# Patent

## Title
Measuring an alignment target with multiple polarization states

## Abstract

An alignment target includes periodic patterns on two elements. The periodic patterns are aligned when the two elements are properly aligned. By measuring the two periodic patterns at multiple polarization states and comparing the resulting intensities of the polarization states, it can be determined if the two elements are aligned. A reference measurement location may be used that includes third periodic pattern on the first element and a fourth periodic pattern on the second element, which have a designed in offset, i.e., an offset when there is an offset of a known magnitude when the first and second element are properly aligned. The reference measurement location is measured at two polarization states. The difference in the intensities of the polarization states at reference measurement location and is used to determine the amount of the alignment error.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to alignment metrology, and in particular to an alignment target and method of use.
2. Discussion of the Related Art
Semiconductor processing for forming integrated circuits requires a series of processing steps. These processing steps include the deposition and patterning of material layers such as insulating layers, polysilicon layers, and metal layers. The material layers are typically patterned using a photoresist layer that is patterned over the material layer using a photomask or reticle. It is important that one layer is aligned with another during processing.
Typically, the photomask has alignment targets or keys that are aligned to fiduciary marks formed in the previous layer on the substrate. However, as the integrated circuit feature sizes continue to decrease to provide increasing circuit density, it becomes increasingly difficult to measure the alignment accuracy of one masking level to the previous level. This overlay metrology problem becomes particularly difficult at submicrometer feature sizes where overlay alignment tolerances are reduced to provide reliable semiconductor devices.
FIGS. 1A and 1B show conventional overlay targets used with conventional imaging metrology methods. FIG. 1A shows a typical Box-in-Box overlay target 2. Target 2 is formed by producing an etched box 4 in a material layer 6 on a substrate. A corresponding smaller box 8 on the photomask or reticle is aligned to the larger box 4 so that the centers of the large and small boxes are aligned.
FIG. 1B shows a Bar-in-Bar overlay target 12, which is similar to target 2 shown in FIG. 1A. Target 12 is produced by etching bars 14 in a material layer 16 on a substrate. The bars 18 on the photomask are aligned to the overlay target alignment bars 14.
After the smaller box 8 or bars 18 are developed, i.e., exposed and etched, the overlay target is imaged to determine whether the photomask or reticle was properly aligned with the underlying layer. Conventionally, high magnification imaging is used to measure overlay alignment. Conventional imaging devices, unfortunately, suffer from disadvantages such as sensitivity to vibration and cost. Moreover, conventional imaging devices suffer from a trade-off between depth-of-focus and optical resolution. Additionally, edge-detection algorithms used to analyze images for the purpose of extracting overlay error are inaccurate when the imaged target is inherently low-contrast or when the target suffers from asymmetries due to wafer processing.
During processing, the substrate is moved from one location to the next so that different areas, e.g., dies, on the substrate can be exposed. The alignment system, e.g., the exposure tool, typically uses an alignment target to properly align the substrate during exposure. FIG. 2 shows a conventional alignment system 50 , which includes a diffraction pattern 52 on the substrate and a second diffraction pattern 54 that is stationary, e.g., is fixed to the lens on the exposure tool. A light source 56 produces coherent light that passes through a beam splitter 58 and is incident on the diffraction pattern 52 after passing through a lens 60 . The light is diffracted by diffraction pattern 52 and passes through lens 60 back to beam splitter 58 . The coherent light beam from source 56 is also reflected off beam splitter 58 , passes through lens 62 and is incident on diffraction pattern 54 . The light diffracted by diffraction pattern 54 passes back through lens 62 to beam splitter 58 . At beam splitter the light diffracted from diffraction patterns 52 and 54 is combined and the combined diffraction patterns is received by light detectors 64 .
Alignment system 50 provides an accuracy of approximately 15 nm. One disadvantage of alignment system 50 is that coherent light is used. Thus, if the diffraction pattern 52 on the sample absorbs the particular frequency used, alignment system 50 cannot provide an accurate measurement. While multiple coherent light sources may be used to avoid this disadvantage, the use of multiple light sources adds complexity and cost.
Thus, there is a need in the semiconductor industry for an improved alignment target for metrology and alignment system.
SUMMARY
An alignment target in accordance with the present invention is used to determine if two elements are in alignment or the amount of the alignment error between the two elements. The alignment target includes periodic patterns on the two elements. The periodic patterns, which may be, e.g., diffractions gratings, are aligned when the two elements are in alignment. The alignment target is measured by producing Light with multiple polarization states that is incident on the alignment target. The intensities of the polarization states are detected after the light interacts with the alignment target. The polarization states can then be compared to determine if the elements are aligned. Additional periodic patterns that have a designed in offset, i.e., a known offset between the two elements when the elements are aligned, may be used to aid in measurement of the alignment error.
In one embodiment, a method includes providing an alignment target on a first element and a second element, the alignment target having a first periodic pattern on the first element and a second periodic pattern on the second element. The first and second periodic patterns are illuminated with light having at least two polarization states. The light may be incident at from one or more directions. The intensities of the polarization states of the light after interacting with the alignment target is detected, and the intensities are compared to determine the alignment of the first element and the second element. One or both of the periodic patterns may be diffraction gratings having periodicities in one or two directions. The method may include moving one element with respect to the other to minimize the difference between the intensities of the polarization states.
The alignment target may further include a third periodic pattern on the first element and a fourth periodic pattern on the second element, the third periodic pattern and the fourth periodic pattern have a designed in offset of a known magnitude such that when the first element and second element are aligned, the third periodic pattern and the fourth periodic pattern are offset by the known magnitude. The third and fourth periodic patterns are illuminated with light having at least two polarization states, and the intensities of the polarization states are detected and compared. The compared intensities from the third and fourth periodic patterns can be used as a reference for the compared intensities of the first and second periodic patterns.
Alternatively, a model may be produced of the periodic patterns and the light with multiple polarization states using e.g., rigorous coupled wave analysis (RCWA). The measured intensities of the periodic patterns are compared with the model to determine the alignment error.
In another embodiment of the present invention, an alignment target for measuring the alignment between a first element and a second element includes a first location having a first periodic pattern on the first element and a second periodic pattern on the second element. The second periodic pattern is aligned to the first periodic pattern when the first element and the second element arc properly aligned. The alignment target also includes a second location having a third periodic pattern on the first element and a fourth periodic pattern on the second element The fourth periodic pattern has a designed in offset of a known magnitude with the third periodic pattern when the first element and the second element are properly aligned.
In another embodiment, an apparatus for determining the alignment of a first element with a second element using an alignment target having a first periodic pattern on said first element and a second periodic pattern on said second element, includes a radiation source for producing radiation having at least two polarization states to be incident on the alignment target. The apparatus further includes a detector for detecting the radiation with at least two polarization states after it interacts with the alignment target; and a computer and a computer-usable medium having computer-readable program code embodied therein for causing the computer to calculate the difference between the intensities of the at least two polarization states to determine if the first element and the second element are aligned.
Where the alignment target includes a second measurement location with a third and fourth periodic patterns, the radiation source produces radiation having at least two polarization states to be incident on both the first and second periodic patterns and the third and fourth periodic patterns, and the detector detects the radiation with at least two polarization states after it interacts with both the first and second periodic patterns and the third and fourth periodic patterns. The computer-readable program code embodied in the computer-usable medium causes the computer to compare the intensities of the polarization states from the light after interacting with the third periodic pattern and the fourth periodic pattern and using the comparison to determine the amount of alignment error between the first element and the second element.



BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A and 1B show conventional overlay targets used with conventional imaging metrology methods.
FIG. 2 shows a conventional alignment system, which includes a diffraction pattern on the substrate and a second diffraction pattern that is stationary, e.g., is fixed to the lens on the exposure tool.
FIGS. 3A and 3B show a top and cross-sectional views, respectively, of an alignment target in accordance with an embodiment of the present invention.
FIGS. 4 and 5 shows the alignment target in accordance with the present invention with an alignment error.
FIG. 6 is a block diagram of an alignment system with which the alignment target may be used.
FIG. 7 shows a perspective view of a substrate and a reticle with a lens and four reference masks disposed between the substrate and reticle.
FIGS. 8A, 8B, 8C show metrology devices that may be used to measure the diffraction from an alignment target in accordance with the present invention.
FIG. 9A, 9B, 9C, 9D, 9E, and 9F show the alignment target being measured from different angles simultaneously.
FIGS. 10 and 11 show a cross-sectional and top view, respectively, of an alignment target in accordance with another embodiment of the present invention.
FIG. 12 shows top view of an alignment target in accordance with another embodiment of the present invention.
FIG. 13 shows measuring non-zero order diffracted light from an alignment mark.



DETAILED DESCRIPTION
An alignment target, in accordance with the present invention, can be used to align two elements. For example, the alignment target can be used to align a substrate and/or a reticle with respect to a stationary element, e.g., the lens, in an exposure tool. Of course, the alignment target is not limited to use in an exposure tool, but may be used to align any two elements. Additionally, the alignment target can be used to measure the amount of alignment error between any two elements, such as two layers on a substrate or any other elements.
The alignment target of the present invention and method of use is similar to the alignment target used to assist in the alignment process and to measure alignment error as described in U.S. Patent Applications “Positioning Two Elements Using an Alignment Target With A Designed In Offset” by Weidong Yang, Roger R. Lowe-Webb, John D. Heaton and Guoguang Li, Ser. No. 10/116,964 “Alignment Target with Designed in Offset” by Weidong Yang, Roger R. Lowe-Webb, and John D. Heaton, Ser. No. 10/116,863; and “Encoder with Alignment Target”, by Weidong Yang, Roger R. Lowe-Webb, and John D. Heaton, Ser. No. 10/116,855, all of which are filed herewith and have the same assignee as the present application and are incorporated herein by reference.
FIGS. 3A and 3 B show a top and cross-sectional views, respectively, of an alignment target 100 in accordance with an embodiment of the present invention. Alignment target 100 includes a periodic pattern 102 on a first element 103 and another periodic pattern 104 on a second element 105 . The periodic patterns 102, 104, which may be diffraction gratings, are designed to be in alignment with respect to each other when layers 103 and 105 are in alignment. The first element 103 and second element 105 may be movable with respect to each other. For example, the first and second element 103 and 105 may be two stages or a substrate and/or reticle and another object, such as a lens or a reference mask coupled to a lens, in an exposure tool. The elements 103 and 105 may also be layers on a substrate, such as a semiconductor wafer, flat panel display or any other structure in which accurate alignment of successive layers is desired. The periodic patterns of alignment target 100 are similar to that described in U.S. Ser. No. 09/960,892 entitled “Spectroscopically Measured Overlay Target”, filed Sept. 20, 2001, which has the same assignee as the present disclosure and which is incorporated herein in its entirety by reference.
The bottom periodic pattern 102 is produced, for example, by providing a layer of appropriate material, such as a 200 nm layer of polysilicon, followed by a layer of photoresist. The desired image including the periodic pattern 102 is exposed in the photoresist, which is then developed. The polysilicon is then etched away leaving periodic pattern 102.
The top periodic pattern 104 is produced using, e.g., photoresist, in a manner similar to the bottom periodic pattern 102 . The top periodic pattern 104 may be separated from the bottom periodic pattern 102 by one or more intermediate layers. Thus, for example, an 800 nm layer of the photoresist may be used to produce top periodic pattern 104. The desired image including the periodic pattern is exposed in the photoresist layer. The photoresist may then be developed to produce periodic pattern 104, or alternatively, a latent image may be used as periodic pattern 104.
It should be understood that the processing steps used to produce periodic patterns 102 and 104 are exemplary. Different or additional layers may be included between substrate and the bottom periodic pattern 102 or between the bottom periodic pattern 102 and the top periodic pattern 104. In fact, if desired, the top periodic pattern 104 may be on the same layer as the bottom periodic pattern 102, in which case, top and bottom refers to the order in which the gratings are produced, i.e., the bottom periodic pattern being first and the top periodic pattern being second. Thus, the alignment target 100 may be used to ensure that a first pattern produced on a first layer on the substrate is aligned with a second pattern produced on the same layer on the substrate. Moreover, the alignment target 100 may be used with two elements that are not connected. Thus, for example, the top periodic pattern 104, and the bottom periodic pattern 102 may be separated by a small distance, e.g., up to approximately 50 μm or more. The dimensions of the patterns and the thicknesses of the layers may be altered. For example, the bottom diffraction gratings 106, 116 need not extend to the top of element 105. It should be understood that the alignment target 100 may be produced using various materials and the dimensions optimized for the materials used. Thus, the dimensions of the alignment target 100 may be altered to maximize sensitivity based on the types of materials used.
To determine if the layers 103, 105 are in alignment, a radiation source 120, such as a broadband light source, produces radiation 121 that is incident on alignment target 100. Source 120 produces light that has a non-normal angle of incidence and has an azimuthal angle that is non-parallel with the direction of periodicity of the periodic patterns in alignment target 100, if the pattern has only one periodicity direction.
The radiation source 120 produces radiation 121 that has a plurality of polarization states, e.g., two polarization states, as illustrated in FIG. 3B. After the radiation interacts with alignment target 100, a detector 122 detects the radiation. The difference in intensity of the polarization states from alignment target 100 vary proportionally with the alignment error. When the elements 103 and 105 are in alignment, periodic patterns 102 and 104 will be in alignment. Consequently, the polarization states in the detected radiation will have equal intensity. However, if there is an alignment error between elements 103 and 105, periodic patterns 102 and 104 will be out of alignment, as illustrated in FIGS. 4 and 5. With the periodic patterns 102 and 104 out of alignment, the intensity of the detected polarization states will be unequal. Thus, by comparing the intensities of the detected polarization states from alignment target 100, it is possible to determine if elements 103 and 105 are in alignment.
The ability to determine if elements 103 and 105 are in alignment is particularly useful in an alignment system. Thus, for example, the present invention may be used to ensure substrate to reticle registration when the substrate is on the exposure tool during processing. The alignment target may be used to assist in the precise alignment of separate elements in any alignment system and is not limited to an exposure tool.
It should be understood that the present invention may be used in both reflection and transmission modes.
The present invention may be used to measure the alignment error down to a fraction of nanometer, while the current industry standard is approximately 15 nm. Thus, the present invention provides a large improvement compared to current technology.
FIG. 6 is a block diagram of an alignment system with which the alignment target 100 may be used. The alignment system is an exposure tool 200 includes X and Y substrate stages 202 and 204 that hold the substrate 201. The exposure tool 200 also includes X and Y reticle stages 206 and 208 that hold the reticle 210. Exposure tool 200 may include two sets of stages, one set for large motions and another set for fine motions. For sake of simplicity, X and Y stages 202, 204, 206, and 208 may be used for both large motion and fine motion.
A control system 212 controls the motion of the stages. A lens 214 or other suitable optics is positioned between the substrate 201 and the reticle 210 and is used to focus light from light source 216 that is transmitted through reticle 210 onto substrate 201. The operation and control of exposure tools is well known in the art.
A reference mask 218 extends from the lens 214 by way of a low thermal expansion arm 219. The distance between the reference mask 218 and the substrate 201 should be small, e.g., between 1 and 10 μm. Spectrometers 220 are positioned above reference masks 218. As shown in FIG. 6, a plurality of reference masks 218 may be used, each having an associated spectrometer 220.
FIG. 7 shows a perspective view of substrate 201 and reticle 210 with lens 214 and four reference masks 218 disposed between the substrate 201 and reticle 210. The spectrometers 220 are not shown in FIG. 16. As can be seen in FIG. 7, a number of separate alignment targets 100 are used, where the top periodic pattern 104 is on the reference masks 218 and bottom periodic pattern 102 is on the substrate 201.
Referring back to FIG. 6, the spectrometers 220 may be coupled to the lens 214 as shown in FIG. 6, or may be connected to another stationary object. The spectrometers 220 communicate with the control system 212. The control system 212 includes, e.g., a computer-usable medium having computer-readable program code embodied therein for causing the control system to calculate the difference between the diffracted light from the two locations and using the difference to determine if the first element and the second element are aligned. The control system 212 is coupled to the stage to adjust the location of the substrate 201 in response to the signals provided by spectrometer 220 until the starting position of the substrate 201 is precisely aligned with the lens 214. Once the substrate 201 is aligned, the control system 212 can move the stages to perform the desired exposure operation.
Alignment target 100 may be used to measure the amount of alignment error, e.g., using several types of metrology devices, e.g., such as that shown in FIGS. 8A, 8B, and 8C. FIG. 8A, for example, shows a block diagram of a nonnal incidence polarized reflectance spectrometer. Spectrometer 300 is discussed in detail in the U.S. Patent Application entitled “Apparatus and Method for the Measurement of Diffracting Structures,” filed Sept. 25, 2000, having Ser. No. 09/670,000, and the U.S. Patent Application entitled “Measurement Of Diffracting Structures Using One-Half Of The Non-Zero Diffracted Orders” filed Apr. 27, 2000, having Ser. No. 09/844,559, both of which have the same assignee as the present disclosure and are incorporated herein by reference. Spectrometer 300 may use rigorous coupled wave analysis (RCWA) as described in Ser. No. 09/670,000, or folded rigorous coupled wave analysis as described in Ser. No. 09/844,559 to measure the alignment error from alignment target 100. In an alignment system, such as that shown in FIG. 6, however, a precise measurement is not necessary. Only a determination of whether the polarization states have the same intensity needs to be made in order to determine if the periodic patterns 102 and 104 are in alignment.
As shown in FIG. 8A, spectrometer 300 includes a polychromatic light source 322 that generates a light beam that is partially reflected by beam splitter 324 along the optical axis 323. The light beam is directed towards a sample 326 having an alignment target, such as alignment target 100, to be measured. Sample 326 may be, e.g., a semiconductor wafer or flat panel display or any other substrate, and is supported by a stage 328, which may be a polar coordinate, i.e., R-θ, stage or an x-y translation stage. Spectrometer 320 includes a rotatable polarizer 330 and a lens 332 (or series of lenses) to polarize and focus the light beam onto the sample 326 at normal incidence. The beam is reflected off sample 326 and the reflected light is transmitted through lens 332 and polarizer 330. A portion of the reflected light is transmitted through beam splitter 324 and is received by a spectrophotometer 334. Spectrophotometer 334 is coupled to processor 336, which analyzes the data provided by spectrophotometer 334. Processor 336 is e.g., a computer with a computer and a computer-usable medium having computer-readable program code embodied therein for causing the computer to determine the overlay error based on the light that is diffracted from the alignment target. Thus, the computer-readable program code causes the computer to calculate the difference between the intensities of the polarization states from the alignment target and use the difference to determine if the alignment target is aligned. One of ordinary skill in the art can program code necessary to determine alignment in accordance with the present invention in view of the present disclosure. For more information on the general operation of a normal incidence polarized reflectance spectrometer, the reader is referred to Ser. Nos. 09/670,000 and 091844,559, which are incorporated herein by reference.
If desired, other measurement devices may be used to measure alignment target 100 including ellipsometry and scatterometry. FIGS. 8B and 8C show block diagrams of a spectroscopic ellipsometer 140 and spectroscopic scatterometer 145. Ellipsometer 140 includes a broadband radiation source 141 and a spectrophotometer 142, which is connected to a processor 143. Spectroscopic scatterometer 145 includes a broadband radiation source 146 and a spectrophotomcter 147, which is connected to a processor 148. As indicated by the arrows in FIG. 8C, one or both of broadband radiation source 146 and spectrophotometer 147 are adjustable to alter the angle of incidence. The operation of an ellipsometer 140 and spectroscopic scatterometer 145 is well known to those skilled in the art. Processor 143 and 148 may be similar to processor 136 shown in FIG. 8A.
It should also be understood, that the present invention may use a single wavelength, a plurality of discrete wavelengths, or a continuum of wavelengths.
If desired, multiple light sources and detectors may be used simultaneously. FIG. 9A for example, shows alignment target 100 being measured from different angles simultaneously with a plurality of radiation beams, 121a, 121b, 121c. Because of the symmetrical properties of the periodic patterns in alignment target 100, the measurement may be made at multiple symmetrical angles.
FIGS. 9B, 9C and 9D illustrate the symmetries of alignment target 100. As can be seen in FIGS. 9B, 9C, and 9D, alignment target 100 has mirror symmetry along the x-z plan, the y-z plan and 180 degree rotation symmetry around the z axis. The y-z plan mirror symmetry and z axis rotation symmetry are broken once the alignment pattern symmetry is broken, i.e., when there is an alignment error.
As illustrated in FIGS. 9B, 9C, and 9D, incident light has polarization components along s and p, with equivalent phase shifts shown in each figure. The light that is detected has polarization states s′ and p′ where there is also equivalent phase shifts shown in each figure. It should be understood that the phase shift in the incident light and the detected light need not be the same. Moreover, the polarization states need not be linear. Because of symmetry, the measurements in FIGS. 9C and 9D are identical and are also identical to the measurement in FIG. 9B, but only when the alignment patter is symmetrical. This difference can be used for alignment as well as shift measurement.
A special case is when the incident light comes in from the y direction as shown in FIGS. 9E and 9F. In this case, the two measurements, a and b, follow the same light path, but with both the incidence and detecting polarizations mirroring each other in the y-z plan. As can be seen in FIGS. 9E and 9F, the polarization angels used in the incident light need not be used in the detection.
It should be understood that multiple polarization states may be used to determine when the symmetry in the alignment target is broken. For example, in one embodiment, white light may be used to determine when the symmetry is broke.
In a special case, the polarization states of the two beams may overlap in either the incident beam or in the detection of the resulting beam.
The present invention may be used to not only determine if the elements are aligned, but to measure the alignment error if any. The alignment error may be measured using alignment target 100, for example, using a modeling technique, such as RCWA. Alternatively, a reference pattern may be used.
To measure the alignment error using a modeling technique, a model of the alignment target and the incident and diffracted light. The modeled light is compared to the measured light to determine if there is an acceptable fit, i.e., the difference between the modeled light and measured light is within a specified tolerance. If an acceptable fit is not found, the alignment target and incident and diffracted light are remodeled and compared to the measured light. Once an acceptable fit between the measured and modeled light is found, it is known that the modeled alignment target accurately describes the actual alignment target. If desired, the difference in the spectra from the two polarization states may be determined before or after the comparison with the modeled light. Of course, if the difference in measured spectra is used, the model light must be the difference in the modeled spectra. Moreover, a number of models of the alignment target, including the modeled light, may be generated a priori and stored in a library.
FIG. 10 shows a cross-sectional view of an alignment target 400 in accordance with another embodiment of the present invention. Alignment target 400 includes two measurement locations, referred to as overlay patterns 402 and 404. Each of the overlay patterns 402, 404 includes a periodic pattern ( 402a, 404a) on a first element 403 and a periodic pattern ( 402b, 404b) on a second element 405. The overlay pattern 402 has no designed in offset, i.e., periodic patterns 402a and 402b are aligned when elements 403 and 405 are in proper alignment. Overlay pattern 404, however, has a designed in offset between the bottom periodic pattern 404a and 404b of a magnitude D.
It should be understood that periodic patterns 402b and 404b or periodic patterns 402a and 404a may be a parts of the same continuous periodic pattern. Because the measurement is made at different locations, however, it is unimportant if the patterns are connected or not.
FIG. 11 shows a top view of alignment target 400. The periodic patterns in overlay patterns 402 and 404 may be oriented at any non-perpendicular angle with respect to each other.
In operation, overlay pattern 404 is used as a reference pattern for alignment target 400. Each measurement location, i.e., overlay patterns 402 and 404, of alignment target 400 is measured at a plurality of, e.g., two, polarization states. When elements 403 and 405 are properly aligned, the intensities of the polarization states from overlay pattern 402 will be equal, but the intensities of the polarization states from overlay pattern 404 will be unequal. When there is an alignment error between the elements 403 and 405, the intensities of the polarization states from overlay pattern 402 will be unequal. Because the difference in the intensities of the polarization states varies proportionally with the alignment error, the difference in intensities of the polarization states from overlay pattern 404 may be used as a reference measurement.
In general, the alignment error e is determined by: 



  
    
      
        e
        =
        
          
            
              φ
              1
            
            
              
                φ
                2
              
              -
              
                φ
                1
              
            
          
          *
          D
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        1
      
    
  




wherein φ1  is the differential spectra at the target location, i.e., overlay pattern 402, φ2  is the differential spectra at the reference location, i.e., overlay pattern 404, and D is the designed in offset at the reference location. By optimizing equation 1, the alignment error e for the entire spectrum, equation 1 the alignment error is determined as: 



  
    
      
        e
        =
        
          
            
              
                ∑
                i
              
              ⁢
              
                
                  φ
                  
                    1
                    ,
                    i
                  
                
                *
                
                  
                    (
                    
                      
                        φ
                        2
                      
                      -
                      
                        φ
                        1
                      
                    
                    )
                  
                  i
                
              
            
            
              
                ∑
                i
              
              ⁢
              
                
                  (
                  
                    
                      φ
                      2
                    
                    -
                    
                      φ
                      1
                    
                  
                  )
                
                i
                2
              
            
          
          *
          D
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        2
      
    
  




where i is the wavelength number in the spectrum.

In another embodiment, the reference location is produced by moving the second element 405 with respect to the first element 403 by a distance D and measuring the pattern in the new position. In this embodiment, the second overlay pattern 404 is not necessary.
When the relationship between the differential spectra and the alignment error is assumed to be a polynomial, the higher orders can be treated by using additional reference patterns. The use of additional reference patterns and a polynomial equation to solve for the alignment error is discussed in more detail in U.S. Patent Application entitled “Alignment Target with Designed in Offset” by Weidong Yang, Roger R. Lowe-Webb, John D. Heaton, and Guoguang Li, which is incorporated herein.
FIG. 12 shows top view of an alignment target 500 in accordance with another embodiment of the present invention. Alignment target 500 is a bi-grating includes two periodic patterns, a bottom periodic pattern 502, shown as a solid squares, and a top periodic pattern 504, shown as empty squares, that have periodicities in two directions. The two periodicities need not be perpendicular and the shapes forming the periodic patterns need not be square. Because the alignment target 500 has two periodicities, it can be used to determine alignment in two directions, shown as the X and Y direction in FIG. 12. Alignment target 500 is measured from two separate directions by beam 506, which is sensitive to alignment error in the Y direction and beam 508, which is sensitive to alignment error in the X direction.
Moreover, it should be understood that one or both of the periodic patterns, e.g., in alignment target 100FIGS. 3A, 3B can be a bi-grating if desired.
Further, if desired, the incident light and the detected light need not share the same azimuthal angle. Thus, as shown in FIG. 13, an alignment mark 600, which is similar to alignment mark 100, may be measured by a light source 620 that produces an incident light beam 621 and a detector 624 detects non-zero order diffracted light 622.
In general, the cross-reflection symmetry may be used for the error measurement and alignment control. The reflection of the light from a surface can be expressed as:

Eout=R•Eout  eq.3

where 



  
    
      
        E
        =
        
          (
          
            
              
                
                  E
                  s
                
              
            
            
              
                
                  E
                  p
                
              
            
          
          )
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        4
      
    
  




and 



  
    
      
        R
        =
        
          [
          
            
              
                
                  r
                  pp
                
              
              
                
                  r
                  sp
                
              
            
            
              
                
                  r
                  ps
                
              
              
                
                  r
                  ss
                
              
            
          
          ]
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        5
      
    
  




rsp and rps are defined as the cross-reflection coefficients. For symmetric grating, the 0th order cross-reflection coefficients are known to be identical but with a sign change in conical mount. With symmetry broken, they no longer have identical magnitude. This property can be exploited for alignment control and overlay error measurement.

Let s as x axis, and p as y axis. In conical incidence, if the grating is symmetrical, 0th orders are antisymmetrical, rps =-rps ≢0, while the higher orders are symmetrical, rsp =rps. For transmission, this relationship is reversed. The 0th orders are symmetrical, while higher orders are antisymmetrical. Assume incidence light has polarization along angle θ, with phase different φ1 between s and p polarizations. Also assume that the 0th order refection is detected at polarization along angle θ2, with phase different φ2 between s and p polarizations. Incidence light can be described as: 



  
    
      
        
          
            E
            in
          
          ⁡
          
            (
            
              
                
                  
                    E
                    s
                  
                
              
              
                
                  
                    E
                    p
                  
                
              
            
            )
          
        
        =
        
          (
          
            
              
                
                  sin
                  ⁡
                  
                    (
                    
                      θ
                      1
                    
                    )
                  
                
              
            
            
              
                
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁢
                      
                         
                      
                      ⁢
                      
                        φ
                        1
                      
                    
                  
                
              
            
          
          )
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        6
      
    
  




0th order reflection: 



  
    
      
        
          E
          out
        
        =
        
          
            R
            ·
            
              E
              in
            
          
          =
          
            
              
                [
                
                  
                    
                      
                        r
                        pp
                      
                    
                    
                      
                        r
                        sp
                      
                    
                  
                  
                    
                      
                        r
                        ps
                      
                    
                    
                      
                        r
                        ss
                      
                    
                  
                
                ]
              
              ·
              
                (
                
                  
                    
                      
                        sin
                        ⁡
                        
                          (
                          
                            θ
                            1
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          cos
                          ⁡
                          
                            (
                            
                              θ
                              1
                            
                            )
                          
                        
                        ⁢
                        
                          e
                          
                            i
                            ⁢
                            
                               
                            
                            ⁢
                            
                              φ
                              1
                            
                          
                        
                      
                    
                  
                
                )
              
            
            =
            
              (
              
                
                  
                    
                      
                        
                          r
                          pp
                        
                        ⁢
                        
                          sin
                          ⁡
                          
                            (
                            
                              θ
                              1
                            
                            )
                          
                        
                      
                      +
                      
                        
                          r
                          sp
                        
                        ⁢
                        
                          cos
                          ⁡
                          
                            (
                            
                              θ
                              1
                            
                            )
                          
                        
                        ⁢
                        
                          e
                          
                            i
                            ⁢
                            
                               
                            
                            ⁢
                            
                              φ
                              1
                            
                          
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          r
                          ps
                        
                        ⁢
                        
                          sin
                          ⁡
                          
                            (
                            
                              θ
                              1
                            
                            )
                          
                        
                      
                      +
                      
                        
                          r
                          ss
                        
                        ⁢
                        
                          cos
                          ⁡
                          
                            (
                            
                              θ
                              1
                            
                            )
                          
                        
                        ⁢
                        
                          e
                          
                            i
                            ⁢
                            
                               
                            
                            ⁢
                            
                              φ
                              1
                            
                          
                        
                      
                    
                  
                
              
              )
            
          
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        7
      
    
  




The measured electric field is: 



  
    
      
        
          
            
              
                E
                measure
              
              =
              
              ⁢
              
                
                  
                    (
                    
                      
                        sin
                        ⁡
                        
                          (
                          
                            θ
                            2
                          
                          )
                        
                      
                      ⁢
                      
                        cos
                        ⁡
                        
                          (
                          
                            θ
                            2
                          
                          )
                        
                      
                      ⁢
                      
                        e
                        
                          i
                          ⁢
                          
                             
                          
                          ⁢
                          
                            φ
                            2
                          
                        
                      
                    
                    )
                  
                  ·
                  
                    E
                    out
                  
                
                =
                
                  
                    (
                    
                      
                        sin
                        ⁡
                        
                          (
                          
                            θ
                            2
                          
                          )
                        
                      
                      ⁢
                      
                        cos
                        ⁡
                        
                          (
                          
                            θ
                            2
                          
                          )
                        
                      
                      ⁢
                      
                        e
                        
                          i
                          ⁢
                          
                             
                          
                          ⁢
                          
                            φ
                            ⁢
                            2
                          
                        
                      
                    
                    )
                  
                  ·
                
              
            
          
        
        
          
            
              
              ⁢
              
                (
                
                  
                    
                      
                        
                          
                            r
                            pp
                          
                          ⁢
                          
                            sin
                            ⁡
                            
                              (
                              
                                θ
                                1
                              
                              )
                            
                          
                        
                        +
                        
                          
                            r
                            sp
                          
                          ⁢
                          
                            cos
                            ⁡
                            
                              (
                              
                                θ
                                1
                              
                              )
                            
                          
                          ⁢
                          
                            e
                            
                              i
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                φ
                                1
                              
                            
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            r
                            ps
                          
                          ⁢
                          
                            sin
                            ⁡
                            
                              (
                              
                                θ
                                1
                              
                              )
                            
                          
                        
                        +
                        
                          
                            r
                            ss
                          
                          ⁢
                          
                            cos
                            ⁡
                            
                              (
                              
                                θ
                                1
                              
                              )
                            
                          
                          ⁢
                          
                            e
                            
                              i
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                φ
                                1
                              
                            
                          
                        
                      
                    
                  
                
                )
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    r
                    pp
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                
                +
                
                  
                    r
                    ss
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁡
                      
                        (
                        
                          
                            φ
                            1
                          
                          +
                          
                            φ
                            2
                          
                        
                        )
                      
                    
                  
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    r
                    sp
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁢
                      
                         
                      
                      ⁢
                      
                        φ
                        1
                      
                    
                  
                
                +
                
                  
                    r
                    sp
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁢
                      
                         
                      
                      ⁢
                      
                        φ
                        2
                      
                    
                  
                
              
            
          
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        8
      
    
  




A second measurement is made along the same light path. Assume the incidence light has polarization along angle θ2, with phase different φ1 'between s and polarizations. Also assume that the 0th order refection is detected at polarization along angle θ1, with phase different φ2 'between s and p polarizations. The measured electric field is: 



  
    
      
        
          
            
              
                E
                measure
              
              =
              
              ⁢
              
                
                  (
                  
                    
                      sin
                      ⁡
                      
                        (
                        
                          θ
                          1
                        
                        )
                      
                    
                    ⁢
                    
                      cos
                      ⁡
                      
                        (
                        
                          θ
                          1
                        
                        )
                      
                    
                    ⁢
                    
                      e
                      
                        i
                        ⁢
                        
                           
                        
                        ⁢
                        
                          φ
                          2
                          ′
                        
                      
                    
                  
                  )
                
                ·
                
                  [
                  
                    
                      
                        
                          r
                          pp
                        
                      
                      
                        
                          r
                          sp
                        
                      
                    
                    
                      
                        
                          r
                          ps
                        
                      
                      
                        
                          r
                          ss
                        
                      
                    
                  
                  ]
                
                ·
                
                  (
                  
                    
                      
                        
                          sin
                          ⁡
                          
                            (
                            
                              θ
                              2
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          
                            cos
                            ⁡
                            
                              (
                              
                                θ
                                2
                              
                              )
                            
                          
                          ⁢
                          
                            e
                            
                              i
                              ⁢
                              
                                 
                              
                              ⁢
                              
                                φ
                                1
                                ′
                              
                            
                          
                        
                      
                    
                  
                  )
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    r
                    pp
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                
                +
                
                  
                    r
                    ss
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁡
                      
                        (
                        
                          
                            φ
                            1
                            ′
                          
                          +
                          
                            φ
                            2
                            ′
                          
                        
                        )
                      
                    
                  
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    r
                    sp
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁢
                      
                         
                      
                      ⁢
                      
                        φ
                        1
                        ′
                      
                    
                  
                
                +
                
                  
                    r
                    sp
                  
                  ⁢
                  
                    cos
                    ⁡
                    
                      (
                      
                        θ
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        θ
                        2
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      i
                      ⁢
                      
                         
                      
                      ⁢
                      
                        φ
                        2
                        ′
                      
                    
                  
                
              
            
          
        
      
    
    
      
        eq
        .
        
           
        
        ⁢
        9
      
    
  




To obtain symmetrical measurements for symmetrical grating using symmetrical reflection or transmission orders, i.e. rsp =rps, or tsp =tps, the following condition has to be satisfied:

ei(φ1+φ2)=ei(φ1'+φ2′)

eiφ1=eiφ1′

eiφ2=eiφ2′  eq.10

which can be simplified as:

 φ1=φ1′

φ2=φ2′  eq.11

To obtain symmetrical measurements for symmetrical grating using antisymmetrical reflection or transmission orders, i.e. rsp=−rpps, or tsp=−tps1, the following condition has to be satisfied:

ei(φ1+φ2)=ei(φ1′+φ2′)

eiφ1=eiφ1′

eiφ2=eiφ2′  eq.10

Some special cases for antisymmetrical orders arc as follows:

    
    
        1) First and second incidence lights have polarization which is mirror symmetrical to s direction linear or non-linear, as does the first and second detection polarization, linear or non-linear.
        2) First and second incidence lights have polarization which is mirror symmetrical top direction linear or non-linear, as does the first and second detection polarization, linear or non-linear.
        3) One of the polarization directions is s or p.
        4) One of the polarization directions is s, the other is p. Effectively, one measurement is done with incidence polarization of p and detection polarization of s, the other is reversed.
    
    


It should be understood that the incidence paths for the two measurements do not need to be along the same path. The incidence paths could be mirror symmetry pair of x-z plan, where x is the grating vector direction.
Although the invention has been described with reference to particular embodiments, the description is only an example of the invention's application and should not be taken as a limitation. Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention as defined by the following claims.

## Claims

1. A method comprising:
providing an alignment target on a first element and a second element, the alignment target having a first periodic pattern on said first element and a second periodic pattern on said second element; 
illuminating said first periodic pattern and said second periodic pattern of said alignment target with light; 
detecting the intensities of at least two polarization states of said light after interacting with said alignment target; and 
comparing said intensities of said two polarization states to determine the alignment of said first element with respect to said second element.

2. The method of claim 1, wherein at least one of said first periodic pattern and said second periodic patterns are diffraction gratings.

3. The method of claim 1, wherein at least one of said first periodic pattern and said second periodic patterns has periodicities in two directions.

4. The method of claim 1, wherein illuminating said alignment target comprises:
producing light having at least two polarization states; and 
focusing said light onto said alignment target.

5. The method of claim 1, wherein the illuminating light has two polarization states.

6. The method of claim 4, wherein said light is non-normally incident on said alignment target, said light having a non-parallel azimuthal angle with respect to the periodicity of said first periodic pattern and said second periodic pattern.

7. The method of claim 1, further comprising moving said first element with respect to said second element if the intensity of one polarization state is not equal to the intensity of a second polarization state.

8. The method of claim 1, wherein said alignment target further includes a third periodic pattern on said first element and a fourth periodic pattern on said second element, said third periodic pattern and said fourth periodic pattern have a designed in offset of a known magnitude such that when said first element and second element are aligned, said third periodic pattern and said fourth periodic pattern are offset by said known magnitude; said method further comprising:
illuminating said third periodic pattern and said fourth periodic pattern of said alignment target with light having at least two polarization states; 
detecting the intensities of the polarization states of said light after interacting with said third periodic pattern and said fourth periodic pattern; and 
comparing said intensities of said polarization states from said light after interacting with said third periodic pattern and said fourth periodic pattern.

9. The method of claim 8, further comprising:
calculating the ratio of the comparison of said intensities of said polarization states from said light after interacting with said third periodic pattern and said fourth periodic pattern and the comparison of said intensities of said polarization states from said light after interacting with said first periodic pattern and said second periodic pattern to determine the amount of alignment error between said first element and said second element.

10. The method of claim 1, further comprising:
producing a model said alignment target and light having at least two polarization states interacting with said alignment target; 
comparing said model of light having at least two polarization states with the detected intensities of the polarization states to determine the amount of alignment error between said first element and said second element.

11. The method of claim 10, wherein said model is stored in a library.

12. A method comprising:
illuminating an alignment target on said first element and said second element with light having at least two polarization states, the alignment target having a first periodic pattern on said first element and a second periodic pattern on said second element; 
detecting the intensities of the at least two polarization states of light diffracted from said alignment target; and 
comparing the intensities of the at least two polarization states of light diffracted from said alignment target to determine the alignment between said first element and said second element.

13. The method of claim 12, wherein said periodic patterns are diffraction gratings.

14. The method of claim 12, wherein at least one of said periodic patterns has periodicities in two directions.

15. The method of claim 12, wherein said alignment target further includes a third periodic pattern on said first element and a fourth periodic pattern on said second element, said third periodic pattern and said fourth periodic pattern have a designed in offset of a known magnitude such that when said first element and second element are aligned, said third periodic pattern and said fourth periodic pattern are offset by said known magnitude;
said method further comprising: 
illuminating said third periodic pattern and said fourth periodic pattern of said alignment target with light having at least two polarization states; 
detecting the intensities of the polarization states of said light after interacting with said third periodic pattern and said fourth periodic pattern; and 
comparing said intensities of said polarization states from said light after interacting with said third periodic pattern and said fourth periodic pattern.

16. The method of claim 15, further comprising:
calculating the ratio of the comparison of said intensities of said polarization states from said light after interacting with said third periodic pattern and said fourth periodic pattern and the comparison of said intensities of said polarization states from said light after interacting with said first periodic pattern and said second periodic pattern to determine the amount of alignment error between said first element and said second element.

17. The method of claim 12, further comprising moving said first element with respect to said second element if the intensity of one polarization state is not equal to the intensity of a second polarization state.

18. A method comprising:
providing an alignment target on a first element and a second element, the alignment target having a first periodic pattern on said first element and a second periodic pattern on said second element; 
illuminating said first periodic pattern and said second periodic pattern of said alignment target with two light beams, each light beam having a different polarization state; 
detecting the intensities of said two light beams after interacting with said alignment target; and 
comparing said intensities of said two light beams to determine the alignment of said first element with respect to said second element.