthal angle of phi=90;   a computing system which utilizes the symmetrical characteristics of a diffraction analysis of the second azimuthal angle so as to reduce the computation complexity of an analysis of the data collected from the diffraction grating at the second azimuthal angle during the determination of at least one characteristic of the diffraction grating.   
     
     
         31 . The optical metrology tool of  claim 30 , wherein the sample is rotated to provide the azimuthal rotation. 
     
     
         32 . The optical metrology tool of  claim 30 , wherein the plane of incidence of the light is rotated to provide the azimuthal rotation. 
     
     
         33 . The optical metrology tool of  claim 30 , wherein the polar angle of the incident light is changeable. 
     
     
         34 . The optical metrology tool of  claim 30 , wherein the light source provides at least VUV wavelengths of light. 
     
     
         35 . The optical metrology tool of  claim 30 , wherein the incident light is provided through a high numeric aperture optic using an aperture stop to allow incident light at only specific angles. 
     
     
         36 . The optical metrology tool of  claim 32 , wherein the numeric aperture optic is configured to transmit multiple azimuthal angles of incident light simultaneously. 
     
     
         37 . A method of measuring characteristics of a diffraction grating structure, comprising:
 providing incident light comprising multiple wavelengths;   providing the incident light in an incident plane of the light that is at a first azimuthal angle of effectively phi=90 with respect to a plane perpendicular to the diffraction grating structure;   detecting light reflected or diffracted from the diffraction grating structure when the incident light is at the first azimuthal angle;   utilizing the detected light as part of a diffraction analysis; and   determining at least one characteristic of the diffraction grating structure by exploiting symmetry properties of the diffraction analysis such that the computation time for data is significantly reduced compared to the conventional computation at the first azimuthal angle, and is approximately the same as or is less than the computation time for the comparable classical mount at the first azimuthal angle and a same polar angle.   
     
     
         38 . The method of  claim 37 , wherein the diffraction analysis comprises utilizing a rigorous coupled wave analysis. 
     
     
         39 . The method of  claim 38 , wherein the symmetry properties comprise symmetry properties of the Fourier expansions of the rigorous coupled wave (RCW) analysis for the first azimuthal angle case, allowing the RCW eigen- and boundary problems to be reduced in complexity. 
     
     
         40 . The method of  claim 39 , wherein the first azimuthal angle boundary problem is reduced to a 4(N+1)×4(N+1) system of equations and the eigen-problem is reduced to two (N+1)×(N+1) eigen-systems for a given truncation order, N. 
     
     
         41 . The method of  claim 37 , wherein two data sets are utilized in the diffraction analysis for each polar angle, the data sets being comprised of two different polarizations at the first azimuthal angle. 
     
     
         42 . The method of  claim 37 , further comprising utilizing multiple polar angles at the first azimuthal angle. 
     
     
         43 . The method of  claim 37 , wherein the computation time for data at the first azimuthal angle case is reduced by a factor of approximately 8 over the conventional first azimuthal angle calculation.