Patent Publication Number: US-6992764-B1

Title: Measuring an alignment target with a single polarization state

Description:
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 feature sizes below approximately 100 nm 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 light 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 to determine 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 a single polarization state. The polarization state of the incident light is perpendicular or parallel to the direction of periodicity of the alignment target. The intensity of the resulting light after interacting with the alignment target is then measured at a single polarization state that is perpendicular or parallel to the polarization state of the incident light. The polarized resulting light will be periodic as a function of relative position of the two elements. The periodicity of the resulting light can be used to determine when the first element and the second element are aligned. 
     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 incident light having a first polarization state. The light interacts with the first and second periodic patterns and the resulting light is polarized. The polarized resulting light is then detected. The alignment of the first element and the second element is then determined based on the detected polarized resulting light. The resulting light may be polarized parallel or perpendicular to the polarization state of the incident light. Moreover, the polarization state of the incident light may be parallel or perpendicular to the periodicity of the first and second alignment targets. 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 while detecting the polarized resulting light. Because the intensity of the polarized resulting light is periodic, it can be determined when the two elements are aligned. 
     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 incident light with a single polarization state. The resulting light is polarized and then detected. The alignment of the first and second elements can then be determined using the detected polarized light from the first and second periodic patterns and the detected polarized light from the third and fourth periodic patterns. The detected polarized light from the third and fourth periodic patterns can be used as a reference for detected polarized light from the first and second periodic patterns. 
     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 the first element and a second periodic pattern on the second element, includes a light source for producing light having a first polarization state, the light is to be incident on the alignment target. The first polarization state may be perpendicular or parallel to the direction of periodicity of the first periodic pattern and the second periodic pattern. The apparatus further includes a polarizing element for polarizing the light after interacting with the alignment target and a detector for detecting the resulting polarized light. The polarizing element polarizes the light with a polarization state that is perpendicular or parallel to the polarization state of the incident light. The apparatus may include a processor to determine when the alignment target is aligned based on the detected resulting polarized light. The apparatus may further include a stage controlled by the processor, the stage moving the first element with respect to the second element to align 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 top and cross-sectional views, respectively, of an alignment target in accordance with an embodiment of the present invention. 
         FIGS. 4 and 5  show 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 ,  8 B,  8 C show metrology devices that may be used to measure the diffraction from an alignment target in accordance with the present invention. 
         FIGS. 9A ,  9 B,  9 C,  9 D,  9 E, and  9 F 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. 
         FIG. 14  shows a top view of an alignment target being illuminated by a single state s type polarization beam and with the resulting p polarized light is detected. 
         FIG. 15  shows a top view of an alignment target being illuminated by a single state p type polarization beam and with the resulting s polarized light is detected. 
         FIGS. 16A and 16B  show side views of an alignment target with the top and bottom periodic patterns in alignment and with an incident beam and a resulting beam, respectively. 
         FIGS. 17A and 17B  show side views of an alignment target with the top and bottom periodic patterns out of alignment and the polarization states of the resulting beams. 
         FIGS. 18 ,  19 , and  20  show graphs of reflected light as a function of shift between the top and bottom periodic patterns, where the light is obliquely incident on the alignment target. 
         FIGS. 21 and 22  show graphs of reflected light as a function of shift between the top and bottom periodic patterns, where the light is normally incident on the alignment target. 
         FIG. 23  shows a graph of the reflected light as a function wavelength and shift between the top and bottom periodic patterns. 
         FIG. 24  shows one embodiment of an encoder that uses an alignment pattern, in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     An alignment target is measured using a single polarization state, in accordance with the present invention, 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. An alignment target suitable for use with the present invention is described in U.S. patent application “Measuring An Alignment Target with Multiple Polarization States” by Weidong Yang and Roger R. Lowe-Webb, Ser. No. 10/116,798, filed Apr. 4, 2002, and which has the same assignee as the present application and is incorporated herein by reference. 
     The alignment target and method of use of the present invention 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 were filed on Apr. 4, 2002, and have the same assignee as the present application and are incorporated herein by reference. 
       FIGS. 3A and 3B  show top and cross-sectional views, respectively, of an alignment target  100  that may be used 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 Sep. 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 grating  102  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 a 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. 7 . As can be seen in  FIG. 7 , a number of separate alignment targets are used, where the top periodic pattern  262  is on the reference masks  218  and bottom periodic pattern  264  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 ,  8 B, and  8 C.  FIG. 8A , for example, shows a block diagram of a normal incidence polarized reflectance spectrometer. Spectrometer  320  is discussed in detail in the U.S. patent application entitled “Apparatus and Method for the Measurement of Diffracting Structures,” filed Sep. 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  320  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 are in alignment. 
     As shown in  FIG. 8A , spectrometer  320  includes a polychromatic light source  322  that generates a light beam that is partially reflected by beam splitter  324  along the optical axis. 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 09/844,559, 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  340  and spectroscopic scatterometer  345 . Ellipsometer  340  includes a broadband radiation source  341  and a spectrophotometer  342 , which is connected to a processor  343 . Spectroscopic scatterometer  345  includes a broadband radiation source  346  and a spectrophotometer  347 , which is connected to a processor  348 . As indicated by the arrows in  FIG. 8C , one or both of broadband radiation source  346  and spectrophotometer  347  are adjustable to alter the angle of incidence. The operation of an ellipsometer  340  and spectroscopic scatterometer  345  is well known to those skilled in the art. Processor  343  and  348  may be similar to processor  336  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,  121   a ,  121   b , and  121   c . Because of the symmetrical properties of the periodic patterns in alignment target  100 , the measurement may be made at multiple symmetrical angles. 
       FIGS. 9B ,  9 C and  9 D illustrate the symmetries of alignment target  100 . As can be seen in  FIGS. 9B ,  9 C, and  9 D, alignment target  100  has mirror symmetry along the x-z plane, the y-z plane and 180 degree rotation symmetry around the z axis. The y-z plane 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 ,  9 C, and  9 D, 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, i.e., parallel to the lines, as shown in  FIGS. 9E and 9F . In  FIG. 9E , a and b represent the polarization states of the incident light for two measurements that follow the same light path and in  FIG. 9F , a′ and b′ represent the polarization states of the resulting light for the two measurements. As can be seen, the two incidence polarization states (a and b) and the two detection polarization states (a′ and b′) mirror each other in the y-z plane. However, as can be seen, the polarization angles used in the incident light need not be used in the detection, i.e., a′ and b′ may differ from a and b, but should be symmetrical about the y-z plane. 
     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 broken. 
     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 is produced. 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 ( 402   a ,  404   a ) on a first element  403  and a periodic pattern ( 402   b ,  404   b ) on a second element  405 . The overlay pattern  402  has no designed in offset, i.e., periodic patterns  402   a  and  402   b  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  404   a  and  404   b  of a magnitude D. 
     It should be understood that periodic patterns  402   b  and  404   b  or periodic patterns  402   a  and  404   a  may be a part 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 φ 1  is the differential spectra at the target location, i.e., overlay pattern  402 , φ 2  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 fitting the alignment error e for the entire spectrum, 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. Further, if desired, a select portion of the full spectrum may be used to provide an optimized result. The portion of the full spectrum to be used may be determined by examining the wavelength dependent signal response to the alignment error either empirically or by modeling.
 
     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 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., alignment target  100  in  FIGS. 3A ,  3 B, 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  that 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: 
         E   out   =R·E   in   eq. 3               where   ⁢           ⁢   E     =     (           E   s               E   p           )             eq   .           ⁢   4                 and   ⁢           ⁢   R     =     [           r   pp           r   sp               r     p   ⁢           ⁢   s             r   ss           ]             eq   .           ⁢   5               
     r sp  and r ps  are defined as the cross-reflection coefficients. For symmetric grating, the 0 th  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. 
     In conical incidence, if the grating is symmetrical, 0 th  orders are antisymmetrical, r sp =−r ps ≠0, while the higher orders are symmetrical, r sp =r ps . For transmission, this relationship is reversed. The 0 th  orders are symmetrical, while higher orders are antisymmetrical. Assume incidence light has polarization along angle θ 1 , with phase different φ 1  between s and p polarizations. Also assume that the 0 th  order refection is detected at polarization along angle θ 2 , with phase different φ 2  between s and p polarizations. Incidence light can be described as: 
               E     i   ⁢           ⁢   n       =       (           E   s               E   p           )     =     (           sin   ⁡     (     θ   1     )                   cos   ⁡     (     θ   1     )       ⁢     ⅇ     i   ⁢           ⁢     ϕ   1                 )               eq   .           ⁢   6             
 
0 th  order reflection: 
               E   out     =       R   ·     E     i   ⁢           ⁢   n         =         [           r   pp           r   sp               r     p   ⁢           ⁢   s             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     p   ⁢           ⁢   s       ⁢     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   ⁢           ⁢   ϕ2         )     ·     (               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 θ 2 , with phase different φ 1 ′ between s and p polarizations. Also assume that the 0 th  order refection is detected at polarization along angle θ 1 , with phase different φ 2 ′ 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     p   ⁢           ⁢   s             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. r sp =r ps , or t sp =t ps , the following condition has to be satisfied:
 
e i(φ     1     +φ     2     ) =e i(φ     1     ′+φ     2     ′)  
 
e iφ     1   =e iφ     1′   
 
e iφ     2   =e iφ     2   ′  eq. (10)
 
which can be simplified as:
 
φ 1 =φ 1 ′
 
φ 2 =φ 2 ′  eq. (11)
 
     To obtain symmetrical measurements for symmetrical grating using antisymmetrical reflection or transmission orders, i.e. r sp =−r ps , or t sp =−t ps , the following condition has to be satisfied:
 
e i(φ     1     +φ     2     ) =e i(φ     1     ′+φ     2     ′)  
 
e iφ     1   =e iφ     1′   
 
e iφ     2   =e iφ     2   ′  eq. (10)
 
Some special cases for antisymmetrical orders are 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 to p 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 plane, where x is the grating vector direction. 
     In another embodiment of the present invention, a single polarization state is used to determine the alignment between a top periodic pattern and a bottom periodic pattern.  FIG. 14  shows a top view of an alignment target  700 , which is similar to alignment target  100  shown in  FIGS. 3A and 3B , being illuminated by a single state polarization beam. As shown in  FIG. 14 , the incident beam  702  is produced by source  710 , which includes polarizer  711  to produce a single polarization state, e.g., s polarization. The beam  702  is incident on alignment target  700  with an azimuthal angle that is parallel with the lines in the periodic pattern of the alignment target  700 . The polarization state of the incident beam  702 , thus, may be parallel to or perpendicular to the direction of periodicity in the alignment target  700 . It should be understood that the alignment target may have periodicities in two directions. e.g., as shown in  FIG. 12 . 
     The intensity of the resulting light with a polarization state perpendicular or parallel to the polarization state of the incident beam is then detected.  FIG. 14  shows the intensity of p′ type polarized light in the resulting beam  704  (where the prime notation is used to indicate that it is the polarization state of the resulting beam  704 ) being detected by detector  712 , which includes a polarizer  713  to select the p type polarized light. If desired, however, a parallel polarization state, i.e., s′ polarized light, may be detected, as indicated by the broken line in  FIG. 14 . Alternatively, as shown in  FIG. 15 , the incident beam may have a polarization state of p, and the detector  712  receives the s′ polarization state of the resulting beam  704  by way of polarizer  713 . Again, if desired, a parallel polarization state, i.e., p′ polarized light, may be detected, as indicated by the broken circle in  FIG. 15 . Based on the intensity of the polarization state of the resulting beam  704 , the alignment between the top periodic pattern and the bottom periodic pattern may be determined. 
       FIG. 16A  shows a side view of alignment target  700  with an incident beam  702  having a single polarization state, i.e., s type.  FIG. 16B  shows the resulting beam  704  from alignment target  700 . When the top and bottom periodic patterns  700   a  and  700   b  are in alignment, as shown in  FIGS. 16A and 16B , the polarization state of the resulting beam  704  will be the same as the polarization state of the incident beam  702 . Consequently, the measured intensity of the p type polarized light in the resulting beam  704  will be approximately zero. 
       FIG. 17A  shows a side view of alignment target  700  with the top and bottom periodic patterns  700   a  and  700   b  slightly out of alignment. As shown in  FIG. 17A , the resulting beam  704  has both an s′ type component and a p′ type component. Consequently, the measured intensity of the p type polarized light in the resulting beam  704  will be non-zero.  FIG. 17B  is another view of alignment target  700  with the top and bottom periodic patterns  700   a  and  700   b  more out of alignment than shown in  FIG. 17A . As shown in  FIG. 17B , the resulting light  704  has an increased p′ type component, and a decreased s′ type component. Consequently, the measured intensity of the p type polarized light in the resulting beam  704  shown in  FIG. 17B  is greater than that measured in  FIG. 17A . 
       FIG. 18  is a graph showing the reflectance of p type polarized light a function of the shift between the top and bottom patterns, where the incident light is s polarized and light has an incident angle of 60 degrees. As can be seen, the resulting reflection has a clear periodic pattern.  FIG. 19  is a graph showing the reflectance of p type polarized light as a function of shift, where the incident light is p polarized and the light has an incident angle of 60 degrees.  FIG. 20  is a graph showing the reflectance of s type polarized light as a function of shift, where the incident light is s polarized and the light has an incident angle of 60 degrees. 
     Thus, as can be seen in  FIGS. 17A and 17B , the intensity of the p type polarized light in the resulting beam increases as the misalignment between top and bottom periodic patterns is increased. The change in the intensity of the light is periodic as can be seen in  FIGS. 18 ,  19 , and  20 . Accordingly, by monitoring the single polarization state (s or p) of the resulting beam as either the top periodic pattern  700   a  or the bottom periodic pattern  700   b  are moved, it may be determined when the top and bottom periodic patterns are aligned. As shown in  FIG. 18 , for cross polarization states, e.g., the incident beam is s type polarized and the p type polarization is monitored in the resulting beam, a minimum will indicate when the patterns are aligned or 90 degrees out of phase. Where the same polarization state is monitored as is incident, e.g., p type polarization is incident and monitored as shown in  FIG. 19 , maxima will indicate when the patterns are aligned or 90 degrees out of phase. Where s type polarization is incident and monitored, as shown in  FIG. 20 , maxima will indicate when the patterns are aligned. 
     As discussed above, normally incident light may be used to monitor the misalignment between the top and bottom periodic patterns, e.g., using a normal incidence metrology device, such as that shown in  FIG. 8A .  FIGS. 21 and 22  show graphs of the reflectance of TE and TM mode light, respectively, as a function of shift between the top and bottom periodic patterns, where the incident light is in TE and TM mode, respectively, and is normal to the substrate. Similar to what is shown in  FIGS. 18 ,  19 , and  20 ,  FIGS. 21 and 22  show that the resulting measurement of the TE and TM modes of the reflected light is periodic and, thus, can be used to determine when the periodic patterns are in alignment. 
     As described in reference to  FIG. 10 , additional alignment targets may be used as reference targets. One of the alignment targets has a designed in offset D. By comparing the measurement alignment target with the reference alignment target, as described in equations 1 and 2, the offset amount may be determined. Moreover, additional alignment targets may be used as described in the U.S. patent application entitled “Alignment Target with Designed in Offset” by Weidong Yang, Roger R. Lowe-Webb, and John D. Heaton, which is incorporated herein by reference. 
     Alternatively, the alignment target  700  can be self-referenced, by taking a measurement at a first location, moving either the top or bottom periodic pattern with respect to the other by a known distance D, and taking a second measurement. The first and second measurements may then be used along with distance D to determine the alignment error, as described in equations 1 and 2. Once the alignment error is determined, either the top or bottom periodic pattern is moved with respect to the other by the amount of the alignment error to minimize the error. If desired, a third measurement may be made. Because the alignment error is minimized, the intensity of the polarization state of the resulting beam should be approximately zero. However, if the intensity of the polarization state of the resulting beam is non-zero, the amount of the current alignment error may be determined by comparing the third measurement with the second measurement, as described in equations 1 and 2, where D is distance that the periodic patterns were previously moved to minimize the alignment error. 
     As discussed above, it should also be understood, that the present invention may use a single wavelength, a plurality of discrete wavelengths, or a continuum of wavelengths.  FIG. 23 , for example, shows a graph of the reflected p type polarized with respect to wavelength, where the incident light is s type polarized.  FIG. 23  shows a plurality of curves for different shifts between the top periodic pattern and bottom periodic pattern. As can be seen in  FIG. 23 , certain wavelengths, e.g., approximately 400 nm, are more responsive to overlay shifts than other wavelengths. 
     It should be understood that the determination of whether two elements are in alignment may be used advantageously with an alignment system, such as that shown in  FIGS. 6 and 7 , or with an encoder device, such as that described in “Encoder with Alignment Target”, by Weidong Yang, Roger R. Lowe-Webb, and John D. Heaton which is incorporated herein by reference. 
       FIG. 24  shows one embodiment of an encoder  800  that uses an alignment pattern  801 , in accordance with the present invention. Encoder  800  includes a sensor head  802  and a scale  804 . The scale  804  includes a continuous periodic pattern  805 , such as a diffraction grating. In operation, the sensor head  802  and the scale  804  are movable with respect to each other, as indicated by arrow  807 . One of the elements, e.g., the sensor head  802 , moves, while the other element, e.g., the scale  804 , is held stationary. Encoder  800  may be used as a linear encoder or as a rotary encoder. 
     In one embodiment, the sensor head  802  may have two or more measurement locations, each of which includes a periodic pattern  806  and  808 . In another embodiment, only one measurement location is used. Sensor head  802  also includes a light source  810 , which may be, e.g., a white LED source. If desired, an external light source may be used, in which case the light source may be coupled to the sensor head  802 , e.g., by a fiber optic cable. Moreover, if desired, more than one light source may be used, e.g., one light source for each measurement location. 
     Sensor head  802  can operate in reflection mode or transmission mode.  FIG. 24  illustrates sensor head  802  operating in reflection mode. As shown, beams splitters  811  and  813  direct the light from light source  802  towards the periodic patterns  806  and  808 , respectively. The light passes through periodic patterns  806  and  808 , and is reflected back by the periodic pattern  805  on the scale  804 . The reflected light passes through beam splitters  811  and  813  and is received by detectors  812  and  814 , respectively. Thus, the two measurement locations include both the periodic patterns  806  and  808  on the sensor head  802  and the periodic pattern  805  on the scale  804 . Thus, it should be understood that periodic patterns  806  and  805  together will be sometimes referred to as measurement location  806 , and likewise, periodic patterns  808  and  805  will be sometimes referred to as measurement location  808 . 
     If desired, multiple light sources may be used in sensor head  802 . Sensor head  802  may use a reflectometer type device to measure the measurement locations  806  and  808 . The operation of reflectometers and similar devices is well known in the art. Moreover, if desired, sensor head  802  may operate in transmission mode. In transmission mode, the light is transmitted through periodic pattern  805  on scale  804 , as opposed to being reflected, and is received by detectors on the other side of scale  804 . 
     The detectors  812  and  814  detect the resulting light and convert the light into electrical signals that are received by processor  820  coupled to the sensor head  802 . 
     Encoder  800  may use a single polarization state to monitor when the top and bottom periodic patterns are in alignment. By determining when the periodic patterns are in alignment, and by knowing the distance between the lines in the periodic patterns, the processor can determine the relative position between the sensor head  802  and the scale  804 . The resolution of the encoder  800  can be further improved by interpolating the position of the sensor head  802  relative to the scale  804  based on a recorded measurement of the signal over one period. 
     Alternatively, the second measurement location  808  may be used in conjunction with the first measurement location  806  as discussed above. 
     Although the invention has been described with reference to particular embodiments, the description is only an example of the invention&#39;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.