Measuring an alignment target with multiple polarization states

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 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 1Bshow conventional overlay targets used with conventional imaging metrology methods.FIG. 1Ashows a typical Box-in-Box overlay target2. Target2is formed by producing an etched box4in a material layer6on a substrate. A corresponding smaller box8on the photomask or reticle is aligned to the larger box 4 so that the centers of the large and small boxes are aligned.

FIG. 1Bshows a Bar-in-Bar overlay target12, which is similar to target2shown in FIG.1A. Target12is produced by etching bars14in a material layer16on a substrate. The bars18on the photomask are aligned to the overlay target alignment bars14.

After the smaller box8or bars18are 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. 2shows a conventional alignment system50, which includes a diffraction pattern52on the substrate and a second diffraction pattern54that is stationary, e.g., is fixed to the lens on the exposure tool. A light source56produces coherent light that passes through a beam splitter58and is incident on the diffraction pattern52after passing through a lens60. The light is diffracted by diffraction pattern52and passes through lens60back to beam splitter58. The coherent light beam from source56is also reflected off beam splitter58, passes through lens62and is incident on diffraction pattern54. The light diffracted by diffraction pattern54passes back through lens62to beam splitter58. At beam splitter the light diffracted from diffraction patterns52and54is combined and the combined diffraction patterns is received by light detectors64.

Alignment system50provides an accuracy of approximately 15 nm. One disadvantage of alignment system50is that coherent light is used. Thus, if the diffraction pattern52on the sample absorbs the particular frequency used, alignment system50cannot 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.

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 3B show a top and cross-sectional views, respectively, of an alignment target100in accordance with an embodiment of the present invention. Alignment target100includes a periodic pattern102on a first element103and another periodic pattern104on a second element105. The periodic patterns102,104, which may be diffraction gratings, are designed to be in alignment with respect to each other when layers103and105are in alignment. The first element103and second element105may be movable with respect to each other. For example, the first and second element103and105may 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 elements103and105may 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 target100are 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 pattern102is 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 pattern102is exposed in the photoresist, which is then developed. The polysilicon is then etched away leaving periodic pattern102.

The top periodic pattern104is produced using, e.g., photoresist, in a manner similar to the bottom periodic pattern102. The top periodic pattern104may be separated from the bottom periodic pattern102by one or more intermediate layers. Thus, for example, an 800 nm layer of the photoresist may be used to produce top periodic pattern104. The desired image including the periodic pattern is exposed in the photoresist layer. The photoresist may then be developed to produce periodic pattern104, or alternatively, a latent image may be used as periodic pattern104.

It should be understood that the processing steps used to produce periodic patterns102and104are exemplary. Different or additional layers may be included between substrate and the bottom periodic pattern102or between the bottom periodic pattern102and the top periodic pattern104. In fact, if desired, the top periodic pattern104may be on the same layer as the bottom periodic pattern102, 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 target100may 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 target100may be used with two elements that are not connected. Thus, for example, the top periodic pattern104, and the bottom periodic pattern102may 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 gratings106,116need not extend to the top of element105. It should be understood that the alignment target100may be produced using various materials and the dimensions optimized for the materials used. Thus, the dimensions of the alignment target100may be altered to maximize sensitivity based on the types of materials used.

To determine if the layers103,105are in alignment, a radiation source120, such as a broadband light source, produces radiation121that is incident on alignment target100. Source120produces 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 target100, if the pattern has only one periodicity direction.

The radiation source120produces radiation121that has a plurality of polarization states, e.g., two polarization states, as illustrated in FIG.3B. After the radiation interacts with alignment target100, a detector122detects the radiation. The difference in intensity of the polarization states from alignment target100vary proportionally with the alignment error. When the elements103and105are in alignment, periodic patterns102and104will be in alignment. Consequently, the polarization states in the detected radiation will have equal intensity. However, if there is an alignment error between elements103and105, periodic patterns102and104will be out of alignment, as illustrated inFIGS. 4 and 5. With the periodic patterns102and104out of alignment, the intensity of the detected polarization states will be unequal. Thus, by comparing the intensities of the detected polarization states from alignment target100, it is possible to determine if elements103and105are in alignment.

The ability to determine if elements103and105are 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. 6is a block diagram of an alignment system with which the alignment target100may be used. The alignment system is an exposure tool200includes X and Y substrate stages202and204that hold the substrate201. The exposure tool200also includes X and Y reticle stages206and208that hold the reticle210. Exposure tool200may include two sets of stages, one set for large motions and another set for fine motions. For sake of simplicity, X and Y stages202,204,206, and208may be used for both large motion and fine motion.

A control system212controls the motion of the stages. A lens214or other suitable optics is positioned between the substrate201and the reticle210and is used to focus light from light source216that is transmitted through reticle210onto substrate201. The operation and control of exposure tools is well known in the art.

A reference mask218extends from the lens214by way of a low thermal expansion arm219. The distance between the reference mask218and the substrate201should be small, e.g., between 1 and 10 μm. Spectrometers220are positioned above reference masks218. As shown inFIG. 6, a plurality of reference masks218may be used, each having an associated spectrometer220.

FIG. 7shows a perspective view of substrate201and reticle210with lens214and four reference masks218disposed between the substrate201and reticle210. The spectrometers220are not shown in FIG.16. As can be seen inFIG. 7, a number of separate alignment targets100are used, where the top periodic pattern104is on the reference masks218and bottom periodic pattern102is on the substrate201.

Referring back toFIG. 6, the spectrometers220may be coupled to the lens214as shown inFIG. 6, or may be connected to another stationary object. The spectrometers220communicate with the control system212. The control system212includes, 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 system212is coupled to the stage to adjust the location of the substrate201in response to the signals provided by spectrometer220until the starting position of the substrate201is precisely aligned with the lens214. Once the substrate201is aligned, the control system212can move the stages to perform the desired exposure operation.

Alignment target100may be used to measure the amount of alignment error, e.g., using several types of metrology devices, e.g., such as that shown inFIGS. 8A,8B, and8C.FIG. 8A, for example, shows a block diagram of a nonnal incidence polarized reflectance spectrometer. Spectrometer300is 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. Spectrometer300may 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 target100. In an alignment system, such as that shown inFIG. 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 patterns102and104are in alignment.

As shown inFIG. 8A, spectrometer300includes a polychromatic light source322that generates a light beam that is partially reflected by beam splitter324along the optical axis323. The light beam is directed towards a sample326having an alignment target, such as alignment target100, to be measured. Sample326may be, e.g., a semiconductor wafer or flat panel display or any other substrate, and is supported by a stage328, which may be a polar coordinate, i.e., R-θ, stage or an x-y translation stage. Spectrometer320includes a rotatable polarizer330and a lens332(or series of lenses) to polarize and focus the light beam onto the sample326at normal incidence. The beam is reflected off sample326and the reflected light is transmitted through lens332and polarizer330. A portion of the reflected light is transmitted through beam splitter324and is received by a spectrophotometer334. Spectrophotometer334is coupled to processor336, which analyzes the data provided by spectrophotometer334. Processor336is 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 target100including ellipsometry and scatterometry.FIGS. 8B and 8Cshow block diagrams of a spectroscopic ellipsometer140and spectroscopic scatterometer145. Ellipsometer140includes a broadband radiation source141and a spectrophotometer142, which is connected to a processor143. Spectroscopic scatterometer145includes a broadband radiation source146and a spectrophotomcter147, which is connected to a processor148. As indicated by the arrows inFIG. 8C, one or both of broadband radiation source146and spectrophotometer147are adjustable to alter the angle of incidence. The operation of an ellipsometer140and spectroscopic scatterometer145is well known to those skilled in the art. Processor143and148may be similar to processor136shown 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. 9Afor example, shows alignment target100being 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 target100, the measurement may be made at multiple symmetrical angles.

FIGS. 9B,9C and9D illustrate the symmetries of alignment target100. As can be seen inFIGS. 9B,9C, and9D, alignment target100has 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 inFIGS. 9B,9C, and9D, 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 inFIGS. 9C and 9Dare identical and are also identical to the measurement inFIG. 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 inFIGS. 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 inFIGS. 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 target100, 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. 10shows a cross-sectional view of an alignment target400in accordance with another embodiment of the present invention. Alignment target400includes two measurement locations, referred to as overlay patterns402and404. Each of the overlay patterns402,404includes a periodic pattern (402a,404a) on a first element403and a periodic pattern (402b,404b) on a second element405. The overlay pattern402has no designed in offset, i.e., periodic patterns402aand402bare aligned when elements403and405are in proper alignment. Overlay pattern404, however, has a designed in offset between the bottom periodic pattern404aand404bof a magnitude D.

It should be understood that periodic patterns402band404bor periodic patterns402aand404amay 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. 11shows a top view of alignment target400. The periodic patterns in overlay patterns402and404may be oriented at any non-perpendicular angle with respect to each other.

In operation, overlay pattern404is used as a reference pattern for alignment target400. Each measurement location, i.e., overlay patterns402and404, of alignment target400is measured at a plurality of, e.g., two, polarization states. When elements403and405are properly aligned, the intensities of the polarization states from overlay pattern402will be equal, but the intensities of the polarization states from overlay pattern404will be unequal. When there is an alignment error between the elements403and405, the intensities of the polarization states from overlay pattern402will 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 pattern404may be used as a reference measurement.

In general, the alignment error e is determined by:e=φ1φ2-φ1*Deq.⁢1
wherein φ1is the differential spectra at the target location, i.e., overlay pattern402, φ2is the differential spectra at the reference location, i.e., overlay pattern404, 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⁢φ1,i*(φ2-φ1)i∑i⁢(φ2-φ1)i2*Deq.⁢2
where i is the wavelength number in the spectrum.

In another embodiment, the reference location is produced by moving the second element405with respect to the first element403by a distance D and measuring the pattern in the new position. In this embodiment, the second overlay pattern404is 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. 12shows top view of an alignment target500in accordance with another embodiment of the present invention. Alignment target500is a bi-grating includes two periodic patterns, a bottom periodic pattern502, shown as a solid squares, and a top periodic pattern504, 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 target500has two periodicities, it can be used to determine alignment in two directions, shown as the X and Y direction in FIG.12. Alignment target500is measured from two separate directions by beam506, which is sensitive to alignment error in the Y direction and beam508, 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 target100FIGS. 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 inFIG. 13, an alignment mark600, which is similar to alignment mark100, may be measured by a light source620that produces an incident light beam621and a detector624detects non-zero order diffracted light622.

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•Eouteq.3
whereE=(EsEp)eq.⁢4
andR=[rpprsprpsrss]eq.⁢5
rspand rpsare defined as the cross-reflection coefficients. For symmetric grating, the0thorder 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, 0thorders are antisymmetrical, rps=-rps ≢0, while the higher orders are symmetrical, rsp=rps. For transmission, this relationship is reversed. The0thorders are symmetrical, while higher orders are antisymmetrical. Assume incidence light has polarization along angle θ, with phase different φ1between s and p polarizations. Also assume that the 0thorder refection is detected at polarization along angle θ2, with phase different φ2between s and p polarizations. Incidence light can be described as:Ein⁡(EsEp)=(sin⁡(θ1)cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1)eq.⁢6
0thorder reflection:Eout=R·Ein=[rpprsprpsrss]·(sin⁡(θ1)cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1)=(rpp⁢sin⁡(θ1)+rsp⁢cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1rps⁢sin⁡(θ1)+rss⁢cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1)eq.⁢7
The measured electric field is:Emeasure=⁢(sin⁡(θ2)⁢cos⁡(θ2)⁢ⅇⅈ⁢⁢ϕ2)·Eout=(sin⁡(θ2)⁢cos⁡(θ2)⁢ⅇⅈ⁢⁢ϕ⁢2)·⁢(rpp⁢sin⁡(θ1)+rsp⁢cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1rps⁢sin⁡(θ1)+rss⁢cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1)=⁢rpp⁢sin⁡(θ1)⁢sin⁡(θ2)+rss⁢cos⁡(θ1)⁢cos⁡(θ2)⁢ⅇⅈ⁡(ϕ1+ϕ2)+⁢rsp⁢sin⁡(θ2)⁢cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ1+rsp⁢cos⁡(θ2)⁢sin⁡(θ1)⁢ⅇⅈ⁢⁢ϕ2eq.⁢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 0thorder refection is detected at polarization along angle θ1, with phase different φ2'between s and p polarizations. The measured electric field is:Emeasure=⁢(sin⁡(θ1)⁢cos⁡(θ1)⁢ⅇⅈ⁢⁢ϕ2′)·[rpprsprpsrss]·(sin⁡(θ2)cos⁡(θ2)⁢ⅇⅈ⁢⁢ϕ1′)=⁢rpp⁢sin⁡(θ1)⁢sin⁡(θ2)+rss⁢cos⁡(θ1)⁢cos⁡(θ2)⁢ⅇⅈ⁡(ϕ1′+ϕ2′)+⁢rsp⁢sin⁡(θ1)⁢cos⁡(θ2)⁢ⅇⅈ⁢⁢ϕ1′+rsp⁢cos⁡(θ1)⁢sin⁡(θ2)⁢ⅇⅈ⁢⁢ϕ2′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.